Mastering the Techniques of Intraocular Lens Power Calculations - 9788184483802

Mastering the Techniques of IOL Power Calculations

Mastering the Techniques of IOL Power Calculations 2nd Edition Editors Ashok Garg MS PhD FIAO (Bel) FRSM ADM FAIMS FICA International & National Gold Medalist, Chairman & Medical Director Garg Eye Institute & Research Centre, 235-Model Town, Dabra Chowk Hisar-125 005 (India) JT Lin PhD Technical Director, Room 826, No. 144, Section 3 Min-Chuan East Road, Salford Quays Taipei, Taiwan-1205 Robert Latkany MD Associate Adjunct Professor NY Eye & Ear Infirmary, Founder Director Dry Eye Center of New York, 115, East 57th Street 10th Floor, New York-10022, USA Jerome Bovet MD Consultant Ophthalmic Surgeon, FMH Clinique de I’oeil, 15, Avenue du Bois-de-la-Chapelle, CH-1213 Onex Switzerland Wolfgang Haigis PhD Associate Professor, Head of the Biometry Department University Eye Hospital, 11, Josef – Schneider – Str D-97080, Wuerzburg, Germany

Forewords Kenneth J Hoffer Jes Mortensen ®

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First Edition: 2005 Second Edition: 2008 ISBN 978-81-8448-380-2 Typeset at JPBMP typesetting unit Printed at Ajanta Press

Dedicated to -

My Respected Param Pujya Guru Sant Gurmeet Ram Rahim Singh Ji for his blessings and motivation. My Respected Parents, teachers, my wife Dr. Aruna Garg, son Abhishek and daughter Anshul for their constant support and patience during all these days of hard work. My dear friend Dr. Amar Agarwal, a leading International Ophthalmologist from India for his continued support and guidance. Ashok Garg

My wife, Jeanette and my sons Alex and Tao, who have been giving me constant support and love. JT Lin

To my beautiful wife Barbara and wonderful kids Brian, Amanda and Luke. I look forward to seeing you each and every day. Robert Latkany

-

Yveric, Luc and Fanny Laure. Silvio Korol, who was not only a teacher but also an intellectual guide and a friend. Jerome Bovet

My wife Katharina and my son Michael. Wolfgang Haigis

Contributors

Alberto Artola Roig MD

Instituto Oftalmologico De Alicante Avda Denia 111, 03015 Alicante, Spain

Amar Agarwal MS FRCS FRC Ophth Consultant Dr Agarwal’s Eye Hospital 19, Cathedral Road Chennai-600086, India

Anand A Shroff MS

Shroff Eye Hospital 222, SV Road Bandra (W) Mumbai-400050 (India)

Antonio Calossi Dip Optom It FAILAC FBCLA Studio Optometrico Calossi Via 2 Giugno, 37 50052, Certaldo (FI) Italy

Aravind R Reddy MS FRCS DNB The Leeds Teaching Hospitals Leeds - LS2 9NS, UK

Arif Adenwala MS DNB FRCS

Consultant Ophthalmologist P Box No 457, Zulekha Hospital Sharjah, UAE

Arturo Pérez-Arteaga MD

Dennis SC Lam MD PhD

Medical Director Centro Oftalmologico Tlalnepantla Dr Perez-Arteaga Vallarta No 42 Tlalnepantla, Centro, Etado de Mexico, 54000 Mexico

Professor of Ophthalmology Department of Ophthalmology and Visual Sciences The Chinese University of Hongkong 3/F, Hong Kong Eye Hospital 147K Argyle Street, Kowloon, HKSAR PRC China, India

Ashok Garg MS PhD FRSM

Medical Director Garg Eye Institute and Research Centre 235-Model Town, Dabra Chowk Hisar-125005 (India)

Ashok Sharma MD

Director Cornea Centre SCO 833-834 (2nd Floor) Sector 22-A, Near Bus Stand Opp Parade Ground Chandigarh-160022 India

Athiya Agarwal MD DO FRSH Consultant Dr Agarwal’s Eye Hospital 19, Cathedral Road Chennai-600086, India

Barun K Nayak MD MNAMS DO

Dimitrii Dementiev MD

Chief and Medical Director Blue Eye Centro di Michro Chirurgia Oculare Eye Clinic Arese 20020 (MI) Via Campo Gallo 21/10 Italy

DM Portaliou MD

Institute of Vision and Optics (IVO) Vardinoyiannion Eye Institute of Crete (VEIC), GR 71 003 Vouters Heraklion, Crete Greece

Eneida de la C Pérez MD

Cuban Institute of Ophthalmology Ramon Pando Ferrer Havana, Cuba

Evelyn Icasiano MD

Vice Chairman Microsurgery Center Cuban Institute of Ophthalmology Ramon Pando Ferrer Havana, Cuba

Consultant and Head Deptt of Ophthalmology PD Hinduja National Hospital and Medical Research Centre Veer Savarkar Marg Mahim, Mumbai-400016 (India)

Arthur Cheng MD

B Vineeth Kumar MD FRCS Ed

Fengju Zhang MD

Armando Capote MD

Department of Ophthalmology and Visual Sciences The Chinese University of Hongkong 3/F, Hong Kong Eye Hospital 147K Argyle Street, Kowloon, HKSAR PRC, China

Fellow in Ophthalmology Arrowe Park Hospital Arrowe Park Road Upton, Wirral CH49 5PE UK

Consultant Ophthalmic Surgeon Dry Eye Center of New York 115, East 57th Street 10th Floor, New York-10022 USA Tianjin Medical University Director, Refractive Surgery Centre Tianjin Eye Hospital and Eye Institute Add : No4, Gansu Rd Tianjin 300020 China

Mastering the Techniques of Intraocular Lens Power Calculations

viii Frank J Goes MD

Director Goes Eye Centre W Klooslaan 6 B2050 Antwerp, Belgium

Frederic Hehn MD

Centre de La Vision (Nations - Vision) 32, Boulevard de l’europe 54500, Vandoeuvre France

GD Kymionis MD

Institute of Vision and Optics (IVO) Vardinoyiannion Eye Institute of Crete (VEIC), GR 71 003 Vouters Heraklion, Crete, Greece

Georges Baikoff MD

Clinique Monticelli 88, Rue du Commandant Rolland 13008, Marsielle France

Gian Maria Cavallini MD

Director Institute of Ophthalmology University of Modena and Reggio Emilia, via de’ Pozzo 71-41100 Modena, Italy

Giovanni Neri MD

Institute of Ophthalmology University of Modena and Reggio Emilia, via de’ Pozzo 71-41100 Modena, Italy

I Howard Fine MD FACS

Oregon Eye Surgery Centre 1550, Oak Street # 5, Eugene, OR - 97401 USA

I-Jong Wong MD PhD

Department of Ophthalmology National Taiwan University Hospital Taipei, Taiwan

IG Pallikaris MD

Jay S Pepose MD PhD Pepose Vision Institute 16216, Baxter Road Suite 205, Chesterfield Missouri - 63017 USA

Jerome Bovet MD Consultant Ophthalmic Surgeon FMH Clinique de I’oeil 15, Avenue du Bois-de-la-Chapelle CH-1213 Onex Switzerland

Jinhui Dai MD Eye and ENT Hospital Fudan University Shanghai China

Jorge L AlióY Sanz MD PhD Director Instituto Oftalmologico De Alicante Avda Denia 111, 03015 Alicante, Spain

Jos J Rozema MD Department of Ophthalmology University Hospital Antwerp Wilrikstraat 10, B-2650 Edegem (Antwerp) Belgium

Jose B Almeida MD Dept Fisica, Physics Department Universidade do Minho Portugal

JT Lin PhD Technical Director New Vision, Inc Room 826, Section 3, No144 Min-Chuan East Road Taipei, Taiwan 105

Professor and Head Institute of Vision and Optics (IVO) Vardinoyiannion Eye Institute of Crete (VEIC), GR 71 003 Vouters Heraklion, Crete Greece

Kenneth J Hoffer MD

Irwin Y Cua MD

Kukrenkov Vetchiaslav MD

St Luke’s Medical Centre Quezon City, Philippine

Clinical Professor of Ophthalmology UCLA, St Mary’s Eye Centre 1441, Broadway, Santa Monica CA-90404, 310-451-2020, USA

Arese 20020 (MI) Via Campo Gallo 21/10, Milan, Italy

Kumar J Doctor MS DNB Director Doctor Eye Institute Spenta Mansion SV Road Andheri (West) Mumbai - 400 058, India

Laure Gobin PhD Department of Ophthalmology University Hospital Antwerp Wilrikstraat 10, B-2650 Edegem (Antwerp) Belgium

Luca Campi MD Director Institute of Ophthalmology University of Modena and Reggio Emilia, via de’ Pozzo 71-41100 Modena, Italy

Lung - Kun Yeh MD Department of Ophthalmology Chang-Gung Memorial Hospital (Linko), Chang-Gung University College of Medicine, Taiwan

M Edward Wilson Jr MD

MUSC Storm Eye Institute 167, Ashley Avenue Charleston SC-29425-5536 (USA)

Manuel Parafita MD Deptt of Ophthalmology Universidad de Santiago de Compostela, Spain Portugal

Marcelino Rio MD Vice Chairman Microsurgery Center Cuban Institute of Ophthalmology Ramon Pando Ferrer Havana, Cuba

Marek E Prost MD Professor of Ophthalmology and Director Department of Ophthalmology Military Institute of Aviation Medicine Kransinskiego 54, 01-755 Warsaw, Poland

Contributors Marie Jose Tassignon MD PhD Professor Department of Ophthalmology University Hospital Antwerp Wilrikstraat 10, B-2650 Edegem (Antwerp) Belgium

Mark Packer MD

Oregan Eye Surgery Centre 1550, Oak Street, # 5, Eugene, OR- 97401, USA

Massimo Camellin MD

Consultant Ophthalmologist Rovigo, Italy

Minshan Jiang MD

Institute for Laser Medical and Bio-Photonics, Shanghai Jiaotong University Shanghai, China

Mujtaba A Qazi MD

Director, Clinical Studies Pepose Vision Institute 16216, Baxter Road Suite 205, Chesterfield, MO 63017, USA

NS Tsiklis

MD

Institute of Vision and Optics (IVO) Vardinoyiannion Eye Institute of Crete (VEIC), GR 71 003 Vouters Heraklion, Crete Greece

Nilesh Kanjani MS

Pooja Deshmukkh MS

Doctor Eye Institute Spenta Mansion SV Road, Andheri (West) Mumbai - 400 058, India

Renyuan Chu MD

Consultant Ophthalmologist Eye and ENT Hospital Fudan University Shanghai, China

Richard S Hoffman

Oregon Eye Surgery Centre 1550, Oak Street, # 5 Eugene OR- 97401, USA

Robert Latkany MD

Associate Adjunct Professor NY Eye & Ear Infirmary Founder Director Dry Eye Center of New York 115, East 57th Street 10th Floor, New York-10022 USA

Roberto Pinelli MD

Director Istituto Laser Microchirurgia Oculare Crystal Palace Via Cefelonia, 70 25124 Brescia, Italy

Rupal H Trivedi MD

Research Assistant Professor MUSC Storm Eye Institute 167, Ashley Avenue Charleston SC-29425-5536 (USA)

Consultant Dr Agarwal’s Eye Hospital 19, Cathedral Road Chennai-60086, India

Sandra Franco MD

Nita Shanbhag MS DOMS

Sonja Hairer MD FMH

Doctor Eye Institute Spenta Mansion SV Road, Andheri (West) Mumbai - 400 058 India

Paul Rolf Preussner MD

Professor of Ophthalmology University Eye Hospital Lagenbeckests-1 D-55101, Mainz-Germany

Dept Fisica, Physics Department Universidade do Minho Portugal Clinique de I’oeil 15, Avenue du Bois-de-la-Chapelle CH-1213 Onex Switzerland

Srinivas K Rao MD

Director Darshan Eye Clinic T 80, Fifth Main Road Anna Nagar, Chennai-600017 India

ix Sumita Karandikar MS

Doctor Eye Institute Spenta Mansion SV Road, Andheri (West) Mumbai - 400 058 India

Sunil Moreker MS Consultant PD Hinduja National Hospital and Medical Research Centre Veer Savarkar Marg Mahim Mumbai-400016 (India)

Sunita Agarwal MS DO PSVH Dr Agarwal’s Eye Hospital 19, Cathedral Road Chennai-600086, India 15, Eagle Street Langford Town Bengaluru, India

Tom Conze MD FMH Clinique de I’oeil 15, Avenue du Bois-de-la-Chapelle CH-1213 Onex Switzerland

Wolfgang Haigis MS PhD Assistant Professor Head of the Biometry Department University Eye Hospital Universitats - Augenklinik Josef - Schneider - Str 11 D-97080, Wuerzburg Germany

Yan Wang MD Professor Tianjin Medical University Director, Refractive Surgery Centre Tianjin Eye Hospital & Eye Institute Add : No4, Gansu Rd Tianjin 300020 China

Yoshiaki Nawa MD Associate Professor Department of Ophthalmology Nara Medical University Kashihara, Nara 6348522 Japan

Foreword to the Second Edition

In my opinion, the most important subject in the field of cataract surgery is the calculation of the appropriate lens implant (IOL) power. The very first complication of lens implantation was an IOL power prediction error of 16 D by Sir Harold Ridley when he implanted his first IOL in 1949. The mistake was repeated in 1950 when he implanted his second lens. He then turned his attention to fixing the problem which allowed lens implantation to proceed. Through the 50s, 60s and early 70s, it became the standard to use an 18.5 D prepupillary IOL for all eyes and the patient would wind up with the same refractive error they had all their life, regardless of how bad it was. Some had devised crude charts allowing a surgeon to vary that power based on the patient’s previous refraction in hopes of getting closer to emmetropia. However, European pioneer surgeons, such as Cornelius Binkhorst and Jan Worst of the Netherlands, were measuring the axial length of the eye using a crude Ascan ultrasound and calculating the target IOL power using a Gaussian optics formula such as that devised by von der Hiedje or Colenbrander. I introduced immersion ultrasound IOL power calculation in the America in 1974 using the original Hoffer formula and stimulated Sonometrics, Inc (Boston) to manufacture the first specific A-scan for IOL power (the DBR-100) in 1975. Over the years, improvements in ultrasound instrumentation and development of more accurate formulas (Haigis, Hoffer Q, Holladay and SRK/T) have made lens power calculation very accurate when there is attention to detail. The introduction of the IOLMaster by Zeiss in 1999 revolutionized this process by making axial length measurement much easier, repeatable and more accurate with only 10-15% of eyes still needing an ultrasound measurement. In the past, patients quietly accepted needing an eyeglass prescription after cataract surgery. That is no longer true. Patient expectations today are that their postoperative refractive error will be what they expect it to be and at no time is this more important than when performing a clear lens extraction to correct ametropia or implanting a phakic IOL. It behoves every surgeon implanting IOLs to become an expert in this subject and this textbook will help in that regard. Obtaining the exact IOL power desired is the biggest practice builder there is. Making patients happy, however, is the most gratifying compensation and what this is all about. I congratulate Dr Garg for assembling such a large group of contributors so as to enable the reader to learn a lot about this important topic, be they novice or expert. I may not completely agree with every statement in this textbook but difference in experience and opinion is what helps move science forward. Kenneth J Hoffer MD FACS Clinical Professor of Ophthalmology, UCLA St. Mary’s Eye Center, 1301 20th St. Suite 250 Santa Monica, CA 90404 , USA 310-451-2020 Mobile: +1-310-387-2013 [After 1 PM PST Only] [email protected] www.KHoffer.com Travel Site www.EyeLab.com IOL Power Site

Foreword to the First Edition In 1999, I visited India for the first time, to meet my now good friend Dr. Amar Agarwal in Chennai. The knowledge and skill I met imbued me with a deep respect for my Indian colleagues, I therefore felt honoured to be asked to write the Foreword to this book. A good textbook should bear the characteristics of an enthusiastic teacher, taking students by the hand and leading them through the tasks to be mastered, leaving them wiser for the experience. The authors of this book have fully understood this process by which we learn. As early as 1870, Placido studied the corneal surface with his Disc. In 1880 Javal in France was already aware of the importance of photographically recording the images to be studied. In 1896, Professor Allvar Gullstrand (1868 – 1930) developed the first photokeratoscope, giving us quantitative data on the form of the cornea. This allowed him to calculate the corneal meridian profiles, which are surprisingly similar to those derived from modern Corneal Topography Analyses. Gullstrand improved the ophthalmoscope, and invented the slit-lamp. He and Helmholtz were the first to describe schematic eye models to approximate the optical properties of a normal eye. As a member of the Swedish Ophthalmological Community for almost 30 years, the work of Professor Gullstrand, who won the Nobel Prize in Physiology or Medicine in 1911, lies close to my heart. Indeed his work in many ways has helped to provide the background to the knowledge presented in this book. I started my Residency in Ophthalmology 1976, and implanted my first IOL in 1983. Biometry and IOL calculations were relatively crude at that time, and postoperative anisometropia was not uncommon, something that we have been able to correct in many cases after introduction of the Excimer laser. In the Spring of 1993, I performed my first PRK. At that time the cornea was viewed as an essentially two-dimensional piece of plastic. There were many satisfied patients but also a number of dissatisfied. This textbook by Internationally Eminent Dr. Ashok Garg and co-authors will explain just why a more complex evaluation of the eye is needed, and will describe the state of the art in the technology we use to ensure the best possible results today. Jes Mortensen MD The Eye Department Örebro University Hospital SE-701 85 Örebro, Sweden Fortunagatan 29 , SE-553 23 Jonkoping, Sweden Telephone: 46 36 129601 e-mail: [email protected] [email protected] [email protected]

Preface to the Second Edition

The First Edition of IOL Power Calculation book released only three years ago is completely sold out much before our expectations with worldwide appreciations and acclamations. We are certainly encouraged by this tremendous response and our publisher has asked us for revised (second) edition. IOL power calculation is a complex and important subject. A number of new formulas have come up for cataract and refractive surgeons which deliver good outcomes and provide another avenue to validate our IOL selections. The Second edition contains 56 chapters covering all aspects of IOL power calculation from basic to advanced IOL power calculations in various clinical and difficult conditions of the eye by International Masters of this field. Precision in IOL power calculations shall lead to accurate vision in cataract and refractive patients with less complications. Our sincere gratitudes are due to publisher specially Sh. Jitendar P Vij (CEO), Mr. Tarun Duneja (General Manager, Publishing) and all staff members of M/s Jaypee Brothers Medical Publishers (P) Ltd. for their dedicated efforts and preparation of second edition in a very short time. We are confident that the second edition covering all clinical conditions and newer formulas shall serve as ready reference to ophthalmologists worldwide in their clinical practice for precise IOL power calculations. Editors

Preface to the First Edition

Intraocular lens power calculation is an important clinical parameter. An accurate and precise biometry is one of the key factors in obtaining a good refractive outcome after cataract surgery. A small preoperative ocular biometry error leads to significant postoperative refractive error posing problems both for patient and surgeon. Inaccurate axial length measurements and inappropriate use of Intraocular lens power formulae generally lead to this problem. Standard keratometry and computed corneal topography are commonly used parameters. Estimation of central anterior chamber depth is vital in new theoretical formulae for IOL power calculation. New technologies have been introduced in this field specially customised IOL power formulae, measurement of axial length (IOL master), customised axial length approach, computerized rotary 3D scanning system, etc. These techniques certainly help the ophthalmologists for proper preoperative assessment to obtain predicted postoperative refractive outcomes. Improved measurement technologies and refinements in IOL power formulae reduce postoperative refractive errors in long and short eyes as well as normal axial length eyes. This International book of IOL power calculations covers all aspects of calculations from normal cornea to after refractive surgery, in Phaco/Microphaco, on irregular corneal surface, in phakic IOLs, in corneal scarring and astigmatism and in pediatric cataract surgery. A number of leading International ophthalmologists who are masters in this field have contributed their experiences in form of chapters for the benefit of ophthalmologists. Our special thanks to the publisher M/s Jaypee Brothers Medical Publishers (P) Ltd. specially Mr. Jitendar P Vij (CEO), Mr. Tarun Duneja (General Manger, Publishing) and all staff members who extended full cooperation and published this International book in a very short time. We are hopeful that this book shall meet the expectation of ophthalmologists in providing complete information in relation to IOL power calculations in their day-to-day clinical practice. Editors

Contents

Section 1: Preliminary Considerations and Various IOL Power Calculation Formulas and Basics 1. Schematic Eye ................................................................................................................................................................ 3 Athiya Agarwal, Amar Agarwal, Ashok Garg (India) 2. A-scan Biometry ............................................................................................................................................................. 5 Sunita Agarwal, Amar Agarwal, Ashok Garg (India) 3. Corneal Topography .................................................................................................................................................... 10 Athiya Agarwal, Sunita Agarwal, Amar Agarwal, Nilesh Kanjani (India) 4. Optical Corneal Tomography .................................................................................................................................... 21 Sandra Franco, Jose B Almeida (Portugal), Manuel Parafita (Spain) 5. Optical Biometry with IOL Master (Partial Coherence Interferometry) ............................................................. 24 Ashok Garg (India) 6. Anterior Chamber Depth in IOL Power Estimation .............................................................................................. 26 Aravind R Reddy (UK) 7. How to Calculate the Constant A ............................................................................................................................... 28 Sonja Hairer, Tom Conze, Jerome Bovet (Switzerland) 8. Axial Length Dependence of IOL Constants .......................................................................................................... 31 Wolfgang Haigis (Germany) 9. IOL Calculations: When, How and Which? ............................................................................................................. 36 Kumar J Doctor, Nita Shanbhag, Sumita Karandikar, Pooja Deshmukkh (India) 10. How to Measure a Correct Central Keratometric Reading for IOL Power Calculation after LASIK Surgery? .................................................................................................................................................. 46 Lung-Kun Yeh, I-Jong Wang (Taiwan) 11. An Update on IOL Power Calculation Formulas .................................................................................................... 51 JT Lin (Taiwan), Ashok Garg (India) 12. The New IOL Formulas based on Gaussian Optics .............................................................................................. 62 JT Lin (Taiwan) 13. Classical vs Modern Formulas for Estimated Lens Position (ELP) ...................................................................... 70 JT Lin (Taiwan) 14. IOL Power Calculations .............................................................................................................................................. 75 Kenneth J Hoffer (Santa Monica, CA, USA)

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Mastering the Techniques of Intraocular Lens Power Calculations 15. The Theoretical Summary of IOL Formulas ........................................................................................................... 92 JT Lin (Taiwan) 16. Error Analysis of IOL Power Calculations ............................................................................................................. 101 JT Lin (Taiwan) 17. The Basics of Accommodating IOLs ...................................................................................................................... 106 JT Lin (Taiwan) 18. IOL Calculation in Long and Short Eyes ................................................................................................................ 114 Wolfgang Haigis (Germany) 19. Customization of IOL Formulas .............................................................................................................................. 121 B Vineeth Kumar (UK)

Section 2: IOL Power Calculations in Cataract Surgery 20. Intraocular Lens Power Selection for Children ..................................................................................................... 127 Rupal H Trivedi (USA), M Edward Wilson Jr (USA) 21. Age Dependent IOL Power Calculations for Pediatric Patients ........................................................................ 136 JT Lin (Taiwan) 22. History & Method of Intraocular Lens Power Calculation for Cataract Extraction Surgery after Corneal Refractive Surgery .............................................................................................................. 142 Alberto Artola Roig, Jorge L Alio Y Sanz (Spain) 23. Intraocular Lens Power Calculations in Phaco and Microphaco ....................................................................... 146 Ashok Garg (India), Arif Adenwala (UAE) 24. Intraocular Lens Power Calculations for High Myopia ....................................................................................... 153 Renyuan Chu, Jinhui Dai (China) 25. Accuracy of Intraocular Lens Power Calculation in Bimanual Microphacoemulsification .......................... 159 Gian Maria Cavallini, Luca Campi, Giovanni Neri (Italy) 26. Clinical Outcomes of Cataract Surgery after Previous Refractive Surgery ...................................................... 164 Frank J Goes (Belgium)

Section 3: IOL Power Calculations in Refractive Surgery (Corneal and Lenticular Refractive Surgery) 27. IOL Power Calculations: A Topographic Method ................................................................................................ 175 Frederic Hehn (France) 28. IOL Power Calculation in Post-hyperopic PresbyLASIK Cataract: Preliminary Results ............................... 180 Roberto Pinelli (Italy) 29. Comparison of Methods for IOL Power Calculation after Incisional and Photoablative Refractive Surgery ............................................................................................................................ 184 Antonio Calossi, Massimo Camellin (Italy) 30. IOL Power Calculations after Corneal Refractive Surgery ................................................................................. 205 Srinivas K Rao (India), Arthur Cheng, Dennis SC Lam (China)

Contents 31. The Latkany Regression Formula for Intraocular Lens Calculations after Myopic Refractive Surgery ....................................................................................................................................... 213 Evelyn Icasiano, Robert Latkany (USA) 32. The Latkany Regression Formula for Intraocular Lens Calculations after Hyperopic Refractive Surgery ................................................................................................................................. 218 Evelyn Icasiano, Robert Latkany (USA) 33. Which IOL Formula to Use after Refractive Surgery ........................................................................................... 221 Sonja Hairer, Tom Conze, Jerome Bovet (Switzerland) 34. Intraocular Lens Power Calculation after Advanced Surface Ablations (ASA) .............................................. 225 Tsiklis NS, Kymionis GD, Portaliou DM, Pallikaris IG (Greece) 35. The Mathematics of LASIK ..................................................................................................................................... 231 JT Lin (Taiwan) 36. Preoperative Evaluation of the Anterior Chamber for Phakic IOLs with the AC OCT .................................. 238 Georges Baikoff (France) 37. Biometry for Refractive Lens Surgery .................................................................................................................... 244 Mark Packer, I Howard Fine, Richard S Hoffman (USA) 38. IOL Power Calculations in Phakic IOLs ................................................................................................................ 252 Dimitrii Dementiev, Kukrenkov Vetchiaslav (Italy) 38. Raytracing Analysis of Accommodating IOL ........................................................................................................ 254 Yoshiaki Nawa (Japan) 40. Analysis of Dual-optics Accommodating IOLs ..................................................................................................... 259 JT Lin (Taiwan) 41. Aspherical IOL Analysis .......................................................................................................................................... 265 JT Lin (Taiwan)

Section 4: Miscellaneous (Recent Advances and IOL Power Calculations in Difficult Situations) 42. Determining Corneal Power for Intraocular Lens Calculations in Patients with Corneal Scarring and Irregular Astigmatism ............................................................................................................................................... 277 Mujtaba A Qazi, Irwin Y Cua, Jay S Pepose (USA) 43. IOL Calculation in Hyperopes ................................................................................................................................. 281 Wolfgang Haigis (Germany), Frank J Goes (Belgium) 44. Consistent IOL Calculation in Normal and Odd Eyes with the Raytracing Program OKULIX .................... 285 Paul Rolf Preussner (Germany) 45. A-scan in Difficult Situations ................................................................................................................................... 292 Anand A Shroff (India) 46. Management of Refractive Surprises after Cataract Surgery ............................................................................. 305 Armando Capote, Eneida de la C Perez, Marcelino Rio (Cuba) 47. Intraocular Lens Power Calculation in the High Myopic Eye ............................................................................. 314 Fengju Zhang, Yan Wang (China) 48. Calculation of Intraocular Lens Power in Cataract with Silicone Oil Eyes ....................................................... 318 Fengju Zhang, Yan Wang (China)

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Mastering the Techniques of Intraocular Lens Power Calculations 49. Intraoperative IOL Power Calculation ................................................................................................................... 320 Arturo Peréz-Arteaga (Mexico) 50. ZEMAX Raytracing Method for Accommodative IOL ......................................................................................... 327 JT Lin (Taiwan), Minshan Jiang (China) 51. Problems of IOL Power Calculation in Pediatric Cataract Surgery ................................................................... 331 Marek E Prost (Poland) 52. Intraocular Lens Calculation after Prior Refractive Surgery ............................................................................... 337 Kenneth J Hoffer (Santa Monica, CA, USA) 53. Cataract Surgery: Calculating the IOL Power in Case of Anisometropia ......................................................... 345 Laure Gobin, Jos J Rozema, Marie-José Tassignon (Belgium) 54. Review of IOL Power Calculation: A Theoretical Analysis of Proposed Formulas ........................................ 356 Laure Gobin, Jos J Rozema, Marie Jose Tassignon (Belgium) 55. IOL Power Calculation for Cornea Triple and Penetrating Keratoplasty with IOL Exchange ..................... 368 Ashok Sharma (India) 56. IOL Power Calculations in Eyes with Irregular Corneas ..................................................................................... 371 Barun K Nayak, Sunil Moreker (India) Index ............................................................................................................................................................................. 375

Athiya Agarwal, Amar Agarwal, Ashok Garg (India)

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Schematic Eye

INTRODUCTION A schematic eye is extremely important to understand as it explains to us the refractive elements of the eye and the way the eye refracts. REFRACTION BY COMBINATION OF LENSES When two lenses are placed in apposition to one another the effect of the combination is additive. This may be expressed more accurately by saying that in a system of lenses, provided these are infinitely thin, infinitely near and are accurately centered on the same optic axis, the total refracting power of the system is equal to the algebraic summation of the refracting power of the lenses. Thus, if a +2 D lens is combined with a –3 D lens, the combination will have a refracting power of –1 D. These simple relations hold when the lenses, which compose the system, are so thin and so close together that their thickness and their distances apart can be neglected. When this cannot be done, however, the determination of the nature and the position of the resultant image becomes more complicated. It involves the construction of the image formed by the first element in the system, its consideration as the object presented to the second element and the construction of the image by this, and so on, through all the component parts of the system. If we take the refraction by two convex lenses A and B (Fig. 1.1) we will see that the image should have been formed by the first lens at A1. This does not happen, because of the refracting power of the second lens. The image is thus formed at F. In the same manner, refraction is caused by a convex and a concave lens combination. The image, which should form at A1 forms at F.

Fig. 1.1: Refraction by combination of lenses

GAUSS’S THEOREM In a complex system such as the eye, such a process would be very tedious. So, Gauss brought out his theorem for simplifying the refraction in the eye. Gauss simplified the refraction occurring by a compound homocentric system as having comprised of Figure 1.2. • Two principal foci—F1 and F2 • Two nodal points—N1 and N2 • Two principal points—H1 and H2. No matter how complex a homocentric system of refractive elements may be, it is obvious that there will always be a ray originating from the object AB running parallel to the axis. This reaches one of the refracting surfaces H2 and then after refraction cuts the axis at a point F2. Another ray originating from the object gets refracted

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Mastering the Techniques of Intraocular Lens Power Calculations The figures in mm are shown in Figure 1.3. The ray of light passes from the object and after refracting at H2 reaches F2. Another ray of light passes from the object and after refracting at H1 reaches F2 again. There are two nodal points N1 and N2.

LISTING’S EYE

Fig. 1.2: Gauss’s theorem

at the first refracting surface H1 and meets the first ray. The third ray passes through the nodal point. The image A1B1 is formed at the point where these three rays meet. The nodal points N1 and N2 correspond to the single optical center of a simple lens. The distance from H1 to F1 is called the anterior focal length D1. The distance from H2 to F2 is called the posterior focal length D2.

Listing felt even Gullstrand’s schematic eye was complicated and thus created the Listing’s eye. In this he felt that the two principal points H1 and H2 could be taken to be one as H. This point could be in between H1 and H2 (Fig. 1.4). This is situated about 1.5 mm behind the cornea. Similarly, the two nodal points could be taken to be one nodal point N. This is because the two nodal points are very near each other and no significant error would arise if they were resolved into one point. This single nodal point is situated about 7.8 mm behind the anterior surface of the cornea. There are two foci F1 and F2. The dioptric power of the eye is 60 D. The other measurements are shown in Figure 1.4.

SCHEMATIC EYE OF GULLSTRAND Using the Gauss’s theorem, a schematic eye of Gullstrand was created. Gullstrand considered the eye to consist of a coaxial homocentric system of lenses. He resolved the eye into 6 cardinal points and 2 focal lengths (Fig. 1.3). 1. H1—Anterior principal point 2. H2—Posterior principal point 3. N1—First nodal point 4. N2—Second nodal point 5. F1—Anterior focal point 6. F2—Posterior focal point 7. D1—Anterior focal length 8. D2—Posterior focal length

Fig. 1.3: Gullstrand’s schematic eye

DONDER’S REDUCED EYE Donder (Fig. 1.4) in the interest of simplicity treated the eye as a single refracting surface. The anterior focal length was 15 mm and the posterior focal length was 20 mm. The nodal point was 5 mm posterior to the principal plane.

Fig. 1.4: Listing’s and Donder’s eye

Sunita Agarwal, Amar Agarwal, Ashok Garg (India)

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A-scan Biometry

INTRODUCTION It is necessary for every ophthalmologist who is working with intraocular lenses to know how to calculate the power of the IOL.

AXIAL LENGTH MEASUREMENT For IOL implantation, the ultrasonic method affords the best way to calculate the axial length and achieves the desired postoperative refraction. The instruments available to make these measurements are of two basic types: i. Instruments with rigid probe tips ii. Instruments with distensible tips or with water baths. Those instruments with distensible membranes on the front of the probe are approximately 5 percent more accurate in making measurements than those with the rigid tip. The reasons why the distensible tip are better are as follows: 1. The distensible tip prevents indenting the cornea when the measurement is made, and does not cause the eye to appear artificially shortened. A rigid tip can cause corneal indentation between 0.1 and 0.3 mm, resulting in error from 0.3 to 1.0 diopters (Fig. 2.1). In other words if one is buying an A-scan, one should get one with a distensible tip. 2. The distensible tip helps to separate the corneal reflection from the signal sent out from the front surface of the transducer, i.e. it makes it more accurate to determine exactly where the front surface of the cornea is, and when it is not in direct contact with the transducer.

Fig. 2.1: Disadvantage of hard tip transducer—note indentation on the cornea

Fig. 2.2: Biometer

KERATOMETRIC MEASUREMENTS The keratometric measurements can be done through a keratometer or through an autokeratometer. Many biometers (Fig. 2.2) have provision for connecting the auto-

Mastering the Techniques of Intraocular Lens Power Calculations

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keratometer to their computer so that once the keratometer reading is taken automatically, the value is entered into the biometer, and one does not have to feed it in again.

IOL FORMULA There are two major categories of IOL formulae.

Theoretical Formula

Introduction

where, D = Dioptric power of IOL in aqueous humor, 1336 = Index of refraction of vitreous and aqueous, r = Radius of curvature of the anterior surface of the cornea, a = Axial length of the globe (mm), and d = Distance between the anterior cornea and the IOL.

Disadvantages

This formula is based on an optical model of the eye. An optics equation is solved to determine the IOL power needed to focus light from a distant object onto the retina. In the different formulae, different assumptions are made about the refractive index of the cornea, the distance of the cornea to the IOL, the distance of the IOL to the retina as well as other factors. These are called theoretical formulae because they are based on a theoretical optical model of the eye. All of these theoretical equations make simplifying assumptions about the optics of the eye, and hence, provide a good (but not perfect) prediction of IOL power. The most popular formula in this group is the Binkhorst formula. This is based on sound theory. All the theoretical formulae can be algebrically transformed into the following P = [N/(L–C)] – [NK/(N–KC)] where, P = Dioptric power of the lens for emmetropia N = Aqueous and vitreous refractive index L = Axial length (mm), C = Estimated postoperative anterior chamber depth (mm), and K = Corneal curvature [D].

Binkhorst Formula Binkhorst has made a correction in his formula for surgically induced flattening of the cornea, using a corneal index of refraction of 1.333. Binkhorst also corrects for the thickness of the lens implant by subtracting approximately 0.05 mm from the measured axial length. Thus with the Binkhorst formula, 0.25 mm is added to the measured axial length to account for the distance between the vitreoretinal interface and the photoreceptor layer, and 0.05 mm is subtracted for lens thickness, resulting in a net addition of 0.20 mm to the measured axial length. The Binkhorst’s formula is: D = 1336 (4r–a)/(a–d) (4r–d)

The problem in the theoretical formula is in the axial length measurement. The reason why it is difficult to measure the axial length accurately is that one must know the exact velocities of the ultrasound as it travels through the various structures of the eye. Because of the variation of the acoustic density of a cataract, these velocities cannot be known exactly. As a result, when cataractous lenses are much more acoustically dense than the average lens, the sound wave will move more rapidly through the lens and return to the transducer much more quickly than would have been expected for a given axial length. As a result of the velocity error, the eyes appear to be shorter. The formula consequently calculates an IOL power for an axial length which is too short. The patient then becomes overminused (too myopic). Theoretical formulae help the surgeon to anticipate what should result, not what will result from implantation.

Regression Formula (Empirical Formula)

Introduction The regression formulae or empirical formulae are derived from empirical data and are based on retrospective analysis of postoperative refraction after IOL implantation. The results of a large number of IOL implantations are plotted with respect to the corneal power, axial length of the eye, and emmetropic IOL power. The best-fit equation is then determined by the statistical procedure of regression analysis of the data. Unlike the theoretical formulae, no assumptions are made about the optics of the eye. These regression equations are only as good as the accuracy of the data used to derive them.

Advantages Implant power calculations can be made much more accurately through the use of regression formulae that are based on the analysis of the actual results of many

A-scan Biometry uncomplicated IOL implantations in previous cataract surgeries. Since regression analysis is based on the results of actual operations, it includes the vagaries of the eye and measuring devices, vagaries that theoretical formulae attempt to address with correction factors.

Sanders-Retzlaff-Kraff (SRK) Formula The most popular regression formula is the SRK formula which was developed by Sanders, Retzlaff and Kraff in 1980. This is:

P = A – 2.5 L – 0.9K where, P = Implant power to produce emmetropia, L = Axial length (mm), K = Average keratometer reading, and A = Specific constant for each lens type and manufacture. The SRK formula calculates the IOL power by linearly regressing the results of previous implants. As this is a linear formula, it will underestimate the power of highpowered lenses and it will overestimate the power of the low-powered lenses compared to the theoretical calculation. For example, if the Binkhorst formula predicts that a 28-diopter lens should be used, the SRK formula will predict that a 26-diopter lens should be used. In lenses with low power, if the Binkhorst formula predicts that a 10-diopter lens is necessary, the SRK will predict that a 12-diopter lens should be used.

RELATION OF EQUIPMENT TO SPECIFIC FORMULAE Most of the instruments calculate the desired power for the IOL at least by three different methods including a regression formula and a theoretical formula. It is the responsibility of the doctor to select which of the formulae he or she wants to use. Rarely, between 18 and 22 diopters, is there a significant difference between the calculated lens powers. But outside this range, there will be a progressive increase in difference between that determined by the theoretical formula and the one calculated by the regression formula. Since the regression formula has turned out to be statistically more accurate, 5 percent at these extremes, it is presently more reliable than the theoretical formulae. The manufacturers vary as to which programs they provide. One should anyway make sure that both the regression and theoretical formulae are included so that one has the opportunity to personally select the most reliable technique for one’s surgery.

TARGETING IOL POSTOPERATIVE REFRACTION The question that comes to one’s mind next is “How to predetermine what postoperative refraction the patient should have?” This is the one parameter which the doctor has to decide upon and feed into the computer. The other parameters like axial length, etc. we have no control over. The answer depends on whether we are doing a monocular or binocular correction.

Monocular Correction If we are considering only one eye (i.e. if the other eye has cataract or is amblyopic), targeting the postoperative refraction for approximately –1.00 diopter is probably the best choice. This is usually best because most people have visual needs for both distance and near. This means that the patient wants to be able to drive and to read without wearing glasses. If we target the postoperative refraction to –1.00D, it will allow the patient to perform most tasks with no glasses. At times, when they need finer acuity, they can wear regular bifocals, which will correct them for distance and near. The second reason for targeting the postoperative refraction to –1.00D is that statistically, between 70 percent and 90 percent of the patients will fall within +1.00D error of the desired postoperative refraction. The errors, as mentioned earlier are due to our inexact measurements. Therefore, the patient will fall between plano and –2.00D 90 percent of the time. This will assure most patients of useful vision without glasses. Hence, the error of the ultrasound is best handled by choosing the postoperative refraction to –1.00D. If we would target for plano, then 90 percent of the patients will be between –1.00 and +1.00D. When the patient’s refraction is on the +1 side he or she has no useful vision at any distance because he or she is hyperopic and does not have the ability to accommodate. Consequently, because it is very undesirable to have a hyperopic correction, targeting for –1.00D not only optimizes the best vision at all distances, but also minimizes the chance for hyperopia that can result from inaccurate ultrasonic measurements.

Binocular Correction When the vision in the other eye is good, its refraction must be considered for binocular vision. One overriding rule when prescribing glasses is that one should never prescribe spectacles which gives the patient a difference in the power between the right and left lens greater than 3D. The reason for this is that even though the patient

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may have 6/6 vision in primary gaze, when the patient looks up or down, the induced vertical prism difference in the two eyes is so great that it will create double vision. In a patient who has good vision in the nonoperative eye, one must target the IOL power for a refraction within 2D of his or her present prescription in the nonoperative eye. Two diopters, not three, due to our 1D A-scan variability. For example, if we have a patient who is hyperopic and has +5D correction in each eye, we cannot target the IOL for a postoperative refraction of –1.00D because this would produce a 6D difference between the two lenses resulting in double vision. We must therefore select the IOL power to obtain a refraction which is approximately 2D less than the nonoperative eye. Consequently, on our patient who is +5D in both eyes, we should target the postoperative refraction in the eye with the cataract for +3D, so that there is a 90 percent probability that there will be less than a 3D difference. In contrast, if the patient were highly myopic in each eye, for example, –10D in both eyes, we should target the IOL power to produce refraction of approximately –8D. Again, we have limited the difference in the spectacles lenses to a 2D difference in the final prescription. Again, target, for a 2D difference not a 3D, because there is approximately a 1D tolerance in the accuracy of the ultrasonic measurement. If the operation on the second eye is to be done shortly after the first, the preoperative spectacles refraction can be ignored, and the patient is treated as if he or she were monocular.

Axial Length Correction Factor

FACTORS AFFECTING ACCURACY OF IOL POWER CALCULATION

Postoperative Change in Corneal Curvature

Many factors can affect the accuracy of the power of the IOL calculated.

Keratometry Keratometers only measure the radius of curvature of the anterior corneal surface. This measurement must be converted to an estimate of the refracting power of the cornea in diopters, using a fictitious index (the true corneal refractive index of 1.376 could be used only if both the anterior and posterior corneal radii of curvature were known). The variability can alter calculated corneal dioptric power by 0.7D.

Axial Length Measurement As explained earlier, indentation of the cornea by the A scan instrument tip can alter the axial length affecting the accuracy of the power of the IOL.

The distance from the vitreoretinal interface to the photoreceptor layer has been estimated to be about 0.15 to 0.5 mm. This distance can affect the accuracy of the IOL power calculated.

Site of Loop Implantation Posterior chamber IOLs may be implanted with both loops in the ciliary sulcus or in the capsular bag, or with one loop in the sulcus and one loop in the capsular bag. Positioning the implants within the capsular bag places the implant further back in the eye and decreases the effective power of the lens. There is usually a 0.5 to 1.5D loss of effectivity by placing the implant in the capsular bag as opposed to the ciliary sulcus. A higher power lens should therefore be used when the implant is placed in the capsular bag.

Orientation of Planoconvex Implants Some surgeons implant planoconvex posterior chamber lenses with the plano surface forward. Such flipping of the implant decreases the effective power of the lens by 0.75D even if the position of the lens is unchanged. An additional 0.5D loss of effectivity occurs because the principal plane of the lens is usually displaced further back into the eye. Thus, a total loss in effectivity of 1.25D is expected by turning the lens around.

Suturing of a cataract incision has a tendency to steepen the vertical meridian. These changes affect the postoperative refraction of the patient.

Density of the Cataract The density of the cataract also makes a difference. In a dense cataract (Fig. 2.3), the ultrasonic waves travel faster whereas in an early cataract (Fig. 2.4) the ultrasonic waves travel slower.

IOL Tilt and Decentration When a lens is tilted, its effective power increases and plus cylinder astigmatism is induced about the axis of the lens tilt. The tilting of the lens occurs if one loop is in the capsular bag and the other in the sulcus (Fig. 2.5). Alternatively, residual cortex being left behind can cause

A-scan Biometry

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Fig. 2.3: Ultrasonic reading in dense cataract Fig. 2.6: Topograph of a patient in whom a wrong power IOL was implanted

Fig. 2.4: Ultrasonic reading in early cataract

Fig. 2.7: Topograph of the same patient as in Figure 2.6 after LASIK

an inflammatory response which causes contraction and pulling unequally on parts of the loops and the optic.

PSEUDOPHAKIC LASIK

Fig. 2.5: Captive iris syndrome

If a patient has had a wrong biometry then the solution can be to remove the IOL and replace it with a correct powered IOL. Another alternative is to perform LASIK and correct the problem. Figure 2.6 is the topograph before LASIK of a patient who had a power of –10.0 diopters after IOL implantation. The patient was referred to us and we did a LASIK as the patient was operated a year back. We felt that the IOL might be fixed firmly in the bag. Figure 2.7 is the topograph after LASIK.

Mastering Techniques of Intraocular Power Calculations Athiya the Agarwal, Sunita Agarwal,Lens Amar Agarwal, Nilesh Kanjani (India)

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3

Corneal Topography

INTRODUCTION Topography is defined as the science of describing or representing the features of a particular place in detail. In corneal topography, the place is the cornea, i.e. the features of the cornea are described in detail. The word topography is derived1, 2 from two Greek words: (i) topos—meaning place, (ii) graphien—meaning to write.

CORNEA There are basically three refractive elements of the eye, namely axial length, lens and cornea. The cornea is the most important plane or tissue for refraction. This is because it has the highest refractive power (which is about + 45 D) and it is easily accessible to the surgeon without going inside the eye. To understand the cornea, one should realize that the cornea is a parabolic curve—its radius of curvature differs from the center to the periphery. It is steepest in the center and flattest in the periphery. For all practical purposes the central cornea, i.e. the optical zone is taken into consideration, when one is doing a refractive surgery. A flatter cornea has less refractive power and a steeper cornea has a higher refractive power. If we want to change the refraction, we must make the steeper diameter flatter and the flatter diameter steeper.

KERATOMETRY The keratometer was invented by Hermann Von Helmholtz and modified by Javal, Schiotz, etc. If we place an object in front of a convex mirror we get a virtual, erect and minified image (Fig. 3.1). A keratometer in relation to

Fig. 3.1: Physics of a convex mirror. Note the image is virtual, erect and minified. The cornea acts like the convex mirror and the mire of the keratometer is the object

the cornea is just like an object in front of a convex reflecting mirror. Like in a convex reflecting surface, the image is located posterior to the cornea. The cornea behaves as a convex reflecting mirror and the mires of the keratometer are the objects. The radius of curvature of the cornea’s anterior surface determines the size of the image. The keratometer projects a single mire on the cornea and the separation of the two points on the mire is used to determine corneal curvature. The zone measured depends upon corneal curvature—the steeper the cornea, the smaller the zone. For example, for a 36 D cornea, the keratometer measures a 4 mm zone and for a 50 D cornea, the size of the cone is 2.88 mm. Keratometers are accurate only when the corneal surface is a sphere or a spherocylinder. Actually, the shape of the anterior surface of the cornea is more than a sphere or a spherocylinder. But keratometers measure the central 3 mm of the cornea, which behaves like a sphere or a spherocylinder. This is the reason why Helmholtz could manage with the keratometer (Fig. 3.2). This is also the reason why most ophthalmologists can manage

Corneal Topography

Fig. 3.2: Keratometers measure the central 3 mm of the cornea, which generally behaves like a sphere or a spherocylinder. This is the reason why keratometers are generally accurate. But in complex situations like in keratoconus or refractive surgery they become inaccurate

management of cataract surgery with the keratometer. But today, with refractive surgery, the ball game has changed. This is because when the cornea has complex central curves like in keratoconus or after refractive surgery, the keratometer cannot give good results and becomes inaccurate. Thus, the advantages of the keratometer like speed, ease of use, low cost and minimum maintenance is obscured. The objects used in the keratometer are referred to as mires. Separation of the two points on the mire are used to determine corneal curvature. The object in the keratometer can be rotated with respect to the axis. The disadvantages of the keratometer are that they measure only a small region of the cornea. The peripheral regions are ignored. They also lose accuracy when measuring very steep or flat corneas. As the keratometer assumes the cornea to be symmetrical, it becomes at a disadvantage if the cornea is asymmetrical as after refractive surgery.

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Fig. 3.3: Keratoscopy

modification is captured by a video camera. This information is analyzed by computer software and the data is then displayed in a variety of formats. To simplify the results to an ophthalmologist, Klyce in 1988 started the corneal color maps. The corneal color maps display the estimate of corneal shape in a fashion that is understandable to the ophthalmologist. Each color on the map is assigned a defined range of measurement. The hot colors are red—steep and the cold colors are blue—flat (Figs 3.4 and 3.5).

NORMAL CORNEA In a normal cornea, the nasal cornea is flatter than the temporal cornea. This is similar to the curvature of the long end of an ellipse. The normal corneal topography can be round, oval, irregular, symmetric bow-tie or asymmetric bow-tie in appearance.

KERATOSCOPY To solve the problem of keratometers, scientists worked on a system called keratoscopy. In this, they projected a beam of concentric rings and observed them over a wide expanse of the corneal surface (Fig. 3.3). But this was not enough and the next step was to move into computerized videokeratography.

COMPUTERIZED VIDEOKERATOGRAPHY In this some form of light like a Placido disk is projected onto the cornea. The cornea modifies this light and this

Fig. 3.4: Topography of a patient with keratoconus. Note the red area which are the steep areas

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Mastering the Techniques of Intraocular Lens Power Calculations

Fig. 3.7: Topography of a normal cornea Fig. 3.5: Topography of a patient after LASIK (Laser in situ keratomileusis). Note the blue color in the center indicating flattening in the center after LASIK

Fig. 3.6: Topography machine

READING A CORNEAL TOPOGRAPHY How does one read a corneal topographic map created by a topographic machine (Fig. 3.6)? Let us look at some corneal topographic maps. First of all let us look at a normal cornea (Fig. 3.7). Whenever you see a corneal topographic picture, look at the red number. In Figure 3.7 you can see two topographic pictures: one of the left eye denoted by the letter L in red, and the other of the right eye denoted by the letter R in red. Below that you see the number written 43.8 D at 80 degrees axis. This is written under the left eye topographic picture. In brackets is written 7.71 in blue under this is written 43.11 D at 170 degrees axis and in brackets is written 7.83. This means that the patient has in the left eye 43.8 D corneal power at axis 80 degrees and 43.11 D at 170 degrees. The brackets indicate the radius of curvature of the cornea in mm. Below these two figures is

written difference 0.69 D in red which means that the patient has an astigmatism (difference between 43.8 and 43.11) of + 0.69 D at axis 80 degrees as it is marked in red. This is for the central 3 mm zone. You can also calculate for further zones like 5 mm zone, etc. In the right eye, the patient has an astigmatism of + 0.45 D at 66 degrees. On the top of the photo you will see color bars and you can see that the red colors are steep and the blue are flat. In Figure 3.8, you can see the patient has in the right eye an astigmatism of + 2.82 D at 90 degrees. This is a classic case of with-the-rule (WTR) astigmatism. If you see the corneal topographic pattern, you will see a bowtie appearance. In other words this is a symmetric bow-tie appearance.

CORNEAL DISEASES The most important corneal disease in which corneal topography is used is keratoconus (Fig. 3.9). In Figure 3.9, you can see a picture of a patient with keratoconus. See the large amounts of red in the picture. Also note the astigmatism as + 11.03 D at axis 107 degrees. See also the radius of curvature (the figure in brackets) is 5.85 mm. If anything is below 7 mm radius of curvature, start thinking of keratoconus. If by chance the patient has keratoconus, laser in situ keratomileusis (LASIK) is not done. Other areas where corneal topography is used is in checking the cornea after a penetrating keratoplasty (Fig. 3.10) or after injuries where corneal scars are formed (Fig. 3.11). If the patient has excessive astigmatism after either penetrating keratoplasty or after corneal scarring, the solution is to perform LASIK on these patients. The problem in such difficult cases is that LASIK is not enough. One should perform topographic-assisted LASIK on these

Corneal Topography

Fig. 3.8: Topography showing a symmetric bow-tie appearance

Fig. 3.10: Topography of a post-keratoplasty patient

Fig. 3.9: Topography showing keratoconus

Fig. 3.11: Topography of a patient with a corneal scar in the right eye

cases. The idea here is to incorporate the topographic machine to the LASIK machine creating a terrific combination.

CONTACT LENS-INDUCED WARPAGE If a patient wears contact lenses, then LASIK should be deferred for at least 2 weeks to a month and then LASIK performed. In the interim period, the patient can wear glasses but no contact lenses. The reason to advise this is that contact lenses produce a slight change in the corneal curvature. If we perform LASIK immediately on the day the contact lenses were removed, then the refraction— which we would be correcting—would be wrong. Let us look at Figure 3.12 to understand this well. This patient was tested for corneal topography on 01/09/97. You can see the astigmatism is 0.8 D. This was tested immediately after the contact lens was removed. Then again corneal topography was performed on 10/10/97 about a month after the contact lenses were removed. The patient did not put on the contact lenses for a month. Now you can see the difference in the two topographic pictures. The

astigmatism has become 1.27 D. In other words, the contact lens induced a change in the corneal astigmatism and once the contact lens was removed for a month, the cornea came back to its normal position. If we had performed LASIK immediately after the contact lens was removed, we would have corrected a wrong refractive number and the patient would not have become emmetropic.

Fig. 3.12: Contact lens induced warpage

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RADIAL KERATOTOMY Radial keratotomy (RK) is still being performed in the world. Figure 3.13 is a topographic picture of a patient after radial keratotomy. In the picture on the left one can see the normal cornea. In the picture on the right one can see the topography after radial keratotomy has been done. Note the blue coloration in the areas where the corneal cuts were made. Both the pictures are of the patient’s left eye. If one has performed radial keratotomy and there is still some astigmatism or power left, then one can perform LASIK on these patients. In Figure 3.14 the picture on the left is of the right eye. The patient had a radial keratotomy done but the power had not become nullified. Note the astigmatism present, which is about 2.29 D. The patient then, had LASIK done. When one does LASIK after RK one should be slightly careful so that the keratotomy cuts do not tear, especially when lifting the flap. The picture on the right shows the patient after LASIK had been done. Note the blue flattening of the cornea indicating LASIK having been done. Also note the astigmatism now has come down to 0.36 D which indicates a very good result. Another point to note is to see that the picture on the left has a corneal power of 44.46 D (figure in red) and after LASIK has been done, the flattening has occurred and the corneal power has reduced to 38.49 D.

LASIK Myopia In myopia the excimer laser is applied in the center. In Figure 3.15 one can understand the topography of a patient

Fig. 3.13: Topography after radial keratotomy. Note the picture on the left of the cornea before RK and the one on the right after RK. Note the blue coloration in the areas of the keratotomy lines

Fig. 3.14: Topography of a patient who had LASIK after RK. Picture on the left is of the patient after RK and on the right after LASIK was done

who had LASIK done to correct myopia. The picture on the left shows the pre-LASIK topograph. This was taken on 03/28/97. Note the corneal power is 45.22 D (figure in red). LASIK was subsequently done and the topograph taken on 04/14/97. Note the corneal power has become 39.31 D indicating flattening of the cornea. Also see the blue coloration at the center indicating the flattening which has occurred after LASIK.

Hyperopia In hyperopia the excimer is applied at the periphery (Fig. 3.16). The pre-LASIK topograph was taken on 02/05/ 97. The corneal power is 43.43 D. Then LASIK was performed and the topograph again taken on 04/19/97. The corneal power has become 49.27 D, in other words, the central cornea has steepened. Note the coloration in the center has become reddish indicating the steepening of the cornea.

Fig. 3.15: Topography of myopic LASIK

Corneal Topography was performed, the topograph was again taken on 04/ 14/97. The corneal power became 37.05 D. See the flattening which has occurred. The patient came again on 10/02/97 after 6 months. There was regression of the refractive power and the corneal topograph showed (as seen in Figure 3.19 in the picture on the right) the corneal power had increased to 38.12 D. This clearly indicates the regression which had occurred.

Hyperopia

Fig. 3.16: Topography of hyperopic LASIK

Astigmatism Astigmatism can be corrected with LASIK (Fig. 3.17). The pre-LASIK topograph was taken on 04/16/97. Note the astigmatism being a symmetric bow-tie appearance. Also see the astigmatism is 3.48 D. LASIK was subsequently done and the topograph repeated on 10/12/97. Note the flattening of the cornea and most important the astigmatic pattern is now missing on the topograph. The astigmatism has reduced to 0.65 D.

Figures 3.20 and 3.21 illustrate regression in a hyperopic patient after LASIK. In Figure 3.20 the picture on the left is the pre-LASIK topograph which was taken on 04/01/97. LASIK was subsequently performed and the topograph repeated on 04/19/97. The corneal power increased from 46.2 D to 52.55 D indicating the steepening of the cornea which had occurred. The patient came back to us after 5 months with regression (Fig. 3.21). The topograph in Figure 3.21 (picture on the right) shows the corneal power has become 51.69 D. This was taken on 09/25/97.

REGRESSION AFTER LASIK Myopia One of the big problems in refractive surgery is regression. This is less in LASIK compared to PRK (photorefractive keratectomy) or RK but it still exists. Figures 3.18 and 3.19 illustrate regression in a myopic patient after LASIK very well. In Figure 3.18 one can see the picture on the left is the pre-LASIK topograph which was taken on 03/28/97. The corneal power is 44.27 D. Once LASIK

Fig. 3.18: Regression after a myopic LASIK

Fig. 3.17: Topography of astigmatic LASIK

Fig. 3.19: Regression after a myopic LASIK

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Fig. 3.20: Re-LASIK

Fig. 3.22: Re-LASIK

Fig. 3.21: Regression after a hyperopic LASIK

Fig. 3.23: Re-LASIK

RE-LASIK

COMPLICATIONS OF LASIK

If regression has occurred or the refractive power not fully corrected, then one might have to perform LASIK once again. It is better to call the patient after a month, so that if regression has occurred the flap can be lifted and ReLASIK done. If the patient comes after 6 months, there are two alternatives—either to lift the flap which is a bit difficult or again perform the keratectomy. Figures 3.22 and 3.23 illustrate the effect of Re-LASIK in a patient. In Figure 3.22 we see the pre-LASIK topograph taken on 08/ 13/97. The corneal power is 44.14 D, LASIK was subsequently performed. The picture on the right in Figure 3.22 shows the flattening of the cornea and the corneal power has reduced to 38.59 D. The patient was not emmetropic and so Re-LASIK was performed after lifting the previous flap. In Figure 3.23 we see the picture on the right showing the topograph of the patient after Re-LASIK was done. Note the corneal power has reduced to 37.9 D.

Central Islands Central islands (Figs 3.24 and 3.25) are an important complication of LASIK. In central islands when the topography is done there will be steepening of the central cornea compared to the surrounding areas. This is because the central area of the cornea is undercorrected. If you see the topographic pictures in Figures 3.24 and 3.25 you will notice a blue flattening of the cornea. In the center of the blue area, there is a green area indicating undercorrection as it is a steeper area compared to the surrounding areas.

Decentered Ablation Figure 3.26 shows a case of decentered ablation. When one performs LASIK, one should be careful that the excimer laser shots are hit in the center of the pupil and perpendicular to the cornea. If it is hit superiorly then the ablation will be decentered. Once you have a decentered

Corneal Topography

Fig. 3.24: Central island after LASIK

17

Fig. 3.26: Decentered ablation

was + 5.25 D at axis 89 degrees. The sutures were subsequently removed, and one can see the astigmatism has become + 0.57 D. Note also the color of the topography in the right side has cooled down—in other words the red areas have nearly disappeared.

Foldable IOL

Fig. 3.25: Central island after LASIK

ablation, the patient will remain dissatisfied. The solution to this problem is very complex once it occurs, so basically one should try to prevent it from occurring. Once it has occurred, then one can treat it with topographic-assisted LASIK.

Let us now look at Figure 3.28. The patient as you can see has negligible astigmatism in the left eye. The picture on the left shows an astigmatism of + 0.56 D at 136 degrees axis. Now, we operate generally with a temporal clear corneal approach, so in the left eye, the incision will be generally at 30 degrees as shown by the cross at the edge of the circle at the 30 degrees mark. Remember we are sitting temporally and it is the left eye. The right hand will enter at about 30 degrees and the left hand at about 300 degrees. Now look at the picture on the right. You will notice a flattening at the site of entry at about the

CATARACT SURGERY Corneal topography is extremely important in cataract surgery. One can reduce the astigmatism or increase the astigmatism of a patient after cataract surgery. The simple rule to follow is that wherever you make an incision that area will flatten and wherever you apply sutures that area will steepen.

Extracapsular Cataract Extraction (ECCE) In Figure 3.27, you can see the topographic picture of a patient after ECCE. You can see the red areas in the picture on the left. Both pictures are of the left eye. The patient had an extracapsular cataract extraction done in which the sutures were applied very tightly. The astigmatism

Fig. 3.27: Topography of a left eye after extracapsular cataract extraction (ECCE). The figure on the left shows astigmatism of + 5.25 D at 89 degrees due to tight sutures. After the sutures are removed, the astigmatism has decreased to + 0.57 D as seen in the figure on the right. Note the red areas in the left have become blue in the right

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Mastering the Techniques of Intraocular Lens Power Calculations

Fig. 3.28: Topography of laser phaco cataract surgery with a foldable IOL implantation. Note no change in astigmatism (see text)

Fig. 3.29: Increase in astigmatism after cataract surgery due to incision being made in the wrong meridian. This is the topography of a phaco with foldable IOL implantation

30 degrees axis. This is shown in the color map as blue. This indicates the area where the clear corneal incision was given. One can also see that the astigmatism has remained more or less unchanged. It is now + 0.6 D at axis 135 degrees. The photo on the left was taken on 03/ 14/97 and the one on the right on 03/31/97. This means that after about two weeks, the astigmatism was unchanged and this shows a good result. This patient had a foldable IOL implanted under topical anesthesia after a laser phaco cataract surgery with the size of the incision being 2.8 mm.

appearance has increased and the astigmatism has also increased from + 1.55 D to + 1.99 D. This shows a bad result. If we had made the incision superiorly at the 105 degrees axis, we would have flattened that axis and the astigmatism would have been reduced. The picture on the left was taken on 09/18/97 and the one on the right on 10/15/97 about a month later.

Astigmatism Increased Figure 3.29 illustrates a case in which astigmatism has increased due to the incision being made in the wrong meridian. The patient had a 2.8 mm incision with a foldable IOL implanted after a phaco cataract surgery under topical anesthesia. Both the pictures are of the right eye. In Figure 3.29, look at the picture on the left. In the picture on the left, you can see the patient has an astigmatism of + 1.55 D at axis 105 degrees. Note also the bow-tie astigmatic appearance of the topographic picture. As this is the right eye, our temporal clear corneal incision is at about 195 degrees as shown by the cross near the 195 degrees mark. Now if we wanted to flatten this case, we should have made the incision where the steeper meridian was. That was at the 105 degrees axis. But because we were doing routinely temporal clear corneal incisions, we made the incision opposite to that at 195 degrees axis. Now look at the picture on the right. The flattening is seen at 195 degrees axis by the blue color in the area where we entered with the diamond knife. As this was in an area exactly opposite what we should have done, the bow-tie

Astigmatism Decreased In Figure 3.30, both pictures are of the left eye. In the picture on the left, one can see an astigmatism of + 2.09 D at 90 degrees. Now as this is the left eye, the clear corneal incision with the diamond knife for laser phaco cataract surgery and implantation of a foldable IOL was done at about 45 degrees. This operation was done under topical anesthesia. Remember once again this is a temporal clear corneal incision shown by the cross and the surgeon is sitting temporally. Note the picture on the right shows a flattening at the site of the incision by the color bluish green. The astigmatism has decreased to + 1.15 D, this is because the incision was close to the area of steepening. But if we had gone a little more towards the 90 degrees axis, the astigmatism could have been totally neutralized as the steep area at 90 degrees would have been flattened.

Basic Rule The basic rule to follow is to look at the number written in red. If the difference in astigmatism is say 3 D at 180 degrees, it means the patient has + 3 D astigmatism at axis 180 degrees. This is against-the-rule astigmatism. In such cases, make your clear corneal incision at 180 degrees so that you can flatten this steepness. This will reduce the astigmatism.

Corneal Topography

Fig. 3.31: Topography of a non-foldable IOL implantation (see text) Fig. 3.30: Decrease in astigmatism after cataract surgery. Topography of a laser phaco cataract surgery with foldable IOL implantation

Non-foldable IOL In Figure 3.31, the pictures are of the right eye. This patient has a preoperative astigmatism of + 1.06 D at axis 107 degrees as seen in the picture on the left. Again, in this case, a temporal clear corneal incision was done followed by laser phaco cataract surgery and the implantation of a non-foldable IOL. This incision should have been made superiorly at axis 107 degrees to neutralize the preoperative astigmatism. On the contrary, a temporal clear corneal incision was done at axis 210 degrees. Now look at the picture on the right. One can see the flattening which has occurred after the clear corneal sutureless incision at axis 210 to 225 degrees. This is denoted in the bluish green color. This has increased the bow-tie appearance and the astigmatism has increased to + 2.9 D. The first picture was taken on 09/26/97 and the second on 11/12/97. The patient was not happy with the result of the surgery. At this stage to solve this problem, one can perform astigmatic keratotomy. We solved the problem by another way. We took the patient to the theater and under topical anesthesia put a tight suture in the center of the incision. Look at Figure 3.32. The picture on the left is the photograph of the patient with the increased astigmatism. Note the bluish green color at axis 210 to 225 degrees. Now after applying the tight suture, we took a photograph, which is the picture on the right. You can see from the cross where we put the suture, the bluish green color has become yellow in the center. This is because this area in the center has become steepened by the suture. Note also the astigmatism has decreased to + 1.58 D. If we would have put two more sutures on either side of the central suture, the astigmatism would have

Fig. 3.32: Topography of a non-foldable IOL implantation (see text)

decreased even more, and there would have been a uniform yellow color.

Unique Case In Figure 3.33, the patient had a temporal clear corneal incision for laser phaco cataract surgery under topical anesthesia with a non-foldable IOL. Both the pictures are of the left eye. The picture on the left shows the postoperative topographic picture. The postoperative astigmatism was + 0.95 D at axis 86 degrees. This patient had three sutures in the site of the incision. These sutures were put as a non-foldable IOL had been implanted in the eye with a clear corneal incision. When this patient came for a follow-up we removed the sutures. The next day the patient came to us with loss of vision. On examination, we found the astigmatism had increased. We then took another topography. The picture on the right is of the topography after removing the sutures. Note the red color in the map. The astigmatism increased to + 5.76 D. We were again in a mess. To solve this problem, we then took the patient to the theater and under topical

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Fig. 3.33: Unique case (see text)

Fig. 3.34: Unique case (see text)

anesthesia, we applied a tight suture in the area of the clear corneal incision. Look at Figure 3.34. The picture on the left is before applying the sutures, and the picture on the right is after applying the sutures. Note the astigmatism has decreased to + 2.18 D. If we had applied two more sutures the astigmatism would have reduced even more.

Phakonit: Cataract Removal through A 0.9 mm Incision Phakonit is a technique devised by Dr Amar Agarwal in which the cataract is removed through a 0.9 mm incision. The advantage of this is obvious. The astigmatism created by a 0.9 mm incision is very little compared to a 2.6 mm phaco incision. This is seen clearly in Figure 3.35. If you will see the preoperative and the postoperative photographs in comparison, you will see there is not much difference between the two. In this case a foldable IOL was not implanted as the patient had high myopia. That is why the incision remains at 0.9 mm. At present there is no foldable IOL, which would go through a 0.9 mm incision, so if an IOL has to be implanted the incision would have to be increased.

SUMMARY Corneal topography is an extremely important tool for the ophthalmologist. It is not only the refractive surgeon who should utilize this instrument but also the cataract

Fig. 3.35: Topography of a phakonit case (cataract removal through a 0.9 mm incision)

surgeon. The most important refractive surgery done in the world is cataract surgery and not LASIK (laser in situ keratomileusis) or PRK (photorefractive keratectomy). With more advancements in corneal topography, topographic-assisted LASIK will become available to everyone with an excimer laser. One might also have the corneal topographic machine fixed onto the operating microscope so that one can easily reduce the astigmatism of the patient.

REFERENCES 1. Gills JP, et al. Corneal Topography: The State-of-the Art. New Delhi: Jaypee Brothers, 1996. 2. Agarwal S, Agarwal A, Sachdev MS, et al. Phacoemulsification, Laser Cataract Surgery and Foldable IOLs (2nd edn) New Delhi: Jaypee Brothers, 2000.

Optical Corneal Tomography Sandra Franco, José B Almeida (Portugal), Manuel Parafita (Spain) 21

4

Optical Corneal Tomography

The knowledge of both corneal topography and thickness has many applications such as ocular surgery,1-3 diagnose and treatment of several corneal pathologies,4,5 contact lens fitting.6,7 So, it seems that the simultaneous measurement of both parameters would be desirable. Recently,8 the authors presented a technique that allows three-dimensional (3-D) mapping of the corneal thickness and topography of both corneal surfaces, obtained with the rotary system. Corneal thickness and topography are computed from optical sections obtained by illumination with a collimated beam expanded in a fan by a small cylindrical lens. This lens is provided with motor driven rotation in order to perform automated rotary scanning of the whole cornea. Two cameras are used to capture the images of the optical sections (Fig. 4.1). In the present configuration it consists of an illuminator and two CCD cameras (COHU, COU 2252) provided with 55 mm telecentric lens connected to a data processing computer. The illumination system comprises a quartz halogen light source, an optical fiber bundle, a collimator, a small rod-shaped cylindrical lens with a diameter of 5 mm, a convex lens and an apodizing aperture slit. After the beam is collimated, a small cylindrical lens expands it in a fan. This lens has the shape of rod with a diameter of 5 mm and is held in a mount that can be rotated to produce rotary scanning of the entire cornea. The fan is focused on the cornea surface by the convex lens and the light diffused from the cornea produces an optical section whose orientation follows the cylinder lens orientation. The rotary scanning of the cornea is continuous and the number of optical sections acquired is only limited by processing time. In order to get results faster and

Fig. 4.1: View of the optical components of the rotary scanning system

considering the processing is not yet optimized, we only acquired images from six meridians (Fig. 4.2). The measurements are taken in steps of 30º but it is possible to decrease this interval at the expense of processing time. In spite of this interval, the centre of the cornea is measured very precisely because of the rotational process. The images of the optical sections are captured by the two cameras placed at 60° with the light beam and defining with the visual axis planes perpendicular to each other. These two cameras act like a single virtual camera

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Mastering the Techniques of Intraocular Lens Power Calculations

Fig. 4.2: Optical sections of the six meridians measured

that can be rotated with the cylinder lens; the advantage of using two cameras is that it allows faster rotation then would be possible if a single camera had to be rotated in synchronism with the lens. The rotary scanning of the whole cornea is automatically performed simultaneously with image acquisition by the cameras. After the image acquisition, the next step consists in the detection of both corneal edges from the optical sections images using a method known as “adaptative thresholding” reposted by Hachicha et al.9 This procedure is done for each measured meridian and gives a set of points from each surface. The topography of both corneal surfaces as well as its thickness are computed from this set of points after some corrections for observation angle and corneal curvature are done. The corneal thickness is compute from the distance between the two corneal edges. The result is a thickness profile along the six meridians and it becomes possible to interpolate the thickness along all meridians and to compute a thickness map of the whole cornea (Fig. 4.3).

Fig. 4.4: Elevation map for the anterior surface

Fig. 4.5: Elevation map for the posterior surface

Fig. 4.3: Corneal thickness maps

The set of points acquired, after the corrections, represent the elevation for each corneal surface related to a plane tangent to the corneal vertex. By interpolation or spline fitting is possible to have information about the entire surface. Figures 4.4 and 4.5 show an elevation map for the anterior and posterior corneal surfaces, respectively. It represents the difference in height from a sphere of 7.75 mm for the anterior surface and from a sphere of 6.45 mm for the posterior one. It’s possible to observe the typical height pattern of an astigmatic surface in Figure 4.4. The posterior surface is apparently spherical.

Optical Corneal Tomography Although not fully developed the system is already capable of delivering clinically meaningful information. The authors plan to increase the scanning speed in order to produce complete topography in 1/60 of a second, avoiding problems with eye movement and equipment vibration. The present implementation does not fully exploit the technique’s capabilities due to camera and software limitations.

REFERENCES 1. Mrochen M, Seiler T. Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery. J Cataract Refract Surg 2001;17:S584-S587. 2. Wilson SE, Klyce SD. Screening for corneal topographic abnormalities before refractive surgery. Ophthalmology 1994;101:147-52. 3. Wirbelauer C, Hoerauf H, Roider J, Laqua H. Corneal shape changes after pars plana vitrectomy. Graef Arch Clin Exp 1998;236:822-28.

4. Avitabile T, Marano F, Uva MG, Reibaldi A. Evaluation of central and peripheral corneal thickness with ultrasound biomicroscopy in normal and keratonic eyes. Cornea 1997;16: 639-44. 5. Owens H, Watters GA. An evaluation of the keratonic cornea using computerised corneal mapping and ultrasonic measurement of corneal thickness. Ophthal Physiol Opt 1996;16:115-23. 6. Myrowitz EH, Melia M, O’Brien TP. The relationship between long-term contact lens wear and corneal thickness. CLAO J 2002;28:217-20. 7. Liu Z, Pflugfelder SC. The effects of long-term contact lens wear on corneal thickness, curvature and surface regularity. Ophthalmology 2000;107:105-11. 8. Franco S, Almeida JB, Parafita M. Corneal thickness and elevation maps computed from optical rotary scans. J Refract Surg 2004;20:S576-S580. 9. Hachicha A, Simon S, Samson J, Hanna K. The use of graylevel information and fitting techniques for precise measurement of corneal curvature. Comp Vis Graph Image 1989;47:131-64.

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Mastering the Techniques of Intraocular Lens Power Calculations Ashok Garg (India)

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5

Optical Biometry with IOL Master (Partial Coherence Interferometry)

INTRODUCTION

Technique

Accurate and precise biometry is one of the key factors in obtaining a good refractive outcome after cataract surgery. An error of only 1.0 mm in Axial Length shall results in a postoperative refractive error of three diopters. With the advent of the IOL MASTER (Zeiss) which uses partial coherence interferometry technology has mostly eliminated operative error and is quite useful for biometric assessment. IOL Master is an indispensable tool for preoperative assessment of cataract patients. The IOL Master can measure axial length, corneal radii and anteprocesses from the measurement of the parameters to the computation of the IOL through the Integrated Biometric formulas and lens database. It is a non-contact technique, local anesthesia is not required and there is no risk of infection.

Axial length measurements with IOL Master (Fig. 5.1) are very easy and quick. Patient is seated on chair with chin resting on chinrest. The overview mode is used for course alignment. The patient looks at small yellow fixation light. The patient then looks at the small red fixation light so that accurate axial length measurements are done. A high degree of flexibility is seen on measuring axial length. The examiner selects a best area and takes measurement from that point. An ideal axial length display is far more important than high signal noise ratio (SNR).

IOL Master The main important reason for improper IOL Power Calculation is an error is measurement of axial length. Initially A-scan biometer using 10 MHz ultrasound probe was used but had limited the resolution to approximately to 0.10 mm. IOL Master is recent method of accurately measuring the axial length. It is non-contact method using partial coherent beam of light. It uses infrared light source and has increased accuracy from 0.10 mm to between 0.02 mm and 0.01 mm. It is about 5 times more accurate. IOL Master uses a modified Michelson Interferometer to measure axial length with good accuracy. This creates a pair of co-axial 780 nm infrared light beam with coherence length of approximately 130 nm.

Ideal Axial Length Recording The characteristics are: i. SNR ratio greater than 2.0. ii. Tall narrow primary maxima, with a thin well center termination and one set of secondary maxima. iii. At least 4 out of 20 measurements should be within 0.02 mm of each other. Advantages: It is useful in eyes with corneal opacities, high myopes or hypermetropics, aphakics and eyes filled with silicone oil. It is more accurate and reproducible than contact ultrasound in providing accurate AL measurements. Axial length, keratometric reading and anterior chamber depth can be measured. This concurs a save in time without need that the patient changes his position. As it is non-contact technique, the risk of corneal lesion and transmission of infection from patient to patient are also excluded.

Optical Biometry with IOL Master

Fig. 5.1: IOL Master

Limitations: IOL Master being optical device, any media opacities in axial region will cause problem in measurement. In case of mature or dark brown/black cataract, corneal scars or vitreous hemorrhages, where there is interference in passage of partial coherent light, the test is not highly accurate. IOL Master measures the central corneal power by Automated Keratometry. The instrument takes five keratometry readings within 0.5 seconds and takes the average. The latest software version (3.01) has improved keratometry software which will send alert signals in cases of highly variable readings. IOL Master also measures anterior chamber depth using lateral slit illumination at approx. 30° to optical axis. The various formulas put in IOL Master are Holladay, SRK/T, Haigis, SRK II and Hoffer Q. The preferred formula which is used is SRK/T. IOL Master software can accommodate as many as 20 doctors, each having 20 preferred IOLs and corresponding lens constants. This with the introduction of IOL Master, there is new era of high resolution lens power calculation which is highly accurate.

INFERENCE Based on various research studies data’s it has been shown that IOL master is an excellent and accurate method of IOL Power Calculation. It has increased the postoperative refractive outcome at par with recent techniques of ophthalmic surgery.

BIBLIOGRAPHY 1. Buschmann W. Ultrasonic measurement\s of the axial length of the eye, Klin Monatsbl Augenheilkd 1964;144:801-15.

2. Connors R III, Boseman P III, Olson RJ. Accuracy and reproducibility of biometry using partial coherence interferometry. J Cataract Refract Surg 2002;28:235-38. 3. Drews RC. Calculation of intraocular power, a program for Hewlett-Packard 97 calculator. Am Intraocular Implant Soc J 1977;3:209-12. 4. Drexler W, Findl O, Menapace R, et al. Partial coherence interferometry: A novel approach to biometry in cataract surgery. Am J Ophthalmol 1998;126:524-34. 5. Eleftheriadis H. IOL Master biometry: Refractive results of 100 consecutive cases. Br J Ophthalmol 2003;87(8):960-63. 6. Findl O, Drexler W, Menapace R, et al. Improved prediction of intraocular lens power using partial coherence interferometry. J Cataract Refract Surg 2001;27:861-67. 7. Fritz KJ. Intraocular lens power formulas. Am J Ophthalmol 1981;91:414. 8. Gantenbein C, Lang HM, Ruprecht KW, Georg T. First steps with the Zeiss IOL Master: A comparison between acoustic contact biometry and non-contact optical biometry, Klin Monatsbl Augenheilkd 2003;220(5):309-14. 9. Kalogeropoulos C, Aspiotis M, Stefaniotou M, Psilas K. Factors influencing the accuracy of the SRK formula in the intraocular less power calculation. Doc Ophthalmol 1994;85(3):223-42. 10. Kielhorn I, Rajan MS, Tesha PM, Subryan VR, Bell JA: Clinical assessment of the Zeiss IOL Master 1. J Cataract Refract Surg 2003;29(3):518-22. 11. Kim JN, Lee DN, Joo CK. Measuring corneal power for intraocular lens power calculations after refractive surgery. JCRS 2002;28(II):1932-38. 12. Kraff MC, Sanders DR, Lieberman HL. Determination of intraocular lens power: A comparison with and without ultrasound. Ophthalmic Surg 1978;9:81-84. 13. Liang YS, Chen TT, Chi TC, Chan YC. Analysis of intraocular lens power calculation. J Am Intraocular Implant Soc 1985;11(3):268-71. 14. Olsen T. Theoretical approach to intraocular lens calculation using Gaussian optics. J Cataract Refract Surg 1987;13:141-45. 15. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992;18:125-29. 16. Olsen T, Thim K, Corydon L. Accuracy of the newer generation intraocular lens power calculation formulas in long and short eyes. J Cataract Refract Surg 1991;17(2):187-93. 17. Ouda B, Tawafik B, Derbala A, Youseif AB. Error correction of intraocular lens (IOL) power calculation. Biomed Instrum Technol 1999;33(5):438-45. 18. Raj PS, Ilango B, Watson A. Measurement of axial length in the calculation of intraocular lens power. Eye 1998; 12(Pt2):227-29. 19. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye 2002;16:552-56. 20. Rose LT, Moshegov CN. Comparison of the Zeiss IOL Master and applanation A-scan ultrasound: Biometry for intraocular lens calculation. Clin Experiment Ophthalmol 2003;31(2):121-24. 21. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. Am Intraocular Implant Soc J 1980;6:263-67. 22. Shammas HJ. A comparison of immersion and contact techniques for axial length measurement. J Am Intraocular Implant Soc 1984;10:444-47. 23. Suto C, Hori S, Fukuyama E, Akura J. Adjusting intraocular lens power for sulcus fixation. J Cataract Refract Surg 2003;29(10):1913-17. 24. Verhulst E, Vrijghem JC. Accuracy of intraocular lens power calculations using the Zeiss IOL Master. A prospective study. Bull Soc Belge Ophthalmol 2001;(281):61-65. 25. Wainstock MA. Ultrasonography: Its role in the success of intraocular implant surgery. Int Ophthalmol Clin 1979;19:43-50.

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Mastering the Techniques of Intraocular Lens Power Calculations Aravind R Reddy (UK)

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6

Anterior Chamber Depth in IOL Power Estimation

INTRODUCTION IOL implantation in the bag has now become standard practice. The position of the IOL in relation to the refractive elements of the eye (effective lens position-ELP) is critical in the final refractive outcome. Errors in prediction of effective lens position (ELP) may account for 20 to 40 percent of the total refractive prediction error. This ELP was wrongly assumed constant for all eyes and the manufacturer recommended values are often based on this. Postoperative ACD measurements have been shown to be significantly different from those published by IOL manufacturers. Mean preoperative ACD values estimated with PCI or raytracing methods correlate well with actual postoperative ACD. Newer formulae for IOL power estimation (Holladay, Hoffer Q and Haigis) aim to reduce this error by utilizing additional preoperative biometric data of the eye, i.e. central anterior chamber depth (ACD), corneal diameter and the refractive error, thus producing personalized ACD constants specific for surgeon, IOL and for each eye.

Methods to Measure ACD Various methods used for the estimation of central ACD are ultrasonography (applanation and immersion), partial coherence interferometry (PCI), scanning-slit topography and other less popular optical methods. Contact ultrasound is the most common method currently used. Ultrasound biometry with a 10 MHz transducer probe has a resolution of approximately 200 to 300 µm and a precision of 150 µm. The Orbscan II topography system (Orbtek Inc.), based on scanning-slit method, initially designed for corneal topography, has been

demonstrated to be a useful tool in anterior segment biometry. This system is claimed to provide accurate and reproducible measurements of ACD. PCI is now being accepted as the gold standard for ACD measurement. The IOL Master (Carl Zeiss) is one such device. Anterior segment biometry with such devices has been reported to have high precision (5 µm), high resolution (~12 µm), and good reliability.

How do the Various Methods Compare? Auffarth compared Orbscan and immersion ultrasound measurements of ACD in eyes prior to cataract surgery and found a high correlation between the two methods (correlation coefficient 0.96, P 26

Little: ALX < 22 Normal : 22 < ALX< 24.5

Mastering the Techniques of Intraocular Lens Power Calculations

30

The formula of the Ref depending only from the variable IOL, K, ACD, SF. To calculate the SF we use only variable like Aref, ALX, K, and ACD, the other are fix number . We give you all the formula that you can calculate our own, the variables are printed with different colors. Here is the formula : Ref = (1000 * na * (na * R – (nc – 1 ) * Alm – IOL * ( Alm – ACD-SF)*(na*R-(nc-1)*(ACD+SF)))/(na*(V*(na*R-(nc1)*Alm)+Alm*R)*0.001*IOL*(Alm-ACD-SF)*(V*(na*R-(nc1)*(ACD+SF))+(ACD+SF)*R)) With : nc=4/3, V = 12 (vertex), R = (337.5/K), Alm = (Alx + 0.2), na = 1.336 Then we want that the target is as near as possible from zero and we find: SF = ((((-(Aref *0.001 * (( Alm * V * (nc – 1)) – (R*(Alm- (V * na )))) – (((nc -1 )*Alm) + (na * R)))) – sqrt(((Aref *0.001 * (( Alm * V * (nc – 1)) – (R*(Alm- (V * na )))) – (((nc -1 )*Alm) + (na * R)))* (Aref *0.001 * (( Alm * V * (nc – 1)) – (R*(Alm- (V * na )))) – (((nc -1 )*Alm) + (na * R))))-(4*((nc-1) – (0.001 * Aref*(( V (nc-1)) – R)))* (Alm * na * R) – (0.001 * Aref *Alm * V * R * na)) –((1000 * na ((na*R)-(((nc-1)*Alm)- (0.001 * Aref *((V*((na*R)-((nc-1)*Alm))) + (Alm * R)))))/l)))))/ (2*((nc-1) – (0.001 * Aref*(( V (nc-1)) – R)))))-ACD) With : nc=4/3, V = 12 (vertex), R = (337.5/K), Alm = (Alx + 0.2), na = 1.336 Then we use Constant A = (SF + 65.6) / 0.5663 and we find Constant A = ((((((-(Aref *0.001 * (((Alx + 0.2) * V * (nc – 1)) – ((337.5/K)*( (Alx + 0.2)- (V * na )))) – (((nc -1 )* (Alx + 0.2)) + (na * (337.5/K))))) – sqrt(((Aref *0.001 * (((Alx + 0.2) * V * (nc – 1)) – ((337.5/K)*( (Alx + 0.2)- (V * na )))) – (((nc -1 )* (Alx + 0.2)) + (na * (337.5/K))))* (Aref *0.001 * (((Alx + 0.2) * V * (nc – 1)) – ((337.5/K)*( (Alx + 0.2)- (V * na )))) – (((nc 1 )* (Alx + 0.2)) + (na * (337.5/K)))))-(4*((nc-1) – (0.001 * Aref*(( V (nc-1)) – (337.5/K))))* ((Alx + 0.2) * na * (337.5/ K)) – (0.001 * Aref *(Alx + 0.2) * V * (337.5/K) * na)) –((1000 * na ((na*(337.5/K))-(((nc-1)* (Alx + 0.2))- (0.001 * Aref

*((V*((na*(337.5/K))-((nc-1)* (Alx + 0.2)))) + ((Alx + 0.2) * (337.5/K))))))/l)))))/(2*((nc-1) – (0.001 * Aref*(( V (nc-1)) – (337.5/K))))))-ACD)) + 65.6) / 0.5663 With : ALX : K: ACD Aref : nc = 4/3 V = 12 (vertex) na = 1.336

axial length keratometry anterior chamber depth stabilited refraction after 1 month

CONCLUSION We still have to perfect all the new formulas which don’t give us enough accurate results for the expectation of the patient. Each modern formula use a constant related to the Aconstant which is calculated with the postoperative results and therefore, the A-constant become more accurate with the number of procedures. We hope this modified formula will be useful for manufacturer and surgeon which use new implants without the A-constant.

REFERENCES 1. Smith ME, Kincaid MC,West CE. Basic Science, Refraction and pathology St Louis MO: Mosby 2002;87-89. 2. Shammas HJ in Intraocular Lens Power calculations. Slack inc. Thorofare NJ,USA 2004. 3. Garg A in Mastering the Techniques of IOL Power calculations. Jaypee Brothers Medical Publishers, New Delhi India 2005. 4. Retzlaff J, Sanders DR, Kraff MC. Lens Implant Power Calculation A manual for ophthalmologists and Biometrists 3rd edition Slack inc. Thorofare NJ, USA 1990. 5. JT Holladay, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14: 17-24. 6. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333-40. 7. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formula. J Cataract and Refract Surg 1993; 19:700-12. 8. Haigis W. IOL calculation according to Haigis 1997. Available at http//www.augenklinik.uni-wuerzburg.de/uslab/ioltxt/ haie.htm.Accessed September 2003. 9. Hill WE. Chossing the right formula Available at http// www.doctor-hill.com/formula.htm.Retrieved January 2003.

Axial Length Dependence of IOL Constants Wolfgang Haigis (Germany)

8

Axial Length Dependence of IOL Constants

With customized constants for a given IOL type and measurement setup, one would expect that these should work equally well for all surgeons with the same instruments and lenses. Optimized IOLMaster constants, for example, are expected to produce the same quality of refractive results for all surgeons. This, however, is not the case in general due to the fact that apart from instrumentation there are additional conditions defining the surgeon’s working environment. Among them is the patients’ axial length distribution. This article tries to elucidate the influence of axial length on optimized IOL constants.

INTRODUCTION In formulas to calculate the necessary power for an intraocular lens (IOL) implant, the IOL itself is represented by its respective lens constants. While the A-constant is the most popular one, it is not the only one: each formula has its own way and hence, its own constant(s) to represent a given IOL type. Table 8.1 gives an overview on popular IOL formulas with their respective constants. A-constants or ACD-constants are usually stated by the lens manufacturers and are meant for an average measurement set-up. In the literature (e.g. there are simple transformation formulas (‘standard’ relations) 1-3 to translate one IOL constant into another. This is the standard situation and the respective constants may be considered as default constants. For a given surgeon’s measurement set-up it is highly probable that the manufacturers’ constants are less than optimum. Thus, it is commonly agreed (e.g. that the published constants must be customized (individualized, personalized, optimized)4,5 in order to make allowance for different surgeon-specific measurement conditions (e.g. different combinations of A-scans and keratometers). Once constants are optimized, the classical (‘standard’) relations between them break down and are replaced by new ones (namely ‘relations between optimized IOL constants’).6, 7 For optical biometry with the Zeiss IOLMaster, such optimized IOL constants are e.g. published in the internet within the framework of the ULIB project.8

MATERIAL AND METHODS To assess the effect of axial length on different IOL constants, two methods were applied: 1. Model calculations on theoretical ametropic eyes derived from the standard Gullstrand eye. 2. Comparison of clinical results for different surgical centers.

Model Calculations Theoretical ametropic eyes were derived from the Gullstrand eye (#2)9 as already described to some extent in a previous paper.10 The anterior segment (corneal radius, anterior chamber depth and lens thickness) was left

Table 8.1: Popular IOL formulas with their respective IOL constants

Formula IOL constant

SRK II

SRK/T

Holladay-I

HofferQ

Haigis

Holladay-II

A

A

sf

pACD

a0, a1, a2

ACD

31

32

Mastering the Techniques of Intraocular Lens Power Calculations Table 8.2: Axial and vitreous lengths, refractions and emmetropia IOL powers of the model eyes used, derived from Gullstrand eye #2. The anterior segment was the same for all eyes: ACD (anterior corneal vertex to anterior lenticular vertex): 3.6 mm; corneal radius: 7.7 mm, (phakic) lens power: 20.282 D. An effective IOL position of 4.419 mm was assumed for all model eyes

Model eye

Axial length [mm]

Vitreous length [mm]

Refraction [D]

Emmetropia IOL power [D]

Hyperopic 10 (h10)

20.149

12.944

+11.007

36.385

Hyperopic 5 (h5)

22.149

14.944

+5.403

26.281

Emmetropic (em)

24.149

16.944

0.00

18.272

Myopic 5 (m5)

26.149

18.944

- 5.214

11.767

Myopic 10 (m10)

28.149

20.944

-10.248

6.379

unchanged. Axial myopia or hyperopia was created by increasing or decreasing the standard vitreous length (16.944 mm) by 2 or 4 mm. Axial and vitreous lengths for each model eye can be found in Table 8.2. Paraxial ray tracing with a custom-made PC program as well as a commercial software package (WinLens Plus, V.1.1.5, Linos, Goettingen, Germany) were applied to determine the refractions of the model eyes. The same technique was used to calculate the equivalent (total) power of an equiconvex PMMA lens (center thickness: 0.8 mm, refractive index: 1.490) positioned 4.819 mm11 behind the anterior corneal vertex which made the respective model eye emmetropic. The same lens thickness of 0.8 mm was used for the IOLs for all eyes. (In real life, lens thickness is a function of its refractive power. The error, however, caused by assuming a constant thickness is considered neglectable within the context of these model calculations). In a second step, ‘clinical’ IOL calculations were performed for all model eyes using the following formulas: SRK II,12 SRK/T,13 Holladay-I,14 HofferQ,15,16 Haigis2: for each formula, the respective IOL constants were iteratively adjusted to give the very emmetropia IOL power which was derived earlier from paraxial ray tracing. The same procedure was applied to study the effect of immersion and contact ultrasound on the IOL constants to be used with these two biometry modes. For the standard emmetropic Gullstrand eye it was assumed that immersion ultrasound measures the correct axial length (24.149 mm), while contact ultrasound produces a value 0.30 mm shorter (i.e. 23.849 mm). Again, the respective IOL constants were iteratively varied to give the same emmetropia IOL power for both biometry techniques.

Clinical Data The results of the model calculations were compared to clinical results, which were retrospectively derived from patient data sent to the author by 11 surgeons from Australia (n=1), Germany (n=2) and the USA (n=8) within the ULIB (User Group for Laser Interference Biometry) project to optimize IOL constants for optical biometry.17 A total of 2095 datasets of patients with an Alcon SN60WF lens were evaluated; further statistical details can be found in Table 8.5. Each set consisted of preoperative biometry (axial length, anterior chamber depth) and keratometry (corneal radii) data obtained with the Zeiss IOLMaster, the spherical equivalent of the stable postoperative refraction at BCDVA and the IOL power implanted. Optimized constants of all popular IOL formulas were derived for each center. For this purpose, custom-made computer programs were applied performing an iterative mathematical process in which the respective IOL constants were incrementally varied until the mean prediction error (achieved – calculated refraction) was zero.

RESULTS Model Calculations Together with biometric data, Table 8.2 lists the primary refractions (‘preoperative’) of the model eyes as well as the respective emmetropia IOL powers determined from paraxial ray-tracing. The IOL constants of the different power formulas necessary to come up with the correct emmetropia IOL are summarized in Table 8.3. Figure 8.1 shows the axial length dependences, thus obtained for the A-constants of the SRK II and SRK/T formulas, Figure 8.2 for the constants sf, pACD and a0 of the Holladay-1, HofferQ and Haigis formulas respectively.

Axial Length Dependence of IOL Constants

Fig. 8.1: Model calculations: A-constants for the SRK II and SRK/T formulas to produce the correct emmetropia IOLs for model eyes of different axial lengths

33

Fig. 8.2: Model calculations: IOL constants sf, pACD and a0 for the Holladay-I, HofferQ and Haigis formulas to produce the correct emmetropia IOLs for model eyes of different axial lengths

Table 8.3: Lens constants of the respective IOL formulas necessary to obtain the correct emmetropia IOL power for each model eye

Model eye

A SRK2

A SRKT

sf

pACD

a0

Hyperopic 10 (h10)

124.20

120.49

2.524

6.067

1.417

Hyperopic 5 (h5)

121.10

119.55

2.055

5.732

1.225

Emmetropic (em)

118.09

118.38

1.508

5.392

1.040

Myopic 5 (m5)

117.09

117.75

1.308

5.269

0.865

Myopic 10 (m10)

116.70

117.48

2.079

5.893

0.721

The results of the simulations of different biometry techniques (immersion and contact ultrasound) are compiled in Table 8.4 for each biometry mode.

Clinical Results The results of the individual constants’ optimizations at the different ophthalmosurgical centers are listed in Table 8.5, together with the axial length means and standard deviations in each center. The optimized constants of the Alcon SN60WF for the pooled data—as they are published on the ULIB website8 (in rounded form)—are also given in Table 8.5.

Figure 8.3 shows the customized A-constants for the SRK/T formula derived from the individual patient data in the 11 ophthalmosurgical centers vs the mean axial length of the respective patient population which was used for the optimization. The corresponding results for the constant a0 in the Haigis formula are plotted in Figure 8.4.

DISCUSSION Our calculations simulating the use of immersion and contact ultrasound clearly demonstrate that constants for

Table 8.4: IOL constants necessary to calculate the correct emmetropia IOL power (18.272 D, cf Tab 8.2) for the standard Gullstrand eye with all IOL power formulas after simulated immersion (24.149 mm) and contact ultrasound (23.849 mm) measurements of the axial length

A SRK2

A SRKT

sf

pACD

a0

Immersion ultrasound

118.09

118.38

1.508

5.392

1.040

Contact ultrasound

117.34

117.56

0.961

4.811

0.415

Mastering the Techniques of Intraocular Lens Power Calculations

34

Fig. 8.3: Customized SRK/T A-constants for the Alcon SN60WF in 11 ophthalmosurgical centers vs mean axial length of the respective patient populations

Fig. 8.4: Customized a0 constants of the Haigis formula for the Alcon SN60WF in 11 ophthalmosurgical centers vs mean axial length of the respective patient populations

Table 8.5: Optimized IOL constants for the different ophthalmosurgical centers, together with the respective numbers of datasets used for constants’ optimization and the axial length means and standard deviations for each center. Extreme values in bold. *): a1=0.4, a2=0.1 . **): published on the ULIB website8

Center #

n

Mean axial length [mm]

A SRK2

A SRKT

sf

pACD

a0 *)

1

325

23.54 ± 0.97

119.12

118.90

1.756

5.549

1.352

2

50

23.26 ± 0.84

119.87

119.30

1.971

5.712

1.546

3

210

23.76 ± 1.19

119.29

119.05

1.858

5.660

1.521

4

279

23.91 ± 1.25

119.09

119.00

1.846

5.654

1.471

5

199

23.73 ± 1.19

119.38

119.08

1.869

5.654

1.508

6

204

24.13 ± 1.21

119.01

118.99

1.824

5.631

1.321

7

50

23.44 ± 0.89

118.97

118.88

1.739

5.514

1.302

8

301

23.70 ± 1.02

119.17

119.02

1.835

5.642

1.502

9

268

23.47 ± 0.94

119.25

118.97

1.801

5.584

1.408

10

144

23.53 ± 0.99

119.49

119.05

1.835

5.613

1.458

11

65

23.49 ± 0.70

119.42

119.13

1.897

5.677

1.427

All **)

2090

23.68 ± 1.09

119.22

119.01

1.829

5.619

1.439

immersion biometry need to be stronger than for contact ultrasound. Since laser interference biometry with the Zeiss IOLMaster was calibrated against immersion ultrasound2 this argument also holds for optical biometry: accordingly, IOL constants for optical biometry must be stronger than for contact ultrasound ! This is the basis of the ULIB constants’ optimization project.17 The model calculations furthermore show a definite dependency of the IOL constants of the different power formulas on axial length. It is strongest for the SRK II A-

constant (Fig. 8.1) and weakest for the a0 constant of the Haigis formula (Fig. 8.2). This behavior is caused by and corresponds to the well-known axial length dependence of the arithmetic refraction prediction errors of these IOL power formulas.18 From the model calculations it follows that the SRK/T A-constant decreases by ≈ 0.4 D per mm axial length, the Haigis a0 constant by ≈ 0.1 mm per mm axial length. The clinical observations are qualitatively and quantitatively in good agreement with these findings: all clinical constants decreased with increasing axial length.

Axial Length Dependence of IOL Constants The customized SRK/T A-constants from different centers were found to vary between 119.3 and 118.9 D in the axial length range of 23.2 to 24.2 mm, while the Haigis a0 constant changes between 1.30 and 1.55 mm. The author is aware of some shortcomings of the presented model calculations: the Gullstrand eye serving as a basis for the model eyes is a theoretical eye for optical and not for biometrical purposes. Also, apart from axial length no other factors (like e.g. corneal radii or anterior chamber depth) influencing refraction predictions and thus, IOL constants were made allowance for. Axial length, however, is the predominant factor in IOL power calculation, and the simplifying model calculations help in understanding why IOL constants necessarily depend upon the axial length average of the patient population from which the constants were derived.

CONCLUSION Best refractive results will only be obtained if individualization is done on the surgeon level. Published constants like the ULIB constants for optical biometry8 are nevertheless a good starting point until enough data for individual optimization is available.

ACKNOWLEDGEMENT The author wishes to thank the following surgeons for providing patient data: Australia: A.Rivett; Germany: U Reinking, R Wiedemann; USA: R Arleo, PC Campanella, J Chappell, DL Cooke, H Geggle, W Hill, WG Myers, P Parden.

REFERENCES 1. Retzlaff J, Sanders DR, Kraff MC: Lens Implant Power Calculation - A manual for ophthalmologists and biometrists, 3rd edition, Slack Inc, Thorofare NJ, USA, 1990. 2. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence

3. 4.

5.

6.

7. 8. 9. 10.

11.

12.

13.

14.

15.

16. 17. 18.

interferometry for IOL calculation according to Haigis, Graefes Arch Clin Exp Ophthalmol 2000;238:765-73. Holladay, JT. International intraocular lens implant registry 2003. J Cataract Refract Surg 2003;29:176-97. Gale RP, Saldana M, Johnston RL, Zuberbuhler B, McKibbin M. Benchmark standards for refractive outcomes after NHS cataract surgery. Eye advance online publication, 24 August 2007, doi:10.1038/sj.eye.6702954. Bissmann W, Haigis W. How to optimize biometry for best visual outcome. In: Methods to achieving best uncorrected vision for your patients. Ocular Surgery News International Edition, May 2000, Slack Inc, Thorofare NJ, USA 2000; 13-15. Haigis W. Relations between optimized IOL constants. Symposium on Cataract, IOL and Refractive Surgery of the American Society of Cataract and Refractive Surgery (ASCRS), Philadelphia, PA, USA, June 1-5, 2002, Abstracts, 2002;112. www.augenklinik.uni-wuerzburg.de/uslab/iolcone.htm, as of March 24, 2005. www.augenklinik.uni-wuerzburg.de/ulib/c1.htm, as of Nov 22, 2007. Le Grand, El Hage SG. Physiological Optics, Springer, 1980. Haigis W. Corneal power after refractive surgery with myopia: the contact lens method. J Cataract Refract Surg 2003;29(7):1397-411. Haigis W. Biometrie. In: Jahrbuch der Augenheilkunde 1995: Optik und Refraktion. Kampik A (Hrsg), Biermann-Verlag, Zülpich, 1995;123-40. Sanders DR, Retzlaff J, Kraff MC. Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg 1988;14:136-41. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16(3):333-40. Holladay JT, Musgrove KH, Prager TC, Lewis JW, Chandler TY, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19: 700-12. Hoffer KJ. Errata in printed Hoffer Q formula. J Cataract Refractive Surg 2007;33:2-3. www.augenklinik.uni-wuerzburg.de/ulib as of Dec 7, 2007. Haigis W. IOL calculations in long and short eyes. In: Mastering intraocular lenses (IOLs). Ashok Garg, JT Lin (eds). Jaypee Brothers Medical Publishers (P) Ltd: New Delhi, India, 2007;92-99.

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Mastering theNita Techniques of Intraocular Power Calculations Kumar J Doctor, Shanbhag, SumitaLens Karandikar, Pooja Deshmukkh (India)

36

9

IOL Calculations: When, How and Which?

IOL MASTER PHYSICS Introduction It was estimated that 67% of the error in refractive outcome is caused by errors in axial length measurement. Currently, axial length measurements are performed with ultrasound. According to the ASCRS survey of 1998, applanation biometry is used by 95% of surgeons. The precision of this widely used ultrasound technique is rather poor with around 100–150 µm.1 With the introduction of the IOL Master (Carl Zeiss Meditec Inc., Dublin, CA) in North America in 2000, refractive outcomes within 0.25D of the targeted refraction became a reality for the first time. Reaching this milestone will now allow us to set our sights on far more sophisticated endeavors, such as the correction of thirdand fourth-order aberrations.

Principle Defined in the 19th century by the German-American physicist Albert Michelson. Partial coherence interferometry (PCI), enables a precision more than 10-fold better than that of ultrasound. The system uses a dual-beam version of partial coherence laser interferometry. The laboratory prototype system IOL Master • Superluminescent diode

• Infrared

• Wavelength: 855 nm

• wavelength: 780 nm

• Resolution - coherence length: 10 µm

• resolution - coherence length: 130 nµ

The use of a dual coaxial beam allows the IOL Master to be insensitive to longitudinal movements and makes axial length measurements mostly distance-independent.

While one mirror of the interferometer is fixed the other mirror is moved at a constant speed by a small motor. This process takes one of the light beams out of phase with the other by twice the displacement of the moving mirror. Both beams of light then illuminate the eye to be measured and are reflected at the level of cornea and the retinal pigment epithelium. After passing through a polarizing beam splitter all light beam components are combined together, producing interference fringes of alternating light and dark bands. The constant speed of measuring mirror causes a Doppler modulation of the intensity of the interference pattern. An optical encoder is then used to sense the position of the moving mirror, which is then translated into an axial length figure.2 The display shows peaks which are much slimmer, resulting in the higher precision of this technique. IOL Master • AL measured from corneal vertex to RPE • Axial-length measurement is based on a very short 780-nm light wave • The time needed for measurement of axial length is about 0.5 sec, with a resolution of 0.1 mm. • IOL Master A – Constant will always be higher than those optimized for applanation— A scans in which there is a variable amount of corneal compression.

Ultrasound A- Scan • AL measured from Corneal Vertex to ILM • Axial-length measurement is based on much longer 10-MHz sound wave • Time required depends on the surgeon • A- Constants due to compression will be lesser than those of the IOL master

IOL Calculations: When, How and Which? Dr Wolfgang Haigis at the University of Wurzberg has recommended the following approach for calculating the initial IOL Master SRK/T A- constant: A IOL Master = AUltrasound + 3x ( AL IOL MasterAL Ultrasound) A IOL Master = Optimized A-constant for IOL Master A Ultrasound = Optimized A-constant for ultrasonography AL IOL Master = Average IOL Master length AL Ultrasound = Average ultrasound axial length There are four situations in which the IOLMaster is best suited for accurate biometry: 1. Nanophthalmia or extreme axial hyperopia, because small errors in axial length are important. 2. Extreme axial myopia, especially in the presence of a peripapillary posterior staphyloma. 3. Prior retinal detachment with silicone oil. 4. Pseudophakia and phakic IOLs. 5. Eyes that develop cataracts after phakic IOL implantation, and the IOLMaster can measure straight through the phakic IOL on the phakic setting with excellent results.4

Limitations5 Because the IOLMaster is an optical device, any significant axial opacity has the potential to be a problem. Clinical situations such as a mature or darkly brunescent lens, central posterior subcapsular plaques, anterior cortical spokes, corneal scars that pass through the visual axis, and vitreous hemorrhages may interfere with the partially coherent light beams and decrease the SNR to the point that may preclude a meaningful measurement.5

IOL POWER CALCULATION FORMULAE: IOL MASTER BASICS, APPLICATION AND FALLACIES Background IOL Power calculation is an important parameter in relation to postoperative visual outcome. In 1967, Fyodorov et al first presented a theoretical formula based on geometric optics using axial length and keratometry. Many Theoretical formulae followed thereafter. The three types of IOL power calculation formulae are:

Theoretical Formulae1 These formulae are based on an optical model of the eye. An optics equation is solved to determine the IOL power

37

needed to focus light from a distant object onto the retina. In the different formulae, different assumptions are made about the refractive index of the cornea to the IOL, the distance of the IOL to the retina as well as other factors. They are based on a theoretical optical model of the eye. Binkhorst Formula

Pe = [N/(L-C)] – [NK/(N-KC)]

Other Theoretical Formulae: Colenbrander’s Formula

Pe = [1366 /L – C – 0.05 ] – [1366/ (1336/ K) - C – 0.05]

Gullstrand’s Formula Pe = 1348 K + 4L Fyodorov’s Formula

Pe = 1336 – LK / (L – C) (1- CK/1336)

Van der Heijde’s Pe = [1336/(L-C)] - [1/(1/K) – Formula (C/1336) ] Pe = Emmetropic IOL power (diopters) L = Axial length of eye (mm) K = Corneal dioptric power (diopters) C = Pseudophakic depth of the anterior chamber r = Average corneal radius (mm) = 337.5/K; A = Constant derived for each type of lens and manufacturer SE = Spherical equivalent N = Aqueous and Vitreous R.I

Binkhorst Formula Binkhorst has made a correction in his formula: The Modified Binkhorst Formula, for surgically flattening of cornea, using a corneal index of refraction of 1.33. He also corrects for the thickness of the lens implant by subtracting approx. 0.05 mm from the measured axial length. Thus with the Binkhorst formula, 0.25 mm is added to the measured axial length to account for the distance between the vitreo-retinal interface and the photoreceptor layer, and 0.05 mm is subtracted for lens thickness, resulting in a net addition of 0.2 mm to the measured axial length. Modified Binkhorst formula: Pe = 1366 (4r – L) / (L – C)(4r – C) Other Modified Theoretical Formulae: Hoffer’s Formula: Pe = [1336/L-C-0.05] – [1336/ (1336/K+E) – C – 0.05] Shammas’s Fudged Formula: Pe = [1336/L-0.1(L-23) – C -0.05 ] – [1/ ( 1.0125/K) –( C+ 0.05/1336)]

Mastering the Techniques of Intraocular Lens Power Calculations

38

Disadvantages: The problem in these formulae is in the axial length measurement. Because of the variation of the acoustic density of a cataract these velocities cannot be known exactly. When cataracts are much more acoustically dense than the average lens, the sound wave will move more rapidly through the lens and return to the transducer much more quickly than would have been expected for a given axial length. As a result of the velocity error, the eyes appear to be shorter. The formula thus, calculates an IOL power for an AL which is too short. The patient then becomes too myopic. Theoretical formulae help the surgeon to anticipate what should result, not what will result from implantation.

Regression (Empirical) Formulae 1 These formulae are derived from empirical data and are based on retrospective analysis of postoperative refraction after IOL implantation. The results of a large number of IOL implantations are plotted with respect to the corneal power, axial length of the eye, and emmetropic IOL power. The best-fit equation is then determined by the statistical procedure of regression analysis of the data. Unlike the theoretical formulae, no assumptions are made about the optics of the eye. These regression equations are only as good as the accuracy of the data used to derive them. Factors important for regression formulae are:

SRK III / Modified SRK II Formula: I = P-cr R This is a new formula which is used to produce a desired postoperative refraction R I = IOL power for desired Ametropia P = Emmetropia Power calculated by SRK II cr = another empirical constant defined as cr = 1 for P < 14 cr = 1.25 for P>14 Other Regression formulas: Axt Formula7 Pe = 120.6 – 2.49 L – 0.97 K Donzis Kastle Gordon Formula7 Pe = A – 0.9 K – 58.75 + 58.75 [(23.5 – L)/L] Pe = Emmetropic IOL power (diopters) L = axial length of eye (mm) K = corneal dioptric power (diopters) A = constant derived for each type of lens and manufacturer Advantages: Implant power calculations can be made much more accurately through the use of regression formulae that are based on the analysis of the actual results of many uncomplicated IOL implantations in previous cataract surgeries. Since regression analysis is based on the results of actual operations, it includes the vagaries of the eye and measuring devices, vagaries that theoretical formulae attempt to address with correction factors.

Axial Length Measurement

Newer/3rd Generation Theoretical Formulae

An error of 1 mm affects the postoperative refraction by 2.5 D approx.(L)

SRK/T: It is a non-linear modified theoretical optical formula empirically optimized for post-op ACD, Retinal thickness, and Corneal RI. This formula is for long eyes >28 mm.

Corneal power: the keratometric reading. (K) Postoperative Anterior Chamber Depth: (pACD) An error of 1 mm affects the post-op refraction by approx. by 1.0 D in myopic eye, 1.5 D in emmetropic eye and up to 2.5 D in hyperopic eye.(pACD) The most popular regression formula is the SRK formula which was developed by Sanders, Retzlaff and Kraff popularized this in 1980. SRK Formula

Pe = A – 2.5 L – 0.9 K

SRK II Formula7 Pe = A1-0.9 K-2.5 L A1 = new constant A1 = A+ 3 if axial length L < 20 mm A1 = A+ 2 if, L is 20 to 21 mm A1 = A+ 1 if, L is 21 to 22 mm A1 = A if, L is 22 to 24.5 mm A1 = A – 0.5 IF, L > 24.5

Haigis Formula In 1991, Wolfgang Haigis, the head of the biometry Department of the University of Würzburg Eye Hospital in Germany, published the Haigis formula. Using the same mathematical backbone as other theoretic formulas, the Haigis formula approaches the problem of IOL power accuracy with three constants (a0, a1, and a2) and adds a measured anterior chamber depth for a third required variable. With the a0 constant optimized in a manner similarly to SRK/T, and the a1 and a2 constants based on schematic eye parameters, the formula performs similar to most thirdgeneration two-variable formulas. When all three constants are optimized by regression analysis based on surgeon-specific IOL data, however,

IOL Calculations: When, How and Which? the range of the Haigis formula can be extended greatly to cover both high-axial hyperopia and high-axial myopia.3,4 This formula uses three constants to set both the position and shape of a power prediction curve. The IOL calculation according to Haigis is based on the elementary IOL formula for thin lenses. D = a0+ (a1x ACD) + (a2 x AL) Uses three constants: a0, a1, a2 D = Effective Lens Position ( ELP ) a 0 = same as lens constants for the different formulas given before a 1 = tied to anterior chamber depth a 2 = measured axial length The constants interact with ACD AND AL. These constant are derived by tracking post-op results specific to the surgeon.2

Hoffer Q Formula The Hoffer Q Formula was published in 1993, based on the earlier work of Kenneth J Hoffer, MD. P = f (A, K, Rx, pACD) It is a function of A: axial length K: average corneal refractive power K=0.5(K1+K2) with ( K1=337.5/R1C & K2= 337.5/R2C) R1C/R2C=corneal radii Rx: refraction = f (A, K, P, pACD) pACD: personalized ACD =ACD –constant=0.583*Aconst-63.89

Holladay Formula: I and II8 Holladay I: In 1988 when Dr Holladay created the Holladay I formula, he used the axial length and keratometry to determine the ELP using the Fyodorov formula to calculate corneal height. Likewise, the SRK/T formula used a similar method to predict the ELP while the Hoffer Q formula also used axial length and K but in a different manner (tangent of K) to predict the ACD. These three formulas became grouped together when Dr Hoffer used all three in the first Windows computer IOL power calculation program for clinical use (Hoffer Programs) and are referred to as third-generation formulas. The Holladay IOL Consultant used a similar system and added the Holladay II formula.

Holladay II: The Holladay II formula uses seven variables to predict lens position, and is derived from the result of a study that Dr Holladay conducted in which he used data on myopic and hyperopic eyes from 35 surgeons (30,000 cases) around the world. In addition to the axial length and keratometry, Dr Holladay and his colleagues asked these surgeons to measure the horizontal? white-to-white? corneal diameter, the ACD, the lens thickness, the refraction, and the age of the patient. The initial formula uses “Basic Surgeon Factor”. It can be calculated from the A constant provided by lens manufacturer. The Holladay II formula, available since 1998, is considered by many to be the most accurate of the theoretic formulas currently offered. The formula is easy to optimize and works well across a wide range of axial lengths. Components of this are: Data screening criteria to identify improbable axial length and keratometric measurement. The modified theoretical formula , which predicts the effective lens position of the IOL based on axial length and average corneal curvature. Personalized surgeon factor that adjusts for any consistent bias on surgeon from any source. It is advance method, which requires patient refractions.

Constant of IOL Formulae7 This value represents where we anticipate the IOL to sit in relationship to the cornea. Specifically how near or far from the cornea. The “constant” will decrease with an ACIOL as compared to a PCIOL. The ACL sits closer to the cornea, hence less power is needed. Currently three constants are in use: The SRK/T USES “A-Constant” The Holladay I uses “Surgeon Factor” The Holladay II and Hoffer Q use “Ant Chamber Depth” These formulae assume that the distance from the cornea to the IOL is proportional to the axial length, i.e. Short eyes have shallow ACD and long eyes will have deeper AC.2

Effective Lense Position3,4,7 In actual practice, the two eyes with same AL and K may have different lens power, this may be due to: • Effective lens position (i.e. Distance of lens from the cornea) • Individual geometry of Lens model.

39

Mastering the Techniques of Intraocular Lens Power Calculations

40

The main part of highly accurate IOL power calculation is ability to correctly predict ‘D’ i.e. The effective lens position for any given patient and IOL. SRK/T ‘D’= A constant Hoffer Q ‘D’= pACD Holladay I ‘D’= Surgeon Factor Holladay II ‘D’= ACD Haigis ‘D’= a0+(a1xACD) +(a2xAL)

Lens Position Constant3,4 Dr Michael Hennessy (MSAC Supporting Committee, 2002) designed a table containing the different lens calculation formulae to teach trainees. Commonly used lens calculation formulae (as devised and used by Dr M Hennessy) Generation Lens Position Constant

Formulae

1st 2nd 3rd

SRK SRK II SRK/T Hoffer Q, Holladay Holladay II

4th

Fixed LPC LPC adjusted by length LPC adjusted by length and K LPC adjusted by length, K, other anterior segment measurements

APPLICATIONS3,4 of various formulae • The Holladay 1 formula which works well for eyes with normal and long axial lengths. • The SRK/T formula, which works well for normal to moderately long axial lengths. • The Hoffer Q formula works well for eyes with short and normal axial lengths. Because most biometry equipment already comes with several theoretic formulas, a simple rule to follow is to use the Holladay 1 formula for normal-to-long eyes and Hoffer Q formula for normal-to-short eyes. The following tabulation would help to pick a particular formula which applies best to a given situation.

Comparison in Efficacy of Formulae Certain comparative studies performed have shown the following: • As can be seen, there are a number of options to choose from when using formulae. In a review of 900 eyes comparing SRK I, SRK II, SRK/T, Holladay, Hoffer and Binkhorst formulae, Sanders et al. (1990) found that the SRK/T and Holladay formulae worked best overall.9 • In a further study of 450 eyes Hoffer (1993) compared regression and theoretical formulae and found that SRK I and II were least accurate.10 • In the same study Hoffer found that there was no statistical difference between SRK/T, Hoffer Q and the Holladay formulae.10 • In conjunction with Dr Holladay, A retrospective review by R Zaldivar concludes that there was no difference in outcomes of Holladay II, Hoffer Q and SRK/T. Also they are statistically superior to SRK I and II.11 • To compare the accuracy of intraocular lens (IOL) power calculations using 4 formulas: Hoffer Q, Holladay I, Holladay II, and SRK/T5. • Results: No formula was more accurate than the others as measured by mean absolute error. The formulas were also equally accurate when eyes were stratified by axial length. • To compare the accuracy of the Hoffer Q and SRK-T formulae in eyes below 22 mm in axial length, using biometry measured with partial coherence inferometry (PCI), without a customised ACD constant.6 • Result: Hoffer Q was found to be more accurate than the SRK-T formula in this series of eyes < 22 mm axial length when customised ACD constants are not used.

Axial Length

Primary

Secondary

Category

< 20 mm

Holladay II

-

High Axial Hyperopia Poly pseudophakia

< 20 mm

Holladay II

Hoffer Q

Moderate to High Axial Hyperopia

20 to 21.99 mm

Holladay II

Hoffer Q

Low to Moderate Axial Hyperopia

22 to 24.49 mm

Holladay II

Holladay I/SRK-T

Emmetropia to low Axial Hyperopia

24.5 to 25.9 mm

Holladay II

Holladay I/SRK-T

Emmetropia to low Axial Myopia

26 to 28 mm

Holladay II

Holladay I

Low to moderate Axial Myopia

28 to 30 mm

Holladay II

Holladay I

Moderate to High Axial Myopia

> 30 mm

Holladay II

Holladay I

High Axial Myopia – Minus power IOL

IOL Calculations: When, How and Which? Fallacies of Newer Formulae3,4

Immersion A-scan Biometry

• Limitations of all third-generation theoretic twovariable formulas are that they work best near schematic eye parameters, apply a number of broad assumptions to all eyes, and, apart from the lens constant, predict the final position of the optic of the IOL based solely on central corneal power and axial length. For example, some formulas assume that the anterior and posterior segments of the eye are mostly proportional, or that there is always the same relationship between central corneal power and the effective thin-lens position, which is not always true, especially in axial hyperopia. • Regression formulas like Binkhorst II, SRK I, and SRK II soon became of historical interest only. Interestingly, SRK II is still used by many in spite of its obvious limitations. • The main limitation to using the Haigis formula for all axial lengths is that only Dr Haigis or Dr Holladay l presently carry out the required regression analysis, and a patient database of approximately 200 cases containing a wide range of axial lengths is required. • Limitation of Holladay formula is that it requires the manual input of seven variables and is relatively expensive to purchase. Surgical practices serious about their refractive outcomes will typically use the Holladay II formulae.

Technique

COMPARISON IMMERSION ULTRASOUND BIOMETRY (IUS) VS PARTIAL COHERENCE INTERFEROMETRY (PCI/OCB) Introduction Accurate estimation of the required power of the intraocular lens (IOL) is central to the success of modern cataract surgery. The average corneal refractive power, anterior chamber depth (A-constant) and axial length of the eye are key determinants of the required lens power. The contact technique or direct applanation on the eye is used commonly but is fraught with problems. Even the skilled technician may have parallax difficulties: in centreing the probe on the cornea there is always the potential of indenting the eye, especially in patients who have lower intraocular pressure. The immersion technique eliminates these problems by using a liquid interface between the eye and the ultrasound probe. 1

The technique described herein can be used with any ultrasound unit equipped with a solid A-scan probe and mobile electronic gates.2-5 1. The patient is placed in a supine position on a flat examination table or in a reclining examination chair and a drop of local anesthetic is instilled in both eyes. 2. A scleral shell is applied to the eye. The most commonly used scleral shells are the Hansen shells and the Prager shells.The Hansen shells are available in 16, 18, 20, 22 and 24 mm diameter. While the 20 mm shell fits most eyes, the larger cup provides a better fit in bigger eyes with large palpebral fissures and the smaller cups fit better in the presence of a narrow palpebral fissure. The newest Prager shell features single handed immersion biometry, a Luer fitting to facilitate tubing changes, an autostop for exact manufacturer specified probe depth, and six centreing guides to ensure perpendicularity. Each shell is polished, allowing direct visualization of fluid levels. Other types of scleral shells are also available from different manufacturers including the Kohn shell. 3. The Hansen shell is filled with gonioscopic solution. Methylcellulose 1% is preferred over the 2.5% concentration (too thick) and over saline solutions (too liquid). The solution should be free of air bubbles; the presence of bubbles causes variations in the speed of sound and is responsible for noise formation within the ultrasound pattern. The easiest way to avoid bubbles is to remove the bottle’s nipple and to pour the solution in the cup. If bubbles do form within the solution, they are removed with a syringe, and, if unsuccessful, the cup has to be emptied, cleaned, repositioned, and refilled with gonioscopic solution. The Kohn shell is designed to hold the probe tightly and allow a better fit on the eye. Because of this tight fit, the coupling fluid used in this shell does not have to be methylcellulose; instead, balanced salt solution or artificial tears could be used. 4. The ultrasound probe is immersed in the solution, keeping it 5 to 10 mm away from the cornea (Fig. 9.1). The patient is asked to look, with the fellow eye, at a fixation point placed at the ceiling. Attention is then focused on the screen. The probe is gently moved until it is properly aligned with the optical axis of the eye and an acceptable A-scan echogram is displayed on the screen (Fig. 9.2).

41

42

Mastering the Techniques of Intraocular Lens Power Calculations

Fig. 9.1: Ultrasound probe and technique

Optical Coherence Biometry The IOL Master is the equivalent of an upright, noncontact, ultra-high-resolution immersion A-scan.

Technique

Fig. 9.2: A-scan pattern obtained by an immersion ultrasound technique

The patient is seated comfortably and positioned in a chin rest similar to what is typically used for a slit lamp. The overview mode is used for course alignment; the patient looks at a small, yellow fixation light. Once the video image of the eye is centred, the operator switches to the axial length measurement (ALM) mode. The patient then views a small red light and the image of the eye is enlarged, with the iris filling most of the video screen. It is best if nothing has touched the corneal surface prior to axial length

IOL Calculations: When, How and Which?

Fig. 9.3: IOL Master

Fig. 9.4: A scan Echogram with IOL master which is similar to the A-scan in ultrasound, however, the peaks are much slimmer, resulting in the higher precision of this technique.7

measurements (e.g., an applanation tonometer or contact lenses) (Fig. 9.3). Measuring axial length with the IOL Master allows a high degree of flexibility. Rather than simply positioning a small, in-focus image in the middle of a set of video screen cross hairs, the operator can instead maneuver the focusing spot anywhere within the measurement reticule, and even focus in or focus out. In this way it is possible to

sample different areas around the visual axis until the best axial length display is obtained. Then, once that best area is discovered, all subsequent measurements are taken from that location.6 This technique is especially useful for eyes with small corneal scars, anterior cortical spokes, posterior subcapsular plaques, or other localized media opacities (Fig. 9.4).

IMMERSION ULTRASOUND vs OPTICAL BIOMETER

OPTICAL BIOMETER • AL measured from corneal vertex to

RPE.8

ULTRASOUND A-SCAN • AL measured from Corneal Vertex to ILM.8

• Axial-length measurement is based on a very short 780nm light wave.8

• Axial-length measurement is based on much longer 10MHz sound wave.8

• The time needed for measurement of axial length is about 0.5 sec, with a resolution of 0.1 mm.8

• Time required depends on the surgeon.8

• Scanning with the IOL Master takes about 1 minute

• Immersion ultrasound takes a few minutes longer

• IOL Master A – Constant will always be higher than those optimized for applanation ( A scans in which there is a variable amount of corneal compression.8)

• A- Constants due to compression will be lesser than those of the IOL master.8

• One advantage is that OCB is not subject to crosscontamination because it is a noncontact procedure.9

• Contact procedure A high chance of cross- contamination with probe.

• In eyes with silicone in the posterior vitreous, the OCB technology is clearly superior to ultrasound.10,11

• John Sammus formulae also gives erroneous results in presence of silicon oil.

• This measurement is important in eyes that are affected by a posterior pole staphyloma, such as those seen in the higher myopes, in which the fovea actually may lie along the slope of the staphyloma wall.

• A staphyloma is erroneously measured as long axial length. H-Mac visualization to locate the fovea and then superimpose A and B scans for the AL measurement.

• There are disadvantages associated with OCB, which does not allow reliable measurements in the presence of any significant axial opacity (e.g.,corneal scars, keratopathy, severe tear film deficiency)10-11

• In axial opacities, corneal scars, keratopathy, severe tear film deficiency ultrasound is better than OCB.

43

Mastering the Techniques of Intraocular Lens Power Calculations

44 Studies

1. The Prager Shell and other immersion approaches have been compared directly with the noncontact interferometer (Zeiss IOL Master) determination of axial length; there is no clinical difference in precision between the two methodologies, although there is a significant difference in cost.10,11 2. A study by Packer and colleagues looked at 50 cataractous eyes and compared the Axis II (immersion ultrasound unit) with the IOL Master (OCB). Results showed a high correlation between the two units in axial length calculation (Pearson correlation coefficient ¼ 0.996). 11 3. The IOLMaster has been calibrated against high precision immersion ultrasound (Haigis et al.2000) and has thus been found to correlate well with immersion techniques.18,11 4. The Zeiss company developed a clinical biometry unit using the PCI technique originating in Vienna. This equipment measures axial eye length. We compared this clinical prototype with our laboratory prototype and with immersion ultrasound. Clinical prototype vs. laboratory prototype vs. immersion ultrasound trial: Results: - laboratory and clinical prototype: high correlation - both measured longer than immersion ultrasound. 7

5. Kiss (2002b) evaluated the refractive outcome of 45 patients from Austria with age related cataracts in both eyes three months post-operatively using PCI as well as IUS. The authors indicate that the refractive outcome in cataract patients using PCI biometry was as good as that achieved with IUS.12,13

Inference Because the patient fixates on a light, the AL of the visual axis is measured using PCI/OCB. However, the laser cannot penetrate advanced or mature cataracts to generate an interference pattern and therefore will not replace US biometry. The main drawback of optical biometry is therefore, its limited usability in the case of fixation problems or advanced cataract.19 While the IOLMaster can match the accuracy and efficiency of immersion ultrasound, it’s an expensive instrument. Also, it can’t be used when patients are unable to fixate or have dense cataracts or other media opacities. Immersion ultrasound is a more cost-effective alternative that can be used with all patients, regardless of cataract

density or visual acuity level. (Even practices that use the IOLMaster will continue to need immersion ultrasound for patients who can’t be measured using optical coherence biometry.) Immersion also provides an accurate measurement of lens thickness and anterior chamber depth, which are needed for current fourth-generation formulas. 20

REFERENCES A 1. Vienna IOL Study Group http://www.meduniwien.ac.at/iol/biometry/ mainpage.htm#Method_Biometry 2. Hill WE. The IOLMaster. Techniques in Ophthalmology. 2003;1:1:6, Hill WE, Byrne SF. Complex axial length measurements and Unusual IOL PowerCalculations. In: Focal Points: Clinical Modules for Ophthalmologists. San Francisco:American Academy of Ophthalmology 2004; 22:9. 3. Vogel A, Dick B, Krummenauer F. Reproducibility of optical biometry using partial coherence interferometry. Intraobserver and interobserver reliability. J Cataract Refract Surg 2001;27:1961-68. 4. Salz JJ, Neuhann T, Trindade F, et al. Consultation section: cataract surgical problem. J Cataract Refract Surg 2003;29:1058-63. 5. Fercher AF, Roth E. Ophthalmic laser interferometer. Proc SPIE 1986;658:48-51.

B 1. Holladay JT, Prager TC, Chandler TY, et al. A three part system for refining intraocular lens power calculations. J Cataract Refract Surg. 1988;14:17-24. 2. Karen Bachman,Cincinnati Eye Institute, 2004. 3. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997;23:1356-70. 4. Holladay JT, Gills JP, Leidlen J, Cherchio M. Achieving emmetropia in extremely short eyes with two piggyback posterior chamber intraocular lenses. Ophthalmology 1996;103:1118-23. 5. Julio Narváez, Grenith Zimmerman, R Doyle Stulting, Daniel H Chang. From the Department of Ophthalmology and School of Allied Health Professions, Loma Linda University, Loma Linda, California, Emory University, USA, 2002. 6. Eye advance online publication 16 March 2007; doi: 10.1038/ sj.eye.6702774 E A Gavin and C J Hammond. 7. “Optical biometry using partialcoherence interferometry priorto cataract surgery” March 2003 MSAC application 1050Assessment report. 8. Jack T Holladay, MD, MSEE, FACS is Clinical Professor of Ophthalmology at Baylor College of Medicine, Houston, Texas. Dr. He may be reached at (713) 668-7337; docholladay @docholladay.com 9. Sanders DR, Retzlaff JA, Kraff MC, et al. Comparison of the SRK/T formula and other regression formulas. J Cataract Refract Surg 1990;16:341-46. 10. Hoffer KJ. The Hoffer Q Formula: A comparison of theoretical and regression formulae. J Cataract Refract Surg 1993;19: 700-12. 11. Zaldivar R, Shultz MC, Davidorf JM, Holladay JT. Intraocular lens power calculations in patients with extreme myopia.J Cataract Refract Surg 2000;26:668-74.

IOL Calculations: When, How and Which? C

1. Thomas C Prager, PhD, MPH, David R. Hardten, MD Benjamin J Fogal, OD. Ophthalmol Clin N Am 2006;435-48. 2. Byrne SF. Standardized echography, Part I: A-scan examination procedures. Int Ophthalmol Clin 1979;19: 267-81. 3. Ossoinig KC. Standardized echography: basic principles, clinical applications and results. Int Ophthal Clin 1979; 19:127-285. 104 CHAPTER 10. 4. Shammas HJ. Axial length measurement and its relation to intraocular lens power calculations. Am Intraocular Implant Soc J 1982;8:346-49. 5. Kendall CJ. Ophthalmic Echography. Thorofare, NJ: SLACK Incorporated; 1990;57-106. 6. Hill, Warren E. MD, FACS. Techniques in Ophthalmology: 2003;1(1);62-67. 7. Drexler W, Findl O, Menapace R, et al. Partial coherence interferometry: a novel approach to biometry in cataract surgery. Am J Ophthalmol 1998;126:524–34. 8. Haigis W, Lege B, Miller N, et al. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation 446 PRAGER et al according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000;238: 765–73. 9. Packer M, Fine IH, Hoffman RS, et al. Immersion A-scan compared with partial coherence interferometry: Outcomes analysis. J Cataract Refract Surg 2002;28:239–42.

10. Kiss B, Findl O, Menapace R, et al. Biometry of cataractous eyes using partial coherence interferometry: clinical feasibility study of a commercial prototype I. J Cataract Refract Surg 2002;28:224-9. 11. Kiss B, Findl O, Menapace R, et al. Refractive outcome of cataract surgery using partial coherence interferometry and ultrasound biometry: clinical feasibility study of a commercial prototype II. J Cataract Refract Surg 2002;28:230–4. 12. Tehrani M, Krummenauer F, Blom E, et al. Evaluation of the practicality of optical biometry and applanation ultrasound in 253 eyes. J Cataract Refract Surg 2003;29:741–6. 13. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye 2002; 16:552–6. 14. Nemeth J, Fekete O, Pesztenlehrer N. Optical and ultrasound measurement of axial length and anterior chamber depth for intraocular lens power calculation. J Cataract Refract Surg 2003;29:85–8. 15. Hill W. Axial length: do you measure up? Ophthalmology Management 2002;6:58–60. 16. Hitzenberger, 1991, Hitzenberger et al., 1993, Haigis, 2002. 17. Rhonda G. Waldron Ophthalmology Manangement N OV 2003.

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Mastering the Techniques of Intraocular Lens Power Calculations Lung-Kun Yeh, I-Jong Wang (Taiwan)

46

10

How to Measure a Correct Central Keratometric Reading for IOL Power Calculation After LASIK Surgery?

INTRODUCTION The refractive surgery such as laser in situ keratomileusis (LASIK) is very popular in recent years. An increasing number of cataract surgeries in eyes after LASIK procedures become to be problematic due to the difficulty in intraocular lens (IOL) power calculation. Application of the measured average keratometric readings (central keratometric diopters) after LASIK into standard IOL power calculation formulas commonly results in substantial undercorrection and postoperative hyperopic or even anisometropia. In this chapter, different methods for improved assessment of central keratometric diopters to minimize IOL power miscalculations after LASIK are introduced.

ERRORS IN IOL POWER CALCULATION Prediction formulas of IOL power in cataract surgery is based on measurements of radius of corneal curvature, axial length, and estimation of postoperative anterior chamber depth (effective lens position, ELP). However, after LASIK surgery, the anterior corneal curvature becomes flatter, whereas the posterior curvature seems no changes or much less change,1,2 which overestimates central keratometric readings using the routine keratometers or the autorefractors. This overestimation may also be caused by different factors and becomes one3 of the reasons for IOL power miscalculations (Fig. 10.1). 1. The ratio between anterior and posterior curvature, measured by standard keratometry or computerized videokeratography, may markedly alter and the central corneal thickness decreases after LASIK procedure. Previously many measurements of corneal power suppose central sphericity and a radius of curvature of

Fig. 10.1: Schematic eye

the posterior cornea 1.2 mm steeper than the anterior radius. After LASIK, there may be significant change of asphericity and there is a flattening of the anterior corneal surface with little or no impact on the posterior radius. This change in relation leads to inaccurate estimations of net corneal power (the difference between anterior and posterior curvature). 2. Inaccurate calculation of anterior corneal power using the standardized value for refractive index of the cornea (1.3375). The index is based on Gullstrand’s model eye rather than on actual measurements.5 In the Gullstrand’s model eye, the cornea is replaced by an ideal thin lens with power equivalent to the cornea and one refractive surface. The total power of the lens is determined using the radius of curvature of anterior and posterior cornea. The anterior corneal curvature is determined using the keratometer, but the posterior corneal curvature could not be directly measured. To overcome this problem, the eye model

How to Measure a Correct Central Keratometric Reading? assumes a fixed ratio between anterior and posterior surfaces, then this ratio is applied to determine posterior corneal curvature. Savini and coworkers presented that myopic PRK and LASIK induce reduction of the keratometric refractive index which is correlated to the amount of attempted correction by excimer laser by the factor of Npost= 1.338+ 0.0009856x attempted correction.4 In recent advancement of measurement of posterior curvature, such as Pentacam and Orbscan, the net power of anterior and posterior cornea could be determined and the refractive index can be recalculated according to the amount of refractive corrections. 3. Incorrect estimation of effective lens position (ELP): One reason for the underestimated for IOL power calculation after LASIK surgery is based on the incorrect effective lens position (ELP) estimation calculated by third-generation theoretical formulas in which the post LASIK surgery Kvalue is applied. Aramberri presented that Double-K modification of the SRK/T formula improved the accuracy of IOL power calculation after LASIK and PRK.5 This method used the pre-refractive surgery K-value (Kpre) for the effective lens position (ELP) calculation and the postrefractive surgery K-value (Kpost) for IOL power calculation by the vergence formula. The Kpre value was obtained by keratometry or topography and the Kpost, by the clinical history method. This method helped in the correction of underestimates the ELP and IOL power, resulting in hyperopia between 1.0 D and 3.0 D. 4. Incorrect axial length measurement: If the biometry is accurate, axial length measurements are unlikely to contribute significantly to IOL power errors after LASIK surgery. Axial length measurements have decreased these errors by refinements in biometry techniques and instruments.6,7 Winkler-von-Mohrenfels and his collegues analyzed axial length before and after excimer keratectomy and found no significant differences.8 Shortening axial length would be expected as tissue is removed from the central cornea after myopic LASIK/PRK,. This may result in IOL power overestimation with unexpected myopia.

METHODS TO MEASURE KERATOMETRIC DIOPTERS

manual keratometry is a simple, reliable methods for determining K values for eyes with unaltered corneas. However, manual keratometry is generally considered to be the least accurate of these methods, because it measures only four points approximately 1.5 mm from the corneal apex. This method assumes that the anterior central cornea is spherical and the radius of posterior corneal curvature is 1.2 mm. This measured zone may be more peripheral to the central flattened area leading to a lower power intraocular lens calculation and postoperative hyperopia. Manual or automated keratometry will both overestimate the change in central refractive power following these procedures. Most keratometers use a corneal index of refraction of 1.3375. (M) However, LASIK surgery changes the fixed ratio based on anterior to posterior curvature and central corneal sphericity (Fig. 10.2). The ratio between anterior and posterior curvature could increase markedly and the central corneal thickness decreases after PRK/ LASIK procedure. Therefore, the default index of refraction used in maual keratometry is no longer accurate in determining the true power of the cornea after LASIK procedure. Rouitne single standard keratometry is not suitable for measuring corneal power after LASIK.

Fig. 10.2: Flatter changes of anterior corneal curvature after PRK/LASIK

Manual keratometry after myopic LASIK overestimates corneal power and underestimates IOL power. Manual keratometry after hyperopic LASIK and PRK theoretically underestimates corneal power and results in IOL power overestimation, For LASIK/PRK, the error causes is directly proportional to the amount of keratectomy.

Keratometry

Manual and Automated Manual and automated keratometry are the most frequently utilized methods for measuring central corneal power to calculate intraocular lens (IOL) power. Although

Topography Access

Placido-based Videokeratography Videokeratoscopes, based on the Placido disk principle, is important to estimate the corneal keratometry.

47

48

Mastering the Techniques of Intraocular Lens Power Calculations Videokeratoscopes measure more than 5000 points over entire cornea and more than 1000 points within the central 3.0 mm and yield a radius of curvature that units automatically convert into diopteric power (simulated keratometry [Sim-K]. Topography uses a preprogrammed refractive index. Although the default index of refraction is 1.3375, Placido-based videokeratography still can provide greater accuracy than manual keratometry in normal eyes and in eyes after radial keratotomy (RK).9, 10 However, the true corneal power in eyes after PRK was overestimated due to the change of the ratio of anterior to posterior curvature.11 These reasons may be due to (1) the cornea is a “true” spherical surface and (2) the power of the paracentral 3 to 4 mm is not significantly different from that of the central cornea. In fact, the cornea is a prolate, aspheric refractive media with progressive flattening toward the periphery. Cuaycong et al compared manual keratometry with keratometry derived from computerized videokeratography to determine IOL power in normal eyes without refractive surgery and found that the computerized videokeratography values were more accurate.12 Celikkol et al. showed that corneal powers derived from computerized videokeratography were more accurate than routine methods. 13 In contrast, Husain et al. concluded that the corneal powers derived from computerized videokeratography were less accurate than that from standard keratometry.14 Seitz et al. also found manual keratometry to be superior to topography-derived values in postmyopic PRK eyes .15

Average Central Power Maeda and Klyce presented the concept of average central power (ACP) which is obtained by the average of corneal powers from Topographic Modeling System (TMS).16 They showed a videokeratographic method to calculate corneal power within the pupil. This method offers advantages in eyes with small optical zones.

Slit-scanning Videokeratography ( Orbscan II) Slit-scanning-based corneal topography systems such as the Orbscan (Orbtek), Orbscan II (Bausch & Lomb) and Pentacam (Oculus GmbH) have the capacity to measure both corneal surfaces to calculate the total corneal power. The Orbscan II system is a Placido-based, slit scanning instrument that projects 20 slits from the right and 20 slits from the left during each 2.1-second scan at a fixed angle of 45 degrees onto the cornea. Each slit was captured by video camera and used to construct mathematical

representations of the ture topographic surfaces. However, the ability of Orbscan II to accurately map the surfaces of human cornea remains unknown due to uncertain variances like microsaccades, light scatter, tear instability and surface irregularities. Srivannaboon et al presented that the Orbscan topography system (Bausch & Lomb) provides K-values that correlate closely with changes in manifest refraction produced by LASIK.17 Qazi et al showed that the Orbscan II 5.0 mm total axial power and 4.0 mm total optical power can be used to more accurately predict true corneal power than the history-based method and may be particularly useful while pre-LASIK data are unavailable.18

Optical Coherence Tomography (OCT) Optical coherence tomography (OCT) is an alternative method to directly measure both corneal surfaces. Current commercial retinal OCT scanners with scan rates of 100 or 400 axial scans (A-scans)/second have been used to measure corneal thickness and LASIK flap.19, 20 However, the results of measurement in anterior corneal power are variable due to the motion error. This motion error could be reduced by using higher scanning speed. Therefore, a high –speed cornea and anterior segment OCT (CAS-OCT, Carl Zeiss Meditec, Inc.) which is capable of 2000 A-scans/ second and operated at a 1.3 um wavelength seems to be better choice to measure corneal power. In 2006, Tang and LI presented that the repeatability of hybrid method that the optical powers of the anterior and posterior surfaces were calculated by the combination of corneal thickness map from OCT and anterior corneal surface from Placido ring corneal topography which was 3 times better than that of the direct method that both corneal surfaces was measured directed by the OCT.21

METHODS TO IMPROVE THE PREDICTION OF INTRAOCULAR POWER Each of these methods has practical limitations.

Clinical History Method K= Pre-RS K+ (Pre-RS SE- Post-RS SE) K: current keratometric reading; Pre-RS K is prerefractive surgery keratometry Pre-RS SE and Post-RS SE are the prerefractive and postrefractive surgery spherical equivalents (SEs).

How to Measure a Correct Central Keratometric Reading? These method requires access to an accurate manifest refraction and keratometry prior to LASIK.

EyeSys Corneal Analysis System (effective refractive index, 1.3375; EyeSys Technologies, Inc., Houston, TX).24

Contact Lens Overrefraction

Maloney Methods

KCL= BC+ D+ (ORCL- MR)

The corneal power at the center of the topographic map is modified according to the formula Central power= (central topographic powerx[376/337.5])-4.9.25

KCL=corneal power; BC is the contact lens base curve ORCL is the SE of the overrefraction, and MR is the SE without contact lens. The contact lens method loses accuracy when visual acuity is lower than 20/80 or worse.22

Single-K versus double-K Method • Equation 1: Preoperative corneal radius of curvature: rpre 337.5/Kpre • Equation 2: Corrected axial length (LCOR): If L < 24.2, LCOR= L. If L > 24.2, LCOR= 3.446 +1.716x L0.0237xL2 • Equation 3: Computed corneal width (Cw): Cw=5.41 + 0.58412 x LCOR + 0.098 x Kpre • Equation 4: Corneal height (H): H=rpre-Sqrt[rpre2(Cw2/4)] • Equation 5: Offset value: Offset=ACDconst-3.336 • Equation 6: Estimated postoperative ELP (ACD): ACDest=H + Offset • Equation 7: Constants: V=12; na=1.336; nc=1.333; ncm1=0.333 • Equation 8: Retinal thickness (RETHICK) and optical axial length (LOPT): RETHICK = 0.65696 - 0.02029 x L. LOPT = L + RETHICK • Equation 10: Emmetropia IOL power (IOLemme): IOLemme = [1000 x na x (n x rpost - ncm1 x LOPT)]/ [(LOPT - ACDest) x (na x rpost - ncm1 x ACDest)] • Variables L = axial length; Kpre = pre-refractive surgery K-value; Kpost = post-refractive surgery K-value; ACDconst = IOL constant (can be computed from Aconstant).

Feiz–Mannis Method After myopic LASIK: Post-myopic LASIK IOL = pre-LASIK IOL+ (change in SE/0.67) After hyperopic LASIK: Post-hyperopic LASIK IOL = pre-LASIK IOL - (change in SE/0.67) 23

Adjusted Effective Refractive Power (EffRPadj) The EffRPadj is calculated by multiplying the LASIKinduced refractive change by 0.15 diopters (D) and subtracting this value from the measured EffRP, which is displayed in the Holladay Diagnostic Summary of the

IOL Formulas (SRK/T, Hoffer Q, Holladay I, and Holladay II) Holladay, Hoffer Q, or SRK/T, appear to improve the accuracy of intraocular lens power calculations following LASIK surgery while compared with regression formulas such as the SRK or SRK II. These methods will discuss in detail in other charpters.

CONCLUSION To avoid underestimation of intraocular lens power after cataract surgery in eyes that previously receiving LASIK refractive surgery, the central corneal power should be measured correctly. Although there are no absolutely reliable methods in determining corneal power in these eyes, different measurements could be considered into the prediction of IOL power. Finally, long-term effects of LASIK on the stability of refraction are not known, and these could have an impact on IOL power calculations and the selection of the postoperative target of refraction.

REFERENCES 1. Wang Z, Chen J, Yang B. Posterior corneal surface topographic changes after laser in situ keratomileusis are related to residual corneal bed thickness. Ophthalmology 1999;106:406-09. 2. Naroo SA, Charman WN. Changes in posterior corneal curvature after photorefractive keratectomy. J Cataract Refract Surg 2000;26:872-78. 3. Olsen T: On the calculation of power from curvature of the cornea. Br J Ophthamol 1986;70:152-54. 4. Savini G, Barboni P, Zanini M. Correlation between attempted correction and keratometric refractive index of the cornea after myopic excimer laser surgery. J of Refractive Surg 2007; 23:461-66. 5. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double-K method. J Cataract Refract Surg 2003;29:2063-68. 6. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. J Am Intraocul Implant Soc 1980;6:263-67. 7. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992;18:125-29. 8. Winkler-von-Mohrenfels C, Gabler B, Lohmann CP. Optical biometry before and after excimer laser epithelial keratomileusis (LASEK) for myopia. Eur J Ophthalmol 2003; 13:257-59.

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Mastering the Techniques of Intraocular Lens Power Calculations 9. Cuaycong MJ, Gay CA, Emery J, et al. Comparision of the accuracy of computerized videokeratography and keratometry for use in intraocular lens calculations. J Cataract Refract Surg 1993;19:178-81. 10. Packer M, Brown LK, Hoffman RS, Fine IH. Intraocular lens power calculation after incisional and thermal keratorefractive surgery. J Cataract Refract Surg 2004;30:1430-34. 11. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Cataract Refract Surg 2000;16:349-61. 12. Cuaycong MJ, Gay CA, Emery J, et al. Comparison of the accuracy of computerized videokeratography and keratometry for use in intraocular lens calculation. J Cataract Refract Surg 1993;19(Suppl):178-81. 13. Celikkol L, Pavlopoulos G, Weinstein B, et al. Calculation of intraocular lens power after radial keratotomy with computerized videokeratography. Am J Ophthalmol 1995; 120:739-50. 14. Husain SE, Kohnen T, Maturi R, et al. Computerized videokeratography and keratometry in determining intraocular lens calculations. J Cataract Refract Surg 1996;22:362-66. 15. Seitz B, Langenbucher A. Intraocular lens calculations status after corneal refractive surgery. Curr Opin Ophthalmol 2000;11:35-46. 16. Maeda N, Klyce SD, Smolek MK, McDonald MB. Disparity between keratometry-style readings and corneal power within the pupil after refractive surgery for myopia. Cornea 1997; 16:517-24. 17. Srivannaboon S, Reinstein DZ, Sutton HFS, Holland SP. Accuracy of orbscan total optical power maps in detecting

18.

19.

20.

21.

22.

23. 24.

25.

refractive change after myopic laser in situ keratomileusis. I Cataract Refract Surg 1999;25:1596-99. Qazi MA, Cua IY, Roberts CJ, Pepose JS. Determining corneal power using Orbscan II videokeratography for intraocular lens calculation after excimer laser surgery for myopia. J Cataract Refract Surg 2007;33:21-30. Bechmann M, Thiel MJ, Neubauer AS, et al. Central corneal thickness measurement with a retinal optical coherence tomography device versus standard ultrasonic pachymetry. Cornea 2001;20:50-54. Maldonado MJ, Ruiz-Oblitas L, Munuera JM, et al. Optical coherence tomography evaluation of the corneal cap and stromal bed features after laser in situ keratomileusis for high myopia and astigmatism. Ophthalmology 2000;107: 81-87. Tang M, Li Y, Avila M, Huang D. Measuring total corneal power before and after laser in situ keratomileusis with highspeed optical coherence tomography. J cataract Refract Surg 2006;32:1843-50. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903. Feiz V, Mannis MJ. Intraocular lens power calculation after corneal refractive surgery. Curr Opin Ophthalmol 2004;15: 342-49. Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651–58. Smith RJ, Chan WK, Maloney RK. The prediction of surgically induced refractive change from corneal topography. Am J Ophthalmol 1998;125:44-63.

An Update on IOL Power Calculation JT Formulas Lin (Taiwan), Ashok Garg (India)

11

An Update on IOL Power Calculation Formulas

INTRODUCTION Both classical and modern formulas have been used for the power calculation of regular IOL or accommodative IOL in aphakic, pseudophakic and phakic eyes. The modern formulas include that of Haigis, Hoffer, Q, Holladay, Olson, SRK/T, SRK I and II, and the more recent formulas by Odenthal et al (the historical method), Aramberri et al (the double-K method), Rosa et al (the Rfactor method) and Jin et al (the Adjusted-K method). Most of these efforts were to improve the prediction of IOLpower by a better prediction of the postoperative anterior chamber depth (ACDpost) or the effective lens position (ELP) defined by ACDpre, corneal height and curvature, lens thickness and axial length. All the existing IOL-power calculations (except Lin’s new formulas) are based on the classical vergence formulas (CVF) of Fyodorov (1975), and van der Heijde (1976) or their revision, the Hoffer Q formula (1981). The CVFs assume a thin-lens (for both corneal and IOL) and are all based on a 2-optics system (the cornea and the IOL) which, strictly speaking, can only apply to aphakic eyes. For pseudophakic or phakic eyes, the 3optics systems are much more complex and the oversimplified 2-optics CVF suffers the following possible drawbacks. It excludes the effects of IOL thickness and shape (configuration) and the role of natural lens or primary IOL. Major error may result from the use of the keratometric power (Kpre or Kpost) rather than the true postoperative corneal power which requires accurate measurement of both the anterior (r1) and posterior radius (r2). In addition, the CVF assumes paraxial ray and spherical surface for the cornea and IOL. Therefore, it also excludes the effects due to corneal surface asphericity change after refractive surgery.

One of the major pitfalls of the existing IOL power calculations is the ignoring of individual true corneal power and using a mean-zero error for the postoperative refraction. Except the Haigis formula and the Lin Z2formula, all other optimization formulas are based on oneconstant like the surgeon factor, the A-constant, the ACDpost or the ELP. The mean-zero error might be the result of the balanced errors of short and long eyes. Therefore, the validity range of axial length for various existing formulas under a linear empirical-fit could not justify their accuracy when they are applied to individual eyes. A true personalized IOL power prediction, in our opinion, should at least individualize the following parameters: the postoperative ELP, axial length, corneal anterior and posterior surface, and the IOL types (or configurations). In this Chapter, we would up-date the IOL formulas and address the critical issues covering 4 subjects: 1. IOL-power, 2. Corneal power after refractive surgery, 3. Piggyback IOL power, and 3. Accommodating IOL. Greater details of subject (3) and (4) may be found in separate Chapters of Lin in this book.

IOL POWER FORMULAS Theoretical Formulas All the theoretical formulas (except Lin’s formulas) for IOL power are based on a two lens systems, i.e. the cornea and the pseudophakic lens focusing images on the retina, where thin-lens is also assumed. Table 11.1 summarizes these formulas.

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52

Mastering the Techniques of Intraocular Lens Power Calculations Table 11.1: For emmetropic IOL power calculations 1. Basic theoretical formulas for emmetropia:

Colenbrander’s formula

P=

1336

1336

–

L – C – 0.05

1336 – C – 0.05 K

Fyodorov’s formula

1336 – LK

P= (L – C)

1 – CK 1336

Van der Heijde’s formula

P=

1336 L–C

1

–

1 K

Binkhorst’s formula

P=

1336

C

–

1336

(4R – L)

(L – C) (4R –C)

Lin’s S-formula (I)

Z’P =

1336 (L-S)

1336

–

1336 – S Dc

2. Modified formulas for ametropia:

Shamman’s fudged formula

1336

P=

–

L – 0.1(L – 23) – C – 0.05

Binkhorst’s adjusted formula

P=

1 1.0125 – C 0.05 + K 1336

1336 (4R – L) (L – C) (4R – C)

Hoffer’s formula

1336 P=

1336 –

L – C– 0.05

1336 - C – 0.05 K+E

Lin’s S-formula (II) (see Table 11.3)

Z’P =

1336 (L-S)

–

1336 – qE – Pn 1336 – S Dc

q = (1 + kP)/Z2 Z = 1 – S (Dc/1336), Z’ = 1 – p’(Pn/1336)

Basic Theoretical Formulas These include Colenbrander’s, Fyodorov’s a, Van-derHeijde’s formula and the Hoffer 1974-formula which yield approximately the same IOL powers. Binkhorst’s formula yield 0.50 D stronger lens power.

Modified Theoretical Formulas These include Hoffer’s 1983-formula, Shamman’s fudged

formula and Binkhorst’s adjusted formula. These formulas are modification of Colenbrander’s formula.

The Modern Formulas These include formulas of Holladay I and II, Hoffer Q, SRK/T formula. The more recent formula of Haigis using 3-constant optimization for all ranges of eye length and IOL types. In Lin’s new formulas presented in this chapter,

An Update on IOL Power Calculation Formulas Table 11.2: Corneal power (Dc) calculation after refractive surgery (1) Clinical-history Method (2) Contact Lens Method

(3) (4) (5) (6) (7) (8)

Shammas Method Maloney Topography Method Koch Method Shammas Refraction Method Hoffer Mean-value Method Lin Gaussian-optics (I) (II) where r1 = cornea front surface radius (postop) r2 = cornea back surface radius (postop) Kpost = postoperative keratometry Kpre = preoperative keratometry

the effective ACD, corneal power and IOL types are personalized.

Dc = Kpre-RC, RC = refractive correction of LASIK DC = B+P+Rw-Rno B = base curve; P = power of CL Rw = refractive error; Rno = bare refraction Dc = 1.114 Kpost – 6.8 Dc = 1.114 Ktopo – 5.5 Dc = 1.114 Ktopo – 6.1 Dc = (1.114 Kpost – 6.8) – 0.23 (RC) Dc = 337.5 (1/r1 + 1/r2)/2 Dc = 1.117 Kpost – 41/r2 Dc = (377/r1)[1 – 0.109 (r1/r2)]

value of 6.5 mm. As pointed out by Lin, each 1.0 diopter of corneal power would result in an error of about (1.3 to 1.6) diopter of IOL-power calculation.

Regression Formulas These formulas are derived empirically from retrospective computer analysis of data of patients who have undergone surgery before. The factors on which IOL power calculation depends are:

Postoperative Anterior Chamber Depth (ACD) It is least important factor in calculation of lens power. An error of 1 mm affects the postoperative refraction or IOL-power by approximate (0.6 to 2.5) diopter depending on the ocular conditions based on Lin’s M-formula.

Axial Length Measurement This is the most important step in calculation of lens power. The IOL Master is a recent method using PCI which gives high accuracy in measurement of axial length. An error of 1 mm affects the postoperative refraction by (1.2 to 2.5) D approximately. It is measured in millimeters (mm).

Corneal Power It is measured either in diopters or in mms (radius of curvature). Keratometer measures the radius of curvature of the central part of anterior corneal surface (r1) and given by K=337.5/r1. All the conventional formulas for corneal power (Kc) is given by (Table 11.2) Kc = 1.114 K – C, with C given by a mean value of 5.1, 5.5 or 6.5 diopter to count for the mean posterior surface power. The Lin’s formula using the personalized p–C = 41/r1 to count for the role of individual posterior corneal surface (r2) which may deviate significantly from the commonly used mean

THE ESTIMATED IOL POSITION (ELP) The main part of highly accurate IOL power calculation is able to correctly predict the estimated IOL position (defined as ELP=d) for any given patient and IOL. Various formulas have been presented as follows: SRK/T, d = A constant Hoffer Q, d = pACD Holladay I, d = surgeon Factor Holladay II, d = ACD Haigis, d = aO + (a1 × ACD) + (a2 × AL) Lin, S = d + gT + Gp (Table 11.3). In actual practice, the two eyes with same axial length and keratometric reading may have different lens power. This may be due to:

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Mastering the Techniques of Intraocular Lens Power Calculations Table 11.3: Lin’s formula for IOL-power in aphakia and phakia (A) 2-optics aphakia/IOL Effective ACD: Thin-IOL: Thick-IOL:

S = d + gT d = ELP (for T = 0) g =1/(1+Z”P1/P2) Z” = 1 – T(P2/1336) (B) 3-optics phakia/IOL S’ = (d + gT) + Gp’ p’ = p + 2.4 mm G = 1/(1+Z’P/Pn) Z’ = 1 - p’(Pn/1336) (C) piggyback-IOL S’ = (d + gT) + g’p’ (D) IOL-power (the most generalized format for 3-optics system) Z’P = 1336 [ 1/X – 1/Y]-Pn - q’E X = L – S – 0.05 mm Y = 1336/Dc – S q’ = (1 + kP)/Z2 Z = 1 – S’ (Dc/1336) where: d = separation of cornea and IOL (or ELP, ACD). p = separation of piggyback and primary IOL, or IOL and natural lens T = thickness of piggyback-IOL P = IOL power (thin lens), or P1/P2 for front/back power (thick-lens) Pn = power of natural lens (or primary-IOL) Dc = corneal power E = refractive error to be corrected (on corneal plane) (g, G) = geometry factor for (thick-IOL, subsystem).

• Effective (or optical) lens position (S) which may be different from the ELP (or d). • Individual geometry of lens types. • Presence of the natural lens or the primary-IOL. Hoffer Q formula is best for short eyes. Holladay for long eyes and SRK/T is best for very long eyes. Overall SRK/T is probably most accurate in majority of cases. It, however, ignores the role of IOL thickness and types and only good for 2-optics aphakic-IOL like others. The Lin’s formula is good for all axial length and IOL types.

ACCURACY OF IOL POWER CALCULATION In spite of recent advances in technology, there is no single method to accurately determine the net central power of these postrefractive surgery eyes. The current method available is limited by lack of clinical experience on large scale and by the theoretic nature of all the calculation methods. The factors, which significantly affect the accuracy of IOL Power calculations, are: 1. The error in preoperative biometry with regard to the difference between post and preoperative axial length measurement. 2. The position of the implantation of intraocular lens. 3. The style of intraocular lens. 4. The preoperative corneal astigmatism.

5. 6. 7. 8. 9.

Surgically induced corneal astigmatism. The postoperative astigmatism. The true corneal power (post-LASIK). The formulas used to find IOL-power. Assumption of thin lens or 2-optics system. Greater details of above will be presented in a Chapter of “Error analysis of IOL-power calculations” by Lin.

THE NEW GENERATION FORMULAS Formulas to be detailed in the following include: SRK (I, II), SRK/T, Hoffer Q, Holladay (I, II), Olson and the more recently formulas of Haigis d-formula and Lin’s S-formula.

SRK Formula

SRK I Formula It is basic regression formula. It is given by: P = A – 0.9K – 2.5 L where P = IOL power for emmetropia K = Keratometric power reading A = A constant L = Axial length in mm.

An Update on IOL Power Calculation Formulas SRK II Formula

Holladay (I) Formula

In this formula, the A constant is adjusted to different axial length ranges. It is given by:

1. Data screening criteria to identify improbable axial length and keratometric measurement. 2. The modified theoretical formula, which predicts the effective position of the IOL based on the axial length and the average corneal curvature. 3. Personalized Surgeon Factor (PSF) that adjusts for any consistent bias on surgeon from any source. It is advance method, which requires patient refractions. The initial formula uses the “Basic Surgeon Factor”. It can be calculated from the A-constant provided by lens manufacturer.

P = A1 – 0.9 K – 2.5 L A1 = adjusted constant A1 = A + 3, if Axial length (L) < 20 mm A1 = A + 2, if L 20 – 21 mm A1 = A + 1, if L 21 – 22 mm A1 = A, if L = 22 – 24.5 mm A1 = A – 0.5, if L > 24.5 mm

SRK/T Formula Regression formula for ACD (or ELP) is used to calculated IOL-power based on Fyodorov formula. This formula is more accurate than SRK I and II. ACD post = ACD – 3.336 + corneal height (H), where ACD is related to the manufacturer’s A-constant by:

Holladay (II) Formula The IOL-power is calculated based on the Binkhorst formula as in the Holladay I.

Olsen Formula Olson proposed his 2003 regression formula for the predicted postoperative ACD as follows: ACDpost = ACDmean + 0.12H + 0.33ACDpre +0.3T’ + 0.1L – 5.18

ACD = 0.62467 A – 68.747.

Hoffer Q Formula The HOFFER Q formula was published in 1993 [HOFFER, 1993] and gives the IOL-power P = f (A, K, Rx, pACD) which is a function of A: axial length K: average corneal refractive power (K-reading) Rx: refraction pACD : personalized ACD (ACD – constant) Likewise, the HOFFER Q refractive error Rx Rx = f (A, K, P, pACD), which depends on A, K, P and pACD. For the calculations, K=337.5 divided by the average radius of curvature the cornea. The personalized ACD (pACD) is set equal to the manufacturer’s ACD – constant, if the calculation was selected to be based on the ACD – constant. In case the A – constant was chosen, pACD is derived from the Aconstant [HOFFER, 1998] according to [HOLLADAY et al, 1988]. pACD = ACD – const = 0.58357 * A – const – 63.896

where H is the corneal height, T’ is the natural lens thickness. Above formula, however, can only apply to phakic eyes. For aphakic or pseudophakic eyes, the coefficients will change.

Haigis Formula It uses three constants to set both the position and shape of a power prediction curve. The IOL calculation according to HAIGIS is based on the elementary IOL formula for thin lenses. d = d = aO + (a1 × ACD) + (a2 × AL) where d = the effective (or optical) lens position ACD = measured anterior chamber depth of the eye AL = axial length of the eye. aO constant = same as lens constants for the different formulas given before a1 Constant = tied to anterior chamber depth

Holladay Formulas

a2 Constant = measured axial length

The components of the three part Holladay system are:

Thus the value for d is determined by a function rather than a single number.

55

Mastering the Techniques of Intraocular Lens Power Calculations

56

The a0 a1 a2 constants are derived by multi-variable regression analysis. The Haigis formula IOL constants will appear different than normal as they interact with the ACD and the AL. The conventional optimization based on one-constant (A-constant, surgeon’s factor, ACD) which could only “parallel shift” the calculated curve to fit the measured data for a predicted mean zero error. Therefore, the validation range of the axial length is limited, where improvement for long eye results more errors for short eye, and vice versa. For example, SRK/T is accurate for long eye (L > 26 mm), but not for very short eye (L < 22 mm) which requires the Hoffer formula. Haigis 3-constant optimization allows the curve-fit by both parallel shift and rotation of the curve such that it covers wider range of axial length. However, the above Haigis formula also assumed thin-IOL and excludes the role of IOL configurations for different IOL types.

Lin’s S-Formula Based on a generalized effective ACD (“S”) derived from Gaussian optics in thick-lens for 2-optics and 3-optics system valid for all range of axial length and IOL types. It also includes the effects due to natural lens and primaryIOL which are totally neglected in all the other formulas presented in above A to E. An effective (or optical) ACD is introduced as S given by, for the case of thick IOL in aphakic eye (Fig. 11.1) S = ELP + gT, (1.a) g = 1/[1+Z”(P1/P2)] (1.b) Z” = 1-T(P2/1336) (1.c) where T is the IOL thickness, and the geometry factor (g) is determined by the ratio of the IOL front and back surface power P1/P2. Note that g could be positive (for P1/P2 > 0) or negative (P1/P2 < 0). Therefore, S could be myopic or hyperopic shifted. Figure 11.1 shows the definition of S in a 2-optics system, where both optics can be either thin or thick lenses. Other formulas for S are summarized in Table 3 for both phakic and piggyback IOL. Greater details of the geometry factors g and G will be presented in a separate Chapter of Lin in this book.

IOL POWER IN APHAKIC EYE This is a simple 2-optics system consisting of the cornea and IOL (with natural lens removed). The IOL-power calculation based on S and the true corneal power (Dc) is also developed by Lin as follows: P = 1336 / X – 1336 / Y – qE, (2.a) X = L – S + 0.05 (2.b) Y = 1336/Dc – S (2.c)

Fig. 11.1: Definition of effective (optical) separation (S) between 2 thin lenses (A) and 2 thick lenses (B). Also shown in the second principal plane position (Q) and the system effective focal length (F)

where q=(1+kP)/Z2 is a nonlinear term, with k about 0.003 and Z=1-S(Dc/1336). E is the remaining refractive error after IOL implant. The above Lin’s new formula contributes two improvements: the S function, defined by Eq (1) and in Table to include the IOL configuration and the true corneal power calculated by Dc = 1.117K – 41/r2

(3)

in which the true corneal power after refractive surgery is personalized by its measured front and back surface radius (r1 and r2). The K-reading is further defined as K=337.5/r1. Because that both S and Dc are personalized, accurate IOL power may be calculated for individual cases without the use of “fudge factors” to fit for mean zero error. Figure 11.2 shows the change of corneal power for various r2 values. The individual effective ACD (the “S”) may be calculated from Eq (1) for a given function of f(P, L, Dc, E) by solving a quadratic equation of S, similar to the dfunction of Haigis. The 3-constant optimization like Haigis, but using S rather than d, allows us to obtain the minimal mean error not only for all range of axial length (L), but also for all IOL types via the g-factor in Eq (1). Greater details of above issues will be presented in other Chapters of this book.

An Update on IOL Power Calculation Formulas

57

c. A new nonlinear term q’ is introduced and given by q’ = (1+kP)/Za2 (6.a) Za = 1-S’ (Dc/1336) (6.b)

Fig. 11.2: Corneal power change at various back surface

IOL POWER IN PHAKIA AND PIGGYBACK-IOL For phakic IOL or piggyback IOL, the IOL power calculations involve with a 3-optics system which has been recently formulated by Lin by generalizing the Eq.(2) of 2-optics (aphakic-IOL) as follow Z’P = 1336/X – 1336/Y - q’E – Pn

(4)

which has the following revisions to count for the effects from the presence of the natural lens or the primary IOL (having a power Pn) and the separation between the cornea and IOL (ACD or ELP); and IOL and natural lens or primary-IOL (p). a. A reduction factor Z’ = 1-p’ (Pn/1336), with p’=p+2.4 mm, is introduced and has a value of Z’=0.95, for p’=6.0 mm for a typical phakic-IOL implanted in front of a natural lens power of 21 D and separated by p=1.0 mm or p’=1.0+2.4=3.4 mm. In comparison, Z’ is about 0.99 for the case of piggyback IOL (with p’=p=1.0 mm). Therefore, a reduction of about 5 and 1% is expected in the IOL-power term (Z’P). b. A new S’=S+Gp’ is introduced, with a system geometry factor given by G=1/[1+Z’(P/Pn)] (5) where P and Pn are the IOL-power and the natural lens (or primary-IOL) power, respectively. The above system geometry factor (G) may be compared to the IOL geometry factor given by g=1/[1+Z”(P1/P2)], with Z”=1-T(P2/1336) and for thick-IOL case S=ACD+gT. Therefore, S’=ACD+gT+Gp’, for the general case of thick-IOL implanted in phakic (or primary-IOL) eye.

which reduces to the 2-optics (aphakia) q’=q, when p’=0, S’=S and Z’=Z as expected. The new 3-optics Za may be further related to the Z in 2-optics aphakicIOL by Za = Z - Gp’ (Dc/1336) (7) where the second term is due to the shifted distance of the second principal plane of the IOL-natural lens or piggyback-IOL and primary-IOL subsystem. d. Conversion function (CF), one may define Zeff derived from Zeff2 = Z’Za to obtain Zeff = 1 – Seff (Dc/1336) (8.a) Seff = S + 0.5p’ (Pn/Dc) (8.b) where Seff is defined as the shifted S by an amount proportional to p’ and the power ratio (Pn/Dc) of the natural lens or primary-IOL(Pn) and the cornea (Dc). For typical values of p’= 3.0 mm, Pn = 20 D, Dc = 43 D, one obtains Seff = S + 0.7 mm. This 0.7 mm shift may result in IOL-power difference about (0.7/S)2 or about 3 to 5%, for S = 3 to 4 mm. Above Eq (8) allows us to calculate a conversion function (CF), defined by CF = -(dE/dP) which may be derived from the deviative of Eq (4) and using Eq (8) as follows: CF = 1-2k’E) Zeff2 (9) Therefore, the CF in 3-optics is lower due to the natural lens (or primary IOL) about 5 to 10% less than 2-optics formula. In other words, the conventional 2-optics formulas overestimate the IOL-power when it is implanted in phakia or pseudophakia, but simplified as aphakia. Greater details will be shown in other Chapter of this book by Lin.

PIGGYBACK IOL POWER Given the CF, the piggyback IOL power to correct a residual ametropia power (E), on the corneal plane (not spectacle plane), may be calculated by P = E/CF

(10)

where CF is given by Eq (9) in general. Comparison of various formulas is shown in Table 11.4. Several critical issues on the previous formulas may be addressed as follows: a. All the formulas, except Lin’s, are based on the spectacle power (E) converted to IOL-power (P). The Es of Lin is defined as E on the corneal plane. Another

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Table 11.4: Piggyback IOL-power (P) formulas for residual ametropia error (1) Sanders and Kraff (1980) based on empirical data of over 2500 IOL lens (2) Feiz and Mannis (2001) (3) Holladay II (1993) based on Hoffer (1981), Colenbrander (1973)

P = E/0.67=1.49 E

P = E/0.7 = 1.43E P = (IOL)1- (IOL)2 (IOL)j = 1336/[1336/Kj-ELP] Kj (j=1,2), for pre- and postop corneal power

for plus IOL, P(+) =1.5E, for minus IOL, P(-) = 1.0E; E is the postop refractive error at spectacle plane. (4) Shammas (2001) P = (E/a)/(138.3-A)-0.5 where a = 0.03 for plus IOL, a = 0.04 for minus IOL. A = A-constant = (ACD+63.896)/0.5836 (5) Gills (1996) P(+) =1.4E+1.0 only for hyperopic correction (6) Lin (2005) P = Ec/(CF) = (1.25 to 1.7) Ec The Z2-formula * CF = (1-2kE)(Ec/Z2) for both plus and minus IOL Z =1-S(Dc/1336) Typical value: CF = (0.6 to -0.8) where: Dc is the corneal power and k is a nonlinear term. S is the effective (optical) lens position, S=ELP+gT+ Gp’ E(Ec) is the refractive error on the spectacle (corneal) plane and may be related by another conversion factor Ec=E/Zs2, with Zs=1-0.012E. For simplified 2 optics, see Eq (9) in the text and Table 11.3 for 3-optics system

b.

c. d.

e.

f.

new formula for spectacle-power conversion to corneal plane is also presented in other Chapter of Lin in this book. Formulas of Sanders-Kraff and Feiz-Mannis are comparable. However, both are based on a mean value of CF=0.7 which may be valid only for average clinical data. Individual CF value could be 10 to 20% deviate from this mean value and would require Lin’s formula. Gills formula is only good for hyperopia and it is also based on average case. Shammas formula might be good for low IOL power, say 5.0 D or less. It includes the dependence of ACD (or the a-constant). However, it does not include the effects due to corneal power or individual IOL types. It also assumes thin IOL and a 2-optics system or aphakic IOL. Holladay II based on Binkhorst uses AL, K, ACD, LT, CD, pre-op Rx and age to calculate the ELP and needs numerical method versus the analytic formula of Lin which also revises ELP by S. Lin’s new formula based on Gaussian optics might be the only one which includes most of the effects due to individual ocular parameter and IOL types, where the effective ACD (S, or Seff) has been rigorously defined

for various systems of aphakic, aphakic or pseudophakic and for both thin and thick IOL. The roles of natural lens or primary-IOL are also included in the new formula (Table 11.4).

Fig. 11.3: IOL-power (P) vs. axial length (L) for a fixed corneal power Dc=43 diopter at various IOL position ELP=3.5, 4.5 and 5.5 mm shown by curve (A), (B) and (C), respectively

An Update on IOL Power Calculation Formulas

Fig. 11.4: Schematics of P vs. L for SRK formula (curve 1), Gaussian optics (curve 2) and Colenbrander (curve 3)

Fig. 11.6: IOL-power vs. corneal power calculated from Gaussian optics (B), SRK-I (C) and Hoffer (A)

Fig. 11.5: IOL-power (P) vs. corneal power (D) for a fixed ELP=4.5 mm for long, normal and short eyes, with L=26, 23.5 and 21 mm shown by curves A, B, C, respectively

ACCOMMODATING IOL (AIOL) The accommodating rate function (M) defined as the accommodation amplitude increase per 1.0 mm forward movement of a plus AIOL may be expressed by the Lin’s M-formula M = (Z/1336)P[2Dc+ZZ’P]

(11)

Above formula is a general form for both phakia and aphakia and also for dual-optics AIOL. As shown in Fig. 3, for the thick-IOL single-optics case, the M value is higher

Fig. 11.7: Schematic comparison of various K-based formulas (dashed lines 1 to 4) and Gaussian-optics formulas (solid lines) at various corneal power for long (A) and short (C) eyes

for convex-concave IOL configuration (having front and back surface power of P1 and P2) which has higher P1 for a given P1+P2, when P21.0 mm and P2>10.0 diopter. Overestimation of the CF (in 2-optics formula) will also underestimate the piggyback IOL power which results in hyperopia post-IOL in a plus piggyback IOL, and vice versa in a minus piggyback IOL. Similarly, the 2-optics formula used for IOL implant in phakic eyes would also suffer errors by ignoring the presence of the natural lens in a “phakic eye”, although it is accurate for “aphakic” system. This error is governed by the reduction factor (BZ’). For typical value of fc=31, d’ = 3.0 and f2 = 60 (all in mm) of a phakic IOL system, BZ’ is about 0.78, which translates to an error of 22% overestimate of 2-optics CF comparing to the EXACT 3optics formula. Hyperopia surprising therefore occurs in plus IOL implant when a 2-optics formula is used.

SPECTACLE POWER AND HOLLADAY FORMULA As shown in Figure 12.7, the conversion from spectacle power (Ds) to IOL power (P), defined by TF=P/Ds=1/ [D’/P)(Ds/D’)], or TF=1/(CF)(CFs), where CF=(D’/P) is defined as the conversion from IOL-power to the refractive error on the corneal plane (D’) which is further converted to the spectacle power (Ds) given by CFs=Ds/D’=10.012Ds. For typical parameters of V=12, fc=31, f2=62, (all in mm), the analytic formula of Eq (7) gives CFs(+) = (94, 88, 82, 76)% for plus spectacle having power of Ds=(5, 10, 15, 20) diopter. For minus spectacle power of (-5, -10, 15, -20) diopter, CFs(-)= (106, 112, 118, 124)%. Following two calculated examples for minus and plus piggyback IOL are shown and compared to that of Holladay, Gills, Habot-Wilner et al.

Error Analysis The presence of the primary-IOL reduces the conversion efficiency of the piggyback IOL (PIOL). This reduction effect is proportional to the power (P2) and distance (d’) of the PIOL or to the shifted effective ACD, S=p+gd’ (with g is about 0.6 to 1.6) and contributes about 10 to 15% which can not be ignored. Therefore, all the existing piggyback IOL-power calculations based on 2-optics assumption and totally ignoring the role of the PIOL, suffer serious errors,

Fig. 12.7: The 3-optics system consists of spectacle (located at a vertex distance V=12 mm), reduced effective distance V’ and the effective anterior chamber depth (ACD) of the phakic eye d’ (about 6.0 mm). Q4 is the second PP position of the cornea and natural lens subsystem and L is the axial length, L=X+d’+0.18 mm and V’=V+gd’

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A minus posterior chamber piggyback IOL, with p=4.0 mm, ACD=5.0 mm and corneal power of Dc=43D, primary IOL-power P2=15.0 D. CF(pig)=71.7% which gives the calculated TF(-)=(132, 125, 119, 113)% for spectacle power of Ds=(-5, -10, -15, -20) D. This example shows that the case studies of Habot-Wilner et al with Ds=(-3 to -8) D shall result in calculated TF(-)=(135 to 125%) or having a mean value about 130%. However, the actual comparison shall require the corneal powers for each eye which were not disclosed in their report. The Holladay I-for-1 formula or TF(-)=100% is only good for spectacle power Ds about -25 D and underestimated about 10 to 32% for minus Ds of -20 D to -5.0 D, for the case of phakic-IOL or piggyback IOL.

Case (2) A plus PIOL under the same condition as (Case 1), TF(+) is calculated to be (149, 159, 171, 184)% for Ds=(+5, +10, +15, +20) D. Therefore, the studied range of Habot-Wilner et al, Ds=(+5 to +8) D shall expect TF(+)=(150 to 160%) or a mean of about 155%. These calculated values based on the new formulas in comparing with Fig. 12.1 of their report, show linear-fit based on TF(+)=140% are underestimated the actual refraction change. This example also demonstrates that the Holladay TF(+) = 150% is only good for Ds about +5.0 D and underestimated 10 to 34% for high Ds of (5.0 to 20) D for the case of ACD = 5.0 mm. For anterior aphakia IOL with ACD = 3.0 mm, TF(+) = (130, 139, 149, 161)%, which shows Holladay’s 1.5-for-1 formula is valid only for Ds about +15.0 D.The major sources of error of Holladay’s calculations are: (a) the assumption of 2-optics, and (b) the use of a mean value of CF about 80% and ignored its dependence on ACD. This mean value method provides the approximate conversion formula only valid for IOL implanted in the anterior chamber (with ACD about 3.0 mm) and limited to spectacle power of about 15 diopters. The new formula show a much wider ranges for TF (-)=110 to 135% and TF(+)=140 to 190% depending on the values of the effective IOL positions (S) and its power. The TFs is also influenced by the corneal power (Dc), where shorter S and/or flattened cornea would have a higher value of CF and therefore, smaller value of TFs, as one may easily see from the formulas of CF and TF. The clinically averaged mean value for TFs may be reasonably accurate, but only when the IOL is anteriorly implanted having S about 2.5 to 3.5 mm. For personalized TFs, one

requires the individual value of S, and the power of Dc, Ds and P related by the new formulas.

CONCLUSION The commonly accepted formulas of TF(-)=100% (1-for-1) and TF(+)=150% (1.5-for-1) in converting the spectacle power to IOL power based on classical vergence formulas could result in significant errors in IOL power calculations, particularly for posterior IOL. Information on the individual power of cornea and primary-IOL are also required to avoid errors using averaged CF values. In addition, the phakic or piggyback IOL power requires an adjusting factor of 1.2 to 1.3 when the conventional 2optics formulas are used. The new formulas presented in this Chapter include the effects resulting from the second principal plane shift, the nonlinear term given by the initial refractive error, and the small influence from the natural or piggyback lens power. The IOL power conversion may be unified to one simple formula for both aphakia and phakia. Applications of the above described new formulas for the calculations of the efficiency of accommodating IOL may be found in other Chapters by Lin in this book.

APPENDIX 3-optics IOL Conventional classical IOL formulas are all based on a 2optics system which is valid only for aphakic-IOL and for thin optics. For phakic-IOL or piggyback-IOL, a 3-optics system is required. The 3-optics system may be reduced to an effective 2-optics by considering the natural lens and IOL as a sub-system (SS) which is further coupled to the cornea and treated as an effective 2-optics, the SS and the cornea. By Gaussian optics, the effective focal length (EFL) of the IOL and natural lens sub-system (SS) is given as (referred to Fig. 12.2) 1/f = 1/f1 + Z’/f2, Z’ = 1 – d’/f1,

(P.1)

where f1 and f2 are the EFL of the IOL and natural lens; d’ is the effective IOL position (away from the natural lens first principal plane location Q1) and given by d’=d+2.4 mm, where d is the IOL position and 2.4 mm is a shifted effective position due to the thickness (about 4.0 mm) of the natural lens. The EFL of the reduced 2-optic system consisting of cornea and SS is then given by 1/F = 1/fc + Za/f Za = 1 – S/fc,

(P.2)

The New IOL Formulas based on Gaussian Optics where the effective distance between the cornea and SS (shown by the distance between Q1 and Q3 in Fig. 12.2) may be calculated from S=p+gd’, where g is a geometry factor given by g = f/f2 = 1/[1 + Z”(f2/f1)] Z” = 1 – d’/f2

(P.3) (P.4)

Greater details of the geometry factor may be found in other Chapters by Lin in this book. It can be readily seen that the 3-optics phakic eye reduces to a 2-optics aphakic eye when the natural lens is removed, or when f2 goes to infinite and g = 0, f = f1. Eq (2) becomes a simple cornea-IOL 2-optics system (or an aphakic IOL) which has the same format as that of corneanatural lens system. By separating all the IOL-power dependence term in Eq (2), or a de-coupling of the f1dependence of the second principle plane with others, and using Za = Z(1 – gd’/Zfc), with Z = 1 – p/fc, one may obtain Eq (1) based on Eq (A.4) in the text by a revised q’. It should be noted that the above method may be easily applied to the 3-optics system of piggyback-IOL (in aphakia) by replacing the natural lens with the primary-

IOL which may be assumed to be a thin lens such that d’ = d, without the extra term of 2.4 mm due to the thick natural lens.

REFERENCES 1. Shammas HJ. Intraocular lens power calculations. Thorofare NJ: SLACK 2004;7-24;59-61;64-65. 2. Holladay JT. Optics and intraocular lens power calculation for phakic intraocular lenses. In: Horden DR. Lindstrom RL. Davis EA, ed. Phakic Intraocular lenses: principles and practice. Thorofare NJ: SLACK 2004;37-44. 3. Lin, JT. Unified refractive-state analysis for customized vision correction. J Refract Surg 2004;20(3):398-400. 4. Lin, JT. New formulas comparing accommodation in human lens and intraocular lens. J Refract Surg 2005;21(2):200-01. 5. Lin JT. A generalized refractive state theory and effective eye model. Chin J Optom and Ophthal 2005;7(1):1-6. 6. Lin, JT. Analysis of refractive state ratios and the onset of myopia. Ophthal Physiol Opt 2005;26(1):97-105. 7. Odenthal MTP, Eggink CA, Melles G et al. Clinical and theoretical results of intraocular lens power calculation for cataract surgery after photorefractive keratectomy for myopia. Arch Ophthalmol 2002;120:431-38. 8. Habot-Wilner Z, Sachs D, Cahane M et al. Refractive results with secondary piggyback implantation to correct pseudophakic refractive errors. J Cataract Refract Surg 2005;31(11): 2101-03.

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13

Classical vs Modern Formulas for Estimated Lens Position (ELP)

INTRODUCTION In the early formulas, the estimated lens position (ELP), also known as the postoperative anterior chamber depth (ACDpost), is assumed as a constant. The modern formulas allow the dependence of ELP on many factors including:, axial length, keratometry, horizontal corneal diameter, corneal height natural lens thickness and preoperative ACD, IOL lens thickness, patient’s age and preoperative refraction. Furthermore, the ELP is not only affected by the preoperative-ACD, but also by the placement of the IOL, whether it is in the anterior chamber, iris-supported, or in the posterior chamber (in the sulcus or in the capsular bag). For a thick IOL, the ELP also needs modification to include the effects due to different types of IOLs, or its configurations. The conventional ELP formulas assuming

a thin-IOL do not take into consideration the differences in IOL types which require a geometry factor (g) to be introduced in this chapter. This chapter will discuss the above issues and compare different formulas to correlate four parameters: the ELP, the A-constant, the surgeon’s factor and the effective (or optical) ACD for an IOL implanted in different positions and for both aphakic and phakic eyes. Comments on the existing formulas based on thin-lens in 2-optics system will be presented by new formulas for thick-lens in 3-optics system.

APHAKIC VERSUS PHAKIC IOL As shown in Figures 13.1A to E, various IOL implants in phakic and aphakic eyes for both a thin and thick lens are defined by the following parameters:

Figs 13.1A to E: Schematic for IOL implant in aphakic and phakic eyes

Classical vs Modern Formulas for Estimated Lens Position (ELP) ELP: distance between the corneal front surface (N1) and IOL front surface (N2), ELP=ACD in aphakic IOL. p: distance between N2 and N3 (natural lens front surface). Q1: first principal plane position (PP) of the IOLnatural lens subsystem. Q2: first PP position of a thick IOL. Q3: second PP of thick IOL. Q4: first PP of a thick natural lens. Q5: second PP position of a thick natural lens. S: effective (or optical) IOL position (or the effective ACD). By above definition, the S is related to ELP and the effective focal length (EFL) of the corneal (fc), IOL(f1) and natural lens or primary-IOL (f2) by equations shown in Table 13.1. It should be noted that the effective or optical ACD (defined as S) is not directly related to the preoperativeACD. It is governed by the postoperative-ACD, the IOL physical position and IOL types (in the case of a thick IOL). Furthermore, it is also determined by the power of the natural lens (in the case of a phakic eye) and the primary-IOL (in the case of a piggyback IOL in an aphakic eye). The new parameter “S” may be rigorously derived from Gaussian optics. Formulas shown in Table 13.1 may be further revised by adding 0.05 mm to the ELP to account for the second PP contribution of a thick-cornea (assumed to be 0.5 mm). The effect of retinal thickness is about 0.18 mm (for a typical axial length of 23.5 mm) and may also be added to the ELP. Thus, the revised ELP becomes

Table 13.1: The Lin’s S-formulas for effective (optical) IOL position (S) for various implants in phakia and aphakia (refer to Fig. 13.1)

Implant types

Relationship of S and ELP

(a) Thin-IOL in aphakia (b) Thin-IOL in phakia

S=ELP=ACD S=ELP+gp’ where g=f/f2=1[1+Z2(f2/f1)], p’=p+2.4 mm, Z2=1-p’/f2 S=ELP+gp S=ELP+g’T, where T=IOL thickness S=ELP+gp’, where p’=p+g’T+2.4 mm

(c) Thin piggyback IOL (c) Thick-IOL in aphakia (d) Thick-IOL in phakia

geometry factor g = 1/(1+Z2P1/P2), g’=1/(1+Z2’P1'/P2') (P1, P2) = (IOL-power, natural lens power) in case (b) = (piggyback, primary IOL) power in case (c) and (e) (P1', P2') = (front, back) surface IOL power in case (d) and (e)

ELP’=ELP+(0.05+0.18) or about 0.23 mm longer than the conventional value which ignores the thickness of the corneal and retina. The ELP or ACD in this chapter is defined from the front corneal surface to the front IOL surface, that is, the corneal thickness is included. This definition is consistent with the anatomical ACD defined by Holladay. Greater details based on Figure 13.1 are shown as follows: Case (a): S = ELP (thin IOL) = ACD for IOL in aphakia (see Fig. 13.1A) Case (b): S = ELP + gp’ (in a thick natural lens) for an IOL in a phakia. where the S is shifted by the first principal plane (FPP) position at Q1 which may be calculated by the geometry factor defined by g = f/f2 = 1[1+Z2(f2/f1)] = 1/[1+Z2(P1/P2)], where P1 and P2 are the power of the IOL and natural lens respectively; f is the EFL of the IOL-natural lens given by 1/f=1/f1+Z1/f2 or 1/f2 + Z2/f1; and Z1=1-p’/f1, Z2=1p/f2 ; p is given by p’=p+2.4 mm, where 2.4 mm is the position of the natural lens FPP, for a typical thickness of 4.0 mm. For example, for an IOL power of +10.0 D (or f1=133.6 mm) and natural lens of +15.0 D (or f2=1336/15=89.1 mm) and p=1.0 mm, Z1=1-3.4/133.6=0.974, f=54.4 mm. Therefore, gp’=0.61x3.4=2.07 mm, and S=ELP+2.07 mm, which is shifted to a larger value than ELP and cannot be neglected for a typical value of ELP=(2.0 to 3.0) mm. Case (c): the piggyback IOL (Fig. 13.1C). Where the primary-IOL could be a thin or thick IOL. For thin IOL case, S=ELP+gp, with g=f/f2, similar to case (b), which is defined by the EFL (or power) of both piggyback (f1) and primary IOL (f2). For example, for primary-IOL power of 20 D (or f2=1336/20=66.8 mm) and piggyback IOL power of -5.0 D (or f1=-267.2 mm), and separated by p=1.0 mm, one may calculate Z1=1+1.0/267.2=1.0037 and f=88.9 mm. Therefore, gp=1.33 mm which is smaller than the gp’=2.07 mm in case (b), because the natural lens thickness of 4.0 mm is greater than p=1.0 mm. For a thick IOL, the S should be further shifted by gT, with T being the IOL thickness as shown in the following case. Case (d): thick-IOL in phakia with two configurations (Fig. 13.1D).

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For the convexo-concave IOL, the FPP is left-shifted (shown by position of Q2) in contrast to that of a biconvex IOL having Q2 right-shifted. For example, in a convexo-concave IOL having front and back surface radii of (R1, R2)=(66.8, 133.6) mm ora power of (P1, P2)=(+20, -10) D, and IOL thickness of T=0.5 mm, we may calculate the geometry factor g which may be approximated by g=1/(1+P1/P2) for small T with Z2=1-T/f2=1.0, we obtain g=-1.0, therefore S=ELP-0.5 mm. In comparison, for a biconvex IOL having the same total power (P1+P2) of +10.0 D, we obtain g=+0.5 and S=ELP+0.25 mm. The smaller S value in a convex-concave lens would require a smaller IOL-power at a given refractive error than that of biconvex lens. The shifted value gT could be neglected only for a thin IOL, or T< 0.2 mm; or when ELP>>gT in posterior chamber case with ELP about 4.0 to 5.5 mm. For an anterior chamber IOL with ELP about 3.0 mm, the shifted amount may contribute about 8-15% and cannot be ignored.

THE ESTIMATED LENS POSITION (ELP) As shown in Table 13.2, the ELP value (or ACD) depends on the IOL implant position. The table also shows the corresponding values for the A-constant and the surgeon factor(s) as defined by Holladay. Table 13.3 shows some typical values of these 3 parameters. By knowing the ELP (or ACD), A-constant or surgeon-factor, the corresponding effective (optical) ACD (or S) may be calculated based on formulas shown in Table 13.1 given by S=ELP+gT (or gp).

NONLINEAR GAUSSIAN-FORMULA The Classical Formula The IOL power may be calculated from the classical vergence formulas developed by Colenbrander (1973), Hoffer (1974), Fyodorov (1975), Binkhorst (1975) or van der Heijde (1976) given by a general format of P = 1336/(L-C) – 1336/(y-C), Y = 1336/(Kc+E),

Case (e):a thick-IOL in phakic eye (Fig. 13.1E).

(1)

where the effects from the shift from PP of both elements should be included and p is defined by the distance between the two second PPs’ position, or Q3 and Q4. A typical value is p’=p+g’T+2.4 mm, with a g factor of the IOL g’=1/[1+Z2(P1'/P2')], Z2=1-T(P2/1336), where P1' and P2' are the front and back surface power of the thickIOL; and S=ELP+gp’, where the g-factor for the IOLnatural-lens system g=f/f2 (similar to case b).

where Kc is the corneal power measured by keratometry and E is the desired postoperative refractive error, and C = ELP. The above formula for an ametropic case was also used by Hoffer (1974) [published in 1981] and more recently by Haigis (2003), where the original formula of Colenbrander or van der Heijde (for the emmetropic case with E=0) was revised to y for ametropia. Unlike the new formula of Lin (to be shown below) which is rigorously

Table 13.2: Typical values of ELP, A-constant and surgeon’s factor(s) for different IOL implants

Table 13.4: Formulas for postoperative estimated IOL position (ELP) and effective/optical ACD (S) and validity range of axial length (L)

IOL Implant

ELP (mm)

A-constant

s-factor

Anterior chamber lens Iris-supported lens Posterior chamber lens in the sulcus in the bag

2.8 – 3.1 3.3 – 3.5

115.0 – 115.3 115.5 – 115.7

-0.7 to -0.4 -0.1 to +0.1

3.7 – 4.1 4.3 – 5.1

115.9 – 117.2 117.5 – 118.8

+0.1 to +0.7 +0.9 to +1.6

Table 13.3: Lens constant conversion table*

A-constant

ELP

114 2.63 115 3.21 116 3.80 117 4.38 118 4.97 119 5.55 * based on the relationships: ELP=0.5836A-63.896 s-factor=0.5663A-65.6

s-factor -1.04 -0.48 0.03 0.66 1.22 1.79

(1) (2) (3) (4)

Formula

L (in mm) Features

SRK/T Holladay I Hoffer Q Olson

> 26.0 24-26 26.0 mm) and the Hoffer Q is good for short eyes (26.0 mm) (5%). In short eyes (0.0001) in an additional large study of 830 short eyes as well as in a multiple-surgeon study by Holladay. Holladay has postulated that the other formulas overestimate the shallowing of the effective lens position (ELP) in these very short eyes. A more recent study41 I performed on 317 eyes, showed that the Holladay 2 formula equaled the Hoffer Q in short eyes but was not as accurate as the Holladay I or Hoffer Q in average and medium long eyes (Table 14.4). Eyes shorter than 19 mm are extremely rare (0.1 %) and may well be benefited by using the Holladay 2 formula. It appears that in attempting to improve the accuracy of the Holladay formula, the addition of more biometric data input has improved the Holladay II formula in the extremes of axial length but deteriorated its excellent performance in the normal and medium long range of eyes (22.0-26.0 mm) which is 82% of the population.

Methodology There are several means by which to use these newer formulas including A-scan instruments, handheld calculators and computer programs that run on DOS, Windows and Macintosh systems as well as for the handheld Palm PDA operating system (Fig. 14.9). You can also program the published ones yourself on a spreadsheet program. It is important to check the errata

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Table 14.4: Results of accuracy of 4 theoretical formulas on 317 eyes using the Holladay IOL consultant for analysis (Shaded = recommended formulas)41

MEAN ABSOLUTE ERROR

ALL 317 EYES

Formula

Short 26.0

Long ± 2D ERROR

Holladay II

0.72

0.56

0.51

0.49

0.50

0.55

-1.60

0%

Holladay I

0.85

0.42

0.37

0.56

0.43

0.43

-1.44

0%

Hoffer Q

0.72

0.43

0.47

0.58

0.50

0.45

-1.61

0%

SRK/T

0.83

0.46

0.35

0.44

0.36

0.44

-1.45

0%

AVERAGE

0.78

0.47

0.42

0.52

0.45

0.47

H-Q H-2

H-Q H-1

S/T H-1

S/T

S/T

BEST

Where M-Long = medium long, V-Long = very long, Long = all long eyes, Max = maximum.

Figs 14.9A to D

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Figs 14.9A to F: Hoffer Programs IOL power program on a palm personal digital assistant; A. Main calculation screen using Hoffer Q, Holladay and SRK/T formulas, B. Next screen showing refractive results of different IOL powers, C. Clinical History method screen, D. Contact Lens method screen, E. Personalization screen for adding new PO eyes, F. Personalization screen for various IOLs.

in references 37 and 38. The most popular commercial programs are the Hoffer Programs System* (1994) and the Holladay IOL Consultant* (1997), which include several formulas and the ability to personalize them as well as routines to deal with odd clinical situations. (*Available from EyeLab, Inc. 1605 San Vicente Blvd, Santa Monica, CA 90402, 310-451-2020, [email protected]).

Personalization The concept of personalizing a formula based on a surgeon’s past experience and data was introduced by Retzlaff 42 using the A constant to refine the formula. Holladay incorporated this concept into backsolving for the Surgeon Factor and Hoffer backsolved for his personalized ACD. Several studies have proved that formula personalization definitely improves formula accuracy significantly. The following parameters are required from postoperative eyes: 1 Axial length (Pre-op) 2 Corneal power (Pre-op) 3 IOL power 4 Postoperative refractive error (Stable) The eyes should all contain the same lens style by one manufacturer implanted by one surgeon. The same biometry instruments and technician should also have been used. Eyes with postoperative surprises or acuity

worse than 20/40 should not be included due to poor accuracy in obtaining refractive error. Personalization involves backsolving for the exact IOL position that would produce the resultant refractive error with that AL and K. Then all the “ideal” IOL positions are averaged to arrive at the personalized value to use in the future. Personalization can be easily performed using the Hoffer Programs or Holladay IOL Consultant computer programs.

CLINICAL VARIABLES Patient Needs and Desires Most surgeons have developed their own plan for deciding on the clinical needs of their patients. It has often been recommended to aim patients for mild postoperative myopia (-0.5 to –1.5 D) so if the error is on the plus side, they will be emmetropic and if on the minus side, they will have reading vision. This is necessary because of the larger range of IOL power errors generally experienced. When the bell-shaped curve of prediction error is squeezed down to 67% within ±0.50 D, it is then possible to aim most patients for emmetropia. This is even more important when implanting a multifocal IOL. Senior citizens are much more active today then in the past and in emergency situations it would be a lot safer if they were emmetropic than looking around for their myopic correction to escape to safety.

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87

There are several exceptions, however, patients who have been life-long myopes are never happy being hyperopes postoperatively. Patients that would wind up with a large anisometropia should be stimulated to be fit with a contact lens in the other eye prior to deciding on an emmetropic IOL. Monocular CL wearers are more successful than binocular. It is wise to document all discussions in unusual situations.

Plager et al45 reported on 38 eyes of 27 subjects receiving an IOL in childhood. Based on their results they recommend the following scheme for the refractive goal for children depending upon their age:

Special Circumstances

In 1991, the author46 reported that to obtain -2.75 D myopia (reading at 14”-16”) the IOL power in the near vision region must be about 3.75-4.00 D stronger than the emmetropic power. I also showed that the amount of this additional power in a bifocal IOL is not affected at all by the axial length and very little by the corneal power. It is affected, however, by the IOL position and an AC lens would need less add power than a PC lens. Obviously, to negate the need for any glasses, it is important to aim for emmetropia, but mild postoperative hyperopia is far better than even the mildest myopia. The distance vision will be reasonable in the former (they can easily obtain readers if necessary); while in the latter it will not. Bifocal IOL patients with myopia are not happy and everything should be done to avoid this situation since minus power “readers” are not readily available. In the future, a PRL could be implanted over the top of the bifocal to make the eye emmetropic.

Monocular Cataract in Bilateral High Ametrope The dilemma is to make the surgical eye emmetropic or match the large ametropia of the other eye, which may never need surgery. Up to now, I have convinced most patients to accept a CL or ignore the other eye and go for the “brass ring” of emmetropia. In the future, those that can’t tolerate CLs could have a PRL either placed in the other eye or placed over the IOL to eliminate aneisikonia and have it removed if the other eye ultimately has surgery.

Pediatric Eyes Children have always posed a dilemma43 in IOL power selection in that the eye will grow in length and become more myopic if a fixed emmetropic power is implanted. The study of pediatric eyes by Gordon and Donzis44 shows a steep axial length growth rate from premature babies to age two, increasing by 6 mm (~20 D), while corneal power drops from 54 D to 44 D offsetting 10 D. If IOLs are used in this age group it might be best to place piggyback lenses with the more posterior IOL having the average adult emmetropic power and the anterior IOL being the added power needed to reach emmetropia now. As the child grows, they can be corrected with myopic glasses until they are old enough to have the anterior IOL removed. Between the ages of two to five years, growth slows to about 0.4 mm per year and only increases another 1 mm from age five to ten while corneal power remains stable. From age 2-10, it might be wise to aim for 1.5-2 D of hyperopia postoperatively which allows for reasonable uncorrected vision and light spectacle correction in amblyopia treatment. When they mature, they will wind up emmetropic or mildly myopic, depending on age at implantation. Growth slows after age 10-15 and emmetropia can be the aim. Future use of implantable phakic refractive lenses (PRL) over the top of IOLs may be very helpful in these kids since they can easily be exchanged as the eye grows, keeping them emmetropic throughout life.

AGE

3

4

5

6

7

8

10

GOAL +5.00 +4.00 +3.00 +2.25 +1.50 +1.00 +0.50

13 Plano

Multifocal IOL

Silicone Oil Refractive Effect The second problem that arises when the vitreous is replaced with silicone oil is that the refractive index of the oil is much less than that of vitreous, and it acts as a negative lens in the eye which must be offset with more power in the IOL. This effect is dependent upon the shape factor of the back surface of the IOL such that a biconvex IOL creates the worst problem and a concave posterior lens (no longer commercially available) causes practically none. In between the two is the plano-posterior lens, which is recommended in these cases. With a plano-convex lens, 2-3 D must be added to the IOL power to compensate for this silicone effect.

Piggyback Lenses Either piggyback lenses can be placed primarily or the second lens placed secondarily over a previously healed IOL. In the former, the anterior IOL forces the posterior IOL more posteriorly a distance equal to the central thickness of the anterior lens. This causes the posterior

88

Mastering the Techniques of Intraocular Lens Power Calculations lens (whose focal point is moved farther behind the retina) to require more power to maintain the same focus. This effect diminishes the thinner (lower power) the anterior lens is and a thinner lens is easier to remove if that should be necessary. Primary piggyback lenses need special calculations to adjust for the posterior lens shift. Secondary lenses can be calculated using the refraction formula or by a more simple formulation based on the fact that the healed primary IOL is more stable. Due to the different effect on vertex power changes between plus and minus lenses, the following formulation works well. Hyperopic: Piggyback IOL = 1.5 × Rx ERROR Myopic Error: Piggyback IOL = 1.0 × Rx ERROR where Rx = PO spherical equivalent refractive error.

Problems and Errors The major problem is an unacceptable postoperative refractive error. The sooner it is discovered, the sooner it can be corrected and the patient made happy. Therefore, it is wise to perform K readings and a manifest refraction on the first postoperative day. Immediate surgical correction47 (24-48 hrs) will allow easy access to the incision and the capsular bag, one postoperative period, and excellent uncorrected vision. The majority of medicolegal cases today are due to a delay in diagnosis and treatment of this iatrogenic problem. Up to now, we could only correct this problem by lens exchange which creates the dilemma of determining which factor created the IOL power error; axial length, corneal power or mislabeled IOL or a combination of the above. Today, with the advent of low powered IOLs, the best remedy may be a piggyback IOL. Using a piggyback IOL, it is not necessary to determine what caused the error or to remeasure the axial length of the freshly operated pseudophakic eye. It is possible to confirm the power of an explanted IOL by using the McReynolds lens analyzer (Vision & Hearing Center, PO Box 488, 1111 Main St. Quincy, IL 62301, 217-222-6656) (Fig. 14.10). It is important to remember that a shallow AC can lead to as much as 3 D of myopia (depending on the power of the IOL) which will disappear when the AC reforms. An RK eye has a propensity for the cornea to flatten postoperatively causing large hyperopic surprises. It may take up to three or four months for the cornea to resteepen, therefore, surgical correction should not be attempted until then.

Fig. 14.10: McReynolds IOL lens power analyzer

Handling the IOL Power Surprise An inappropriate PO refractive result is disappointing to both the patient and the surgeon. It is often difficult to determine what caused this prediction error. A. According to most studies, the most common cause is an error in measuring axial length. I. This is most commonly seen in eyes longer than 25 mm which have a higher incidence of staphyloma. The problem with staphylomas is that they can vary in size and position. If the macula is located at the deepest end of the staphyloma the anatomical AL will equal the visual AL. Most often the macula lies somewhere else along the slope of the staphyloma and the ultrasound measures the anatomical AL which is longer than the real visual AL. Usually these errors are ones of too long AL and too weak an IOL power (hyperopic error). II. Contact applanation ultrasound artificially shortens the AL and this built in variable error is worse as the AL becomes shorter. Though this fact has been well-accepted, still 90% of clinicians use this procedure and add a fudge factor to correct for it. This would be acceptable if the amount of artificial shortening was approximately the same for every eye but it is not. Some eyes are shortened by as much as a 1 mm and others are not shortened at all. This shortening leads to a too short an AL and too strong IOL power (myopic errors). III. Technician inexperience or just plain error is another cause for incorrect AL measurements.

IOL Power Calculations IV. Using the wrong average ultrasound velocity is another cause for measurement errors. Many use an average velocity of 1550 m/sec which is incorrect. As proven by Hoffer,42 the correct value to be used for a phakic cataractous eye is 1555 m/sec. The problem is that the average speed for a short 20 mm eye is 1560 m/sec and for a long 30 mm is 1550 m/sec. V. Poor IOLMaster readings that are not recognized by the examiner is also a cause of error in AL and are more common as the cataract is more dense or the patient is not able to fixate properly. VI. Silicone oil filled eyes are an especially vexing problem since the ultrasound wave is so slowed down crossing the posterior segment that it is often impossible to get a reading at all. It is also difficult to determine what percentage of the vitreous body is filled and what parts the beam is going through. VII. Lastly there is the problem of the eye that “JUST CAN’T BE MEASURED”! This situation is rare but unfortunately real. No one has offered a complete explanation for this. B. Correct measurement of the corneal power is the second most common reason for IOL power error. I. Overestimation of the corneal power (K) is the rule in eyes that have had previous corneal refractive surgery. This is due to the fact that there has not yet been a keratometer or keratometer attachment that will allow the measurement of the true central corneal power in these eyes. Two factors are at play here. The first is the fact that most keratometers measure at the central 3.2 mm (wider if the cornea is flatter) of the cornea and not able to get the mosre central flat area that is being used by the eye. The second is the change in the refractive index of the cornea that is difficult to correct for in any individual eye because it is dependent upon the amount that cornea has been thinned. II. It is important to have a schedule of calibrating all keratometers to prevent errors in measurement. III. The IOLMaster has a setup screen that allows the operator to change the index of refraction (IR) (most users are unaware of this). The manufacturer did this to cause the instrument to produce K readings equivalent to that obtained by the manual keratometer used in the clinician’s office. American keratometers are set at an IR of 1.3375 and European ones at 1.336. Hoffer recently discovered that if the IOLMaster IR is not set for 1.3375, the Hoffer Q

Formula will be in error. He has not tested the Holladay I & II or the SRK/T formulas. IV. In cataract patients that wear contact lenses, there is a corneal warping factor that produces incorrect K readings compared to what they would be without the CLs (the state the eye will probably be after IOL surgery). This is especially true in eyes wearing hard CLs. 10 years ago a medico-legal case was lost in Louisiana because the judge ruled that the CLs should have been kept out for a minimum of 2 weeks prior to keratometry exam. V. Corneal scaring especially in the center can cause a great problem in measuring the corneal power. VI. Eyes that will need corneal transplantation also pose a problem in predicting preoperatively what the ultimate healed corneal power will be. C. The third and least effective factor in prediction error is the healed effective position of the IOL in the eye. This is referred to as the A constant, the surgeon factor (SF) or the Hoffer anterior chamber depth (ACD). Holladay instituted the replacement term, effective lens position (ELP), since most IOLs today are not in the anterior chamber. I. Errors may occur if the IOL settles in a deeper or shallower position than that predicted by the formula or what would be expected in an eye with that particular IOL, AL and K. Sometimes this can be a temporary situation in the early PO period. II. Another cause of error is when the ACD constants have not been personalized to the individual IOL style, surgeon and clinic. D. Formulas are a cause of IOL power error especially for those using regression formulas and most definitely with those using the SRK I regression formula in eyes outside the normal AL range of 22-24.5 mm. This has been shown in some many studies14 over the past 12 years it would be impossible to reference them all here. E. There are other miscellaneous causes for IOL power errors that can be just as serious as those mentioned above. A rare manufacturer labeling error can be very serious and very difficult to pick up before the patient is discharged from the facility. If the OR nurse hands the surgeon the wrong IOL power during the surgery this may not be easily recognized in time to correct the error. Lastly, transcription mistakes can cause some of the largest errors seen.

89

90

Mastering the Techniques of Intraocular Lens Power Calculations Prevention of Common Errors • Use immersion A-scan and/or IOLMaster to measure the AL. • Suspect a staphyloma in eyes >25 mm: Use IOLMaster and/or Shammas A/B-scan technique. • Use CALF method: measure eye using 1532 m/sec and add +0.32 mm to the result to correct for any error in sound velocity. • Employ a well-trained, experienced technician. • Regularly calibrate manual keratometers. • Carefully evaluate the IOLMaster scan for reliability. • Keep CL out for 2 weeks prior to keratometry (at least in one eye.) • Silicone oil eyes need IOLMaster if possible or ultrasound AL times 0.71. • Use the Hoffer® Q formula in eyes 0 (for near vision accommodation) when dS>0 defined by a movement toward the cornea. The values of M ranging (0.5 to 1.9) depends on ocular conditions. Examples are shown as follows. Case (1): fixed X = 18.8 mm and S = 5.0 mm, (or L = X + S = 23.8 mm). M = (1.1, 1.29, 1.45, 1.62) (diopter/mm) for corneal power of Dc = (45, 43, 41, 39 ) diopter and the required IOL-power for emmetropia P = (17, 20, 22.4, 25.6) diopter. It shows that higher IOL power, in general, produces higher accommodation for a given amount of anterior movement (dS).

Case (5): fixed P = 20 diopter, S = 5.0 mm. M = (1.38, 1.26, 1.19) for L = (22, 24, 26) mm and X = (17, 19, 21) mm. Case (6): fixed Dc = 43 diopter and S = 5.0 mm (with L varies for emmetropic state). M = (0.6, 0.93, 1.29, 1.68), for P = (10, 15, 20, 25) diopters.

Three-optics Formulas (Lin. 2006)

Mobile Front-optics Case As shown in Figure 15.6, a doublet IOL (dual-optics) consists of 2 optics separated by p’, where the front optic separates from the corneal vertex surface by a distance p. M = Z (D1/1336)(2Dc+ZD1)- Delta,(9.a) (9.b) Delta = Z2(D1D2/1336), Z = 1-S(Dc/1336), (9.c) where S (in the unit of mm) being the effective anterior chamber depth (ACD) of the IOL; D1, D2 and Dc are, respectively, the front and back IOL power and corneal power. The accommodation rate (M function) is almost linearly proportional to the moving front IOL-power (D1). M is positive for positive-power moving optics, that is an increase of p’ (or dp’>0 and dp0 for forward movement (toward the cornea), and dS 0), the natural lens (W’ < 0) and the IOL (W”< 0) such that W(total) is minimum. The Coddington shape factor (S) and the surface radius ratio (X) provide comprehensive and analytical formulas which are Table 15.7: The age-dependent refractive error given by Lin’s double-rate theory dDe = -(MN)(A’ – A) M = (P’ + ZP)2/1336 where: dA = (A’ – A) is the age change from A to A’. dL = the axial length growth (in mm). N = (dL/dA) = axial length growth rate per year (mm/year) dDe = the refractive error increase due to axial growth after cataract surgery M = (dDe/dL) = refractive change rate per 1.0 mm change of axial length (D/mm) P and P’ = power of the IOL and the cornea, respectively.

Table 15.6: The adjusted mean power (Wilson et al, 2005) at age of surgery (Ao) Ao (year)

0.1

0.2

0.4

1-2

2-4

4

5

6

7-10

10-14

>14

Dadj (Wilson)

+12 +9

+8

+6

+5

+4

+3

+2

1.5-1.0

0.5

Plano

100

Mastering the Techniques of Intraocular Lens Power Calculations consistent to the numerical results of Want et al and Atchison (Figs 15.8 and 15.9).

REFERENCES

Fig. 15.8: Coddington shape factor (S) for various IOL configurations

Fig. 15.9: The adjusted IOL-power (Dadj) versus cataract surgery age (Ao) for emmetropic IOL-power (Po) being higher than equal to, or lower than the mean value, shown by curve (a), (b) and (c), respectively

1. Shammas HJ. Intraocular lens power calculations. Thorofare NJ: SLACK. 2004;7-24;59-61;64-65. 2. Holladay JT. Optics and intraocular lens power calculation for phakic intraocular lenses. In: Horden DR. Lindstrom RL. Davis EA (Ed). Phakic Intraocular lenses: principles and practice. Thorofare NJ:SLACK 2004;37-44. 3. Lin JT. Unified refractive-state analysis for customized vision correction. J Refract Surg 2004;20(3):398-400. 4. Lin JT. The generalized refractive state theory and effective eye model. Chinese J Optom and Ophthal 2005;7:1-6. 5. Lin JT. New formulas comparing accommodation in human lens and intraocular lens. J Refract Surg 2005;21(2):200-01. 6. Lin JT. A generalized refractive state theory and effective eye model. Chin J Optom and Ophthal 2005;7(1):1-6. 7. Lin JT. Analysis of refractive state ratios and the onset of myopia. Ophthal Physiol Opt 2005;26(1):97-105. 8. Lin JT. Update on IOL power calculation formulas. In: Garg A, Lin JT (Ed). “Mastering Intraocular Lenses[IOLs]: Principles, Techniques and Innovations”, New Delhi: Jaypee Brothers, 2006;17-29. 9. Lin JT. The new IOL formulas based on Gaussian optics. In: Garg A, Lin JT (Ed). “Mastering Intraocular Lenses[IOLs]: Principles, Techniques and Innovations”, New Delhi: Jaypee Brothers, 2006;56-65. 10. Atchison DA. Design of aspherical IOLs. Ophthal Physiol Opt 1991;11:137-46. 11. Pedrotti LS, Pedrotti FL. Optics and vision. Upper Saddle River, NJ. 1998;122-41. 12. Smith G et al. The spherical aberration of the crystalline lens of the human eye. Vision Res 2001;41:235-43. 13. Wang XJ, Jin CP, Wang QM. Aberration with IOLs based on different optical designs. Chinese J Optom and Ophthal 2003;5:209-11.

Error Analysis of IOL Power Calculations

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JT Lin (Taiwan) 101

Error Analysis of IOL Power Calculations

INTRODUCTION Recent advances such as partial coherent interferometry (PCI, or so called IOLMaster) and the advanced image devices called Orbscan have improved the accuracy of ocular biometry, particularly for eyes after cataracts or refractive surgeries. However, errors in the prediction of IOL power still exist in almost all methods, in which some of the error factors are intrinsic either clinically or theoretically. The existing methods (except Haigis’ and Lin’s) of IOL power calculation are all based on the meanzero-error (MZE) concept, where the empirically fit parameters (such as ELP, estimated lens position) are defined by regression formulas with one-constant optimization. Improvement of accuracy was developed by 3-constant optimization proposed by Olsen and Haigis. However, errors of IOL-power are inevitable when the MZE methods are applied to individual eyes. The current MZE methods had personalized the following factors for improved accuracy. • Axial length (L) • Corneal power (based on keratometry-reading) • Corneal height (H) natural lens thickness (T) • Anterior chamber depth (ACD) Modern formulas of Olson predicted the postoperative ACD by a regression formula consisting of the preoperative parameters of (L, H, T, ACD). Haigis proposed the optical ACD given by the solution of a quadratic equation based on Colenbrander formula and the use of 3-constant for optimization which extended the valid range of axial length for both short and long eyes. In Lin’s S-formula, a geometry factor was introduced to further personalize the IOL types, where the effects of

IOL thickness and configuration are included. Lin also presented the Gaussian optics formula for the true corneal power such that the intrinsic errors existing in all keratometry-based formulas may be eliminated by personalizing the posterior surface radius of the cornea, particularly for eyes after refractive surgery. Based on Olsen’s 500 patients study, the total error of IOL power is contributed to 3 major components: 54% to axial length errors, 38% to errors in the ACD estimation, and 8% to corneal power errors. With the optimized ACD calculation (e.g., the Binkhorst I formula), the predicted ACD (postoperative) may be reduced to half. However, for eyes after refractive surgeries, the errors due to postoperative corneal power may increase. Most of the reported studies about the errors of IOL power due to the factors described above are limited to estimated, or qualitative discussion and lack of specifics on individual eyes.

SUMMARY AND NOTATIONS This Chapter will present formulas and examples for indepth guidance and quantitative discussion on IOL power errors (E) resulting from each or combined factors of the following: 1. True corneal power (Dc): Each 1.0 diopter error in corneal power will cause about 1.2 to 1.5 diopter in IOL power error (defined as E) depending on IOL positions. It is more sensitive for anterior implanted IOL. In addition, each 1.0 diopter error in K-reading will result in E = (1.3 to 1.7) diopter. 2. Estimated lens position (ELP) or effective ACD: Each 1.0 mm error of ELP (or ACD) may result in E=(0.5 to 2.5) diopter.

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3. Axial length (L) or vitreous depth (X): Each 1.0 mm error of L or X may result in E=(1.5 to 2.7) diopter, in which shorter eyes and/or steeper cornea is more sensitive to the errors. 4. Manufacturer labeling error or surgeon’s implant error: Depending on IOL types and thickness, E=(0.5 to 3.5) diopter may occur and the higher the IOL power, the higher the error will be. It also has a greater error effects in IOLs having smaller ACD. 5. Error from formulas used: IOL-power error of E= (0.5 to 2.5) diopter may result from eyes having abnormal axial length or posterior corneal surface, where the mean-zero-method based on K-reading of most of the existing formulas fail. Gaussian optics formulas based on true and personalized corneal power should be used to minimize these errors.

NOTATIONS In the following discussion, we will use the definition below: E: error of IOL-power (P) defined as E = -dP (IOLpower change) E>0 (for resultant myopia) or (a plus-IOL power is underestimated), or (a minus-IOL power is overestimated) E 0) M: IOL error per 1.0 mm (or 1.0 diopter) change/ error of Q

Therefore E = -M(dQ), with Q=(L, X, ELP, ACD, Dc, gT): The sign of E depends on the sign of -M since dQ is defined as positive. For example, in a hyperopia, plusIOL implant an overestimated corneal power (dDc>0) will result in an underestimated IOL-power (P), or E = dP 0, therefore E < 0 for dS>0

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Mastering the Techniques of Intraocular Lens Power Calculations based on Eq.(3), this is the case that a plus IOL-power is underestimated and results in a myopia due to the overestimation of S (or ACD).

AXIAL LENGTH ERROR As discussed earlier, L = S+X, therefore for a fixed ACD (or S), the error of L is due to the error of X (or dL = dX) and the associated IOL-power error may be expressed by Lin’s M2-formula (for emmetropic state) E = -M2(dL), (5) M2 = 1336 / (XZ)2, or M2 = 1336/F2, 1/F = (Dc + ZP)/1336 Above formulas show that E is proportional to the IOLpower (P), but inverse proportionally to X (or axial length L). That is, IOL-power errors are more sensitive to short eyes and it is higher for higher P. For example, for fixed corneal power of Dc = 43 D and S = 5.0 mm, Z = 0.839, M2 = (1.66, 1.98, 2.68) (D/mm) for IOL-power of P = (5, 10, 20) D. Therefore, the IOL-error rate function M2 due to per 1.0 mm error of axial length (or strictly speaking, X) is about 1.5 times of M1 (due to error of S or ACD). It should be noted that if both S and X have errors, the total IOL-power error is given by E = (M1 + M2) (dS) + M2(dX). (6)

1.0 will result in gT = 0.5 mm, or the S value increases by 0.5 mm. The associated IOL-power error is E = -0.5 (M1), or about -0.25 to -1.25 diopter. EXAMPLE #3, for a convex-concave IOL with (P1, P2) = (+20, -10) D, gT = -0.5 mm. A mis-labeling or mis-implant of reversed direction with (P1, P2) = (-10, +20) D, having g=+2.0 and gT = +1.0 mm (noting that gT changes from – to +). Substantial errors in IOL power E = -1.5 (M1), or about -0.75 to -3.75 diopter may occur.

CONCLUSION As summarized in Table 16.1, the IOL-power error (E) associates to the error of the corneal power (Dc), axial length (L, or X), ACD (or S) and mis-labeling (by the g-

For the special case of dX = -dS, E becomes E = M1(dS) or Eq.(3); and Eq.(6) reduces to Eq.(5) when dS=0, as one should expect.

MIS-LABELING ERROR

Fig. 16.1: IOL-power error (E) versus IOL-position (S) for 1.0 diopter error of corneal power

For thick IOL, the effective (or optical) ACD (defined as “S”) is shifted by the first principal plane location of the IOL and is given by the geometry-factor defined earlier S = ACD + gT, (7) g = 1 / (1+Z’P1/P2) EXAMPLE #1, for an IOL having a thickness T = 0.5 mm and a biconvex structure having front and back surface power of (P1, P2) = (+5, +10) D, g = 0.666, gives gT = 0.33 mm; whereas a mis-labeling (or surgeon’s mis-implant) with a reverse structure of (P1, P2) = (+10, +5) D, g = 0.333, gives gT = 0.167 mm which causes a S value difference of about 0.16 mm, or IOL-power error of E = -0.16 (M1) which is about (0.1 to 0.4) diopters, for M1 = (0.5 to 2.5) (D/mm). EXAMPLE #2, for a convex-plano IOL (P1, P2) = (+10.0, 0) D, gT = 0 (for the convex surface facing the cornea). A misimplant of the plano surface facing the cornea with g =

Fig. 16.2: IOL-power error (E) for 1.0 mm error of ACD and axial length (L), given by curves M1 and M2, respectively

Error Analysis of IOL Power Calculations factor) may be expressed by analytic formulas, the Lin’s M1, M2, g and Z2-formula. Depending on IOL and ocular conditions, these calculated error functions have a wide range of value, covering most of the reported clinical data. However, most of the existing analysis assumed a mean value without specifying the ocular conditions. Finally, it should be noted that the discussions of this Chapter are based on 2-optics aphakic system. For 3-optics phakic IOL or piggyback IOL, the errors (E) caused by dX and dS would be about 10 to 25% smaller in the 3-optics system. The error caused by corneal power error may be also reduced by about 5 to 10%. Greater details of 3-optics system will be presented in other Chapter of this book.

BIBLIOGRAPHY 1. Atchison DA. Optical design of intraocular lens. I. On-axis performance. Optom Vis Science 1989;66:492-506. 2. Ho A, Manns F, Pham T, et al. Predicting the performance of accommodating intraocular lens using ray tracing. J Cataract Refract Surg 2006;32:129-36.

3. Landenbucher A, Reese S, Jakob C, Seize B. Pseudophakic accommodation with translation lenses-dual optic vs. monooptic. Ophthalmic Physiol Opt 2004:24:450-57. 4. Langenbucher A, Nguyen NX, Sertz B, Gusek-Schneider GC, Kuchle M. Measurement of accommodation after implan-tation of an accommodating posterior chamber intraocular lens. J Cataract Refract Surg 2003;29:677-85. 5. Lin JT. Accommodating IOL: efficiency and optimal design. In: Garg A, Lin JT (Ed.), Mastering IOLs: Principles and Innovations, Jaypee Brothers Med Pub New Delhi, India. 2006. 6. Lin JT. Unified formulas for phakic-aphakic IOL and spectacle-cornea power conversion. J Refract Surg 2006;22:(in press). 7. Lin, JT. New formulas comparing accommodation in human lens and intraocular lens. J Refract Surg 2005;21:200-01. 8. Lin, JT. Unified refractive-state analysis for customized vision correction. J Refract Surg 2004;20:398-400. 9. Mcleod SD, Portney V, Ting A. A dual optic accommodating fordable intraocular lens. Br J Ophthalmol 2003;87: 1083-85. 10. Nawa Y, Ueda T, Nakatsuka M et al. Accommodation obtained per 1.0 mm forward movement of a posterior chamber intraocular lens. J Cataract Refract Surg 2003;29: 2069-72. 11. Wang XJ, Jin CP, Wang QM. Aberration with IOLs based on different optical design. Chinese J Optom and Ophthal (in Chinese). 2003;5:209-11.

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Mastering the Techniques of Intraocular Lens Power Calculations JT Lin (Taiwan)

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17

The Basics of Accommodating IOLs

INTRODUCTION Analytic formulas for accommodating intraocular lens with forward movement pseudo-accommodation (or apparent accommodation) in various intraocular lenses (IOLs) has been reported including 1CU lens (Human Optics, Inc.), AT-45 lens (C&C Vision) and MA30 lens (Eyeonics Vision, Inc.). 1-4 The preoperative and postoperative corneal power (or keratometry) or the estimated lens position (ELP), are believed to be the important factors in comparing the outcomes of different IOLs. The accommodation (A) per 1.0 mm anterior movement (defined as M) was measured 3-5 to be about M=(0.9 – 1.9) (diopter/mm) and calculated by Nawa et al6 to be (0.8 – 2.3) (diopter/mm) by ray tracing method. It was known that widely scattered values of M may result from various ocular conditions such as corneal power, IOL power and axial length. These features are explored by numerical calculations based on a ray-tracing equation, where the roles of each of the ocular parameters have not been fully explored. This Chapter will cover the following subjects: • Accommodation of single and dual-optics IOL (in aphakia) • Accommodation of single-optics IOL (in phakia) • Design aspects for maximal efficiency and minimal spherical aberration. Analytic formulas for M in single-optics IOL will be derived (in the Appendix) to demonstrate explicitly the parameters determining M. These include the corneal and IOL power, the IOL postoperative effective position (S), the effective vitreous cavity length (X), axial length (L) and the remaining refractive error. For example, M should be determined by X and S, rather than the axial length alone, where M varies even for the same axial length. Six

different ocular situations showing the roles of each of the parameters will be discussed.

CATEGORIES OF AIOL As shown in Figure 17.1A, the accommodation of a singleoptics accommodating IOL (AIOL) in aphakic eye (without the natural lens) may be achieved by the forward movement of the optics, and L = S + X, where S = p (position of the IOL) for thin-lens and S = p + gT, for thick-lens to include the geometry factor (g) and its thickness. Note that gT > 0 for biconvex and gT < 0 for convex-concave, and gT = 0 for convex-plano. Figure 17.1B shows the 3-optics system where the AIOL is implanted in a phakic eye. Figure 17.1C shows the dual-optics AIOL in which the accommodation may be achieved by the forward (or backward) movement of the front (or back) optics. The net result depending on various situations that either front or back or both optics may be mobile, while the other optics could be immobile determined by the ciliary-body contraction on the AIOL and its configurations. Dualoptics AIOL is much more complex than the single-optics and will be presented in other Chapter of this book.12

THE BASIC PRINCIPLES Single-optics IOL (referred to Fig. 17.2) By the definition of M = -dDe/dS (in diopter/mm), the accommodation amplitude (A) per mm axial movement of the lens is given by (see Appendix for derivation) A = -M(dS), (1) M = M2-M1, (2) M2 = 1336/F2, (3.a) M1 = 1336/fc2, (3.b)

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Fig. 17.2: The basics of accommodation (3-component analysis) due to axial movement in a positive-power IOL, where SSP is the position of second principal plane

b myopic-shift due to the effective power (1336/F) increase when S decreases (or dS < 0) since d(1/F) = dS/(fcf2), d(1/F) > 0 when dS < 0; c. hyperopic-shift due to the back-shift of the second principal plane (SSP) resulting from the decrease of (SF). Component (a) gives M2, and (b) + (c) give a net hyperopic shift given by M1. Typically, the contribution percentage of each component is: (b) = 33%(a), and (c) = 80% (a). Therefore the net A = (1+0.33-0.80)(a) = 0.53(a). For example, for F = 22 mm, fc = 31 mm, f2 = 62 mm, (a) = M2 = 2.76, (b) = 0.92, and (c) = -2.1, therefore A = 1.58 (diopter). Some of the published articles had wrongly assumed that A mainly attribute from d(1/F). Furthermore, the contribution from the SSP-shift, about 33% of (a), could not be ignored. Comparison of positive and negative A (for a plus IOL):

A>0 A 0) due to lens axial forward movement (dX > 0 and dS < 0) may be expressed by 3 components: a. myopic-shift due to dX > 0, increase of vitreous cavity length (X);

dS

dX

axial movement

0

>0 0) or negative (P < 0) lens, where I define dS0 for backward movement. Greater detail of dual-optics IOL is shown in a separate Chapter of Lin in this book.

Dual-optics IOL (Referred to Fig. 17.4) Above single-optics IOL formula of Eq.(3) may be generalized to a dual-optics IOL having a front and back optics power of P1 and P2. The A for dual-optics IOL is then attributed to both movements of the dual optics and given by A = M1(dS1) + M2(dS2), Mj (j=1,2) = (Z/1336)Pj[2P’+ZPj].

Case (1): fixed X = 18.8 mm and S = 5.0 mm, (or L = X+S = 23.8 mm). M = (1.1, 1.29, 1.45, 1.62) (diopter/mm) for corneal power of D1 = (45, 43, 41, 39 ) diopter and the required IOL-power for emmetropia D2 = (17, 20, 22.4, 25.6) diopter calculated from Eq.(2). These calculated data show that IOL with a higher power, in general, produces higher accommodation for a given amount of anterior movement (dS), in consistent with the measured 1 and calculated values using a ray tracing method6 (Fig. 17.5).

(5.a) (5.b)

As shown by Figure 17.2(a), a positive A may be achieved for presbyopia eyes after cataract surgery. In contrast, shown by Figure 2(b), a negative A is required for pediatric eyes in order to compensate (accommodate) the myopicshift due to the axial elongation of the pseudophakic eye (after IOL implant). In Eq.(5), I had re-defined dSj>0 for forward movement.

Fig. 17.5: Accommodation rate M (per 1.0 mm of forward movement) versus IOL-power at various axial length L=(22, 24, 26) mm

Fig. 17.4: Image shift caused by a dual-optics IOL for (A) positive-negative pair, and (B) negative-positive pair

Case (2): fixed corneal power D1 = 43 diopter and axial length L = 23.8 mm. M = (1.08, 1.14, 1.2, 1.29, 1.36) (diopter/mm), for S = (2.0, 3.0, 4.0, 5.0, 6.0) mm. These values show that M is an increasing function of the IOL position, where X

The Basics of Accommodating IOLs

Fig. 17.6: M versus IOL position (S) for: (A) fixed IOL-power at 20 diopter, and (B) fixed corneal power at 43 diopter, for a fixed axial length L=23.8 mm in both cases

Fig. 17.7: M versus axial length (L) with Curve (A) and (B) having the same conditions as Figure 17.5, but for a fixed S=5.0 mm, and L and X change

decreases when S increases for a fixed axial length L = X+S. See Figure 17.6, Curve (B). Case (3): fixed IOL-power D2 = 20 diopter and L = 23.8 mm. M = (1.36, 1.34, 1.32, 1.29, 1.25) (diopter/mm), for S = (2, 3, 4, 5, 6) mm. The decrease of M for larger S is the net result of the competing factors from the decrease of X = L- S, and the emmetropic condition which requires a higher corneal power for a given IOL power. See Figure 17.6, curve (A). Case (4): fixed P’ = 43 diopter and S = 5.0 mm M = (0.56, 0.82, 1.22, 1.87) (diopter/mm), for IOL-power D2 = (9.5, 12.4, 19.1, 27.3) diopter and axial length L = (27, 26, 24, 22) mm calculated from L = X + S. This example shows that, for a given corneal power, longer eye with lower IOL power result in a smaller M, in consistent with that of Nawa.6 See Figure 17.7, curve (B). Case (5): fixed P = 20 diopter, S = 5.0 mm. M = (1.38, 1.26, 1.19) for L = (22, 24, 26) mm and X = (17, 19, 21) mm. See Figure 17.6, Curve (A). Case (6): fixed P’ = 43 diopter and S = 5.0 mm. M = (0.6, 0.93, 1.29, 1.68), for P = (10, 15, 20, 25) diopters, calculated from Eq.(4.a) for the linear case

Fig. 17.8: M versus plus IOL-power P for fixed corneal power at 43 diopter and S=5.0 mm, where Curve (A) shows the linear function based on Eq.(3) which is lower than curve (B) with nonlinear term included

shown by curve (A), and the nonlinear case, curve (B) in Figure 17.8. The above examples may be used to analyze and explain why the measured values of M have a wide range of 0.8 to 1.9 (diopter/mm) even they have been averaged over various ocular conditions. More details are shown as follows. Calculations of Case (1) are shown by Figure 17.5 for the role of IOL-power (P). The general feature of M being

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Mastering the Techniques of Intraocular Lens Power Calculations an increasing function of P may also be easily seen by Eq.(4.b), in which the minus term – P/1336 is minor and the front term (P)Z2 is the dominating term. Also shown in Figure 17.2 are the comparison of M vs. P for axial length L = (22, 24, 26) mm, where longer eyes results in smaller M for a given P’, P and S. This may be realized by Eq.(4.b) showing M is proportional to 2/X, and X = L-S. Therefore a longer eye results in a smaller M. In addition, for a given axial length, steep corneas normally require a lower IOL power to achieve the emmetropic state, De = 0 in Eq.(1), which also obtain a lower accommodate rate than that of a flat-cornea with high-power IOL. This trend is consistent with that of Nawa et al using lengthy numerical calculation which is readily available from Eq. (4.b). Figure 17.6 shows the results for Case (2) and (3) which have opposite trends when S increases. This feature may be further analyzed as follows. Case (2) shown by Curve (B) of Figure 17.5 indicates that given the same axial length and corneal power, posterior chamber implant (such as 1CU) is more efficient than that of anterior implant (such as AT-45), because higher IOL-power is needed for larger S to achieve an emmetropia. In contrast, Case (3) shown by Curve (A) with a fixed IOL-power and L, larger S requires smaller X and higher corneal power (P’) to meet the emmetropic condition. Calculations based on parameters of Case (3) show a net increase of M, in contrast to Case (2), when S increases. These features were not explored in the ray-tracing method of Nawa et al. Furthermore, the statement made by these authors that longer eye with lower IOL-power results in higher M is only partially correct. As shown in this study, Case (2) and (3), and Eq.(4.b), M is governed by the combined function of Z2(P)/X, rather than their absolute values. As shown in the above example, M may be a decreasing or increasing function of S or X even for the same axial length (L). The role of axial length should be broken down by L = S+X to separate the roles of S and X as shown by Case (2), (3) and (6).The roles of S, X and L were not differentiated in the calculations of Nawa et al. In other words, a longer eye does not necessarily result in a higher M which is also subject to the relative value of S and X. Results of Case (4) and (5) are shown by Curves (B) and (A) of Figure 17.7 and demonstrate that M is a decreasing function of L in both Cases, because X is an increasing function of L when S is fixed, and larger X results in a smaller M as shown by Eq.(4.b). The calculated values in Case (4) with M = (0.56 – 1.87) (D/mm) for L = (27-22) mm are consistent with that of Nawa, M = (0.8-

1.9) (D/mm), where the small difference is due to the difference in corneal power chosen. The measured data of 0.9 and 2.02 (D/mm) for axial length of 21 and 25.8 mm also showed the similar trend, although their values are higher due to higher IOL powers are used. Figure 17.7 (Curve-B) shows that M is a strongly decreasing function of L (from 1.87 to 0.82) in Case (4) with a fixed corneal power and various IOL powers, in comparing to a weak dependence of L in Case (5) (CurveA) with a fixed IOL-power and various corneal powers. In other words, M has a stronger dependence on IOLpower than on corneal-power. Figure 17.8 shows the nonlinear behavior of M versus P (about 1% higher per diopter) as shown in Case (6). This nonlinear feature resulted from the second term of Eq. (3) was not shown by Nawa et al using a ray tracing method. As shown in the Appendix, M, in general, is a function of six parameters (De, P’, P, S, X, L), where De is the refractive error after IOL implant (if any) and may contribute about 6% (for De = 10.0 diopter) of the value of M at emmetropic state. The M value for ametropic state (post-IOL) may be calculated by adding an extra term of 2(1/X – 1/f2)De to Eq.(4.b). This ametropic term contributes about 0.06 (diopter/mm) for each diopter of De to the M value at emmetropic state.

THREE-OPTICS SYSTEM (IN PHAKIA) The 3-optics IOL system include: (a) single-optics IOL in phakia, (b) piggyback-IOL, and (c) dual-optics IOL in aphakia. Case (c) for dual-optics IOL is much more complex due to the variety of configurations and the movement dynamics of each optics which will be presented in a separate Chapter by Lin in this book. We shall now present the formulas for case (a) and (b). Using Gaussian optics, Lin had derived the formula for the dual-optics accommodating IOL which may also apply to the single-optics IOL in phakic eye by replacing the back-optics of the dual-optics-IOL as the natural lens (for phakic-IOL) or the primary-IOL (for piggyback-IOL). The M function of 2-optics system shown by Eq. (1) or (3) is revised as follows for a 3-optics phakic-IOL (Lin, 2007) M’ = (f/f2)M – Delta, (6.a) Delta = 1336Z2/(f2f3), (6.b) where f2 and f3 are the EFL of the IOL and the natural lens (NL), respectively and 1/f = 1/f2+Z’/f3, with Z’ = 1p’/f3, p’ = p+2.4 mm. Above formula reduces to the 2optics (M) when f3 = infinity (or aphakic eye) and f = f2, Delta = 0. The second term, Delta, is a reduction factor of

The Basics of Accommodating IOLs M due to the presence of the NL. The configuration factor G = f/f2 may be re-expressed as G = 1/[1+Z’(Pn/Pi)] (7) where Pn and Pi are the NL-power and IOL-power, respectively. M’ may be further expressed as the power of the cornea (P’), Pn and Pi as follows M’ = (Z/1336)Pi (2 P’+Z’ZPi), (8.a) Z’ = 1-p’/f3, Z = 1-S’/f1, (8.b) S’ = S+gp’, g=1/[1+Z’(Pi/Pn)]. (8.c) where p’=p+2.4 mm in phakic IOL and S=ELP is the position of the IOL (thin lens) or S=ELP+g’T (for thick lens), where g’ is a geometry factor of the IOL having a thickness T and front and back surface power ratio of D12, g’=1/(1+D12). Eq. (6) may also be derived from the IOL-power (Pi) of phakic 3-optics system given by (Lin, 2007) Pi = (Pio + C)/Z’, C = (pGM’)/Z2,

(9.a) (9.b)

and by using the conversion factor CF=dDe/(Z’PiPio)=Z2, where dDe is the system power change (or accommodation A) due to the axial movement (from p=0 to p). Pi and Pio are the IOL-power for emmetropia at p and at p=0. Comparing M’ of Eq.(6) for IOL in phakic eye with Eq.(4) for the aphakia M, one may easily conclude the following: 1. For a given IOL-power, M’ in phakia is always smaller than that of the aphakia (M) by a reduction factor determined by Z and Z’=1-p’/f3, in which Z’1, for meniscus (or convex-concave) with more curved surface facing cornea; R = -1, for plano-convex; R = +1 for convex-plano; R>-1 for biconvex and R = 0 for equi-convex. According to Smith and Liu, the optimal value of R = +1.1 or a convex-concave IOL (with convex facing cornea) in order to produce positive SA and balance the negative corneal SA for minimal overall SA of the eye. Based on the Gaussian formula of M’ and M, the convexconcave configuration also provides higher accommodation rate.

CONCLUSION By Gaussian optics, the accommodation rate (diopter/ mm) function (M) may be derived analytically for both aphakia and phakia IOL and piggyback IOL. The M value is determined by the combined factor of the products of ZPiPc(2+Z’ZPi/Pc) shown by Eq.(3). Following features of AIOL may be summarized: • M is proportional to the product of Z and the IOL (Pi) and corneal power (Pc) and extra nonlinear term Z’ZPi/Pc which is influenced by the power of the natural lens (for the case of phakic-IOL), or by the primary-IOL power (for the case of piggyback-IOL) by Z’ and S’ = S = gp’; • The Z’ reduction term is a function of the IOL and natural lens (or primary-IOL) separation and their power, Z’ = 1-p’(Pn/1336), having a value of about 0.96 to 0.98. • The effective ACD (S) is shifted to S’ = S+gp’, where g is a geometry factor given by g = 1/(1+Z’Pi/Pn) about 0.6 to 0.82. • The M’ function (for phakia) is about 10 to 30% lower than M (for aphakia). • The general trend is that higher M or M’ for eyes with shorter axial length (L or X), flatter cornea or smaller ACD (or S) and for high IOL power. • IOL with convex-concave structure has a higher M’ and may achieve lower surface aberration of the eye comparing to other structures. Above features are for single-optics IOL in phakia or aphakia, or piggyback-IOL. For dual-optics IOL accommodation, see other Chapter of Lin in this book.

APPENDIX (SINGLE-OPTICS IOL) By Gaussian optics theory,8 the refractive error (De) after an IOL is implanted in an aphakic eye (a two-optics system) may be described by: 9,10

De = 1336[1/(L-L2) – 1/F],

(A-1)

where L is the axial length, L2 is the position of the second principal plane and F is the effective focal length (EFL) of the cornea-IOL system related to the EFL of the cornea (f1) and IOL (f2) by 1/F = 1/f1 + Z/f2,

(A-2)

where Z = 1-S/f1, S being the effective anterior chamber depth of the IOL which equals to the postoperative estimated lens position (ELP) when a thin IOL lens is assumed. Using the relation of L2 = S(1-F/f1) (for thin lens) 8,10 and substituting Eq.(A-2) to (A-1), one obtains qDe = 1336/X – P’/Z- P, q = 1/Z2,

(A-3) (A-4)

where the effective vitreous length defined by X = L-S, and P’ and De are the power of the cornea and lens, respectively. To formulate the accommodation amplitude (A) per 1.0 mm forward movement of a single-optics IOL, I define a rate function M = -dDe/dS = A/dS, which may be obtained by taking the derivative of Eq.(A-3) with respect to X (or S) dDe = -M(dS), M = M1 – M2, M1 = 1336(1+dS/X)(Z/X)2, M2 = 1336/f12,

(A-5) (A-6.a) (A-6.b) (A-6.c)

where the high-order term dS/X contributing about 5% for dS = 1.0 mm since X is about 18 mm. In deriving above formulas, I had also used dX = dL-dS = -dS, since dL = 0, that is axial length remains the same when the IOL is anterior shifted; and dZ = -dS/f1. At emmetropic state (De = 0), Eq.(A-3) gives the formula for IOL-power P = 1336/X – P’/Z,

(A-7)

which may be used to eliminate the second term in Eq.(A6) since P’ = 1336/f1 and to obtain a more practical formula for M as shown in Eq.(1.b), where I also used the relationship of F = X/Z for emmetropic state in deriving Eq.(1.b) in which the high-order terms of (A-6) are neglected. Eq.(A-7) may be compared with the classical vergence formula of Heijde 11 by relating X = L-ELP and corneal power by the keratometric power (K). It was known that error occurs in using K for cornea power, therefore Eq.(A-7) is more accurate than all the classical vergence

The Basics of Accommodating IOLs formulas which have been used in combining with the modern formulas for ELP. The approximated Eq.(A-3) is derived by decoupling the second principal plane position P2 = SF/f1 from L2 = S-P2. Alternatively, one may use the following equation for exact numerical calculation for both De and M De = 1336/(X+P2) – 1336/F,

(A-8)

which is just a rearrangement of Eq.(A-1) without using the decoupling approximation. Above equation also allows us to check the accuracy of the analytic approximate formulas of Eq.(1). For example, for P = 20.0 diopter with a fixed P’ = 43 diopter, S = 5.0 mm and L = 23.7 mm, M = 1.30 (diopter/mm) calculated from the exact Eq.(A-3) in comparing to M = 1.298 calculated from analytic formula, Eq.(1), which is only about 0.15% error. Alternatively, one may also derive Eq.(A-6) by taking the derivative of Eq.(A-1) and using the relationship of Eq.(A-2). A third method is to take the Taylor secondorder expansion of De in Eq.(A-7) or (A-8) with respect to the change of X. For example, 1/(X+dX) = 1/X-(dX/X2)[1dX/X]. All the above described three different methods lead to the same formula of (A-6) and justify the derivation of M. Above formulas are for 2-optics system. Much complex algebra is involved in 3-optics system for thin-IOL in phakic eye or dual-optics IOL in aphakia. The detailed derivation will be shown in a separate Chapter of Lin in this book.

REFERENCES 1. Langenbucher A, Nguyen NX, Sertz B, Gusek-Schneider GC, Kuchle M. Measurement of accommodation after implantation of an accommodating posterior chamber intraocular lens. J. Cataract Refract Surg. 2003;29:677-85. 2. Cumming JS, Slade SG, Chayet A. Clinical evaluation of the model AT-45 silicone accommodating intraocular lens. Ophthalmology 2001;108:2005-09. 3. Koeppl C, Findl O, Kriechbaum K et al. Change in IOL position and capsular bag size with an angulated intraocular lens early after cataract surgery. J Cataract Refract Surg 2005;31:348-53. 4. Stachs O, Schneider H, Steve J, Guthoff R. Potentially accommodating intraocular lenses-an in vitro and in vivo study using three-dimensional high-frequency ultrasound. J Refract Surg 2005;21:37-45. 5. Holladay JT, Chandler TY et al. Refractive power calculation for the phakic eye. Am J Ophthalmol 1993;116:63-66. 6. Nawa Y, Ueda T, Nakatsuka M et al. Accommodation obtained per 1.0 mm forward movement of a posterior chamber intraocular lens. J Cataract Refract Surg 2003; 29:2069-72. 7. Lin JT. The roles of corneal power and anterior chamber depth on the accommodation of aphakic intraocular lenses. J Refract Surg 2005;21:765-66. 8. Pedrotti Ls, Pedrotti FL. Optics and Vision. Upper Saddle River; NJ 1998;74-78. 9. Lin, JT. Analysis of refractive state theory and the onset of myopia. Ophthal Physiol Opt 2006;26:97-105. 10. Lin, JT. The generalized refractive state theory and effective eye model. Chin J Opt and Ophth 2005;7:1-6. 11. van de Heijde GL. The optical correction of unilateral aphakia. Trans Am Academy Ophthal Otolaryngol 1976;81:80-88. 12. Lin JT. Analysis of dual optics accommodating IOL. In: Garg A, Lin JT (Ed), Mastering Intraocular Lenses (IOLs): Principles, Technologies and Innovations. New Delhi: Jaypee Brothers Med Pub 2006;434-39. 13. Wang XJ, Jin CP, Wang QM. Aberration with IOLs based on different optical design. Chinese J Optom and Ophthal (in Chinese). 2003;5:209-11. 14. Atchison DA. Optical design of intraocular lens. I. On-axis performance. Optom Vis Science 1989;66:492-506.

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IOL Calculation in Long and Short Eyes

Biometry and IOL calculation play an important role in cataract surgery and even more in refractive surgery. Surveys among members of the ASCRS and ESCRS have shown again and again in the last years that incorrect IOL powers are the number one cause of explantation or secondary surgical intervention.12 This is of special importance when it comes to long and short eyes: in these highly ametropic patients often undergoing refractive lens exchanges correct measurements and appropriate use of IOL formulas are absolutely mandatory. In the following, an attempt will be made to shed light on some of the problems in biometry and IOL calculation which are typical for or more pronounced in short and long eyes than in normal eyes.

results (n = 15, 123, unpublished data) of cataract patients and setting the axial length (AL) limits to 20 and 27 mm, we find 0.3 percent short eyes with AL < 20 mm and 4.1 percent long eyes with AL > 27 mm. If, however, we set the cutoff points to 22 mm for short and 25 mm for long eyes, then we have some 11 percent in each category of extreme eyes leaving ≈ 78 percent ‘normal’ eyes with 22 mm < AL < 25 mm. Table 18.1 gives an overview on ocular dimensions of cataract patients who underwent preoperative measurements in our laboratory. In all cases, biometry was performed by high precision immersion ultrasound (Grieshaber Biometric System GBS); for keratometry either a Zeiss ophthalmometer (‘Zeiss bomb’) or an Alcon handheld keratometer (Renaissance series) was used.

LONG AND SHORT EYES

Short Eyes

How are we to define long and short eyes? Analyzing our database with preoperative biometry and keratometry

In 1981, KJ Hoffer9 published his well-known paper on the short eye problem. He described that the combination

INTRODUCTION

Table 18.1: Ocular dimensions (mean ± standard deviation, unpublished data), based on n=15,123 preoperative biometries and keratometries of cataract patients. Results for all eyes (left) and split into short, normal and long eyes (right). Distances measured by high precision immersion ultrasound (Grieshaber biometric system GBS); keratometries obtained with Zeiss ophthalmometer (‘Zeiss bomb’) and Alcon handheld keratometer (Renaissance series)

All eyes

Short < 22

Axial length (mm) Normal 22 - 25

Long >25

Anterior chamber depth (mm)

3.13 ± 0.51

2.69 ± 0.50

3.14 ± 0.47

3.48 ± 0.46

Lens thickness (mm)

4.48 ± 0.71

4.69 ± 0.76

4.46 ± 0.70

4.40 ± 0.71

23.48 ± 1.68

21.44 ± 0.58

23.27 ± 0.72

27.09 ± 2.08

7.67 ± 0.27

7.45 ± 0.26

7.69 ± 0.25

7.76 ± 0.31

n

15,123

1,678

11,812

1,633

n (%)

100%

11.1

78.1

10.8

Axial length (mm) Corneal radius (mm)

IOL Calculation in Long and Short Eyes of the Binkhorst formula and an applanation type biometry device resulted in an overestimation of the implant lenses by 0.5 D. On the other hand, with ultrasound biometry in immersion technique and another optical formula like the Colenbrander-Hoffer, these eyes presented no difficulties. So, the problem was basically bound to an axial length measured too short by the biometrical technique used and to an IOL formula, which applies a negative correction to the measured length thus making things even worse. Trying to fix the formula part of the problem actually led to the development of the SRK I regression formula. Nevertheless, Hoffer concluded in his paper that “... regression formulas are not necessary ... if the immersion method ... and a theoretic formula other than Binkhorst’s is used.” Some years ago,3 we were wondering whether short eyes would still pose specific problems if current procedures and measurement methods were applied. We revisited the short eye problem by performing model calculations for twins with axial lengths of 21 mm. The twins consulted two perfect surgeons performing perfect measurements using state-of-the-art equipment. They asked for equiconvex silicone IOLs (7 mm optic, edge thickness 0.2 mm, A-constant 118.05); both surgeons used the SRK/T formula.15 The calculations carried out in Gaussian thick lens optics showed that one of the twins ended up hyperopic (+2.67 D) while the other one came out nearly emmetropic (+ 0.19 D). The reasons for these results lay in the different measurement techniques (surgeon A: immersion ultrasound and Javal-type keratometer, surgeon B: applanation ultrasound and Zeiss keratometer) and different labeling principles applied to the IOL powers calculated by each surgeon. Table 18.2 shows a summary of the model calculations. As a result, differences in predicted refraction of up to 2.4 D were obtained; biometry contributed 0.7 D and keratometry 0.5 D. Lens specific factors were responsible for up to 1.2 D. Figure 18.1 gives a schematic representation of the individual error contributions. Manufacturing tolerances (allowed in this power range: ± 0.5 D) were not considered in the above model calculations and would add in real life to the errors already mentioned. This hypothetical IOL implantation in twins showed that the combination of different working conditions can still lead to a ‘short eye problem’. Apart from the wellknown influences of measurement techniques, an essential contribution was found to be due to specifications of modern IOLs (power declaration method used, lens shape). These IOL related difficulties may in part be

Fig. 18.1: Error contributions of biometry (A scan), keratometry and IOL labeling policies for hypothetical IOL implantation in twins. Overall refractive error as calculated by thick lens optics: 2.4 D

overcome by appropriate international standards to come into effect in the future. In the meantime, the possible differences in optical behavior of lenses of different manufacturers must be accounted for by suitable fudging techniques. This can be done, e.g. by a thorough personalization of IOL constants in different axial length ranges. Another important influence on short eye results comes from biometry. Measurement errors become more effective if the measured axial length value is small in comparison to longer eyes. This holds especially for the effective lens position, which apart from the SRK II formula is a function of axial length in all IOL power formulas. For the average short (21.44 mm), normal (23.28 mm) and long (27.09 mm) eyes of Table 18.1, the following changes Δ Rx in refraction relative to changes Δd in effective lens position can be derived: short eye: Δ Rx/Δ d ≈ 1.9 D/mm; normal eye: Δ Rx/Δ d ≈ 1.4 D/mm; long eye: Δ Rx/Δ d ≈ 0.6 D/mm. From this it follows that the refractive effect due to an uncertainty in IOL position is ≈ 3 times larger in a short eye than in a long eye. These numbers, by the way, also explain why an ‘accommodative’ intraocular lens based on the optic shift principle has a better if any chance to work in a hyperope than in a myope.

Long Eyes Long eyes, too, like short eyes, deserve the best of biometry technique available, especially if a clear lens extraction is planned. While immersion ultrasound is known to be superior to contact ultrasound, contact A scan ultrasonography is still applied in a majority of ophthalmo-surgical centers, e.g. exclusively in 65 percent of the centers in the UK.2 Recently, optical biometry based on partial coherence interferometry (PCI) has become

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Mastering the Techniques of Intraocular Lens Power Calculations Table 18.2: Short eye problem revisited: Data for simulated IOL implantation in twins who consult two perfect surgeons using different state-of-the-art equipment and procedures. Biometry and keratometry for twins: True axial length=21 mm, anterior chamber depth=2.59 mm, corneal radius=7.44 mm. The nominal power of the IOL implanted by surgeon A stood for the back vertex power at room temperature (20°C), while surgeon B’s IOL was labeled as effective (total) power at in situ temperature (35°C)

Surgeon A

Surgeon B

US biometry technique ... results in ...

Immersion axial length

Applanation axial length - 0.3 mm

keratometer index ... results in ...

nC = 1.338 K = 338/RC

nC = 1.332 K = 332/RC

(back) vertex power 20 °C

effective (total) power 35 °C

Twin A

Twin B

21.00 mm 45.44 D 26.43 D 26.5 D + 2.67 D

20.70 mm 44.64 D 28.32 D 28.5 D + 0.19 D

IOL power stands for ... at temperature ...

Measured axial length Measured corneal power Calculated emmetropia IOL Implanted IOL Resultant refraction

available in the Zeiss IOL Master.5,6,8 PCI biometry is particularly beneficial for measurements in more challenging eyes (e.g. those containing silicone oil, pseudophakic eyes, eyes of children, extremely short nanophthalmic or extremely long myopic eyes with posterior staphylomata). The incidence of staphylomata increases significantly with axial length1 and it is these eyes which may cause considerable trouble in ultrasound measurements. However, these eyes are ideal candidates for optical biometry, the reasons lying in the different axes of measurement. Ultrasound is aimed along the optical axis of the eye in order to meet all interfaces perpendicularly, while PCI measures along the visual axis which the patient uses for fixation during the measurement. Thus, there is no question in optical biometry which axial length is the correct one. An example is given in Figure 18.2 showing PCI and ultrasound biometry in a myopic eye with a staphyloma.13 The axial length was 27.06 mm by ultrasound and 29.19 mm by PCI. A myopic refractive surprise of ≈ 5 D would have been created if the ultrasound value would have been used for IOL power calculation. Keratometry, next to biometry, plays also an important role for the outcome in IOL implantation. High myopes asking for refractive surgery are often young and active persons wearing contact lenses (CL). Especially hard contact lenses if not removed a sufficient time before examination have the potential to skew refractive results

Fig. 18.2: Optical (PCI, bottom) and acoustical (US) biometry in a myopic eye with a staphyloma. Ultrasound axial length was 27.06 mm, PCI length 29.19 mm. A myopic refractive surprise of ≈ 5 D would have been created if the ultrasound value would have been used for IOL power calculation

by up to 1 or even 1.5 D. It is therefore very important to make sure in these cases that keratometry results are not compromised by preceding CL wear.

IOL POWER FORMULAS It is obvious that high quality measurement procedures are mandatory to obtain good results in extreme eyes.

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Table 18.3: Common IOL power formulas and their respective IOL constants

Formula IOL constants

Haigis

Hoffer Q

Holladay

SRK/T

SRK II

a0, a1, a2

pACD

sf

A-const

A-const

However, entering excellent input data into an inappropriate formula will nevertheless produce erroneous outcomes. The most commonly applied IOL power formulas today are those by Sanders, Retzlaff and Kraff: SRK II16 and SRK/T.15 According to a recent survey in the UK,2 49 percent used SRK/T, 17 percent SRK II and 34 percent other formulas. In Germany, the respective percentages are 40 percent for SRK II, 22 percent for SRK/ T, 23 percent for Haigis5,7 and 15 percent for other formulas.14 The Royal College of Ophthalmologists17 in the United Kingdom has set up some guidelines—based on the work of KJ Hoffer—which formula works best for short, normal and long eyes. According to these recommendations the Hoffer Q10 should be used in cases of short eyes, SRK/T in long eyes and an average of Hoffer Q, SRK/T and Holladay11 for medium eyes. If the performance of IOL power formulas is to be compared it is essential that the respective IOL constants are customised (optimized, personalized). Table 18.3 gives an overview of commonly applied formulas and their respective IOL constants. If ‘raw’ manufacturer’s constants are used there may still be systematic shifts between different formulas. This can be seen in Figure 18.3 which shows differences between calculated and necessary IOL powers for 11 different IOL types for SRK II, SRK/T and Haigis,4 (partly unpublished data). With standard (manufacturer’s) constants, there is a tendency for SRK II and SRK/T to produce IOL powers a bit too small thus causing a slight hyperopia while the Haigis formula is characterized by the opposite behavior. Optimizing lens constants is equivalent to iteratively adjusting the lens constant(s) in question such as to produce a mean zero prediction error between truly achieved and calculated refraction. The resulting set of IOL constants will then, for each formula, lead to a mean arithmetic error (ME) of 0 D. Today’s biometry equipment offers optimization programs as part of the instrument (Zeiss IOL Master as well as modern ultrasound A scan machines). For optical biometry, the User Group for Laser Interference Biometry (ULIB)18 has analyzed more than 9800 patient data sets publishing optimized constants for more than 73 popular IOL types in the internet.

AXIAL LENGTH DEPENDENCE OF PREDICTION ERROR A mean arithmetic error of 0 D does not necessarily mean that an IOL formula has the same performance over the total axial length range. Errors occurring at small eyes may well be compensated by respective errors for long eyes with opposite sign. To study the axial length dependence of the prediction error, a total of 771 eyes supplied with an AMO SI40 lens in the bag after continuous curvilinear capsulorhexis and phacoemulsification by one surgeon (JB) was retrospectively analyzed (unpublished data). Optimization was carried out on the basis of all 771 eyes for the commonly used IOL power formulas. For the Haigis formula, two cases were considered: (1) optimization of a0 alone with a1 and a2 kept constant (denoted by Haigis,1 (2) optimization of all three constants a0, a1 and a2 (triple optimization, denoted by Haigis (3). The lens constants thus obtained were subsequently used to calculate the postoperative refraction in all eyes, in a subgroup of n=78 short eyes and in a subgroup of n = 43 long eyes. For all three groups, the mean arithmetic (ME) error, the mean absolute error (MA), and the percentages of correct refraction predictions within ± 0.5 D, ± 1.0 D and ± 2.0 D were determined. The results are compiled in Table 18.4 and graphically displayed in Figures 18.4 to 18.6. From the Table as well as from the figures we can clearly see that SRK II has the worst performance of all: mean arithmetic and mean absolute errors are largest for SRK II, followed by SRK/T. While Figure 18.4 shows a mean arithmetic error of zero D for all formulas due to the very optimization process it is obvious from Figures 18.5 and 18.6 how this comes about: errors of opposite signs for short and long eyes cancel each other out. This effect, again, is most pronounced for SRK II and SRK/T, least for Hoffer Q and Haigis. The latter formulas thus turn out to be least axial length dependent. Mean absolute errors for all but the SRK II formula are of the order of 0.4 D over the total axial length range. For small eyes, Haigis and Hoffer Q show again some 0.4 D, while ≈ 0.3 D are reached by Haigis with single as well as triple optimization. The best results in terms of correct predictions within ± 0.5 D, ± 1.0 D and ± 2.0 D were achieved by Haigis with triple optimization for all eyes

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Fig. 18.3: Systematic shifts between different IOL formulas if IOL constants are not customized: differences between calculated and necessary IOL powers for 11 different IOL types for SRK II, SRK/T and Haigis

Fig. 18.4: Mean arithmetic (ME) and mean absolute (MA) deviation between true and calculated refraction (true-calc) for all n=771 eyes supplied with a AMO SI40 lens. Customized constants were used for all formulas. Haigis(1): single optimization (only a0 optimized); Haigis(3): triple optimization (all three constants optimized)

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Table 18.4: Mean arithmetic (ME) and mean absolute (MA) deviation (mean ± standard deviation) between true and calculated refraction (true-calc) and percentages of correct refraction predictions within ±0.5D, ±1D and ±2D for all, short and long eyes. Constants were optimized for each formula on the basis of all eyes. Haigis(1): single optimization (only a0 optimized); Haigis(3): triple optimization (all three constants a0, a1, a2 optimized)

formula

ME [D]

MA [D]

n ± 0.5 D [%]

n ± 1.0 D [%]

n ± 2.0 D [%]

all AL, n=771 Haigis(1) SRK/T SRK II Holladay Hoffer Q Haigis(3)

0.00 ± 0.60 0.00 ± 0.62 0.00 ± 0.74 0.00 ± 0.59 0.00 ± 0.60 0.00 ± 0.59

0.42 0.44 0.52 0.42 0.43 0.42

± ± ± ± ± ±

0.42 0.44 0.52 0.42 0.42 0.42

72.4 69.5 61.6 70.8 69.6 73.4

92.5 90.7 86.4 92.6 91.4 93.0

98.7 98.3 97.8 98.8 99.1 99.1

AL=25, n=43 Haigis(1) SRK/T SRK II Holladay Hoffer Q Haigis(3)

0.02 ± 0.47 -0.29 ± 0.55 -0.62 ± 0.67 -0.12 ± 0.55 0.03 ± 0.56 -0.06 ± 0.49

0.33 0.43 0.68 0.42 0.41 0.35

± ± ± ± ± ±

0.33 0.45 0.61 0.37 0.38 0.34

83.7 69.8 39.5 69.8 67.4 88.4

90.7 95.3 81.4 95.3 90.7 90.7

100.0 95.3 93.0 100.0 100.0 100.0

Fig. 18.5: Mean arithmetic (ME) and mean absolute (MA) deviation between true and calculated refraction (true-calc) for a subgroup of n=78 short eyes with AL < 22 mm supplied with a AMO SI40 lens

Fig. 18.6: Mean arithmetic (ME) and mean absolute (MA) deviation between true and calculated refraction (true-calc) for a subgroup of n=43 long eyes with AL >25 mm supplied with a AMO SI40 lens

(73.4% within ± 0.5 D, 93.0% within ± 1.0 D, 99.1% within ± 2.0 D). Hoffer Q obtained the best results for short eyes eyes (70.5% within ± 0.5 D, 94.9% within ± 1.0 D, 100% within ± 2.0 D), while Haigis with triple optimization was best in long eyes (88.4% within ± 0.5 D, 90.7% within ± 1.0 D, 100% within ± 2.0 D).

CONCLUSION It goes without saying that high quality results expected from excellent surgery and high-end refractive devices will be spoiled or even made impossible by erroneous IOL powers calculated by the wrong formula from low quality measurement data. Therefore it is especially

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important in short and long eyes to apply high quality methods, procedures and techniques in surgery, measurement as well as IOL calculation. This implies using immersion ultrasound and/or optical biometry (especially for high myopes) instead of applanation ultrasound. At this point it may be noted that for immersion ultrasound—since it had served as a basis to calibrate PCI biometry5—the same IOL constants may be used as for optical biometry. As a general rule of thumb only those IOL formulas and lenses for which personalized IOL constants are available should be considered in extreme eyes. The SRK II formula should not be used any longer. It should never be applied in short eyes and it would also be better not to use it for long eyes either. In nan-ophthalmic eyes with hyperopia, Hoffer Q and Haigis perform best. In young patients booked for refractive surgery one should be aware of wearers of contact lenses with its implicatons for keratometry. Finally, surgeons should check the plausibility of all measured data, for instance ensuring that axial length correlates with refraction and that corneal radii measurements correlate with astigmatism. By following these guidelines and reducing variables to a minimum, surgeons can take advantage of improved measurement technologies and refinements in IOL power formulas to reduce postoperative refractive errors in long and short eyes as well as eyes of normal axial length.

ACKNOWLEDGEMENT The author wishes to thank the surgeon, J Brändle, MD (Private Practice, Füssen, Germany), for providing patient data.

REFERENCES 1. Curtin BJ, Karlin DB. Axial length measurements and fundus changes of the myopic eye. Am J Ophth 71(1):42.

2. Gale RP, Saha N, Johnston RL. National biometry audit. Eye 2004;18:63-66. 3. Haigis W. The short eye problem - revisited. 13th Congress of the European Society of Cataract and Refractive Surgeons (ESCRS), Amsterdam, 1995;1-4. 4. Haigis W. Lens shape, IOL constants and the calculation of intraocular lens power. Symposium on Cataract, IOL and Refractive Surgery of the American Society of Cataract and Refractivce Surgery (ASCRS), San Diego, USA, 1995;1-5, Book of Abstracts, 1995. 5. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefe’s Arch Clin Exp Ophthalmol 2000;238:765-73. 6. Haigis W. Optical coherence biometry. In: Kohnen T (Ed): Modern Cataract Surgery. Dev Ophthalmol, Basel, Karger 2002;34:119-30. 7. Haigis W. The Haigis formula. In: Shammas HJ (Ed): Intraocular Lens Power Calculations. Slack Inc, Thorofare, NJ, USA, 2003;41-57. 8. Haigis W. Optical biometry using partial coherence interferometry. In: Shammas H (Ed): Intraocular Lens Power Calculations. Slack Inc, Thorofare, NJ, USA, 2003;141-57. 9. Hoffer KJ. Intraocular lens calculation: The problem of the short eye. Ophthalmic Surgery 1981;12(4):269-72. 10. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19: 700-12. 11. Holladay JT, Musgrove KH, Prager TC, Lewis JW, Chandler TY, Ruiz RS. A three-part system for refining intraocular lens power calculations, J Cataract Refract Surg 1988;14:17-24. 12. Leaming DV. Practice styles and preferences of ASCRS members - 2003 survey. J Cataract Refract Surg 2004;30: 892-900. 13. Lege BAM, Haigis W. Laser interference biometry versus ultrasound biometry in certain clinical conditions. Graefes Arch Clin Exp Ophthalmol 2004;242(1):8-12. 14. Ober S, Reuscher A, Wenzel M. Umfrage von DGII und BVA zum derzeitigen Stand der Katarakt- und refraktiven Chirurgie. www.dgii.org/info/umfrage2002_ergebnis.html, Jan 2005. 15. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16(3):333-40. 16. Sanders DR, Retzlaff J, Kraff MC. Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg 1988;14:136-41. 17. The Royal College of Ophthalmologists. Cataract Surgery Guidelines, www.rcophth.ac.uk, Feb.2001. 18. User Group for Laser Interference Biometry (ULIB): www.augenklinik.uni-wuerzburg.de/ulib, Jan.2005.

Customization of IOL formulas

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B Vineeth Kumar (UK) 121

Customization of IOL Formulas

INTRODUCTION

Preoperative Planning

Cataract surgery has evolved significantly since the advent of phacoemulsification. To obtain accurate IOL power calculations and a good refractive outcome following cataract surgery we need to optimize technical and surgical factors.1-7 The various technical factors are keratometry technique, method of axial length measurement, IOL power calculation formula, optimized lens constant, and configuration of the capsulorhexis, all individually influence the final refractive outcome. For this reason, focussing on a just the axial length measurement or the IOL power calculation formula is usually insufficient to ensure consistent accuracy over a wide anatomical range of eyes. The surgeon must consider the process as a whole while optimizing each component simultaneously. When properly personalized, any of the modern IOL power calculation formulas will do a good job for normal axial lengths and normal central corneal powers. However, in unusual cases such as very long or short eyes, or for eyes with very flat or very steep corneal powers, consistently accurate IOL power calculation has remained elusive. Available third generation formulas include the SRK/ T, Hoffer Q, Holladay II, and Haigis. These are essentially theoretical formulas. The previous formulas included the regression models such as SRK and SRK II. The thought process in improving accuracy with our refractive outcomes is to consider the effective lens position of the IOL placed in the capsular bag with a good capsulorhexis. In this chapter we shall discuss the various third generation formulas in the process to customise and improve refractive outcomes following cataract surgery.

Proper examination and counseling before listing a patient for cataract surgery is important. Patient’s expectations have to be taken into consideration to achieve the planned result. Preoperative assessment includes examination of the eye, biometry, and decision on the IOL implant. Examination of the eye includes assessment of the cataract and other pathology which may coexist to affect the success of the cataract operation. Biometry is a highly skilled process the results of which are crucial for the success of the cataract surgery. An experienced technician or the ophthalmologist can do biometry. There are two components to the biometry process: Measuring the axial length which can be done by various techniques such as ultrasound A scan or immersion method, non-contact by using laser interferometry (IOL Master). Corneal curvature measurement which can be done by keratometer or corneal topography. The axial length and keratometry measurements must be done accurately as they can have a significant bearing on the outcome. Optical biometry’s (laser interferometry) use of a shortwavelength light source (instead of a longer-wavelength sound beam) increases axial length measurement accuracy by fivefold when compared with ultrasound. There accuracy is very good in challenging cases, e.g. in eyes containing silicone oil, extremely short nanophthalmic eyes, or extremely long myopic eyes with posterior staphylomata). Disadvantage of the technique is that it is an optical method. Axial opacities such as a corneal scar, dense posterior subcapsular plaque or cataract, or vitreous hemorrhage may decrease the

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reliability. Immersion method is a very reliable method but is limited by poor resolution and the applanation A scan biometry can produce false axial length measurements especially in the hands of an inexperienced technician or an anxious patient. After this incorporating them into the right formula is important. Validation of biometry measurements eliminates most implant power calculation problems.

Constants Various studies by Dr Holladay1 have revealed that standardizing the constants for keratometry, ultrasonic biometry, and IOL power calculations can significantly improve the predictability of refractive outcomes. There are about seven preoperative variables which have been found to be useful in significantly improving the prediction of effective lens position (ELP) in eyes that range from 15.0 to 35.0 mm in axial length. They are axial length, corneal power, horizontal corneal diameter, phakic anterior chamber depth, phakic lens thickness, preoperative refraction, and age. It is understood that not only the variables that improve prediction but improved technical skills of the surgeons who perform proper capsulorhexis and proper placement of the IOL in the capsular bag enhance the refractive result. Axial misplacement can contribute to refractive surprises which vary with the power of the lens and amount of displacement. Surgeons must personalize the lens constant (Holladay 1 Surgeon Factor; SRK/T A-constant; Holladay 2 or Hoffer Q anterior chamber depth; Haigis a0, a1, and a2) for a given formula in order to make adjustments for a variety of practice-specific variables, including different styles of IOLs, keratometers, and variations in A-scan biometry calibration. Most IOL power calculation programs provide either internal software or specific recommendations for how to go about lens constant optimization.

IOL Power Calculation Formulas We presently have third generation formulas that are supposed to increase the predictability of postoperative refraction. These formulas are theoretical based (SRK/T, Holladay II, Hoffer Q, Holladay, I etc) rather than the regression models (SRK II, SRK I, etc) which existed previously. Studies have compared the efficiency of these new models in various axial length groups. All studies have divided the eyes on the basis of their axial length as short (< 22 mm), intermediate (22-24.5 mm), long (24.5-26 mm) and very long eyeballs (> 26 mm).

The salient features of these studies are, Hoffer published a series of 450 cases in November1993 2 that were single surgeon, single technician, and single IOL style. For SRK-II, SRK-T, Holladay and Hoffer Q an error of SD 0.5D was present in 57%, 62%, 65%, and 66% respectively and for errors (SD 1.0D) the results were88%, 92%, 93%, and 93%. Hoffer found that SRK-T, Holladay and Hoffer were statistically similar and all were better than SRK-II with axial lengths greater than 26.0 mm. Hoffer’s analysis published in August 20003 compared the accuracy of Holladay II formula against the original for different axial length groups using a retrospective means comprising 317 eyes operated by 1 surgeon, 1 technique, and 1 IOL type. He concluded that Holladay II equals the Hoffer Q in short eyes, the Holladay I and Hoffer Q are equivalent in average eyes , and the SRK/T and Holladay II perform equally in medium long eyes, but the SRK/T produces a trend toward better results in very long eyes. Retzlaff et al4 used an unselected data set of 1677 cases published in May 1990, compares the formulas of SRK-T, Holladay, SRK-II, Hoffer and Binkhorst II. For errors < 0.5D the percentages achieved were 50%, 50%, 48%, 42%, and 47% respectively. For errors 10

17 19 21 24

12 14 16 19

45 44 43 43

57 43 32 23

For individual ocular parameters (or IOL-power needed for emmetropia) deviated from the above “mean” values, the adjustment of Dadj may be calculated based on the following situations. (i) For same P’, but different Po due to different X: dM = (2Z2/X)(dPo) = C(dPo), (5.a) dPo = Po’ – Po, (5.b)

P(2)=(Ppre-P”)/B,

(8)

where Ppre is the pre-IOL refractive error and P” is the residual error, B is a conversion factor given by B=Z2, with Z=1-S(P’/1336), P’ being the corneal power. For example, for P’=43 D, B=(0.82, 0.7), for S=(3, 5) mm, respectively, depending on the secondary IOL position. (f) For early age stage (0 to about 2 year), the rate function of the anterior chamber depth (m1) is proportional to the corneal power square, shown by Eq.(1.d). Therefore, steeper cornea results in a higher myopic progress due to the growth of S, the same trend as that of steep lens (or higher IOL-power), and a higher Dadj is needed. Figure 21.4 summarizes the above adjustment factors for revised Dadj accordingly. Comparing to the Wilson’s Dadj (which is only valid for average population), the Dadj (new) of Lin is

Age Dependent IOL Power Calculations for Pediatric Patients customized based on the estimated pre-operative rates functions m and N which, in general, are age dependent.

CONCLUSION The myopic-shift after pediatric cataract surgery may be compensated by a new adjusted IOL-power which is agedependent and governed by rate functions (mj and Nj, with j=1,2). In comparison to the mean-value method of Wilson et al, the Lin’s new Dadj is personalized by the measured (or estimated) pre-operative mj and Nj which may deviate from their mean (typical) values. Greater details for the discussion of Lin’s double-rate theory was published elsewhere.2

REFERENCES 1. Lin JT. The new IOL formulas based on Gaussian optics. In: Garg A and Lin JT, Ed. Mastering IOLs: Principles and Innovations. New Delhi: Jaypee Brothers, 2006;56-65. 2. Lin JT. Analysis of refractive state ratios and the onset of myopia. Ophthal Physiol Opt 2006;26:97-105. 3. Wilson ME, Trivedi RH. Eye growth after pediatric cataract surgery. Am J Ophthalmol 2004;38:1039-40. 4. Trivedi RH, Wilson ME. Intraocular lens power calculation for children. In: Mastering the Techniques of IOL power calculations. Garg A et al, (ed). Jaypee Brothers: New Delhi 2005;98-108. 5. Vasavada AR, Raj SM, Nihalani B. Rate of axial growth after congenital cataract surgery. Am J Ophthalmol 2004;138: 915-24. 6. Gordon LA, Donzis PB. Refractive development of the human eye. Arch Ophthalmol 1985;103:785-89.

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Mastering the Techniques of Intraocular Lens Power Alberto Artola Roig,Calculations Jorge L Alió Y Sanz (Spain)

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History & Method of Intraocular Lens Power Calculation for Cataract Extraction Surgery after Corneal Refractive Surgery

INTRODUCTION Refractive surgical procedures changed the ophthalmic world in the early 1990s. The surge in the growth of the number of refractive surgeries in the early nineties of the last century was followed by another surge in cataract extraction in the same patients a few years later. Most of the patients were at an age theoretically prone to cataract development. This led ophthalmologists to face a previously existing problem with more decisive solutions. In 2001, the annual volume of cataract surgeries performed by the American Society of Cataract and Refractive Surgery (ASCRS) members exceeded 2.5 million.1 This growth in number of refractive surgeries led to a significant increase over this decade in the number of patients requiring cataract extraction following refractive surgery. Today´s refractive surgical patient expects to attain a higher level of uncorrected visual acuity compared with several years ago. These patients are likely to have similar expectations from their cataract surgery. The typical surprise of hyperopia in the post myopic LASIK eye is not uncommon and quite debilitating.2 It is essential, therefore, to develop accurate techniques for calculating appropriate IOL powers in the postrefractive surgery cataract patient. Today´s IOL power calculation formulas are extremely reliable for the majority of eyes with physiologic prolate corneas. These formulas can be broken down into empirical regression or threoretical formulas. The most popular regression formula is the SRK-T.3 The theoretical optical formulas (Hoffer-Q, Holladay 2) are based on a standardized schematic eye in which several assumptions are made for parameters that are not possible to measure.

In eyes operated upon by refractive surgeries, altered corneas possess new criteria upon which traditional ways of Intraocular lens (IOL) calculation are not applicable. These alterations are: Improper evaluation of anterior corneal curvature by standard keratometry or computerized videokeratography.4 Improper conversion of K reading into diopters due to change in index of refraction.5 Improper evaluation of the effective lens position.6

Myopic Treatments Unfortunately, in the postrefractive surgery eye, the keratometric power cannot be measured accurately using current instrumentation. Current instruments make assumptions about the corneal anatomy that no longer hold. Traditional keratometers and topographers assume that the cornea is a spherical surface. The normal cornea does approximate a spherical surface over the central 2 to 3 mm. However, in the postrefractive surgery eye, even the central cornea may no longer approximate a sphere, due to the oblate aspherical shape caused by the surgery. The corneal power (P) , measured in keratometrics diopters, is derived from the measured radius of curvature (r) of the anterior corneal surface and an effective index of refraction (n) according to the formula : P = (n – 1)/r. This index of refraction, taken to be 1.3375 in most keratometers and topographers, is based on the assumption that the posterior surface has a radius of curvature that averages 1.2 mm less than anterior curvature.7 Due to the fact that the entire basis of myopic LASIK and photorefractive keratectomy (PRK) is to decrease the anterior curvature of the cornea, this relation

History & Method of Intraocular Lens Power Calculation for Cataract Extraction Surgery does not hold postoperatively unless the posterior curvature decreases by the same amount. Accurate measurement of the posterior corneal curvature remains difficult. The introduction of scanning slit-beam topography has allowed us to obtain measurements of the posterior corneal curvature. The issue of how the posterior corneal curvature changes following refractive surgery has been even more controversial.8-12 Patel et al13 have a theory to explain the discrepancy between measured keratometric diopters and actual refractive change following LASIK/PRK. They also suggest that a change in the refractive index of the cornea could be at the heart of the problem, but propose this is due to a 6.5% increase in stromal hydration during the postoperative period rather than an alteration of the anterior/posterior curvature ratio. In postradial keratotomy (RK) the main error is probably the inability to measure the power in the center, and not the anterior/posterior curvature disparity, because the relation between the anterior and posterior curvatures in RK is thought to be maintained relatively constant.14 As a result, K of a previously myope eye is overestimated. Subsequently, the IOL power is underestimated and a residual hyperopia ensues.

Hyperopic Treatments Refractive procedures for hyperopia are beginning to increase with the advent of larger available optical treatment zones for LASIK. In the case of hyperopic treatments, in contrast to myopia, the anterior curvature is steepened and made more prolate. Assuming there is not a significant change in the posterior curvature following hyperopic LASIK., this change in the anterior/posterior curvature relation would lead to an underestimation of the keratometric diopters and, consequently, a myopic surprise after IOL implantation.15 Several methods to estimate keratometric power after refractive surgery have been described. They include the clinical history method,6, 16, 17 contact lens overrefraction method,6, 7, 18 double-K adjustment,19 vertexed IOL power method18, effective refractive power calculated from corneal topography using the Holladay Diagnostic Summary,20 intraoperative autorefraction,21 Gaussian optics formula for paraxial imagery,22 Feiz-Mannis method,23 BEESt formula,24 method bypassing corneal power,25 No History method,26 and others. The perioperative (previously known as clinical history method)6, 16, 17 is the most popular one.

THE CLINICAL HISTORY METHOD Since we currently have no accurate method for directly measuring the keratometric diopters following keratorefractive surgery, an indirect method of deriving the postoperative keratometric diopters is currently the gold standard technique. It was introduced by Holladay in 1989.6, 27 This method involves subtracting the change in spherical equivalent refraction induced by the refractive procedure from the known preoperative keratometric power. This clinical history method or perioperative data method, well established in the literature.2, 6, 7, 14, 28 requires knowledge of preoperative keratometric power and refractions as well as stable postoperative refraction (prior cataract). Three measurements are needed to calculate effective postrefractive surgery keratometric diopters: 1. Preoperative manifest refraction 2. Preoperative keratometric power 3. Stable postoperative manifest refraction Given these parameters, the postoperative keratometric diopters are given by: Kpost = Kpre - ΔSEQ Example: Patient is a – 8 spheric myopic equivalent prior to LASIK. His preoperative average K is 43.00 D. The patient undergoes LASIK for correction of the full –8 D and has a stable postoperative refraction at 1 year of –0.5 D. His ΔSEQ = – 0,5 D – (– 8 D) = + 7.5 D. Thus, the patient´s effective postoperative keratometric diopters K post = 43.00 D – 7.5 D = 35.5 D. This new value is utilized in one of the recent IOL calculation formulae such as SRK/T or Holladay II to reach the desired IOL power.4 It is important to note that this calculation makes use of refractions relative to the spectacle plane. Should these be corrected for the vertex distance to the corneal plane to match the preoperative keratometric diopters also used in the formula? A study by Odenthal 21 found that correcting the spectacle plane refraction to the corneal plane in cases of myopic PRK resulted in higher estimated postoperative keratometrics diopters and, thus, a larger hyperopic surprise. The errors correlate with attempted correction and with higher attempted corrections leading to worse errors. Therefore, it has been recommended to use the spectacle plane refractions in the clinical history method calculations. This recommendation is supported by others.2, 29 This method is only as good as the availability of the correct data. The main problems are:

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1. Are the preoperative measurements available? 2. How stable is the postoperative refraction ? 3. Is the postoperative refraction corrupted by an incipient cataract ?. An study by Feiz et al30 suggested that this method assumes a one-to-one relation between change in refraction and change in corneal dioptric power, an assumption that may not necessarily hold with higher keratorefractive corrections.

CONCLUSION IOL calculation after refractive surgeries is one of the present challenges in ophthalmology. Many researches have been carried out into this issue; however still many questions remain to be answered. The difficulty arises from the fact that present instruments are unable to determine the keratometric value to be used in IOL calculating formulae. K value is overestimated in myopia and underestimated in hyperopia. Instruments either do not measure the curvature properly or utilize improper refractive index to represent the cornea. The perioperative method is the most famous solution. It takes into consideration the refractive change done by the refractive surgery and refers it to the spectacle plane or corneal plane. This method requires the presence of old values that might not be available (the refractive information before and after refractive surgery and before cataract formation). In our center (VISSUM Instituto Oftalmológico de Alicante) we relied upon the historical method for many reasons. First, it has a long standing credibility (since 1989). Second, most of the published work on this issue has used the same method. Thus comparison of the results would have more significance. Lastly, all our patients had properly preserved long-term medical records. When the prerefractive surgery data is unavailable, several other methods may be used to estimate keratometric diopters. Patients who are candidates for cataract surgery following refractive surgery should be appropriately counseled that current methods for IOL power calculation are not entirely accurate and that there may be a need for a second procedure to provide the appropriate refractive correction.

REFERENCES 1. Leaming DV. Practice styles and preferences of US ASCRS members: 2001 survey with international comparisons. Ocular Surgery News 2002;20:16-18. 2. Speicher L. Intra-ocular lens calculation status after corneal refractive surgery. Curr Opinion Ophthalmol 2001;12:17-29.

3. Retzlaff JA, Sanders Dr, Kraff MC. Development of thr SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333-40 4. Wang L, Booth MA and Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology 2004;111:1825-31. 5. Speicher L. Intra-ocular lens calculation status after corneal refractive surgery. Current opinion in Ophthalmology 2001; 12:17-29. 6. Holladay JT. Comment in Consultations in refractive surgery. Refract Corneal Surg 1989;5:203. 7. Holladay JT. Cataract surgery in patients with previous keratorefractive surgery (RK, PRK and LASIK). Ophthalmic Pract 1997;15:238-44. 8. Seitz B, Langenbucher A, et al. Refractive power of the human posterior corneal surface in vivo in relation to gender anda ge. Ophthalmolge 1998;95:S50. 9. Hernández-Quintela E, Samapunphong S, et al. Posterior corneal surface changes after refractive surgery. Ophth 2001; 108:1415-22. 10. Naroo SA, Chaman WN. Changes in posterior corneal curvature after photorefractive keratectomy. J Cataract Refract Surg 2000;26:872-78. 11. Seitz B, Torres F, et al. Posterior corneal curvature changes after myopic laser in situ keratomileusis. Ophth 2001; 108:666-73. 12. Kamiya K, Oshika T, et al. Influence of excimer laser photorefractive keratectomy on the posterior corneal surface. J Cataract Refract Surg 2000;26:867-71. 13. Patel S, Alió JL, Perez-Santonja JJ. A model to explain the difference between changes in refraction and central ocular surface power alter laser in situ keratomileusis. J refract Surg 2000;16:330-35. 14. Seitz B, Langenbucher A. Intraocular lens calculations status after corneal refractive surgery. Curr Opinion Ophthalmol 2000;11:35-46. 15. Feiz V and Mannis MJ. Intraocular lens power calculation after refractive surgery. Current opinion in Ophthalmology 2004;15:342-9. 16. Holladay JT, Prager TC, Ruiz RS, et al. Improving the predictability of intraocular lens power calculations. Arch Ophthalmol 1986;104:539-41. 17. Koch DD, Liu JF, hyde LL, et al. Refractive complications of cataract surgery after radial keratotomy. Am J Ophthalmol 1989;108:676-82. 18. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Cataract Refract Surg 2000;16:349-61. 19. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003;29:2063-68. 20. Holladay JT. Corneal topography using the Holladay Diagnostic Summary. J Cataract Refract Surg 1997;23: 209:221. 21. Odenthal MTP, Eggink CA, Melles G, et al. Clinical and theoretical results of intraocular lens power calculation for cataratct surgery after photorefractive keratectomy for myopia. Arch Ophthalmol 2002;120:431-38. 22. Olsen T. On the calculation of power from curvature of the cornea. Br J Ophthalmol 1986;70:152-54. 23. Feiz V, Mannis MJ, Garcia-Ferrer F, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a standard approach. Cornea 2001;20: 792-7. 24. Borasio E, Stevens J, Smith GT. Estimation of true corneal power after keratorefractive surgery in eyes requiring cataract surgery: BESSt formula. J Cataract Refract Surg 2006; 32:2004-14.

History & Method of Intraocular Lens Power Calculation for Cataract Extraction Surgery 25. Walter KA, Gagnon MR, Hoopes PC, Dickinson PJ. Accurate intraocular lens power calculation after myopic laser in situ keratomileusis bypassing corneal power. J Cataract Refract Surg 2006;32:425-29. 26. Shammas HJ, Shammas MC. No-history method of intraocular lens power calculation for cataract surgery after myopic laser in situ keratomileusis. J Cataract Refract Surg 2007;33:31-36.

27. Holladay JT. IOL calculations following radial keratotomy. Refract Corneal Surg 1989;5:203 28. Hoffer KJ. Intraocular lens power calculations for eyes after refractive keratotomy. J Refract Surg 1995;11-490-93. 29. Holladay JT. IOLs in LASIK patients: how to get them right the first time. Rev ophthalmol 8/9/2000:59 30. Feiz V, Mannis MJ, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia. Cornea 2001;20:792-97.

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Mastering the Techniques of Intraocular LensAshok Power Calculations Garg, Arif Adenwala (India)

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Intraocular Lens Power Calculations in Phaco and Microphaco

INTRODUCTION The various technological advances in phacoemulsification, phaco machines and IOL design have resulted in increase in expectation of both surgeon and patient. One of the important step in postoperative visual outcome is A scan biometry and IOL power calculations. The major components of IOL power calculations are axial length, keratometry measurements and use of accurate IOL formula. Thus it is important that each ophthalmic surgeon should have good knowledge of biometry and recent lens power calculations methods. Recently a new technology using laser interferometry (IOL Master) has been developed to improve the accuracy of axial length measurement.

A SCAN BIOMETRY The different A scan techniques available are: A. Applanation A scan. B. Immersion A scan. C. Immersion vector A/B scan.

Fig. 23.1: Normal contact echogram (A—Anterior lens capsule; P—Posterior lens capsule; R—Retina; S—Sclera)

4. Retina 5. Sclera 6. Orbit. The main disadvantage of this technique is compression of cornea due to applanation. This can lead to error in measurement of axial length. The error is between 0.14 to 0.28 mm. The main advantage is minimal learning curve and very easier to perform in minimum time.

Applanation A Scan Biometry

Immersion A Scan Biometry

In cases of A scan biometry using applanation method, the ultrasound probe is placed directly on the corneal surface. Initially topical anesthetic eye drop is instilled in the eye and then probe is placed on cornea. This can be done at slit lamp or by holding the probe with hand which is commonly used. The various spikes seen by these techniques are (Fig. 23.1): 1. Initial spike (cornea) 2. Anterior lens capsule 3. Posterior lens capsule

In this technique, the ultrasound probe does not come in contact with the cornea directly. A coupling fluid is placed between the eye and probe in this technique. It requires the use of Prager Scleral Shell or set of Ossoinig Scleral Shells. The shell is placed between eyelids over the cornea. It is then filled with mixture of goniosol and dacrtose. The probe is then placed on the solution avoiding contact with the cornea. The display screen will exhibit 6 spikes in the phakic patient than 5 because probe and cornea are no longer contact with each other, thus appearing separate.

Intraocular Lens Power Calculations in Phaco and Microphaco When the ultrasound probe is properly placed, we can see few spikes on the screen and they are steeply rising. The few spikes are of cornea, anterior and posterior lens capsule, retina and sclera.

Advantage It is more accurate than applanation method as it removes the error due to corneal indentation. It also reduces technician dependency. Important: Change the settings on the machine to immersion mode if it is not done automatically.

Immersion Vector A/B Scan Biometry In this recent technique, there is two dimensional B scan display with the A scan spikes. The A scan vector is adjusted such that it passes through center of cornea and thus the vector will intersect the retina in region of the fovea. The main advantage being direct axial length measurement from and the region of the fovea. The technique is very useful on area of posterior staphyloma, mature cataract and high myopia.

Disadvantage It is more expensive and requires greater level of skill to perform the technique.

IOL MASTER The main important reason for improper IOL power calculation is an error is measurement of axial length (Fig. 23.2). Initially A scan biometer using 10 MHz ultrasound probe was used but had limited the resolution to approximately to 0.10 mm. IOL Master is recent method of accurately measuring the axial length. It is non-contact method using partial coherent beam of light. It uses infrared light source and has increased accuracy from 0.10 mm to between 0.02 mm and 0.01 mm. It is about 5 times more accurate. IOL Master uses a modified Michelson Interferometer to measure axial length with good accuracy. This creates a pair of co-axial 780 nm infrared light beam with coherence length of approximately 130 nm.

Technique Axial length measurements with IOL Master are very easy and quick.31 Patient is seated on chair with chin resting

Fig. 23.2: IOL Master

on chinrest. The overview mode is used for course alignment. The patient looks at small yellow fixation light. The patient then looks at the small red fixation light so that accurate axial length measurements are done. A high degree of flexibility is seen on measuring axial length. The examiner selects a best area and takes measurement from that point. An ideal axial length display is far more important than high signal noise ratio (SNR).

Ideal Axial Length Recording The characteristics are: i. SNR ratio greater than 2.0. ii. Tall narrow primary maxima, with a thin well center termination and one set of secondary maxima. iii. At least 4 out of 20 measurements should be within 0.02 mm of each other. Advantages: It is useful in eyes with corneal opacities, high myopes or hypermetropics, aphakics and eyes filled with silicone oil. It is more accurate and reproducible than contact ultrasound in providing accurate AL measurements. Axial length, keratometric reading and anterior chamber depth can be measured. This concurs a save in time without need that the patient changes his position. As it is non-contact technique, the risk of corneal lesion and transmission of infection from patient to patient are also excluded.

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Mastering the Techniques of Intraocular Lens Power Calculations Limitations: IOL Master being optical device, any media opacities in axial region will cause problem in measurement. In case of mature or dark brown/black cataract, corneal scars or vitreous hemorrhages, where there is interference in passage of partial coherent light, the test is not highly accurate. IOL Master measures the central corneal power by automated keratometry. The instrument takes five keratometry readings within 0.5 seconds and takes the average. The latest software version (3.01) has improved keratometry software which will send alert signals in cases of highly variable readings. IOL Master also measures anterior chamber depth using lateral slit illumination at approx. 30 to optical axis. The various formulas put in IOL Master are Holladay, SRK/T, Haigis, SRK II and Hoffer Q. The preferred formula which is used is SRK/T. IOL Master software can accommodate as many as 20 doctors, each having 20 preferred IOLs and corresponding lens constants. This with the introduction of IOL Master, there is new era of high resolution lens power calculation which is highly accurate.

FORMULAS FOR CALCULATING IOL POWER Theoretical Formulas All the theoretical formulas used for calculation of lens power are based on a two lens systems, i.e. the cornea and the pseudophakos lens focussing images on the retina. 1. Basic theoretical formulas: These include Colenbrander’s, Fyodorov’s and Van der Heijde’s formula which yield approx. the same IOL powers. Binkhorst’s formula yield 0.50 D stronger lens power. 2. Modified theoretical formulas: These include Hoffer’s formula, Shamman’s fudged formula and Binkhorst’s adjusted formula. The fudged formula is a modification of Colenbrander’s formula. The various formulas are described in Table 23.1.

Regression Formulas These formulas are derived empirically from retrospective computer analysis of data of patients who have undergone surgery before. The factors on which IOL power calculation depends are:

Table 23.1: For emmetropic IOL power calculations

Intraocular Lens Power Calculations in Phaco and Microphaco 1. Axial Length Measurement: This is the most important step in calculation of lens power. The IOL Master is recent method which gives high accuracy in measurement of axial length. An error of 1 mm affects the postoperative refraction by 2.5 D approximately. It is measured in millimeters (mm). 2. Corneal Power: It is measured either in diopters or in mms (radius of curvature). Keratometer measures the radius of curvature of the central part of anterior corneal surface. K = 1000 (n – 1) n = corneal index of refraction R 1.3375 for Haag- Streit and Bausch and Lomb. 3. Postoperative anterior chamber depth (ACD): It is least important factor in calculation of lens power. It is important in cases of Haigis formula. An error of 1 mm affects the post operative refraction by approx. 1.0 D in myopic eye, 1.5 D in emmetropic eye and upto 2.5 D in hyperopic eye. The recent 3rd generation 2 variable formulas use commonly are given below.

SRK Formula 1. SRK I Formula: It is basic regression formula. It is given by: P = A – 0.9K – 2.5 L Where P = IOL power for emmetropia K = Keratometric power reading A = A constant L = Axial length in mm. 2. SRK II Formula: In this formula, the A constant is adjusted to different axial length ranges. It is given by: P = A1 – 0.9 K – 2.5 L A1 = new constant A1 = A + 3 if axial length (L) < 20 mm A1 = A + 2 if L 20 – 21 mm A1 = A + 1 if L 21 – 22 mm A1 = A if L = 22 – 24.5 mm A1 = A – 0.5 if L > 24.5 mm 3. SRK III Formula: This is new formula which is used to produce a desired postoperative refraction R. I = P – cr R where P = Power which is calculated by SRK II cr = Another empirical constant defined as cr = 1 for P < 14 cr = 1.25 for P > 14

Hoffer Q Formula The Hoffer Q formula was published in 1993 [Hoffer, 1993], based on the earlier work of Kenneth J Hoffer, MD (cf. references).

The Hoffer Q IOL power is given by: P = f (A, K, Rx, pACD) It is a function of A: axial length K: average corneal refractive power (K-reading) Rx: refraction pACD: personalized ACD (ACD – constant) Likewise, the Hoffer Q refractive error Rx Rx = f (A, K, P, pACD) depends on A, K, P and pACD. For the calculations, the corneal radii, R1C and R2C in [mm] are converted into K in [D] according to: K = 0.5 (K1 + K2) with K1 = 337.5/R1C and K2 = 337.5/R2C. The personalized ACD (pACD) is set equal to the manufacturer’s ACD – constant, if the calculation was selected to be based on the ACD – constant. In case the A – constant was chosen, pACD is derived from the A – constant [Hoffer, 1998] according to [Holladay et al, 1988] pACD = ACD – const = 0.58357 * A – const – 63.896

Haigis Formula On of the final frontiers in ophthalmology is the consistent accurate calculation of intraocular lens power in all the eyes. The more recent formula which is developed, to increase the accuracy of lens power calculation is Haigis Formula. This formula was given by Dr. Wolfgang Haigis. It uses three constants to set both the position and shape of a power prediction curve. The IOL calculation according to Haigis is based on the elementary IOL formula for thin lenses. d = a0 + [a1 × ACD] + (a2 × AL) where d = the effective lens position ACD = measured anterior chamber depth of the eye AL = axial length of the eye a0 constant = same as lens constants for the different formulas given before a1 constant = tied to anterior chamber depth a2 constant = measured axial length Thus the value for d is determined by a function rather than a single number. The a 0 , a 1 and a 2 constants area derived by multivariable regression analysis. The Haigis formula IOL constants will appear different than normal as they interact with the ACD and the AL.

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The main part of highly accurate IOL power calculation is able to correctly predict ‘d’ for any given patient and IOL. ‘d’ for the five formulas commonly in use are: SRK/T d = A constant Hoffer Qd = pACD Holladay 1d = surgeon Factor Holladay 2d = ACD Haigis d = a0 + (a1 × ACD) + (a2 × AL). In actual practice, the two eyes with same axial length and keratometric reading may have different lens power. This may be due to: Effective lens position, i.e. distance of the lens from the cornea Individual geometry of lens model. Commonly used lens constants in different 3rd generation 2 variable formulas are: SRK/T Formula – uses A constant Holladay I Formula – uses Surgeon Factor Holladay II Formula – uses Anterior Chamber Depth (ACD) Hoffer Q Formula – uses Anterior Chamber Depth (ACD) These constants are usually interchangeable All the above formula has limited axial length range of accuracy. Holladay I – works well for normal – moderately long axial length and Hoffer Q – works better for shorter axial length. Hoffer Q formula is best for short eyes. Holladay for long eyes and SRK/T is best for very long eyes. Overall SRK/T is probably most accurate in majority of cases.

Holladay Formula The components of the three part Holladay system are:1. Data screening criteria to identify improbable axial length and keratometric measurement. 2. The modified theoretical formula, which predicts the effective position of the IOL based on the axial length and the average corneal curvature. 3. Personalized surgeon factor (PSF) that adjusts for any consistent bias on surgeon from any source. It is advance method, which requires patient refractions. The initial formula uses the “Basic Surgeon Factor”. It can be calculated from the A constant provided by lens manufacturer.

Intraocular Lens Power Calculation after Corneal Refractive Surgery Keratorefractive surgeries done to decrease the refractive errors have gained enormous popularity among patients

and the doctors. Most of these techniques permanently and irreversibly alter the corneal shape and its effective power. Thus the routine formula used for IOL power calculation cannot be used these patients. Increased accuracy has increased both the surgeon and the patient’s expectation for precise outcome and more so in patients having undergone refractive surgery. The different methods available for IOL power calculations are:

Hard Contact Lens Method This method uses a hard contact lens of known power and base curve to determine true corneal powers. After refraction is over, a plano hard contact lens is placed on the eye and over refraction is performed. If no differences exist between refraction, then the corneal dietetic power is the same as the contact lens base curve. If the over refraction is more myopic than refraction without the contact lens, the lens is steeper than the cornea. The change in refraction is subtracted from the contact lens base curve to yield the corneal power. If over refraction is more hyperopic than the contact lens refraction, the cornea is steeper than the lens. The change in refraction is then added to the contact lens base curve to calculate corneal power. In this situation, the clinical relationship: C base + C power + R cl + R bare = K true Generally holds true, if the following are known: C base = base curve of the contact lens in diopters, and C power = spherical power of the contact lens in diopters, and R cl = spherical equivalent refractive error with the contact lens and R bare = spherical equivalent refractive error without the contact lens, then K true = the estimated corneal power after refractive surgery To give accurate information, the refractive numbers (R cl and R bare) must retain their corresponding plus (hyperopic) and minus (myopic) signs, and be corrected for vertex distance.

Clinical History Method It was first described by Holladay and later by Hoffer for corneal power estimation as Kp + Rp – Ra = Ka. Where, Kp = the average keratometry power before refractive surgery,

Intraocular Lens Power Calculations in Phaco and Microphaco Rp = the spherical equivalent before refractive surgery, Ra = the stable spherical equivalent after refractive surgery, Ka = final central corneal power after refractive surgery. This method requires knowledge of keratometry prior to refractive surgery, as well as induced refractive change, i.e. changes in spherical equivalent (SE) before the development of cataract. A. For postmyopic procedure patients; Corneal diopteric powers = prerefractive surgery Ks – change in SE B. For posthyperopic procedure patients; Corneal dioptric power = prerefractive surgery + change in SE Calculated corneal dioptric power is then used for IOL determination.

Feiz and Mannes IOL Power Adjustment Method In this technique, initially the IOL power is calculated using the pre-LASIK corneal power. The pre-LASIK IOL power is then increased by the amount of refractive change at spectacle plane divided by 0.7 IOL power = (IOL) pre + DD/0.7 DD = the refractive change after LASIK.

Modified Maloney Method In this method, the central corneal power is obtained by using the Axial Map of Zeiss Humphery Atlas Topographer (Cccp) (Cccp × 1.114) – 6.10 = post-LASIK adjusted corneal power.

Nomogram-based Correction The following formula is used to predict IOL power to maintain emmetropia after refractive surgery. After myopic LASIK; Post-LASIK IOL = Pre-LASIK IOL + (change in SE/ 0.67) After hyperoic LASIK; Post-LASIK IOL = Pre-LASIK IOL – (change in SE/ 0.67).

IOL Power Calculations in Silicone Filled Eyes Silicone oil in the vitreous causes an error in axial length measurement. This occurs due to change in the velocity of sound through silicone oil. The error may be 3 to 4D. Axial

length measurement should be done prior to injection of silicone oil. Regarding the spike pattern, it is difficult to get good retinal spikes. The axial length obtained can be corrected by the following formula: Axial length = AL × Velocity (corrected)/Velocity (measured)

ACCURACY OF IOL POWER CALCULATION Inspite of recent advances in technology, there is no single method to accurately determine the net central power of these postrefractive surgery eyes. The current method available is limited by lack of clinical experience on large scale and by the theoretic nature of all the calculation methods. The factors, which significantly affect the accuracy of SRK in IOL power calculations, are: 1. The error in preoperative biometry with regard to the difference between post and preoperative axial length measurement. 2. The position of the implantation of intraocular lens. 3. The style of intraocular lens 4. The preoperative corneal astigmatism 5. Surgically induced corneal astigmatism 6. The postoperative astigmatism.

CONCLUSION According to various studies it has been seen that IOL Master is very good, accurate method of IOL power calculation. It has increased the postoperative refractive outcome at par with recent techniques of cataract surgery like microphaco.

BIBLIOGRAPHY 1. Aramberri. Intraocular lens power calculation after corneal refractive surgery; double K method 3CRS 2003;29(11):200308. 2. Binkhorst RD. Pitfalls in the determination of intraocular lens power without ultrasound, Ophthalmic Surg 1976;76:6982. 3. Buschmann W. Ultrasonic measurements of the axial length of the eye, Klin Monatsbl Augenheilkd 1964;144:801-15. 4. Connors R III, Boseman P III, Olson RJ. Accuracy and reproducibility of biometry using partial coherence interferometry. J Cataract Refract Surg 2002;28:235-38. 5. Determining Corneal power following LASIK and PRK. 6. Drews RC. Calculation of intraocular power, a program for Hewlett-Packard 97 calculator, Am Intraocular Implant Soc J 1977;3:209-12. 7. Drexler W, Findl O, Menapace R, et al. Partial coherence interferometry: A novel approach to biometry in cataract surgery. Am J Ophthalmol 1998;126:524-34.

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Mastering the Techniques of Intraocular Lens Power Calculations 8. Eleftheriadis H. IOL Master biometry. Refractive results of 100 consecutive cases. Br J Ophthalmol 2003;87(8):960-63. 9. Findl O, Drexler W, Menapace R, et al. Improved prediction of intraocular lens power using partial coherence interferometry. J Cataract Refract Surg 2001;27:861-67. 10. Fritz KJ. Intraocular lens power formulas. Am J Ophthalmol 1981;91:414. 11. Gantenbein C, Lang HM, Ruprecht KW, Georg T. First steps with the Zeiss IOL Master: A comparison between acoustic contact biometry and non-contact optical biometry, Klin Monatsbl Augenheilkd. 2003;220(5):309-14. 12. Kalogeropoulos C, Aspiotis M, Stefaniotou M, Psilas K. Factors influencing the accuracy of the SRK formula in the intraocular less power calculation. Doc Ophthalmol 1994;85(3):223-42. 13. Kielhorn I, Rajan MS, Tesha PM, Subryan VR, Bell JA. Clinical assessment of the Zeiss IOL Master 1: J Cataract Refract Surg 2003;29(3):518-22. 14. Kim JN, Lee DN, Joo CK. Measuring corneal power for intraocular lens power calculations after refractive surgery. JCRS 2002;28(II):1932-38. 15. Kiss B, Findl O, Menapace R, et al. Biometry of cataractous eyes using partial coherence interferometry: Clinical feasibility study of a commercial prototype I. J Cataract Refract Surg 2002;28:224-29. 16. Kraff MC, Sanders DR, Lieberman HL. Determination of intraocular lens power: A comparison with and without ultrasound, Ophthalmic Surg 1978;9:81-84. 17. Lal H. Biometry and IOL Power Calculation, Manual of Phaco Technique. 33-37 Haigis W, Lege B, Miller N, Schneider B: Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. 18. Liang YS, Chen TT, Chi TC, Chan YC. Analysis of intraocular lens power calculation. J Am Intraocular Implant Soc 1985;11(3):268-71. 19. Olsen T. Theoretical approach to intraocular lens calculation using Gaussian optics. J Cataract Refract Surg 1987;13: 141-45. 20. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992;18:125-29.

21. Olsen T, Thim K, Corydon L. Accuracy of the newer generation intraocular lens power calculation formulas in long and short eyes. J Cataract Refract Surg 1991;17(2): 187-93. 22. Ouda B, Tawafik B, Derbala A, Youseif AB. Error correction of intraocular lens (IOL) power calculation. Biomed Instrum Technol 1999;33(5):438-45. 23. Raj PS, Ilango B, Watson A. Measurement of axial length in the calculation of intraocular lens power. Eye 1998:12(Pt2):227-29. 24. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations Eye 2002;16:552-56. 25. Rose LT, Moshegov CN. Comparison of the Zeiss IOL Master and applanation A scan ultrasound: Biometry for intraocular lens calculation. Clin Experiment Ophthalmol 2003:31(2): 121-24. 26. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data, Am Intraocular Implant Soc J 1980;6:263-67. 27. Shammas HJ. A comparison of immersion and contact techniques for axial length measurement. J Am Intra-Ocular Implant Soc 1984;10:444-47. 28. Suto C, Hori S, Fukuyama E, Akura J. Adjusting intraocular lens power for sulcus fixation. J Cataract Refract Surg 2003;29(10):1913-17. 29. Tromans C, Haigh PM, Biswas S, Lloyd IC: Accuracy of intraocular lens power calculation in paediatric cataract surgery. Br J Ophthalmol 2001;85(8):939-41. 30. Understanding the Haigis formula.www.doctor-hill.com. 31. Vahid Feiz, Mark J Mannis. Intraocular lens power calculation after corneal refractive surgery – current opinion in ophthalmology 2004;15:342-49. 32. Verhulst E, Vrijghem JC. Accuracy of intraocular lens power calculations using the Zeiss IOL Master. A prospective study, Bull Soc Belge Ophthalmol 2001 (281):61-65. 33. Wainstock MA. Ultrasonography: Its role in the success of intraocular implant surgery, Int Ophthalmol Clin 1979;19: 43-50. 34. Warren E Hill. The IOL Master – Techniques in Ophthalmology. 2003;1:62-67.

Intraocular Lens Power Calculations for Renyuan High Myopia Chu, Jinhui Dai (China)

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Intraocular Lens Power Calculations for High Myopia

INTRODUCTION There is a high prevalence rate of myopia in the public. Sanders et al.1 reported that people of high myopia with axial length > 27mm accounted for 1.1% of the whole population. And as people of high myopia tend to have complicated cataract, the prevalence rate of cataract among them is higher than that in the public. As the development of cataract extraction surgery with IOL implantation, the formulas for IOL power calculation from first-generation to third-generation have been continuously optimized. Since the current empirical formulas are based on the parameters acquired from eyes with average axial length, these formulas are quite accurate for normal eyes while have some errors in calculation for highly myopic eyes with longer axial length and posterior staphyloma which decrease the accuracy of preoperative biometry. Hence there tend to be more errors in preoperative prediction of IOL power for high myopia. The postoperative refraction after IOL implantation is determined by three factors:1) Surgical procedure including surgical skills, incision size, suturing technique, position of IOL and patients’ responses which can affect patients’ postoperative visions. 2) Accuracy of preoperative biometry: axial length and radius curvature of the cornea are the most important parameters in the IOL power formulas and anterior chamber depth (ACD) is a key parameter in the theoretical formulas, the accuracy of the instruments and the measuring process will influence the outcome. 3) Accuracy of the IOL power formulas. The development of small-incision phacoemulsification has reduced the occurrence of postoperative corneal astigmatism to the utmost extent. And circular capsulorhexis and intracapsular IOL

implantation which has fixed the IOL in the capsule has lessened the influence of eccentricity and incline of the IOL on the postoperative vision. Thereby, errors from biometry and IOL power calculation formulas are the main cause of prediction inaccuracy especially for eyes with long axial length which contain more errors during measurement. Errors in IOL power calculation may cause postoperative refractive errors or anisometropia. And severe anisometropia would make patients inconvenient even ask for another IOL replacement surgery. So how to reduce the errors from the preoperative biometry and select the proper calculation formula for IOL power is crucial for cataractous patients with high myopia to achieve a satisfactory postoperative refractive status.

INTRAOCULAR LENS POWER CALCULATION FORMULAS Intraocular lens power calculation formulas include theoretical and empirical formulas. All theoretical formulas are based on the schematic eye according to the geometric method of optical calculations derived from Gaussian Formula.2 The first-generation theoretical formulas containing Fyodorov Formula, Colenbrander Formula, Binkhorst-I Formula are based on the same fundamental equation3: P=N/(L-C)-NK/(N-KC), P=IOL power for emmetropia, N=refractive indices of aqueous and vitreous, L=axial length, K=corneal curvature, C=estimated postoperative anterior chamber depth (ACD). Predictive value of postoperative ACD differs in different formulas. It is changeable in Fyodorov formula while is a constant in other formulas. Since it was proved to vary with the axial length(AL) 4 , the ACD is commonly deeper in eyes with long AL while more shallow with short AL.

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Mastering the Techniques of Intraocular Lens Power Calculations So a big error will certainly occur in calculation with a fixed value of ACD which would bring postoperative myopia to eyes of long AL with overestimating power of IOL while hyperopia to short AL with underrating power of IOL. Therefore the theoretical formulas of firstgeneration provide poor accuracy. The empirical formulas of first-generation include SRK-I formula and Lloyd formula and so on, based on the postoperative data of IOL with multiple regression analysis, are more accurate than the first-generation theoretical ones5. SRK-I formula, P=A-2.5L-0.9K (P=IOL power for emmetropia, A=A-constant, L=axial length, K=corneal curvature), was derived by Sanders, Retzlaf and Kraff on the multiple regression analysis of the postoperative data from thousands of patients undergoing IOL implanted in 1980. A-constant, provided by manufacturers, is determined by the material, type and intraocular position of IOL. SRK-I formula, representative of the first-generation empirical formulas, performs quite accurately in eyes with normal axial length but poorly with abnormal axial length. Then SRK-II Formula6 was described by Sanders, Retzlaff and Kraff in 1988 by multiple regression analysis through the postoperative data of 2068 patients with posterior chamber intraocular lens: P = AL-2.5L-0.9K (when L< 20.0 mm, AL = A + 3; 20 mm = L < 21.0 mm, AL = A + 2; 21 mm = L < 22 mm, AL = A + 1; 22 mm = L< 24.5 mm, AL= A; L = 24.5 mm, AL = A - 0.5). SRK-II formula, modified by three steps in eyes with axial length < 22mm while only one allowance in myopia of axial length >24.5mm, was clinically proved to be highly accurate in hyperopia and emmetropia while obviously inaccurate in high myopia. The second-generation theoretical formula includes Binkhorst-II7, Hoffer8, and Shammas formula9 developed in1980s. The estimated postoperative ACD, which vary with AL, surgical procedure and IOL type, is a key parameter for postoperative refraction. Olsen10 had found that the predictive error of ACD accounted for 20%, 40% of the total error. Low accuracy of the original theoretical formula is not due to the inaccuracy of the geometric method of optical calculations but to the poor method for prediction of the postoperative ACD which is generally described as a constant. And since it can provide a better predictive result of ACD, second-generation formulas are evidently superior to the previous ones. The third-generation theoretical formulas include Holladay formula11, Olsen formula12, SRK/T formula13, and so on. The equation for prediction of ACD of Holladay formula, which has increased the accuracy, is described

as: ACDpost=H+SF , H= cornea elevation, SF (surgeon factor)=a new constant, a distant from iris –anterior chamber angle level to the optic surface of IOL. Olsen 14 found that the postoperative effective ACD was significantly correlated with 5 preoperative variables (in decreasing order): axial length, preoperative ACD, keratometry reading, lens thickness, refraction. A new postoperative effective ACD algorithm was derived from the five preoperative variables by multiple linear regression. With the new algorithm, the refractive prediction error decreased by 10% from the error associated with a previous 4-variable algorithm and decreased 28% from the error using no individual ACD method. Because of better prediction of ACDpost, third-generation theoretical formulas outperform the second-generation especially in eyes with high myopia. Calculation by theoretical formulas usually results in postoperative myopia in eyes with short AL due to overcorrection and hyperopia with long AL because of undercorrection. On the contrary, empirical formulas just perform in the opposite way 15. Second-generation formulas and third-generation theoretical formulas provide equivalent accurate result in eyes with average axial length16. But for high myopia, the latter are superior to the former17 since the empirical formulas just cover a small number of eyes with abnormal AL while thirdgeneration theoretical formulas, a integration of theory and empirical, are based on both geometric optics and empirical data like A-constant in SRK/T formula or SF in Holladay formula. However, more clinical data should be collected for eyes with extremely long AL. Comparing the accuracy of these formulas,1,6,16,18 the percentage of eyes with error within ± 1D was 56-77% in second theoretical formulas such as Hoffer and BinkhorstII formula, 79–80% in SRK-II, 81–82% in Holladay and SRK/T formula. The percentage with error greater than ± 2D is 4.5–11.0% in Hoffer and Binkhorst—II formula, 3.0–4.7% in SRK-II, 2.5–2.8% in Holladay, 2.6% in Olsen and SRK/T formula. It shows that Holladay, Olsen and SRK/T formula were a little more accurate than Hoffer, Binkhorst-II and SRK-II formula. In eyes with short AL, SRK-II, Holladay, Olsen, SRK/T formula provided almost the same accuracy and the latter three formulas were slightly superior to former one. In long eyes, predictive errors became higher in all the formulas especially in SRKII. Narváez J et al19 reported that Hoffer Q, Holladay 1, Holladay 2, and SRK/T were equally accurate for high

Intraocular Lens Power Calculations for High Myopia myopic patients. Coburn15 reported that when AL > 24.5 mm, the percentage of eyes with postoperative error greater than ± 2D was 9% in SRK-II, 10% in Binkhorst-II, 8% in Holladay formula. And Sanders, Retzlaff and Kraff reported that the percentage was 28% in SRK-II, 3.5% in Holladay and SRK/T for AL > 28,4 mm. Yalvaç IS et al.20 reported that the SRK-II formula was not very accurate in axial myopic patients. When AL > 24.5 mm, the mean absolute error of the SRK II formula in axial myopia was 1.16 ± 0.78 D, and the percentage with absolute refractive error > 1 D and >2D was 41.8% and 15.3%,respectively. Since axial length can reach above 35 mm and SRK-II ,which comprises not enough long eyes, has only one value -0.5 for rectification in eyes with long AL, the accuracy of SRK-II is poor in long eyes. Dai et al 21 proposed a rectified SRK-II formula in high myopia(SCDK formula) by multiple regression analysis of postoperative data of 176 patients with high axial myopia(AL=26mm). The SCDK formula is as follows: P = A-2.5L – 0.9K – 1.46 (26 mm < L < 30mm) P = A-2.5 × L-0.9 × K-0.99 (L > 30mm) (P = IOL power for emmetropia, A=A-constant, L=axial length, K=corneal curvature), Rectification value -1.46 and -0.99 is respectively -0.96 and -0.49 larger than the value-0.5 in SRK-II formula. Dai et al22compared the accuracy of SRK-II formula, SRK/T formula and SCDK formula in high myopic patients. The mean absolute refractive error of SRK-II formula, SRK/T formula and SCDK formula was 1.42D, 0.84D and 0.89D, respectively. The percentage of the eyes with prediction error greater than 2D was 15.53%, 4.74% and 5.26%, respectively. SRK/T formula and SCDK formula were more accurate than SRK-II formula in the eyes with axial length above 26mm and there was no significant difference between SRK/T formula and SCDK formula. Compared with second-generation formulas, thirdgeneration formula is superior for high myopia. Donoso23 reported that among the third-generation formulas, SRK/ T performed best. Hoffer24 found that in extremely long eyes, Holladay II formula had the highest accuracy but didn’t reach a statistically significant difference from the other third-generation formulas. Still, third-generation formulas provide some error. MacLaren et al.25 reported that current third-generation formulas underestimated –1.00D to –4.00D of IOL power in high myopia resulting in a tendency toward hyperopia postoperatively.

PREOPERATIVE BIOMETRY Axial length and corneal refractive power are the main parameters in determining the power of IOL. There is high accuracy to measure corneal refractive power. The error of measurement is mainly occured in axial length measurement, especially in high myopia. As a result of low capacity of instruments and operational errors, errors of biometry are obvious in early days. Holladay 26 found that 43-67% errors over ±2D stemed from inaccurate measurement. Olsen10 observed 584 eyes with IOL and noticed that 62% postoperative errors of refractive power resulted from measuring errors, and 54% of which was related to axial length. If recalculating the power of IOL in terms of postoperative axial length and corneal refractive power, the accuracy will improve 54% and 10% respectively. The accuracy of measurement improves significantly with the development of new biometry instruments. The error of axial length measurement can be controlled less than 0.1mm by means of repeated measurement in normal axial length eyes. Though biometry instruments have been improved, measuring errors are still in evidence in long axial eyes, especially with posterior sclera staphyloma. How to reduce measuring error in long axial eyes is the important aspect on increasing accuracy of prediction. The following are the causes of axial length measurement error: (1)Ultrasonic probe pressing into cornea or there is tear liquid between the probe and the cornea, which may lead to shorter or longer axial length; (2)The probe is not in the center of the conea; (3)Exist of posterior sclera staphyloma. High myopia is often associated with posterior sclera staphyloma and a slight deviation of the probe will result in distinct error. This is the main cause of less accuracy in measuring axial length in highly myopic eyes;(4)The impact of ultrasonic velocity27. The velocity of ultrasound is different for cornea, aqueous humor, crystal lens and vitreous body, so calculating by the mean velocity will produce errors. Because the proportion of volume of the lens is larger in short eyes compared with normal eyes and is smaller in long eyes, calculating by mean velocity will result in smaller axial length in short eyes and larger in long axial length eyes. Olsen28 reported that, with the mean velocity, the acquisition should increase 0.07mm when axial length is less than 20mm, and the result should decrease 0.05mm when axial length is more than 30mm. In addition, the velocity is also different if the hardness of the lens is different ,.(5)Patients’ poor cooperation. In little children, poor cooperation will result in measurement

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Mastering the Techniques of Intraocular Lens Power Calculations errors. The causes which lead to measurement errors on corneal refractive power are:(1) The measuring region is not in the center of the cornea. (2) Keratometer is not consistent with the ocular axis.(3)The corneal epithelium is not integral.(4) Patients’ poor cooperation, and so on. The measurement error for axial length is obviously larger than that for corneal refractive power. So the key to reduce error is to improve the accuracy for axial length measurement. The following are the key aspects to reduce the measurement error of axial length:(1)Utilizing advanced instruments.(2)It is better to apply immersion process if possible. Avoiding pressing into the cornea with the probe and existing lacrimal liquid between the probe and the cornea if applying applanation process. (3)The A-scan probe should be on the center of the cornea and keeping the measuring direction consistent with the center of ocular axis. (4) Measuring several times and taking the mean value. (5) For high myopia, B-scan examination is necessary to identify if the posterior sclera staphyloma is exist and the relation of macular and stapyloma. The axial length from B-scan can be a reference to A-scan measurement. (6) Comparing between the two eyes. (7) Referring to the former refraction. (8) Adopting the respective velocity of ultrasound for cornea, aqueous humor, crystal lens and vitreous body. (9) It is better to remeasure it by another manipulator if the difference is obvious among results of repeated measurement or between the two eyes. The IOL Master29, which has become available in recent years, is a combined instrument for axial length measurement and biometry evaluation for corneal radius of curvature, anterior chamber depth and cornea diameter. The principle of IOL Master is the same as OCT utilizing partial coherence interferometry (PCI) of infrared(ë= 780nm). and it has high precision and repeatability. The parameters can be directly input into computer for the calculation of IOL power. Eleftheriadis30 reported that it is more accurate than traditional A-scan and B-scan ultrasonography. However, it shows a poor accuracy in measuring eyes with severe cataract.

SATISFACTORY POSTOPERATIVE REFRACTIVE STATUS With modern techniques, a perfect postoperative refractive outcome has become a symbol of success for the cataract surgery. As to eyes of average axial length, both postoperative emmetropia and low myopia are acceptable. But considering patients of high myopia who are used to

this kind of refractive error for a long time, a postoperatively low myopic refraction should be recommended. Kora et al31 regarded that a postoperative refraction of 0 to -3D should be given to patients of high myopia with satisfying best spectacle-corrected visual acuity while -5D maybe the target refraction for those with poor BCVA in order to avoid blurry near vision postoperatively. Ophthalmologists should choose an appropriate postoperative refraction for each patient according to their education backgrounds, life habits and occupations etc. Clinically, even a slightly high myopic refraction postoperatively is agreeable to most patients of extreme high myopia. However, once postoperative hyperopia occurs on either the operative eye for single-eye operation or one of the two operative eyes, life will be seriously inconvenient for these patients. Hence the preserved myopic refraction should be increased properly especially for those always doing prolonged close-up work while suitably reduced for those who need agreeable distantvision. IOL power calculation for postoperative emmetropia is different for different formulas. Usually, the IOL power for emmetropia is figured out first, then it is converted to the power of IOL to be implanted for patients according to target postoperative refraction by conversion ratio F (the change of IOL power equal to 1D change of spectacle lens).So the accuracy of F value is significantly important. In SRK-I, the ratio of F is 1:1.5; in SRK-II, the ratio is 1 £º 1.25 when the lens power for emmetropia >14D while the ratio changes to 1:1 for power ≤ 14D; in the SRK/T formula, the F value is 1:1.25 and 1:1 for lens power>16D and ≤16D respectively. That is to say F value is gradually close to 1:1 with the development of axial length. But contrarily according to the theoretical formulas derived from Gaussian Formula, the value has nothing to do with the axial length but a positive correlation with the corneal curvature and ACD meanwhile an evident correlation with postoperative refraction21. Commonly there is 0.01 change of F value corresponding to 0.1mm change of ACD or 1D change of corneal curvature. And there is also a negative correlation between the postoperative myopic refraction and F value meantime a positive correlation between the hyperopic refraction and F value with about 0.02 change in F value corresponding to every 1D change of postoperative refraction. For example, as to an eyeball with AL of 24mm, ACD of 4.2mm, keratometry reading of 44D and postoperative refraction expectation of -1D, F value is 1:1.33. Personalized modification may be made

Intraocular Lens Power Calculations for High Myopia according to individual ACD, corneal curvature and postoperative refraction.

REFRACTIVE INDEX OF CORNEA AND A-CONSTANT The actual refractive index of cornea is 1.376. And the corneal refraction is estimated based on the curvature radius of anterior surface of the cornea since the curvature radius of the back surface is difficult to measure. The commonly used refractive index is assumed to be 1.337532. Setting 7.8 mm as the value of curvature radius of anterior surface and 1.3375 as the refractive index, the curvature radius of the back surface of the cornea will be 8.11mm derived from the geometric method of optical calculations. But as we all know that the radius of back surface curvature is smaller than the anterior one, the value of 1.3375 seems to be a little higher to consist with the fact. So 1.333 is recommended in SRK/T formula, 1.3(4/3) is applied in Holladay and Binkhorst formula while 1.3315 is used in Olsen formula. A-constant, commonly given by manufacturers, is an important parameter for empirical calculation which is determined by the intraocular position and the type of IOL. Different manufacturers provide IOL of different Aconstant. As an example, for 720C Pharmacia IOL and UPB380 Allergan IOL, both single-piece PMMA, 13.5 mm long with an optic diameter of 6.5 mm and 10 degree haptic angulation , A-constant is 118.8 and 118.0 respectively with a notable discrepancy of 0.8. Therefore, a retrospective analysis through a large number of clinical cases is necessary to improve the accuracy of A-constant. From capsular bag to ciliary sulcus, the IOL position change will make the optical effective ACD about 0.2mm alter which mostly the same with eyes of different axial length. And A-constant in SRK formula changes with the ACD shift which affects the IOL power. According to the theoretical formula derived from Gaussian Formula21, an alter of 0.2mm on optical effective ACD will lead to 0.31D shift on IOL implanted when the axial length is 24mm and 0.06 D shift when axial length is 29mm. Thereby values of A-constant for IOL in ciliary sulcus and capsular bag are mostly the same for eyes of long axial length and even identical for those of axial length>29mm.

CONCLUSION With the increasingly spread of phacoemulsification with intracapsular IOL implantation and improvement of micro-instrument for surgical procedure, the cataract

surgery outcome is increasingly satisfying and more emphasis is being placed on the prediction accuracy of IOL power. The two main factors influencing the predictive accuracy are the preoperative biometry and IOL power formulas which are considered accurate for eyes of average axial length. But as to extreme high axial myopia, the error of axial length measurement becomes higher and the accuracy of all the IOL formulas turns lower due to the higher prevalence of posterior staphyloma. So it is utmost of significant to improve the predictive accuracy of IOL power for extreme high axial myopia. The following measures can be helpful: detecting posterior staphyloma with B-ultrasound preoperatively, repeating measure to reduce errors, selecting IOL formulas which is most suitable to high axial myopia like the thirdgeneration formulas and the empirical regression formula based on the postoperative data from cataract patients with high myopia.

REFERENCES 1. Sanders DR,Retzlaff J, Kraff MC,et al. Comparison of the SRK/T formula and other theoretical and regression formulas. J Cataract Refract Surg 1990;16:341-46 2. Miller D. Optics and refraction. Gower medical publishing. NewYork: London 1991;12:7 3. Jaffe NS,Horwitz J. Lens and cataract. Gower medical publishing. NewYork: London 1991;10:6 4. Olsen T, Olesen H, Thim K, et al. Prediction of pseudophakic anterior chamber depth with the newer IOL calculation formulas. J Cataract Refract Surg 1992;18:280. 5. Sanders DR, Retzlaff J, Kraff MC, et al. Comparison of the accuracy of the Binkhorst,Colenbrander,and SRK implant power prediction formulas. Am Intra-Ocular Implant Soc J 1981;7:337. 6. Sanders DR, Retzlaff J, Kraff MC. Comparison of the SRK-II formula and other second generation formulas. J Cataract Refract Surg 1988;14:136. 7. Jaffe NS,Horwitz J. Lens and cataract. Gower medical publishing. NewYork: London 1991;10:6. 8. Hoffer KJ. Intraocular lens calculation: The problem of the short eye. Ophthalmic Surg 1981;12:269. 9. Shammas HJF. The fudged formula for intraocular lens power calculations. Am Intra-Ocular Implant Soc J 1982;8:350. 10. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992;18:125. 11. Holladay JT, Praeger TC, Chandle TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17. 12. Olsen T, Thim K, Corydon L. Theoretical versus SRK-I and SRK-II calculation of intraocular lens power. J Cataract Refract Surg 1990;16:217. 13. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333. 14. Olsen T. Prediction of the effective postoperative (intraocular lens) anterior chamber depth. J Cataract Refract Surg 2006;32:419-24.

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Mastering the Techniques of Intraocular Lens Power Calculations 15. Olsen T, Denmark A. Theoretical,computer-assisted prediction versus SRK prediction of postoperative refraction after intraocular lens implantation. J Cataract Refract Surg 1987;13:146. 16. Coburn RM, Grandon SC, Grandon GM. Intraocular lens implant power calculations:Investigations controlling for lens type. J Cataract Refract Surg 1990;16:457. 17. Olsen T, Thim K, Corydon L. Accuracy of the newer generation intraocular lens power calculation formulas in long and short eyes. J Cataract Refract Surg 1991;17:187. 18. Brandser R, Haaskjold E, Drolsum L. Accuracy of IOL calculation in cataract surgery. Acta Ophthalmol Scand 1997;75:162. 19. Narváez J, Zimmerman G, Stulting RD, et al. Accuracy of intraocular lens power prediction using the Hoffer Q, Holladay I, Holladay II, and SRK/T formulas. J Cataract Refract Surg 2006;32:2050-53. 20. Yalvaç IS, Nurözler A, Unlü N, et al. Calculation of intraocular lens power with the SRK II formula for axial high myopia 1996;6:375-78. 21. Jinhui Dai, Renyuan, Guosheng Lu. Study of intraocular lens power Calculation formula in High myopic. Chin J Ophthalmol 2000;36(1):69-70. 22. Jinhui Dai, Renyuan Chu, Guosheng Lu. Comparison of intraocular lens power calculation foumula. Rec Adv Ophthalmol 2001;21(4):283-85. 23. Donoso R, Mura JJ, Lopez M, et al. Emmetropization at cataract surgery. Looking for the best IOL power calculation

24. 25. 26. 27. 28. 29.

30. 31. 32.

formula according to the eye length. Arch Soc Esp Oftalmol 2003;78:477-80. Hoffer1 KJ. Clinical result using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000;26: 1233-37. MacLaren RE, Sagoo MS, Restori M, et al. Biometry accuracy using zero- and negative-powered intraocular lenses. J Cataract Reract Surg 2005;31:280-90. Holladay JT, Prager TC, Ruiz RS, et al. Improving the predictability of intraocular lens power calculations. Arch Ophthalmol 1986;104:539. Hoffer KJ. Ultrasound velocities for axial eye length measurement. J Cataract Refract Surg 1994;20:554. Olsen T, Corydon L, Gimbel H. Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm. J Cataract Refract Surg 1995;21:313. Vogel A, Dick HB, Krummenauer F. Reproducibility of optical biometry using partial coherence interferometry: intraobserver and interobserver reliability. J Cataract Refract Surg 2001; 27:1961-68. leftheriadis H. IOL¡¡Master biometry:refractive results of 100 consecutive cases. Br J Ophthalmol 2003;87:960£-63. Kora Y, Yaguchi S, Inatomi M, et al. Preferred postoperative refraction after cataract surgery for high myopia. J Cataract Refract Surg 1995;21:35-38. Colliac JP. Matrix formula for intraocular lens power calculation. Invest Ophthalmol Vis Sci 1990;31:374.

Accuracy of Intraocular Lens Power Calculation in Bimanual Gian Maria Cavallini, LucaMicrophacoemulsification Campi, Giovanni Neri (Italy)

25

Accuracy of Intraocular Lens Power Calculation in Bimanual Microphacoemulsification

INTRODUCTION Cataract surgery is the most common intraocular surgery procedure performed in the world. From 1967, year in which Kelman introduced the phacoemulsification technique,1 begun a new era for cataract surgery: more invasive procedures were abandoned, and we assisted in a decrease in incision size from the 10.0 mm required for the intracapsular cataract extraction to 7.0 for extracapsular cataract extraction and ultimately to the small incisions (3.2 to 2.8 mm) used for phacoemulsification.1, 2 The use of smaller surgical instruments, foldable intraocular lenses (IOLs), and more advanced management software for the phaco units, further allowed to reduce incision size and tissue trauma and to promote faster functional recovery. Clinical trials have found that the length of the incision is directly proportional to the amount of induced astigmatism and inversely proportional to its stability over time.3 The bimanual microincision phacoemulsification technique is a less invasive variation of traditional coaxial phacoemulsification and allows cataract extraction through incisions of 1.5 mm or smaller.4, 5 So nowadays, cataract surgery, is considered both a therapeutic procedure to remove cataract and a refractive surgery, as patients often claim to obtain a postsurgical excellent visual rehabilitation increasingly refractive expectations. A remaining problem, however, is the accurate calculation of intraocular lens (IOL) power which is necessary for attaining the desired postoperative refraction. Nevertheless, in surveys of members of the American Society of Cataract and Refractive Surgery and the European Society of Cataract and Refractive Surgeons about the complications of foldable IOLs that require explantation or secondary intervention, incorrect IOL

power is the most common indication. For the three most commonly used IOLs (3-piece acrylic, 3-piece silicone, and 1-piece acrylic), incorrect power is the leading indication for removing or exchanging an IOL. These trends have been consistent over the past 4 years.6 Highly accurate IOL power calculations result from optimizing a collection of interconnected details. The keratometry technique, method of axial length measurement, IOL power calculation formula, optimized lens constant, and configuration of the capsulorhexis, all individually influence the final refractive outcome. For this reason, focusing on a single item such as the axial length measurement or the IOL power calculation formula is usually insufficient to ensure consistent accuracy over a wide anatomical range. The surgeon must consider the process as a whole while simultaneously optimizing each component.7

KERATOMETRY Ophthalmologists and often accept without question corneal power measurements by keratometry or simulated keratometry, but not all measurements have the same level of accuracy or reproducibility. It should be remembered that keratometry errors have a 1:1 correlation with postoperative refractive errors at the spectacle plane. For example, if the keratometry reading is off by 0.50 D, the result will be a 0.50 D postoperative refractive error at the spectacle plane, even if all other aspects of the IOL power calculation and surgery are perfect. Add in other small errors such as variable corneal compression induced by applanation A-scan biometry or the use of an older 2 variable formula in axial hyperopia, and a 1.00 D deviation from the target refraction is not difficult to imagine.8

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Mastering the Techniques of Intraocular Lens Power Calculations To maximize keratometry accuracy, first, make the decision to use a single instrument for all pre- and postoperative measurements in order to limit the number of variables. For manual measurements, switching to a Javal-Schiotz–style keratometer will to help improve accuracy. Autokeratometry is quick and easy, but it typically requires multiple measurements to confirm accuracy. The simulated keratometry feature of many topographers is an excellent way to objectively determine the axis of astigmatism, but it can sometimes be less accurate than careful manual keratometry for measuring the central corneal power. Second, regularly check your keratometer against a set of standard calibration spheres and consider keeping a logbook of these evaluations . Third, if the results for any patient vary, ask a second staff member to confirm the measurements to ensure accuracy. Finally, if the keratometry mires are unreliable or distorted, obtaining a topographic axial map may help uncover something unsuspected such as a false form of keratoconus.

AXIAL LENGTH MEASUREMENTS One of the most common reasons for an incorrect IOL power is an error in the axial length measurement. The familiar and trusted 10 MHz applanation A-scan biometry is probably no longer accurate enough to consistently satisfy contemporary patients’ expectations. The reason is that measurements by the applanation technique produce a falsely short axial length and sometimes widely different results due to varying degrees of corneal compression and axial alignment. Immersion A-scan biometry is unquestionably a more reliable method. This technique causes no corneal compression and measurements can be of very high quality and quite reproducible. At present, optical coherence biometry using the IOL Master (Carl Zeiss Meditec AG, Jena, Germany) is unquestionably the most accurate way to measure axial length prior to cataract surgery. Optical coherence biometry’s use of a short-wavelength light source (instead of a longer wavelength sound beam) increases axial length measurement accuracy when compared with ultrasound.9 For challenging axial length measurements (e. g., in eyes containing silicone oil, extremely short nanophthalmic eyes, or extremely long myopic eyes with posterior staphyloma), the accuracy of optical coherence biometry is unparalleled. The one disadvantage of the technique is that it is an optical method. Axial opacities such as a

corneal scar, dense posterior sub capsular plaque, or vitreous hemorrhage may decrease the signal-to-noise ratio to the point that reliable measurements are not possible. In the typical North American ophthalmology practice, optical coherence biometry is unable to measure between 5% and 15% of patients, and immersion ultrasound is required.

IOL CONSTANT OPTIMIZATION Surgeons must personalize the lens constant (Holladay 1 Surgeon Factor; SRK/T A-constant; Holladay 2 or Hoffer Q anterior chamber depth; Haigis a0, a1, and a2) for a given formula in order to make adjustments for a variety of practice-specific variables, including different styles of IOLs, keratometers, and variations in A-scan biometry calibration. Most IOL power calculation programs provide either internal software or specific recommendations for how to go about lens constant optimization.10

SURGICAL TECHNIQUE The configuration of the capsulorhexis can affect refractive outcomes if a surgeon is implanting a single-piece acrylic or a three-piece assembled IOL. If the capsulorhexis’ diameter is larger than the lens optic, the forces of capsular bag contraction may anteriorly displace the IOL, a situation resulting in an increased effective lens power and more myopia than anticipated. A simple “rhexis rule” is that the capsulorhexis should be round, centered, and slightly smaller than the optic. In order for the IOL power calculation formula to be most consistent and accurate, the capsular bag should completely contain the IOL. Attention to this detail can help maximize refractive accuracy.11 In this chapter we will describe our experience of intraocular lens power calculation in that patients who underwent cataract surgery with bimanual microphacoemulsification technique.

PATIENTS AND METHODS A retrospective review was conducted of 690 consecutive eyes with cataracts of grade 2 to 4 according to LOCS III classification operated with bimanual microphacoemulsification and IOL implant into capsular bag by one surgeon (GMC). Inclusion criteria were: transparent central cornea, good preoperative pupil dilation, no history of previous eye surgery or glaucoma, no history of retinal disease, astigmatism lower than 3.0 diopters (D).

Accuracy of Intraocular Lens Power Calculation in Bimanual Microphacoemulsification the error; final refraction was performed 4 weeks after surgery.

SURGICAL TECHNIQUE

Fig. 25.1: IOL master

Two 1.4 mm trapezoidal incisions were made in the clear cornea at 10 o’clock and 2 o’clock with a precalibrated diamond knife (E. Janach) (Fig. 25.3). A continuous curvilinear capsulorhexis (CCC) with a diameter between 5.0 mm and 6.0 mm was made with a cystotome. Hydrodissection was performed with a 26 gauge cannula and phacoemulsification, with a 20 gauge, 30 degree-angled sleeveless probe and an irrigating chopper (E. Janach) (Fig. 25.4). Phaco fracture was by the stop-and-chop technique. Irrigation/aspiration (I/A) was performed with a 20 gauge probe with an oval section (American Medical Optics) introduced through the microincisions. 12,13 Gradual suction of the cortical remnants and epinucleus was done with the aspiration probe in the dominant hand and the irrigation probe in the other, using the continuous infusion mode to avoid sudden collapse of the anterior chamber. With the irrigation probe, the lens fragments were directed toward the aspiration probe to simplify the procedure and lower turbulence in the anterior chamber.

Fig. 25.2: Ultrasound biometry

Fig. 25.3: Microincision with precalibrated diamond knife

Preoperatively all eyes had ocular biometry with IOL Master (Carl Zeiss Inc.) (Fig. 25.1) and ultrasound biometry (Fig. 25.2) when no reading could be taken with IOL Master especially those with dense cataracts or sub capsular opacities; manual keratometry was obtained in all cases. Eyes were stratified into groups of short, average and long axial length (< 22 mm, 22 to < 24,5, and > 24,5 respectively). Data were entered into IOL software program and we chose Hoffer Q formula for short eyes, SRK II formula for average eyes and SRK T formula for long eyes. We compared the predicted final spherical equivalent (SE) refractive error in each eye with the actual postoperative manifest refraction SE and calculated the difference as

Fig. 25.4: Bimanual microphaco technique

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Fig. 25.5: IOL for microincision (1.8 mm) implanted

Table 25.1: Surgical parameters for the Sovereign WhiteStar setup

Parameter

Values

Power (%) Aspiration flow (cm3/min) Vacuum (mmHg) Unoccluded Occluded Cortical remnant I/A (mmHg)

20 – 25 24 – 28

Fig. 25.6: Akreos M160

60 – 250 80 – 300 450

I/A = irrigation/aspiration

After the half of the capsular bag opposite the entry site was polished with the aspiration probe, the instruments were passed from one hand to the other, retracting the aspiration probe first.14 The remaining capsular bag was cleaned in the same way. Then, the IOL was inserted through a third 1.8 mm incision created at 12 o’clock (Fig. 25.5). The phacoemulsificator used (Sovereign WhiteStar, AMO Inc, CA, USA) was the same for all surgeries and was used with the same setting parameters (Table 25.1). We implanted two different foldable, acrylic, microincision IOLs: Akreos MI60 (Fig. 25.6) and Acri.Smart 48S (Fig. 25.7). The first IOL has hydrophilic properties and has a great uveal biocompatibility, while the second one is hydrophobic, and has a better capsular biocompatibility (Table 25.2).15-17

RESULTS The results are underlined in Table 25.3. We haven’t note differences than data reported in literature.7-10

Fig. 25.7: Acri.Smart 48 S

Table 25.2: Technical features of implanted IOLs

Characteristics

Akreos MI60

Acri.Smart 48S

Shape

single piece

single piece

Optic

biconvex, aspheric standard, anterior and posterior biconvex, symmetric

Optic diameter

6.0

5.5 mm

Overall length

10.7 mm

11.0 mm

Haptic angulation 10°

0°

Material

foldable acrylate

foldable acrylate

Surface

hydrophilic

hydrophobic

A-costant (optic) 118.9

118.3

Accuracy of Intraocular Lens Power Calculation in Bimanual Microphacoemulsification Table 25.3: Mean absolute error by formula Mean Absolute difference, predicted vs actual postoperative SE refraction (D) ± SD

Axial Length, mm (range)

Eyes

Hoffer Q

SRK II

SRK T

< 22 (20.71-21.95)

31

-

-

22 to < 24.5 (22.02-24.48)

483

0.62 ± 0.53 0.05 to 1.73 -

-

> 24.5 (24.52-31.54)

176

-

0.49 ± 0.45 0.00 to 1.84 -

0.54 ± 0.65 0.04 to 2.32

SE: Spherical equivalent

DISCUSSION The smaller incision used for cataract extraction today make the surgery less invasive and safer, result in less invasive and safer resulting in less postoperative intraocular inflammation, fewer incision-related complications, lower surgical induced astigmatism and shorter total surgical time. These factors provide faster postoperative visual recovery and increased patient satisfaction. Increasingly, patients expect good refractive outcomes after cataract surgery in adition to the therapeutic benefits from treating the pathology. Bimanual microincision phacoemulsification is an effective and safe technique to manage all types of cataract. Also the accuracy of IOL calculation for new microincisional intraocular lenses is at least comparable to results reported in literature.

REFERENCES 1. Kelman CD. Phaco-emulsification and aspiration; a new technique of cataract removal; a preliminary report. Am J Ophthalmol 1967;64:23–35. 2. Paton D, Ryan S. Present trends in incision and closure of the cataract wound. Highlights Ophthalmol 1973;14:3–10. 3. Aliò JL. What does MICS require? The transition to microincisional surgery. In: Aliò JL, Rodriguez-Prats JL, Galal A, eds, MICS Micro-Incision Cataract Surgery. El Dorado, Republic of Panama, Highlights of Ophthalmology International, 2004;1–4. 4. Cavallini GM, Masini C. Microfacoemulsificazione bimanuale; origine e definizione. In: Cavallini GM, eds, Microfacoemulsificazione Bimanuale nella Chirurgia della Cataratta. Modena, Athena Ed, 2006;15–16. 5. Cavallini GM, Lugli N, Campi L, et al. Surgically induced astigmatism after manual extracapsular cataract extraction or after phacoemulsification procedure. Eur J Ophthalmol 1996;6:771-78.

6. Mamalis N. Complications of foldable IOLs requiring explantation or secondary intervention—2001 survey update. J Cataract Refract Surg 2002;28:2193-201. 7. Kiss B, Findl O, Menapace R, Wirtitsch M, Drexler W, Hitzenberger CK and FercherAF: Biometry of cataractous eyes using partial coherence interferometry: clinical feasibility study of a commercial prototype I. J Cataract Refract Surg 2002;28:224–29. 8. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye 2002;16:552–56. 9. Findl O, Drexler W, Menapace R, Heinzl H, Hitzenberger CK & FercherAF: Improved prediction of intraocular lens power using partial coherence interferometry. J Cataract Refract Surg 2001;27:861–67. 10. Narvaez J, Zimmerman G, Doyle Stulting R, Chang D. Accuracy of intraocular lens power prediction using the Hoffer Q, Holladay 1, Holladay 2, and SRK/T formulas. J Cataract Refract Surg 2006;32:2050-53. 11. Holladay J. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997;23(9):1356-70. 12. Cavallini GM, Campi L, Masini C, Pelloni S, Pupino A. Bimanual microphacoemulsification versus coaxial miniphacoemulsification: Prospective study. J Cataract Refract Surg 2007;33:387-92. 13. Gimbel HV, Neuhann T. Development, advantages and methods of the continuous circular capsulorhexis technique. J Cataract Refract Surg 1990;16:31. 14. Fine IH. Corneal tunnel incision with a temporal approach. In: Fine IH, Fichman RA, Grabow HB. Clear corneal cataract surgery and topical anesthesia. Slack, Thorofare: NJ, 1993: 5-26. 15. Cavallini GM. Microfacoemulsificazione bimanuale; tecnica bimanuale. In: Cavallini GM, Eds. Microfacoemulsificazione Bimanuale nella Chirurgia della Cataratta. Modena, Athena Ed, 2006. 16. Tsuneoka H. Minimally Invasive bimanual phaco surgery and foldable IOL implantation through the smalllest incision. In: Garg A, Fine IH, Chang DF, Tsuneoka H, Eds. Step by Step Minimally Invasive Cataract Surgery. Jaypee Brothers Medical Publishers (P) LTD; New Delhi, 2005;186-209. 17. Cavallini GM, Pupino A, Masini C, Campi L, Pelloni S. Bimanual microphacoemulsification and Acri.Smart intraocular lens implantation combined with vitreoretinal surgery. J Cataract Refract Surg 2007;33(7):1253-58.

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Mastering the Techniques of Intraocular Lens Power Calculations Frank J Goes (Belgium)

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Clinical Outcomes of Cataract Surgery after Previous Refractive Surgery

INTRODUCTION In this chapter we would like to share with you our clinical experience of more than 100 cataract and IOL Implant surgeries in eyes that had previous refractive surgery such as Radial keratotomy-Excimer laser surgery- LTK surgery. We started Radial keratotomy in 1981and performed more than 1300 surgeries. We started Excimer laser surgery in 1991 and have performed more than 12,000 cases until now. We started LTK in 1998 and have performed 450 cases. The purpose of this chapter is not to analyze IOL power calculations although we will discuss it briefly but to discuss: Indications - Safety and Predictability –and Outcomes of Cataract surgery after previous refractive surgery. We have probably more results and follow-up of cataract surgery after previous refractive surgery than any other clinic in the world since we are in Excimer laser business since 1991 and have an excellent follow-up in our own clinic. We will review three different groups: • Cataract surgery after previous Myopia Excimer laser surgery • Cataract surgery after previous Hyperopia laser surgery • Cataract surgery after previous Radial Keratotomy surgery We will report also on the incidence and type of cataract after previous refractive surgery-the age of cataract patients in the different refractive groups- discuss the surgical technique and describe the follow-up after surgery.

We will analyze in detail 75 eyes with sufficient follow up: 53 cataractous eyes after myopia surgery and 22 cataractous eyes after previous hyperopia surgery. The primary refractive surgery procedures were as follows: LASIK 24 eyes, PRK 40 eyes, Radial Keratotomy 7 eyes and, LTK 4 eyes. There were in the whole group 47 female and 28 male eyes; this corresponds to the distribution of patients coming in for refractive surgery purposes; more women than men.

DELAY OF CATARACT SURGERY AFTER PREVIOUS REFRACTIVE CORNEAL SURGERY The mean time interval between the Excimer refractive surgery and the cataract surgery was 2588+/-937 days for the myopia group and 2377+/-977 days the hyperopia group. No significant differences were seen between these two groups as far as time delay is concerned.

TYPE OF CATARACT AFTER REFRACTIVE SURGERY In the series of eyes operated upon after Radial Keratotomy no particular type of cataract was predominant; the majority being cortical cataracts as we see them in the similar age population. This is explained by the fact that these post Radial Keratotomy patients never were really highly myopes since we limited ourselves to treat eyes below 6 diopters and never performed more than 8 incisions as a primary treatment. In the series of cataracts after previous Myopic Laser surgery –the real long myopic eyes-nearly always a nuclear-sometimes fast progressive- cataract was present. In the early years 1990-1995 myopia till -15 was treated

Clinical Outcomes of Cataract Surgery after Previous Refractive Surgery with Excimer laser and we published on that topic at that time. Most of our cataract patients after previous Myopic Excimer laser surgery had nuclear cataracts. We reviewed the literature on that subject and our clinical findings were confirmed (See Chapter Prevalence of cataract). In the series of Hyperopic Excimer laser cases developing cataract the cataract was not of any typical type since all forms of cataract were present: mostly cortical cataracts were seen similar to what we see in the routine population of that age. Cataracts after previous LTK were mostly cortical cataracts as we see them in a routine population.

PATIENT’S AGE AT TIME OF CATARACT SURGERY In the Myopia group the mean patient’s age of surgery for cataract was much lower than the mean age in the general population-57.1+/7.8 years versus 74 years in our normal cataract population. We know that myopic eyes develop cataract much earlier than emmetropic eye but these differences were striking. As a rule of thumb, 10 diopters of myopia equals 10 years earlier manifestation of cataract. But here the differences were more important since the mean myopia before surgery in this group was -10.3+/2.7 Dptr. The literature confirms the earlier manifestation of cataracts in myopic eyes compared to emmetropic and hyperopic eyes. In the Hyperopia group the mean age was also younger than in our normal population but the difference was less important; 61.5+/-9.8 years in this group compared to 74 years .This difference could be explained by the fact that many of these patients came in for refractive surgery at their first visit they had their lens removed when the hyperopia progressed too much and not necessary when the cataract only was the reason for the visual deterioration. So some patients in this group are refractive lensectomy patients. The mean hyperopia before surgery in this group was 3.78+/1.9 Dptr. In the group of Radial Keratotomy patients the mean age was also closer to our normal values: 62.1+/12 years. Although this cohort includes also myopic eyes, the mean myopia of these patients before their refractive surgery:5.3+/1.7 Dptr. This is much lower than in the Excimer laser surgery myopia group. In the group of cataracts after LTK primary refractive surgery again the mean age - 59+/-12 years- was similar

to the hyperopia group since also here some lenses with beginning cataract causing a progressive hyperopia were removed as part of refractive lensectomy surgery procedure.

LITERATURE: PREVALENCE OF CATARACT IN MYOPIA AND MANIFESTATION OF CATARACT IN MYOPIA In the literature several papers discussed the association between cataract and refractive errors - specifically myopia- but not so many data were found between the age of manifestation of cataract and the different refractive groups. McCarty CA, et al. in 19991 described the prevalence and risk factors for cataract in an Australian population aged 40 years and older. In the urban and rural cohorts, age, female gender, rural residence, brown irides, diabetes diagnosed 5 or more years earlier, myopia, age-related maculopathy, having smoked for greater than 30 years, and an interaction between ocular ultraviolet B exposure and vitamin E were all risk factors for nuclear cataract. The rate of posterior subcapsular cataract was 4.08% (95% confidence limits, 3.01%, 5.14%), whereas the overall rate of posterior subcapsular cataract including previous cataract surgery was 4.93% (95% confidence limits, 3.68%, 6.17%). Wong et al in 20012 described the relation between refractive errors and incident age-related cataracts in a predominantly white US population: All persons aged 43 to 84 years of age in Beaver Dam, Wisconsin, were invited for a baseline examination from 1988 through 1990 and a follow-up examination 5 years later from 1993 through 1995. When age and gender were controlled for, myopia was related to prevalent nuclear cataract (odds ratio [OR], 1.67; 95% confidence interval [CI], 1.23-2.27), but not to cortical and posterior subcapsular cataracts. Myopia was not related to 5-year incident nuclear, cortical, and posterior subcapsular cataracts, but was related to incident cataract surgery (OR 1.89; CI 1.18-3.04). Hyperopia was related to incident nuclear (OR 1.56; CI 1.25-1.95) and possibly cortical (OR 1.25; CI 0.96-1.63) cataracts, but not to posterior subcapsular cataract or cataract surgery. Their data support the cross-sectional association between myopia and nuclear cataract seen in other population-based studies. Younan C, et al 3 in 2002 assessed whether an association exists between myopia and incident cataract and cataract surgery in an older population-based cohort study. Their epidemiologic data provided some evidence

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Mastering the Techniques of Intraocular Lens Power Calculations of an association between myopia and incident cataract and cataract surgery.

Prevalence of Cataract in Myopia Wong TY et al in 20034 described the relationship of refractive errors and axial ocular dimensions and agerelated cataract. In a Population-based, cross-sectional survey of ocular diseases among Chinese men and women aged 40 to 81 years (n = 1232) living in the Tanjong Pagar district in Singapore., nuclear cataract was associated with myopia (-1.35 D vs. -0.11 D, P < 0.001, Cortical cataract was associated with thinner lenses (4.67 mm vs. 4.79 mm, P = 0.001, comparing right eyes with and without cortical cataract), but not with refraction and other biometric components. Posterior subcapsular cataract was associated with myopia. Their population-based data supported the associations between nuclear and posterior subcapsular cataracts and myopia reported in previous studies. Chang MA et al 5 found significant associations between myopia and both nuclear and posterior subcapsular opacities. For nuclear opacity, the odds ratios (ORs) were 2.25 for myopia between -0.50 diopters (D) and -1.99 D (P – 12D

1.3355 1.3286 1.3237 1.3172

The new keratometry reading is obtained by using the equation K = [rN – 1 / Ra] Ra = anterior corneal curvature in meters, measured after refractive surgery, using an automated instrument. The authors also describe an alternate formula to determine rN for eyes in which the change in refraction after LASIK is known, rN = 0.0014SEc + 1.3375 SEc – Spherical equivalent change after LASIK

STRATEGIES TO BE USED WHEN PRIOR DATA IS NOT AVAILABLE Corneal Topography13 The reasons why standard keratometry results in poor refractive outcomes after IOL implantation in eyes that have had corneal refractive surgery, have already been described. Most of the currently available computerized videokeratography units provide color-coded maps of corneal power distribution. The basic principles adopted

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Mastering the Techniques of Intraocular Lens Power Calculations by the Placido-based devices remain very similar to those in manual keratometers. Hence they are subject to the inaccuracies described earlier. However, in post-RK eyes, some degree of accuracy can be attained by ignoring the simulated keratometry values provided by the machine (measured from a 3 mm zone), and deriving the value from the center of the zone of flattening indicated in the topographic map. This is more accurate since these devices use data from more points on the corneal surface including the cornea within the 3 mm zone measured by the keratometer. This method would not however be useful in eyes that have had excimer surgery, due to the inaccuracy in conversion mentioned earlier. To further improve the accuracy of this method, Maloney suggested the following modification to the power obtained from the center of the corneal topographic map14 Adjusted central corneal power = [Measured central topographic power × (376/337.5)] – 4.9. Koch et al, using data from 11 eyes suggested the use of 6.1D instead of 4.9D as the value for the posterior corneal power.

The Hard Contact Lens Method15 In this technique, a hard contact lens of known base curve is placed on the eye with lens changes, and refraction is performed. The subjective refraction with the contact lens in place is compared with the refraction obtained without the contact lens. These values are used to derive the corneal power, using the following relationship, Keratometry (D) = Contact lens base curve (D) + contact lens power (D) + (refraction with the contact lens) – (refraction without the contact lens) Example If refraction without the contact lens (base curve 38.0D) is – 5.0D, and with the contact lens in place is plano, it means that the cornea underlying the lens is steeper than the contact lens by 5D. Hence the corneal power would be contact lens power plus 5D (assuming that the contact lens power was zero). Thus, Keratometry = 38 + 0 + (0) – (– 5) = 38 + 5 = 43.0D. This method is advantageous because it does not require access to patient data. However, it is accurate only if the cataract allows refraction and the patient has have a best-corrected visual acuity of at least 6/18 (to ensure that the refraction is accurate). If the cataract is very dense or total, and accurate refraction is not possible, or if the

visual acuity in the cataractous eye cannot be improved beyond 6/24, then the accuracy of this method is open to question. More recently, the contact lens overrefraction method was reviewed and modified by Haigis.16 He explains that the formula described above may provide a clinically acceptable estimate of the corneal back vertex power in normal eyes without previous corneal surgery. However, in eyes that have had corneal surgery, the formula may lead to overestimation of keratometry. To overcome this, he suggests the use of the following formula PCe = 1.119 × PCLO – 5.78 PCe – Equivalent corneal power PCLO – Power from the contact lens over-refraction method.

Regression Derived Clinical Method17 The authors used a dataset of eyes undergoing LASIK to derive the following equation using regression equations. Kc.cd = 1.14Kpost – 6.8 Kc.cd = Clinically derived post refractive surgery keratometry. Kpost = Measured postrefractive surgery keratometry. Example If the measured postrefractive surgery keratometry is 40.0D. The value according to the above equation would be = (1.14 × 40) – 6.8 = 38.8D.

Intraoperative Retinoscopy18 In this technique, cataract surgery is completed and retinoscopy is performed intraoperatively in the aphakic eye. From the aphakic refraction, the IOL power can be determined. Alternatively, the IOL chosen can be implanted and then retinoscopy is performed, although IOL exchange would be necessary if there was a significant error. It would also be necessary to consider the loss of aseptic technique that may occur during this intraoperative maneuver. These issues were addressed in a recent study and the authors derived a regression equation to help determine the IOL power required using the intraoperative aphakic automated refraction obtained during surgery.19 Predicted final adjusted IOL power = 2.01449 × intraoperative SE refraction.

IOL Power Calculations after Corneal Refractive Surgery In another similar approach, the authors suggest performing a manifest aphakic refraction 30 minutes after cataract surgery and using the following equation to calculate the IOL power.20 Predicted final adjusted IOL power = 1.75 × manifest SE refraction.

The Gaussian Optics Formula21 This is a theoretical approach that uses the values for anterior and posterior corneal curvatures measured after refractive surgery – using the Orbscan or the Pentacam, with the pachymetry – to derive the corneal power. The values obtained are used with the formula described below. Corneal power = P1 + P2 – [d / n1] × P1 × P2 P1 = [1 / r1 (n1 – n0)] P1 = [1 / r2 (n2 – n1)] P1 = Power of the anterior corneal surface P2 = Power of the posterior corneal surface n0 = refractive index of air (1.0) n1 = refractive index of cornea (1.376) n2 = refractive index of aqueous humor (1.336) d = corneal pachymetry r1 = anterior corneal radius of curvature (mm) r2 = posterior corneal radius of curvature (mm)

Theoretical Variable Refractive Index Method

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The authors used a dataset of post PRK eyes to derive a theoretical variable refractive index correlated to axial length. This was used to derive the corrected value for post PRK keratometry using the measured value. Theoretical refractive index (TRI) = [– 0.0006(AL × AL) + (0.0213 × AL) + 1.1572] Corneal power = (TRI – 1)/r AL – Axial length in mm R – Corneal curvature in mm The availability of these various techniques has resulted in improved accuracy in IOL power calculations for eyes that have had refractive surgery.23 However, there is still scope for improvement. Concerns exist with some of the methods described – especially those that are theoretical derivations, which require verification with actual patient datasets. With techniques that require access to prerefractive surgery patient data, it is important that such data be accurate. 24 Especially with postrefractive surgery refractive error, it is vital that this be obtained before the onset of cataract alters the value. With methods such as the contact lens over refraction, the degree of cataract and

visual function affect the accuracy of the outcome, as also the contact lens fit and centration. Finally, even if all these are accurate, the quality of the refractive ablation is very important in determining the outcomes of these calculation techniques. If there has been a very small, irregular or decentered ablation zone, the outcomes can still be suboptimal. Thus, in dealing with these patients, it is important to have access to as much of the available prerefractive surgery data as possible, perform a careful preoperative examination of the eye and corneal profiles, use as many of the methods described as possible, choose the least keratometry value obtained (ensuring that it is fits with the data available), calculate the IOL power required using the third and fourth generation formulae, choose the highest IOL power determined (for eyes that have had myopic refractive surgery), and aim for a slight postoperative myopia of 0.75 to 1.0 D. Despite all this, it may be necessary also to discuss with the patient the issues involved and explain the possible need for some further procedures, should the desired result not be obtained. Finally, it is important to keep a database of these patients, to help improve our ability to improve refractive outcomes after cataract surgery.

REFERENCES 1. Holladay JT. Consultations in refractive surgery. Refract Corneal Surg 1989;5:203. 2. Feiz V, mannis MJ, Garcia-Ferrer F, Kandavel G, Darlington JK, Kim E, Caspar J, Wang JL, Wang W. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia. Cornea 2001;20:792-97. 3. Hamed HA, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651-58. 4. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double K method. J Cataract Refract Surg 2003;29:2063-68. 5. Koch DD, Wang L. Calculating IOL power in eyes that have had refractive surgery. J Cataract Refract Surg 2003;29: 2039-42. 6. Jarade EF, Tabbara KF. New formula for calculating intraocular lens power after laser in situ keratomileusis. J Cataract Refract Surg 2004;30:1711-15. 7. Stakheev AA, Balashevich LJ. Corneal power determination after previous corneal refractive surgery for intraocular lens calculation. Cornea 2003;22:214-20. 8. Walter KA, Gagnon MR, Hoopes PC, Dickinson PJ. Accurate intraocular lens power calculations after myopic laser in situ keratomileusis, bypassing corneal power. J Cataract Refract Surg 2006;32:425-29. 9. Latkany RA, Choksi AR, Speaker MG, Abramson J, Soloway BD, Yu G. Intraocular lens calculations after refractive surgery. J Cataract Refract Surg 2005;31:562-70. 10. Masket S, Masket SE. Simple regression formula for intraocular lens power adjustment in eyes requiring cataract surgery after excimer laser photoablation. J Cataract Refract Surg 2006;32:430-34.

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Mastering the Techniques of Intraocular Lens Power Calculations 11. Feiz V, Moshirfar M, Mannis MJ, Reilly CD, Garcia-Ferrer F, Caspar JJ, Lim MC. Nomogram-based intraocular lens power adjustment after myopic photorefractive keratectomy and LASIK. Ophthalmology 2005;112:1381-87. 12. Jarade EF, Abi Nader FC, Tabbara KF. Intraocular lens power calculation following LASIK: Determination of the new effective index of refraction. J Refract Surg 2006;22:75-80. 13. Celikkol L, Pavlopoulos G, Weinstein B, Celikkol G, Feldman S. Calculation of intraocular lens power after radial keratotomy with computerized videokeratography. Am J Ophthalmol 1995;120:739-50. 14. Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology 2004;111:1825-31. 15. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg 1995;11:490-93. 16. Haigis W. Corneal power after refractive surgery for myopia: Contact lens method. J Cataract Refract Surg 2003;29: 1397-411. 17. Shammas HJ, Shammas MC, Gabaret A, Kim JH, Shammas A, LaBree L. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol 2003;136:426-32.

18. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000;16:349-61. 19. Ianchulev T, Salz J, Hoffer K, Albini T, Hsu H, LaBree L. Intraoperative optical refractive biometry for intraocular lens power estimation without axial length and keratometry measurements. J Cataract Refract Surg 2005;31:1530-36. 20. Mackool RJ, Ko W, Mackool R. Intraocular lens power calculation after laser in situ keratomileusis: Aphakic refraction technique. J Cataract Refract Surg 2006;32: 435-37. 21. Cheng ACK, Lam DSC. Keratometry for intraocular lens power calculation using Orbscan II in eyes with laser in situ keratomileusis. J Refract Surg 2005;21:365-68. 22. Ferrara G, Cennamo G, Marotta G, Loffredo E. New formula to calculate corneal power after refractive surgery. J Refract Surg 2004;20:465-71. 23. Cheng AC, Lam DS. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol 2004;137:970. 24. Cheng AC, Rao SK, Tang E, Lam DS. Pachymetry assessment with Orbscan II in postoperative patients with myopic LASIK. J Refract Surg 2006;22:363-66.

The Latkany Regression Formula for IOL Calculations afterIcasiano, Myopic Refractive Evelyn Robert Surgery Latkany (USA)

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The Latkany Regression Formula for Intraocular Lens Calculations after Myopic Refractive Surgery

INTRODUCTION Refractive surgery has been performed for over a decade now. These patients whom have undergone laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK) have grown accustomed to excellent uncorrected vision and have understandably high expectations. As these patients develop cataracts, it is becoming increasingly important to determine appropriate intraocular lens (IOL) powers to achieve emmetropia. The two approaches to solving this problem are (1) determining a postrefractive total corneal power and (2) calculating an accurate IOL power. Ideally, one would be able to calculate corneal power and IOL power without the need for prerefractive measurements. Numerous methods have been suggested, but most of those published have not been tested clinically, or have been performed only on a small number of cases. Existing IOL formulas assume a predictable relationship between the anterior and posterior surfaces of the cornea. Ablative keratorefractive surgery changes the relationship between the anterior and posterior surfaces of the cornea. Postrefractive keratometry readings appear higher than their actual values in previously myopic eyes because of the resultant flattening of the anterior cornea, leading to an underestimation of IOL power. The corneal power is overestimated by about 1 diopter (D) for every 7 D of refractive surgery correction.1 This falsely low IOL power results in undesirable postoperative hyperopia. Much work has been done to try to determine more accurate ways of determining IOL power for patients undergoing cataract surgery with a previous history of refractive surgery.

In determining corneal power, keratometers measure corneal curvature and relate this measurement to an assumed relationship between the anterior and posterior corneal surfaces. A 3.2 millimeter (mm) optical zone of the central cornea is measured. An average of measurements taken from 4 discrete points on the anterior cornea is used, assuming a spherical cornea. Most manual keratometers and topographers use a corneal index of refraction of 1.3375 based on the assumption that the posterior cornea has a radius of curvature 1.2 mm less than the anterior cornea. After refractive surgery to correct myopia, the cornea becomes aspheric whereupon the relationship between the anterior and posterior cornea is altered.1-5 There are numerous methods of determining corneal refractive power after refractive surgery.6,7 Computerized videokeratography (VKG) derived keratometry readings using Placidobased or slit scanning have been used.8 Alternatively, methods of calculating total corneal power after refractive surgery have been developed and will be discussed further. In determining IOL power, there are a number of formulas that have been proposed. We can divide them into two groups: those requiring preoperative keratometry and those that do not. When prerefractive keratometry readings are available, there are formulas that can be used based on whether or not the preoperative spherical equivalent (SE) is available. In a comparison of the various methods, it was found that the double-K clinical history method, methods of separate consideration of anterior and posterior corneal curvatures, and both Latkany regression formulas gave the most accurate IOL powers. These methods were the only ones that seemed to neither over- nor underestimate IOL power relative to the preoperative refraction.6 These methods will be discussed further.

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When Prerefractive Keratometry and Refraction are Available The clinical history method calculates corneal power from the refractive and keratometry measurements before and after refractive surgery. When all pre-refractive information is available, one can use the refractive change following refractive surgery or the spherical equivalent change in refraction. This value is then used to determine the mean postoperative corneal power. These calculations can be done either at the spectacle plane or at the corneal plane. For myopic refractive surgery, the corneal power is lowest when calculated by the spherical equivalent method at the spectacle plane and greatest when calculated at the anterior corneal surface method.1,9 K = Kpreop + Rpreop – Rpostop Kpreop = preoperative keratometry Rpreop = preoperative refraction Rpostop = postoperative refraction The Feiz-Mannis method of determining IOL power involves first determining the IOL power as if the patient had not undergone refractive surgery. The IOL power is calculated using prerefractive corneal power values and axial length before surgery. Then the induced change in refractive error is determined. This value divided by 0.7 is added to the prerefractive IOL power.10 IOLpre IOLpre ΔRE IOLpost

= = = =

ΔRE/0.7 = IOLpost IOL calculated using prerefractive keratometry Stable postrefractive refractive error Estimated IOL power after refractive surgery to be implanted.

When Only Preoperative Keratometry is Available When the only preoperative data available is the keratometry reading one option is to consider the anterior and posterior surfaces separately.11,12 This method is based on the assumption that the total power of the cornea is the sum of the power of the anterior cornea and the posterior cornea: P = Pa + Pp = (n2-n1)/r1 + (n3-n2)/r2; where n1 is the refractive index of air; n2 is the refractive index of the cornea; and n3 is the refractive index of aqueous humor.

If preoperative keratometry is available the following formula can be used to calculate the anterior corneal power: Pa = Pa = Kpre =

Kpre × 1.114 power of anterior cornea prerefractive keratometry 1.114 corresponds to 376/337.5

The power of the posterior corneal surface can be calculated by subtracting the prerefractive corneal power from the power of the anterior corneal surface. Pp = Pa – Kpre Pp = power of posterior cornea According to this method the total corneal power can then be calculated by adding the postoperative Pa to the preoperative Pp. The post-operative posterior corneal power is thought to be relatively unchanged. K = postop Pa + preop Pp

When Only Preoperative Refraction is Available The Feiz-Mannis nomogram10 can be utilized when the only information available is prerefractive surgery refractive error. The clinician can use the postrefractive keratometry and axial length to determine an IOL power. This IOL power is then adjusted based on the change in refraction induced by refractive surgery. The adjustment would be: – 0.231 + (0.595 × change in spherical equivalent) This value is then subtracted from the target IOL power (absolute value). The Latkany regression formulas13 are especially useful when the myopic spherical equivalent (SE) is the only preoperative value available. No previous keratometry values are needed. This method only requires keratometry readings based on postrefractive measurements, either flattest readings or average readings. Twenty-one patients who underwent uneventful cataract surgery with IOL implantation after previous refractive surgery for myopia were evaluated in a retrospective case series analysis. These formulas were derived by first determining a theoretical keratometry reading by repeatedly entering K-values into the SRK/T formula while keeping all other values the same constant until a keratometry value that achieved the patients’ postcataract surgery refraction was achieved Kexact. This value was then used in the SRK/T formula to determine the IOL power to achieve emmetropia, IOLexact. Different methods

The Latkany Regression Formula for IOL Calculations after Myopic Refractive Surgery were compared including the clinical history method, the Feiz-Mannis method, a back-calculated method based on prerefractive spherical equivalent, and methods as described above whereupon IOL powers were chosen based on either average post-refractive keratometry or flattest postrefractive keratometry. These methods were ompared to IOLexact. A paired t test showed that the adjusted IOLflatK was not statistically different from IOLexact. When the average postrefractive or flattest postrefractive keratometry readings were used and inserted into the SRK/T formula the following adjustment factors were determined based on linear regression analysis: For IOLflatK the adjustment factor is: – (0.47x +0.85) For IOLavgK the adjustment factor is: – (0.46x +0.21) x = prerefractive SE Note: Final IOL result should be rounded to the highest 0.50 D The clear advantage of this method is the ability to predict an accurate IOL power when prerefractive keratometry is not available. The only pre-refractive information needed is the SE. Although no head to head study was performed to see if there was a statistically significant difference between IOLflatK and IOLavgK, anecdotal evidence appears to favor IOLflatK. A clinical example follows:

Example Pre-refractive surgery Refraction: – 6.00 – 1.00 x 90 Pre-refractive spherical equivalent: – 6.50 Post-refractive keratometry 38.0 D, 38.5 D Flattest K: 38.0 D Axial Length: 24.0 mm A constant: 118.4 IOL calculation using flattest K in SRK/T formula: For target goal – 0.20 D → +25.0D lens Adjustment factor – (0.47(– 6.5) + 0.85) = +2.21 Adjusted IOLflatK to the highest 0.50 D: +27.5 D Shammas et al, derived a formula to determine a refraction-derived corrected keratometric value14. They observed a correlation between the amount of refraction at the corneal plane and the overestimation of corneal power measured after refractive surgery. Kc.rd = Kpost (– 0.23 × CRc) Kpost = postrefractive keratometry CRc = amount of myopia corrected at the corneal plane.

When No Preoperative Data are Available The contact lens method involves using a hard contact lens with a known base curve. Accurate measurement of the change in refraction before and after placement of the hard contact lens must be obtained. This value is then added to the known value of the base curve of the contact lens used. When evaluated clinically, this method was found to be unreliable.15 K = B + P + RCL – RnoCL B = base curve P = power RCL = manifest refraction with contact lens RnoCL = manifest refraction without contact lens Another method that is useful is the separate consideration of anterior and posterior corneal curvatures. As previously mentioned, this method is based on the assumption that the total refractive power of the cornea can be calculated by adding the power of the anterior and posterior corneal surfaces.11,12 This method can be utilized with or without preoperative data. It is useful when preoperative keratometry is missing and a standard value for the posterior corneal power is needed. If preoperative keratometry is not available, the Maloney method can be used16. K = Kpost × 1.114 – 4.98 Kpost = corneal power measured on an axial map This method was then modified by Wang et al11. It has been referred to as the Modified Maloney method. K = Kpost × 1.114 – 6.1 A variation of the method described previously by Shammas et al, is used to determine a clinically derived corrected keratometry where no clinical history is needed14. Kc.cd = 1.14Kpost – 6.8 Rosa et al, developed a method using a correction factor to determine corneal power. The postoperative radius as measured by videokeratography is multiplied by a factor between 1.01 and 1.22 depending on the axial length.17 K = (1.3375 – 1)/(Kpost × correction factor)/1000)) Ferrara et al, proposed the theoretical variable refractive index (TRI) where the change in the corneal

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Mastering the Techniques of Intraocular Lens Power Calculations refractive index after laser surgery is correlated to the axial length.18 TRI = – 0.0006 × (AL × AL) + 0.0213 × AL + 1.1572 AL = axial length Corneal power can then be calculated: K = (TRI – 1)/r r = corneal curvature in meters

INTRAOCULAR LENS POWER CALCULATION Determining corneal power is only part of the challenge. Furthermore, there is inaccuracy in the IOL power calculation even when postrefractive corneal power is determined. The Holladay, SRK/T and Hoffer Q formulas use axial length and keratometry to calculate the effective lens position (ELP) or anterior chamber depth. The ELP, axial length and keratometry are then used in the vergence formula to calculate the IOL power. After refractive surgery where the anterior corner is flattened, these formulas will falsely assume a shallow ELP and therefore a lower intraocular lens power. The double-K method uses the prerefractive keratometry reading to calculate effective lens position and post refractive keratometry measurement for the vergence formula and IOL calculation. This formula was assessed clinically in a small group of patients and predictability was found to be 90% within + 1.0 D of SE.19 Double-K Method: Use Kpre to calculate ELP & Kpo to calculate IOL power.

PROSPECTIVE ANALYSIS OF LATKANY REGRESSION FORMULA Twenty eyes of 14 patients who had previous uncomplicated myopic refractive surgery, followed by cataract extraction with IOL implantation were evaluated after calculation of the IOL implanted was based on the Latkany regression formula using flattest keratometry readings and spherical equivalent before refractive surgery. This method was compared to the clinical history method and the double-K method. Twelve of the 20 eyes had sufficient data to evaluate the statistical relationships among the three formulas as compared to a backcalculated IOL for emmetropia. The Latkany regression formula resulted in refractive error within 1.00 D of intended refractive aim (range: 0.78 to –1.00) in all cases. The absolute mean deviation was 0.59 + 0.39 D. Paired t test demonstrated no statistical difference between the IOL powers determined by the Latkany regression formula and the back-calculated IOL power for emmetropia. This

method has been shown to provide a simple and accurate method of IOL calculation.20 Undoubtedly more work needs to be done to optimize methods of obtaining accurate IOL powers for patients whom have undergone myopic refractive surgery and are considering cataract extraction with IOL implantation. Ideally a method that is independent of pre-refractive measurements would be most convenient. In the meantime, it is useful to become familiar with the many existing formulas. Two very useful websites that highlight these formulas include: http://www.eyelab.com/01% 20HofferSavini.htm and http://www.doctor-hill.com/ physicians/physician_main.htm. It will be important for the proposed methods to be tested clinically in prospective studies to further validate them. It is advocated that all patients undergoing refractive surgery should be given records regarding their prerefractive keratometry, prerefractive refraction, and stable postrefractive refraction. Additionally, patients should be appropriately counseled regarding the possible need for a second procedure in order to achieve emmetropia. Until we have a universally accepted formula, the Latkany regression formula has been clinically proven, although in a relatively small number of patients, to be an attractive option for postrefractive cataract surgery IOL power determination.

REFERENCES 1. Hoffer, KJ. Calculating intraocular lens Power After Refractive Corneal Surgery. Arch Ophthalmol 2002;120:500-01. 2. Norrby, S. Keratometry after Corneal Refractive Surgery. J Cataract Refract Surg 2005;31(2):256-57. 3. Anera, RG et al. Changes in corneal asphericity after laser in situ keratomileusis. J Cataract Refract Surg 2003;29:762-68. 4. Sonego-Krone, S et al. A direct method to measure the power of the central cornea after myopic in situ keratomileusis. Arch Ophthalmol 2004;122:159-66. 5. Twa, MD et al. Response of the posterior corneal surface to laser in situ keratomileusis for myopia. J Cataract Refract Surg 2005;31:61-71. 6. Savini G et al. Intraocular lens Power Calculation after Myopic Refractive Surgery. Ophthalmology August 2006;113(8): 1271-82. 7. Hoffer/Savini Tool: http://www.eyelab.com/01%20Hoffer Savini.htm 8. Qazi, MA et al. Determining Corneal Power Using Orbscan II Videokeratography for Intraocular Lens Calculation After Excimer Laser Surgery for Myopia. J Cataract Refract Surg 2007;33:21-30. 9. Basic and Clinical Science Course. Sect 11. Lens and Cataract. AAO, 2004;151. 10. Feiz V, et al. Intraocular Lens Power Calculation After Laser in situ keratomileusis for myopia and hyperopia: a Standardized Approach. Cornea 2001;20(8):792-97. 11. Speicher, L. Intraocular lens calculation status after corneal refractive surgery. Curr Opin Ophthalmol 2001;12:17-29.

The Latkany Regression Formula for IOL Calculations after Myopic Refractive Surgery 12. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000;16(3):349-61. 13. Latkany RA et al. Intraocular lens Calculations after Refractive Surgery. J Cataract Refract Surg 2005;31:562-70. 14. Shammas HJ et al. Correcting the Corneal Power Measurements for Intraocular Lens Power Calculations After Myopic Laser in situ Keratomileusis. Am J Ophthalmol 2003;136: 426-32. 15. Wang L et al. Comparison of Intraocular Lens Power Calculation Methods in Eyes That Have Undergone LASIK. Ophthalmology 2004;111(10):1825-30.

16. Smith, RJ et al. The prediction of surgically induced refractive change from corneal topography. Am J Ophthalmol 1998; 125:44-53. 17. Rosa N et al. A New Method of Calculating Intraocular Lens Power After Photorefractive Keratectomy. J Refract Surg 2002;18:720-24. 18. Ferrara, G et al. New formula to calculate corneal power after refractive surgery. J Refract Surg 2004;20:465-71. 19. Aramberri, J. Intraocular lens Power Calculation After Corneal Refractive Surgery: Double-K Method. J Cataract Refract Surg 2003;29:2063-68. 20. Khalil, M et al. Prospective Evaluation of Intraocular Lens Calculation after Myopic Refractive Surgery. J Refract Surg 2008.

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The Latkany Regression Formula for Intraocular Lens Calculations after Hyperopic Refractive Surgery

INTRODUCTION As patients whom have undergone refractive surgery are advancing in age and developing cataracts, it becomes increasingly important to find more accurate ways to determine intraocular lens powers. It is of course essential to discuss with patients that cataract surgery following refractive surgery remains an area that is inexact and that there is a potential need for glasses or additional surgery. Much work has been done to try to calculate more precise intraocular lens (IOL) powers for cataract patients after refractive surgery.1-11 Few reports have been published to date regarding IOL calculations specifically following hyperopic refractive surgery.3,12,13 In previously hyperopic patients who have had refractive surgery, the keratometric power is underestimated resulting in undesirable myopia after cataract surgery. The difficulty lies in the fact that after ablative refractive surgery the anterior corneal curvature is changed while the posterior curvature of the cornea remains relatively unchanged. Existing intraocular lens equations assume a predictable relationship between the anterior and posterior cornea. Using post-refractive keratometry measurements will lead to an inaccurate measure of the estimated lens position and an apparent deep anterior chamber. This misleading measurement leads to an overestimation of IOL power and therefore a myopic result. Manual keratometers and topographers measure anterior corneal curvature based on a predictable relationship between the anterior and posterior corneal surfaces. Four paracentral points are averaged in order to estimate corneal curvature. Therefore, a steeper central region induced after hyperopic refractive surgery would be inaccurately measured3.

Methods of overcoming inaccurate postoperative keratometric readings have included the hard contact lens method14 and the refraction-derived clinical history method.15 However, the contact lens method depends on obtaining an adequate refraction that may be influenced by visually significant cataract. Also a visual acuity of at least 20/80 is necessary. The clinical history method requires knowledge of prerefractive keratometry and prerefractive refraction.12 In determining IOL power, the Holladay, SRK/T and Hoffer Q formulas use axial length and keratometry to calculate the effective lens position (ELP) or anterior chamber depth. The ELP, axial length and keratometry are then used in the vergence formula to calculate the IOL power. Because of the induced changes on the corneal surface, the ELP is inaccurately estimated following refractive surgery. The double-K method uses the prerefractive keratometry reading to calculate effective lens position and postrefractive keratometry measurement for the vergence formula and IOL calculation. This formula was assessed clinically in a small group of patients and predictability was found to be 90% within + 1.0 D of SE.11 Correction tables have been devised for each of these formulas utilizing the double-K method. These tables can be easily viewed at the following website: http://www. doctor-hill.com/iol-main/prior-keratorefractive.htm The Latkany hyperopic regression formula for previously hyperopic patients has shown promising results in a retrospective case series analysis. This formula was derived by first repeatedly entering keratometry values into the SRK/T formula while keeping all other unknowns constant until a keratometry value that achieved the patients’ postcataract surgery refraction was achieved Kexact. This value was then used in the SRK/T

The Latkany Regression Formula for IOL Calculations after Hyperopic Refractive Surgery formula to calculate an IOL for emmetropia (IOLexact). These IOL powers were then compared to the IOL measurements based on the average (IOLavgK) and the steepest (IOLsteepK) keratometry readings after refractive surgery. Regression analysis determined the amount of overestimation for IOLavgK can be predicted if the prerefractive spherical equivalent (SE) is known. The adjustment factor is – (0.27x + 1.53) where x is the prerefractive SE. In a retrospective case series it was found that there was no statistical difference from IOLexact. Again, the advantage of using the Latkany regression formula is that the only prerefractive information needed is the SE. This method was evaluated in twenty patients that underwent phacoemulsification with IOL implantation after hyperopic LASIK. Seven different methods of calculating IOL power were compared. These methods included the clinical history method adjusted for the corneal plane, the clinical history method in the spectacle plane, the Feiz-Mannis method, a back-calculated method based on prerefractive spherical equivalent, the SRK/T method using the double-K method, and methods as described above whereupon IOL powers were chosen based on either average postrefractive keratometry and steepest post-refractive keratometry13. For IOLavgK the adjustment factor is: – (0.27x + 1.53) x = prerefractive spherical equivalent

EXAMPLE Prerefractive refraction: +3.00 -1.00 × 180 Prerefractive spherical equivalent: +2.50 Postrefractive keratometry: 44.5 D, 45.0 D Average K: 44.75 D Axial length: 22.5 mm A constant: 118.4 IOL calculation using average K in SRK/T formula: For target goal: - 0.05 → +22.5 D Adjustment factor – (0.27 (+2.5) + 1.53) = – 2.21 Adjusted IOLavgK rounded to highest 0.5D: +20.5 D The Feiz-Mannis method of determining IOL power involves first determining the IOL power as if the patient had not undergone refractive surgery. The IOL power is calculated using prerefractive corneal power values and axial length before surgery. Then the induced change in refractive error is determined. This value divided by 0.7 is added to the prerefractive IOL power2. IOLpre = ΔRE/0.7 = IOLpost

IOLpre = IOL calculated using prerefractive keratometry ΔRE = stable postrefractive refractive error IOLpost = estimated IOL power after refractive surgery to be implanted The Feiz-Mannis nomogram3 can be utilized when the only information available is prerefractive surgery refractive error. The clinician can use the postrefractive keratometry and axial length to determine an IOL power. This IOL power is then adjusted based on the change in refraction induced by refractive surgery. The adjustment would be: 0.751 – (0.8632 x change in spherical equivalent) The Feiz-Mannis method and the back-calculated methods appear to produce accurate IOL calculations. However, for increasing amounts of prerefractive surgery hyperopia, these methods calculate a less powerful IOL. These methods require prerefractive keratometry and refraction. When this information is not available, there is a clear additional benefit in utilizing the Latkany regression formula that only requires pre-refractive spherical equivalent. Retrospective analysis yields 80% accuracy within 1 D of theoretic emmetropia. Almost half of the patients are within 0.5 D, and only 5% are > 2 D off.3 In order to validate these results clinically, more work needs to be done in a prospective study. To date, very little has been published regarding IOL calculation methods in patients whom have undergone hyperopic refractive surgery. While we are awaiting a more universal and accurate formula, the Latkany hyperopic regression formula offers a relatively accurate and simple method in dealing with posthyperopic refractive surgery cataract patients in IOL power determination. Until then, it is important to be aware of the new challenges that are presenting themselves in this new era where patients whom we have performed refractive surgery on for many years now desire cataract surgery and whose expectations for uncorrected visual acuity remain high. Patients need to be counseled regarding the potential need for additional surgery or glasses to achieve emmetropia.

REFERENCES 1. Hoffer, KJ. Calculating intraocular lens power after refractive corneal surgery. Arch Ophthalmol 2002;120:500-01. 2. Savini, G et al. Intraocular lens power calculation after myopic refractive surgery. Ophthalmology Aug 2006;113(8): 1271-82. 3. Feiz V, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a Standardized Approach. Cornea 2001;20(8):792-97.

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Mastering the Techniques of Intraocular Lens Power Calculations 4. Speicher, L. Intraocular lens calculation status after corneal refractive surgery. Curr Opin Ophthalmol 2001;12:17-29. 5. Seitz, B and Langenbucher, A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000;16(3):349-61. 6. Latkany, RA et al. Intraocular lens calculations after refractive surgery. J Cataract Refract Surg 2005;31:562-70. 7. Shammas, HJ, et al. Correcting the corneal power measurements for intraocular lens power calculations after myopic laser in situ keratomileusis. Am J Ophthalmol 2003; 136:426-32. 8. Wang, L et al. Comparison of intraocular lens power calculations methods in eyes that have undergone LASIK. Ophthalmology 2004;111(10):1825-30. 9. Rosa, N et al. A new method of calculating intraocular lens power after photorefractive keratectomy. J Refract Surg 2002; 18:720-24.

10. Ferrara, G et al. New formula to calculate corneal power after refractive surgery. J Refract Surg 2004;20:465-71. 11. Aramberri, J. Intraocular lens power calculation after corneal refractive surgery: Double-K Method. J Cataract Refract Surg 2003;29:2063-68. 12. Wang, L. Methods of estimating corneal refractive power after hyperopic laser in situ keratomileusis. J Cataract Refract Surgery 2002;28:954-61. 13. Chokshi, AR et al. Intraocular lens calculations after hyperopic refractive surgery. Ophthalmology 2007;114(11):2044-49. 14. Zeh WG, Koch DDD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903. 15. Holladay JT. Consultations in refractive surgery. Refract Corneal Surg 1989;5:203 [letter].

Which IOL Formula Use after Refractive SonjatoHairer, Tom Conze,Surgery Jerome Bovet (Switzerland)

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Which IOL Formula to Use after Refractive Surgery

INTRODUCTION Corneal refractive surgery is gaining in popularity as the method of choice for the correction of near sightedness in young adults. More patients in their 40s and 50s are now undergoing refractive corneal surgery in their quest to achieve emmetropia. A number of these patients will develop cataracts, and they will probably expect excellent uncorrected postoperative visual acuity, just like after their refractive surgery. However, early experience with eyes that had undergone refractive surgery has shown that the refractive predictability after cataract surgery is relatively poor.1-4 The corneal power has to be corrected after corneal refractive surgery, whether this surgery was radial keratotomy (RK), photorefractive keratectomy (PRK), or laser in situ keratomileusis (LASIK) (Table 33.1).

Corneal refractive surgery corrects refractive errors by modifying the anterior surface of the cornea. The problem appears years later when these patients develop cataracts and require lens extraction surgery and intraocular lens (IOL) implantation. The question arises about which should be the basis for calculating this lens implant. Being able to determine the accurate power of the IOL to be implanted in a patient undergoing cataract surgery is a big challenge, even more so when the patient has had prior refractive surgery. With standard intraocular lens (IOL) power calculations using the post-LASIK K readings (Kpost), the power of the implant used during cataract surgery is usually underestimated, resulting in a postoperative hypermetropic surprise. Different investigators have shown that after refractive surgery, the true value of the

Table 33.1: IOL calculation after refractive surgery

Type of Operation Without modification of K

Methods IOL Calculation

Hypermetropia postoperative: 3 to 6D Edema inside the line KR Regression after 3 months K error, 3 mm centralis, very variable

Corneal topography History

Can’t measure true corneal power Index of refraction of cornea changed.

Old method Estimate true corneal power (K) Fudge the target IOL power

Clear lens extraction Intracorneal ring Radial Keratotomy

With modification of K PRK-LASIK

With modification of biometry

Characteristic

Phake IOL

Contact lenses K-1

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Table 33.2: Methods IOL calculation for PRK-LASIK Old method

Oldest methods 1989: Clinical history method 1948: Contact lens method:

RC= Rxpre – Rxpo K = Kpre + RC K = B + P + Rcl – Rbare

Estimate true corneal power

With history

Clinical history Speicher (Selz) method Adjusted:

Without history

CL method Shammas Koch/Maloney topo Savini/Barboni/Zanini Ronje method Adjusted:

IR Savini Camelin Jarade

IR methods Ferrara

Rosa Oculus pentacam Zeiss OCT Fudge the target IOL power

With history

Without history

Felz-Mannis method Latkany method Masket method Wake Forest Method Aramberry double K method use prelasik K Aphakic methods lanchulev in OR refraction Mackool secondary IOL Aramberry double K method use 43D

corneal power is actually lower than the K readings measured by keratometry or by topography. Formulas for calculating the IOL power include multiple variables, but with the current standardized cataract surgery techniques, these are reduced to only three: lens constant, corneal diopter power and axial length of the eye. The lens constant is standard for each lens model; refractive corneal surgery does not change axial length;5-7 however, postrefractive surgery produces a significant change in corneal curvature. At present, the best system for measuring corneal curvature is computerized corneal topography, although this method overestimates the central diopter power of a flattened cornea resulting from corneal refractive surgery. Consequently, the IOL power calculation will depend primarily on how accurately the cornea’s central refractive power is calculated.8,9 The refractive success of cataract surgery in eyes with prior refractive corneal surgery will depend mainly on the ability to calculate the current keratometric power of

the cornea accurately. This requires knowledge of the patient’s ocular history before and after refractive surgery, as well as of the current ocular status Routine IOL power calculations in cataractous eyes that had undergone previous corneal refractive surgery have been very unpredictable. The IOL power is usually underestimated, resulting in a high incidence of postoperative unintentional hyper metropia.10,11 The history-derived method and the refraction-derived method to correct the corneal power require access to the refractive surgery data (pre-LASIK K readings and/ or amount of myopia corrected). In this chapter we will described the proposed methods for measurement the IOL power calculation formulas of axial length (Table 33.2).

HISTORY DERIVED METHOD The most accurate way to obtain the correct keratometric values is to use the history-derived method (also known as the clinical history method) where the myopic

Which IOL Formula to Use after Refractive Surgery correction achieved at the corneal plane is algebraically added to the prerefractive corneal power. However, this method requires knowledge of the prerefractive corneal power and the amount of myopic correction obtained with the refractive surgery. Care should be taken not to include in the calculations any myopic shift induced by the cataract. The problem arises when neither the preLASIK K readings nor the amount of myopia corrected are known. Many patients will not know or be able to obtain the preoperative refractive data when the cataract surgery is planned, which could be many years after LASIK.

ESTIMATE TRUE CORNEAL POWER WITHOUT HISTORY CL METHOD Trial Hard Contact Lens Method This method requires a plano hard contact lens12 with a known base curve and a patient with a cataract, which allows us to see the retinoscopy, shadows during the refraction. The patient’s spherical equivalent refraction is determined by normal refraction. The refraction is repeated with a hard contact lens in place. If the spheroequivalent refraction does not change with the contact lens, the patient’s cornea must have the same power as the base curve of the plano contact lens. If there is a hyperopic shift in the refraction, then the base curve of the contact lens is weaker than the cornea by the shift amount If the patient has a myopic shift, then the base curve of the contact lens is stronger than the cornea by the shift amount The appropriate algebraic formula for each case is then made, taking into account that spheroequivalent values greater than: t4.00 D must be converted to corneal plane. This method is limited by the accuracy of the refraction, which is in turn limited by the amount and type of the cataract.

the corneal fixation center and, therefore, outside the area of refractive treatment in many high myopic patients. The pentacam central measurement is better for the estimation on the true central keratometry.

FUDGE THE TARGET IOL POWER WITHOUT HISTORY MACKOOL SECONDARY IOL One of the simpliest method is to operate the cataracte, then at the end of the procedure when the patient is aphake to calculate exactly the refraction and to do the implantation in the same session or to wait one to three week to stabilize the cornea like we do for radial keratotomy.

USING A MODIFIED HOFFER Q FORMULA FOR IOL POWER CALCULATIONS AFTER LASIK15,16 The Hoffer Q formula has an advantage over the other formulas in these cases because it calculates a stronger power IOL for emmetropia than the other formulas in presence of a very flat cornea and it does not require a correction in its ELP calculations.

THE CONSENSUS-K TECHNIQUE FROM JB. RANDLEMAN17,18 The consensus-K technique from JB. Randleman generated refractive outcomes similar to those in the control group and was better than with all other K- or IOL-generating techniques (Fig. 33.1) except the classic refractive history method. The consensus method showed less variability and higher predictability than all other methods tested.

ESTIMATE TRUE CORNEAL POWER WITHOUT HISTORY KOCH/MALONEY TOPO CENTRAL K (CENTRAL KERATOSCOPE READING)13,14 Corresponds to the central topographic area within the central 3 mm of the cornea which coincides with the visual axis and whose value may be obtained from the center of the topographic map and the color code bar in diopters It is very important to bear in mind that rings 6, 7 and 8 are on the outer limit of the three central millimeters of

Fig. 33.1: IOL power calculation after LASIK: the concensus K method, J Brian Foster et al

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Refractive corneal surgery induces changes on the corneal surface and, consequently, in topographic readings. After refractive corneal surgery, corneal power may be calculated using the data of the patient’s refractive history. Comparisons between the keratometric values obtained with the refractive history method (“calculated K”) and the topographic data, allow us to conclude that the central keratometric value shown by topography (“central K”) is the closest to the calculated value. For this reason, they cannot reflect the true value of the central cornea or, in other words, the keratometric value of the center of the cornea. Therefore, in calculating the IOL, these topographic values would lead to an undercorrected power calculation, thus inducing a final hyperopic refractive error. Although the calculation method will continue to be used until the computerized system of modern videokeratoscopes allows us to obtain objective central keratometric values, topographic “central K” may be useful when the refractive history is not available. We recommend recording refraction values pre- and postrefractive surgery, corneal topography values and axial length measurements in all patients who will be subjected to corneal refractive surgery, in order to facilitate calculation of intraocular lens power in the future, when the patient requires cataract surgery. None of these formulas provide the desired result if the central corneal power is measured incorrectly. On the first day following cataract surgery, patients usually exhibit a hyperopic shift primarily due to transient postoperative corneal edema and intraocular pressure changes. These patients also exhibit the same daily fluctuation during the early postoperative period after cataract surgery. Because refractive changes are expected and vary significantly among patients, no lens exchange should be considered until after the first postoperative week or until after the refraction has stabilized, whichever is longer.

REFERENCES 1. LyleWA’, Jin GJ. Intraocular lens prediction in patients who undergo cataract surgery following previous radial keratometry. Arch Ophthalmol 1997;115:457-61.

2. Gimbel H, Sun R, Kaye GB. Refractive error in cataract surgery after previous refractive surgery J.Cataract Refract Surg 2000;26:142-44. 3. Koch DD, Liu J, Hyde LL, et al. Refractive complications of cataract surgery after radial keratotomy. AmJ OphthalmoI 1989;108:676-82. 4. Holladays JT. IOL Calculation following radial keratotomy surgery. Refractive and Corneal Surg 1989;5:36A. 5. Shammas HJ. Intraocular lens power calculations. In: Azar DT, ed. Intraocular Lenses in Cataract and Refractive Surgery. Philadelphia: WB Saunders, 2001;60-61. 6. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refractive Surg 1990;16(3):333-40. 7. Holladay JT, Prager TC, Chandler TY, Musgrove KH. A threepart system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. 8. Sanders DR, Koch DD, et al. Atlas of corneal topography. 1st edn. Thorofare, NJ: Slack Incorporated, 1993;209. 9. Kly’ce SD, Dingeldein SA. The topography of normal corneas. Arch OphthalmoI1989;107:512-18. J Cataract Refract Surg 1991;17:187-93. 10. Seitz B, Langenbucher A, Nguyen NX, Kus MM, Kuchle M. Underestimation of intraocular lens power for cataract surgery after myopic photorefractive keratectomy. Ophthalmology 1999;106:693-702. 11. SeitzB, Langenbucher. A Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000;16:349-61. 12. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903. 13. Feiz V, Mannis MJ, Garcia-Ferrer F, Kandavel G, Darlington JK, Kim E, Caspar J, Wang JL, Wang W. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a standardized approach. Cornea 2001; 20:792-97. 14. Odenthal MTP, Eggink CA, Melles G, Pameyer JH, Geerards AJM, Beekhuis WH. Clinical and theoretical results of intraocular lens power calculation for cataract after photorefractive keratectomy for myopia. Arch Ophthalmol 2002;120:431-38. 15. Hoffer KJ. The Hoffer Q formula: A comparison of theoretical and regression formulas. J Cataract Refract Surg 1993; 19:70012. 16. Hoffer KJ. The Hoffer-Q formula: a comparison of theoretic and regression formulas. JCataract Refract Surg 1993;19: 700-12. 17. Hamed AM, Wang L, Misra M, Koch D. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651-58. 18. Randleman JB, Foster JB, Loupe DN, Song CD, et al. Intraocular lens power calculations after refractive surgery: Consensus-K technique. J Cataract Refract Surg 2007; 33:1892-8.

Intraocular Lens Power Calculations after Advanced SurfaceDM, Ablations (ASA)IG (Greece) Tsiklis NS, Kymionis GD, Portaliou Pallikaris

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Intraocular Lens Power Calculation after Advanced Surface Ablations (ASA)

INTRODUCTION Advanced Surface Ablation (ASA) is the abbreviation for all surface ablation techniques. ASA is indicated for Myopic, Hyperopic and Astigmatic corrections. The epithelium in surface treatments can be removed with several ways. The oldest method is to scrape the epithelium off with a blade or a rotating brush.1, 2 Alternatively the epithelium can be removed with the laser (Transepithelial Keratectomy3) or the use of alcohol (LASEK4). Another approach is Epi-Lasik.5 With this method a blunt blade is used to remove the epithelium in a sheet. The sheet is replaced after the laser treatment and provides theoretically a natural shield over the treaded surface. Adjuvant, mitomycin C (MMC) could be used after the laser ablation. The application of MMC minimizes the incidence of haze formation and improves the quality of patients’ vision.6-8 The main advantages of ASA over Laser in Situ Keratomileusis (LASIK) is that it is a less invasive, safer procedure with fewer complications and less induced high order aberrations since there is no corneal flap.9-14 On the contrary, LASIK offers faster vision rehabilitation and less postoperative pain.15-17 As the refractive surgery comes to maturity, an important issue is raised: how to calculate the exact power of the Intraocular Lens for these patients when undergo a cataract surgery. The main problem to calculate the exact IOL power is the changes in normal corneal anatomy. During excimer laser treatment, selective removal of corneal tissue results in a change of the corneal thickness and curvature.18 The anterior surface of the cornea becomes flatter (after a myopic treatment) or steeper (after a hyperopic treatment), while the posterior surface remains almost unchanged in

uncomplicated cases19. Therefore, after corneal refractive surgery (CRS) the ratio between anterior and posterior curvature alters significantly while the central corneal thickness decreases, approximately 10 μm/D of correction. Contact ultrasound techniques are unable to detect such small changes in axial length and this inevitably lead to a 0.30D to 0.50D error in IOL power calculation in an eye of average axial length. Thus, more accurate devices using non-contact ultrasound techniques and the IOL Master should be preferred. Moreover, manual keratometers and topography units can not measure anterior corneal curvature accurately after CRS. Both instruments make assumptions about the corneal anatomy that no longer exist. First, they assume that the cornea is a spherical surface and second, they reduce corneal power (P) by using anterior corneal curvature (r) and an “effective” index of refraction (n) according to the formula: P = (n - 1)/r The index of refraction is 1.3375 in most keratometers and topographers, based on the assumption that the posterior surface has a radius of curvature that averages 1.2 mm less than the anterior curvature20. This correlation is no longer valid after laser refractive surgery. Besides that, the use of the postrefractive surgery keratometry readings will lead to an inaccurate estimation of the Effective Lens Position (ELP). This is true for most IOL calculation formulas except the Haigis formula. As a result of these inaccuracies the measured keratometric values for previously myopic patients are usually higher than the actual power, leading to hyperopic results. On the contrary, after a hyperopic refractive

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surgery, the keratometric power is usually underestimated leading to overestimation of IOL power and subsequently, a myopic result. In order to overcome those problems and measure the appropriate IOL power for cataract surgery in post-ASA patients, a variety of methods have been developed. Some of them are quite successful, but none can be characterized as the “perfect” or “ideal” method. Ideally the “perfect” method should provide the correct corneal power measurement, independent from the availability of perioperative data. Such method does not exist yet.

For example REF preop -4.50D (vertex distance 12 mm) at the corneal plane is -4.50 / (1-[0.012x -4.50]) = -4.26D. The Double K method can be applied in other available modalities for the IOL power calculations improving the final outcome.

Requiring Preop Keratometry and Preop Refraction

Feiz-Mannis Formula

Requiring Preop Keratometry and Preop, Postop Refraction

The Feiz–Mannis Formula is a method with high predictability that can be used when preoperative keratometry and refraction are available. It is relied on the assumption that for every diopter of change in IOL power the change in refractive power is 0.7D, achieved at the spectacle plane24. This is due to position of the IOL behind the iris as opposed to the spectacle plane with a vertex distance of 12 – 13 mm.

Clinical History Method

The corresponding equation is:

PROPOSED METHODS All the current proposed methods can be subdivided into the following categories:

It is considered the gold standard method in the issue of IOL calculation after ASA but refractive surprises cannot be excluded. The advantage of this method of calculation is that a direct measurement of the post-refractive corneal power can be obviated, but it requires preoperative information. The corneal power (K) can be calculated by the following equation: K = K preop + (REF preop – REF postop) 21, 22 where K preop is the preoperative corneal power, REF preop is the preoperative refraction and REF postop is the postoperative refraction. The refraction should be performed at a stable time after refractive surgery (e.g. six months postoperatively) to avoid the influence of refraction by nuclear sclerosis of the crystalline lens. For example if preop K is 43.00D, REF preop is -4.50D and REF postop is - 0.50D then K= 43.00 + [-4.50 + (-0.50)] = 39.00D.

Double K Method One way to ensure even greater accuracy and to avoid hyperopic surprises is to use the preoperative keratometry to determine the effective lens position and the postoperative keratometry to determine the IOL power with the vergence formula.23 The main advantage is that the spherical equivalent is obtained at the corneal plane with optimum results.

K = preop K ± (preop REF /0.7) where preop K is the preoperative keratometry and preop REF the preoperative refraction (attempted correction). The IOL power for emmetropia can be calculated by adding (for myopic corrections) or subtracting (for hyperopic corrections) the preoperative refraction divided by 0.7 to the preoperative keratometry. For example if preop K is 41.00D and preop refraction is -4.00D then K = 41.00 + (4.00/0.7) = 46.71D If preop refraction is + 4.00D then K = 41.00 – (4.00/ 0.7) = 35.285D The main drawback of this method is that it can lead to underestimation in eyes with high myopic or hyperopic corrections. If that’s the case, it is recommended to aim for a final refraction of ±0.50D to avoid under/over corrections. The Double K method is not applicable in the Feiz Mannis Formula.

Requiring Preoperative Keratometry

Separate Consideration of Anterior and Posterior Corneal Curvatures (Seitz and Speicher) This method can give efficient results only with the availability of the preoperative keratometry. It is based on

Intraocular Lens Power Calculations after Advanced Surface Ablations (ASA) the assumption that the anterior and the posterior corneal power when added give the total refractive power.25, 26 P = Pa + Pp = (n2-n1)/r1 + (n3-n2)/r2 where P is the total refractive power, Pa the anterior refractive power, Pp the posterior refractive power and n1, n2, n3 are the refractive indexes of air (1), cornea (1.376) and aqueous humor (1.336) respectively. The power of the anterior corneal curvature can be calculated preoperatively and postoperatively by the following equation: Pa = Sim – K × 1.114 Sim – K is the simulated keratometry reading given by a computerized videokeratography system and 1.114 corresponds to 376/337.5. The power of the posterior corneal curvature can be easily calculated as the difference between the total and the anterior surface corneal power Pp = Pa – P = (Sim – K × 1.114) – Sim – K In order to obtain the real corneal power (K) and not the one altered by the refractive surgery the formula mentioned below must be used K = postop Pa + preop Pp = postop Sim – K × 1.114 + [(preop Sim – K × 1.114) - preop Sim – K. For example if preop Sim – K is 40.00D and postop Sim – K is 38.00D then K = (38.00 × 1.114) + [(40.00 × 1.114) – 40.00] = 42.332 + 2.332 = 46.892D This method can be further improved when the Double – K method is applied. Another significant advantage is that it doesn’t require stable postoperative refraction. The separate consideration of anterior and posterior corneal curvatures is not widely used so there are not many comparative studies in order to be evaluated meticulously.

Requiring Preoperative Refraction

Corrected Refractive Index of Refraction It is clear that the standard keratometric index (n=1.3375) used when calculating an IOL in order to translate into diopters the anterior corneal curvature is not applicable in eyes that have undergone refractive surgery. After ASA both corneal eccentricity (the measure of corneal asphericity) and ratio between anterior and posterior corneal surface curvature change leading to incorrect

measurements. Different proposals aim in providing high precision in the calculation of the corrected refractive index. Camellin27 and associates proposed the calculation of a relative refractive index (Nrel) Nrel = 1.3319 + 0.00113 × SIRC where SIRC is the surgically induced refractive change. Savini28 and associates suggest that the postoperative surgery index of refraction (Postop in.ref) can be calculated by the formula Postop in. ref. = 1.338 + 0.00009856 × SIRC Once the corrected refractive index is known the corneal power (P) is given by the following equation: P = n-1/r where n is the corrected refractive index, 1 is the refractive index of the air and r the corneal radius. The application of the Double K method is possible.

Not Requiring Preoperative Data When preoperative data of the patient is not available, it is very difficult to measure accurately the corneal power after any refractive surgery. There are several proposals from many investigators but none of them is considered as a reliable method.

Contact Lens Over-refraction The contact lens over-refraction procedure starts with a manifest refraction that determines the spherical equivalent. Then a plano hard contact lens with a known base curve is applied and a second manifest refraction is performed. If the refraction does not change after the lens trial, it is presumed that the cornea has the exact same power as the contact lens.29-34 If the refraction is more myopic or hyperopic the corneal power is lower or higher than the base curve of the contact lens. The corneal power (K) can by calculated as follows: K = BCL + DCL + (ORCL - MR) where BCL is the contact lens base curve, DCL is the contact lens power, ORCL is the contact lens overrefraction and MR is the manifest refraction. For example, if BCL is 8.7mm, DCL is 40.00D, ORCL is +1.00D and MR is +0.50D then K = 40.00 + [+1.00 – (+0.50)] =40.50D. The main question that arises is whether it is possible to have patient collaboration and consequently accurate measurements, when the visual acuity is low (less than 20/80) due to cataract formation.34 This is a serious limitation of this method.

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Mastering the Techniques of Intraocular Lens Power Calculations It is possible to apply the Double K method to ensure greater accuracy of this method.

Separate Consideration of Anterior and Posterior Corneal Curvature Methods (Savini-Barboni-Zanini, Maloney, Koch) It is a variable of the method by Seitz and Speicher 25, 26 described earlier when the preoperative keratometry is missing. Instead of calculating the postoperative posterior corneal curvature power a fixed value is used. According to Savini-Barboni-Zanini this value is -4.98D and according to Maloney and Koch is -6.10D.28, 33, 34 The equations are: K = postop Pa + (-4.98) = postop Sim – K × 1.114 – 4.98 K = postop Pa + (-4.98) = postop Sim – K × 1.114 – 6.10 K is the original corneal power and postop Pa the anterior corneal curvature Power. For example if postop Sim – K is 44.50D then K = (44.50 × 1.114) – 4.98 = 44.593D or K = (44.50 × 1.114) – 6.10 = 43.473D Double – K method is applicable here and it is strongly recommended.

Aphakic Refraction Technique (Ianchulev, Mackool, Leccisotti) An empiric model for IOL estimation is to calculate the IOL power after removal of the crystalline lens and before the implantation. Ianchulev and associates used a portable Retinomax Autorefractor (Nikon) to perform aphakic retinoscopy at a vertex distance of 13.1 mm in the operating room with excellent results.35 The procedure added only 3 - 4 minutes operating time and the IOL power was next calculated by the formula P = 2.01449 × AR + (A-118.84) where AR is the aphakic refraction and A the constant for intended IOL type. For example if AR is 10.00D then P = 2.01449 × 10.00 + (A) = 20.14D. Mackool and associates suggested that manifest aphakic refraction should be held in an examing room 30 minutes after surgery and IOL insertion approximately 1 hour after the crystalline lens removal. The IOL power (P) was calculated based on the Mackool algorithm.35 P = 1.75 × AR + (A-118.84) where AR is the aphakic refraction and A the constant for intended IOL type.

For example if AR 5.50D then P = 1.75 × 5.50 + (A) = 9.625D. Mackool’s method is quite accurate but it can cause great inconvenience for the patient that has to leave the operating room and return back after an hour. Leccisotti36 performed intraoperative autorefraction after crystalline lens removal and used 2 different equations in order to convert spherical equivalent refraction into IOL power. For myopias less than -4.75D he used the Iachulev formula37. P = 2.01449 × AR + (A-118.84) For myopias more than -4.75 he used a different formula36 P = 1.3 × AR + 1.45 For example if AR is 7.00 D then P = 1.3 × 7.00 + 1.45 = 10.55D Leccisotti discovered that the relation between intraoperative autorefraction and IOL power for emmetropia can be expressed by a parabolic function: y = 0.07x2 + 1.27x +1.22 where x is the independent variable (AR) and y the dependent variable (IOL power). This function proves that there are different linear regression formulas for different myopic ranges. Double K method is not applicable.

Gaussian Optics (Orbscan II, Pentacam) A lot of approximations are applied in all the methods used to calculate the IOL power. The Gaussian optics formula when applied can determine the original corneal power (P) without any assumptions, since posterior corneal curvature can be measured directly. The corresponding equation is: P = P1 + P2 – (d/n) × (P1 × P2) where P1 is the power of the anterior corneal surface, P2 is the power of the posterior corneal surface, d the corneal thickness and n the refractive index of air (1). This equation can be transformed into P = (n1-n)/r1 + (n2-n1)/r2 – (d/n1) × [(n1-n)/r1] × [(n2-n/r2)] × 1000 where r1 and r2 are the radius of curvature of the anterior and posterior corneal curvature, n1 the refractive index of the anterior corneal surface (1.376) and n2 the refractive index of the posterior corneal surface (1.336).

Intraocular Lens Power Calculations after Advanced Surface Ablations (ASA) Only the Orbscan II38 (Bausch&Lomb, Rochester NY) and the Pentacam39 (Oculus Optikgeräte, GmbH, Wetzlar Germany) can measure directly the r2 of the posterior curvature, but it is very difficult to verify the accuracy of these values. The Gaussian optics formula without any adjustments can lead to underestimations of the corneal power compared with the clinical history method or the data from videokeratography in non operated eyes.

CONCLUSION In conclusion, all the current methods described herein have their advantages and disadvantages. None of them is the ideal method. They majority of them have limited clinical application and need further investigation, while others (clinical history method) are already been used in the everyday practice of ophthalmology with fairly good results. Finally, patients who are candidates for cataract extraction after refractive surgery must be informed that IOL calculation is still inaccurate and there might be a need for a second procedure to achieve the desired refraction. Refractive surgeons should provide all their patients with a “wallet card” of their preoperative keratometry, refraction and a postoperative stable refraction.

REFERENCES 1. Trokel SL, Srinivasan R, Braren B. Excimer laser surgery of the cornea. Am J Ophthalmol 1983;96:710-15. 2. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg 1988;14:46-52. 3. Clinch TE, Moshirfar M, Weis JR, Ahn CS, Hutchinson CB, Jeffrey JH. Comparison of mechanical and transepithelial debridement during photorefractive keratectomy. Ophthalmology 1999;106:483-89. 4. Lee JB, Seong GJ, Lee JH, Seo KY, Lee YG, Kim EK. Comparison of laser epithelial keratomileusis and photorefractive keratectomy for low to moderate myopia. J Cataract Refract Surg 2001;27:565-70. 5. Pallikaris IG, Katsanevaki VJ, Kalyvianaki MI, Naoumidi II. Advances in subepithelial excimer refractive surgery techniques: Epi-LASIK. Curr Opin Ophthalmol 2003;14: 207-12. 6. Majmudar PA, Forstot SL, Dennis RF et al. Topical Mitomycin-C for subepithelial fibrosis after refractive corneal surgery. Ophthalmology 2000;107:89-94. 7. Maldonado MJ. Intraoperative MMC after excimer laser surgery for myopia. Ophthalmology 2002;109:826. 8. Gambato C, Ghirlando A, Moretto E, et al. Mitomycin C modulation of corneal wound healing after photorefractive keratectomy in highly myopic eyes. Ophthalmology 2005; 112:208-18. 9. Epstein D, Frueh BE. Indications, results, and complications of refractive corneal surgery with lasers. Curr Opin Ophthalmol 1995;6:73-78.

10. Rajan MS, Jaycock P, O’Brart D, et al. A long-term study of photorefractive keratectomy; 12-year followup. Ophthalmology 2004;111:1813-24. 11. Kymionis GD, Tsiklis N, Pallikaris AI, et al. Fifteen-year follow-up after LASIK: case report. J Refract Surg 2007;23:937-40. 12. Alió JL, Muftuoglu O, Ortiz D, et al. Ten-year Follow-up of Laser in Situ Keratomileusis for High Myopia. Am J Ophthalmol 2008;55-64. 13. Ambrósio R, Wilson S. LASIK vs LASEK vs PRK: Advantages and indications. Semin Ophthalmol 2003;18:2-10. 14. Moreno-Barriuso E, Lloves JM, Marcos S, et al. Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing. Invest Ophthalmol Vis Sci 2001;42:1396-403. 15. Pallikaris IG, Papatzanaki ME, Stathi EZ, et al. Laser in situ keratomileusis. Lasers Surg Med 1990;10:463-68. 16. Tahzib NG, Bootsma SJ, Eggink FAGJ, et al. Functional outcomes and patient satisfaction after laser in situ keratomileusis for correction of myopia. J Cataract Refract Surg 2005;31:1943-51. 17. Solomon KD, Fernandez de Castro LE, Sandoval HP, et al. Refractive surgery survey 2003. J Cataract Refract Surg 2004;30:1556-69. 18. Seiler T, McDonnell PJ. Excimer laser photorefractive keratectomy. Surv Ophthalmol 1995;40:89-118. 19. Wilson SE, Klyce SD, McDonald MB, et al. Changes in corneal topography after excimer laser photorefractive keratectomy for myopia. Ophthalmology 1991;98:1338-47. 20. Holladay JT. In discussion of Determining the power of an intraocular lens to achieve a postoperative correction of 1.00D. Refract Corneal Surg 1989;5:202-03. 21. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg 1995;11:490-93. 22. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double-K method. J Cataract Refract Surg 2003;29:2063-68. 23. Rosa N, Capasso L, Lanza M. Double-K method to calculate IOL power after refractive surgery. J Cataract Refract Surg 2005;31:254-55. 24. Feiz V, Mannis MJ, Garcia-Ferrer F, et al. Intraocular lens power calculation after laser in situ keratomileusis for myopia and hyperopia: a standardized approach. Cornea 2001; 20:792-97. 25. Seitz B, Langenbucher A. Intraocular lens power calculation in eyes after corneal refractive surgery. J Refract Surg 2000;16:349-61. 26. Speicher L. Intra-ocular lens calculation status after corneal refractive surgery. Curr Opin Ophthalmol 2001;12:17-29. 27. Camellin M, Calossi A. A new formula for intraocular lens power calculation after refractive corneal surgery. J Refract Surg 2006;22:187-99. 28. Savini G, Barboni P, Zanini M. Correlation between attempted correction and keratometric refractive index of the cornea after myopic excimer laser surgery. J Refract Surg 2007;23: 461-66. 29. Ridley F. Development in contact lens theory. Trans Ophthalmol Soc UK 1948;68:385-401. 30. Soper JW, Goffman J. Contact Lens fitting by Retinoscopy Ed. Soper JW. In: Contact Lenses Stratton Intercontinental Medical Book Corp. New York: NY 1974;99. 31. Zeh WG, Koch DD. Comparison of contact lens over-refraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903. 32. Haigis W. Corneal power after refractive surgery for myopia: contact lens method. J Cataract Refract Surg 2003;29:

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Mastering the Techniques of Intraocular Lens Power Calculations 1397-1411. Erratum in: J Cataract Refract Surg 2003;29:1854. 33. Wang L, Booth MA, Koch DD. Comparison of intraocular lens power calculation methods in eyes that have undergone LASIK. Ophthalmology 2004;111:1825-31. 34. Savini G, Barboni P, Zanini M. Intraocular lens power calculation after myopic refractive surgery: theoretical comparison of different methods. Ophthalmology 2006;113:1271-82. 35. Mackool RJ, Ko W, Mackool R. Intraocular lens power calculation after laser in situ keratomileusis: Aphakic refraction technique. J Cataract Refract Surg 2006;32: 435-37.

36. Leccisotti A. Intraocular lens calculation by intraoperative autorefraction in myopic eyes Graefes Arch Clin Exp Ophthalmol 2007. 37. Ianchulev T, Salz J, Hoffer K, et al. Intraoperative optical refractive biometry for intraocular lens power estimation without axial length and keratometry measurements. J Cataract Refract Surg 2005;31:1530-36. 38. Cheng AC, Lam DS. Keratometry for intraocular lens power calculation using Orbscan II in eyes with laser in situ keratomileusis. J Refract Surg 2005;21:365-68. 39. Elbaz U, Barkana Y, Gerber Y, et al. Comparison of different techniques of anterior chamber depth and keratometric measurements. Am J Ophthalmol 2007;143:48-53.

JT Lin (Taiwan) 231

The Mathematics of LASIK

35

The Mathematics of LASIK

INTRODUCTION The combined technologies of scanning laser, eye tracking, topography and wavefront sensor advance the corneal reshaping (the refractive surgery) one step further from the conventional ablation of spherical surface to the customized ablation of aspherical surface. Therefore, the theory (or mathematics) behind LASIK is also expanded from the simple paraxial formula to the high-order nonlinear formulas involving the change of the corneal asphericity and the LASIK-induced surface aberrations. This Chapter provides a summary of the classical and modern formulas with comprehensive examples to illustrate the application or clinical aspects of LASIK. The mathematics (formulas) for the following subjects (principles) is covered: • Refraction power of human eye including corneal and lens and the definition of refractive error. • Ablation rate of LASIK. • Mixed (compound) astigmatism • Bifocal (or presby-LASIK). • LASIK ablation profiles for both spherical and aspherical surface. • Second-order (paraxial) and high-order approximation. • Prediction and control of corneal asphericity. Greater detail of the derivations of the formulas presented in this Chapter may be found in the cited references. A related subject of vision correction using IOL can be found in a separate book Chapter by Lin (The mathematical handbook of IOL).

REFRACTION POWER Total power of a natural human eye (Lin, 2005)

P = Dc + ZP’ (1) Z = 1 – S(Dc/1336). Corneal power Dc = 377/r1 – 41/r2 + at (2) Lens power P’= 84 (1/R1 – 1/R2) – bT (3) Corneal power is also related to the keratometry power (K) by Dc=1.117K-41/r1. Where S is the effective anterior chamber depth given by S=ACD+2.4 mm for a typical lens thickness of 4.0 mm; and refractive indexes of 1.377, 1.42 and 1.336, respectively, for the cornea, lens and aqueous (vitreous). (r1, r2) and (R1, R2) are the (anterior, posterior) surface radius for the cornea and lens, respectively (in mm). The small correction term due to the corneal thickness bt is about 0.25% of Dc (may be ignored for t=0.5 mm), but the lens thickness term (-bT) about 1.5% of P’ can not be ignored (since T=4.0 mm).

REFRACTIVE ERROR (D) In LASIK procedure, the refractive error is defined by the difference of the preoperative (R) and postoperative (R’) front surface radius of the cornea D = 377(1/R – 1/R’),

(4)

where D in diopter (or 1/m) and R and R’ in mm, therefore (as shown by Fig. 35.1) myopia (D < 0), R’ > R, hyperopia (D > 0), R’ < R. EXAMPLE (for preoperative R = 7.7 mm), see (Fig. 35.1). D -1 -5 -10 0 +2 +5 +10 R’

8.0

8.6

9.7

7.7

7.4

7.0

6.4

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232

Fig. 35.1: The corneal post-LASIK front surface radius vs. refraction correction power (D), for initial radius R = 7.7 mm

LASIK ABLATION RATE Given the laser fluence (F, in mJ/cm2) or energy (E) per unite area and repetition rate (Rp, in Hz), the ablation rate (A) is proportional to their product, or A ~ Rp(F-F*),

(5)

where F* is the threshold fluence (about few mJ/cm2) depending on the corneal surface condition. Therefore the LASIK procedure time (per diopter correction) is inverse proportionally to A, that is, T~1/A, or T’=T/D ~ 1/(F-F*)Rp ~ (E-E*)Rp/ s2,

(6)

where s is the laser spot size (diameter) and E is the laser energy per pulse (in mJ). For example: for T’=3 seconds, for a typical set of parameter (Rp, F, s)=(100 Hz, 200 mJ/ cm2, 1.0 mm), the proportional formulas of T’ gives us: T’ = 1.5 second, for fixed F, but s=2.0 mm or higher repetition rate of Rp=200 Hz. T’ = 6.0 second, for lower Rp=50 Hz, or lower (F-F*)= 100 mJ/cm2, or smaller beam spot s=0.71 mm. A more rigorous formula for Eq.(5) is given by, for A being the ablation depth per pulse (Deutsch, 1983) F/F* = exp(-aA),

(7)

where a is the absorption coefficient of the cornea (stroma) at 193 nm, about 2.9 (1/um) and F* is about 60 mJ/cm2.

Other factors may influence A or T include: • Re-absorption of the laser energy by the tissue plume • Corneal (or stroma) hydration level • Non-normal incident angle of the beam (in peripheral area) • PMMA calibration reading error • Ablation nomogram (or algorithm) used in the system (to be detailed later). Most of the manufacturers of LASIK systems use a fudge factor (m) to clinically adjust the conversion between in the PMMA power and the corneal correction power with m=(0.3 to 0.35) depending on laser systems and algorithm used. For example, -5.0 diopter in PMMA ablation corresponding to about -1.5 diopter in actual corneal power change, that is, the corneal tissue ablation rate is about 3 times of the PMMA. This m-factor may smear out part of the factors affecting the ablation rate or errors from algorithms.

BIFOCAL (PRESBY-LASIK) The corrections powers of Table 35.1 below are based the following general formulas developed by Lin (unpublished) for general case of (spherical, presbyopia)=(a, NA), where NA=near addition. For CM: W(ring) needs D=a (to achieve plano at peripheral) and W(center 4.0 mm) needs D’=a+NA (for Table 35.1: Strategies of presbyopia-LASIK using either a center-myopia island (CM) or peripheral-myopia ring (PM) to see both near and far

Preoperative cases

Correction diopter (zone size) PM CM

(a) Plano NA* = +2.0 D

+2.0 (W = 7.0) - 2.0 (W = 4.0)

+2.0 (W = 4.0) No Wring needed

(b) Hyperope +1.0 NA = +3.0 D

+4.0 - 3.0

+1.0 (Wring) +4.0 (W =4.0)

(c) Myope -2.0 D NA = +3.0 D

+3.0 - 5.0

-2.0 +1.0

(d) Myope -4.0 D NA = +2.0 D

+2.0 -6.0

-4.0 -2.0

* NA stands for the near addition power of a presbyopic eye. ** Each treatment consists of two steps: for PM, a large (W=7.0 mm) followed by a small (W=4.0 mm) zone correction; for CM, a ring-zone Wring (4/7 mm) followed by a central zone W = 4.0. CM has the advantage of less tissue removed comparing to PM, however, it may suffer worse contrast (Lin, 2006).

The Mathematics of LASIK myopia to see near) which corrects with the spherical error and presbyopia (or NA). For PM: W(7.0 mm) to see near needs D = a + NA (if a > 0), NA (if a < 0); and D’ (for W = 4.0 mm to achieve plano) = NA (if a > 0), (a – NA) (if a < 0).

ASPHERICITY COMPARISON The difference of shape factor (dP) or asphericity (dQ) between CM and PM depends on the areas of the cornea. A. Central zone (within W = 4.0 mm) The net refractive error pf PM is given by a (for both a > 0 and a < 0), whereas CM has (a + NA). Therefore, the p-factor difference, defined as dp = p’(PM) may be derived from Eq.(4.a) with C defined by a (for PM) and (a+NA) (for CM) as follows: (dp)/p = 0.0408(NA) – 0.0612[(a+NA)2 – a2], where NA>0 (the presbyopia near addition power), therefore dp>0, or CM always has a smaller p-factor (or more prolate) than PM (Figs 35.2 and 35.3) B. Peripheral zone (between W=4.0 to 7.0 mm) In this area, CM has the refractive error of D1=a and PM has D2 = (a+NA) (for a > 0), NA (for a < 0). The refractive error difference is D12 = D1 – D2 = a – (a+NA) (for a > 0), or D12 = (a – NA)(for a < 0). Therefore, dp = 0.0408 d12 – 0.0612(D12 – D22). In contrast to the central zone, the peripheral zone shows p’(CM)>p’(PM), that is, the CM has less prolate than PM in the peripheral, as opposed to the central zone.

Fig. 35.3: Same as Figure 35.2, but for fixed ablation zone (W = 6.0 mm) at different myopic-power changed for single-zone (A) and multi-zone (B)

Above formulas allow us to calculate dp for all the cases shown in Table 35.1. Case (a) (b) (c) (d) ——————————————————————— (dp/p) (A) -0.08 -0.1 -0.13 -0.09 (B) +0.08 +0.1 +0.2 +0.26 ——————————————————————— +(A) for central zone, (B) for peripheral zone Comparisons of CM and PM for the corneal shape and spherical aberration (SA) is summarized as follows. CM PM Corneal shape (A) Central large small (degree of prolate) (B) Peripheral small large ——————————————————————— Spherical aberration (A) Central small large (B) Peripheral large small The above comparison implies that CM offers better image quality (by smaller SA) in the central zone for near, but worse than PM in the peripheral zone far vision whereas the reversed benefits offered by PM.

MIXED ASTIGMATISM

Fig. 35.2: Central ablation depth (Ho) in myopic-LASIK vs. ablation diameter (W) for a given correction of -5.0 D, where (A) for paraxial approximation and (B) for high-order increased by (1+C)

It was known that (Lin, 1994) the strategy of using positive cylinder correction (followed by spherical) for the treatment of compound (mixed, toric) astigmatism and benefiting less corneal tissue removal and faster procedure.

233

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234

The corneal shape change of the above 2-step sequential ablation (with correcting powers of D and D’) is given by the formulas below. As shown in Table 35.2, case (a) and (b) are equivalent having the same SE; and (c) = (d). They are converted by the formula for a general case of [spherical, Cylinder, Angle], noting that the negative and positive cylinder are rotated by 90 degrees. Shape factor (P) change: (P = Q+1, Q=asphericity) Δ = -2B(1-1.5 B)P, (8) Δ > 0 (less prolate, after myopic LASIK) Δ < 0 (more prolate, after hyperopic LASIK) B = (D’ + D)R/377, (9) R = preoperative corneal front surface radius D and D’ = correction power in sequential ablation Table 35.2: Converting mixed astigmatism Conversion formula: [a, b × A1] = [1+b, -b x(A1 - 90)] Spherical equivalent (SE) = (a+b)/2 (a)[+5.0, -3.0 × 180] = (b) [+2.0, +3.0 × 90] (SE = +3.5) (c)[-3.0, -2.0 × 180] = (d) [-5.0, +2.0 × 90] (SE = -4.0)

LASIK ABLATION NOMOGRAM Spherical Surface • Paraxial (second-order): hyperopia: H(y) = 4 Dy2/3 myopia: H’(y) = H(y) – H(d) • High-order hyperopia: H”(y) = H(1+C) myopia: H”(y) = H”(y) - H”(d) where: C = 0.19 (W/r1)2 is the high-order term d = ablation radius (in mm) W= ablation zone (W=2d)

(10.a)

(10.b)

a. Central ablation depth of single-zone H’o = H’ (y=0) = -(DW2/3) (1 + C) (11) • For fixed W=6.0 mm (C=0 case) D -2 -5 -10 (in diopter) ———————————————————— H’o 24 60 100 (in um) • Effect of ablation diameter (W) (for fixed D= -5.0 diopter, C=0) W (mm) 4.0 5.0 6.0 6.5 —————————————————— H’o (um) 26.7 41.7 60.0 70.4 • Effect of high-order term (C) (for r1 = 7.7 mm, or K = 43.2 D): W (mm) 6.0 6.5 7.0 —————————————— C (%) 11.2 13.2 16.5

b. Central ablation depth for multi-zone Ho (3-zone) = Rd Ho (single-zone), where the reduction factor Rd=(0.70 to 0.85) depending on the algorithms used which define the power and radius of each zone. For example, comparing to a single zone with W=6.5 mm, a multizone depth will reduces to 71.6% (or Rd=0.716) when a smaller inner zone of 5.5 mm is used.

Aspherical Surface a. Conicoid surface Z(y) = [R – (R2 –py2)1/2]/p (12) where: Z: distance along the optical axis y: distance from the optical axis R: vertex radius of the corneal front surface P: shape-factor, P=Q+1. Q: corneal asphericity, Q=P-1. b. Polynomical expansion of Z(y) Z(y) = Zo + Z2 + Z4 + Z6 + ......

(13)

c. LASIK ablation profile Hyperopia: H(y) = Z(R’, p’, y) – Z(R, p, y) = H2 + H4 + H6 + ···• (14) Myopia: H’(y) = H(y) – H(d) (15) 2 H2 = (4D/3)y (16) H4 = (1/8R3)y4(p-Bp’) H6 = (1/16R5)y6 (p2-B5/3 p’2) B = (R/R’)2 d. Central depth (myopia) Ho = -(DW2/3)(1+C’), (17) C’ = 0.19p(W/R)2, which reduces to that of spherical case when p=1.0 (or Q=0) e. Superposition two LASIK procedures with correction power of D1 and D2 may be calculated by f12=f1+f2 defined as follows (Lin, 2006). f1(y) = -(1.33D1)(d2-y2) + (C1/8R3)(d4-y4), (18.a) f2(y) = (1.33D2)y2 – (C2/8R3)y4, C1 = p1-Bp2, C2 = p2-Ap3, B = (R/R’)3, A = (R’/R”)3, Therefore the combined ablation profile f12 = Z0 (1-aCd2) + 1.33D12 (1-aC’y2), C = (p1-Bp2)/D1 C’ = (p2-Ap3)/D12 a = 3/(32R3) and Zo = -4Dd2/3.

(18.b)

The Mathematics of LASIK Asphericity Control

Correlated Case The shape factor post-LASIK (p’=Q’+1) is correlated to its initial (or preoperative) value (p) by p’ = (R’/R)mp = Mp, M = 1/(1+RD/377)m, = 1/(1+0.0204 D)m, for typical R=7.7 mm.

(19.a) (19.b)

where the m-power depends on the ablation algorithms used: m = 2 (for nth-order approx of Lin.) m = 3 (for second-order approx of Jimenez.) m = (4.5 to 6.0) (fit to measurements)* * For 30% adjusted area m=2 cases For myopia (R’>R): p’ > p (more prolate) For hyperopia (R’Q*

Myopic

PRO OB

Less PRO —————

OB more OB

Hyperopic

PRO OB

more PRO PRO

————less OB

*where Q* is a transition value defined by when Q’=0. Shorthand notations used: PRO for prolate and OB for oblate (referred to Figs 35.4 and 35.5).

If p’ and p are not correlated, particularly for actual LASIK procedures in which the ablation rate (and profile) affected by biomechanical factors, then the ablation for hyperopiaLASIK is given by H(y) = H2(y) + H4(y) + Hcontrol, (20) = H2 (1+C’) + Hcontrol Hcontroly) = M(dp), (21) M = y4/(8R3), C’ = (3p/4R2)y2

235

236

Mastering the Techniques of Intraocular Lens Power Calculations For corneal radius of (post-LASIK) r=(7.2, 7.7, 8.2) mm, M = (27.1, 22.2, 18.4) microns for per 1.0 change of p (at y=3.0 mm). The Hcontrol is the extra ablation profile to generate the desired extra change (decrease, dp < 0, if Hcontrol > 0) of the corneal shape factor (or asphericity Q) such that the cornea becomes more prolate to minimize the positive spherical aberration of the whole eye.

SURFACE ABERRATION As shown in Table 35.4, optical aberration may be defined by the Zernike polynomials which are similar to the expansion coefficients of the Z(y) defined by Eq. (13) and (14) Table 35.4: Summary of optical aberration defined by Zernike coefficients (A) Monochromatic Defocus (second-order) Coma (third-order) Spherical (fourth-order) Field curvature (second-order) Astigmatism (second-order) Distortion (first-order) (B) Chromatic Longitudinal, Transverse (1) Seidel Aberration (surface contribution, relaxed eye) Cornea (+80%, -10.4%), cornea-lens separation (-5.6%) Lens (+13.1%, +22.9%), total power 60.29 diopter. For (r1, r2) = (7.8, 6.5), (R1, R2) = (10.5, 6) and S = 6(all in mm) (2) Typical aspherical data (Q-value) for (front, back) surface Cornea (-0.3, -0.66), ideal surface Q=-0.527 Lens (-0.94, +0.96), for relaxed eye (Louis and Brennar)

a. For a given final state asphericity (Q’) and corneal anterior surface radius R2, the prime spherical aberration (PSA) is given by (Manns et al, 2000) Sj = Wjb4, (22.a) W1 = -0.046 (0.535 + Q’)/R3, (22.b) where j=1, 2, 3, 4 stands for the PSA of anterior and posterior surface of the cornea and lens, b is the ray height on the corneal surface. Therefore, the change of corneal PSA is given by dS1 = 0.046(b4/R3)(dp’), b. Change of shape-factor in (p’=Q’+1) dp’ = dH/M’ M’ = 0.263B(d4-y4),

(22.c) (23.a) (23.b)

where dH is the ablation depth change. As an example, for d = 3.0 mm and D1 = – 2.0 diopter, B = 0.882, M’ = (16.4, 13.3) microns at y = (1.0, 2.0) mm. Therefore, the PSA change due to corneal shape change at y = 2.0 mm, and for post-myopic LASIK radius of R = 8.15 mm as an example, dS1 = 0.244(dH), or a positive PSA increase of

0.244 microns per 1.0 micron corneal surface ablation depth which causes the increase of the corneal asphericity. This is in consistent with the reported data that induce positive PSA were found in myopic LASIK procedures. The calculated value of M’ is also consistent with that of Manns et al (2002). c. Refractive error (De) of myopic-shift induced by corneal positive SA for optimal image (Atchison and Smith, 2000) (24.a) De = -2Wb2, W = (198.6 + 376Q)/R3 (24.b) For typical value of W=+0.038, De=-0.29 diopter at pupil diameter (b) of 6.0 mm comparing to b=2.0 mm. The ideal corneal surface with W=0 gives Q=Q*= -0.528 as seen from above formula.

CONCLUSION The formulas presented in this Chapter for LASIK procedures are based on the available, published articles. They may be revised, updated or even corrected by further newer developments.

BIBLIOGRAPHY 1. Anera R, Jimenez JR, Barco LJ. Equation for corneal asphericity after corneal refractive surgery. J Refract Surg 2003;19:65-69. 2. Anera RG, Jimenez JR, Barco LJ, Hitta E. Change in corneal asphericity after laser refractive surgery, including reflection loss and nonnormal incidence upon the anterior cornea. Opt Lett 2003;15:417-19. 3. Atchison DA, Smith G. Optics of the human eye. Boston, MASS: Butterworth Heinemann 2000. 4. Avalos G, Silva A. Presbyopia LASIK-the PMMA technique. In: Agarwal A. ed. Presbyopia, a surgical textbook. Thorofare NJ: SLACK; 2004;139-46. 5. Azar DT, Primack JD. Theoretical analysis of ablation depths and profiles in laser in situ keratomileusis for compound hyperopic and mixed astigmatism. J Cataract Refract Surg 2000;26:1123-36. 6. Cantu R, Rosales MA, Tepichin E, et al. Objective quality of vision in presbyopic and non-presbyopic patients after pseudoaccommodative advanced surface ablation. J Refract Surg 2005(Suppl.);21:S603-05. 7. Deutsch TF, Geis MW. Self-developing UV photoresist using excimer laser exposure. J Appl Phys 1983;54:7201-04. 8. Gatinel D, T Hoang-Xuan, Azar D. Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model. Invest Ophthalmol Vis Sci 2001;42:1736-42. 9. Jimenez JR, Anera RG, Diaz J, Diaz A, Perez-ocon F. Corneal asphericity after refractive surgery when the Munnerlyn formula is applied. J Opt Soc Am (A) 2004;21:98-103. 10. Lee H, Oh JR, Reintein DZ, et al. Conservation of corneal tissue with wave-front-guided laser in situ keratomileuse. J Cataract Refract Surg 2005;31:1153-58. 11. Lin JT. Multiwavelength solid state laser for ophthalmic applications. Proc SPIE 1992;1644:266-75.

The Mathematics of LASIK 12. Lin JT. Mini-excimer laser corneal reshaping using a scanning device. Proc SPIE 1994;2131:228-36. 13. Lin JT. Scanning laser technology for refractive surgery. In: Garg et al. Mastering the techniques of corneal refractive surgery. New Delhi, India, Jaypee Brothers 2005;20-36. 14. Lin JT. Critical review on refractive surgical lasers. Opt. Engineer. 1995;34:668-75. 15. Lin JT. Bifocal profiles and strategies of presbyopic-LASIK for pseudo-accommodation. J Refract Surg 2006;22:736-38. 16. Lin JT. A new formula for ablation depth in 3-zone LASIK. J Refract Surg 2005;21:413-14. 17. Lin JT. The generalized refractive state theory and effective eye model. Chinese J Optom and Ophthal 2005;7:1-6.

18. Lin JT. Prediction and control of corneal asphericity after refractive surgery. J Refract Surg 2006;22:848-49. 19. Lin JT. A New Algorithm for Controlling Corneal Asphericity in LASIK. In: Garg A. Lin JT. Ed. “Mastering the Techniques of LASIK, EPILASIK and LASEK (Techniques & Technology)”. New Delhi: Jaypee Brothers, 2006. 20. Manns F, Ho A, Parel JM, Culbertson W. Ablation profile for wavefront-guided correction of myopia and primary spherical aberration. J Cataract Refract Surg 2002;28:766-74. 21. Pinelli R, Ngassa N, Scaffidi E. Sequential ablation approach to the correction of mixed astigmatism. J Refract Surg 2006;22:787-94.

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Preoperative Evaluation of the Anterior Chamber for Phakic IOLs with the AC OCT

INTRODUCTION Today, the increasingly popular development of phakic implants as well as the FDA agreement obtained for the VERISYSE implant, means that a very precise preoperative evaluation of the dimensions of the anterior chamber is essential. Axial measurements are evaluated with ultrasonography (A-scan, B-scan),1,2 with optical procedures (Slit Lamp,3 IOL Master,4). The relationship between different eye structures can be studied in reduced areas with ultrasonography (A-scan, B-scan, ultrasound biomicroscopy (UBM),5 and posterior segment optical coherence tomographer.6 The Scheimpflug technique7 gives a complete image of the anterior chamber, but the complex and inaccurate mathematical reconstructions make it difficult to evaluate the anterior segment precisely. The disparities in the obliquity of the cross sectional and projection plane of photographic images can sometimes lead to measurements being obtained through extrapolation. It is only recently that complete axial cross sections of the anterior segment are possible with ultra high frequency ultrasound equipment (ARTEMIS)8 and with the anterior chamber optical coherence tomography (AC OCT).9 Not only is the OCT simple to use but it is possible to obtain a very precise analysis of anterior segment modifications during accommodation and ageing of the eye. Development of this new imaging technique has enabled us not only to show that in certain cases there is a possibility of contact between a phakic implant and the anatomical structures of the eye but also to evaluate the internal dimensions of the anterior chamber with precision.

Optical Coherence Tomography Technology for the Anterior Chamber Today, the AC OCT with its 820 nm wavelength, is a wellknown posterior segment imaging device,6 and by 1994 Izatt et al9 had already suggested using it for anterior segment imaging. It was only in 2001, with the introduction of a high speed AC OCT using a 1310 nm wavelength that good quality, easy to interpret images, were obtained.10,11 Analysis of the eye is a non-contact procedure during which the patient fixes an optical target. The target’s focus can be adjusted with positive or negative lenses to compensate the patient’s spherical ametropia and obtain images of the eye unaccommodated. The target can be defocussed by using negative lenses to induce natural accommodation of the studied eye. There is no undue pressure on the anterior segment because there is no contact, the images are obtained in just a few seconds and only modifications to the studied eye are taken into account under physiological conditions. This examination is therefore very different from the ultrasound explorations which require stimulation of the fellow eye or the Scheimpflug technique where pilocarpine drops are used to obtain an artificial accommodation. The image acquisition system provides a video image of the examined zone and stores the last seven images taken at a rate of 8 frames per second. At the end of the examination, the images are reviewed by the examiner and only the best shots are retained. The chosen image is then interpreted with specific software which re-adjusts the dimensions of the images by eliminating the distortions induced by corneal optical transmission differences. After reconstruction of the

Preoperative Evaluation of the Anterior Chamber for Phakic IOLs with the AC OCT image, all the required anterior chamber measurements can be done: anterior chamber diameter, anterior chamber depth, corneal pachymetry, crystalline lens radius of curvature, crystalline lens thickness, irido-corneal angle opening. The prototype’s resolution is approximately 14 µm. The infra-red light beam is stopped by the pigments, therefore a satisfactory view of the different structures situated behind the epithelium pigment layer of the iris or of the anterior uvea is not possible.

Interest of the AC OCT and the Study of Accommodation when Implanting Phakic IOLs

Measurement of the Anterior Chamber’s Internal Diameter One of the key points in improving anterior chamber anglesupported implant tolerance lies in correctly adapting its size with the anterior chamber’s internal diameter. Until today, we had to rely on approximate measuring methods, such as white-to-white, sometimes improved by using a graduated plastic sizer when inserting the implant. However, these measuring means are relatively inaccurate and do not give a precise evaluation of the anterior chamber’s diameter. Figure 36.1 clearly demonstrates the interest of this type of anterior segment preoperative imaging (AC OCT, Scheimpflug, ultra high frequency ultrasound) to evaluate the internal diameter dimensions before surgery.

Fig. 36.2: In 74 percent of normal non-operated eyes, the vertical diameter is greater than the horizontal diameter (Courtesy: Elsevier)

large diameters. The average difference is approximately 300 µm (Fig. 36.2), which is more than the examination measuring or reproducibility error which is not more than 50 µm. In the future, this phenomenon must be taken into account in order to chose the implant. The largest diameter must be taken into account when choosing an anglesupported implant. Indeed, if one chooses an implant with an overall diameter equal to the eye’s horizontal diameter, which is generally the smaller of the two diameters, there is a risk that the implant rotates or is unstable. On the contrary, to avoid implant rotation and ensure its stability, it is essential that the implant is fitted both in size and orientation to the largest diameter, i.e. generally the vertical one. This is to avoid an implant that is too big being placed on the smaller diameter which would inevitably lead to oversizing and pupil ovalization.

Endothelium Safety Distance

Fig. 36.1: Aspect/dimension of the anterior segment photographed with the AC OCT (Courtesy: Elsevier)

We were surprised12 when we compared the anterior chamber’s diameter on the 0°, 45°, 90° and 135° axes. The vertical diameter appeared larger than the horizontal diameter in 74 percent of the cases. The mean difference between the vertical and horizontal axis is more significant for eyes with small diameters than eyes with

Retrospective studies have shown that a 1.5 mm distance must be respected between the edge of the IOL’s optic and the corneal endothelium. This minimum safety distance avoids the risk of endothelial cell loss secondary to contact between the implant and the endothelium in particular when the patient rubs his eyes. Anterior segment imaging software should therefore include this safety distance. Studying accommodation and crystalline lens ageing13,14 has shown that the crystalline lens increases in volume with age and during accommodation. Developing software that simulates anterior segment distortions with the variations of the crystalline lens volume should allow us to define a safety-free zone in the anterior chamber where the optic of the implant should

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Fig. 36.3: Endothelial safety distance (Courtesy: Elsevier)

Fig. 36.5: Forward thrust of crystalline lens with ageing

be situated in order to reduce the risk of complications, because of contact with the endothelium or with the crystalline lens (Fig. 36.3).

In a previous work,13 we demonstrated that because the crystalline lens thickens with age, there is a forward movement of its anterior pole which reduces the depth of the anterior chamber by 18 to 20 µm per year. As the iridocorneal angle recesses remain fixed, the crystalline lens distorts and pushes the iris forward modifying its relationship with an angle-supported implant and or iris fixated implant. We also found16 that with ARTISAN phakic implants, there was an unusually high percentage (6%) of pigment dispersions in hyperopes. This has been confirmed by Saxena and Landesz.17 In this study, we measured the distance between the crystalline lens’ anterior pole and the line represented by the horizontal internal diameter of the anterior chamber (Fig. 36.6). In subjects having developed pigment dispersion, this rise was much higher than average. If the crystalline lens rise is above 600 µm, there is a 75 percent risk of developing pigment dispersion (Fig. 36.7) and this complication can lead to removal of the implant and even extraction of the crystalline lens. If the crystalline lens rise is known on the day of surgery, as well as the statistical forward movement of the crystalline lens, it is possible to estimate the ARTISAN implant tolerance period knowing

Possibility of Contact Crystalline Lens/Implant Having studied numerous series of phakic implants,15 we were able to show evidence of contact of different models of implants with the crystalline lens. Having dilated a hyperopic patient with an ARTISAN implant, we discovered a contact between the lower edge of the implant and the crystalline lens. Likewise, during accommodation, the posterior face of a hyperopic patient’s PRL phakic implant came into contact with the crystalline lens. In a patient implanted 10 years ago with an anglesupported IOL, we noticed that the crystalline lens came into contact with the implant’s posterior face because the crystalline lens had increased in volume with age (Fig. 36.4). These different elements should encourage manufacturers to include in their software the profiles of the different implants available so as to be able to simulate their position in the anterior segment either accommodated or unaccommodated. Simulating anterior segment ageing would give us an indication of how long an implant will be tolerated (Fig. 36.5).

Fig. 36.4: Contact between a ZB5M implant and the crystalline lens 10 years after implantation (Courtesy: Elsevier)

Fig. 36.6: Crystalline lens rise. Distance between anterior pole of the crystalline lens and the line connecting two angle recesses at 3 o’clock and 9 o’clock (Courtesy: Elsevier)

Preoperative Evaluation of the Anterior Chamber for Phakic IOLs with the AC OCT

Fig. 36.7: Diagram: Crystalline lens rise vs AC depth. Eyes having developed pigment dispersion are displayed in red (Courtesy: Elsevier)

Fig. 36.9: AC OCT anterior segment cut of an ARTISAN implant in a case of pigment dispersion. Note: the presence of iris pigments between the crystalline lens and the implant and flattening of iris (Courtesy: Elsevier)

that the critical level is around 600 µm according to the following formula:

T = number of safe years, S = danger level in microns, F = rise measured in microns on the day of examination, Δ = yearly reduction of anterior chamber or yearly progression of crystalline lens’ anterior pole in microns (Figs 8.8 and 8.9). This notion of the crystalline lens rise should also be applied to angle-supported anterior chamber implants. The implant’s vault measures the implant’s posterior face rise with regards to the baseline joining the tip of the implant’s footplates. It is therefore easy to understand that if the crystalline lens has a rise equal to or superior to

Fig. 36.10: Different anterior chamber safety distances measured from the angle recess to recess baseline (Courtesy: Elsevier)

the implant’s vault, there will be contact between the posterior face of the implant and the crystalline lens. It is necessary today to take into account the implant’s vault and the crystalline lens rise when considering surgery to know whether an angle-supported anterior chamber implant is indicated or not and for how many years it will be tolerated. We consider this notion to be just as essential as anterior chamber depth. To ensure safe anterior chamber implantation, endothelial safety distances as well as crystalline lens safety distances must be respected. With ageing, endothelial safety distances remain constant whereas the distance between implant and crystalline lens gradually decreases over the years (Fig. 36.10).

Can Anterior Segment Imaging Indicate that One Particular Implant is Preferable Over Another? Fig. 36.8: Clinical aspect of pigment dispersion behind an ARTISAN implant (Courtesy: Elsevier)

Studying accommodation in an albino patient18 showed that all the structures of the anterior uvea were malleable

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and mobile. The only stable elements of the anterior segment are the cornea and the uvea insertion at the corneoscleral junction, that is to say the iridocorneal angle; the iris, the sulcus, the ciliary body and the crystalline lens show significant modifications during accommodation. In our opinion, these elements define the irido-corneal angle as the most stable structure and the least affected by accommodation. This could be another fact in favour of angle-supported implants, as long as the problem of pupil ovalizations has been definitely solved as they are the result of inaccurate preoperative measurements. Studying the ciliary body and the sulcus in an albino patient showed evidence of important diameter variations of these two structures during accommodation.18 In its present state, the Visante™ OCT technology does not allow us to routinely study the posterior chamber in a normal subject. Liliana Werner et al studied the internal diameter of the anterior chamber on 20 phakic and pseudophakic cadaver eyes with the ARTEMIS (L Werner et al. Poster ASCRS San Diego 2004, Poster SFO Paris 2004, oral communication AAO/ISRS Subspecialty Day Meeting New Orleans 2004) and found, as we did, that in most cases, the anterior chamber’s internal vertical diameter and the sulcus’ vertical diameter were statistically larger than their horizontal diameters. More recently, in a patient with an ICL and having developed bilateral cataract, we were able to establish that the patient had a very high crystalline lens rise (Fig. 36.11). This complication is probably due to the forward thrust of the crystalline lens, Gonvers19 demonstrated that in ICL patients, the risk of cataract dramatically increased with age.

SUMMARY In the light of these studies, it appears that the AC OCT or other similar techniques (Scheimpflug, ultra high frequency ultrasound) available in everyday practice are going to become essential when scheduling a phakic implant in a patient where LASIK is contraindicated. Static and dynamic study of the anterior segment as well as new software are going to become necessary to simulate the anatomical relationship of the implant and the anterior chamber during accommodation and ageing. The safety distances required in the anterior segment will be specified and we will probably be able to predict a safety period during which the implant will be well-tolerated and after which it will probably be necessary to remove it.

Fig. 36.11: High crystalline lens rise in a patient having developed cataract after an ICL (Courtesy: Elsevier)

REFERENCES 1. Kurtz D, Manny R, Hussein M. COMET study group. Variability of the ocular component measurements in children using A-scan ultrasonography. Optom Vis Sci 2004;81,1: 35-43. 2. Hamidzada WA, Osuobeni EP. Agreement between A-mode and B-mode ultrasonography in the measurement of ocular distances. Vet Radiol Ultrasound 1999;40,5:502-07. 3. Krogsaa B, Fledelius H, Larsen J, et al. Photometric oculometry. II. Measurement of axial ocular distances with slit-lamp microscopy. Clinical evaluation and comparison with ultrasonography. Acta Ophthalmol (Copenh). 1984;62,2:290-99. 4. Sheng H, Bottjer CA, Bullimore MA. Ocular component measurement using the Zeiss IOLMaster. Optom Vis Sci 2004;81,1:27-34. 5. Mishima HK, Shoge K, Takamatsu M, et al. Ultrasound biomicroscopic study of ciliary body thickness after topical application of pharmacologic agents. Am J Ophthalmol 1996;121,3:319-21. 6. Puliafito C, Hee MR, Schuman JS, et al. Optical Coherence Tomography of Ocular Diseases, Thorofare NJ Slack Inc, 1996. 7. Boker T, Shequem J, Rauwolf M, et al. Anterior chamber angle biometry: A comparison of Scheimpflug photography and ultrasound biomicroscopy. Ophthalmic Res 1995;27 Suppl 1:104-09. 8. Kim DY, Reinstein DZ, Silverman RH, et al. Very high frequency analysis of a new phakic posterior chamber intraocular lens in situ.Am J Ophthalmol 1998;125,5: 725-29. 9. Izatt JA, Hee MR, Swanson EA, et al. Micrometer-scale resolution imaging of the anterior eye in vivo with optical coherence tomography. Arch Ophthalmology 1994; 112,1,584-89. 10. Radhakrishnan S, Rollins AM, Roth JE, et al. Real-time optical coherence tomography of anterior segment at 1310 nm, Arch Ophthalmology 2001;119,8:1179-85. 11. Huang D, Swanson EA, Lin CP, et al. Optical Coherence Tomography. Science 1991;254:1178-81. 12. Baikoff G, Bourgeon G, Jitsuo Jodai H, et al. Evaluation of the measurement of the Anterior Chamber’s internal diameter and depth: IOLMaster vs AC OCT. J Cataract Refract Surg (submitted). 13. Baikoff G, Lutun E, Ferraz C, et al. Static and dynamic analysis of the anterior segment with optical coherence tomography. J Cataract Refract Surg 2004; 30:1843-50. 14. Koretz J, Strenk S, Strenk L, Semmlow J. Scheimpflug and high-resolution magnetic resonance imaging of the anterior segment: A comparative study. J Opt Soc Am 2004;21: 346-54.

Preoperative Evaluation of the Anterior Chamber for Phakic IOLs with the AC OCT 15. Baikoff G, Lutun E, Ferraz C. Contact between 3 phakic intraocular lens models and the crystalline lens: An anterior chamber optical coherence tomography study. J Cataract Refract Surg 2004;30:2007-12. 16. Baikoff G, Bourgeon G, Jitsuo Jodai H, et al. Pigment dispersion and Artisan implants. The crystalline lens rise as a safety criterion. J Cataract Refract Surg (submitted). 17. Saxena R, Landesz M, Noordzij B, Luyten G. Three-year follow-up of the Artisan phakic intraocular lens for hypermetropia: Ophthalmology 2003;110:1391-95.

18. Baikoff G, Lutun E, J Wie, Ferraz C. Anterior chamber optical coherence tomography study of human natural accommodation in a 19-year-old albino. J Cataract Refract Surg 2004;30:696-701. 19. Gonvers M, Bornet C, Othenin Girard P. Implantable contact lens for moderate to high myopia: Relation of vaulting to cataract formation. J Cataract Refract Surg 2003;29(5): 918-24.

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Biometry for Refractive Lens Surgery

INTRODUCTION Axial length measurement remains an indispensable technique for intraocular lens power calculation. Recently, partial coherence interferometry has emerged as a new modality for biometry.1 Postoperative results achieved with this modality have been considered “analogous” to those achieved with the ultrasound immersion technique.2 Reportedly “user-friendly” and less dependent on technician expertise than ultrasound methods, non-contact optical biometry is, however, limited by dense media, e.g., posterior subcapsular cataract. A second limitation of the optical method is the lack of a lens thickness measurement, which is a required variable in the Holladay II IOL power calculation software, version 2.30.9705. On the other hand, according to Holladay, the lens thickness can be estimated by the formula 4.0 + (age/ 100). Also, optical biometry can provide keratometry measurements, obviating the need for a second instrument. Immersion ultrasound has long been recognized as an accurate method of axial length measurement, generally considered superior to applanation ultrasound techniques.3 , 4 The absence of corneal depression as a confounding factor in measurement reduces the risk of inter-technician variability in technique. In addition to having a short learning curve, immersion ultrasound has no limitations in terms of media density and measurement capability. On the other hand, optical biometry may be superior in eyes with posterior staphyloma because of more precise localization of the fovea. We have compared axial length measurements obtained by optical biometry using the IOLMaster (Zeiss Humphrey Systems, Jena, Germany) with measurements obtained by immersion ultrasound using the Axis II

(Quantel Medical, Clermont-Ferrand, France). We have also examined the post-operative refractions of patients undergoing cataract extraction with posterior chamber intraocular lens implantation to determine the accuracy of the immersion ultrasound technique. Fifty cataractous eyes underwent preoperative axial length measurement with both the Axis II and the IOLMaster. For the Axis II immersion technique the Praeger shell was employed. Patients were placed in a sitting position in an examination room chair with the head reclined gently against the headrest. The average “Total Length” reported by the unit was entered into the Holladay II IOL power calculation formula. For the IOLMaster the selected axial length with the highest signal to noise ratio was used as the basis for comparison. The measured axial lengths were plotted and a linear regression trendline fit to the data. The Pearson correlation coefficient was determined to assess the relationship between the immersion and the optical measurements according to the formula ρ = 1/(1 - n) Σ ((x – μ)/s)((y – μ)/s). Keratometry was performed with the IOLMaster. The three reported sets of values were compared for consistency and correlated with the axis and magnitude of the eye’s preoperative astigmatism. Either an averaged value of three measurements or of the two closest measurements (in case one measurement appeared to be an outlier) was entered into the formula. In selected cases autokeratometry (HARK 599, Zeiss Humphrey Systems, Jena) and/or computerized corneal topography (EyeSys Technologies, Houston) were utilized to better delineate the preoperative keratometry. The corneal white-to-white diameter was determined with the Holladay-Godwin Corneal Gauge.

Biometry for Refractive Lens Surgery One surgeon (IHF) performed all surgery. The Holladay II IOL power calculation formula was used to select the intraocular lens for implantation in each case. This program automatically personalized the surgeon’s A constant during the course of the study. To provide uniform results, the Collamer IOL (CC4204BF, Staar Surgical, Monrovia, CA) was implanted in all 50 eyes. The surgical technique has been previously described.5 Briefly, a temporal clear corneal incision is followed by continuous curvilinear capsulorhexis, cortical cleaving hydrodissection and hydrodelineation, and nuclear disassembly utilizing horizontal chopping with high vacuum and flow but very low levels of ultrasound energy. The intraocular lens is inserted into the capsular bag via an injection device. All patients underwent autorefractometry (HARK 599, Humphrey Zeiss Systems, Jena) and subjective manifest refraction 2 -3 weeks postoperatively. Only eyes obtaining 20/30 or better best-corrected visual acuity were included in the study. The post-operative refraction was then entered into the Holladay IOL Consultant (Holladay Consulting, Inc., Bellaire, TX). Utilizing the Surgical Outcomes Assessment Program (SOAP) the spherical equivalent prediction error was measured and analyzed.

AXIAL LENGTH MEASUREMENTS The axial length measurements obtained with the Axis II and the IOLMaster correlated very highly (Pearson correlation coefficient = 0.996, Fig. 37.1). The mean of the

axial lengths measured by immersion was 23.40 (range 21.03 to 25.42), while the mean of the optically measured axial lengths was 23.41 (range 21.13 to 25.26). Technicians noted that immersion measurements required five minutes, while optical measurements required about one minute.

SURGICAL OUTCOMES ASSESSMENT The Holladay IOL Consultant report reflects a personalized A constant of 119.365 (ACD 5.512), as compared to the manufacturer’s suggested constant of 119.0 (ACD 5.55). The frequency distribution of postoperative spherical equivalent prediction error reveals that 48% of eyes precisely achieved the targeted refraction. The cumulative distribution graph demonstrates that 92% of eyes measured within ±0.5 D of the targeted refraction, and 100% of eyes measured within ± 1.00 D of the targeted refraction (Fig. 37.2). The mean absolute error measured 0.215 D, while the mean error of – 0.105 reflected the trend toward myopia. The near perfect correlation of immersion ultrasound and optical coherence biometry measurement techniques indicates the high level of accuracy of both of these methodologies. Our high rate of achieving the targeted refraction by utilizing immersion ultrasound measurements and the Holladay II formula compares favorably with previously reported results. For example, Haigis achieved accurate prediction within ± 1.00 D in 85.7% of

Fig. 37.1: Comparison of axial length measurements with immersion ultrasound (abscissa) and optical coherence interferometry (ordinate). The linear regression trendline reflects the very high correlation between the two sets of values

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Fig. 37.2: Holladay IOL consultant surgical outcomes analysis. Introduction

eyes by utilizing immersion ultrasound.2 Additionally, Sanders, Retzlaff and Kraff have indicated that achievement of about 90% of eyes within ± 1.00 D of the targeted refraction and a mean absolute error of approximately 0.5 D represents an acceptable outcome.6 Technicians report that the immersion ultrasound method with the Praeger shell is well tolerated by patients and relatively easy to learn. Its applicability to all types of cataracts and its ability to generate a phakic lens thickness represent significant advantages, especially for surgeons who utilize the Holladay II calculation formula.

KERATOMETRY AFTER KERATOREFRACTIVE SURGERY Intraocular lens power calculations for cataract and refractive lens exchange surgery have become much more precise with the current theoretical generation of formulas and newer biometry devices.7 However, intraocular lens power calculation remains a challenge in eyes with prior keratorefractive surgery. The difficulty in these cases lies in determining accurately the corneal refractive power.8 10

In a normal cornea standard keratometry and computed corneal topography are accurate in measuring four sample points to determine the steepest and flattest meridians of the cornea, thus yielding accurate values for the central corneal power. In irregular corneas, such as

those having undergone radial keratotomy (RK), laser thermal keratoplasty (LTK), hexagonal kerototomy (HK), penetrating keratoplasty (PKP), photorefractive keratectomy (PRK) or laser in situ keratomileusis (LASIK), the four sample points are not sufficient to provide an accurate estimate of the center corneal refractive power. 11 Traditionally there have been three methods to calculate the corneal refractive in these eyes.12 These include the historical method, the hard contact lens method, and values derived from standard keratometry or corneal topography. However, the historical method remains limited by its reliance on the availability of refractive data prior to the keratorefractive surgery. On the other hand, the contact lens method is not applicable in patients with significantly reduced visual acuity.13 Finally, the use of simulated or actual keratometry values almost invariably leads to a hyperopic refractive surprise.14 It has been suggested that using the average central corneal power rather than topography derived keratometry may offer improved accuracy in IOL power calculation following corneal refractive surgery.15 The Effective Refractive Power (Eff RP, Holladay Diagnostic Summary, EyeSys Topographer, Tracey Technologies, Houston, TX) is the refractive power of the corneal surface within the central 3mm pupil zone, taking into account the Stiles-Crawford effect. This value is commonly known as the spheroequivalent power of the cornea within the 3 mm pupil zone. The Eff RP differs from simulated

Biometry for Refractive Lens Surgery keratometry values given by topographers. The simulated K-readings that the standard topography map gives are only the points along the 3mm pupil perimeter, not the entire zone. As with standard keratometry, these two meridians are forced to be 90 degrees apart. The higher the discrepancy between the mean simulated K-readings and the Eff RP, the higher the degree of variability in the results of intraocular lens calculations.9 Aramberri recently reported the advantages of using a “double K” method in calculating IOL power in postkeratorefractive surgery eyes.16 Holladay recognized this concept and implemented it in the Holladay IOL Consultant in 1996. 17 The Holladay II IOL power calculation formula (Holladay IOL Consultant, Jack Holladay, Houston, TX) uses the corneal power value in two ways: first, in a vergence formula to calculate the refractive power of the eye, and second, to aid in the determination the effective lens position (ELP). The formula uses a total of 7 variables to estimate the ELP, including keratometry, axial length, horizontal white-towhite measurement, anterior chamber depth, phakic lens thickness, patient’s age and current refraction. The Holladay II program permits the use of the Eff RP as an alternative to keratometry (Alt K) for the vergence calculation. For the ELP calculation the program uses either the K-value entered as the Pre-Refractive Surgery K or, if it is unknown, 43.86, the mean of the human population (personal communication, Jack Holladay, February 3, 2004). We performed a retrospective analysis of all patients in our practice who underwent cataract or refractive lens exchange surgery after incisional or thermal keratorefractive surgery in whom the Eff RP and Holladay II IOL calculation formula were utilized for IOL power determination. Between 2/23/00 and 10/28/02, a total of 20 eyes met these criteria. Fourteen eyes had undergone radial keratotomy, three eyes hexagonal keratotomy, and three eyes laser thermokeratoplasty with the Sunrise Sun1000 laser (Sunrise Technologies, Fremont, CA). Preoperative evaluation included a complete ophthalmic examination. Axial length measurements were performed with the IOL Master (Carl Zeiss Meditec, Dublin, CA). The protocol for axial length measurements with the IOL Master allowed up to 0.15 mm of variation within 10 measurements of one eye and up to 0.20 mm of variation between the two eyes, unless explained by anisometropia. The signal to noise ratio was required to read 1.6 or better, and a tall, sharp “Chrysler Building” shaped peak was preferred. If any of these criteria were

not met the measurements were repeated with immersion ultrasonography (Axis II, Quantel Medical, Bozeman, MT). The corneal white-to-white distance was measured with a Holladay-Godwin Gauge in the initial 14 eyes, and with the newly available frame grabber software on the IOL Master in the final 6 eyes. The phakic lens thickness was estimated as 4 plus the patient’s age divided by 100 (e.g., a 67 year old patient’s lens thickness was estimated as 4.67) or determined by immersion ultrasonography. The Holladay II formula was used for all IOL power calculations (Holladay IOL Consultant, Bellaire, TX). “Previous RK” was set to “Yes,” and the Eff RP value from the Holladay Diagnostic Summary of the EyeSys Corneal Analysis System was input in the “Alt. K” area. This procedure instructs the formula to use the Eff RP value in place of standard keratometry for the vergence calculation. In no case was the pre-refractive surgery keratometry known, so the formula used 43.86 as the default value to determine the effective lens position. The “Alt. K” radio button was highlighted, and the Eff RP value was printed on the report as a confirmation that the formula had utilized it in the calculation. In every case the targeted post-operative refraction was emmetropia. Preoperative astigmatism was addressed at the time of cataract or lens exchange surgery by means of limbal relaxing incisions performed with the Force blade (Mastel Precision Surgical Insturments, Rapid City, SD) as described by Gills18 and Nichamin.19 In general, withthe- rule corneal astigmatism equal to or greater than 1.00 D and against-the-rule corneal astigmatism equal to or greater than 0.75 D were considered appropriate for correction. The surgical technique, including clear corneal cataract extraction with topical anesthesia and the use of power modulations in phacoemulsification, has been described previously.20 8 eyes of 5 patients received the Array SA 40 multifocal IOL (AMO, Santa Ana, CA), 5 eyes of 3 patients received the AQ2010V (STAAR Surgical, Monrovia, CA), both eyes of 1 patient received the CLRFLXB (AMO, Santa Ana, CA), both eyes of 1 patient received the SI 40 (AMO, Santa Ana, CA) and 1 eye of 1 patient each received the CeeOn Edge 911A (Pfizer, NY, NY), the Tecnis Z9000 (Pfizer, NY, NY) and the Collamer CC4204BF (STAAR Surgical, Monrovia, CA). The deviation of the achieved postoperative spherical equivalent from the desired postoperative goal for each eye was determined. Each group of keratorefractive

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Mastering the Techniques of Intraocular Lens Power Calculations patients was also analyzed separately. The differences between the Eff RP value and the corneal refractive power derived from the corneal topographer and autokeratometer were also analyzed. All data were placed in an Excel spreadsheet and statistical analyses were performed. In the RK group, the number of radial incisions ranged from four to twenty, with the majority having eight incisions. Fifty percent of the RK patients had astigmatic keratotomy performed in addition to radial keratotomy. For all eyes, the mean duration from intraocular lens surgery to the last postoperative refraction was 6.73 months (range 1 to 24 months). The RK group had the longest follow up, averaging 9.25 months (range 2.5 to 24 months). The mean deviation from the calculated postoperative refractive goal for all patients was 0.13 ± 0.62 D (range – 1.49 to 1.03 D). The difference from the postoperative refractive goal for each group of keratorefractive eyes was 0.27 ± 0.51 D for the RK group, -0.07 ± 0.44 D for the LTK group and -0.32 ± 1.10 D for the HK group. The targeted versus achieved spherical equivalent correction is shown in Figure 37.3. A linear regression equation fitted to the data, Achieved Correction = 0.9266 (Targeted Correction) + 0.1233 D demonstrates the slightly hyperopic trend in achieved spherical equivalent correction. All eyes achieved a

postoperative refraction within 1.5 D of emmetropia, and 80% were within 0.50 D of emmetropia (Fig. 37.4). The mean difference between standard automated keratometry readings (IOL Master, Carl Zeiss Meditec, Dublin, CA) and the Effective RP values was 0.01 ± 0.66 D (range –1.5 to 2.00 D). These results are shown in Fig. 37.5. Within the individual groups, the difference was 0.12 ± 0.65 D (range 0.47 to 2.00 D) for the RK eyes, 0.05 ± 0.29 D (range –1.5 to 0.24 D) for the LTK eyes, and 0.48 ± 0.91 D (range –0.26 to 0.28 D) for the HK group. The mean difference between standard simulated keratometry readings from topography and Effective RP values was -0.85 ± 0.73 D (range –2.28 to 0.31 D). Within the individual groups, the mean difference was -1.03 ± 0.74 D (range –2.28 to –0.19 D) for the RK eyes, -0.01 ± 0.28 D (range –1.08 to –0.5 D) for the LTK group and -0.84 ± 0.30 D (range - 0.13 to 0.31 D) for the HK eyes. Axial lengths in all eyes averaged 24.78 ± 1.54 (22.31 – 27.96) mm. In the RK group the mean axial length measured 25.38 ± 1.40 (23.04 – 27.96) mm; in the LTK group the mean axial length measured 23.21 ± 1.26 (22.31 – 24.65) mm; in the HexK group the mean axial length measured 23.57 ± 0.43 (23.08 – 23.82) mm. No significant correlation between axial length and post-operative spherical equivalent was found (Pearson correlation coefficient = 0.08). The eye with -9.88 D preoperative spherical equivalent refraction deserves a brief comment because of its position as an outlier and the unusual features of the case. This

Fig. 37.3: Targeted correction in SE calculated by the Holladay II formula compared with the achieved postoperative SE correction. Linear regression analysis (y = 0.9266x + 0.1233) demonstrated a slightly hyperopic trend

Biometry for Refractive Lens Surgery

Fig. 37.4: The frequency distribution of eyes (%) determined by the postoperative SE refractions

Fig. 37.5: The average keratometry reading (IOL Master) compared with the EffRP determined by the Holladay Diagnostic Summary. Although the mean difference was small, the range of differences was broad (-1.50 to +2.00). Equivalency lines show the range ± 1.0 D

patient presented 22 years after “failed” RK in this eye. She had never proceeded with surgery on the fellow eye. No other history was available. The fellow unoperated eye had a spherical equivalent of -4.86 D, with keratometry of 42.82 X 44.34 @ 98 and axial length of 25.13. Her preoperative best-corrected acuity in the operated eye was 20/30 with a correction of -10.75 + 1.75 X 33. Keratometry in the operated eye was

41.31 × 42.67 @ 64, yielding an average K of 41.99. Simulated keratometry was 41.36 × 42.55 @ 70. The calculated Eff RP was 41.90 D, and the axial length was 26.59 mm. Exam revealed moderate nuclear sclerosis. The Holladay II Formula predicted a postoperative spherical equivalent refraction of – 0.02 D. The eye achieved a final best-corrected visual acuity of 20/20 with a correction of + 0.25 +0.75 × 55, indicating a predictive error of 0.64 D.

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Mastering the Techniques of Intraocular Lens Power Calculations The determination of IOL power following keratorefractive surgery remains a challenge for the cataract and refractive surgeon. Using a combination of measured and calculated K values with the historical and contact lens methods, as well as a myopic target refraction, Chen and coauthors achieved a postoperative refractive outcome of 29.2% within ± 0.50 D of emmetropia in a series of 24 eyes with a history of RK.14 They suggested that “corneal power values that involve more central regions of the cornea, such as the effective refractive power in the Holladay diagnostic summary of the EyeSys Corneal Analysis System, would be more accurate K-readings in post-RK eyes.” Our results would tend to support that conclusion. Accurate biometry also plays an important role in IOL power determination. The use of partial coherence interferometry (IOL Master, Carl Zeiss Meditec, Dublin, CA) for axial length measurement improves the predictive value of postoperative refraction,21 and it has been shown equivalent in accuracy to immersion ultrasound.22 It is interesting to note the smaller difference between simulated keratometry and the Eff RP in the LTK group as compared to the incisional keratorefractive surgery groups. One possible explanation of this difference is that the LTK corneas had undergone regression from treatment and therefore returned to a less distorted anatomy. The IOL calculation formula plays a critical role in obtaining improved outcomes. The Holladay II formula is designed to improve determination of the final effective lens position by taking into account disparities in the relative size of the anterior and posterior segments of the eye. To accomplish this goal the formula incorporates the corneal white-to-white measurement and the phakic lens thickness, and uses the keratometry (or Eff RP) values not only to determine corneal power but also to predict effective lens position. We have found that the use of the Holladay II formula has increased the accuracy of our IOL power calculations.23 Our study has been limited to eyes which have undergone incisional and thermal keratorefractive surgery. Ongoing research will help to determine the most effective methods of calculating IOL power in eyes which have had lamellar keratorefractive surgery such as photorefractive keratectomy or laser in situ keratomileusis. It appears that further modification is necessary in these situations because of the inaccuracy of the standardized values of index of refraction.24 We continue to tell our patients as part of the informed consent process that IOL calculations following keratorefractive surgery remain a challenge, and that

refractive surprises do occur. We explain that further surgery (e.g., placement of a piggyback IOL) may be necessary in the future to enhance uncorrected visual acuity. We defer any secondary procedures until a full three months postoperatively and document refractive stability before proceeding.

REFERENCES 1. Drexler W, Findl O, Menapace R, et al. Partial coherence interferometry: a novel approach to biometry in cataract surgery. Am J Ophthalmol 1998;126:524-34. 2. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens power calculation according to Haigis. Graefes Arch Clin Exp Ophthalmol 2000;238: 765-73. 3. Giers U, Epple C. Comparison of A-scan device accuracy. J Cataract Refract Surg 1990;16:235-42. 4. Watson A, Armstrong R. Contact or immersion technique for axial length measurement? Aust NZ J Ophthalmol 1999; 27:49-51. 5. Fine IH, Packer M, Hoffman RS. Use of power modulations in phacoemulsification. J Cataract Refract Surg 2001;27: 188-97. 6. Sanders DR, Retzlaff JA, Kraff MC. A-scan biometry and IOL implant power calculations. Focal Points. San Francisco, CA, American Academy of Ophthalmology 1995;13(10). 7. Fenzl RE, Gills JP, Cherchio M. Refractive and Visual Outcome of Hyperopic Cataract Cases Operated on Before and After Implementation of the Holladay II Formula. Ophthalmology 1998;105:1759-64. 8 . Hoffer KJ. Intraocular lens power calculation in radial keratotomy eyes. Phaco & Foldables 1994;7(3):6. 9. Holladay JT. Understanding Corneal Topography, The Holladay Diagnostic Summary, User’s Guide and Tutorial, EyeSys Technologies, Inc, Houston, TX, 1995. 10. Celikkol L, Pavlopoulos G, Weinstein B, Celikkol G, Feldman ST. Calculation of intraocular lens power after radial keratotmy with computerized videokeratography. Am J Ophthal 1995;120:739-50. 11. Speicher L. Intraocular lens calculation status after corneal refractive surgery. Curr Opin Ophthalmol 2001;12(1):17-29. 12. Hamilton DR, Hardten DR. Cataract surgery in patients with prior refractive surgery. Curr Opin Ophthalmol 2003;14(1): 44-53. 13. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25(7):898-903. 14. Chen L, Mannis MJ, Salz JJ, Garcia-Ferrer FJ, Ge J. Analysis of intraocular lens power calculation in post-radial keratotomy eyes. J Cataract Refract Surg 2003;29(1):65-70. 15. Maeda N, Klyce SD, Smolek MK, McDonald MB. Disparity between keratometry-style readings and corneal power within the pupil after refractive surgery for myopia. Cornea 1997;16(5):517-24. 16. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: double K method. J Cataract Refract Surg 2003;29:2063-68. 17. Koch DD, Wang L. Calculating IOL power in eyes that have had refractive surgery (editorial). J Cataract Refract Surg 2003;29:2039-42. 18. Gills JP, Gayton JL. Reducing pre-existing astigmatism. IN: Gills JP, Cataract surgery: The state of the art. Thorofare, NJ: SLACK, 1998;53-66.

Biometry for Refractive Lens Surgery 19. Nichamin L. Refining astigmatic keratotomy during cataract surgery. Ocul Surg News 1993. 20. Fine IH, Packer M, Hoffman RS. Use of power modulations in phacoemulsification. Choo-choo chop and flip phacoemulsification. J Cataract Refract Surg 2001;27(2):188-97. 21. Rajan MS, Keilhorn I, Bell JA. Partial coherence laser interferometry vs conventional ultrasound biometry in intraocular lens power calculations. Eye 2002;16(5):552-56. 22. Packer M, Fine IH, Hoffman RS, Coffman PG, Brown LK. Immersion A-scan compared with partial coherence

interferometry: Outcomes analysis. J Cataract Refract Surg 2002;28(2):239-42. 23. Packer M, Fine IH, Hoffman RS. Refractive lens exchange with the array multifocal intraocular lens. J Cataract Refract Surg 2002;28(3):421-24. 24. Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651-58.

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Mastering the TechniquesDimitrii of Intraocular Lens Power CalculationsVetchiaslav (Italy) D Dementiev, Kukrenkov

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38

IOL Power Calculations in Phakic IOLs

INTRODUCTION The last years more and more refractive surgeons are looking to use not only the corneal refractive procedures (RK, KM, LASIK, PRK, LASEK) for myopia and hyperopia correction, but also the phakic implants. It was just approved that the quality of vision after the refractive implants is much better that after corneal procedures, especially in high refractive error eyes. The evidence of reversibility, stability (no regression was noticed) and high predictability of the final refractive effect of the implants make this kind of surgery to become more popular among the refractive surgeons all over the globe. In this chapter we shall describe the criteria for IOL Power Calculation in Phakic IOL which is crucial for the successful postoperative visual outcome.

PRL POWER CALCULATION It is important to obtain a precise refraction of the eye (with accurate vertex distance measurement) as well as an accurate axial length and corneal power readings to use the various methods (Table 38.1). The spherical equivalent of the most accurate refraction of the eye is used to interpolate the power of the posterior chamber PRL. These powers are based on a simple vertex correction from 12 mm to the corneal plane. This does not seem to make sense optically, but so far has resulted in excellent accuracy in our experience.

CLINICAL RULES 1. Cycloplegic Rx must be less minus than Manifest Rx in Myopes. 2. Cycloplegic Rx must be more plus than Manifest Rx in Hyperopes.

3. If cycloplegic Rx is different, see if patient can accept full cycloplegic correction. 4. Best to attempt correction of cycloplegic Rx in Hyperopes and Manifest Rx in Myopes. 5. Hyperopic patients 18-35 can accommodate a small undercorrection (up to +1.00). 6. Myopic patients 18-35 should not be overcorrected but left emmetropic or small myopia. 7. All patients 36-50 must obtain emmetropia or slight overcorrection (up to –1.00). 8. If cylinder is not to be corrected, using the SE plans for PO mixed astigmatism. 9. If correcting cylinder prior to PRL, use the SE of the resultant healed refraction. 10. If correcting cylinder after the PRL: a. If your astigmatic surgical correction will not change the average K, use the SE. b. If your astigmatic surgical correction will change the average K (flatten), use the Sphere only.

BIBLIOGRAPHY 1. Baikoff G, Colin J. “Intraocular lenses in Phakic Patients” Ophthalmol Clin North Am 1992;5. 2. Davidorf JM, Zaldivar R, Oscherow S. “Posterior Chamber Phakic Intraocular Lenses for Hyperopia of +4 to +11 Diopters“ and “Posterior Chamber Phakic Intraocular lenses for Myopia of –8.0 to –19.0 Diopters” J Refract Surg 1998;14:N.3. 3. Dementiev D, Rozakis G, Hatsis A, Hoffer K, Sborgia G, Marucchi P. “The 5 Years Experience in the Phakic Refractive Posterior Chamber IOL Implantation for the correction of High Ametropia” Binkhorst Symposium during XXVIII International Congress of Ophthalmology, 1998 June,Amsterdam, Holland. 4. Fechner PU. Intraocular lenses for the correction of myopia in phakic eyes: Short long success and long-term caution. Refract Corneal Surgery 1990;6:242-44.

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Table 38.1: CIBA–Medennium PRL power table Based on 12 mm Vertex Formula: PRL=Rx/(1 – 0.012*Rx) EACH PRL CAUSES WHAT RX?

MYOPIA

EACH Rx NEEDS WHAT PRL?

HYPEROPIA

MYOPIA

HYPEROPIA

PRL

RX

PRL

RX

RX

PRL

RX

PRL

–3.0

–3.11

3.0

2.90

–3.0

–2.90

3.0

3.11

–3.5 –4.0 –4.5 –5.0 –5.5 –6.0 –6.5 –7.0 –7.5 –8.0 –8.5 –9.0 –9.5 –10.0 –10.5 –11.0 –11.5 –12.0 –12.5 –13.0 –13.5 –14.0 –14.5 –15.0 –15.5 –16.0 –16.5 –17.0 –17.5 –18.0 –18.5 –19.0 –19.5 –20.0

–3.65 –4.20 –4.76 –5.32 –5.89 –6.50 –7.00 –7.64 –8.24 –8.85 –9.50 –10.09 –10.72 –11.36 –12.00 –12.67 –13.34 –14.00 –14.71 –15.40 –16.11 –16.83 –17.50 –18.29 –19.00 –19.80 –20.50 –21.36 –22.15 –23.00 –23.78 –24.61 –25.50 –26.32

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0

3.36 3.82 4.27 4.72 5.16 5.60 6.00 6.50 6.88 7.30 7.71 8.12 8.50 8.93 9.33 9.72 10.11 10.50 10.87 11.25 11.62 12.00 12.35 12.71 13.07 13.42

–3.5 –4.0 –4.5 –5.0 –5.5 –6.0 –6.5 –7.0 –7.5 –8.0 –8.5 –9.0 –9.5 –10.0 –10.5 –11.0 –11.5 –12.0 –12.5 –13.0 –13.5 –14.0 –14.5 –15.0 –15.5 –16.0 –16.5 –17.0 –17.5 –18.0 –18.5 –19.0 –19.5 –20.0 –20.5 –21.0 –21.5 –22.0 –22.5 –23.0 –23.5 –24.0 –24.5 –25.0 –25.5 –26.0 –26.5

–3.36 –3.82 –4.27 –4.72 –5.16 –5.60 –6.03 –6.46 –6.88 –7.30 –7.71 –8.12 –8.53 –8.93 –9.33 –9.72 –10.11 –10.49 –10.87 –11.25 –11.62 –11.99 –12.35 –12.71 –13.07 –13.42 –13.77 –14.12 –14.46 –14.80 –15.14 –15.47 –15.80 –16.13 –16.45 –16.77 –17.09 –17.41 –17.72 –18.03 –18.33 –18.63 –18.93 –19.23 –19.53 –19.82 –20.11

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0

3.65 4.20 4.76 5.32 5.89. 6.47 7.05 7.64 8.24 8.85 9.47 10.09 10.72 11.36 12.01 12.67 13.34 14.02 14.71 15.40

C 2001 Hoffer–Dementiev

5. Hatsis H. Phakic posterior IOLs for the correction of high hyperopia and high myopia, ASCRS 1997, boston,USA. 6. Holladay JT. Refractive power calculation for intraocular lenses in the phakic eye. Am J Ophthalmol 1993;116:63-66 24.

7. Pallicaris I. “Barraquer lecture” AAO annual meeting 1997 San Francisco, USA. 8. Werblin T. “Barraquer lecture” AAO annual meeting 1998 New Orleans, USA.

Mastering the Techniques of Intraocular Lens Power Calculations Yoshiaki Nawa (Japan)

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39

Raytracing Analysis of Accommodating IOL

INTRODUCTION Accommodative intraocular lenses (IOLs) have recently entered the market. Forward movement of the IOLs is postulated to create most of the accommodation in eyes with such IOLs.1-4 For example, AT-45 R (C&C Vision, Aliso Viejo, California, USA) was reported to move forward by 0.7 mm. 5 ICU R (Humanoptics, Spardorfer, Erlangen, Germany) was reported to move forward by 0.78 mm.6 Recently it has been reported that a double-optic IOL could obtain more accommodation than a single-optic.7-9

THE METHODS OF ACCOMMODATION In this chapter, I describe 1. The method of calculating accommodation in eyes with accommodating single-optic IOLs using raytracing analysis. 2. Accommodation obtained per 1mm forward movement IOL highly correlates with IOL power. 3. Methods to enhance the effect of accommodating IOLs; double-optic IOLs, and combination of corneal surgery and IOL.

The Method of Calculating Accommodation in Eyes with Single-optic Accommodating IOL A ray-tracing analysis of pseudophakic eyes is obtained by analyzing each spherical surface of the eye. 10 The method is shown in the appendix 1. In this chapter the computer software Mathematica R (Wolfram, Champaign, Illinois, USA) was used to calculate refractions of the model eye used here. We can analyze mutual relationship between several parameters of the eye using this equation as described in

Fig. 39.1: The relationship between anterior chamber depth, axial length, and ocular refraction in a pseudophakic eye model. By using the equation of Appendix 1, we can analyze mutual relationships between several different parameters of the eye

the past report.4 Figure 39.1 shows an example that plotted the relationship between anterior chamber depth, axial length, and ocular refraction. Here I investigated accommodation obtained per 1mm forward movement of IOL using a more detailed eye model than that used in the past report.4 I varied anterior corneal radius of curvature of the cornea from 7.2 to 8.4 mm and axial length from 21 to 27 mm. Other parameters were assumed as follows: posterior radius of curvature of the cornea: 6.8 mm; anterior radius of curvature of the cornea; 7.7 mm; thickness of the cornea: 0.5 mm; anterior chamber depth (posterior surface of cornea to anterior surface of IOL): 4.0 mm; IOL: MA30BA (10 - 30 D, Alcon Japan, Tokyo); refractive index of the cornea: 1.376; refractive index of the anterior chamber and vitreous: 1.336; anterior and posterior radius of curvature of IOL, IOL thickness, and refractive index of IOL: provided by the manufacturer.

Raytracing Analysis of Accommodating IOL Amount of accommodation for a 1 mm forward movement of IOL(D)

Fig. 39.2: The relationship between corneal curvature, axial length, and amount of accommodation for a 1mm forward movement of IOL. Shorter eyes with high power IOLs can obtain more accommodation per 1 mm forward movement of IOL

Fig. 39.3: The correlation between IOL power and amount of accommodation for a 1mm forward movement of IOL. They are highly correlated. Other models of single-optic IOLs show similar trends

The IOL power in each theoretical eye with different parameters (corneal radius of curvature and axial length) was selected for the refraction of the model eye to become the least minus power (nearest to emmetropia). Then I plotted the relationship between the amount of myopic shift of the theoretical eye for a 1 mm forward movement of IOL, and axial length, corneal curvature, and IOL power. The summary of the analysis is shown in Table 39.1 and plotted in Figure 39.2. The analysis revealed that 0.65 to 2.07 diopter of accommodation was obtained per 1mm forward movement of IOL, depending on corneal curvature, axial length, and IOL power. The amount of accommodation for a 1 mm forward movement of IOLs should be determined individually in each eye. Long eyes with small power IOLs will obtain a small myopic shift, and short eyes with high power IOLs will obtain a large myopic shift, for a 1 mm forward shift of accommodative IOLs. This kind of analysis can be done for any type of singleoptic IOLs.

forward movement of IOL. These two parameters are highly correlated (y = 0.0723 × – 0.1159, R2 = 0.9862). It is similar to that shown by McLeod7 (y = x/13). The difference may stem from the differences of assumed parameters.

Methods to Enhance the Effect of Accommodating IOLs; Double-optic IOL, Combination of Corneal Surgery and IOL To enhance the effect of accommodating IOLs, doubleoptic IOLs have been developed.7-9 Ray-tracing analysis of double-optic IOLs can be similarly done by inputting each parameter of spherical surfaces of the components of the eye and IOL into an equation of double-optic IOL. Appendix 39.2 shows an equation of double-optic IOL.

Accommodation Obtained per 1mm forward Movement IOL Highly Correlates with IOL Power McLeod described that using the ray-tracing analysis the amount of accommodation for a 1mm forward movement of IOL was approximately (1/13) × IOL power.7 I also evaluated the relationship. Under the assumption of section 1, I analyzed and plotted the relationship between IOL power and accommodation per 1 mm forward movement of IOL. Figure 39.3 shows the relationship between the IOL power and the amount of accommodation for a 1 mm

Fig. 39.4: The relationship between myopic correction, IOL power, and accommodation/1mm forward movement of IOL. Combination of myopic PRK and IOL implantation fairly enhance the effect of accommodating IOL

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Mastering the Techniques of Intraocular Lens Power Calculations

256

Table 39.1: Summary of analysis Anterior radius of curvature of cornea (mm) Axial length(mm) 21

22

23

24

25

26

27

8.4

8.2

8.0

7.8

7.6

7.4

7.2

IOL power (D)

29.0

Predicted refraction (D)

–0.24

Myopic shift for a 1mm movement of the IOL (D)

2.07

IOL power

29.0

27.5

25.5

23.5

Predicted refraction

-0.14

-0.27

-0.15

-0.18

Myopic shift for a 1mm movement of the IOL (D)

2.00

1.90

1.80

1.68

IOL power

29.0

27.5

26.0

24.5

22.5

21.0

19.0

Predicted refraction

–0.26

–0.20

–0.26

–0.32

–0.10

–0.27

–0.27

Myopic shift for a 1mm movement of the IOL (D)

1.93

1.83

1.74

1.67

1.54

1.45

1.33

IOL power

24.5

23.0

21.5

20.0

18.5

17.0

15.0

Predicted refraction

–0.09

–0.01

–0.06

–0.09

–0.19

–0.35

–0.33

Myopic shift for a 1mm movement of the IOL (D)

1.59

1.50

1.39

1.32

1.24

1.14

1.00

IOL power

21.0

19.5

18.0

16.5

15.0

13.5

11.5

Predicted refraction

–0.25

–0.16

–0.20

–0.22

–0.30

–0.31

–0.29

Myopic shift for a 1mm movement of the IOL (D)

1.33

1.21

1.14

1.04

0.98

0.89

0.78

IOL power

17.5

16.0

15.0

13.5

12.0

10.0

Predicted refraction

–0.13

–0.03

–0.40

–0.29

–0.36

–0.16

Myopic shift for a 1mm movement of the IOL (D)

1.10

1.03

0.93

0.84

0.77

0.65

IOL power

14.5

13.5

12.0

10.5

Predicted refraction

–0.00

–0.24

–0.26

–0.27

Myopic shift for a 1mm movement of the IOL (D)

0.88

0.81

0.73

0.69

Ho9 analyzed the accommodation performance of 14 design variations for 2 configurations of two-optic IOL. These represented 4 possible combinations (positive/ negative, mobile/static, front/back element). Configurations with high positive-power front element returned the best amplitude of accommodation (up to approximately 3.0D/mm when the front element power was + 40D). This paper shows many good examples of ray-tracing analysis of two-optic IOLs. Here I describe another possible method to enhance the effect of accommodating IOLs. As described above section 2, higher power IOLs are able to elicit more

accommodation per 1 mm forward movement of IOL. Combined myopic PRK and IOL would increase IOL power. I assumed as follows; anterior corneal radius of curvature of the cornea: 7.7 mm; axial length: 24 mm; posterior radius of curvature of the cornea: 6.8 mm; thickness of the cornea: 0.5 mm; anterior chamber depth (posterior surface of cornea to anterior surface of IOL): 4.0 mm; IOL: VA60BB (HOYA, Tokyo, Japan); refractive index of the cornea: 1.376; refractive index of the anterior chamber and vitreous: 1.336; anterior and posterior radius of curvature of IOL, IOL thickness, and refractive index of

Raytracing Analysis of Accommodating IOL IOL: provided by the manufacturer. The IOL power in each theoretical eye with different parameters (corneal radius of curvature and thickness) was selected for the refraction of the model eye to become the least minus power (nearest to emmetropia). In this initially assumed condition, 19 diopters of IOL was the most appropriate with the refraction of the eye – 0.21D, and accommodation per 1mm forward movement was 1.26D. Next, three different amounts (–5, –10, –15D) of myopic PRK was assumed in the theoretical eye model. The ablation depth was assumed to be 12 × (micrometer). A maximum of 2.28D of accommodation was obtained when –15D of myopic PRK was performed with 39D of IOL implanted. Figure 39.4 shows the summary of the analysis. It revealed that a modest amount of accommodation could be obtained.

REFERENCES 1. Binkorst RD. The optical design of intraocular lens implants. Ophthalmic Surg 1975;6:17-31.

2. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. 3. Holladay JT, Maverick KJ. Relationship of the actual thick intraocular lens optic to the thin lens equivalent. Am J Ophthalmol 1998;126:339-47. 4. Nawa Y, Ueda T, Nakatsuka M, et al. Accommodation obtained per 1mm forward movement of a posterior chamber intraocular lens. J Cataract Refract Surg 2003;29:2069-72. 5. Cumming JS, Slade SG, Chayet A. AT-45 Study Group. Clinical evaluation of the model AT-45 silicone accommodating intraocular lens. Ophthalmology 2001; 108:2005-2010. 6. Langenbucher A, Huber S, Nguyen NX, et al. Measurement of accommodation after implantation of a new accommodative posterior chamber intraocular lens (1CU). J Cataract Refract Surg 2003;29:677-85. 7. McLeod SD, Portney V, Ting A. A dual optic accommodating foldable intraocular lens. Br J Ophthalmol 2003;87:1083-85. 8. Langenbucher A, Reese S, Jakob C, et al. Pseudophakic accommodation with translation lenses-dual optic vs mono optic. Ophthalmoc Physiol Opt 2004;24:450-57. 9. Ho A, Manns F, Pham T, et al. Predicting the preformance of accommodating intraocular lenses using ray tracing. J Cataract Refract Surg 2006;32:129-36. 10. Horiuchi I, Akagi Y. A new theoretical formula for the intraocular lens power caliculation by the ray tracing method. J Jpn Ophthalmol Soc 2001;105:619-27.

257

258

Mastering the Techniques of Intraocular Lens Power Calculations APPENDIX 1 Ray-tracing analysis of pseudophakic eyes Rs= 1/[1/(1/{1/[1/(1/{1/[1/(1/t5 – p4) +t4] – p3} +t3) – p2] +t2} – p1) +v] Rs: Refraction (diopters) in glasses; v: Vertex distance (meters); t: Corneal thickness (meters); ACD: Anterior chamber depth (meters); d: IOL thickness (meters); VIT: Length of vitreous space (meters); AXL: Axial length (meters); ti: Reduced vergence of t, ACD, IOL thickness, and VIT (t2= t/n2, t3= ACD/n3, t4= d/n4, t5= VIT/n5); pi: Refractive power of each interface (diopters); R1: Anterior radius of curvature of cornea (meters); P1= (n2 – n1)/ R1; R2: Posterior radius of curvature of cornea (meters); P2= (n3 – n2)/R2; R3: Anterior radius of curvature of IOL (meters); p3= (n4 – n3)/R3; R4: Posterior radius of curvature of IOL (meters); p4= (n5 – n4)/R4; VIT= AXL-t-ACD-d; ni: Refractive index of each tissue; 1: Air; 2: Cornea; 3: Anterior chamber; 4: IOL; 5:Vitreous

APPENDIX 2 Ray-tracing analysis of pseudophakic eyes with piggyback IOL or double-optic IOL Rs= 1/{1/[1/(1/{1/[1/(1/{1/[1/(1/{1/[1/(1/t7 – p6) +t6] – p5} +t5) – p4] +t4} – p3) +t3] – p2} + t2) – p1] +v} Rs: Refraction (diopters) in glasses; v: Vertex distance (meters); t: Corneal thickness (meters); ACD: Anterior chamber depth (meters); d1, d2: IOL thickness (meters); x: Distance between IOLs (meters); VIT: Length of vitreous space (meters); AXL: Axial length (meters); ti: Reduced vergence of t, ACD, d1, d2, x, and VIT (t2 = t/n2, t3 = ACD/n3, t4 = d1/n4, t5 = x/ n5, t6 = d2/n6, t7 = VIT/n7); pi: Refractive power of each interface (diopters); R1: Anterior radius of curvature of cornea (meters); p1 = (n2 – n1)/ R1; R2: Posterior radius of curvature of cornea (meters); p2= (n3 – n2)/R2; R3: Anterior radius of curvature of IOL1 (meters); p3= (n4 – n3)/R3; R4: Posterior radius of curvature of IOL1 (meters); p4= (n5 – n4)/R4; R5: Anterior radius of curvature of IOL2 (meters); p5 = (n6 – n5)/R3; R6: Posterior radius of curvature of IOL2 (meters); p6= (n7 – n6)/R6;VIT= AXL-t-ACD-d1-x-d2; ni: Refractive index of each tissue; 1: Air; 2: Cornea; 3,5: Anterior chamber; 4,6: IOL; 7 : Vitreous

Analysis of Dual-optics Accommodating IOL

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JT Lin (Taiwan) 259

Analysis of Dual-optics Accommodating IOL

INTRODUCTION Accommodating IOLs (AIOL) including single-optics and two-optics configurations have been designed and analyzed by many researchers.1-11 The accommodation rate (M) defined by the accommodation amplitude per 1.0 mm of the IOL axial movement has been studied both analytically by Gaussian optics and numerically by raytracing method.2,3,5 Single-optics AIOL is much simpler than the dual-optics AIOL which has been analyzed recently by Ho et al using raytracing method. However, analytic formulas are not yet available. This Chapter presents and derives analytic formulas for dual-optics AIOL, in which either or both the front and back optics are allowed to move in both forward and backward directions. Calculated results are consistent with that of raytracing method used by Ho et al. However, analytic formulas provide more insight features which are not readily available in raytracing. The dual-optics formulas may be also compared to the single-optics AIOL in phakia or piggyback IOL which are presented by Lin in other Chapters of this book.

THE ACCOMMODATING RATE (M)

Figs 40.1A and B: Schematics for the 3-optics system, shown in (A) consisting of the cornea and 2-optics IOL separated by p and p’. Also shown are the principal plane locations of IOL (Q1 and Q2) and the second principal plane of the reduced 2optics system (P2), effective focal length (F) and effective distance (S) shown in (B)

Mobile Front-optics Case As shown in Figure 40.1A, a doublet IOL (dual-optics) consists of 2 optics located at N2 and N3 and separated by p’, where the front optic separates from the corneal vertex surface by a distance p. As derived in the Appendix, the 3-optic system consisting of the cornea and the dual-optics IOL may be reduced to an effective 2-optic system shown in Figure 40.1B by Gaussian optics and the system refractive error (De) is given by Lin’s image equation 9,11

De = 1336 [1/(X) + P2 – 1/F],

(1)

By taking the derivative of De with respective to the IOL front optic position (p), the accommodation rate (M), defined as the increase of system power due to per 1.0 mm forward movement of the front IOL (assuming the backoptics is immobile), or M = – dDe/dp, may be derived (see Appendix) and expressed in an analytic format.

260

Mastering the Techniques of Intraocular Lens Power Calculations M = Z (D1/1336)(2Dc + ZD1), Z = 1 – S (Dc/1336),

(2a) (2b)

where S (in the unit of mm) being the effective anterior chamber depth (ACD) of the IOL; D1, D2 and Dc are, respectively, the front and back IOL power and corneal power. The validation of the analytic formula, Eq.(2), is checked by comparing to the exact numerical value of M by calculating the De in Eq.(1) for different IOL position (p) given by M = (0.59, 2.32, 2.94, 3.62) (dioper/mm) for the configurations of (a) to (e) defined earlier. These numerical data show that the error of analytic formula is about 1 to 3%. Comparing to the numerical ray-tracing results of Rana et al,2 the analytic results of this study are also within 5% in difference due to the choice of the effective ACD(S), corneal power and refractive index of the humors (1.333 in Rana vs. 1.336 of this study). Validation of Eq.(2) may be also justified by the following special case. In the convex-plano configuration, D2 = 0 and S = p, the 3-optics formula reduces to the formula for a 2-optics, cornea plus single-IOL system or IOL implanted in an aphakic eye.7,8 Based on Eq.(2) and for typical IOL position of p = 3.0 mm, p’ = 1.0 mm, corneal power Dc = 43 diopter, the calculated values M = (0.57, 1.41, 2.35, 2.89, 3.65) (diopter/ mm), respectively, for various IOL doublet configurations with (front, back) power, (D1, D2) equals: (a) (+ 10, + 10), (b) (+ 20, 0), (c) (+ 30, –10), (d) (+ 35, – 15) and (e) (+ 40, – 20) diopters. The above 5 configurations have the same total IOL power of +20 diopter but different in shapes of biconvex, convex-plano and convex-concave. The nonlinearly increasing feature of M by the front-IOL power (D1) is shown in Figure 40.2 for the plus front-optics IOL which has a higher M value than that of the absolute value of M in minus front-optics IOL due to the cancellation of the second term in Eq.(2a). The following significant features of the dual-optics accommodative IOL, which may not be readily available by numerical raytracing method, can be easily addressed based on the analytic formula of Eq.(2): (a) The accommodation rate (M function) is nonlinearly proportional to the moving front IOL-power (D1) as shown by Eq.(2). M is positive for positive-power moving optics, that is an increase of p’ (or dp’ > 0 and dp < 0) or a forward movement to the cornea is needed in order to have increasing accommodation (or myopic shift) for near vision of a presbyopia. These features are consistent with the numerical finding of Rana et al 2 and Ho et al 5. (b) M is insensitive to the corneal power change due to the

Fig. 40.2: Accommodation rate function (M) versus IOL frontoptic power (D1) for various configurations with a fixed IOL total power of 20 diopter

combined factor of ZDc, where Z = 1 – S (Dc/1336) is a decreasing function of Dc and therefore cancellation occurs in M value when Dc increases. In contrast, M is a decreasing function of S, or the corneal-IOL separation (p). For example, given Dc = 43 diopter, p’ = 1.0 mm, and the configuration with (D1, D2) = (+30, –10) diopter, g = – 0.5, M = (2.39, 2.35, 2.29), for p = (2.5, 3.0, 3.5) mm or S = (2.0, 2.5, 3.0) mm, respectively. (c) As shown by the second term of Eq. (2), cancellation occurs when D1 < 0. Therefore, a positive-power would have a greater M (absolute value) than that of negativepower moving optics. For example, Dc = 43 D, S = 3.5 mm, Z2 = 1.0 and Z = 0.887; the calculated M = +0.99 (D/mm) for D1 = +15 D and M = –0.724 (D/mm) for D1 = –15 D, which is about 27% smaller (comparing the absolute values). This novel feature is consistent with that of Ho et al using raytracing method. (d) For a given IOL total power of Dt = D1 + Z1D2, with Z1 = 1 – p’(D1/1336), the M value for front positive and backnegative IOL is always larger than that of both optics are positive. This feature may be readily observed from Eq.(2) by re-expressing the moving front-optics power D1 = Dt – ZD2 has a higher value when D2 < 0.

Mobile Back-optics Case Eq.(2) is derived for the case that the forward moving element is the front-optics of the dual-optics IOL, where the back-optics is static. In general, both optics may be

Analysis of Dual-optics Accommodating IOL mobile in practice. By symmetry feature of the dual-optics IOL, one may also derive the case for mobile-back (with immobile-front) to obtain (see Appendix)

261

Similar to the mobile front-optics, the M’ value is proportional to the power of the mobile optics and slightly influenced by the immobile optics, via Z1 and the third term of the formula which is absent in the front mobile case.

for positive accommodation A (or myopic shift), A > 0. – : for negative accommodation A (or hyperopic shift), A < 0. ← : forward movement of the IOL (toward cornea) or dS > 0. → : backward movement of the IOL (away from cornea), or dS < 0. • : static (immobile) CX = convex, CA = concave

Both Optics Mobile

Example #1 (Fig. 40.3A)

In order to have a “positive” accommodation (for myopic shift), forward movement (toward the cornea) is needed if the moving optics has a positive power. In contrast, a backward movement is needed for a negative power moving optics. Therefore cancellation effect may occur when both optics having opposite-power are moving in the same directions or 2 optics having the same power sign but moving in the opposite directions. The actual amount of each components, M and M’, shall depend on the structure and implant configuration of the IOL, where contraction of the ciliary body results the direction and amount of each movement. Furthermore, one may also expect a small contribution from the non-linear coupling effect of M and M’, when both optics are allowed to shift in either direction. Therefore, the total (net) amount of accommodation (A) may be expressed as follows, in general,

For the (front, back) optics are CX – CA (with positive power) and CA – CX (with negative power), respectively. The movement direction, for example, (←, →) means (front-optics move forward, back-optics move backward); (+, +) means the resultant accommodations are both positive, and A1 > 0, A2 > 0; (←,•) means front-optics forward moving and back-optics static and the result is given by (+, 0) for A1 = positive, A2 = 0. By these definitions, the 8 possible cases are (Fig. 40.3A’).

M = Z(D2/1336)(2Dc+ZD2) – Delta.

A = M(dS1) + M’(dS2) + N(dS1)(dS2), = A1 + A2 + A12

(3)

+ :

Moving direction (←, •)

(4a) (4b)

where dS1 and dS2 are the movement amount (including directions) of the front and back optics, respectively, and N is a nonlinear coupling factor. Cancellation occurs when A1 and A2 have opposite signs. Figure 40.3 shows the possible combinations for various IOL configuration. Because we had defined the sign of M and M’ are the same as the power of the moving optics, we also need to defined dS > 0 for forward movement (toward the cornea), and dS < 0 for backward (toward the retina) movement.

PERFORMANCE AND CONFIGURATIONS Definition As shown in Figure 40.2, there are many possible combinations of front-back optics configurations and movement directions. They can be described by the following definition:

Accommodation (A1, A2) (+, 0)

(→, •)

(–, 0)

(•, →)

(0, +)

(•, ←)

(0, –)

(→, →)

(–, +)

(→, ←)

(–, –)

(←, →)

(+, +)*

(←, ←)

(+, –)

* case for both A1 and A2 are positive for maximal myopic accommodation.

Example # 2 (Figs 40.3B and C) For (front, back) optics = (CX – CA, CX = CA) or both are bi-CX having positive power for both optics. The possible combinations are shown as follows: Direction (←, •)

(←, •) (•, ←) (•, →)

(←, ←)* (←, →) (→, ←) (→, →)

(A1, A2)

(–, 0)

(+, +)

(+, 0)

(0, +)

(0, –)

(+, –)

(–, +)

(–, –)

* The optimal movement (both are forward) for maximal A = A1 + A2.

Maximal Accommodation Among the above configurations and movement directions, the following cases produce maximal-myopic accommodation having both A1 and A2 are positive:

Mastering the Techniques of Intraocular Lens Power Calculations

262

Fig. 40.3: Configurations and movement direction of various dual-optics accommodating IOL, where (←, ←, O) stands for movement direction of (forward, backward, immobile) with respect to the cornea position; (+, –) stands for (positive, negative)

Power

Direction

(D1, D2) (+, –) (+, +) (–, +) (–, –)

(front, back) (←, →) (←, ←) (→, ←) (→, →)

SOURCE ABERRATION Based on the Coddington shape factor analysis, 8,12,13 it was known that IOL with convex-concave configuration is desired in order to compensate the remaining negative spherical aberration in a normal eye having corneal asphericity about –0.2 to –0.6. Therefore dual-optics AIOL having both optics being convex-concave and the more-curved surfaces facing the cornea is preferred for minimal overall surface aberration. Furthermore, the positive-positive power configuration has the advantage of higher accommodation when both optics are moving forward to the cornea.

CONCLUSION In this Chapter, analytic formulas are presented for dualoptics AIOL which could have the front or back-optics being the mobile element or both. The important features of the accommodation rate function (M) include: • M is proportional to the moving optics power. • Positive accommodation amplitude, A=A 1 +A 2 , requires combination of plus-power optics moving forward to the cornea and minus-power optics moving backward to the retina. • Convex-concave or bi-convex configuration for both front and back optics having positive power offers maximal A when both are moving forward to the cornea. Dual-optics AIOL provides higher accommodation rates (M) via optical configurations. However, the combined surface aberration (SA) to compensate the balanced SA of cornea and natural lens for minimal high-order SA should also be considered in the IOL design.

Analysis of Dual-optics Accommodating IOL APPENDIX: DERIVATION OF LIN’S M-FORMULA 8,9 the

By Gaussian optics, effective focal length (EFL) of the dual-optics IOL is given as 1/f = 1/f1 + Z’/f2, Z’ = 1 – p’/f1,

(A-1)

where f1 and f2 are the EFL of the IOL and front and back optics separated by a distance p’ and related to their power by f1=1336/D1, f2=1336/D2, respectively; S is the effective anterior chamber depth (ACD) as shown in Figure 40.1A. The EFL of the reduced 2-optic system consisting of cornea and IOL is then given by (referring to Figure 40.1A) 1/F = 1/f + Z/fc, Z = 1 – S/fc,

(A-2)

where the effective distance between the cornea and the front IOL optic (shown by the distance between N1 and Q1 in Fig. 40.1) may be calculated from S = p + gp’, p is the estimated IOL position (away from the corneal vertex surface) and g = 1/(1+Z’f2/f1) is a geometry factor of the dual-optics IOL. It can be readily seen that the 3-optics system reduces to a 2-optics system when f2 goes to infinite and f = f1. Eq.(A-2) becomes a simple cornea-IOL 2-optics system (or a single-optic aphakic IOL) which has the same format as that of cornea-natural lens system.10 The refractive error of the reduced 2-optics system is given by 9-11 (for humors refractive index of 1.336). De = 1336/(X + P2) – 1336/F

(A-3)

where the effective vitreous cavity depth (X) is related to the axial length by X = L – p – p’ + p12 with p12 = p’f/f1 being the IOL second principal plane position, or the distance between Q2 and N3 as shown in Figure 40.1A. In Figure 40.1B, P2 = SF/f1 is the position of the system second principal plane. In this study, all the length parameters are in mm, except refractive power in diopter.

263

dX = – (f/f1)(1+p’f/f1f2)(dp), (A-5) dP2 = (F/fc)(dS) – (SF2/fc)d(1/F), (A-6) where dS and d(1/F) may be further expressed as dS = Gdp d(1/F) = – dS/(ffc)+(Z/f1f2)dp, G = 1 – (f/f2)(1+p’f/f1f2).

(A-7a) (A-7b) (A-7c)

In deriving Eq.(A-5) and (A-7), I had also used the basic relation that dp’= –dp to count for the fact that the forward movement of the front IOL causes a decrease of p and an increase of p’ given that p’+ p = constant. Substituting Eq.(A-5) to (A-7) to Eq.(A-4) and after lengthy but straightforward algebraic manipulation, I obtained the final analytic formula for M M = 1336 [af/(f1F2) – G(a/F – Z”/f)/fc-Z”Z/(f1f2)], (A-8) where Z”=1 – aS/fc. Above formula may be further simplified by eliminating F by Eq.(A-2) and using the approximated value of a = 1.0, ignoring the contribution from Din, if system is initially at emmetropic state; G = f/ f1, ignoring the small term (less than 0.5%) of p’f/(f1f2) in Eq. (A-7.c) for typical value of p’ = (0.5 – 1.0) mm; and for a fixed value of IOL effective power 1336/f = (10 to 25) diopters. M = (f/f1) Mo - Delta, Mo = 1336 [1/F2-1/fc2], Delta = Z2/(f1f2).

(A-9.a) (A-9.b) (A-9.c)

The validation of the above analytic formulas may be justified by their special cases and comparison to the exact numerical results based on Eq.(A-3). See detailed discussion in the text. Above formula may be further expressed by the corneal power (Dc) and IOL front and back optic power D1 and D2 as shown in the text Eq.(2) for the emmetropic case a=1 and Z”=Z.

Case (1): Front Optics Mobile To find the accommodation rate (M) defined by the accommodation amplitude (or system power increase) due to the forward movement of the front IOL (assume backoptics is immobile), one may take the derivative of Eq.(A3) with respective to the IOL front optic position (p), or M = – dDe/dp, to obtain M = (1336a/F2)(dX+dP2)+1336d(1/F) (A-4) where a is a nonlinear term given by a = (1 + FD in/1336) to count for the effect of the initial refractive error Din. dX and dP2 are derived from the earlier definitions as follows

Case (2): Back Optics Mobile Similar technique may be used to derive the rate function (M’) for the case that front-optics is immobile and backoptics is mobile, where (A-5) and (A-7) change to dX = (f/f1 – 1)(dp’), dS = (f/f2)(dp’).

(A-10) (A-11)

Therefore one obtains M’, similar to Eq.(A-9), M’ = (f1/f2) Mo – Delta,

(A-12)

Mastering the Techniques of Intraocular Lens Power Calculations

264

In terms of the IOL power and after some algebra, Eq.(A12) gives Eq.(3) in the text. It should be noted that Eq.(A-4) and (A-12) are symmetry.

REFERENCES 1. Shammas HJ. Intraocular lens power calculations. Thorofare NJ, SLACK Inc.,2004. 2. Rana A, Miller D, Magnante P. Understanding the accommodating intraocular lens. J Cataract Refract Surg. 2003;29:2284-87. 3. Nawa Y, Ueda T, Nakatsuka M, et al. Accommodation obtained per 1.0 mm forward movement of a posterior chamber intraocular lens. J Cataract Refract Surg 2003;29:2069-72. 4. Missotten T, Verkamme T, Blanckaert J, et al. Optical forumula to predict outcomes after implantation of accommodating intraocular lens. J Cataract Refract Surg 2004;30:2084-87.

5. Ho A, Manns F, Pham T et al. Predicting the performance of accommodating intraocular lens using ray tracing. J Cataract Refract Surg 2006;32:129-36. 6. Mcleod SD, Portney V, Ting A. A dual optic accommodating fordable intraocular lens. Br J Ophthalmol 2003;87:1083-85. 7. Landenbucher A, Reese S, Jakob C, Seize B. Pseudophakic accmoodation with translation lenses-dual optic vs. mono optic. Ophthalmic Physiol Opt 2004:24:450-57. 8. Pedrotti LS, Pedrotti FL. Optics and Vision. Liper Saddle River, NJ, Prentice Hall. 1998;74-87;92-95. 9. Lin, JT. Unified refractive-state analysis for customized vision correction. J. Refract Surg 2004;20:398-400. 10. Lin, JT. New formulas comparing accommodation in human lens and intraocular lens. J Refract Surg 2005;21:200-01. 11. Lin, JT. Analysis of refractive state ratios and the onset of myopia. Ophthal Physiol Opt 2005;26:97-105. 12. Atchison DA. Optical design of intraocular lens. I. On-axis performance. Optom Vis Science 1989;66:492-506. 13. Wang XJ, Jin CP, Wang QM. Aberration with IOLs based on different optical design. Chinese J Optom and Ophthal (in Chinese). 2003;5:209-11.

Aspherical IOL Analysis

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JT Lin (Taiwan) 265

Aspherical IOL Analysis

INTRODUCTION Customized laser reshaping of corneal surface for supervision recently becomes available by the two combined technology of flying-spot scanning laser patented by JT Lin (Lin, US Pat 5,144,630; 5,520,679) and the advanced wavefront devices1. However, the existing laser ablation algorithms are believed to rely on the parabolic approximation of the Munnerlyn formula2,3 which provides no information about the change of the corneal asphericity (or its shape) even high-order or exact formula are used.4-6 Discrepancy was found in measured postoperative corneal asphericities and predictions based on several proposed algorithms including the optical surface loss of laser energy and other biomechanical effects.7-9 However, the existing theories for laser ablation profiles are based on a known preoperative asphericity and treat the postoperative asphericity as a non-correlated free parameter.5,7,10 For customized laser ablations, a control optimized algorithm is desired to maintain a prolate or more prolate) cornea over the scotopic pupil to compensate for age-related changes and reduce the laserinduced spherical aberration. In the recent article by Cantu and associates,11 the authors proposed an ablation algorithm to increase spherical aberration (SA) and corneal asphericity (Q) to create an improved prolate ablation profile in both myopic and hyperopic patients. A related article by Lee et al,12 also proposed a two-step algorithm for the improvement of overall visual performance, where they use the standard Munnerlyn’s parabolic approximation (PA) formula for plano correction and followed by a second-step to eliminate the high-order aberration (HoAs) without removing too much extra corneal tissue, a strategy contrast

to the zone-enlargement method which suffers the risk of thin remaining corneal bed. However, the actual ablation algorithms used in their studies were not disclosed. It was believed that most of the existing ablation nomogram on the market was based on the PA since these are no initial corneal radius or asphericity assigned as the input parameter. This Chapter will cover the following subjects: • A new algorithm based on aspherical conicoid corneal surface • Correlation of the initial and final corneal asphericity • New strategies for controlling corneal shape with minimal ablation depth • An asphericity chart as guidance for the prediction of post-LASIK asphericity • Strategy of using positive cylinder for the treatment of mixed astigmatism • Strategy to increase the postoperative asphericity of the cornea to reduce the myopic-LASIK induced SA.

ASPHERICA PROFILE Most of the LASIK algorithms only include the preoperative refractive error (D) and ablation radius (d). Therefore, the parabolic approximation 2 (PA) of the ablation profile given by the center depth of Ho = -4Dd2/ 3 (for the case of myopia) was believed to be used in the algorithms. The high-order term 4,13 requiring also the preoperative corneal anterior surface radius (R) or its keratometric power and preoperative asphericity (Q) or shape-factor (p with R = Q+1), I believe, had not been programmed in most of the existing systems.

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Mastering the Techniques of Intraocular Lens Power Calculations For an aspherical corneal surface, the ablation profile may be expressed as follows (up to the 4th-order power of d) for a myopic correction.13,18,19 H(y) = Z2 + Z4 + Hcontrol Z2 = -(4D/3) (d2-y2), Z4 = 103[(d4-y4)/8R3] (p1–Bp2), Hcontrol = 103[By4/8R3](p2'-p2).

(1.a) (1.b) (1.c) (1.d)

where p1 and p2 are the preoperative and postoperative corneal shape-factor related to its asphericity by pj = Qj + 1 (j = 1, 2); B = (R/R’)3 defined by the ratio of the corneal anterior surface radius R (preoperative) and R’ (postoperative); y is the distance away from the optical axis and d is the ablation radius. In the above expression, H in micron, D in diopter and R, d, y in mm. A controlled ablation profile Hcontrol is introduced for further change of the post-LASIK asphericity or shape factor (p2). The significance of Hcontrol is that it allows us to remove a minimal corneal tissue but change substantially corneal asphericity without perturbing too much of the plano refractive state of the post-LASIK eye. One example was reported by Cantu et al 11 and second example by Lee et al.12 The algorithm of Lee et al corresponds to the situation when all three terms included in Eq(1.a) and Hcontrol allows the second-step of creating more prolate profile to reduce the LASIK-induced increase of positive SA while keeping the corneal plano. Similarly, Cantu et al reported the change of initially oblate eyes (with positive Q1, or p1>1.0) to prolate (with negative Q2, or p2R, therefore p’>p, that is, an increase of p or the asphericity (Q). In contrast, hyperopic-LASIK results in R’Q1*

Myopic

PRO OB

Less PRO N/A

OB more OB

Hyperopic

PRO OB

more PRO PRO

N/A less OB

* where Q1* is a transition value defined by when Q2=0 where Q1* is negative (positive) for myope (hyperope) correction (referred to Figure 41.1). Shorthand notations are used: PRO for prolate and OB for oblate.

Mastering the Techniques of Intraocular Lens Power Calculations

268 Example # 2

As shown by Figure 41.1(C) for hyperopia of + 0.5 D Q2 = 0.826 (Q1 + 1) –1. Therefore, an initial Q1 = +0.1 (oblate) results in Q2 = –0.09 (prolate); and Q1 = +0.4 results in Q2 = 0.16 (less oblate). Figure 41.1 and Table 41.1 provide a guideline for the prediction of postoperative corneal shape for a given preoperative shape which could be prolate or oblate. Furthermore, the controlled ablation algorithm may be used to modify corneal shape without changing its refractive power.

CENTRAL ABLATION DEPTH The central ablation depth (in myopia) or the maximal depth (in hyperopia), in general, is proportional to B (the correlation power) and has a higher value for hyperopia than myopia. For example, a typical value of R = 7.7 mm and d = 3.0 (mm), B = (0.724, 0.882) for myopia D = (–5.0, –2.0) diopters; B = (1.13, 1.34) for hyperopia D = (+2.0, +5.0) diopter. Hcontrol in Eq(1.d) is proportional to R’ and the shape-factor change (p2' – p2) and it is ydependent. It may be easily calculated, for each 1.0 change of the controlled asphericity or shape factor change, Hcontrol = 3.9 microns (at y = 2.0 mm), and 19.7 micron (at y = 3.0 mm) for R = 7.7, R’ = 8.0 mm, B = 0.89. These results are consistent with the measured data of Lee et al that Hcontrol is about 10% of the total ablation depth.

POSITIVE CYLINDER FOR MIXED ASTIGMATISM The recent article by Pinelli et al22 presented the advantages of their sequential ablation method (positive cylinder followed by myopic correction) over the conventional hyperopic spherical and negative cylinder method for the correction of mixed astigmatism. They had also demonstrated that less tissue removal and faster procedure using their new method and the bitoric (cross cylinder) LASIK in consistent with the theoretical study of Azar and Primack.2 However, the detail of the PlanoScan nomogram (system made by Bausch and Lomb) used in their study was not disclosed, and I believe that the paraxial approximation (PA) algorithm was built in the system since there was no initial corneal front surface radius (or keratometry power) or its asphericity mentioned as the input parameters in their nomogram. It was known that ablation algorithm under PA based on a “spherical” corneal surface could not provide information of the aspherical shape change postoperatively. In the following I would present the converted positive-cylinder

comparing to the negative-cylinder in the treatment of mix astigmatism based on the change of the cornea asphericity Q which is related to the corneal shape factor (P) by Q = P – 1. After LASIK procedures as discussed earlier, the corneal shape factor may increase or decrease depending on the procedure in myopic or hyperopic and the postoperative shape factor (P’) is correlated to its initial value (P) by Lin’s nth-order 19 P’ = (R’/R)2P, where R’ and R are the corneal post- and pre-operative from surface radius and related to the refractive error (D) by 1/R’ = 1/ R+D/377 (for the refractive index of vitreous humour n = 1.377). Therefore, one may derive the shape factor change defined by Δ = P”– P for sequential ablation of D and D’ power correction with initial P changed to P’ and then P’ to P”; and the corneal radius changes from R to R’ and from R’ to R” as follows: Δ = –2B (1 – 1.5B)P,

(2)

where B = (D’+D)R/377 = 0.0204 (D’ – D) for a typical value of R = 7.7 mm. The above formula allows us to calculate the change of the P values in various methods of correcting mixed astigmatisms. As shown in Table 41.3, four examples will be analyzed, where case (a) and (b) have the same spherical equivalent (SE) of +3.5 D and (c) and (d) have SE = –4.0 D. The converted positive-cylinder cases (b) and (d) have less tissue removed as previously reported.22 However, the postoperative P value may be different depending not only on the refractive correction power (D), but also on the direction (or angle) of the corrected meridian either parallel to the cylinder angle (defined as A2). The refraction correction power of the spherical and cylinder will be presented as D and D’, respectively, in the following analysis. Case (a), [+5.0, –3.0 × A1], the P value change along A1 is determined only by the spherical power D = +5.0 (diopter), therefore Eq(1) gives Δ = –0.17, where the decrease of P (or Δ < 0) was induced by hyperopic correction as expected. However, along the direction of A2 a smaller Δ’ = –0.08 is calculated by the combined correction power of D’ + D = –3.0 + 5.0 = +2.0 diopter. In comparison, case (b) with [+2/0, +3.0 × A2], gives Δ = –0.08 (with D = +2.0) and Δ’ = –0.17 (with D’ + D = +5.0) which are 90 degree in angle converted but have the same magnitude of P changes. Similarly, in case (c) and (d), Δ equals +0.13 and +0.24 (along A1) Δ’ equals +0.24 and +0.13 (along A2), respectively.

Aspherical IOL Analysis Table 41.2: Aspherical corneal surface ablation profile in myopic LASIK H(y,d) = Z2 + Z4 Z2 = –1.333D(d2-y2) Z4 = (1/8R3)(p1-Bp2)(d4-y4) B = (R/R’)3, 1/R’ = 1/R + D/377. ———————————————————————— Z2: ablation depth under parabolic approximation (PA). Z4: the 4th-power of y for an aspherical cornea p1 and p2: pre and postoperative shape-factor p=Q+1. R and R’: pre and postoperative anterior surface radius. y: distance from the optical axis. d : radius of the ablation zone (d=W/2).

Table 41.3: Converting mixed astigmatism and corneal shape changes (a) [+5.0, -3.0 x 180] = (b) [+2.0, +3.0 x 90] (SE = +3.5) (c) [-3.0, -2.0 x 180] = (d) [-5.0, +2.0 x 90] (SE = -4.0) Conversion formula: [a, b × A1] = [1+b, -b × (A1 + 90)] Spherical equivalent (SE) = (a+b)/2 Shape factor (P) change: Δ = P’-P = -2B(1-1.5 B)P Δ >0 (less prolate after myopic LASIK) Δ –0.19. Furthermore, a cornea will become more oblate, if it is initially oblate for all Q1. In comparison, a cornea after hyperopic correction will become more prolate for all Q1, if it is initially prolate; whereas an initially oblate cornea will become less oblate when Q1 > +0.21. These features are summarized in Table 41.1. Most of the previous studies treat the final state asphericity (Q2) as a freely adjustable parameter to make a general statement of increases in the shape factor (p2) for myopes and decreases for hyperopes5-7 without specifying the threshold values of Q 1 * (or p 1 *). Furthermore, the correlation power of N = 1 reported earlier 6 results in Q1* = B – 1 or Q1* = (–0.28, +0.34) versus (–0.19, +0.21) based on N = 2/3 for D = (–5, +5) diopters. The high-order Munnerlyn formula 6 on the other hand, having a correlation of Q2 = Q1/B which gives Q1* = 0, a conclusion conflicting with clinical measurements.7

Application # 3 The above analytic formulas may be further modified to include the effects due to reflection loss, non-normal laser incidence, would healing and other biomechanical factors which were reported as the predominant factors in explaining the discrepancy between the clinical findings and the theoretical calculations.7-9 Taking the difference of the ablation profile, Eq.(1.a), up to their 4th-power of y and d, one obtains the change of ablation due to the change of the final shape factor from p2 to p2'. ΔH = -C2 (B’p2' –Bp2)

(10)

Using the approximate expression of B’p2'–Bp2 = B(Δp2) – p2(ΔB),

(11)

Eq.(10) may be further simplified as ΔH = (1 + 0.5p2/d2)[103B (y4 – d4)/8R13],

(12)

where ΔH in micron and R1 and d in mm. Above formula reduces to that of Manns et al,10 if the p2(ΔB) term, about

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Mastering the Techniques of Intraocular Lens Power Calculations 6%, is ignored. However, it is substantially different from that of Gatinel et al,5 in which the authors assumed B = 1.0 and ignored p2 (ΔB) term. As calculated earlier, B = (–0.59 to 1.57) for D = (–8 to +8) diopter, significant errors (over 50%) are expected in the results of Gatinel based on B = 1.0 and independent to D. For example, they predicted 7.0 micron of central epithelial-hyperphasia to induce an oblate final corneal contour which is about 34% overestimated comparing to that of our new formula, only needs about 5.2 micron using a +5.0 diopter hyperpic correction. The sources of error of Gatinel et al may come from two factors, their Eq.(5) approximated (R1/R2)3 = 8R1D/1000 which should be (8R1D/1000)(1+0.02D), an error of 10% for D = –5.0 diopter; and their Eq.(9) assumed B = 1, or R2 approximated by R1 which results in additional errors as shown above.

COMPARISON OF CENTRAL ABLATION DEPTHS The calculated central ablation depth defined by Hcen = H(y = 0) in this Chapter may be compared to that of others as follows. The second-order approximation of Eq(1) gives Hcen = H0 + M0 (1 – B1/3)p1, (13.a) 3 4 3 Mo = 10 (d /8R1 ). (13.b) where H0 = 4Dd2/3 is the parabolic approximation 2 (PA) of Munnerlyn formula having a second-order approximation (SOA) of 4 Hmun = H0+ M’(1 – B), which does not provide any information about the corneal shape factor even high-order or exact formula is used. Furthermore, a correlation of Q2 = Q1/B was reported in a least-square method using SOA and Munnerlyn exact formula,6 where the mixture of spherical ablation profile and a postoperative aspherical corneal surface result in a correlation conflicting with the measured postoperative asphericity,7 and worse than the data predicted from PA having a correlation of p2 = p1/B. In comparison, the correlation of this study, p2 = p1/B2/3, is based on an algorithm in which both the ablation and final profiles are aspherical to avoid the artificial effects caused by the mixture of spherical and aspherical profiles. Eq.(13) is also substantially different from that of Gatinel et al, 5 in which the authors treated the postoperative shape factor p2 as a freely adjustable parameter non-correlated to its preoperative value p1. The non-correlated central depth may be derived from Eq(1.a) as follows (up to the 4th power of d)

Hcen = H0 + M0 (p1 – Bp2),

(14)

which may underestimate the central depth in comparing to the correlated formula of Eq.(13), since p2 is a free parameter. For example, for R1 = 7.7 mm, d = 3.0 mm, p1 = 0.8 and D = –5.0 diopter, Mo = 22.18 um, B = 0.724, B1/3 = 0.9, ? = Hcen – H0 = 1.8 um for the correlated case from Eq(14); and Δ = 22.18 (0.8 – 0.724p2) = 3.3 um, for p2 = 0.9 in non-correlated case of Eq (14); and Δ = 22.18 (1 – 0.724) = 6.12 um (independent to p1) for the SOA of Munnerlyn formula. The above examples demonstrate that the central depth changes are governed by the B-factor, the correlated values of p1 and p2 at a given ablation zone size (d) and intended refractive correction power (D). However, the significant contribution from the second term of Eq(13) is on the change of corneal shape or its asphericity, rather than the ablation depth, only about 2 to 5% of H0 as shown in the above examples. These features allow us to control or optimize the postoperative asphericity with a minimal change of its central depth which affects the intended power correction and ablation size.

COMPARISON OF THEORY AND MEASUREMENTS As mentioned earlier, the measured corneal asphericity (or shape factor) changes after LASIK were greater than the predicted values due to the algorithm used and the surface energy loss.20 The postoperative and preoperative p-factors are correlated as shown by Eq(14) p’ = B-Np = Ap, (15.a) A = 1/(1+0.0204 D)m, (15.b) where m = 2 (for n th order approximation of Lin19), m = 3 (for 2nd-order approximation of Anera et al 14), m = (4.5 to 6.0) (for adjusted to measured data20). In Eq.(15), I have used R/377 = 0.0204, for R = 7.7 mm. The slope function A for the above 3 cases are calculated as follows for various myopic and hyperopic corrections, for B’ = 1+0.0204 D = (R/R’), D -2 -5 -10 +2 +5 +10 ———————————————————————————

B’ A(1) A(2) A(3)*

0.96 1.09 1.13 1.42

0.9 1.24 1.38 1.62

0.8 1.58 1.98 2.6

1.04 0.92 0.89 0.64

1.1 0.82 0.75 0.57

1.204 0.65 0.53 0.37

———————————————————————————

* where the measured values A(3) are assumed to be 30% higher or lower than the nth-order approximation A(1),

Aspherical IOL Analysis depth which is only about 1.5 to 3.0 microns per 0.1 change of the shape factor p2. Customized ablation of prolate (or oblate) corneal surface requires the accurate information of the laser fluence (or energy per unit area) and spot size, the corneal anterior surface curvature, and its preoperative asphericity (Q1) or shape factor (p1). The conventional Munnerlyn formula can not account for the change of asphericity even a high-order approximation or exact equation is used.

REFERENCES

Fig. 41.2: The preoperative (p) vs. postoperative (p’) corneal shape-factor for 3 cases based on (1) nth-order approximation (Lin), (2) 2nd-order approximation (Anera et al), and (3) adjusted to measurements (Marcos et al) for myopic (-5.0 D) and hyperopic (+5.0 D) LASIK

that is, A(3) = 1.3A(1) for myopia and A(3) = 0.7A(1) for hyperopia correction. These values also allow us to calculate the corresponding power m = 4.5 (myopia) and 6.0 (hyperopia). Comparison of above three cases are shown in Figure 41.2 for D = +/–5.0 diopter. It should be noted that the trends of p’ increasing (decreasing) after myopia (hyperopia) remain the same for all 3 cases although their absolute values may be different and proportional to the power of corrections. From the above Table, it may be seen that the asphericity change may deviate 10% to 30% depending on the power function (m).

CONCLUSION The new algorithm of this Chapter based on Z4 term to account for the asphericity change was totally ignored in parabolic approximation (PA) or the exact formula of Munnerlyn. The relationship between p1 and p2 given by the correlation power N depends on the ablation algorithm and the Z4 value may be significantly affected by the choice of this relationship. For example, p1 = (R1/ R2)2P2 (or N = 2/3) when an exact conicoid surface is used in the ablation depth, whereas N = 1/3 in PA. The significant impact of the Z4 term is on the change of the corneal shape (or its asphericity) rather than the ablation

1. Mackee SM, Krueger RR, Applegate RA, in Customized Corneal Ablation, edited by SM Mackee, RR Krueger and RA. Applegate (SLACK, Thorofare, NJ, 2001), 3-9. 2. Lin JT. “Critical review on refractive surgical lasers”, Opt Engineer. 1995;34:668-75. 3. Twa MD, Lemback RG, Bullimore MA, Roberts C. “A prospective randomized clinical trial of laser in situ keratomileusis with two different lasers”. Am J Ophthalmol 2005;140:173-83. 4. Lin JT. “A new formula for ablation depth in 3-zone LASIK”, J Refract Surg 2005;21:413-14. 5. Gatinel D, Joang-Xuan T, Azar D. “Determination of corneal asphericity after myopia surgery with the excimer laser: a mathematical model”. Invest Ophthalmol Vis Sci 2001; 42:1736-42. 6. Jimenez JR, Anera RD, Diaz JA, Perez-ocon F. “Corneal asphericity after refractive surgery when the Munnerlyn formula is applied”. J Opt Soc Am (A) 2004;21:98-103. 7. Marcos S, Cano D, Barbero S. Increase in corneal asphericity after standard laser in situ keratmileusis for myopia is not inherent to the Munnerlyn algorithm. J Refract Surg 2003; 19:S592-S96. 8. Mrochen M, Seiler T. “Influence of corneal curvature on calculation of ablation patterns used in photorefractive laser surgery”. J Refract Surg 2001;17:S584-S87. 9. Anera RG, Jimenez JR, Barco LJ, Hitta E. “Change in corneal asphericity after laser refractive surgery, including reflection losses and nonnormal incidence upon the anterior cornea”, Opt Lett 2003;15:417-19. 10. Manns F, Ho A, Parel JM, Culbertson W. “Ablation profile for wavefront-guided correction of myopia and primary spherical aberration,”. J Cataract Refract Surg 2002;28: 766-74. 11. Cantu R, Rosales MA, Tepichin E, et al. Objective quality of vision in presbyopic and non-presbyopic patients after pseudoaccommodative advanced surface ablation. J Refract Surg 2005(Suppl.);21:S603-05. 12. Lee H, Oh JR, Reintein DZ, et al. Conservation of corneal tissue with wave-front-guided laser in situ keratomileuse. J Cataract Refract Surg 2005;31:1153-58. 13. Lin JT. A prospective randomized clinical trial of laser in situ keratomileusis with two different lasers. Am J Ophthalmol 2006;[Correspondence] (in press).

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Mastering the Techniques of Intraocular Lens Power Calculations 14. Anera R, Jimenez JR, Barco LJ. Equation for corneal asphericity after corneal refractive surgery. J Refract Surg 2003;19:65-69. 15. Holladay JT, Bains HS. Optimized prolate ablation with the NIDEK CXII excimer laser. J Refract Surg 2005;21:S595-97. 16. El-Danasoury, Baines HS. Optimized prolate corneal ablation: case report for the first treated eye. J Refract Surg 2005;21:S595-602. 17. Jenkins TCA. Aberration of the eye and their effects on vision. Br J Physiol Opt 1963;20:59-91. 18. Atchison DA, Smith G. Optics of the human eye. Woburn, MA: Butterworth-Heinemann 2000;14-16,143-147,160-62.

19. Lin JT. A New Algorithm for Controlling Corneal Asphericity in LASIK. In: Garg A. Ed. Mastering the Techniques of LASIK, EPILASIK and LASEK (Techniques & Technology)”. New Delhi: Jaypee Brothers, 2006. 20. Marcos S et al. Increase in corneal asphericity after standard LASIK for myopia is not inherent to the munnerlyn algoritym. J Refract Surg 2003;19:S592-S96. 21. Chen CC et al. Corneal asphericity after hyperopic LASIK. J Cataract Refract Surg 2002;28:1539-45. 22. Pinelli R, Ngassa N, Scaffidi E. Sequential ablation approach to the correction of mixed astigmatism. J Refract Surg 2006;22:787-94. 23. Smith G et al. The spherical aberration of the crystalline lens of the human eye. Vision Res 2001;41:235-43.

Determining Corneal Power

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Mujtaba A Qazi, Irwin Y Cua, Jay S Pepose (USA)

42

Determining Corneal Power for Intraocular Lens Calculation in Patients with Corneal Scarring and Irregular Astigmatism

INTRODUCTION Manual keratometry and corneal topography remain the most frequently utilized techniques for measuring central corneal refractive power for the calculation of intraocular lens implant (IOL) power in cataract surgeries. While both instruments provide good accuracy when applied to healthy, unoperated corneas with regular astigmatism, their use in measuring corneas that have irregular astigmatism1 or corneas that have undergone refractive surgery2-5 can lead to significant postoperative refractive “surprises.” The manual keratometer measures the corneal power at only four discrete, paracentral points on the anterior cornea and assumes that the average of these approximates the refractive power of the central cornea.2 The diopter values assigned to these four points incorporate thin lens-like contributions from the posterior cornea, by assuming that the central cornea is comprised of two spheres, with the posterior sphere or cornea having a radius of curvature 1.2 mm steeper than its anterior counterpart.2 While this relationship between the anterior and posterior corneal surfaces generally holds true for normal corneas, it is often altered in eyes that have undergone refractive surgery, or have central corneal scarring or irregular astigmatism.1-4 Additionally, there may be a change in the index of refraction in regions of corneal scarring due to local alteration of water content and collagen lamellae. The literature2-5 is replete with strategies to better determine corneal power of eyes that have undergone refractive surgery. Among the most commonly employed methods are refraction based calculations, rigid contact lens over-refraction (CLO), and computerized videokeratography (CVK). The latter two techniques can

also be applied to improve the accuracy of IOL calculations in eyes with corneal scarring and irregular astigmatism.1

TWO CASES OF IOL CALCULATIONS IN EYES WITH CENTRAL CORNEAL SCARS Two patients were referred to our institute for recalculation of IOL power because of greater than 5 diopters (D) of postcataract surgery refractive surprise due to errors in measurement of corneal power.1 The patients had irregular astigmatism related to (1) subepithelial, nummular stromal scarring from herpes simplex virus (HSV) keratitis, and (2) full-thickness corneal laceration repair. They were seen prior to IOL exchange. Manual keratometry data was compared to contact lens over-refraction and various curvature and power maps obtained from the Atlas (Humphrey-Zeiss) and Orbscan (Bausch and Lomb) computerized videokeratography (CVK) systems. In the first case, there was flattening involving the central 2 mm of the scarred cornea. The four paracentral points measured at 3 mm by the manual keratometer gave significantly higher values than the overall central corneal power, resulting in a hyperopic refraction following cataract surgery. This was confirmed by back calculating the corneal power using the Holladay IOL Consultant (Holladay Consulting, Inc.), which provides the “true” corneal power after axial length, IOL model, IOL power, and post-cataract surgery refraction are entered into a lens calculation formula. In the second case, manual keratometry readings could not be reliably recorded due to distorted mires. Most likely, the corneal power used for IOL calculation in the initial cataract surgery was based upon keratometry of the contralateral, unaffected eye. The total axial power map

278

Mastering the Techniques of Intraocular Lens Power Calculations Table 42.1: Mean corneal power measurements (D) in patients with (1) central, nummular stromal scarring secondary to HSV keratitis, and (2) corneal laceration repair Technique* Mean corneal power, Mean corneal power, patient 1 (D) patient 2 (D) Manual Keratometer Power (Atlas) Axial Keratometric Power (Orbscan) Total Axial Power (Orbscan) Total Optical Power (Orbscan) Rigid Contact Lens Over-refraction Back-calculated Power (Holladay)

43.00 41.37 41.82 38.64 39.11 36.37 37.60

Irregular mires 47.75 47.40 47.37 46.13 46.25 47.33

Axial

* Mean videokeratography measurements were the average power value of a central 3.0 mm diameter area of interest.

(Orbscan), total optical power map (Orbscan) and contact lens over-refraction methods provided the most accurate estimates of central corneal power (Table 42.1).

Computerized Videokeratography Computerized videokeratography is based upon computer analysis of placido disk images projected onto the corneal surface. CVK measures more than 5000 points over the entire cornea and more than 1000 points within the central 3 mm.2 This additional information can provide greater accuracy than manual keratometry for measuring corneal power in normal6,7 and postradial keratotomy (RK)8 eyes. However, Ladas et al9 report two cases post-RK in which topography-derived corneal power resulted in inaccurate IOL power implantation. Topography systems utilize an index of refraction that assumes a fixed relationship between the anterior and posterior curvatures to derive corneal power. Seitz and colleagues10 have demonstrated that topography may overestimate true corneal power in patients with previous photorefractive keratectomy (PRK), as the ratio of anterior to posterior curvature has been surgically altered. In patient 2, topographic data describes the corneal power with good accuracy, as the full-thickness laceration repair likely maintained the pretrauma relationship between the anterior and posterior corneal curvatures. Hence, the standardized index of refraction remained fairly accurate in estimating the corneal power in this case (Table 42.1, Patient 2). Our patient with anterior stromal scarring from HSV keratitis had flattening of the central 1 to 2 mm, which resembled the topographic changes typically seen after refractive surgery. Axial maps, which provide curvature and not refractive power values, overestimated the central corneal power (Table 42.1, Patient 1) in this patient by over +3 D. CVK that relies on

analysis of the anterior corneal surface may not be accurate in all cases of central corneal scarring or irregular astigmatism. The Orbscan topography system combines Placidodisk and slit-scanning technology to measure elevation and power of both the anterior and posterior corneal surfaces.11 Using this information, total axial power and total optical power can be calculated. The total optical power map (Fig. 42.1) applies ray tracing analysis through the anterior and, then, posterior corneal surfaces, along with weighting for the Stiles-Crawford effect, to calculate the cornea’s total effective power.11 Sonego-Krone and colleagues12 determined that direct measurement of central corneal power after myopic laser in situ keratomileusis (LASIK) using total mean power and total optical power Orbscan maps provided accurate postrefractive surgery corneal power, independent of historical refractive data. In the two cases presented above, the total axial power maps and total optical power maps were more accurate in estimating the true corneal power than the axial curvature and keratometric maps. However, the application of slit-scanning CVK to cases of corneal scarring may be limited to cases with milder corneal opacity, as dense regions of scarring and intracorneal opacities may obscure the image of the posterior cornea and introduce artifact into total corneal power calculations. Additionally, the reliability of posterior corneal measurements has not been fully established, particularly for postrefractive surgery eyes.13

Rigid Contact Lens Over-refraction The contact lens over-refraction method requires that a hard contact lens of known base curve and power be placed over the eye. Refraction is performed prior to and after the

Determining Corneal Power

Fig. 42.1: The Orbscan total optical power (TOP) map of a patient with central, nummular stromal scarring from herpes keratitis. Average total optical power for the central 3 mm of this cornea was obtained using the “STATS” feature found under the “TOOLS” menu. The “ANALYZE AREA- STATISTICS” mode for the “ANALYZE AREA” sub-menu was then selected. The cursor was dragged from the central cornea to create a 1.5 mm radius central circle of analysis. An internal calculation, applying ray tracing to both the anterior and posterior corneal surfaces, provided a mean TOP value for this area of interest

placement of the contact lens. The corneal power is estimated with the following formula: K = BC + D + (OR – SE)1,2 K = Corneal power, BC = Base curve of rigid contact lens, D = Contact lens power, OR = Spherical equivalent of contact lens over-refraction, and SE = Spherical equivalent without contact lens. The advantages of this technique include detection of vision loss from corneal surface-irregularities, use of the physiologic optical pathway, and applicability regardless of etiology or mechanism of corneal scarring.4 One of the limitations of this technique is that the patient must have good enough visual acuity to obtain an accurate refraction.2,4 Zeh and Koch4 advise that contact lens overrefraction would be acceptable in patients with preoperative best-corrected visual acuity of 20/70 or better.

Examination and Surgical Planning An evaluation of a patient with concurrent corneal scarring and cataract involves uncorrected and bestspectacle correct visual acuity testing, evaluation of pupillary response and ocular motility, intraocular pressure assessment, gonioscopy, contact lens over-

refraction, videokeratography, and fundoscopy. If both structures are significantly contributing to vision loss, a combined penetrating keratoplasty and cataract removal with IOL placement is advised. Many surgeons use a default corneal power of 43 D to calculate the IOL power for triple procedures. Several authors have advocated development of personalized surgeon’s constants for this cohort.14,15 In cases where traumatic injury to the lens and cornea requires simultaneous lens extraction and corneal laceration repair, as in our second patient, it may be better to stage a secondary lens implantation after the corneal repair has healed, so that direct measurements of corneal power and axial length can be obtained. There is no conclusive advantage to one modern theoretical IOL calculation formula over others when applied to corneas with scarring or irregular astigmatism. Among the formulas used for RK and LASIK eyes with good efficacy include the Binkhorst, Holladay and Hoffer Q formulas.16,17 In general, the lowest corneal power value and a myopic target should be selected to minimize the risk of postcataract hyperopia.

CONCLUSION Although manual keratometry and placido-based topography are the most frequently utilized methods for determining central corneal refractive power in patients undergoing cataract surgery, both have limited efficacy for measuring corneas with irregular astigmatism or central scarring. Contact lens over-refraction can provide better estimation of corneal power in cases with visual acuities of 20/70 or better. Computerized videokeratography that analyzes both the anterior and posterior corneal surfaces may more accurately predict true corneal power than manual keratometry or maps that analyze the anterior surface alone.

REFERENCES 1. Cua IY, Qazi MA, Lee SF, Pepose JS. Intraocular lens calculations in patients with corneal scarring and irregular astigmatism. J Cataract Refract Surg 2003;29:1352-57. 2. Holladay JT. Intraocular lens power calculations for the refractive surgeon. Oper Tech Cataract Refract Surg 1998;1:105-11. 3. Hamed AM, Wang L, Misra M, Koch DD. A comparative analysis of five methods of determining corneal refractive power in eyes that have undergone myopic laser in situ keratomileusis. Ophthalmology 2002;109:651-58. 4. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-03.

279

280

Mastering the Techniques of Intraocular Lens Power Calculations 5. Gimbel HV, Sun R. Accuracy and predictability of intraocular lens power calculation after laser in situ keratomileusis. J Cataract Refract Surg 2001;27:571-76. 6. Cuaycong MJ, Gay Ca, Emery J, Haft EA, Koch DD. Comparison of the accuracy of computerized videokeratography and keratometry for use in intraocular lens calculation. J Cataract Refract Surg 1993;19 Suppl:17881. 7. Husain S, Kohnen T, Maturi R, Er H, Koch DD. Computerized videokeratography and keratometry in determining intraocular lens calculations. J Cataract Refract Surg 1996;22:362-66. 8. Celikkol L, Pavlopoulos G, Weinstein B, Celikkol G, Feldman ST. Calculation of intraocular lens power after radial keratotomy with computerized videokeratography. Am J Ophthalmol 1995;120:739-50. 9. Ladas JG, Boxer Wachler BS, Humkeler JD, Durrie DS. Intraocular lens power calculations using corneal topography after photorefractive keratectomy. Am J Ophthalmol 2001;132:254-55. 10. Seitz B, Langenbucher A, Nguyen NX, Kus MM, Kuchle M. Underestimation of intraocular lens power for cataract surgery after myopic photorefractive keratectomy. Ophthalmology 1999;106:693-702. 11. Srivannaboon S, Reinstein DZ, Sutton HFS, Holland SP. Accuracy of Orbscan total optical power maps in detecting

12.

13.

14.

15.

16. 17.

refractive change after myopic laser in situ keratomileusis. J Cataract Refract Surg 1999;25:1596-99. Sonego-Krone S, Lopez-Moreno G. Beaujon-Balbi OV, Arce CG, Schor P, Campos M. A direct method to measure the power of the central cornea after myopic in situ keratomileusis. Arch Ophthalmol 2004;122:159-66. Prisant O, Calderon N, Chastang P, Gatinel D, Hoang-Xuan T. Reliability of pachymetric measurements using Orbscan after excimer refractive surgery. Ophthalmology 2003; 110:511-15. Crawford GJ, Stulting RD, Waring GO 3rd, Van Meter WS, Wilson LA. The triple procedure. Analysis of outcome, refraction, and intraocular lens power calculation. Ophthalmology 1986;93:817-24. Flowers CW, McLeod SD, McDonnell PJ, Irvine JA, Smith RE. Evaluation of intraocular lens power calculation formulas in the triple procedure. J Cataract Refract Surg 1996;22: 116-22. Feiz V, Mannis MJ. Intraocular lens power calculation after corneal refractive surgery. Curr Opin Ophthalmol 2004; 15:342-49. Odenthal MT, Eggnick CA, Melles G, Pameyer JH, Geerards AJ, Beekhuis WH. Clinical and theoretical results of intraocular lens power calculation for cataract surgery after photorefractive keratectomy for myopia. Arch Ophthalmol 2002;120:421-38.

Wolfgang Haigis (Germany), Frank J Goes (Belgium)

43

IOL Calculation in Hyperopes

INTRODUCTION Hyperopia, usually linked to short eyes, presents special problems for biometry and IOL calculation. The term ‘short eyes’ needs to be defined: setting the limit at an axial length of 22 mm leaves some 11% short eyes smaller than 22 mm an0d ≈ 89% normal and long eyes.1 With ultrasound biometry, it is often difficult to obtain good-quality echograms, since the ocular interfaces are not well centered in these eyes. A-scans like the one shown in Figure 43.1 are rather exceptions from the rule. The echogram stems from a short eye with an axial length of 19 mm and was taken in ultrasound immersion technique. This technique or – preferentially - optical biometry are the methods of choice for short eyes; contact ultrasound should not be used. Apart from the difficulties in obtaining precise axial lengths, there are more problems specific to these eyes.1

The IOL position, e.g. is critical: the refractive effect if the lens deviates from its anticipated position is 3 times more pronounced in a short eye than in a long eye. Short eyes require stronger IOL powers than long eyes. For highpowered lenses, however, larger manufacturing tolerances are allowed than for normal IOL powers2 hence creating an additional problem for eyes in need of high powers. The selection of a suitable IOL power formula, too, is critical for short eyes. In KJ Hoffer’s classical paper on the ‘short eye problem’3 an overestimation of the lens power in these eyes was described which eventually led to the development of the SRK I and II formulas.4-6 The authors of these formulas, however, did their job too well, causing now underestimations of the necessary IOL powers in short eyes which make SRK I and II definitely the wrong formulas for these eyes (e.g. [1]). The purpose of the present work was to analyze the refractive outcomes of hyperopic patients and compare the results to predictions of the different IOL power formulas which are implemented in the Zeiss IOLMaster.

MATERIAL AND METHODS

Fig. 43.1: A-scan echogram of a short eye (axial length = 19 mm) measured in ultrasound immersion technique. The anterior chamber depth is shallow, the lens thick, the vitreous length short

In this retrospective study, 91 (48 right, 43 left) eyes of 50 hyperopic patients (18 males, 32 females) presenting for clear lens extraction (CLE) in the Goes Eye Center, Antwerp, Belgium, were enrolled. Their mean age was 46.7 ± 10.5 yrs (median: 47.6 yrs, range: 23.8/65.8 yrs), their mean preoperative refraction (spherical equivalent SEQ) 5.4 ± 1.2 D (median: 5.3 D, range: 3.0/9.5 D), sphere: + 5.8 ± 1.3 D (median:+ 5.8 D, range: + 3.0/+ 9.5), cylinder: –0.8 ± 1.1 D (median: – 0.5 D, range: – 5.0/0 D). All patients underwent uneventful phaco surgery, predominantly with superior incision, with continuous

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curvilinear capsulorhexis. Two types of intraocular lenses (IOL) were implanted: Alcon SA60AT (n = 55) and Alcon SN60AT (n = 36). In all cases, biometry (axial length, anterior chamber depth ACD) and keratometry (corneal radii) were performed with the Zeiss IOLMaster. Postoperative manifest refraction was determined 57 ± 55 days (median: 39 days, range: 1/367 days) after surgery at best distance corrected visual acuity (BCVA). The mean postoperative refraction (spherical equivalent SEQ) at BCVA was – 0.4 ± 0.8 D (median: – 0.4 D, range: – 2.9/+1.8 D) , sphere: 0.0 ± 0.8 D (median: 0.0 D, range: –2.5/+1.8 D), cylinder: – 0.7 ± 0.9 D (median: – 0.5 D, range: – 4.0/0.0 D). The mean IOL power implanted was 30.4 ± 2.0 D (median: 30.0 D, range: 26.0/34.0 D). For each patient, the actually achieved postoperative SEQ was compared to the predicted refractions of the following IOL power formulas: Haigis, 7 HofferQ, 8 Holladay-1,9 SRK/T,10 SRK II.6 Since the two IOL types implanted differed only by the color of their optics, the IOL constants of the Alcon SN60AT published on the ULIB website11 were used for both lens types: Haigis constants: a0 = 0.183, a1 = 0.227, a2 = 0.167; HofferQ constant: pACD = 5.40; Holladay I constant: sf = 1.62; Aconstant for SRK/T = 118.7; A-constant for SRK II = 119.0. Main outcome measures were the mean arithmetic (ARE) and mean absolute (ABE) prediction errors (= achieved (SEQ) – calculated refraction) and the percentages of correct refraction predictions within ± 0.5, ± 1 and ± 2 D. Results are reported as means ± standard deviations (sd), medians and ranges defined by minimums and maximums. Statistical evaluations were carried out using Microsoft Excel 2000 (Microsoft Corp.) and SigmaStat 3.5 (Systat Software Inc.) To test for normal distribution, the KolmogorovSmirnov test was applied. For the comparison of means, a one-way repeated measures ANOVA was carried out. If

Table 43.1: Preoperative biometric and keratometric patient data N=91

Axial length [mm]

Anterior chamber Mean corneal depth [mm] radius [mm]

Mean ± sd

21.23 ± 0.57

2.87 ± 0.31

7.81 ± 0.26

Median

21.27

2.92

7.82

Range

20.02 … 22.62

2.21 … 3.75

7.18 .. 8.46

normality failed, a Friedman repeated measures ANOVA on ranks was performed instead. The Tukey test was used for pairwise multiple comparisons. A p-value < 0.05 was considered significant.

RESULTS Table 43.1 lists the preoperative biometric and keratometric patient data. It can be seen that the range of axial lengths was comparatively small in contrast to the ranges of anterior chamber depth and mean corneal radius. Table 43.2 shows the means and medians of the arithmetic (ARE) and the absolute (ABE) prediction errors together with the percentages of correct refraction predictions within ± 0.5D, ± 1D and ± 2D for the different IOL power formulas in the IOLMaster with the lens constants from the ULIB website. The medians of the arithmetic prediction errors were significantly different (p < 0.05) in all pairs except between the HofferQ and Haigis formulas. Likewise, the medians of the absolute prediction errors were significantly different (p < 0.05) in all combinations except for the pairs Holladay/Haigis, Holladay/HofferQ and HofferQ/Haigis. The best results were evidently obtained with the Haigis and HofferQ formulas with mean arithmetic errors of – 0.07 ± 0.68 D and – 0.03 ± 0.68 D respectively and median absolute errors of 0.40 D and 0.45 D respectively. Also, the

Table 43.2: Mean and median arithmetic (ARE) and absolute (ABE) prediction errors (achieved – calculated refraction) and percentages of correct refraction predictions within ±0.5D, ±1D and ±2D for different IOL power formulas with ULIB IOL constant

ARE [D]

ABE [D]

% within

Formula

Mean ± sd

Median

Mean ± sd

Median

± 0.5 D

± 1.0 D

± 2.0 D

Haigis

–0.07 ± 0.68

0.00

0.52 ± 0.44

0.40

59.3

82.4

100.0

HofferQ

–0.03 ± 0.68

0.03

0.54 ± 0.41

0.45

54.9

86.8

100.0

Holladay-I

+0.37 ± 0.65

0.40

0.62 ± 0.43

0.56

46.2

81.3

98.9

SRK/T

+0.76 ± 0.65

0.79

0.85 ± 0.52

0.79

26.4

64.8

98.9

SRK II

+1.33 ± 0.68

1.39

1.33 ± 0.67

1.39

13.2

29.7

85.7

IOL Calculation in Hyperopes

Fig. 43.4: Arithmetic prediction error of the Haigis formula vs axial length

Fig. 43.2: Arithmetic prediction errors ARE for the following IOL formulas: Haigis (HAI), HofferQ (HOF), Holladay I (HOL), SRK/T (SRKT) and SRK II (SRK2)

Fig. 43.5: Arithmetic prediction error of the HofferQ formula vs axial length

DISCUSSION

Fig. 43.3: Absolute prediction errors ABE for the IOL formulas of Figure 43.2

percentages of correct refraction predictions within ± 0.5, ± 1.0 and ± 2.0 D were highest for these 2 formulas. SRK II produced the worse results. This can also be seen from Figures 43.2 and 43.3, which show boxplots of the ARE and ABE. In Figures 43.4 and 43.5, the axial length dependence of the arithmetic prediction error is plotted for the Haigis and Hoffer Q formulas. The slope of the regression line for the Haigis formula is smaller than for the HofferQ. In both cases, the slope is significantly different from 0 (p < 0.03) and the correlation coefficients are small (Haigis: 0.23, Hoffer Q: 0.37).

In this study 91 eyes of 50 hyperopic patients were examined who had undergone biometry and keratometry with the Zeiss IOLMaster. The IOL powers implanted ranged from 26 to 34 D. The Haigis and HofferQ formulas turned out to show the best performance in these eyes. These findings are in perfect agreement with a recent study from Moorfields Eye Hospital, London, UK,12 in which 76 IOL datasets from 56 patients were evaluated. In this largest-ever series so far published with IOL powers 30 D or greater, the authors found the Haigis formula to be the most accurate, followed by HofferQ, Holladay-1 and SRK/ T. The very same results concerning the ranking of the formulas had been obtained in a former study at our lab,1 based on the analysis of 771 eyes (of which 78 had an axial length £ 22 mm) with an AMO SI40B lens. In the original HofferQ publication,8 Hoffer also compared several IOL formulas with respect to their performances in different axial length ranges. For eyes with axial lengths < 22 mm, he observed mean absolute errors of 0.52 D (HofferQ), 0.61 D (Holladay-1), 0.76 D (SRK/T) and 0.83

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D (SRK II). The respective results in the present study were 0.54 D (HofferQ), 0.62 D (Holladay-1), 0.85 D (SRK/ T) and 1.33 D (SRK II). In a second paper13 dealing with the same subject, Hoffer included the Holladay-II formula in his analysis. Unfortunately, this formula is not published but only available as a computer software. For 10 eyes shorter than 22 mm he concluded that the Holladay-II equals the HofferQ in short eyes. The mean absolute errors for both formulas were 0.72 D. The good performance of the Haigis, HofferQ and Holladay-II formulas in these eyes is also reported by Hill.14 Based on IOLMaster axial length data and his experience with several popular posterior chamber lenses, he reports mean absolute prediction errors for different IOL power formulas and different axial length ranges. Hence, for eyes < 22 mm, absolute errors of 0.25–0.50 D are only obtained with the Haigis, HofferQ and Holladay2 formulas. Other formulas would produce prediction errors > 0.25 D.

CONCLUSION The best results in IOL calculation for hyperopes were obtained with the Haigis and HofferQ formulas.

REFERENCES 1. Haigis W: IOL calculations in long and short eyes. In: Mastering intraocular lenses (IOLs). Ashok Garg, JT Lin (eds), Jaypee Brothers Medical Publishers (P) Ltd, New Delhi, India, 92-99, 2007 and in: Mastering the techniques of IOL power

2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12.

13. 14.

calculations. Ashok Garg, Jairo E. Hoyos, Dimitrii Dementiev (eds), Jaypee Brothers Medical Publishers (P) Ltd, New Delhi, India, 2005;75-85. European standard prEn ISO 11979-2, August 1999: Ophthalmic implants – intraocular lenses. Part 2: Optical properties and testing procedures ISO/FDIS 1999;11979-2. Hoffer KJ. Intraocular lens calculation: the problem of the short eye. Ophthalmic Surgery 1981;12(4):269-72. Retzlaff J. A new intraocular lens calculation formula, Am Intra-Ocular Implant Soc J 1980;6:148-52. Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. Am Intra-Ocular Implant Soc J 1980;6:263-67. Sanders DR, Retzlaff J, Kraff MC. Comparison of the SRK II formula and other second generation formulas. J Cataract Refract Surg 1988;14:136-41. Haigis W, Lege B, Miller N, Schneider B. Comparison of immersion ultrasound biometry and partial coherence interferometry for IOL calculation according to Haigis, Graefes Arch Clin Exp Ophthalmol 2000;238:765-73. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas. J Cataract Refract Surg 1993; 19:700-12. Holladay JT, Musgrove KH, Prager TC, Lewis JW, Chandler TY, Ruiz RS. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17-24. Retzlaff J, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16(3):333-40. http://www.augenklinik.uni-wuerzburg.de/ulib/c1.htm, table as of Nov 22, 2007. Maclaren RE, Natkunarajah M, Riaz Y, Bourne RRA, Restori M, Allan BS. Biometry and formula accuracy with intraocular used for cataract surgery in extreme hyperopia. Am J Ophthalmol 2007;143:920-31. Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000;26: 1233-37. Hill W. Choosing the right formula. www.doctor-hill.com/ iol-main/formulas.htm as of Dec.21, 2007.

Paul Rolf Preussner (Germany)

44

Consistent IOL Calculation in Normal and Odd Eyes with the Raytracing Program OKULIX

ABSTRACT Purpose: To provide a highly accurate IOL power calculation method which can be used without modification in “normal” as well as in “odd” eyes, particularly after corneal refractive surgery. Method: Classical formulae which are based either on Gaussian optics or on empirical adjustments are replaced by a raytracing calculation of the whole pseudophakic eye. The input data of the calculation are the true physical measurements of ocular parameters and the true manufacturing data of the IOL. Corneal surface is given by topography, and axial eye length is measured by partial coherence interferometry (PCI) or by an ultrasound device calibrated relative to PCI. IOL manufacturing data are anterior and posterior curvature radii, central thickness and index of refraction, thus avoiding ambiguously defined “power” values. Powers are only used for the IOL labeling. In case of aspheric IOL, also the asphericity of the anterior or posterior IOL surface is included. Most of the data of the leading IOL manufacturers are already included in the OKULIX data base. The IOL position is estimated by a simple scaling algorithm. The parameters of this algorithm are calibrated in a collective of 189 eyes in Vienna University Eye Hospital and tested in a different collective of 65 eyes in Mainz University Eye Hospital. Results: For “normal” eyes operated by a standard surgical procedure the prediction error of the method is negligibly close to zero, i.e. no “individualization” is necessary. Also for the small number of eyes after corneal refractive surgery included so far no systematic bias can be observed. Particularly, the hyperopisation common with classical formulae is avoided.

PRINCIPLE The following subsections shall describe the physical principle of the raytracing and the input data needed to perform this calculation. These data are the manufacturer’s IOL parameters, the axial eye length and the corneal topography for the extraction of corneal radii and asphericity.

Raytracing The raytracing procedure is used in order to avoid the inaccuracies of classical Gaussian optics which is a poor

approximation of the human eye. A schematic crosssection of the eye with the principle of the raytracing approach is shown in Figure 44.1. IOL power selection is done by calculation of the refraction in corneal plane for all power levels of a preselected IOL model. The power levels closest to the wanted target refraction are proposed to the user.

Fig. 44.1: Ray diagram (two-dimensional section) Two rays are shown, one is the optical axis, and one is an off-axis ray, which intersects the optical axis in the fovea (left side). The latter ray has an angle W to the optical axis in the fovea. This ray undergoes four refractions on four surfaces, where the refractive index changes. Calculation is done from fovea to cornea, which is allowed, since geometric optical pathways can always be mirrored. The refractive indices are: The intravitreal index I, the index of the lens B, of the aqueous humor K and of the cornea C. The shape of the surfaces is primarily described by their central curvature radii: R for the anterior corneal radius, E for the anterior lens and Z for the posterior lens radius. All of the curves can be circles, ellipses, parabolae or hyperbolae. They are distinguished by their numerical eccentricity e, which is 0 for a circle, between 0 and 1 for an ellipse, = 1 for a parabola and > 1 for a hyperbola. For the inner corneal radius we assume a value of 90% of the outer one as default. The total axial length L is the sum over corneal thickness H, anterior chamber depth V, lens thickness D and vitreous depth G. As result of the calculation, for the ray under consideration the distance from optical axis and the angle to it are calculated at the point where the ray leaves the eye. From these two values, the refraction error can be determined. The lens can be decentrated by the decentration A. If A6 ≠ 0, first a ray through fovea and central cornea is iteratively determined. This ray is then used as the reference ray instead of the optical axis. The angle between this ray and the straight line at the center of the cornea perpendicular to corneal surface is calculated in addition

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Table 44.1: IOL types

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Acritec: 73N/733D/737D Acritec: 44S/53N Acritec: 43TS Acritec: 81C Acritec: 14C Acritec: 27SF Acritec: 82C/86CS Acritec: 85C Acritec: 88CS Alcon: LX90BD Alcon: MA30BA Alcon: MA50BM Alcon: MA60AC Alcon: MA60BM/MA Alcon: MZ30BD Alcon: MZ40BD Alcon: MZ60BD Alcon: SA30AL Alcon: SA60AT AMO: Sensar AR40e AMO: Array SA40N (Silic.) AMO: Array SA40N (Acryl) AMO: SI30NB AMO: Clariflex AMO: SI40NB AMO: VERISYSE 50 AMO: VERISYSE 50 aph. AMO: VERISYSE 60 AMO: 351C AMO: 722A/C AMO: 751A AMO: 757C AMO: 808C AMO: 809C AMO: 811B/C/E AMO: 812A/C AMO: 911A AMO: 912A AMO: 920 AMO: Tecnis Z9000 Bausch&Lomb: Meridian Bausch&Lomb: Soflex 2 Bausch&Lomb: EZE-55 Bausch&Lomb: EZE-60/P492UV Bausch&Lomb: Akreos Disk Bausch&Lomb: Akreos Fit Bausch&Lomb: Akreos Adapt Corneal: ACR6DSE Corneal: Ultima Corneal: A6 Corneal: Concept360 Domilens: VisAcryl Hoya: AF-1(UV) Hoya: AF-1(UY) Human Optics: Microcryl Human Optics: Microcryl

ACDM

ØOpt

dpt

n

ASRK

ACDA

5.00 4.90 4.90 4.80 4.70 4.70 5.20 5.20 5.20 5.35 5.49 5.49 5.49 5.50 5.35 5.35 5.35 5.00 5.00 5.20 4.70 4.70 4.40

6.00 6.00 5.80 6.00 7.00 7.00 6.00 5.00 6.50 5.75 5.50 6.50 6.00 6.00 5.50 5.00 6.00 5.50 6.00 6.00 6.00 6.00 6.00 6.00 6.00 5.00 5.00 6.00 6.0 5.5 6.5 6.5 6.5 5.0 6.0 5.5 6.0 5.5 6.0 6.0 6.00 6.00 5.50 6.00 5.50 5.50 5.75 6.00 6.00 6.00 6.00 5.25 6.00 6.00 6.0 6.0

+10.0/+44.0 +1.0/+39.0 +1.0/+39.0 +1.0/+39.0 +10.0/+35.0 +5.0/+30.0 +1.0/+39.0 +1.0/+39.0 +1.0/+39.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 –5.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +6.0/+34.0 +10.0/+34.0 –10.0/+30.0 +6.0/+30.0 +6.0/+30.0 +6.0/+30.0 –10.0/+30.0 +6.0/+30.0 –23.5/+12.0 +10.0/+30.0 -15.0/-3.0 +9.0/+29.5 +8.0/+30.0 +8.0/+30.0 -10.0/+7.0 +8.0/+30.0 +8.0/+30.0 +8.0/+30.0 –10.0/+30.0 +12.0/+28.0 +5.0/+30.0 +5.0/+25.0 +5.0/+30.0 +10.0/+35.0 +1.0/+30.0 +0.5/+34.0 +0.5/+34.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 –5.0/+36.0 +4.0/+40.0 +4.0/+40.0 +10.0/+31.0 +10.0/+30.0

1.430 1.4480 1.4480 1.4920 1.4920 1.4920 1.4920 1.4920 1.4920 1.491 1.5542 1.5542 1.5542 1.5542 1.491 1.491 1.491 1.5542 1.5542 1.47 1.46 1.47 1.46 1.46 1.46 1.492 1.492 1.492 1.4915 1.4915 1.4915 1.4915 1.4915 1.4915 1.4915 1.4915 1.458 1.430 1.430 1.458 1.4747 1.427 1.493 1.493 1.459 1.459 1.459 1.465 1.465 1.465 1.465 1.458 1.517 1.516 1.460 1.460

118.5 118.5 119.0 118.0 118.9 118.9 118.9 118.9 118.9 118.7 118.9 118.9 118.4 118.9 118.7 118.7 118.7 118.4 118.4 118.4 117.73 118.4 117.4 118.05 118.05

4.31 4.10 4.35 4.01 4.30 4.30 4.45 4.57 4.38 4.29 4.39 4.26 4.25 4.24 4.25 4.33 4.16 4.30 4.31 4.09 3.86 4.09 3.68 4.05 4.05 2.5 2.5 2.5 2.49 4.27 4.26 3.50? 3.85 4.07 3.83 4.03 3.97 3.75 4.03 3.97 4.11 3.87 4.11 4.05 3.89 3.89 3.89 4.46 3.03 4.42 4.96 3.96 4.42 4.41 3.83 3.82

4.70

3.33 5.43 5.10 4.50 4.97 4.91 4.79 4.91 5.14 4.85 5.02 5.14 5.14 4.75 5.02 5.02 4.96 4.96 4.96

4.97

HD K3

115.2 118.8 118.8 117.2 118.0 117.9 117.7 117.9 118.3 117.8 118.6 118.3 118.3 118.1 118.1 118.1 118.0 118.0 118.0 119.0 116.5 119.0 120.0 118.0 118.7 118.7 118.4 118.1

ACDL

4.29

4.25

4.20 4.00 4.10

4.00

4.00

Contd...

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287

Contd... ACDM

ØOpt

dpt

n

ASRK

ACDA

4.73 5.02 5.02 5.02 5.61 5.26 5.02

6.10 6.10 5.10 6.60 6.00 6.00 6.00 5.00 5.00 6.00 5.80 6.0 6.0 5.75 5.75 6.25 5.5 6.40 5.10 5.10 5.50 5.75 6.00 6.00 6.40 5.00 6.0 6.0 5.75 6.0 6.5 6.0 6.0 6.0

–6.5/+28.0 +5.0/+35.0 +5.0/+35.0 +5.0/+35.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0 –23.5/+12.0 +10.0/+30.0 –15.0/-3.0 0.0/+30.0 +10.0/+30.0 +10.0/+30.0 8.0/+34.0 –7.0/+34.0 –10.0/+25.0 0.0/+34.0 0.0/+34.0 0.0/+34.0 0.0/+34.0 –7.0/+40.0 +8.0/+30.0 0.0/+34.0 –7.0/+34.0 0.0/+34.0 +6.0/+27.0 +10.0/+30.0 0.0/+35.5 +10.0/+30.0 0.0/+33.0 –16.0/+33.0 +10.0/+30.0 +10.0/+30.0 +10.0/+30.0

1.4906 1.4906 1.4906 1.4906 1.465 1.465 1.465 1.492 1.492 1.492 1.4607 1.457 1.430 1.4600 1.4600 1.4600 1.4915 1.4915 1.4915 1.4915 1.4915 1.4600 1.4915 1.4915 1.4915 1.4915 1.43 1.457 1.4585 1.492 1.492 1.473 1.430 1.457

117.6 118.1 118.1 118.1 119.1 118.5 118.1

4.35 4.01 4.16 3.93 4.55 4.22 4.09 2.5 2.5 2.5 4.12 3.85 3.93 4.03 4.03 4.01 4.21 4.25 4.10 4.10 4.08 3.94 3.85 4.21 4.25 2.96 3.73 3.85 4.07 4.24 3.90 4.34 3.93 3.85

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Morcher: 21S Morcher: 25/25L/65S Morcher: 27A/67G Morcher: 53E/66 Morcher: 92S Morcher: 97A Morcher: 98 OPHTEC: ARTISAN 50 OPHTEC: ARTISAN 50 aph. OPHTEC: ARTISAN 60 Physiol /W2O: CareFlex Polytech: Polylens A60 Polytech: Polylens S80 Rayner: 570C Rayner: 570H Rayner: 620H Rayner: 230U Rayner: 276U Rayner: 510A Rayner: 512A Rayner: 552A Rayner: 574R Rayner: 602A Rayner: 604A Rayner: 645A Rayner: 870U Technomed: 411/412 Technomed: AL-MP301/601 Technomed: Softec I/AL-SP101 Technomed: P2030 Technomed: P2540 Technomed: Ciba-Vision Memory Tekia: TEK-Lens Model 411 Tekia: TEK-Lens Model 614

– – – – – – –

ACDM: Manufacturer’s ACD value [mm] ØOpt: Optical cross diameter [mm] dpt refractive power range in diopters n: Index of refraction ASRK: A-constant of SRK-formula ACDA: ACD value as calculated from A-constant [mm] ADCL: ACD value as measured by laser interferometry [mm].

4.96 4.23

5.26 5.37 4.97 4.97 5.02 4.97 5.14 5.26 5.37 3.80 4.85 4.96 5.10 4.90 4.70 5.60 4.23 4.96

Currently Available IOL Types Table 44.1.

Axial Eye Lengths If axial eye lengths are measured by partial coherence interferometry (IOL Master, Zeiss, Germany), the resulting mean prediction error with OKULIX3 is negligibly close to zero, see also Table 44.3. However, the true axial lengths are not the values read from the IOL Master’s display.

118.4 118.0 118.2 118.4 118.4 118.4 118.5 118.7 118.0 118.0 118.1 118.0 118.3 118.5 118.7 116.0 117.8 118.0 118.0 118.5 118.0 119.0 118.2 118.0

ACDL

Inside the IOL Master the measured values are transformed by a formula given by Haigis: Aacu = 1.0448 × Aopt – 1.3617 with Aopt: optical and Aacu: acoustical eye length.1 The reason for Haigis to do so was to adjust the optical measurements to formulae using ultrasound values. In OKULIX this transformation is inverted thus restoring the originally measured optical data: Aopt = 0.9571 × Aacu + 1.3033

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But also ultrasound axial eye lengths can be used with OKULIX, with only little loss of accuracy. The measured acoustical values are transformed into optical ones by a corresponding linear transformation. The parameters for such a transformation have been measured in 131 eyes8 for the AL2000 (Tomey, Japan). The relation is valid also for all other devices of the Tomey company.

CORNEAL RADII In “normal” eyes keratometry is sufficiently accurate to determine corneal radii. Keratometers, however, are adjusted to spherical or to moderately prolate corneae. In case of an aspheric cornea the vertex radii are overestimated for prolate and underestimated for oblate curvatures (Fig. 44.2). After corneal refractive surgery of previously myope eyes corneal curvature often becomes oblate, resulting in an underestimation of corneal vertex radii and therefore hyperopic shift after cataract surgery. The amount of the effect is graphically shown in Figure 44.3. The resulting error can be avoided if corneal asphericity is taken into account exactly. In OKULIX a three-dimensional model of the cornea based on topographic measurements is used to extract the corneal vertex radii6 together with corneal asphericity. The topographic data of Tomey TMS2 or TMS4 (Japan), Technomed C scan (Germany), Zeiss/Humphrey Atlas (Germany) or Oculus Keratograph/Easygraph (Germany) can be used for input in OKULIX.

Fig. 44.2: Curvature measurements in aspherical cornea. The lower curve shows the section through a spherical cornea, the upper one through an aspherical one (exaggerated for better visualization). The central curvature radius is the same for both curves. Ray 1 is reflected from the lower curve at the same angle as ray 2 from the upper one. In Littmann’s keratometer, the curvature radius is determined from the distance between the central ray and the ray fulfilling the reflection criterion, because for this ray, the investigator sees the coincidence of the projected test figures. In order to measure the curvature radius correctly, the measuring position should be position 1. Position 2 suggests a larger radius

Fig. 44.3: Keratometry in aspherical cornea. In the upper image the measurement deviation [mm] between the assumed and the actual reflection point (Fig. 44.2) is plotted as a function of the numerical eccentricity e [dimensionless]. The curves are labeled by the distance of the reflection point from the optical axis for a spherical cornea of 7.8 mm radius. For the classical Littmann keratometer, this distance is 1.3 mm.2 In the lower image the refraction error [dpt] in emmetropic paraxial IOL calculation caused by the effect of the upper image is shown. e > 0.6 occurs in case of a keratoconus. e < 0 corresponds to oblate corneae after myopia correction in corneal refractive surgery. The labels have the same meaning as above

With this topography-based approach, IOL calculation for “normal” eyes and eyes after corneal refractive surgery can be performed by the same procedure. With respect to IOL calculation, the cataract surgeon even does not necessarily need to know about previous corneal surgery.

IOL POSITION Other than axial eye lengths or corneal radii the postoperative IOL position cannot be measured but only estimated in a model. In most of the IOL formulae the IOL position is more or less hidden to the user. A straightforward approach preferably should separate the IOL position into two parts: a mean value which only

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Table 44.2: Mean ACD and mean position of IOL center

IOL-type

A

N

T

Vpci

VA

Cpci

CA

Alcon: MA30BA Alcon: MA60BM/MA Alcon: SA30AL Alcon: SA60AT AMO: Sensar AR40 Pharmacia: 911A Sum/mean

118.9 118.9 118.4 118.4 118.4 118.3

19 20 17 11 74 48 189

0.67 0.84 0.67 0.65 1.00 1.14

4.29 4.25 4.19 4.00 4.10 4.00

4.39 4.24 4.30 4.31 4.09 3.97

4.625 4.67 4.525 4.325 4.602 4.57 4.580

4.725 4.660 4.635 4.635 4.591 4.540 4.587

A: Best-known A-constant as provided by the manufacturer N: Number of eyes T: Mean central thickness [mm] of the IOL type Vpci: Mean anterior chamber depth [mm] as measured by PCI VA: Mean anterior chamber depth [mm] as calculated from A-constant5 Cpci: Mean distance between the center of the IOL and the posterior corneal surface [mm] as calculated from T and Vpci CA: Mean distance between the center of the IOL and the posterior corneal surface [mm] as calculated from T and VA

resulting value becomes independent on the particular IOL type, at least for the IOL types investigated so far. The difference between the calculated and the measured means is only 7 µm,8 Table 44.2, bold faced numbers in the last line. The most probable individual IOL position can surprisingly be described by the simple linear scaling model shown in Figure 44.4, as could be shown by a comparison of different approaches from literature.8

CLINICAL RESULTS IN “NORMAL” EYES Fig. 44.4: Simple scaling model. The length ratio C/(C+b) is invariant. For each IOL type the mean offset Toff has to be measured only once. The individual ACD is then given by ACD = C + Toff –0.5·D with D: central IOL thickness. In mean over all IOL types, C has a value of 4.6 mm, Table 44.2

depends on the IOL type, and an individual offset relative to this mean value which only depends on the parameters of the individual eye. IOL positions can be described by the anterior chamber depth (ACD). The determination of the mean ACD of a given IOL type can be done in two different ways. It can be re-calculated from the A-constants of the SRK formulae,5 and it can be directly measured with a PCI.7 A comparison of the results of both approachs shows highly accurate coincidence, Table 44.2. If the ACD (distance between posterior cornea and anterior IOL) is replaced by the distance between posterior cornea and IOL center, the

The accuracy of any IOL calculation method can best be described by the prediction error, i.e. the difference between preoperatively predicted and postoperatively measured spherical equivalent of the refraction. The prediction error should not only be as small as possible in mean, but it should also be independent on the individual parameters of the investigated eyes, particularly on the axial eye lengths. Therefore, the prediction error as function of the axial length is an adequate description. The steepness of the regression line is a good measure of the trend (bias) for short or long eyes, Figure 44.5 and Table 44.3.

CLINICAL RESULTS AFTER CORNEAL SURGERY Eyes after corneal refractive surgery have been cataract operated so far in Mainz University Eye Hospital, Table 44.4. Figure 44.6 shows the details of a typical example.

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Mastering the Techniques of Intraocular Lens Power Calculations Table 44.3: Comparison of different IOL calculation methods*

Hoffer Q Holladay SRK T 0 SRK II 0 OKULIX

Offset [dpt]

Standard deviation [dpt]

0.546 0.498 467 666 0.036

0.75 0.75 0.76 0.82 0.72

Trend [dpt/mm] 0.0184 0.0149 – 0.0598 – 0.1008 0.0084

Table 44.3 shows a comparison of the differences between predicted and measured postoperative refractions (diopters, spherical equivalent). All calculations are performed with the same input data. Even if the offset (first column) can be eliminated by “individualization” in the other methods, this is not necessary with OKULIX. The “trend” (steepness of the regression line, Fig. 44.5) is a measure for the systematic bias in prediction error for long or short eyes. In an ideal method, all numbers should be as close to zero as possible. The data are taken from 65 “normal” eyes

Table 44.4: Error contributions after corneal refractive surgery*

Corneal radius SRK/T formula Holladay formula

Mean

Range [min. / max.]

+1.34 dpt +0.59 dpt +0.85 dpt

+0.49 dpt / +2.64 dpt –0.24 dpt / +1.40 dpt +0.13 dpt / +1.22 dpt

* 7 previously myopic eyes with axial length in the range from 26.1 to 32.2 mm all achieved target refraction within ±1.0 dpt. The table shows the errors that would have occurred with other methods. The major error in the sense of a hyperopic shift would have occurred if corneal radii would have been taken from keratometry (first line). This error is avoided by the OKULIX model extraction from topography. But also with the correctly extracted corneal radii an additional error in the sense of an additional hyperopic shift would result if the noted formulae would have been applied instead of the raytracing. The total error with the other methods thus would be the sum of the errors in the first line and either the second or the third line

DISCUSSION

Fig. 44.5: Prediction of postoperative refraction. The difference between preoperatively calculated and postoperatively measured spherical equivalent of the refraction is shown as function of the axial eye length. The ACD is predicted by the – linear scaling approach as described in the text with c = 4.6 mm. The steepness of the regression line is 0.0084 mm/dpt, Table 44.3 for comparisons

The IOL calculation with OKULIX can be performed in “normal” eyes as well as in “odd” ones, e.g. after corneal refractive surgery, without any modifications. Individualizations as proposed by several authors are not necessary, provided the surgical procedure is standardized. This means intact, circular capsulorhexis, in-the-bag implantation and a corneal or sclerocorneal incision without systematic influence on refraction. However, the resulting prediction errors are not zero and not below the recognition threshold. They are relatively higher for shorter than for longer eyes, Figure 44.5. There are two reasons. One is the higher error contribution from deviations between assumed and actual ACD. The other one is the higher influence of manufacturing errors for IOL with higher powers. Also, the allowed tolerances in the ISO standards are higher for IOL with higher power levels.

Consistent IOL Calculation

Fig. 44.6: IOL after eccentric PRK Upper left : Corneal radius [mm, pseudocolors] as a function of location [mm-grid] ten years after PRK. Upper right : Meridional refraction [dpt, pseudocolors] with an 12.5 dpt AMO Sensar Ar40 as function of location [mm-grid]. Axial length is 30.5 mm, ACD 4.645 mm. Lower right : Simulated visual impression of this pseudophakic eye for a pupil width of 2.5 mm. The Landolt’s ring corresponds to a visual acuity of 0.8 (16/20) which was achieved after cataract surgery with the IOL mentioned above. The small circles represent the retinal receptor grid. More details of generating the Landolt’s rings are described in4 Lower left : with (0.25/–0.75/37°), the best correcting prescription glass. The remaining asymmetric halo resulting from the eccentric ablation cannot be corrected by an IOL nor by a prescription glass

REFERENCES 1. Haigis W, Lege BAM. Optical and acustical biometry. Symposion on cataract, IOL and refractive surgery, ASCRSMeeting, 10.-14.4.1999, Seattle, Washington State, USA. 2. Littmann H. Grundsätze zur Ophthalmometrie. Bericht ¨uber die 56. Zusammenkunft der DOG in Heidelberg, 1950:33-39. 3. WWW.OKULIX.DE. 4. Preussner PR, Wahl J. Konsistente numerische Berechnung der Optik des pseudophaken Auges. Ophthalmologe 2000;97:126-41.

5. Preussner PR, Wahl J, Lahdo H, Findl O, Dick B. Ray-tracing for IOL calculation. J Cataract Refract Surg 2002;28: 1412-19. 6. Preussner PR, Wahl J, Kramman C. Corneal Model. J Cataract Refract Surg 2003;29:471-77. 7. Kriechbaum K, Findl O, Preussner PR, Köppl C, Wahl J, Drexler W: Determining postoperative anterior chamber depth. J Cataract Refract Surg 2003;29:2122-26. 8. Preussner PR, Wahl J, Weitzel D, Berthold S, Kriechbaum K, Findl O: Predicting postoperative anterior chamber depth and refraction. J Cataract Refract Surg 2004;30:2077-83. 9. Preussner PR, Wahl J, Weitzel. Topography based IOL power selection. J Cataract Refract Surg (in press) 2004;l.

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Mastering the Techniques of Intraocular Lens Power Calculations Anand A Shroff (India)

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A-scan in Difficult Situations

INTRODUCTION Progress in microsurgery, sophisticated new measurement techniques, and improvements in IOL calculation algorithms offer excellent chances to restore good vision in today’s cataract patients. Whereas most patients benefit from this progress without restrictions, a subgroup presents special problems in IOL calculation.1 Because more than two thirds of the eye’s total refractive power is provided by the cornea, its refractive power must be determined as accurately as possible for IOL calculation. Refractive surgery alters the corneal shape considerably; changes in corneal radii of 20 to 25 percent are fairly normal in formerly myopic eyes. As a consequence, classic keratometry in these eyes produces erroneous results, which in turn affect the accuracy of IOL calculations. Thus, the future holds increasing problems in IOL calculation when patients with previous refractive surgery develop cataract.2 Holladay describe 5 ways to estimate corneal power in eyes after corneal refractive surgery. They are, in descending order of accuracy, refractive history, contact lens over-refraction (CLO), videokeratography, automated keratometry, and manual keratometry. The refractive history method is considered to be the procedure of choice if all necessary information is available. If not, the CLO method is recommended.3 Although manual keratometry is still widely used to measure corneal curvature, cases involving IOL exchange highlight the limitation of keratometry-based measurement of corneal power in cases with central corneal flattening, such as postrefractive surgery or corneal anterior stromal scarring.

KERATOMETRY IN CORNEAL SCARRING/LACERATIONS Cases such as those of herpes keratitis have anterior stromal scarring, which results in central flattening of the anterior aspect of the cornea with little change in the posterior curvature. Central corneal flattening overlying these corneal scars resemble changes induced by laser refractive surgery. These scars are at the 1.0 to 2.0 mm zone with a steeper area surrounding the 3.0 mm zone. The 4 paracentral points measured at 3.0 mm by the keratometer measure higher corneal curvature in these areas than in the central zone and overestimate the true corneal power. This results in a hyperopic “surprise” after cataract surgery of the magnitude of 5.0 D. In cases of corneal trauma/lacerations, corneal power cannot be reliably estimated from manual keratometry because of markedly irregular mires secondary to the corneal scarring. Computerized videokeratography measures more than 5000 points over the cornea; thus, it provides greater accuracy than manual keratometers in corneas with irregular astigmatism. Even with the additional information, the axial map of placido-based corneal topography systems grossly overestimates the central corneal power. Corneal power determination by topography uses the anterior surface curvature multiplied by an index of refraction that assumes a fixed relationship between the anterior and posterior curvatures to arrive at a corneal power. Current instruments assume that the central cornea can be compared to a sphere and that the posterior radius of curvature is 1.2 mm steeper than the anterior corneal radius. While this is generally true in normal corneas, it is often not the case in eyes with

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Table 45.1: The mean corneal power (D) calculated from axial map (Humphrey corneal topography systems) orbscan curvature and power maps, manual keratometry and contact lens over-refraction. IOL Calculations in patients with irregular astigmatism

Optical zone (mm) 1.0 2.0 3.0 4.0 5.0

Axial map (atlas) 38.95 40.25 41.37 42.08 42.09

Axial Total axial Total optical Manual keratometric power map power map keratometry map (Orbscan) (Orbscan) (Orbscan) 40.17 41.03 41.82 42.34 42.20

38.00 38.21 38.64 39.14 39.61

irregular astigmatism or in eyes that have had laser refractive surgery.3 In corneas in which the relationship between the anterior and posterior surfaces is markedly changed, as in laser refractive surgery, the default index of refraction used by most topography systems is not accurate. Table 45.1 shows determination of mean corneal power at various optical zones using different methods. Many studies of modifying the conversion index for corneal power calculation after refractive surgery have been reported. 4-7 Recently, Holladay and Waring recommended using the refractive index of the anterior stroma (n = 1.376), corresponding to a corneal power correction factor of 1.114 (1.376/1.3375), to calculate the change in anterior corneal curvature measured by keratometry or videokeratography after PRK.6 Hugger et al suggest that a higher refractive index of 1.4083, corresponding to a correction factor of 1.21, is necessary to equalize the change in the SE (spherical equivalent) of the subjective manifest refraction and anterior corneal refractive power averaged over the central 3.0 mm. These higher values for the refractive index are used to calculate the change in corneal refractive power; they cannot be used to directly calculate corneal refractive power from measured values of the radius of curvature. 7 While the central corneal power derived from computerized videokeratography significantly overestimates corneal power in cases that are post-refractive surgery or herpes keratitis, the power from computerized videokeratography provides a reasonable estimation in corneal lacerations. This can be attributed to differences in the corneal scarring in the 2 types of cases. In a corneal laceration, the patient has full-thickness corneal scarring, likely resulting in similar changes in the anterior and posterior radii of curvature. Thus, the standardized index of refraction remains fairly accurate in estimating true corneal power. The Orbscan topography system combines Placido disk and scanning-slit technology to measure

38.44 38.84 39.11 40.61 40.49

43.00 -

Contact lens over-refraction 36.37 -

corneal curvature and power. From the video-captured slit images, the anterior and posterior corneal surfaces can be reconstructed. Using this information, the total axial power of the anterior and posterior corneal surfaces can be calculated. The total optical power map applies raytracing analysis through the anterior corneal surface and, subsequently, the posterior corneal surface to calculate the cornea’s total effective power. In corneas that have had refractive surgery, these maps should theoretically be more accurate than maps that analyze the anterior surface alone. Understanding the topographic changes induced by corneal incisions and sutures has resulted in specific recommendations for suturing lacerations to minimize corneal astigmatism.8 Thirty percent of ocular lacerations have associated lens damage, and removal of the traumatic cataract at the time of primary repair of the laceration seems to be technically easier and have less morbidity than when the cataract is removed as a secondary procedure.9 Recent studies generally calculate IOL power using measurements from the non-injured eye. Although this methodology is successful in most cases, there may be instances in which secondary IOL implantation is advisable.10-12 Simply relying on measurements of the contralateral normal eye can be problematic. One study reports that keratometry and axial length measurements of the injured eye, presumably affected by the corneal laceration, were ignored, leading to a 4.00 D surprise. The corneal laceration was central, large, and shelved, confounding calculation of the IOL power due to the resulting corneal topography. When an eye has this specific type of corneal laceration associated with a traumatic cataract, consideration should be given to using the axial length and the keratometry of the injured eye to calculate the IOL power. Difference in the axial lengths between the eyes, of 0.75 mm, could have been due to a change in corneal shape caused by the laceration. The

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Mastering the Techniques of Intraocular Lens Power Calculations axial length difference could have been present before the trauma occurred. The difference in axial lengths accounts for 1.875 D of the 4.00 D surprise. Thus, relying on corneal curvature and axial length measurements in the normal eye caused 4 D of error.10 Specific recommendations for suturing a corneal laceration obtain a spherical central cornea at the conclusion of the primary surgery. Whether these recommendations affect the final topography after sutures are removed and the laceration is healed is unproven. The success of IOL power calculation based on measurements from the fellow eye in patients with corneal lacerations and traumatic cataracts has been documented.10-12 Removal of a traumatic cataract and implantation of an IOL can be successfully performed at the time of primary repair of the corneal laceration. However, although there is evidence that a cornea has topographic memory after removal of sutures from a laceration, a long, shelved, central corneal laceration can confound calculation of IOL power because this type of laceration tends to have a large amount of irregular astigmatism. In this circumstance, secondary IOL implantation may be considered. It may be prudent to wait until the corneal laceration is healed and the sutures are removed and then calculate IOL power based on the simulated keratometry and the axial length measurement in the injured eye. When a cornea has traumatically induced, irregular, central astigmatism, simulated keratometry from videokeratoscopy may contribute to a more accurate calculation of the IOL power by using many corneal locations to determine the steepest and the flattest meridians. Also, a healed central corneal laceration might affect the axial length measurement in the injured eye.13

POSTREFRACTIVE SURGERY IOL CALCULATION Accurate calculation of the intraocular lens (IOL) power in postrefractive surgery eyes is a challenge for cataract surgeons. Using standard IOL calculation methods has resulted in many cases of postoperative hyperopia. This complication is not only a refractive surprise but may also be a refractive disaster for the patient, requiring IOL exchange. In postrefractive surgery eyes, the corneal power is often overestimated by standard keratometry (K) and topography. The keratometer measures the central 3.2 mm (manual) or 2.6 mm (automated) area of the cornea. Corneal topography instruments sample 1000 points within the central 3.0 mm and 5000 points over the entire

cornea. After refractive surgery, the central cornea is significantly flatter. Because of small optical zones of less than 3.0 mm in post-RK eyes, incorrect measurements of the corneal power are often made in the region of the knee between the directly treated portion of the cornea and the indirectly altered effective optical zones. This will result in overestimation of the corneal power and hence underestimation of the IOL power. As a result, patients are hyperopic after cataract surgery. The hyperopia may be exaggerated by the flattening induced by the cataract incision.14,15 The corneal power changes measured by automated keratometry and corneal topography analysis are reported to underestimate corneal flattening after photorefractive keratectomy (PRK) by an average of 24 percent. The greatest source of the underestimation is the corneal power changes measured by keratometry and videokeratography. A 1.0 diopter (D) error in the keratometric reading results in nearly a 1.0 D error in the postoperative refractive power. To avoid underestimating the IOL power and hyperopia after cataract surgery in postphotorefractive surgery eyes, the measured corneal power values must be corrected.16 Changes in corneal power measured by the first ring on videokeratography were closest to the change in the manifest refraction. The slope of the regression line in one study was 0.92 for the first keratoscopic ring, 0.88 for Sim K, and 0.74 for standard keratometry.7 Measuring the corneal power at the first videokeratographic ring appears to be a clinically practical and simple method for determining corneal power after photorefractive surgery.7 Table 45.2 shows IOL power calculation variation using various IOL formulas and different methods of determination of corneal power. Although central K was closer to the actual corneal power than the other K values, it varied slightly from the refractive changes. The possible reasons for the discrepancies include the following: The subjective refraction obtained by spectacle correction has several limitations, including the inability to correct for some small irregular astigmatism; the use of red-green and sunburst balanced tests results in subjective differences among patients; the real central corneal power cannot be measured on topography directly, and the power of the first ring is measured instead; the corneal anatomic center may be different from the visual axis, especially in patients with a large kappa angle.7 To minimize hyperopia after cataract surgery, many surgeons recommend using refraction-derived K values

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Table 45.2: Intraocular lens power (D) calculating using the mean corneal power derived from manual keratometry, CVK and contact lens over-refraction (Case 1)

Mean corneal power (D)

Method Axial map (Atlas) Axial keratometric map (Orbscan) Total axial power map (Orbscan) Total optical power map (Orbscan) Manual keratometry Contact lens derived corneal power

41.37 41.82 38.64 39.11 43.00 36.37

SRK/T

SRK II

Holladay 1

Holladay 2

22.0 (–1.66)* 21.5 (–1.62) 24.5 (–1.51) 24.0 (–1.48) 20.0 (–1.28) 26.5 (–1.36)

21.5 (1.29) 21.5 (–1.61) 24.0 (–1.32) 24.0 (–1.68) 20.5 (–1.68) 26.5 (1.69)

22.0 (–1.40) 21.5 (–1.40) 25.0 (1.41) 24.5 (–1.41) 20.5 (–1.55) 27.5 (–1.49)

23.5 (–1.67) 23.0 (–1.67) 28.0 (–1.39) 25.5 (–1.37) 21.5 (–1.56) 28.5 (–1.56)

CVK = Computerized videokeratography * Numbers in parenthesis are the predicted refractive outcome (D) based on the IOL calculation formulas.

Table 45.3: Back-calculated postoperative refraction error (D) based on IOL formulas using corneal power derived from CVK maps, manual keratometry and contact lens over-refraction (Case 1)

Formula

Manual keratometry 43.00 D*

Axial map (Atlas) 41.37 D*

Holladay 1 Holladay 2 Hoffer Q SPK/T SPK II

4.69 3.72 4.82 4.85 4.71

3.25 2.36 3.14 3.60 3.54

Total axial Axial map power map (Orbscan) (Orbscan) 41.82D* 38.64 D* 3.65 2.73 3.60 3.96 3.86

0.88 0.16 0.41 1.43 1.57

Total optical power map (Orbscan) 39.11D*

Contact lens over-refraction 36.37 D*

1.29 0.53 0.87 1.81 1.91

–1.05 –1.58 –1.76 –0.39 –0.06

All CVK maps of 3.0 mm optical zone * Mean corneal power.

instead of keratometry-derived or videokeratographyderived K values since the former may be more accurate. Many surgeons target for myopia in calculating the IOL power to counteract the tendency toward hyperopia. Koch et al report both a transient and a permanent hyperopic shift in corneal power in RK patients who had cataract surgery.14 Table 45.3 shows the back-calculated postoperative refractive error in the patient using corneal powers derived from the various topographical maps, manual keratometry, and contact lens over-refraction measurements entered into various IOL formulas. Contact lens over-refraction followed by the total axial power map derived from the Orbscan topography system give the most accurate determination of keratometric values when entered into standard IOL calculation formulas. Clinically, a significant hyperopic result from the target refraction can be experienced when doing cataract surgery in post-RK eyes, even when a refraction-derived keratometric value was used in the IOL power calculation. The hyperopic shift partly regresses with time. This shift

is not seen as much in post-PRK eyes as in post-RK eyes. One reason may be that the RK incisions do not heal sufficiently to provide normal corneal refractive stability, and the curvature is affected more by corneal edema than it would be in a normal cornea. In contrast, the integrity of the cornea is not as significantly reduced after PRK surgery. The refraction appears relatively stable in postPRK eyes.17

HARD CONTACT LENS METHOD Introduced by Holladay, the hard contact lens method is based on determining the difference between the manifest refraction with and without a rigid “plano” contact trial lens of a known base curve. An unchanged refraction indicates that the tear lens between the cornea and contact lens has zero power and that the effective anterior corneal radius is equal to the posterior radius (base curve) of the trial lens. If a myopic shift in refraction occurs with the contact lens, the base curve is steeper (i.e. the tear lens forms a plus lens and vice versa). The idea is to determine corneal radius by finding the trial lens that does not change the refraction with and without contact lenses

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Mastering the Techniques of Intraocular Lens Power Calculations and then read the power from the contact lens base curve. One limitation of this method is that the patient must have adequate visual acuity to obtain an accurate refraction.18 Holladay sets the lower limit of visual acuity at 20/ 80. Refraction should, of course, not be influenced by changes caused by cataract. Furthermore, contact lens decentration may cause problems particularly in highly irregular corneas. Hill recommends monitoring the lens position during the measurement, which should be performed as trial frame refraction and not as an autorefraction.19 The advantages of this method include detection of secondary visual loss due to irregular astigmatism, use of the physiologic optical cornea over the entrance pupil, and independence from the mechanism or magnitude of corneal alteration and changes in the index of refraction.18 Corneal power is calculated from the contact lens overrefraction using the following formula: K = BC + D + (OR – MR) where K = corneal power, BC = contact lens base curve (D), D=contact lens power [usually zero], OR =spherical equivalent of contact lens over-refraction, and MR = spherical equivalent of the manifest refraction without contact lens.20 A rigorous analysis of equation 1 reveals that the formula is not mathematically correct. It may give a clinically acceptable estimate of the corneal back vertex power in normal eyes without previous corneal surgery. In eyes with surgically reshaped corneas, however, equation 1 would theoretically lead to equivalent and vertex powers of the cornea that are too high by 1.00 to 2.00 D.

REFRACTIVE HISTORY METHOD To minimize the errors, Holladay suggests that the refraction-derived keratometric value rather than the actual keratometric value be used to calculate the IOL power.21 This involves subtracting the DSEQco (spherical equivalent at the corneal plane) induced by the refractive surgery from the mean corneal power measured before surgery.16,22 In most cases of advancing nuclear sclerotic cataract, a myopic shift in the refraction is seen (index myopia). Unless the surgeon knows what the early postrefractive surgery refraction was, this myopic shift may not be recognized. Ideally, when using refractionderived keratometric values to calculate IOL power, one should also consider the amount of myopic shift that was

induced by the cataract progression. For example, if the refractive procedure caused 4.00 D of corneal flattening and then a progressive cataract reversed 2.00 D of this effect through index myopia, the refraction-derived keratometric value would overestimate the “steepness” of the cornea as used in the lens power calculation formula. Thus, a less powerful IOL would be chosen, resulting in postoperative hyperopia. To obtain an accurate IOL power calculation, good clinical records that document refractions and keratometry measurements during cataract progression are needed. The myopic shift that is often observed in early nuclear sclerosis and opalescent cataracts must be factored in. Because it does not truly represent corneal steepening, its effect on refraction-derived keratometric values must be accounted for when choosing an appropriate IOL power for the cataract patient who has had refractive surgery.

ADJUSTING INTRAOCULAR LENS POWER FOR SULCUS FIXATION Although small-incision cataract surgery is a wellestablished technique, intraoperative posterior capsule rupture still occurs and sulcus fixation of the IOL is thus sometimes necessary. With sulcus fixation, the IOL shifts anteriorly to the intended position; thus, the spherical equivalent (SE) shows a myopic shift from the predicted value 23. As a consequence, when sulcus fixation is required, the planned IOL power should be changed. However, there is no consensus on how much the planned power should be reduced. In general, surgeons empirically subtract 0.50 to 1.50 diopters (D) from the IOL power calculated before surgery. However, there have been no studies of the changes in IOL power and the refraction after sulcus fixation. Sulcus fixation of an IOL of a preoperatively planned power results in a myopic shift because the lens is more anterior than an in-the-bag IOL.23 Suto et al report the mean difference between the postoperative SE and the preoperative refraction was 0.78 ± 0.47 D after sulcus fixation. This shows a significant myopic shift compared with that in contralateral eyes with in-the-bag IOL fixation. When the virtual power of the IOL for in-the-bag fixation that would achieve the same SE as that observed after sulcus fixation was calculated using the SRK/T formula, the virtual power was about 1.00D higher than the power of the IOL actually fixated in the sulcus. This suggests that the power of an IOL for sulcus fixation should be 1.00 D less than the planned power.24

A-scan in Difficult Situations Hayashi and co-authors used Scheimpflug videophotography to compare AC depth (ACD) values among 3 groups that had trans-scleral suture, sulcus, or in-thebag fixation and found a significant difference between sulcus and in-the-bag fixation. The difference in ACD was 0.73 mm, and the authors recommend a 0.50 D reduction in the intended power for sulcus fixation because the postoperative SE showed a significant myopic shift. However, they found no correlation between ACD and the postoperative SE.25

INTRAOCULAR LENS POWER CALCULATIONS IN PATIENTS WITH EXTREME MYOPIA Intraocular lens (IOL) power calculations pose difficulties for cataract surgeons planning surgery in eyes with extreme myopia.26 Since the velocity used in long eyes should be closer to that used in the aphakic eye (1532 msecond), it is recommended that the axial lengths be measured at, or converted to a distance for, 1532 m/second (AL1532), to which a nominal value of 0.28 mm is added to obtain the true ultrasonic axial length (ALU).27 Using Holladay’s technique for accurate axial length measurements in long eyes, values leading to minimal changes in axial length between these 2 velocity measurements are calculated.28 The difficulties in IOL power calculations for longer eyes may be partly due to the anatomy of the posterior pole. The fovea is approximately 4.5 mm (3 disk diameters or 15 degrees) from the center of the optic nerve. Holladay and others have performed high-resolution B scans using horizontal sections through the optic nerve and measuring the distance from the corneal vertex to a point 4.5 mm temporal to the center of the optic nerve. In eyes with axial lengths longer than 30.0 mm, a posterior pole staphyloma temporal to the fovea was common and the corneal vertex– fovea distance was approximately 0.5 to 1.5 mm shorter than the distance from the corneal vertex to the bottom of the staphyloma, which is where the A scan usually finds the perpendicular axis and records the axial length.29 When back calculations are performed, in most cases, using the back-calculated (shorter) axial length improves the ability to predict emmetropia. As the power calculations for cases requiring minus power IOLs tended to suggest IOLs of higher minus power than the empiric ideal IOLs, it is clear that by using shorter axial lengths, the results would empirically improve.30 On diagnostic B-scan ultrasonography an obvious posterior pole staphyloma is found temporal to the optic nerve and

macula in many eyes with axial lengths longer than 30.0 mm. In lieu of these findings, preoperative B scans must be performed in all eyes longer than 27.0 mm having IOL implantation, and an adjusted axial length used in power calculations in patients with a posterior pole staphyloma. While standard B-scan ultrasonography can help identify a posterior pole staphyloma, it is difficult to consistently locate the center of the fovea using current B-scan units. Therefore, the problem of identifying the appropriate site of axial length measurement remains unsolved.30 In eyes with axial lengths longer than 27.0 mm having cataract extraction with IOL implantation, current thirdand fourth-generation lens calculation formulas have a tendency to over minus patients between 21.0 and 24.0 D, leaving patients with postoperative hyperopia. The performance of these formulas appears better for plus power IOL implantation than for minus power IOL implantation, which is related to the higher incidence of posterior pole staphyloma in eyes with axial lengths longer than 30.0 mm. The use of B-scan ultrasonography to identify the location of a posterior pole staphyloma, along with refinements in preoperative measurement techniques and equipment, lens calculation formulas, and IOL design, may help improve the accuracy of IOL calculations in eyes with extreme myopia.30

INTRAOCULAR LENS POWER CALCULATION FOR LENS EXCHANGE Several studies have assessed IOL power calculation in eyes with a long or short axial length or after corneal refractive surgery. Although clinical studies have evaluated power calculation for IOL exchange, it is important not to leave patients with another large refractive error after the second surgery. There is no statistically significant difference in corneal refractive power before and after cataract surgery. Therefore, errors in corneal refractive power do not likely contribute to the large refractive error after cataract surgery. However, if the corneal refractive power changes by more than 1.00 D, it indicates that the corneal refractive power should be carefully evaluated before IOL exchange. Considered together, the axial length and A scan manufacturer are important factors in predicting refractive power after IOL exchange. Errors in axial length measurement can be caused by several factors. One is the difference between contact and immersion A scan biometry. Applanation

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testing gives shorter axial length measurements than immersion testing, in which the ultrasound probe is placed in the solution, never coming in contact with the cornea. Thus, the immersion method may be more accurate than the contact method. Another possible cause of inaccurate axial length measurement is ultrasound velocity. Velocities recommended by the A-scan manufacturers are generally used. Hoffer reports that axial length measurement can be more accurate by correcting the ultrasound velocity based on the measured axial length.31 Axial length measurements may also be inaccurate in eyes with a posterior staphyloma. A B-scan examination should be performed in these cases.

METHODS OF ESTIMATING CORNEAL REFRACTIVE POWER AFTER HYPEROPIC LASER IN SITU KERATOMILEUSIS The clinical history method has been proposed as the most reliable, and this has been tentatively confirmed by studies involving small numbers of eyes.32-34 In hyperopic LASIK, computerized videokeratography tends to slightly overestimate the refractive change for low corrections. However, for refractive change above 1.0 to 1.5 D, CVK tends to underestimate actual corneal power. This underestimation could lead to selection of an excessively strong intraocular lens (IOL), resulting in unexpected myopia following cataract and IOL surgery.35

CHANGES IN KERATOMETRIC CORNEAL POWER AND REFRACTIVE ERROR AFTER LASER THERMAL KERATOPLASTY Laser thermal keratoplasty (LTK) changes the corneal curvature by heat-induced shrinkage of collagen fibers. Non-contact holmium:YAG (Ho:YAG) LTK can produce a moderate amount of hyperopic correction with minimal

regression and induced astigmatism. Laser thermal keratoplasty has enabled presbyopic patients to regain near vision by inducing myopia through changes in the corneal refractive power. Laser thermal keratoplasty is used to steepen the central cornea by a cinching effect in the peripheral cornea and to induce myopia in the treated eye. Experience with eyes after photorefractive keratectomy (PRK) and laser in situ keratomileusis (LASIK) indicate that calculating intraocular lens (IOL) power with the mean keratometric readings frequently results in substantial undercorrection and a “hyperopic surprise” after IOL implantation. The hyperopic refraction may disappoint patients who anticipated excellent uncorrected visual acuity after cataract surgery. Individuals who have refractive surgery during the fifth and sixth decades of their lives may develop cataractous lens changes later. Reports indicate a stable spherical equivalent refraction at 12 months with non-contact Ho:YAG LTK.36

REFRACTIVE CHANGES IN PEDIATRIC PSEUDOPHAKIA Implantation of posterior chamber intraocular lenses (IOLs) in the eyes of selected children having cataract surgery has become common. The efficacy and safety of this procedure, at least in the short and intermediate terms, have been documented in many studies.37-41 Data exist for the normal refractive change in phakic children and in long-term follow-up of aphakic children.42 Studies show a long-term myopic shift in children with pseudophakia, particularly in those younger than 2 years but also in older children in the first decade.39,42-46 In a study by Plager et al (Table 45.4) the mean myopic shift per year of follow-up was greatest in the younger age groups (0.81 diopter [D] per year) and gradually

Table 45.4: Age at surgery, refractive change, follow-up and refractive change per year by age at surgery

Age at Surgery 2-3 6-7 8-9 10-15

n

Mean Age (Yrs) + SD

Mean Refractive Change (D) + SD

9 7 10 11

3.0 + 0.61 7.2 + 0.47 9.0 + 0.52 13.6 + 1.98

– 4.60 + 3.48 – 2.88 + 1.89 – 1.25 + 1.28 – 0.61 + 0.68

All CVK maps of 3.0 mm optical zone

Mean Follow-up (Yrs + SD 5.8 5.8 6.8 5.7

+ 0.75 + 1.03 + 1.20 + 1.09

Mean Refractive Change (D) per Year + SD – 0.81 + 0.63 – 0.54 + 0.46 – 0.17 + 0.18 – 0.10 + 0.11

A-scan in Difficult Situations decreased in children who had surgery when they were older than 10 years (0.10 D per year). The variability in refractive change, measured by standard deviation, decreased from ±3.48 D per year in the youngest group to ±0.68 D per year in the oldest.47 Using these follow-up data, surgeons have tried to determine which IOL power to use in a child to achieve the desired long-term postoperative refraction. However, these studies ultimately rely on the surgeon’s ability to select an IOL that achieves the initial postoperative desired refraction. If the target is not achieved, the outcome may be poor and the long-term data not applicable. Some disagreement exists among physicians about the postoperative refractive goal. Some suggest that children should be made emmetropic at surgery with the thought that amblyopia treatment will be more effective or more easily carried out. The inevitable myopic shift that occurs can be treated optically or surgically when the child becomes an adult. Others do not support this thinking—it is their goal for children to ultimately have a plano or low myopic refractive error when fully grown. Studies show that IOL power calculation in children has an error range of 2.5 to 5.0 diopters (D). Other studies suggest that newer theoretical formulas, such as the Holladay 1, Hoffer Q, and SRK/T predict postoperative refraction more accurately than older regression formulas such as the SRK and SRK II.48-50 Mezer et al found all the above 5 formulas to be at best only fair to good at successfully achieving the target refraction. Although the difference was probably not clinically significant, the theoretical formulas performed slightly better than the regression formulas.13 Why do these formulas appear to be less accurate for pediatric eyes despite long records of success in adults? Several authors have devised a logarithmic formula to predict the myopic shift in pseudophakic eyes from infancy to adulthood.51 Within six months after surgery, little shift should occur and the refraction should remain close to the surgical target. Instead a much larger range of refractive errors at 2 to 3 months is observed, the change between 2 months and 6 months being towards greater hyperopic errors.13 Between 2 months and 6 months postoperatively, factors such as continued molding of the soft pediatric sclera and progressive posterior capsule fibrosis may play a role. Although previous data can be helpful in predicting the correct surgical target refraction, they are only useful if the target is achieved. Some children have longer eyes than the average in adults.

Corneal compression is the most common cause of a shortened axial length measurement.52 There are more accurate ways to perform axial length measurements such as partial coherence interferometry. The speed and the noninvasive nature of these non-contact methods might make them preferable in the pediatric population.13 According to Plager et al “It has been our experience (unpublished) and that of others that our current ability to predict what refractive change to expect for a given infant is not good”.47 Do other factors influence the accuracy of the newer theoretical formulas? The ACD is the sum of the corneal thickness, corneal height, and another value. Corneal height is calculated using axial length and keratometry readings. In the Holladay and SRK/T formulas, the distance from the iris plane to the IOL principal plane is called the SF, while the Hoffer Q formula uses only the ACD. The mean and range of the corneal curvature in one study of pediatric patients (43.99 ± 1.96 D and 38.50 to 49.25 D, respectively) were close to the normal values in adults reported in the literature (mean 43.81± 1.60 D, range 39.38 to 43.37 D).53 This is not surprising as the mean corneal curvature in babies rapidly reaches that of adults (mean 48.4 ± 1.7 D in neonates, mean 45.9 ± 2.3 D at 1 month, mean 42.9 ± 1.3 D at 36 months).54 Corneal thickness in children 2 years of age is also equivalent to adult readings of 0.52 mm.54 The distance from the iris plane to the IOL’s principal plane (SF) is calculated from a series of postoperative adult eyes. Pseudoaccommodation amplitude in pediatric pseudophakic patients can cause a mean anterior IOL movement of 0.42 mm at near, perhaps because of the increased scleral elasticity in children.55 Residual capsule fibrosis is more aggressive in children than in adults and can occur in 51 to 96 percent of cases if no posterior capsulotomy is done at the time of surgery. Both factors could affect the IOL’s position in the eye, perhaps making it less predictable than in adults. This would have an adverse affect on all the formulas. Another source of error might be difficulty obtaining axial length and corneal curvature measurements in uncooperative children. An experienced technician or surgeon on compliant awake children, or the surgeons should take measurements with the child under general anesthesia. If the technician is concerned about accuracy, it must be indicated and the surgeon re-measures with the patient under anesthesia, preferably with optical coherence tomography, which is highly reproducible and fast when compared to immersion biometry.56

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Mastering the Techniques of Intraocular Lens Power Calculations Measurements must be taken under anesthesia when there is a concern about the accuracy or unfeasibility of data taken with the patient awake. Postoperative refraction in children can be difficult. Normal phakic eyes elongate rapidly during the first 2 years of life. The axial growth continues at a slower pace until it stabilizes toward the end of the first decade. Corneal curvature decreases markedly during the first year of life and then changes only minimally thereafter. Lens growth, the third factor affecting overall refractive change in normal eyes, occurs throughout childhood. In the ideal phakic situation, these 3 variables change in concert over time so that the eye remains emmetropic. When the crystalline lens is surgically removed during the developmental years, a trend toward decreasing hyperopia (myopic shift) should be inevitable as a result of ongoing axial elongation. Studies have shown that axial elongation is greater in the pseudophakic eye than in the normal eye, while others have shown a variable reduction in growth of the pseudophakic eye when surgery was performed before 4 months of age.57,58 McClatchey et al pooled the data from 7 centers to accumulate 100 eyes of 83 pseudophakic patients with surgery between 3 months and 10 years of age and a minimum follow-up of 3 years. When compared to the aphakic population reported previously, the pseudophakic eyes showed a slightly lower rate of refractive growth. However, because of the optical effects of an IOL in an elongating eye, the mean quantity of myopic shift was greater in the pseudophakic eyes.44 Enyedi and coauthors report refractive change in 83 pseudophakic eyes with an average follow-up of 26 months. They found a larger and more rapid myopic shift in younger children than in older ones, although the rate of change never became zero during the follow-up.46 Another study of 38 eyes followed for more than a mean of 6 years. Data were generated at one clinical center using a consistent surgical technique and included only primary IOL implantation. The data show 2 clear trends: The rate of myopic shift decreases with age, and the variability among individuals decreases with age.47 For instance, in a pilot study of 11 infants in the Infant Aphakia Treatment Study, myopic shifts in the first 2 years after IOL implantation ranged from –2.00 to –14.00 D. Although individual variations can be significant even among non-infants, very rarely does a patient have an unexpectedly large myopic shift; possibly the child’s large myopic shift was likely genetically predisposed. In the distant future, it may be possible to take parentage into account when choosing IOL power; however, such prediction is beyond our reach at present.

In infants and children, the cornea and sclera are more elastic and distensible than in adults.59 Elastic fibers in the sclera can be stretched beyond their limit of elasticity when not supported by a fully developed collagen structure. The entire globe can therefore be distended until approximately 3 years after birth. Corneal compression during axial length biometry might, therefore, be more common and greater than in adults. In a more elastic pediatric eye, the propensity and magnitude of this measurement error may increase.60 The axial length of the globe is indirectly recorded by multiplying the assumed velocity and the time it takes the sound wave to reflect back to the ultrasound machine from various structures in the eye, such as the anterior capsule of the lens, posterior capsule of the lens, and retina. It relies on the assumed speed of sound within the aqueous, lens, and vitreous. Some biometry units use an average sound wave velocity to determine the axial length. This assumption may not be accurate in the pediatric eye, in which a relatively greater intraocular volume is occupied by the crystalline lens and in which tissue viscosities may be different than in adults.13 Inaccurate axial length measurements contribute to prediction error. In summary, despite efforts in selecting the appropriate targets for postoperative refraction in pediatric IOL implantation to achieve the desired longterm refractive outcome, our ability to achieve that target may be unsatisfactory. Factors that may contribute to this inaccuracy include axial length errors, especially contact ultrasound; K-reading errors; pseudoaccommodation; capsule fibrosis; measurement errors in children; corneoscleral elasticity; and differences in media viscosity compared to the normal adult values. In children younger than 2 years, axial length, corneal curvature, and corneal thickness differences from those in adults may make the inaccuracy even greater. If the target is not achieved, the effects of long-term expected refractive change with the child’s growth might be amplified to create even greater adverse outcomes. The pseudophakic refractive change tends to follow alogarithmic regression curve. McClatchey and Parks too have showed that this myopic shift tends to follow a logarithmic decline with age in children left aphakic.42 Based on the results of these studies, it is now recommended that an immediate postoperative refractive goal be selected for children between 2 and 15 years old at the time of implantation. This should, on average, yield a refraction of –1.00D at 20 years of age. This goal should

A-scan in Difficult Situations be tempered by the refraction in the fellow eye in unilateral cases to keep induced anisometropia at a reasonable level. Unfortunately, the significant variability among individuals makes precise prediction of refractive change for a given patient difficult. The variability decreases significantly with time, which means IOL power can be chosen more confidently in older children. At the other end of the spectrum, the variability among younger children is great. We will not know for certain what longterm refractive changes to expect in children until a generation or 2 have grown into adulthood. In the meantime, as more data with longer follow-up are accumulated, we should be able to at least improve our ability to select the appropriate IOL power for a growing child’s eye. As we move from the excellent refractive control of aphakic contact lenses toward the continued expansion of IOL implantation in pediatric eyes, this becomes increasingly important.

INTRAOCULAR LENS POWER CALCULATION AFTER MACULAR HOLE SURGERY The most common complication of macular hole surgery is the progression of nuclear sclerotic cataract.61 The thickness of the retina ranges from 0.13 mm at the umbo to 0.55 mm at the foveal edge.62 As macular holes range in size from 200 m in stage 2 to 600 m in stages 3 and 4, the depth of the foveolar crater after successful macular hole surgery can range up to 0.5 mm. If this is not taken into consideration when determining the axial length, a falsely long axial length will be used to calculate the IOL power and the patient will end up hyperopic.63 In conclusion, until we have a way of measuring the exact depth of the foveolar defect, such as with optical coherence tomography, the surgeon should estimate the depth of the crater and subtract it from the measured axial length to obtain the functional axial length for lens calculations.

AXIAL LENGTH MEASUREMENT AND ASTEROID HYALOSIS The main sources of axial length measurement errors are inaccurate measurement technique and misleading conditions of the eye such as vitreous opacities.64 Such opacities produce low, or in some cases highly reflective, spikes. These high spikes, especially in eyes with asteroid hyalosis, can be confused with a retinal spike, leading to short axial length measurements.65,66

Asteroid hyalosis is a generally unilateral and benign condition of the vitreous characterized by suspended brilliant bodies consisting of calcium and phospholipids. It is frequently seen in people older than 50 years, with a reported incidence of 0.16 to 0.90 percent in the general population. 65 Asteroid hyalosis is usually found incidentally during examination for another reason. One might encounter eyes with both cataract and asteroid hyalosis. Biometry in these patients require special attention. Automated biometry may lead to short measurements and thus erroneous IOL power selection. Martin and Safir66 reported 2 cases of asteroid hyalosis that resulted in axial length measurement errors significant enough to require IOL explantation and exchange. Asteroid bodies forming an acoustic interface with enough reflectivity were misinterpreted as the anterior retinal surface by automated biometry. This would explain the reason for shorter axial length measurements in eyes with asteroid hyalosis. 66 Most biometry instruments provide a choice of manual and automated measuring modes. In the automated mode, the instrument rather than the examiner selects the scan to be measured. Automated measurements are beneficial for performing rapid measurements in an otherwise normal cataractous eye. The manual measurement mode is usually recommended for aphakic and pseudophakic eyes as well as phakic eyes in which the measurement is difficult to obtain. With the manual mode, the examiner can take more time to align the sound beam along the optical axis of the eye to select the best scan for measurement. In general, axial length measurement accuracy is accepted to be within 0.1 mm. A 1.0 mm error in the axial length of the eye could result in a 2.5 to 3.0 diopter error in postoperative refraction.67,68 In one study, a patient had a 6.23 mm difference between automated and manual measurements in the eye with asteroid hyalosis; this would result in a significantly erroneous IOL power selection. However, this finding alone does not make a significant difference because biometry may be subject to observer and other errors.69 Axial lengths in control eyes (measured by both automated and manual biometry) were not statistically different from those in the eyes with asteroid hyalosis. This suggests that the uninvolved control eye measurement can be used if the measurement of the asteroid hyalosis eye is doubtful, provided there is no history of anisometropia. 69 A significant difference between the axial lengths in 2 eyes suggests a problem in the measurement technique or an abnormality in 1 or both eyes. Asteroid hyalosis is usually

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Mastering the Techniques of Intraocular Lens Power Calculations unilateral. If one detects a significant difference between 2 eyes, the possibility of a missed diagnosis of asteroid hyalosis should be considered. Allison and co-authors reported that the density of asteroid opacities correlated with the errors in automated biometry.65 However, even mild asteroid bodies can result in erroneous measurements.69 Dense cataract precludes visibility of vitreous opacities. Before extraction of a dense cataract, a good practice is to perform B-scan ultrasonography. One might find an unknown vitreoretinal pathologic condition. Another advantage of B-scan ultrasonography is that it seems to detect the presence of asteroid hyalosis. If asteroid hyalosis is diagnosed, biometry should be performed carefully.

BILATERAL MICROCORNEA AND UNILATERAL MACROPHTHALMIA RESULTING IN INCORRECT INTRAOCULAR LENS SELECTION Microcornea usually coexists with microphthalmia. Infrequent reports of microcornea occurring in eyes of normal axial length exist. The finding of symmetrical microcornea and unilateral colobomatous macrophthalmia is extremely rare. This morphology results in incorrect intraocular lens (IOL) selection. Microcornea is defined as an adult corneal diameter of 11 mm or less. 2 cases of true microcornea with degenerative myopia are reported.70 Judisch and coauthors were the first to confirm by ultrasound the presence of microcornea with globes of normal axial length in a family with oculodentodigital dysplasia.71 Bateman and Maumence described a defect named “colobomatous macrophthalmia with microcornea” in patients without extraocular features.72 Affected patients had uveal coloboma. Most had microcornea, high myopia, and posterior staphyloma, with axial lengths ranging from 21.9 to 27.55 mm. The inheritance was consistent with an autosomal dominant mode with variability and incomplete penetrance. The patient’s family history was negative for myopia, microcornea, and macrophthalmia. The patient could represent a new dominant mutation with variable expression of the colobomatous macrophthalmia with microcornea defect. The accurate selection of IOL refractive power requires accurate biometry results. This case illustrates the difficulty of IOL selection when asymmetrical results occur in the presence of symmetrical anterior segments. It also illustrates the finding that

symmetrical anterior microphthalmos does not always coexist with symmetrical posterior microphthalmos. Newer IOL formulas that use additional measurements of the anterior segment (lens thickness, anterior chamber depth, white-to-white horizontal corneal diameter) will more accurately predict the actual position of the IOL and make smaller errors for emmetropia in such eyes.73 It is important to be aware of the association of unilateral colobomatous macrophthalmia and symmetrical microcornea. Awareness of this association may aid appropriate IOL selection in cases with similar features.

REFERENCES 1. LeGrand Y, El Hage SG. Physiological Optics. New York, NY, Springer, 1980. 2. Haigis W. Corneal power after refractive surgery for myopia: Contact lens method. Journal of Cataract and Refractive Surgery 2003;29:1397-1411. 3. Holladay JT. Intraocular lens power calculations for the refractive surgeon. Oper Tech Cataract Refract Surg 1998;1:105-17 . 4. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: A technique for laser refractive surgery. J Cataract Refract Surg 1988;14:46-52. 5. Gobbi PG, Carones F, Brancato R. Keratometric index, videokeratography, and refractive surgery. J Cataract Refract Surg 1998;24:202-11. 6. Holladay JT, Waring GO III. Optics and topography of the cornea in radial keratotomy. In: Waring GO, (Ed): Refractive Keratotomy for Myopia and Astigmatism. St Louis, MO, Mosby Year Book, 1992;62. 7. Hugger P, Kohnen T, La Rosa FA, et al. Comparison of changes in manifest refraction and corneal power after photorefractive keratectomy. Am J Ophthalmol 2000;129: 68-75. 8. Rowsey JJ. Ten caveats in keratorefractive surgery. Ophthalmology 1983;90:148–55. 9. Muga R, Maul E. The management of lens damage in perforating corneal lacerations. Br J Ophthalmol 1978;62: 784–87. 10. Lamkin JC, Azar DT, Mead MD, Volpe NJ. Simultaneous corneal laceration repair, cataract removal, and posterior chamber intraocular lens implantation. Am J Ophthalmol 1992;113:626-31. 11. Rubsamen PE, Irvine WD,McCuen BW II, et al. Primary intraocular lens implantation in the setting of penetrating ocular trauma. Ophthalmology 1995;102:101–07. 12. Bowman RJC, Yorston D, Wood M, et al. Primary intraocular lens implantation for penetrating lens trauma in Africa. Ophthalmology 1998;105:1770–74. 13. Mezer E, Rootman DS, Abdolell M, Levin AV. Early postoperative refractive outcomes of pediatric intraocular lens implantation. J Cataract Refract Surg 2004;30:603–10. 14. Koch DD, Liu JF, Hyde LL, et al. Refractive complications of cataract surgery after radial keratotomy. Am J Ophthalmol 1989;108:676–82. 15. Celikkol L, Pavlopoulos G, Weinstein B, et al. Calculation of intraocular lens power after radial keratotomy with computerized videokeratography. Am J Ophthalmol 1995;120:739–50.

A-scan in Difficult Situations 16. Seitz B, Langenbucher A, Nguyen NX, et al. Underestimation of intraocular lens power for cataract surgery after myopic photorefractive keratectomy. Ophthalmology 1999;106: 693–702. 17. Gimbel HV, Sun R, Furlong MT, van Westenbrugge JA, Kassab J. Accuracy and predictability of intraocular lens power calculation after photorefractive keratectomy. J Cataract Refract Surg 2000;26:1147–51. 18. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity. J Cataract Refract Surg 1999;25:898-903. 19. Hill W, unpublished data, 2002. 20. Koch DD. Cataract surgery following refractive surgery. Focal Points, Clinical Modules for Ophthalmologists. American Academy of Ophthalmology 2001;19(5):1-7. 21. Holladay JT. IOL calculation following radial keratotomy surgery. Refract Corneal Surg 1989;5(suppl):36A. 22. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy. J Refract Surg 1995;11:490–93. 23. Olsen T. Sources of error in intraocular lens power calculation. J Cataract Refract Surg 1992;18:125-29. 24. Suto C, Hori S, Fukuyama E, Akura J. Adjusting intraocular lens power for sulcus fixation. J Cataract Refract Surg 2003;29:1913–17. 25. Hayashi K, Hayashi H, Nakao F, Hayashi F. Intraocular lens tilt and decentration, anterior chamber depth, and refractive error after trans-scleral suture fixation surgery. Ophthalmology 1999;106:878-82. 26. Drews RC. Results in patients with high and low power intraocular lenses. J Cataract Refract Surg 1986;12:154–57. 27. Holladay JT. Standardizing constants for ultrasonic biometry, keratometry, and intraocular lens power calculations. J Cataract Refract Surg 1997;23:1356–70. 28. Holladay JT, Prager TC. Accurate ultrasonic biometry in pseudophakia (letter). Am J Ophthalmol 1993;115:536–37. 29. Byrne SF. A scan Axial Eye Length Measurements; a Handbook for IOL Calculations. Mars Hill, NC, Grove Park Publishers, 1995;62–64. 30. Zaldivar R, Shultz MC, Davidorf JM, Holladay JT. Intraocular lens power calculations in patients with extreme myopia. J Cataract Refract Surg 2000;26:668–74. 31. Hoffer KJ. Ultrasound velocities for axial eye length measurement. J Cataract Refract Surg 1994;20:554–62. 32. Kalski RS, Danjoux J-P, Fraenkel GE, et al. Intraocular lens power calculation for cataract surgery after photorefractive keratectomy for high myopia. J Refract Surg 1997;13: 362–66. 33. Gimbel H, Sun R, Kaye GB. Refractive error in cataract surgery after previous refractive surgery. J Cataract Refract Surg 2000;26:142–44. 34. Gimbel HV, Sun R. Accuracy and predictability of intraocular lens power calculation after laser in situ keratomileusis. J Cataract Refract Surg 2001;27:571–76. 35. Wang L, Jackson DW, Koch DD. Methods of estimating corneal refractive power after hyperopic laser in situ keratomileusis. J Cataract Refract Surg 2002;28:954–61. 36. Park CY, Ji YH, Chung ES. Changes in keratometric corneal power and refractive error after laser thermal keratoplasty. J Cataract Refract Surg 2004;30:867–72. 37. Gimbel HV, Basti S, Ferensowicz M, DeBroff BM. Results of bilateral cataract extraction with posterior chamber intraocular lens implantation in children. Ophthalmology 1997;104:1737-43. 38. Buckley EG, Klombers LA, Seaber JH, et al. Management of the posterior capsule during pediatric intraocular lens implantation. Am J Ophthalmol 1993;115:722–28.

39. Dahan E, Drusedau MUH. Choice of lens and dioptric power in pediatric pseudophakia. J Cataract Refract Surg 1997;23:618-23. 40. Rosenbaum AL, Masket S. Intraocular lens implantation in children. Am J Ophthalmol 1995;120:105–07. 41. Cheng KP. Treatment of pediatric cataracts. Ophthalmology. Clin North Am 1996;9(2):239–47. 42. McClatchey SK, Parks MM. Theoretic refractive changes after lens implantation in childhood. Ophthalmology 1997;104:1744–51. 43. Andreo LK, Wilson ME, Saunders RA. Predictive value of regression and theoretical IOL formulas in pediatric intraocular lens implantation. J Pediatr Ophthalmol Strabismus 1997;34:240–43. 44. McClatchey SK, Dahan E, Maselli E, et al. A comparison of the rate of refractive growth in pediatric aphakic and pseudophakic eyes. Ophthalmology 2000;107:118–22. 45. Spierer A, Desatnik H, Blumenthal M. Refractive status in children after long-term follow-up of cataract surgery with intraocular lens implantation. J Pediatr Ophthalmol Strabismus 1999;36:25-29. 46. Enyedi LB, Peterseim MW, Freedman SF, Buckley EG. Refractive changes after pediatric intraocular lens implantation. Am J Ophthalmol 1998;126:772–81. 47. Plager DA, Kipfer H, Sprunger DT, Sondhi N, Neely DE. Refractive change in pediatric pseudophakia: 6-year-followup.J Cataract Refract Surg 2002;28:810–15. 48. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg 1988;14:17–24. 49. Hoffer KJ. The Hoffer Q formula: A comparison of theoretic and regression formulas. J Cataract Refract Surg 1993;19:700–12; errata, 1994;20:677. 50. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333–40; correction, 528. 51. McClatchey SK. Intraocular lens calculator for childhood cataract. J Cataract Refract Surg 1998;24:1125–29. 52. Binkhorst RD. The accuracy of ultrasonic measurement of the axial length of the eye. Ophthalmic Surg 1981;12:363–65. 53. Hoffer KJ. Biometry of 7,500 cataractous eyes. Am J Ophthalmol 1980;90:360–68; correction, 890. 54. Weale RA. A Biography of the Eye; Development, Growth, Age. London, HK Lewis, 1982. 55. Lesiewska-Junk H, Kaluzny J. Intraocular lens movement and accommodation in eyes of young patients. J Cataract Refract Surg 2000;26:562–65. 56. Shroff AA. Unpublished data.. 57. Sorkin JA, Lambert SR. Longitudinal changes in axial length in pseudophakic children. J Cataract Refract Surg 1997;23:624–28. 58. Flitcroft DI, Knight-Nanan D, Bowell R, et al. Intraocular lenses in children: Changes in axial length, corneal curvature, and refraction. Br J Ophthalmol 1999;83:265–69. 59. Waring GO III, Rodrigues MM. Congenital and neonatal corneal abnormalities. In: Tasman W, Jaeger EA (Eds): Duane’s Ophthalmology on CD-ROM. Philadelphia, PA, Lippincott Williams and Wilkins, 1999. 60. Watson P. Diseases of the sclera and episclera. In: Tasman W, Jaeger EA (Eds): Duane’s Ophthalmology on CD-ROM. Philadelphia, PA, Lippincott Williams and Wilkins, 1999. 61. Thompson JT, Glaser BM, Sjaarda RN, Murphy RP. Progression of nuclear sclerosis and long-term visual results of vitrectomy with transforming growth factor beta-2 for macular holes. Am J Ophthalmol 1995;119:48–54. 62. Gass JDM. Stereoscopic Atlas of Macular Diseases: Diagnosis and Treatment, 3rd edn. St Louis, MO,Mosby, 1987; vol 1, 4.

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Mastering the Techniques of Intraocular Lens Power Calculations 63. Intraocular lens power calculation after macular hole surgery. David B. Cohen, MD J Cataract Refract Surg 2002;28: 1485–86. 64. Byrne SF, Green RL. Ultrasound of the Eye and Orbit. St Louis, MO, Mosby Year Book, 1992. 65. Allison KL, Price J, Odin L. Asteroid hyalosis and axial length measurement using automated biometry. J Cataract Refract Surg 1991;17:181–86. 66. Martin RG, Safir A. Asteroid hyalosis affecting the choice of intraocular lens implant. J Cataract Refract Surg 1987;13: 62–65. 67. Hoffer KJ. Preoperative cataract evaluation. In: Caldwell DR (Ed): Transactions of the New Orleans Academy of Ophthalmology. New York, NY, Raven Press, 1988;24.

68. Shammas HJ. Atlas of Ophthalmic Ultrasonography and Biometry. St Louis, MO, CV Mosby, 1984. 69. Erkin EF, Tarhan S, Ozturk F. Axial length measurement and asteroid hyalosis. J Cataract Refract Surg 1999;25:1400–03. 70. Batra DV, Paul SD. Microcornea with myopia. Br J Ophthalmol 1967;51:57–60. 71. Judisch GF, Martin-Casals A, Hanson JW, Olin WH. Oculodentodigital dysplasia; four new reports and a literature review. Arch Ophthalmol 1979;97:878–84. 72. Bateman JB, Maumence IH. Colobomatous macrophthalmia with microcornea. Ophthalmic Paediatr Genet 1984;4:59–66. 73. Holladay JT, Gills JP, Leidlein J, Cherchio M. Achieving emmetropia in extremely short eyes with two piggyback posterior chamber intraocular lenses. Ophthalmology 1996;103:1118–23.

Armando Capote, Eneida de la C Pérez, Marcelino Río (CUBA)

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Management of Refractive Surprises after Cataract Surgery

INTRODUCTION The development of advanced Formulas for calculation of IOL power and of more accurate tools for measuring the eye dimensions and curvatures has allowed a very high precision in reaching the desired postoperative refraction after lens surgery. The perfection of surgical techniques with a more precise and reproducible placement of the Intraocular lens (IOLs), as well as the exactness of State of the art IOLs permits a prediction of refraction within a limit of only between 0.25 Diopters and 0.50 Diopters of error in the majority of our patients. There is however a number of cases where even after performing a technically perfect surgery, both the Patient and the Ophthalmologist feel disappointment due to the poor uncorrected vision or undesired refractive result. With the high standards of precision mentioned we could consider as a refractive surprise, an obtained refraction of 0.50 D outside of the target refraction. This depends on the equipment and meticulousness of the Surgeon in question. The term is usually left for larger degrees of induced ametropias that cause a serious discomfort for the patient due to poor uncorrected visual acuity, anisometropia, etc. This is relatively rare in eyes with standard morphology, but becomes frequent in eyes outside average dimensions, either big, small, with not proportional depths of anterior and posterior segments, or with atypical corneal curvatures as happens in patients who previously underwent corneal refractive surgery. Also in eyes who have silicone oil as vitreous substitute, among others. In these cases the formulas do not provide good results or the measurements of the globe lack of accuracy.

An important issue for achieving patient satisfaction with the obtained refraction is choosing an adequate target refraction for each patient. Although emmetropia is the most frequently desired goal, it is not always the best choice to offer. Each case must be individually analyzed by the surgeon and discussed with the patient taking into consideration alternatives as monovision or bilateral myopia giving priority to near vision. In monocular cataracts with ametropic noncataractous eye, we should decide to give priority to monocular or binocular vision taking into consideration the desire and feasibility of the patient to wear contact lens or undergo refractive surgery in the contralateral eye. A myopic target refraction may bring less complains with regard to refractive surprise because if there is hyperopic turn the patient is closer to emmetropia and if to myopic still may provide good near vision. Even a mild degree of astigmatism might bring functional benefits for the patient without affecting significantly the uncorrected visual acuity. So the Doctor should choose the right target and then use all the available technology in diagnostic and measuring devices, performing the tests with great care by experienced personnel. Use the best formulas for each particular eye lengths previously customized for his practice. Select a good quality reliable IOL and perform a clean surgery with a low induction of astigmatism and a stable lens implantation within the bag that provides a correct Effective Lens Position. Still then, even in the hands of the most qualified professionals the refractive surprise will eventually happen. It´s incidence is very variable, from 7.11 to 20% as reported by the European Cataract Outcome Study (ECOS)2 for postoperative refractive errors of 1.0 D and depends on the excellence of preoperative studies. The

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Mastering the Techniques of Intraocular Lens Power Calculations best possible treatment is prevention because once present the dissatisfaction is also there and the necessity of a second surgery or of using unexpected Contact Lenses or glasses may disqualify the outcome with the consequent medico-legal claims. The most frequent causes of refractive surprises are biometric mistakes, wrong selection of formulas and difficult eyes with dimensions, or structural changes far of usual ones. Staff mistakes writing or supplying the IOL are also a frequent source of errors. Recommended preventive measurements are: - Precise biometric measurements performed by qualified personnel. - Use of IOL Master when available and possible, otherwise Immersion Biometry or careful Applanation Biometry, taking into consideration that 1mm of indentation means 2.5 D mistake in lens power, and this is magnified in shorter eyes. - Select formula based in the patient biometry and personalized. (Hoffer Q or Holladay II < 22 mm; in eyes between 22-24.5 use SRK T or average of several formulas; Holladay I for 24.5-26 mm ; SRK T > 26 mm) - Silicone oil filled eyes should be measured with IOL master or adjusting US Biometry. In cases where refractive surprise could not be avoided there are different approaches to correct this inconvenience. The right moment to correct the obtained defect is a matter that needs discussion and requires an individual analysis in each patient as several factors are involved. In general we consider necessary to refract the eyes at risk for less predictability in the first days after the surgery, even more if the patient expresses discontent with the visual result achieved, because in most cases our criteria is that the solution to the problem should be provided the sooner the better in order to give rapid satisfaction and prevent the healing of he wound and capsular fibrosis that make surgery more complex and aggressive. Nevertheless several factors need to be taken into consideration to avoid iatrogenic proceedings. Not in all patients it is appropriate to surgically correct a refractive surprise. The anatomic condition of the eye should be considered in first place. If the patient has a low corneal endothelial cell count that puts in danger corneal transparency by performing a second surgery. If chamber depth is rather small or iris defects or sinequias are present. If the stability of the IOL may be compromised by an unstable capsular support or by the risk of breaking

it during the secondary procedure. In patients with associated conditions like advanced glaucoma and senility with higher possibility of serious complications like suprachoroidal hemorrhage. Patients with Cystoid Macular Edema or Myopes with retinal tears or degenerations at risk of Retinal Detachment should also be taken into consideration. The way the cataract surgery was conducted is important, for example if the patient was uncooperative, if the eye presented some technical difficulties like positive vitreous pressure or Floppy iris, etc. The advantages, disadvantages and risks of surgical correction of a refractive surprise should be carefully balanced giving priority to the organic integrity of the eye. The demands of the patients should also be considered at the time of deciding whether to perform a surgical correction or not. In cases of not highly demanding patients who do not express dissatisfaction it may be wise not to suggest or insist on surgery. On the contrary some others may demand solution for small defects that we would not consider in the majority of our patients. Once again risks and benefits should be carefully considered. Some particular cases are mandatory for surgical correction like large not tolerated anisometropia, specially in patients who can not wear contact lenses. In patients with some facial defect that make impossible the use of frame glasses and individuals with professions that require excellent uncorrected monocular or binocular vision like pilots or professional drivers or that can´t wear optical correction like in certain sports. Such situations even in the presence of any of the previously mentioned limiting factors make necessary considering the surgical approach. Once it has been decided that the surgical correction of the Refractive surprise will be done, the surgeon must decide which is the right option in his hands for each particular case either by choosing an intraocular or a corneal approach.

INTRAOCULAR LENS EXCHANGE This is perhaps the most frequently used method to correct Post-cataract Surgery Refractive Surprise and is feasible in the majority of the eyes. It results easier if lens surgery was performed recently, as the same wound and side port incisions may be used to remove the incorrect lens and insert the right one, and the inconvenience of creating a second wound in a scarred area or in a different meridian is avoided, and so is the necessity of two periods of healing

Management of Refractive Surprises after Cataract Surgery for this patient. But the most important fact to perform the surgery the sooner, is the capsular bag fibrosis. When this is present it may be difficult to release the lens from the strongly sticked anterior and posterior capsular bags. Maneuvers should be done very carefully with a thin spatula and the use of viscoelastics to dissect them without breaking the capsule or zonules at the time of taking the lens out of the bag. Patience should prevail over rush, not forgetting that we are performing a refractive surgery and we should not transform a merely refractive problem to a more serious mess by rupturing the vitreous barrier, performing vitrectomy or even compromising a stable support requiring more invasive and unwanted solutions like scleral or iris fixation of a Posterior Chamber Intraocular lens or the implantation of an Anterior Chamber Intraocular Lens. If it results impossible to release a haptic from the adhered capsules it may be wiser to cut it from its joint to the optic zone with scissors or forceps depending on the material and leave it within the eye. When the lens is out of the bag, in the anterior chamber, the size of the wound necessary to take it out should be considered. If PMMA, the wound should of course be the same size of the lens optic zone diameter and if foldable it is not necessary to enlarge the original wound for implantation. The surgeon can cut the lens optic in two pieces with scissors and remove the two halves with forceps. This demands the introduction of sharp instruments all the way across the Anterior Chamber, so a less traumatic solution would be to cut the lens optic only up to half its diameter. In this way scissors are less deeply introduced in the Anterior Chamber (AC). This cut is enough to remove the IOL through an incision half its size by pulling it out with forceps. Explantation Surgical sets with devices like Cutting Loops, Haptic Cutters, etc. exist in the market. It is possible to fold the lens inside the eye, within the AC and remove it folded as inserted. A paracenthesis is done 180° away from the main incision. With viscoelastic, spaces are created under and over the lens to protect the capsule and cornea respectively, an iris spatula is introduced behind the lens through the paracenthesis and a foldable lens implantation forcep is positioned in front of the lens exerting opposite strength with both instruments the lens is folded carefully, the spatula is removed and the lens is turned and gently removed with care of not contacting or damaging intraocular structures. No sharp instruments have to be used inside the eye (Fig. 46.1).

The newly calculated lens whenever possible should be implanted inside the capsular bag, this provides a more anatomical position and achievement of a more correct effective lens position and consequently a satisfactory refractive result, as well as organic advantages as the lens has no contact with the iris nor ciliary body, decreasing the possibility of anterior segment inflammation and Cystoid Macular Edema. In eyes with very fibrosed or ruptured capsules the implantation in the bag may be impossible or produce lens descentration or instability. If fixation in the ciliary sulcus is decided the lens power has to be adjusted to the new position. Its power should be decreased by 0.50 D to 1.50 D. Dr. Hills scheme subtracts -1.5 D in IOLs from 28.5 to 30 D of lens in the bag power, -1.0 from 17.5 D to 28 D and – 0.50 in Bag powers from 9.5 to 17.0 D. Smaller power lenses do not need change when implanted in the sulcus according to this author (doctorhill.com). The calculation of the lens to be implanted can be done by the Clinical method 3: P = (R x C) + I P: Power of the new lens R: Refractive error to correct (Spherical Equivalent) I: Implanted Lens C: 1.0 if I < 14.0 D 1.25 if I > 14 D This is only possible if we know the power of the implanted IOL. And may lead to mistake if it was not the one planned because of error of the Operating Room staff or incorrect packaging by the manufacturer. If the method to be used is to repeat the exams for the IOL calculation it is important to be aware of performing the biometry in the IOL Master or if using Ultrasound Biometer, it should be set in Pseudophakic mode with the right ultrasound speeds depending on the lens material. The best formula for the ocular size should be employed as this may have been the source of the error. Several investigators have proposed methods for calculating the IOL powers in difficult cases like lens surgery after corneal refractive surgery based only in the intraoperative aphakic refraction either performing subjective refraction or autorefraction. That could be used after explantation. Different variants have been proposed by authors like Silguero, Leccisotti and Ianchulev 4, 5, 6among others. Escaf 7, refracts the eye in the operating room after emulsifying the lens, aspirating the cortex and pressurising the eye to the same value previous to the surgery. This aphakic refraction is simply multiplied by 2 and the value obtained is the power of the PC IOL (A constant=118) to be implanted.

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Mastering the Techniques of Intraocular Lens Power Calculations SECONDARY PIGGYBACK INTRAOCULAR LENS IMPLANTATION The implantation of a second IOL in front of a previously placed lens is another alternative to correct refractive surprises posterior to lens surgery. Although apparently less conventional, this approach provides a less traumatic choice particularly in patients who were operated months or years before. Diminishes the risk of breaking the lens capsules and zonules and may avoid disastrous complications for the vitreous and retina. The predictability of the lens power calculation is higher compared to lens exchange, as depends only on the refraction, and mistakes in the implanted IOL power or differences in the position of the exchanged lenses do not affect the result. On the other hand the implantation of a second IOL may be impossible or controversial in eyes with small or not space between the lens in the bag and the iris; in eyes with primary lenses in the sulcus or placed in the bag without good stability; nor in eyes with big diameters of anterior segment exceeding 12.5 mm or 13 mm which would not warranty a good fixation in the sulcus for these lenses. Patients with history of uveitis are contraindicated for the procedure. Hyperopic refractive surprises require positive power IOls, and minus power lenses are implanted for myopic errors. Calculation of the second IOL is based on refraction. The desired change in spherical equivalent is multiplied by 1.5 in hyperopic surprises and by 1.0 in myopic defects. So if we have an eye with +4.00 spherical equivalent and the target is emmetropia (4 × 1.5= 6), the patient needs a 6.0 D PC IOL, if in the same eye our goal is a –1.0 D myopia then a 7.5 D lens should be implanted. In a – 4.0 D undesired sphere targeting emmetropia (4 × 1= 4), a –4.0 D PC IOL is planned. Gills 8 goes farther in the calculation of positive surprises by secondary piggybacking and proposes to have into consideration the axial length: AL < 21 mm: Lens Power = (1.5 × Sph. Eq.) + 1 AL – 22 mm to 26 mm: Lens Power = (1.4 × Sph. Eq.) + 1 AL> 27 mm: Lens Power = (1.3 × Sph. Eq.) + 1 Clear Lens Refractive Exchange (RLE) is performed more frequently every time. The eyes chosen for this technique have usually either very long or short Axial Lengths, so the inaccuracy of IOL power calculation makes necessary that a percentage as high as nearly a quarter of this patients require an enhancement procedure. Secondary Piggyback is a very accurate and less invasive choice for these cases. It has been performed with multifocal lenses. In such case the target refraction should be emmetropia or mild hyperopia. Piggyback technique

with the use of a multifocal IOL9 permits distance and near vision and reduces the optical aberrations of extremely high-powered IOLs. Mark Packer MD has reported experience with piggyback IOL enhancement after RLE with an accommodative IOL. (Crystalens AT45) High astigmatism can be corrected by implanting 2 toric IOLs.10 Corneal surgery inconveniences can be avoided solving the astigmatism problem during the same procedure. There is the problem of finding the exact axis and keeping the right position in the postoperative period. Complications like Interlenticular Opacification (Red Rock Syndrome) is only anecdotal report in secondary piggyback. This complication, as well as hyperopic shift was occasionally described with primary piggyback in the times when the two lenses were implanted in the bag.11-13 Here the secondary lens is placed in the sulcus, so the phenomenon of blocking migration of equatorial cells deviating it to the interlenticular space is not produced. Pupil incarceration of the lens may be found as the lens is placed anteriorly due to fibrosed posterior capsule that doesn´t move backward, so the pupil should be closed by intracameral myotics, and postoperative pupil dilatation should be avoided or delayed. IOLs with small Optics are not recommended, Lenses with optic diameters of 6 mm are much less likely to be trapped by the pupil. Anyway this is a rare circumstance in our experience. In small eyes without sufficient space between the lens and the iris it is wise to perform a peripheral iridectomy during surgery or a peripheral iridotomy with Yag Laser previous to the second lens implantation. This could prevent the development of Secondary Pupillary Block Glaucoma. 14 An IOL design that is appropriate for implantation in the ciliary sulcus must be chosen, one piece acrylic lenses do not guarantee adequate central position. There are occasions when the combination of the two previously explained techniques is necessary (PIGGYBACK LENS EXCHANGE) (Fig. 46.1). It is the case when a refractive surprise is found in an eye that was done primary Piggyback. The exchange of the anterior lens for one with the right power is then necessary. This is technically safe as the lens in the bag serves as a protective barrier for the capsule. Just an observation is necessary to prevent problems in this possible event. Whenever a Piggyback IOL implantation is done it must be registered in details the power of the implanted lenses

Management of Refractive Surprises after Cataract Surgery

Fig. 46.1: Surgical sequence of Piggyback Lens exchange by intraocular folding of the implant

specifying the one in the bag and the one in the sulcus. Otherwise it is impossible to know the right power for the substitute lens and may make necessary the substitution of both lenses with the negative economic and technical consequences. Corneal refractive surgery, that is not particularly desired due two the high microkeratome vacuum in LASIK with a lens in the sulcus would be another unlikable alternative in this situation.

CORNEAL REFRACTIVE SURGERY Corneal refractive surgery is a widely used way to correct postcataract surgery refractive surprises. Its main advantage is that it allows to manage astigmatism as well as spheric errors. LASIK is a good enhancement procedure in cases with astigmatism that are not candidate or have not responded to Limbal Relaxing Incisions. Other

alternatives are PRK, LASEK and CK.These techniques can be used to treat postoperative refractive errors, either expected or not. Incisional surgery in its different modalities like Limbal Relaxing Incisions (LRIs), Straight or Arcuate Tranverse Corneal Incisions are usually used to treat up to 4.0 D of astigmatism. If a patient will need cylinder correction, a second procedure can be avoided, the astigmatism can be corrected at the moment of the cataract operation. Limbal Relaxing incisions can be performed postoperatively to correct astigmatic surprise, with good results if applying the stablished nomograms like the ones from Gills, Nichamin, Cristobal-Mateo, and buzzard15, 16 and precise surgical technique, but results are not as accurate and predictive as excimer laser modalities. It is indeed a more simple, economic and accessible solution.

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Mastering the Techniques of Intraocular Lens Power Calculations LASIK was first combined with phakic IOLs, the latest to reduce the majority of the refractive spherical equivalent and the laser to fine tune any remaining sphere or astigmatism. This combined procedure was denominated Bioptics by Zaldivar, and extended its range to lens surgery in patients who have large amounts of corneal astigmatism or are expected to have refractive error. 17 Corneal flaps are created using the mechanical microkeratome or more recently the femtosecond laser, better one to two weeks before the cataract or Lens Exchange Surgery. After the refraction and corneal topography are stable, the Flap previously created can be lifted and excimer laser ablation performed to correct the residual defect. This period to reach stability depends much on the incision performed and the postoperative evolution of the patient regarding corneal edema, inflammation, and Intraocular pressure. There are not well stablished criteria about the exact time. For a standard phacoemulsification through an incision of around 3 mm, with a good quiet evolution, 2 to 4 weeks is usually enough for the LASIK ablation. In the majority of postcataract surgery undesired refractions, no previous flaps have been created. This has several inconveniences. The high vacuum of the microkeratome should be delayed for several months until the cataract wound is perfectly healed, this takes longer for clear corneal incisions (3 to 6 months). Authors like Dr. Nichamin 18 consider save a period of 4 to 6 weeks in incisions of 3 mm on clear cornea. If cataract surgery had any complication that causes poor lens stability, LASIK may be contraindicated. The high vacuum can also cause pupillary trap of the IOL in sulcus fixated lenses, or more serious problems in AC IOL or iris fixated lenses, reasons why in general such patients don’t qualify to be performed LASIK flaps. Excimer Laser postcataract error correction can provide very accurate results, through wavefront or topography guided ablations it can correct aberrations and improve the quality of vision. Nevertheless even in patients where you expected a possible refractive surprise or have high pre-existing astigmatism, usually results are better than expected, and subjectively satisfactory for the patient, so the creation of corneal flaps should be carefully analyzed and maybe left for patients very interested in reaching the most accurate refractive results. Surgeons should avoid to unnecessarily increase the risk of complications like the ones related with the flap and interface.

CASE REPORTS Case 1 IPL is a 36-year-old female patient with history of high hyperopia. The patient could never get used to Contact Lenses and never wears Glasses for esthetic reasons and because is not satisfied with the visual quality they provide. There is very poor Uncorrected Visual Acuity, of 0.1 RE and 0.09 LE. Refraction RE: + 10.00 – 1.50 x 90 CVA- 0.9 LE: + 9.75 - 1.50 x 10 CVA- 0.8 Keratometric measurements as follows: RE 48.00 × 90 /46.5 × 180 and LE 47.75 × 80/46.25 × 170 and Ultrasound Biometry was RE 2.97, 3.25, 18.83 and LE 2.92, 3.30, 18.79. (ACD, Lens thickness, AL). Media was clear in both eyes, including the lens. And no relevant findings on ocular examination were observed. The patient´s Axial Lengths resulted to be the smaller registered on our data base of more than 50 000 operated eyes. This young active woman could not find an acceptable solution in conservative optical aids, so had been searching for a surgical approach for several years and came to our center after being rejected in various hospitals. Considering her poor quality of vision and life, and her high motivation for surgery we analyzed the possible surgical alternatives in our hands. Excimer Laser surgery either by LASIK or surface ablation can only correct up to 6.00 D of hyperopia. In this particular patient with steep corneas, only a lower amount of defect could be eliminated, so a high residual hyperopia would be left still not considering the regression. This was considered unacceptable even knowing that hyperopic patients feel satisfied by experiencing reduction of their error. Phakic IOL implantation was impossible with the alternative in our hands as Artisan/Artiflex lenses shouldn´t be implanted in Anterior Chamber Depths below 3.0 mm. Clear Lens Extraction was considered, but IOL calculation using Hoffer Q Formula gave a lens power of 35.00 D PC IOL LE to achieve emmetropia. Such high power was not available and is not a desirable pseudophakic correction due to the poor optical quality. Bioptics wasn´t planned as the patient had only a very mild degree of astigmatism and steep cornea. We did not consider appropriate to work with the two structures (Cornea and Lens), when a less traumatic solution that

Management of Refractive Surprises after Cataract Surgery provides excellent optical results as polipseudophakia was in or hands. The patient was performed uneventful phacoemulsification LE through clear corneal incision and a 20.00 D three pieces foldable PC IOL was implanted in the bag and a 15.00 D equal lens implanted in the ciliary sulcus. Post operative refraction after one week LE was: +3.75 -0.75 × 160° BCVA: 0.6 and even though the patient expressed satisfaction we suggested as solution to exchange the more anterior IOL, the patient accepted but for personal reasons preferred to wait 3 more weeks and we did not object given the easy exchange of a sulcus fixated IOL even after longer periods. Multiplying the spherical equivalent by 1.5 the lens in the sulcus was exchanged by a 20.00 D lens. Surgery was uncomplicated, removal was done by folding the lens in the Anterior Chamber and implanting the newly calculated lens in the sulcus. Refraction after 1 week was: +0.25 – 0.50 x 160º UCVA: 0.8 and BCVA: 1.0 with a great patient satisfaction. In the right eye even taking all care, repeating the biometry and doing the necessary adjustments, a mild degree of hyperopia was obtained, satisfactorily solved in the same way.

(K= Kt x (376/337.5)-5.5). SRK T formula was used for calculation. The next table shows the evolution of refraction in both eyes after surgeries. DATE

IOP 16 mmHg OU Examination reveals four RK cuts scars OU. Mild nuclear lens opacity OU, and myopic fundus without risky peripheral retinal degenerations or tears. The patient is offered the possibility of cataract surgery and is explained the lower predictability of IOL calculation because of the previous corneal refractive surgery and the possibility of a second surgery. He was interested due to handicap for certain activities as driving and desire to correct high hyperopic defect. Preoperative tests were done in the IOL Master and Corneal Topographer using Maloney´s formula for adjusting the Keratometric values based in the Central Topography (Kt)

RIGHT EYE

16/11/06

LEFT EYE SURGERY PHACOEMULSIFICACIÓN + PC IOL (24.5 FOLDABLE ACRYSOF)

21/11/06

UCVA 0.1 Ref: +6.00 -1.00 × 180 1.0

6/12/06

PHACOEMULSIFICACIÓN + PC IOL (25.5 PLEGABLE ACRYSOF)

13/12/06

UCVA 1.0 Ref: Plano 1.0

UCVA O.5 Ref: +2.75 -1.75 × 115 1.0

28/12/06

UCVA 0.5 Ref –2.00 1.0

UCVA O.6-1 Ref: +2.00 -1.25 × 120 1.0

18/01/07

UCVA 0.2 Ref: –3.25 1.0

UCVA O.8-2 Ref: +0.50 -2.25 × 110 1.0

20/02/07

UCVA 0.4-1 Ref: –2.75 1.0

UCVA O.6+1 Ref: +1.00 – 2.75 × 110 1.0

9/4/07

INTRAOCULAR LENS EXCHANGE (PC IOL 23.0D FOLDABLE MEDIPHACOS IOFLEX)

28/05/07

UCVA 0.4-1 Ref: –1.75 –1.25 × 60 1.0

UCVA O.5 Ref: -1.00 × 110 1.0

15/06/07

UCVA 0.4-1 Ref: –1.75 –1.25 × 60 1.0

UCVA 1.0 (DIF) Ref: –1.00 × 150 1.0

11/09/07

UCVA 0.4-1 Ref: –2.75 –1.25 × 60 1.0

UCVA 0.7 -1 Ref: –1.25 –1.00 × 155 1.0

Case 2 VAB is a 55-year-old male patient with history of glaucoma (Controlled with Timolol and Xalatan) who was done Radial Keratotomy (RK) both eyes approximately 20 years ago (Four Cuts) to correct a mild myopia and ended with a high overcorrection. Used Contact Lenses in the last 8 years and comes to us complaining of glare and mild visual acuity decrease. UCVA OU: 0.1 Refraction RE: +6.00 -1.00 x 180 1.0 LE: +7.00 -1.50 x 110 1.0

311

UCVA 1.0 Ref. Plano 1.0

The low predictability of IOL calculation in such cases is a well known fact. Nevertheless in this patient what really causes frustration is the great instability of the refraction for a period as long as 10 months. This patient had an unusual degree of overcorrection with only four cuts of RK. And Post Phacoemulsification Refraction through 3 mm clear corneal incisions produced an unexpected long instability. In both eyes the early refraction was amazingly Plano, but satisfaction lasted shortly because subjective visual quality deterioration presented and refraction shifted from plano to -hyperopia to myopia LE and to myopia RE that progressed to – 2.75 -1.25 × 60 even after exchanging IOLs at four months after Phacoemulsification. Hoffer K19 described the postoperative corneal flattening and hyperopia of RK patients with stabilization after 3 or 4 months tipically. This case is an example of how altered the corneal biomechanics can be (As shown in the

Mastering the Techniques of Intraocular Lens Power Calculations

312

Fig. 46.2 : RE pre and postoperative corneal topography

Fig. 46.3 : LE pre and postoperative corneal topography

follow up Corneal topographies) in postrefractive surgery patients, and teaches the importance of waiting for complete stabilization of the refraction before deciding any secondary surgical correction (Figs 46.2 and 46.3).

REFERENCES 1. Lledó Pérez C, Acebal Bernal A Sorpresa Refractiva Tras La Cirugía De La Catarata Actas De La Soc Esp De Enf En Oft. Volumen I Enero-Diciembre 2004. 2. Paul B, Chell MB Refractive targeting in cataract surgery. Focus On: Refractive Targeting In Cataract Surgery. Focus Published By the Royal College of Ophthalmologists. Issue Twenty Eight: Winter 2003. 3. Pérez Silguero MÁ, Pérez Silguero D, Bernal Blasco I, Pérez Hernández FR, Jiménez García A. Nuevo Método Para El Cálculo De Lio En Situaciones Difíciles. Microcirugía Ocular Número 1 - Marzo 2002. 4. Pérez-Silguero D, Pérez-Silguero Ma, Pérez-Hernández Fr.. Intraocular Lens Power Calculation In Complicated Cases:

5. 6.

7.

8. 9.

10.

The «Silguero» Method. Arch Soc Esp Oftalmol 2005;80(10): 80:589-96. Leccisotti A, Bioptics: Where do things stand? Current Opinion in Ophthalmology 2006;17(4):399-405. Ianchulev T, Salz J, Hoffer K, Albini T, Hsu H, LaBree L. Introperative optical Refractive Biometry for intraocular lens power estimation without axial length and Keratometry measurements. J Cataract Refract Surg 2005;31:1530-36. Escaf LJ, Campo T, Tello A, Gonzales A. Método de Escaf para el cálculo del LIO en pacientes con Cirugía Refractiva Previa basado en la refracción afáquica intraoperatoria. Oftalmología Basada en la Evidencia. Libro del Cristalino de las Américas. Livraria Santos Edit. 2007;123-30. Zacharias W. Ecobiometria e Calculo da Lente Intra-ocular para irurgiao de catarata. In: Libro del Cristalino de las Américas. Livraria Santos Edit. 2007;79-93. Alfonso JF, Fernández-Vega L, Begoña M. Secondary diffractive bifocal piggyback intraocular lens implantation. Journal of Cataract and Refractive Surgery, 2006;32(Issue 11):1938-43. Nichamin LD. Treating astigmatism at the time of cataract surgery. Cataract surgery and lens implantation. Current Opinion in Ophthalmology 2003;14(1):35-38.

Management of Refractive Surprises after Cataract Surgery 11. Gayton JL, Apple DJ, Peng Q, et al. Interlenticular opacification: clinicopathological correlation of a complication of piggyback posterior chamber intraocular lenses. J Cataract Refract Surg 2000;26(3):330-6. 12. Shugar JK, Schwartz T. Interpseudophakos Elschnig pearls associated with late hyperopic shift: a complication of piggyback posterior chamber intraocular lens implantation. J Cataract Refract Surg 1999;25:863-67. 13. Shugar JK, Keeler S. Interpseudophakos intraocular lens surface opacification as a late complication of piggyback acrylic posterior chamber lens implantation. J Cataract Refract Surg 2000;26:448-55. 14. Shane K Kim, Ralph C Lanciano Jr., Michael E Sulewski. Pupillary block glaucoma associated with a secondary

15. 16. 17. 18. 19.

piggyback intraocular lens. Journal of Cataract and Refractive Surgery. 2007;33(10):1813-14. Cristobal JA, Faus F, Mateos A. Incisiones y efecto astigmático en la cirugía del cristalino. In: Cristobal JA. Corrección del Astigmatismo. Ed. Mac Line. Madrid 2006;129-41. Chu YR, Hardten DR, Lindquist TD, Lindstron RL. Astigmatic Keratotomy. In: Duane´s Ophthalmology. Lippincott Williams and Wilkins, 2005. Probst LE, Smith T. Combined refractive lensectomy and laser in situ keratomileusis to correct extreme myopia. Journal of Cataract and Refractive Surgery 2001;27(4):632-35. Nichamin L. How to Get the Best From Bioptics. Review of Ophthalmology 10(03). Hoffer KJ. Solving IOL Power Calculation Problems. In Garg A. Mastering the techniques of IOL power calculation. Jaypee Brothers 2005;16:131-60.

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Mastering the Techniques of Intraocular Lens Power Calculations Fengju Zhang, Yan Wang (China)

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47

Intraocular Lens Power Calculation in the High Myopic Eye

INTRODUCTION Cataract surgery is the most common intraocular surgical procedure performed in all over the world. Although the complications are not the main problem due to modern techniques, patients still have very high expectations for the refractive outcomes. In order to achieve optimum results, preoperative biometry must be accurate and an accurate IOL power formula must be used. The theoretical formula was first described by Fedorov and coauthors in 1967.1 All theoretical formulas are based on the same fundamental equation: P = n/ACD – AL – nxK/n –K × A.L (P = IOL power for emmetropia, n = refractive indices of aqueous and vitreous, ACD = estimated postoperative anterior chamber depth, AL = axial length, and K = corneal curvature). Since then, other ophthalmologists (i.e. Binkhorst, Holladay, Hoffer, and Shammas) have refined the existing theoretical formulas.2-5 The Sanders-RetzlaffKraff (SRK) formula, P = A – 2.5AL – 0.9K (P = IOL power for emmetropia, A = A – constant, AL = axial length, K = corneal curvature), was the first regression formula designed for practical calculation6 . It does not include anterior chamber depth (ACD) and is less accurate in eyes with extreme axial length (ALs). With the development of the posterior chamber IOLs, the ACD was proved to vary with the AL7. The second-generation SRK II formula was designed by combining lines regression analysis with stepwise adjustments for long and short eyes. The third-generation formulas (Holladay I, SRK/T, and Hoffer Q) aimed to predict the position of the IOL more accurately, incorporating the effect of corneal curvature. Fourth-generation formulas such as the Holladay II use other factors, such as corneal diameter

and lens thickness, in an attempt to better predict the final position of the IOL. Patients with high myopia are often inclined to suffer from cataract which are called complicated cataract. It is always a manifestation of nuclear cataract or posterior subcapsular cataract. Because of the special anatomical characteristics of high myopia, such as the deeper anterior chamber depth (ACD)¡¢the longer axial length and posterior scleral staphyloma, determining the power of the IOL to be implanted is a crucial factor in the postoperative refractive status and visual acuity. The refractive outcome following cataract surgery depends on a series of factors, including axial length measurement, keratometry, anterior chamber depth, IOL power formulae, A constant and the quality of the IOL. Of all these factors, inaccurate axial length measurements and the inaccurate selection of IOL power calculation formula were shown to be the major deterrent to the predictability of the refractive outcome, especially for the high myopic eyes.

THE FORMULAS OF IOL POWER CALCULATION The First Regression Formula SRK: P = A – 2.5AL – 0.9K (P = IOL power for emmetropia, A = A – constant, AL = Axial length K = Corneal curvature) It is the first regression formula designed for practical calculation. It does not include anterior chamber depth (ACD) and is less accurate in eyes with extreme axial lengths.

Intraocular Lens Power Calculation in the High Myopic Eye The Second-generation Formulas SRK-II, Binkhorst-II The SRK-II formula is the representative one which considers the anterior chamber depth varies with the axial length. It is always used for calculating IOL power in usual situation.

The Third-generation Formulas SRK/T, Holladay I, Hoffer Q. They considered ACD not only varying with the AL but varying with corneal curvature. They aimed for better estimation of IOL power in eyes with extreme AL.

AXIAL LENGTH MEASUREMENT A-scan and B-scan Ultrasonography A-scan uses the echo delay time to measure intraocular distances. It has a longitudinal resolution of 200µm and an accuracy of 100-120 µm in measuring axial length. The difficulties in IOL power calculation for longer axial eye may be partly due to the anatomy of the posterior pole. The forvea is approximately 4.5 mm (3 disc diameters or 15 degrees) from center of the optic nerve. Holladay and others have performed high-resolution B-scans with the Innovative Imaging System using horizontal sections through the optic nerve and measuring the distance from the corneal vertex to a point 4.5 mm temporal to the center of the optic nerve. In eyes with axial length longer than 30.0 mm, a posterior pole staphyloma temporal to the forvea was common and the corneal vertex-forvea distance was approximately 0.5-1.5 mm shorter than the distance from corneal vertex to the bottom of the staphyloma, which is where the A-scan usually finds the perpendicular axis and records the axial length. So for the longer axial eyes, standard B-scan ultrasonography can help to identify a posterior pole staphyloma, where could locate the center of the forvea easily, and measure the accurate axial length.

IOL-Master Optical Coherence Biometry (IOL-Master) has found its clinical application in preoperative biometry. This technique aims to improve the precision in axial length measurements using the principle of partial coherence laser interferometry (PCLI). Partial coherence laser interferometry is a non-contact method and offers the ease of obtaining keratometry values, anterior chamber depth and AL measurements in a single

sitting. This is a significant advantage when compared to conventional ultrasound biometry, which demands topical anesthesia for corneal applanation and is time consuming. Both partial beams are reflected at the corneal surface and the retina (RPE), which defines the long atitude of axial from corneal surface to RPE. So the axial lengths are measured approximately 100 µm longer than with applanation ultrasound. PCLI has an advantage over ultrasound biometry in measuring the AL of eyes with silicone oil or posterior staphyloma. Accurate data of axis length can be obtained by combining results of A-scan, B-scan ultrasonography and IOL-master for high myopia with cataract, especially for patients with posterior scleral staphyloma. A study8 on the accuracy of IOL power calculation formulas in the cataract eyes with high axial myopia showed that the eyes with high axial myopia with AL longer than 25 mm, the Hoffer Q provided the best predictive result and the Holladay I and SRK/T were comparable choices for IOL power calculation. The SRK-II was the least preferable. In studies by Retzlaff and coauthors,9 the Hoffer Q, SRK/T, and Holladay I are superior to the SRK-II in eyes with AL longer than 28.4 mm. In the recent study of Narvaez,10 643 eyes were collected to compare the refractive outcomes with four different formulas (including Hoffer Q, Holladay I, Holladay II and SRK/T), the eyes were stratified into groups average, medium long, and very long axial length 22.0 to < 24.5 mm, 24.5 to 26.0 mm, and > 26.0 mm. In conclusion from the results, there was no difference in the accuracy of IOL power prediction with the Hoffer Q, Holladay I, Holladay II, and SRK/T formulas in all eyes and in 4 subsets of axial lengths. The 4 formulas were equally accurate at all axial lengths. From the clinic study,9 the eyes with axial lengths longer than 27.0 mm having cataract with IOL implantation, current third- and fourth-generation lens calculation formulas have a tendency to over minus partients between -1.0 and -4.0D, leaving patients with postoperative hyperopia. The performance of these formulas appears better for plus-power IOL implantation than for minus-power IOL implantation, which is related to the higher incidence of posterior pole staphyloma in eyes with axial length longer 30.0 mm. So it better to combine the different examination results with the different methods for the extreme longer eyes in order to improve the accurate result.

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Mastering the Techniques of Intraocular Lens Power Calculations IOL POWER CALCULATION OF EYES AFTER CORNEAL REFRACTIVE SURGERY As for the myopic cataract eyes received the corneal refractive surgery, the corneal curvature and anterior chamber depth have changed after corneal refractive surgery, the IOL calculation for these eyes should be more accurate. In Gimbel’s study11 , Refractive outcomes in six cataract surgery and lensectomy eyes after previous laser in situ keratomileusis (LASIK) were analyzed retrospectively. Target refractions based on measured and refraction-derived keratometric values were compared with postoperative achieved refractions. Differences between target refractions calculated using five IOL formulas and two A-constants and achieved refractions were also compared. The refractive results appeared more accurate and predictable when the Holladay II or Binkhorst II formula was used for IOL power calculation. They made the conclusion that hyperopic error after cataract surgery in post-LASIK eyes was significantly reduced by using refraction-derived keratometric values for IOL power calculation. Chan 12 retrospectively reviewed 34 eyes that had undergone routine phacoemulsification and IOL implantation after photorefractive keratectomy (PRK)or LASIK. Sixteen eyes were included in the final analysis. Four methods were used to obtain keratometric values combined with three common IOL formulae (Holladay II, SRK/T and Hoffer Q) and Koch’s published Double-K nomogram. The Double-K method13 was also used in conjunction with the Holladay II formula. The results were that the Clinical History method at the spectacle plane produced the lowest mean K-values. Shammas adjustment formula combined with the Holladay II and Hoffer Q produced results closest to emmetropia. The Double-K methods produced the least number of hyperopic results. The conclusion were that no method produces acceptably consistent results because modern IOL formulae were designed for presurgical eyes. Accuracy will only be improved when new IOL formulae based on the anatomy of post refractive eyes become available. LASIK corrects myopia by flattening the central cornea, thereby reducing the diopter power of the cornea. The more higher myopia is, the more flatter the cornea is. However, this flattening is not uniform. The greatest degree of flattening is found most centrally, and there is a gradual steep toward the periphery of the treatment zone, which in turn converts the normal prolate convexity of the anterior cornea to an oblate convexity. As a result, the mean refractive power of the cornea is reduced and the

effective refractive zone shifts. Corneal topographers may be used to measure the various zones of the cornea. In the Gelender’s clinical study14 , they proved the hypothesis that the keratometric value derived from Orbscan II mean power maps, when used in an IOL calculation formula, at a specific measurement zone, namely 1.5 mm, will accurately determine the power of an IOL for planned cataract surgery in patients who have undergone prior myopic LASIK. The specific measurement was identified as the Orbscan II-derived mean power of the cornea at 1.5 mm. This represents a direct and simple technique to measure the effective keratometric value of the cornea in patients who have had prior myopic LASIK. When applied to IOL calculation formulas, such as the SRK-T formula, it affords an accurate measurement of IOL power for planned cataract surgery. Patients can achieve excellent uncorrected visual acuity with minimal induced refractive error using this method. Borasio E15 described a new formula, BESSt, to estimate true corneal power after keratorefractive surgery in eyes requiring cataract surgery. The BESSt formula, based on the Gaussian optics formula, was developed using data from 143 eyes that had keratorefractive surgery. The formula takes into account anterior and posterior corneal radii and pachymetry (Pentacam, Oculus) and does not require pre-keratorefractive surgery information. A software program was developed (BESSt Corneal Power Calculator), and corneal power was calculated in 13 eyes that had keratorefractive surgery and required cataract surgery. Target refractions calculated with the BESSt formula were statistically significantly closer to the postoperative manifest refraction (mean deviation 0.08 diopters [D] +/- 0.62 [SD]) than those calculated with other methods as follows: history technique (–0.07 +/– 1.92 D; P = .05); history technique with double-K adjustment (0.13 +/– 2.39 D; P = .05); Holladay II with Kvalues estimated with the contact lens method (-0.76 +/1.36 D; P = .03); Holladay II with K-values from Atlas topographer (Humphrey) (-0.55 +/– 0.61 D; P 6 years of age. - Plager and coworkers25 suggest aiming for +5 D in a 3 year old child, +4 D in a 4 year old, +3 D in a 5 year old, +2.25 D in a 6 year old, +1.5 D in a 7 year old, +1 D in an 8 year old, +0.5 D in a 10 year old child and plano in patients 13 years of age and older. - Raina and coworkers26 use a 10% standard reduction in IOL power for children aged 2 to 8 years and emmetropic correction for older children. - Trivedi and Wilson27 use extended undercorrection scheme of predicted IOL outcomes. It is presented in Table 51.1.

Problems of IOL Power Calculation in Pediatric Cataract Surgery Table 51.1: Expected postoperative residual refraction based on patient age at cataract surgery recommended by Trivedi and Wilson27

-

Patient age

Residual refraction

1st month 2nd – 3rd months 4th – 6th months 6 - 12 months 1 – 2 years 2 – 4 years 4 years 5 years 6 years 7 years 8 – 10 years 10 – 14 years >14 years

+ 12,0 Diopters + 9,0 + 8,0 + 7,0 + 6,0 + 5,0 + 4,0 + 3,0 + 2,0 + 1.5 + 1,0 + 0.5 Plano

Author basing on the changes of axial length, corneal power and IOL power with age has calculated that between 1 and 2 years of age the power of the IOL should be undercorrected by 20%, at 2 to 4 years by 15%, at 4 to 8 years by 10% and emmetropia at > 8 years of age (Table 51.2).28 Using these recommendations we have calculated that residual refractive error should be no more than +3,5 D immediately after IOL implantation in childhood and –2,0 D in adulthood (Fig. 51.8). Table 51.2: Simple guidelines for IOL power calculations in children28

1. 2. 3. 4. 5.

1 - 2 years 2 - 4 years 4 - 8 years > 8 years Undercorrect

= IOL formula- 20% = IOL formula- 15% = IOL formula - 10% = IOL formula if results questionable

Factors Influencing Predicted IOL Power Values

Status of Fellow Eye One should adjust the end result of IOL calculation to the refractive status of the second eye to minimize the anizeikonia between both eyes. High anizeikonia is amblyogenic and it will interfere with spectacle correction and amblyopia treatment.

Probability of Inborn Refractive Error One have to undercorrect more if one or both parents are myopic because of greater possibility of myopia development in the school age.

Visual Acuity If deep amblyopia is expected to be find in the operated eye it is advisable to calculate less undercorrection because high hyperopia interferes with amblyopia treatment. Children with small hyperopia or myopia accept better amblyopia treatment because they see better for the near.

Parents Compliance with Amblyopia Treatment Regime If parents noncompliance with amblyopia treatment and eyeglasses or contact lens wearing regime is expected it is advisable to leave less hyperopia to have the least possible error during the most sensitive period of amblyopia treatment.

Sulcus Implantation If during the surgery IOL can not be implanted in-the-bag but is inserted in the ciliary sulcus IOL power should be decreased by 0.75 to 1.0 D.

Fig. 51.8: Approximate IOL power for implantation using above presented guidelines28

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336 CONCLUSION

Author’s preferred method of IOL power calculation in children: 1. Axial length measurement with A-scan ultrasound applanation method + 0,3 mm 2. Keratometry with the use of Retinomax K plus without the use of an eyelid speculum and general anesthesia 3. IOL power calculation with 5 different formulas (SRKT, Holliday I and II, Hoffer Q, Haigis) and then use the average of three most closest predictions 4. Undercorrection of IOL power by 20% in children aged 1 to 2 years, by 15% in patients aged 2 to 4 years, by 10% at 4 to 8 years and emmetropia at > 8 years of age 5. If it is possible do not implant IOL in children younger than 1 year to avoid wide range of residual refractive error in the adulthood.

REFERENCES 1. Prost M. (ed.): Development of the human eye in children. Children’s Memorial Health Institute Publications, 2000, Warsaw, Poland. 2. Gordon RA, Donzis PB. Refractive development of the human eye. Archives of Ophthalmology 1985;103:785-89. 3. McClatchey SK, Hofmeister EM. Intraocular lens power calculation for children. In: Wilson ME, Trivedi RH, Pandey SK, editors. Pediatric Cataract Surgery: Techniques, Complications and Management. Baltimore: Lippincott Williams & Wilkins. 2005;30-38. 4. Eibschitz-Tsimboni M, Archer SM, del Monte LA: Intraocular lens power calculation in children. Surv Ophthalmol 2007; 52:474-82. 5. O’Brien C, Clark D. Ocular biometry in pre-term infants without retinopathy of prematurity. Eye 1994;8:662-65. 6. Inagaki Y. The rapids change of corneal curvature in the neonatal period and infancy. Arch Ophthalmol 1986;104: 1026-27. 7. McClatchey SK, Parks MM. Myopic shift after cataract removal in childhood. J Pediatr Ophthalmol Strabismus 1997; 34:88-95. 8. McClatchey SK, Parks MM: Theoretic refractive changes after lens implantation in childhood. Ophthalmology 1997;104: 1744-51. 9. Enyedi LB, Peterseim MW, Freedman SF, Buckley EG. Refractive changes after pediatric intraocular lens implantation. Amer J of Ophthalmol 1998;126:772-81. 10. Hutchinson AK, Drews-Botsch C, Lambert SR. Myopic shift after intraocular lens implantation during childhood. Ophthalmology 1997;104:1752-57.

11. McClatchey SK, Dahan E, Maselli E et al. A comparison of the rate of refractive growth in pediatric aphakic and pseudophakic eyes. Ophthalmology 200;107:118-22. 12. Wilson ME, Bartholomew LR, Trivedi RH. Pediatric cataract surgery and intraocular lens implantation: practice styles and preferences of the 2001 ASCRS and AAPOS memberships. J Cataract Refract Surg 2003;29:1811-20. 13. Dahan E, Drusedau MU. Choice of lens and dioptric power in pediatric pseudophakia. J Cataract Refract Surg 1997;23 Suppl 1:618-23. 14. Mittelviefhaus H, Gentner C: Messungenauigkeiten der Keratometrie bei der Intraokularlinsenberechnung für Säuglinge. Ophthalmologe 2000;97:186-88. 15. Schelenz J, Kammann J. Comparison of contact and immersion techniques for axial length measurement and implant power calculation. J Cataract Refract Surg 1989; 15:425-28. 16. Andreo LK, Wilson ME, Saunders RA. Predictive value of regression and theoretical IOL formulas in pediatric intraocular lens implantation. J Pediatr Ophthalmol Strabismus 1997;34:240-43. 17. Arffa RC, Donzis PB, Moegan KS et al. Prediction of aphakic refractive error in children. Ophthamic Surg 1987;18:851-54. 18. Mezer E, Rootman DS, Abdolell M, Levin AV. Early postoperative refractive outcomes of pediatric intraocular lens implantation. J Cataract Refract Surg 2004;30:603-10. 19. Neely DE, Plager DA, Borger SM et al. Accuracy of intraocular lens calculations in infants and childrenundergoing cataract surgery. J AAPOS 2005;9:160-65. 20. Tromans C, Haigh PM, Biswas S et al. Accuracy of intraocular lens calculation in pediatric cataract surgery. Brit J Ophthalmol 2001;85:939-41. 21. Eibschitz-Tsimboni M, Tsimboni O, Archer SM et al. Discrepancies between intraocular lens implant power prediction formulas in pediatric patients. Ophthalmology 2007;114:383-86. 22. Ashworth JL, Maino AP, Biswa S, Lloyd IC. Refractive outcome after primary intraocular lens implantation in infants. Brit J Ophthalmol 2007;91:596-99. 23. Crouch ER, Crouch ER Jr, Pressman SH. Prospective analysis of pediatric pseudophakia: myopic shift and postoperative outcomes. Journal of AAPOS, 2002;6:277-82. 24. Hardwig PW, Erie JC, Buettner H. Preventing recurrent opacification of the visual pathway after pediatric cataract surgery. Journal of AAPOS, 2004;8:560-65. 25. Plager DA, Kipfer H, Sprunger DT, Sondhi N, Neely DE. Refractive change in pediatric pseudophakia: 6-year followup. J Cataract Refract Surg 2002;28:810-15. 26. Raina UK, Mehta DK, Monga S, Arora R. Functional outcomes of acrylic intraocular lenses in pediatric cataract surgery. J Cataract Refractive Surg 2004;30:1082-91. 27. Trivedi RH, Wilson ME: Intraocular lens power calculation in children. Magazyn Okulistyczny (Poland), 2005;4(8): 294-300. 28. Prost ME. IOL calculations in cataract operations in children. Klinika Oczna 2004;106:691-94.

Intraocular Lens Calculation after Prior Refractive Kenneth J HofferSurgery (Santa Monica, CA, USA)

52

Intraocular Lens Calculation after Prior Refractive Surgery

INTRODUCTION What could possibly be more important for patients choosing a refractive or multifocal intraocular lens (IOL) than the accurate calculation of the IOL power? This subject is considered a routine affair in most practices and the results are usually acceptable in the standard cataract patient. That may not be true in patients who are expecting (perhaps demanding) perfection and possibly paying extra for the IOL. It behooves every surgeon entering this area of surgical treatment to become completely familiar with every method to improve the accuracy of IOL power calculation in their practice. A special dilemma arises in eyes that have previously had refractive surgery; either by corneal surgery or by a phakic IOL. Let’s solve the biphakic eye problem first.

BIPHAKIC EYES (PHAKIC EYE WITH A PHAKIC INTRAOCULAR LENS) The problem here is eliminating the effect of the sound velocity through the phakic lens when measuring the axial length (AL) using ultrasound. I published a method1 to correct for this potential error by using the following formula: ALCORRECTED = AL1555 + C × T where AL1555 = the measured AL of the eye at sound velocity of 1555 m/sec, T = the central axial thickness of the phakic IOL and C = the material-specific correction factor of +0.42 for PMMA, –0.59 for silicone, +0.11 for collamer, and +0.23 for acrylic. My publications1,2 on this subject contain tables showing the central thickness based on the dioptric power for each phakic IOL on the market today. The least error is

caused by a very thin myopic collamer lens (eg, ICL) and the greatest error is seen with a thick hyperopic silicone lens (eg, PRL).

CORNEAL REFRACTIVE EYES Instrument Error The problem of IOL power calculation errors in corneal refractive surgery eyes was first described by Koch et al3 in 1989. The first problem that arises is that the instruments we use cannot accurately measure the corneal power needed in the IOL power formula in eyes that have had radial keratotomy (RK), photorefractive keratectomy (PRK), laser-assisted intrastromal keratomileusis (LASIK) and laser-assisted epithelial keratomileusis (LASEK). This major cause of error is due to the fact that most manual keratometers measure at the 3.2 mm zone of the central cornea, which often misses the central flatter zone of effective corneal power; the flatter the cornea, the larger the zone of measurement and the greater the error. The instruments usually overestimate the corneal power, leading to a hyperopic refractive error postoperatively.

Index of Refraction Error The second problem is that the assumed index of refraction of the normal cornea is based on the relationship between the anterior and posterior corneal curvatures. This relationship is changed in PRK, LASIK, and LASEK but not in RK eyes. RK causes a relatively proportional equal flattening of both the front and back surface of the cornea, leaving the index of refraction relationship relatively the same. The other refractive procedures flatten the anterior surface but not the posterior surface thus changing the refractive index calculation, which creates an

337

Mastering the Techniques of Intraocular Lens Power Calculations

338

overestimation of the corneal power by approximately 1 diopter for every 7 diopters of refractive surgery correction obtained. A manual keratometer measures only the front surface curvature of the cornea and converts the radius (r) of curvature obtained to diopters (D) using an index of refraction (IR) of usually 1.3375. The formula to change from diopters to radius is [r = 337.5/D] and from radius to diopters is [D = 337.5/r].

Before finishing the Tool, we asked each formula author to beta test it to make sure they agreed with our calculations and assumptions. We have converted formula abbreviations to maintain consistency. The legend for these abbreviations is listed on Sheet #3 in the Tool and at the end of this discussion.

Methods To Estimate True Postoperative Corneal Power

Formula Error The third problem is that most of the modern IOL power formulas (Hoffer Q,3 Holladay I,4 and SRK/T5 but not the Haigis6) use the AL and corneal power (K) reading to predict the position of the IOL postoperatively. The flatter than normal K in RK, PRK, LASIK, and LASEK eyes causes an error in this prediction because the anterior chamber dimensions do not really change in these eyes.

HISTORY OF SOLUTIONS In 1989, Holladay8 was the first to publish and popularize two methods to attempt to predict the true corneal power in refractive surgery eyes. I referred to them as the Clinical History Method and the Contact Lens Method.9,10 The latter was first described by Frederick Ridley11 in the United Kingdom in 1948 and introduced in the United States by Soper and Goffman12 in 1974. Over the years many researchers and authors have proposed multiple methods to solve this problem. No one procedure has yet to be proven to be the most accurate in all cases. In this regard Giacomo Savini of Bologna, Italy and I collaborated, over a 2-year period to create an Excel spreadsheet tool that would automatically calculate most all the proposed methods and also provide a place to store all the data collected and entered. All the information could be stored in one place and it could be printed out on one sheet and stored in the patient’s chart. The Hoffer/ Savini LASIK IOL Power Tool (Fig. 52.1) was finished on July 4, 2007 and can be downloaded at no cost from www.EyeLab.com by clicking on the IOL Power button and then the Hoffer/Savini button. In the creation of the tool, we divided all the published methods into those that attempt to predict the true power of the cornea and those that fudge the target IOL power calculated with the standard data. We then divided each group into those methods that need historical data regarding the status of the patient’s eye prior to refractive surgery and those that do not need any historical data.

Those Needing Clinical History Clinical History Method1-9 K = K PRE + RPRE – RPO or [K = KPRE + RCC] This method is based on the fact that the final change in refractive error the eye obtains from surgery was due only to a change in the effective corneal power. If this refractive change the patient experienced is algebraically added to the presurgical corneal power, we will obtain the effective corneal power the eye has now. Obviously this requires knowledge of the K reading and refractive error prior to refractive surgery. Originally it was recommended to vertex-correct the refractive errors to the corneal plane. Odenthal et al13 showed that clinical results were better if they were not corrected. We have decided to use vertex correction in the Hoffer/Savini Tool because this is more scientifically accurate. Several IOL power calculation computer programs calculate the Clinical History method automatically when needed [Hoffer® Programs and Holladay® IOL Consultant]. Hamed-Wang-Koch Method14 K = TKPO – (0.15*RC) – 0.05 This method requires knowledge of the refractive change from the surgery and the postoperative Sim-K from the topography unit. Speicher15 (Seitz16,17) Method K = 1.114*TKPO - 0.114*TKPRE This method requires obtaining the pre- and postoperative topographic Sim-Ks. Jarade Formula18 K = TKPRE-(0.376*(TKPOr - TKPREr)/(TKPOr*TKPREr) This method requires obtaining the pre- and postoperative topographic Sim-Ks in radius of curvature, not diopters. Ronje Method19 K = KPOFLAT + 0.25*RC This method requires knowledge of the refractive change from the surgery and the postoperative flattest K reading measured now.

Intraocular Lens Calculation after Prior Refractive Surgery

Fig. 52.1: Hoffer/Savini LASIK Tool for IOL power calculation in refractive surgery eyes

Adjusted Refractive Index Methods These methods attempt to “correct” the index of refraction to better predict the corneal power. The first two methods require knowing the surgically induced refractive change at the spectacle plane and the average radius of curvature of the cornea now. The third method requires knowing the surgically induced refractive change at the corneal plane and the average radius of curvature of the cornea now. a. Savini20 Method: K = ((1.338 + 0.0009856*RCS) – 1)/ (KPOr/1000) b. Camellin21 Method: K = ((1.3319 + 0.00113*RCS) – 1)/ (KPOr/1000) c. Jarade22 Method: K = ((1.3375 + 0.0014*RCC) – 1)/ (KPOr/1000)

Those Not Needing Clinical History Contact Lens Method11,12 K = BCL + PCL + RCL - RNoCL The Contact Lens Method was first described by Frederick

Ridley 11 of England (the inventor of NaOH IOL sterilization) in 1948 and taught by Jospeh Soper12 in 1974. This method is based on the principle that if a hard PMMA (not rigid gas permeable) contact lens (CL) of plano power (PCL) and a base curve (BCL) equal to the effective power of the cornea is placed on the eye it will not change the refractive error of the eye. Therefore, the difference between the manifest refraction with the contact lens (RCL) and without it (RNoCL) is zero. The formula above computes the effective corneal power if there is a difference in any of these parameters. Originally it was recommended to vertex-correct the refractive errors to the corneal plane. Odenthal et al13 showed that clinical results were better if they were not corrected. We have decided to use vertex correction in the Hoffer/Savini Tool because this is more scientifically accurate. Several IOL power calculation computer programs calculate this method and the Clinical History Method automatically when needed [Hoffer® Programs

339

340

Mastering the Techniques of Intraocular Lens Power Calculations Table 52.1: Rosa correction factor conversion table based on axial length Rosa Correction Factor Table 22 - > fOS: (A3) Calculating aniseikonia as a function of image magnification M of both eyes, we obtain: (A4)

Contd...

Mastering the Techniques of Intraocular Lens Power Calculations

350 Contd...

B. Predicting postoperative aniseikonia: in case of axial anisometropia In the case of cataract surgery planned in pure axial anisometropia, aiming at emmetropising both eyes, postoperative aniseikonia can easily be estimated by making the ratio of the axial lengths only (Fig. 53.2). The focal length is expressed in function of the axial length: (A5) with PP being the second principal plane of the eye (about 1.6mm for the Gullstrand eye). As PP is only 8-10% of the ocular axial length, and can be considered as equal in both eyes, the ratio of both eyes’ axial lengths can be used as a quick approximation of the ratio of the focal lengths. Combining equations (A4) and (A5), we can estimate the postoperative aniseikonia after emmetropisation using a preoperative axial anisometropia: (A6)

Example: LOD = 23.1 mm and LOS = 25.9 mm → the theoretical aniseikonia in case emmetropisation of both eyes is the aim, will be 12%.

Fig. 53.3: Subjective aniseikonia measured by Winn’s eikonometer with respect to the calculated aniseikonia using our formula as in Appendix A after having implemented the data provided by Winn16

To Predict Postoperative Aniseikonia in the Case of Preoperative Anisometropia Based on the calculation developed in Appendix A, it is possible to calculate the theoretical aniseikonia in patients presenting anisometropia and seeking for lenticular correction. In the case of planned cataract surgery (correction in the lenticular plane), a corneal anisometropia of 8 D or an axial anisometropia of more than 1 mm should warn the surgeon for possible postoperative aniseikonia if emmetropia would be the goal. Because corneal anisometropia of 8 D is not so frequent (mainly after penetrating keratoplasty), axial

anisometropia will be the main cause for postoperative aniseikonia of 4% or more. The usefulness of the theoretical aniseikonia calculation will be illustrated by four clinical cases. In Appendix B, we developed the derivations to calculate aniseikonia in patients presenting pure axial anisometropia. In these cases, the calculation of aniseikonia can be significantly reduced to the ratio of both axial lengths (L). The theoretical aniseikonia is calculated over 360° allowing us to draw the aniseikogram. The highest degree of positive and negative aniseikonia can be deduced (= objective aniseikonia).

-3.5 -5@10°

R

-3%@120° 2.5%@26°

26.3

-14 -4@170°

3.1@75°

15.0

4 -3.75@175°

4.0@81°

48.3@171°

21.4 mm

-3%@80° 1%@170°

22.6(*)

0 -0.5@150°

1.4@83°

45.6@173°

21.6 mm

LE

18.2

24.6

0 0@0°

1.0@103°

41.7@13°

22.4 mm

LE

-3.5%@ 84° -0.5%@174°

7 -2.25@75°

2.4@86°

45.2@176°

20.0 mm

RE

HV (M, 4 years old)

10(*)

LE

10

0 0@0°

1.2@178°

42.1@88°

28.0 mm

-16%@68° 9%@158°

10 -16@67°

16.6@67°

33.2@157°

26.5 mm

RE

VBA (F, 80 years old)

L: axial length; K1: flattest meridian keratometry, ΔK: difference between keratometries of both eyes = astigmatism; R: subjective best-corrected spherical equivalent; ACD: anterior chamber depth; Plens: power lens; RE: right eye; LE: left eye; F: female; M: male (green: right eye, red: left eye, dashed line 0% aniseikonia)

Color legend RE LE Gullstrand

Preoperative aniseikogram

Objective aniseikonia

17.9

4.7@97°

ΔK

Plens

41.8 @7°

K1

42.2@165°

28.2 mm

25.1 mm

L

RE

VHF (F, 75 years old)

Table 53.4: Aniseikogram of four different types of anisometropia

LE

LBM(M, 25 years old) RO

Eye

Patient

Cataract Surgery

351

LE

LE

3.5%@80°

-11%@34°

2 -4@175° = 0

-0.5%@170°

0

RE

VHF (F, 75 years old)

-17%@128°

2.5 -5@10° = 0 2 -4@170° = 0

RE

LBM (M, 25 years old)

-8%@174°

-8%@ 84°

1 -2@75° = 0

RE 0

LE

HV (M, 4 years old)

RE: right eye; LE: left eye; R: target spherical equivalent to achieve emmetropia. M: male; F: female (green: right eye, red: left eye, dashed line 0% aniseikonia)

Color legends RE LE Gullstrand

Aniseikogram in case of emmetropia

Estimated aniseikonia in case of emmetropia

R

Eye

Patient

6%@158°

-18%@68°

8 -16@67° = 0

RE

0

LE

VBA (F, 80 years old)

Table 53.5. Estimated postoperative aniseikonia in four different types of anisometropia considering the patients needed cataract surgery and were implanted with an IOL aiming at emmetropia

352 Mastering the Techniques of Intraocular Lens Power Calculations

2 -4@97

Targeted refraction -4%@125° 1%@30°

-7 -2@161

18

——-

LE

3 -3.75@175°

-0.5%@170° 3.5%@80°

0

20

RE

0 0@0

———

LE

-3.5%@80° -1.7%@170°

6 -2.5@86°

21.5

RE

HV (M, 4 years old)

LE

0 0@0

——

-2.5%@60° 6%@155°

0 -6@120°

anterior chamber IOL

+12 -7.5@160°

RE

VBA (F, 80 years old)

RE: right eye; LE: left eye; R: target spherical equivalent to achieve emmetropia; PIOL: power of the IOL; M: male; F: female (green: right eye, red: left eye, dashed line 0% aniseikonia)

Corresponding aniseikogram

Minimally aniseikonia

16

PIOL (D)

LE

RE

Eye

VHF (F, 75 years old)

Table 53.6: Targeted refraction to achieve a minimally acceptable postoperative aniseikonia

LBM (M, 25 years old)

Patient

Cataract Surgery

353

354

Mastering the Techniques of Intraocular Lens Power Calculations In Table 53.5, the aniseikogram is simulated in case emmetropia was the goal to achieve postoperatively for both eyes. When looking at the results, it is obvious that only VHF would benefit from emmetropia after cataract surgery. LBM and HV would present an aggravation of their theoretical aniseikonia and VBA’s aniseikonia would remain unchanged postoperatively. Vice versa, this aniseikogram can be used to calculate the aimed postoperative refraction in order to achieve a clinically acceptable postoperative aniseikonia. Considering our clinical examples (Table 53.6), the refractive outcome of LBM’s left eye should be targeted at –7 (–2 à 161°) in order to limit postoperative aniseikonia to a maximum 4%, which was approximately his preoperative aniseikonia. Emmetropising his left eye would induce an aniseikonia up to 17%. VHF would be fine by emmetropisation of both eyes. His postoperative aniseikonia would remain unchanged compared to the preoperative one. HV presented about 4% of aniseikonia preoperatively, which was well tolerated. Emmetropisation of his right eye would induce 8% of aniseikonia. In order to reduce this aniseikonia from 8 to 4%, the targeted postoperative spherical equivalent refraction of his right eye should be +4.75 D in order to limit postoperative aniseikonia to 3.5%. The situation of VBA is very complex. She is already pseudophakic in her right eye and in addition presents a very important corneal astigmatism after penetrating keratoplasty. Emmetropisation of her right eye would result in 18% aniseikonia (Table 53.5), which is similar to her actual aniseikonia. Intraocular lens (IOL) exchange would not help that much since no toric IOL of that power is available. In order to limit her postoperative aniseikonia to about 6%, we proposed to implant an anterior chamber IOL, type toric Artisan (Ophtec®), of +12 (–7 à 160°) and to correct the remaining corneal astigmatism by means of laser surgery or spectacles.

To Validate the Method Winn16 proposed the evaluation of aniseikonia of 18 patients with high anisometropia, providing the full biometry. He also measured aniseikonia with another eikonometer than ours. By implementing the refractive data of 18 patients, as published in Winn’s paper,16 we have been able to compare the theoretical aniseikonia calculated with our method to the one that had been measured with their eikonometer. The correlation coefficient between their measurements and our theoretical aniseikonia was 0.82. This correlation factor is very good when considering that

subjective aniseikonia does not only reflect the optical properties of the eye, but also the retinal and/or cerebral properties.31

DISCUSSION In a large study including 5023 students between 6 and 18 years old,25 6% of anisometropia were reported. This number is very close to the 7.6% found in our series. Looking at myopic children, 17% presented anisometropia.26 These results suggest that the importance of anisometropia and the possible associated aniseikonia are not so uncommon. In clinical practice, ophthalmologists will have to deal with 6 to 7.6% of anisometropic patients at risk of developing some degree of induced aniseikonia after cataract or refractive surgery. Improvement of stereopsis in anisometropic children having had refractive surgery to correct their anisometropia has been found in only 10 to 33%.27-29 However, none of these studies clearly distinguished which type of anisometropia they were dealing with. It would have been more interesting to evaluate in which type of anisometropia the best success rate was found. When considering children presenting congenital cataracts, poorer results in visual performance were found in axial anisometropic children.30 These poor results can be explained by the postoperative differences in image size. We could not make the calculation because the dioptrical data were missing. Calculating the theoretical aniseikonia is timeconsuming. It is easier for the surgeon to get the objective aniseikonia at once in each anisometropic patient planned for cataract surgery. In complicated cases, the results obtained can be simulated by means of contact lenses prior to surgery.24 The subjective aniseikonia can then be measured by means of the eikonometer. In this way, the surgeon and the patient will be more confident to do or to undergo the surgery. Combining the theoretical aniseikonia with the subjective one is clinically very useful. The difference between the objective and subjective aniseikonia could be considered to correspond to a certain degree to the retina/ brain causes for aniseikonia.30 An orthoptic exam should be performed routinely in anisometropic patients32 to evaluate the degree of suppression of the recessive eye. Managing aniseikonia is one of the key issues in preserving the ocular balance. Lenticular anisometropia will be corrected after IOL implantation aiming at emmetropia, but axial anisometropia (from 1 mm on) cannot be corrected after IOL implantation without inducing aniseikonia. In patients presenting preoperative suppression, this

Cataract Surgery aniseikonia can be well tolerated, but not in patients with good binocular vision. Based on our theoretical model of anisometropic correlated aniseikonia, the following rules regarding correction of the various types of anisometropia should be considered: • Pure axial anisometropia should preferentially be corrected by means of spectacles. In case cataract surgery is necessary in axial anisometropia, the aim should be to emmetropize the dominant eye. The power of the IOL of the recessive eye should be the difference between the emmetropizing power for the recessive eye minus the difference between both axial powers (cf. HV, Table 53.4 and therapeutic proposal). • Corneal anisometropia can either be corrected by means of contact lenses, refractive surgery or cataract surgery. • Lenticular anisometropia would best be corrected by cataract surgery in older patients. In younger patients, it may be corrected by means of refractive surgery. • Combined anisometropia must be decomposed into its components (axial, corneal and lenticular) and the balance of the induced aniseikonia should be calculated by function of the planned surgical procedure.

13. 14. 15.

16. 17.

18. 19. 20.

21.

REFERENCES 1. Romano PE. “Editorial: Aniseikonia? Yech!”, Binocular vision and strabismus quarterly, Third quarter 1999;14:173-76. 2. Ciuffreda KJ, Xiaonlong L, Mordi J. “Rapid, short term adaptation to optically induced oblique aniseikonia”. Binocular Vision Quarterly, 1991;6:217-25. 3. Stewart CE, Whittle J. “Optical correction of aniseikonia in anisometropia can enhance stereoacuity”. Binocular vision and strabismus quarterly, First quarter of 1997;12:31-34. 4. Lubkin V, Kramer P, Meininger D, Shippman S et al. “Aniseikonia in relation to strabismus, anisometropia and amblyopia”. Binocular vision and strabismus quarterly, Third quarter 1999;14:203-07. 5. Corbé C, Menu JP, Chaine G, Traité d’optique physiologique et clinique, DOIN Editeurs, Risse JF. “Chapitre 14: Anisométropie, Anisophorie induite, aniséiconie”, 285-301. 6. Troutman RC. “Artiphakia and aniseikonia”, Trans Am Ophthalmol Soc 1962;60:590-658. 7. Troutman RC. “Artiphakia and aniseikonia”. Am J Ophth 1963;S6:602-39. 8. Troutman RC. More evidence of aniseikonia in pseudophakia from another expert, with a “seconding” of a warning to corneal, refractive and implant surgeons. Binocul Vis Strabismus Q 1999;14(4):263. 9. Häring G, Gronemeyer A, Hedderich J, et al. Stereoacuity and aniseikonia after unilateral and bilateral implantation of the Array refractive multifocal intraocular lens. J Cataract Refract Surg 1999;25:1153-56. 10. Kramer P, Lubkin V, Pavlica M et al. Symptomatic aniseikonia in unilateral and bilateral pseudophakia. A projection space eikonometer study. Binocular vision and strabismus quarterly, Third quarter 1999;14:183-90. 11. Huber C, Binkhorst CD. Iseikonic lens implantation in anisometropia. Am Intra-Ocular Implant Soc J 1979;5: 194-202. 12. Adams M. A comparison of conventional and aniseikonic slides used as a synoptophore screening test for binocular

22. 23. 24. 25. 26. 27.

28.

29.

30.

31. 32.

function in unilateral aphakia. Brit Orthopt J 1966;23: 90-95. Romano PE. The importance of correcting aniseikonia to facilitate binocularity in neonatal/Infantile unilateral aphakia. Binocular Vision Quarterly 1990;5:117-18. Romano PE, Von Noorden GK. Knapp’s law and unilateral axial high myopia. Binocular vision and strabismus quarterly, Third quarter 1999;14:215-22. Kramer P, Shippman S, Bennett G, et al. A study of aniseikonia and Knapp’s law using a projection space eikonometer. Binocular vision and strabismus quarterly, Third quarter 1999;14:197-201. Winn B, Ackerley RG, Brown CA, Murray FK, et al. Reduced aniseikonia in axial anisometropia with contact lens correction. Ophthalmic Physiol Opt 1988;8(3):341-4. Awaya S, Von Noorden GK. Aniseikonia measurement by phase difference haploscope in myopic anisometropia and unilateral aphakia (with special reference to Knapp’s law and comparison between correction with spectacle lenses and contact lenses). Binocular vision and strabismus quarterly, Third quarter 1999;14:223-30. Hillman JS, Hawkswell A. A biometric study of aniseikonia. KC Ossoinig (Editor), Ophthalmic Echography, ISBN 1987;0-89838-873-2. Elkington AR, Frank HJ. Clinical Optics. 123, ISBN 0-63-04989-8 Blackwell Science, 1999. Sanders DR, Retzlaff J, Kraff MC. Comparison of the accuracy of the Binkhorst, Colenbrander and SRKTM implant power predication formulas. Am Intra-Ocular Implant Soc J 1981;7:337-40. Sanders DR, Retzlaff J, Kraff MC. Development of the SRK/ T intraocular lens implant power calculation formula. J Cataract Refract Surg 1990;16:333-40. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract refract Surg 1988;14:17-24. Preussner PR, Wahl J, Lahdo H, Dick B, Findl O. Ray tracing for intraocular lens calculation. J Cataract Refract Surg 2002; 28:1412-19. Jenkins F, Harvey WE. Fundamentals of optics (fourth edition), Chapter 5 “Thick lenses”. 78-97, Dover Publication Inc, New York, 1981, ISBN 0-486-68328-1. Czepita D, Goslawski W, Mojsa A. Occurrence of anisometropia among students ranging from 6 to 18 years of age. Klin Oczna. 2005;107(4-6):297-9. [Article in Polish] Lesueur L, Chapotot E, Arne JL, Perron-Buscail A, Deneuville S. Predictability of amblyopia in ametropic children. Apropos of 96 cases. J Fr Ophtalmol. 1998;21(6):415-24. Autrata R, Rehurek J. Clinical results of excimer laser photorefractive keratectomy for high myopic anisometropia in children: four-year follow-up. J Cataract Refract Surg. 2003;29(4):694-702. Paysse EA, Hamill MB, Hussein MA, Koch DD. Photorefractive keratectomy for paediatric anisometropia: safety and impact on refractive error, visual acuity, and stereopsis. Am J Ophthalmol. 2004;138(1):70-78. Phillips CB, Prager TC, McClellan G, Mintz-Hittner HA. Laser in situ keratomileusis for treated anisometropic amblyopia in awake, autofixating pediatric and adolescent patients. J Cataract Refract Surg 2004;30(12):2522-28. Ledoux DM, Trivedi RH, Wilson ME Jr, Payne JF. Pediatric cataract extraction with intraocular lens implantation: visual acuity outcome when measured at age four years and older. J AAPOS 2007;11:218-24. De Wit GC. Retinally-induced aniseikonia. Binocular Vision and Strabismus. 2007;22(2):96-101. Godts D, Tassignon MJ, Gobin L. Binocular vision impairment after refractive surgery. J Cataract Refract Surg 2004;30(1):101-9.

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Mastering the Techniques of Jos Intraocular Lens Power Calculations Laure Gobin, J Rozema, Marie-José Tassignon (Belgium)

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54

Review of IOL Power Calculation: A Theoretical Analysis of Proposed Formulas

INTRODUCTION Since the early 70s many formulas have been proposed for intraocular lens (IOL) power calculation with the aim of emmetropizing an eye after cataract surgery. These formulas estimate the IOL power as a function of the corneal refractive power k, the ocular axial length L and, in some cases, the preoperative anterior chamber depth ACDpreop. Currently the most commonly used formulas are the SRK/T1 and Holladay2 . Considering that currently there are over 1350 IOLs on the market (2002 figures3 ), these formulas may not give the most adequate results for all of them. Because of this very large number of IOL types neither the industry nor the surgeons have made a database of the clinical outcome for each type of IOL and the predictions by each formula up till now. If this were done the formulas giving the best clinical outcome for that particular lens should then be used as final choice. However, creating such a database for all available IOL types is impractical. Moreover since most formulas or algorithms are currently incorporated in the measuring devices, most surgeons do not realize which formula has been used to calculate the IOL power of their patients. In recent years, obtaining spectacle independence after cataract surgery has become the goal which resulted in the advent of a series of implants capable of restoring part of the patients’ natural accommodation. In the light of this trend, this chapter aims to review a number of IOL power calculation formulas for their capability to achieve a full emmetropization of the patient. Starting from the Binkhorst formula, we provide a framework in which all first, second and third order formulas can be redefined.

The first generation of IOL calculation formulas are all adaptations of the Binkhorst one, while the second generation formulas has been established empirically by performing a parameter fit of the axial length L, the corneal curvature k and the emmetropizing IOL power P. However, also most of them are derived from the Binkhorts formula exept for the SRK I4-6 and SRK II7 formulas, which are entirely empirical. In summary, this paper will demonstrate that formulas of the first generation can all be reduced to the Binkhorst formula and that those of the second generation are in fact derived from a Taylor expansion of the Binkhorst formula. For three of these formulas (SRK II, Donzis8 and Thompson9 ) we will demonstrate how each can be considered as a derivation from a first or the second order Taylor development of the Binkhorst formula. Finally a theoretical calculation is made of the differences in values using five different formulas. Based on this study, we consider the SRKII formula as our reference formula because of its simplicity. Next the different third generation formulas are compared in terms of their predicted postoperative ACD. Indeed, since 1988, the only difference between all proposed formulas lies in the extrapolation of ACDpostop: the Binkhorst, SRK/T, Hoffer-Q, Olsen, Holladay and the Haigis formulas, the third generation formulas are discussed in more detail. We also compiled a list of commonly used formulas in order to compare their predictive performances in emmetropizing the patient. The fourth generation IOL power calculations, such as the Holladay II,10 Clarcke neural networks11 and Preussner ray tracing,12 are incorporated in patented software.10-12 As they provide no theoretical insight, these models will not be discussed for evident reasons.

Review of IOL Power Calculation

Fig. 54.1: Scheme of the eye and the equivalent thin lens optical model (two side arrows)

DEFINITIONS BASED ON THE BINKHORST FORMULA Cataract surgery consists of replacing a natural crystalline lens that has become opaque over time by an IOL. In order to determine the IOL power required for emmetropizing the pseudophakic eye, Binkhorst1 proposed a theoretical model based on the axial length L and corneal curvature k. This model relied on the assumption that the postoperative optical system, comprising the cornea and IOL, can be described by a combination of two equivalent thin lenses. The first lens, corresponding to the cornea, is located in the corneal posterior principal plane K and the second lens, equivalent to the IOL, is placed in the IOL posterior principal plane B (Fig. 54.1). The Binkhorst formula can be rewritten as (Appendix I):

(1) with (2) where k is the corneal curvature (in diopter), L the axial length (in mm), ACDpostop the predicted postoperative ACD (in mm) and n the refractive index of the cornea. Parameters k and L can easily be obtained from corneal topography and ultrasound biometry. Other formulas, such as the Holladay formula2 , also include the optical axial length (defined as the distance KB ¯¯ between K and the retina R). The only undetermined parameter is ACDpostop as it depends on the postoperative position of the IOL in the

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eye. However this can be accurately estimated by determining the positions of the posterior principal plane of the cornea K, the vertex of the anterior cornea A, the principal image plane of the entire eye H, the posterior principal plane of the IOL B and the retina R. We would like to point out that there is an important difference in the definitions of the preoperative and postoperative ACD. Preoperatively the ACD is given by the distance from the anterior corneal vertex A to the anterior lens vertex. For ACDpostop however two different, but nearly equivalent, definitions exist, namely ACDpostop = ¯¯(“effective ¯¯(Binkhorst’s definition) and ACDpostop = AB KB 14,3 thin lens position” proposed by Holladay ). However these two conventions are nearly equivalent provided the cornea is considered a thick lens. By filling in the numerical values provided by Gullstrand4 there is a 5 0 µ m distance between the secondary principal plane of the cornea and the corneal vertex, corresponding to a 0.08D difference in IOL power for the Holladay formula. In this work we choose the first definition, as it will enable us to compare predicted versus achieved postoperative ACD.

Similarity of First Generation Formulas Table 54.1 shows a list of 6 first generation formulas, starting with the Binkhorst formula. Bringing these formulas to a common denominator (as is shown in Appendix II), a strong similarity can be noted, indicating that for normal eyes they will propose similar IOL powers. The only exception is the Thijssen formula5 , which is based on Binkhorst but has two additional parameters: the IOL thickness and the refractive index.

Deriving the Second Generation Formulas from Binkhorst The SRK II formula (Table 54.2) may be derived from the theoretical Binkhorst formula (1) by taking its first order Taylor derivation in a point x0 = (k0, L0, ACDpostop,0):

(3)

Numerical estimations of the parameters a, ak and aL can be obtained by using the averaged L, k and C values as studied by Hosny et al6 on 211 eyes (Table 54.3). Note that the equation (3) has quite some similarities with SRK II and the Thompson formula for short eyes (L < 24.5 mm), proposing linearities in keratometry k

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Table 54.1: First generation formulas (derived theoretically from the Binkhorst)

Original form

Remarks

Binkhorst13

n = 4/3. Binkhorst II:

Fyodorov22

the refractive index is considered n = 1.336

Van der Heijde22

the refractive index is considered n = 1.336

Colenbrander22

the refractive index is considered n = 1.336

Shammas1 Thijssen17

t: IOLthickness ni: IOL refractive index

Table 54.2: Empirical second generation formulas

Original form SRK II7

with

Donzis8

Thompson9

Remarks Parameter A = IOL specific constant

Parameter A = IOL specific constant Take L0 = 23.5mm

If L < 24.5 mm: P = 131.94 - 2.78L - 1.10k If L > 24.5 mm: P = 63.162 - 0.854L - 0.00187L2 + 0.261k -0.0143k2

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Table 54.3: Calculation of the parameters a, ak and aL using the Hosny biometrical data

L (mm)

k (D)

ACD (mm)

a

ak

aL

21

43.54

3.14

168.4

-1.27

-4.18

23.5

43.74

3.5

152.4

-1.31

-3.34

Medium long eyes

26

43.21

3.72

133.8

-1.3

-2.6

Long eyes

28

43.72

3.48

123.5

-1.31

-2.22

SRK II

A-constant

-0.9

-2.5

Thompson

131.94

-1.1

-2.78

Short eyes Medium eyes

and axial length L. The Donzis8 formula is a variation of (3), where L is replaced by L0(1-(L0-L)/L) and L0 = 23.5 mm. For longer eyes (L > 24.5 mm), however, the Thompson formula9 can be derived from the second order Taylor expansion of (1). This demonstrates that, despite the obvious differences in mathematical form, the second generation formulas can all be reduced to (an approximation of) the original Binkhorst model.

The Different Formulas for the Estimation of ACDpostop The third generation, corresponding to the Holladay I,2,14,15 the Olsen,1-4 the Hoffer-Q5 , the SRK/T1 and the Haigis6 formulas are described in Table 54.4. These formulas are based on the theoretical Binkhorst formula given in equation (1) with this difference that the ACDpostop is predicted in function of the keratometry k, axial length L, crystalline lens thickness T and ACDpreop. As an illustration of the minor differences between the third generation formulas, we propose our own formula for ACDpostop (Table 54.4). Considering the IOL as a thin lens, this formula assumes that the final postoperative position of the IOL center coincides with the center of the natural lens by setting ACDpostop equal to the sum of the distance C from the anterior cornea vertex A to the anterior crystalline lens vertex and the half of crystalline lens thickness T (see Fig. 54.1). In an effort to compare the ACDpostop values predicted by the third generation formulas, we had plotted the different formulas with respect to various parameters. All numerical applications as shown in Table 54.5, use the average ocular biometries published by Hoffer7 and the constants of the Acritec 44S IOL as optimized8 for each of the third generation formulas. We plotted ACDpostop parameter in function of a variable axial length L and a fixed k value (Fig. 54.2A) and a variable keratometry k with a fixed L (Fig. 54.2B). Here we assumed

Fig. 54.2: Predicted ACDpostop with respect to the axial length L using Hoffer-Q, SRK/T, Olsen, Holladay I and Haigis. (A) ACDpredicted in function of the axial length L; (B) ACDpredicted in function of the keratometry k. The following values were used: ACD preop = 3.14 mm, k = 43.81 D, L = 23.65 mm and T = 4.5 mm

the following values: ACDpreop = 3.14 mm, k = 4 3 . 8 1 D, L = 23.65 mm and T = 4 . 5 m m. It can be seen that there are considerable differences in the ACDpostop predictions given by each model and that three models (Holladay, Hoffer Q and SRT/T) show unnatural bends in their curves. As our own model does not depend on k or L, it was not included in the graphs.

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Table 54.4: Third generation formulas

Original form

Remarks

Lepper and Trier20

ACDmean = mean postoperative ACD for a particular IOL type

Holladay2

SF = 0.9704ACDpreop - 3.595 (‘surgeon factor’)

SRK/T1

If L < 24.2 mm: Lc = L If L > 24.2 mm: Lc = -3.446 + 1.715L - 0.0237L2

Hoffer-Q23

pACD = personalized ACD (Hoffer-Q constant) If ACDpostop > 6.5mm → ACDpostop = 6.5mm If ACDpostop < 2.5mm → ACDpostop = 2.5mm

R = Rx/(1-0.012Rx) with Rx the spectacle correction

Olsen19 (1991)

ACDmean = mean postoperative ACD for a particular IOL type

Olsen21 (1995)

ACDmean = mean postoperative ACD for a particular IOL type T = lens thickness (mean: 4.5 mm)

Olsen (2004)

ACDmean = mean postoperative ACD for a particular IOL type

Haigis24 Our formula

Review of IOL Power Calculation

Fig. 54.4: Predicted IOL power with respect to keratometry k for Hoffer-Q SRK/T, Olsen, Holladay, Haigis and SRK II. The average axial length is 23.65 mm

Fig. 54.3: (A) Predicted IOL power with respect to the axial length L for Hoffer-Q SRK/T, Olsen, Holladay I, Haigis and SRK II for an average corneal power of 43.81 D. (B) Detail of (A). The following constant values were used: C =3.14 mm, k = 43.81D and the lens thickness T = 4.5 mm

Table 54.5: Constants of the Acritec 44S IOL for the different formulas SF (Holladay)

1.43

pACD (Hoffer Q)

5.17

A-constant (SRK II)

118.4

Haigis (a0, a1, a2)

0.93

0.4

0.1

Keeping the same parameters as before, additional graphical comparison can be made of the predicted IOL powers calculated by the various formulas (Hoffer Q, SRK/ T, Olsen, Haigis, SRK II and Holladay) in function of L in intervals ranging from 15 to 35 mm (Fig. 54.3A) and from 22 to 25 m m (Fig. 54.3B) and in function of the keratometry in an interval ranging from 38 to 50 D (Fig. 54.4). Studying Figures 54.2 to 54.4 we found that whereas in Figure 54.2 the predicted ACDpostop can vary significantly between the different models, their predicted IOL powers are very similar and remain within the range of

± 1D. This is especially the case for the formulas derived from the Binkhorst formula (i.e. Hoffer-Q, SRK/T, Olsen, Holladay and Haigis) in the range L = 2 2 - 2 4 . 5 m m (Figs 54.2A and 54.3B). This suggests that the choice of ACD prediction formula does not play a large role in the precision of the predicted IOL power for medium sized eyes. However for short eyes the second generation formulas deviate more from the others due to the use of linear regression P (e.g. SRK II). In Figure 54.5A the IOL powers predicted by the different models (Hoffer-Q, SRK/T, Olsen, Haigis, SRK II) were subtracted from those predicted by the Holladay formula. It can be seen that for any axial length values the average difference between the different models and the Holladay model is lower than ±0.5 D, which may explain the similarity in the reported performances of the formulas1,21,23. It also confirms the limited importance of the predicted ACDpostop. We would like to stress that these results need to be interpreted with caution. While the previous figures consisted of theoretical comparisons by varying k and L, the influence of the parameters ACDpreop as used in Haigis and ACD preop and T as used in Olsen, may be underestimated. For this reason we studied the complete biometry of 28 patients (49 eyes) scheduled for cataract surgery and applied their data in the different formulas. The preoperative tests included an Ophtascan echographic biometry and an EyeSys keratometry, providing us with the corneal curvature and thickness, aqueous humor depth, natural lens thickness T and axial length L. This data was entered in a spreadsheet computing the predicted ACDpostop according to the Holladay, SRK/T, Olsen and our formulas. The Olsen

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Mastering the Techniques of Intraocular Lens Power Calculations Because important information is missing from the different papers we studied models were, such as the correlation coefficients of the different regression models with respect to the raw data or the comparison of the effective with the predicted ACDpostop, it is not possible to come to any further conclusions. As many of the original papers contained numerous typographical errors we listed these in Appendix III with the corrections.

DISCUSSION

Fig. 54.5: (A) Differences between the IOL power calculations given by several formulas (Hoffer-Q, SRK/T, Olsen, Haigis and SRK II) and the Holladay formula. The average corneal power is taken 43.81D (value taken from [25]). (B) Averages of the curves in (A)

model was included as a reference because it differentiates between ACDpreop and ACDpostop. Olsen also introduced a correlation coefficient between the predicted and the achieved ACDpostop (Fig. 54.5B). The results are shown in Figure 54.6A, where the predicted ACDpostop according to SRK/T is compared to that of the Holladay model. The result shows a reasonable correlation (R² = 0.82) between these models. The fact that these formulas provide similar refractive outcomes confirms that the anterior chamber prediction model is not crucial.1,21,23 Figures 54.6B to D give the predicted ACDpostop values according to respectively the Holladay, the SRK/T and our own model when compared to the Olsen model. The correlation coefficients between the first two models with the Olsen formula are rather low (respectively 0.39 and 0.42), while our own model shows a quite strong correlation (R ² = 0 . 7 1). The leveling off in Figures 54.6A and B can be explained by the fact that in the Holladay formula, the ACDpostop is set equal to 6.8 mm for axial lengths longer than 2 5 m m.

Surgeons these days would like to use the formula that can calculate the IOL power close to emmetropia, regardless of the patient’s preoperative biometry. By using measured biometric data and making direct numerical comparisons between the predicted and achieved ACDpostop, a ranking of the formulas can beproposed. It is imperative however that one keeps in mind that, no matter how elaborate the eye model used is, the implanted lens will not necessarily stay exactly on the same place the surgeon implanted it. This assumption is based on the knowledge that the remaining lens epithelium cells (LECs) will in many cases proliferate over the posterior capsule or transform into fibroblasts or myofibroblasts and contract the capsule. This may lead to postoperative complications such as posterior capsule opacification (PCO) and contractions of the capsular bag. As these are relatively rapid and violent processes, causing IOL shifts or tilts in the first postoperative months, this can cause refraction changes, increased higher order wavefront aberrations and increased stray light. Given the fact that third generation formulas distinguish themselves only by the way they calculate ACDpostop, we would like to emphasize the importance of correct definitions for the preoperative, predicted postoperative and achieved postoperative ACD. As an illustration, we refer to a recent article by Kriechbaum et al1 in which ACDpostop values were measured for several lens types using Partial Coherence Interferometry (PCI) with the purpose of comparing the predicted and achieved ACDpostop. The authors chose to average the ACDpostop over a number of patients for each IOL in order to determine the IOL constants and found a 1 m m difference between the mean ACDpostop values given by the manufacturers and the measured one. This difference can be explained by the fact that PCI calculates the ACDpostop from the corneal apex till the IOL apex (in

Review of IOL Power Calculation

Fig. 54.6: Calculation of the theoretical postoperative ACD using the biometrical values of 49 patients. (A) Comparison of the results of the SRK/T formula and the Holladay formula; (B) Comparison of the results of the Holladay formula and the Olsen formula; (C) Comparison of the results of the SRK/T formula and the Olsen formula; (D) Comparison of the results of our formula and the Olsen formula

Figure 54.1), while the ACD postop used in formulas provided by manufacturers are determined from the posterior principle plane of the cornea to the IOL. By adding the distance between IOL apex and the IOL posterior principal plane to the values given by Kriechbaum they should correspond with those given by the manufacturers, where the position of this IOL principal plane can derived from the average IOL power and the IOL refractive index. By introducing our formula we wanted to show that compared to the IOL power the predicted ACDpostop value is relatively unimportant. The third generation formulas prdicting the anterior chamber depth, require the following parameters: the axial length, corneal power, preoperative anterior chamber depth, white to white distance. Haigis22 published the correlation coefficient of the achieved ACDpostop with a number of preoperative biometric parameters (axial length L, keratometry k) which can be measured by IOL Master instead of by 4 different

devices as it is the case with the Olsen formula. The advantage of the Olsen formula, however, is that only one constant must be optimized whereas in Haigis formula, 3 constants need optimization. We prefer the use of the Olsen formula although the Haigis formula is very acceptable as well. A comparison of the accuracy of the main third generation formulas is proposed in the Hill’s website2 , where the mean absolute prediction errors of Haigis, Hoffer Q, Holladay, Holladay II, and SRK/T are reported with respect to the axial length. All formulas are equivalent for average eyes (22-28 mm). Surgeon must be careful: for (L < 2 2 m m and L > 2 6 m m), SRK/T is not accurate. The Holladay I formula is the best of the first published third generation formulas. The inconvenient of all the third generation formulas is that they must be optimized by the surgeon which exercize most of the surgeons don’t do. A German website3 collected the results obtained from different

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APPENDIX I: DERIVATION OF THE BINKHORST FORMULA The Binkhorst approach consists in assuming that the eye is an optical system made of a doublet of thin lenses: the cornea and the IOL. The cardinal points of the equivalent thick lens made with the doublet of thin lenses are then easy to calculate using classical geometrical optics. The principal planes of the biconvex IOL coincide with the geometrical centre of the lens and as such, the IOL is taken as a thin lens31. The cardinal points of the cornea are easy to define since its curvature is known. For the calculation of the IOL power achieving emmetropia, several positions on the optical axis have to be defined and presented in Figure 54.1: • K: cornea equivalent thin lens position (posterior principal plane of the cornea) • A: anterior cornea • B: secondary principal plane of the lens / IOL • H: principal image plane of the whole system (cornea and lens) • R: retinal plane as well as several distances: • L: axial length of the eye, distance AR ¯¯ • h: distance KH ¯¯ between the posterior principal plane of the cornea and posterior principal plane of the entire eye. ¯¯ between the secondary principal plane of the cornea and the secondary principal plane of the lens / IOL. • ACDpostop: distance KB The corneal power k is determined from corneal topography. For the vitreous and aqueous humors, the refractive index is chosen. Using these definitions, the power of an emmetropic eye is given by: (I-1) where theoretically31 the distance h is given by:

(I-2)

Solving this equation gives: (I-3) The value of h decreases with increasing axial length L, which means that the principal plane of the whole eye (that is cornea and lens) comes closer to the anatomical anterior cornea. The emmetropic eye power can also be expressed using the thick lens formula16: (I-4) Combining equations (I-1) and (I-4), we obtain:

Replacing h by the equation (I-3), we obtain:

(I-5)

(I-6) The formula has given by Binkhorst in 197513 was: (I-7) with

the corneal radius of curvature. Formula (I-7) can be converted into (I-6) using the approximation n ˜ ncornea: (I-8)

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APPENDIX II: EQUIVALENCE OF THE FIRST GENERATION FORMULAS In this appendix demonstrate that all first generation IOL calculating formulas are variations of the Binkhorst formula and that the differences are negligible. Binkhorst13, Fyodorov22 and Van der Heijde22 This is in fact three times exactly the same formula. However in the literature they are often used next to each other. Starting from formula (I-6) we can find a common form to which all of these formulae can be reduced:

(II-1) Using replacing the value 1.336 by the more general symbol for refractive index n, we can also see that (I-6) and the Fyodorov formula are identical. The Van der Heijde formula can be written as follows:

which is equal to (II-1) after bringing the two terms to a common denominator. Colenbrander22 This formula can be written in the form:

which equals (II-1) apart from a 0.05 mm term. This gives a difference of about 1.5% in the ACDpostop value for ACDpostop = 3.25 mm. Shammas30 This reduces to:

which gives a 0.015% difference for L = 23.45 mm and a 1.25% difference for n. Thijssen17 Here we can write:

with t the implant thickness and ni the implant refractive index. Since the refractive indices n = 1.336 and ni = 1.5 (about 10% difference) this new term may have a relevant influence on the result. The Thijssen formula can therefore be considered as different from the original Binkhorst.

surgeons. They proposed a table where they clearly indicated whether the given constant is reliable or not. Finally we would like to highlight the fact that the empirical formulas of the different authors were established in different regions of the planet, which to our knowledge has never been taken into account. In such

articles the average biometry parameters should be added in order to verify the comparability of the eye populations upon which the models are based.

CONCLUSION In this chapter we reviewed the IOL power calculation formulas using preoperative biometry and proposed a

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APPENDIX III: LIST OF PRINTING ERRORS FOUND IN ORIGINAL ARTICLES Several remarks are applicable to many articles reviewed by the authors. The formulas are often printed in an illegible and incomprehensible way, which is probably the cause of many of the errors given below. The absence of uniform definitions and symbols between the authors also increases the chance of mix-ups and misinterpretations. Holladay2 (1988)

• The estimation of ACDpostop in this article presents a 0.56 offset that does not exist in other articles. • In the formulas given in the appendix the refractive index of the cornea is taken 4/3 = 1.333 while that of the aqueous is given 1.336. The corneal refractive index should be 1.37.

Retzlaff1 (1990)

• On p.335 (1st column): LCOR = 3.446 + 1.715L - 0.237L²; On p.339 formula (2): LCOR = 3.446 + 1.716L - 0.0237L². Actually, the correct formula is: LCOR= -3.446 + 1.715L - 0.0237L² This sign error, also found in Barrett1 (1993) (second column, p.715), was correctly reported in Olsen20 (1992). • In the appendix the reverse SRK II formula is used instead of the reverse SRK/T for the determination of the individual constant: this is inconsistent. The axial length limit used in the SRK/T formula is 24.2 mm on p.335, but 24.4 mm in the appendix (p.339).

Olsen20 (1992)

• On p.282 the axial length limit for SRK/T is reported to be 24.2 mm instead of 24.4 mm. • The Holladay2 formula is not correctly reported with the corneal width maximum value being 13 mm instead of 13.5 mm (page 282, end of first column).

Hoffer23 (1993)

• In formula (4) (p.702) the expression “(tan(0.1(G-A)2))” in the results section cannot be interpreted for several reasons: o tan(k) has no physical meaning (the tangent function can only be applied on nondimensional numbers, while k has the unit of diopter) o tan(k) is discontinuous: it has a period of p and has no finite solution exists at 13p, 14p and 15p, i.e. for k = 40.8, 44.0, 47.1 D. o The tangent argument should actually be reported in angular degrees and not radians. • Inconsistent definition for the axial length: sometimes it is called A and sometimes AL. • Inconsistent definition for the anterior chamber depth in the appendix (p.712): sometimes it is called C and sometimes ACD. • Other errors exist, but have been reported in a later erratum2 .

Olsen21 (1995)

• On one occasion the units are not consistent with the ultrasound speed (p.314): 1550 ms is given instead of 1550 m/s.

Holladay14 (1998)

• The secondary principal plane of the cornea (Figure 3 and p.342) is represented at 50 µm behind the cornea instead of in front, as can be found on p.82 and p.84 of Fundamentals of Optics31. ALo should be equal to Alu+0.3 mm. Holladay underestimated by this the optical axial length of 2x50µm = 0.1 mm which induces an error of 0 . 2 D.

Shammas22 (2004)

• The description of the Holladay equation is incomplete and is therefore unusable. • Incorrect power in the first equation on p.17: aACD = 0.56 + R[R2 - (AG2)(1/4)]-2 should be: aACD = 0.56 + R-[R2 - (AG2)(1/4)]0.5

new formula for the prediction of ACDpostop. Theoretical and practical graphs have been calculated to emphasize the differences between the formulas. The prediction of ACDpostop has little weight in the calculations, which explains why poorly correlated ACD formulas still give nearly the same IOL power values. Many significant inaccuracies in the literature have been tabulated and corrected. The first order derivation of the theoretical formula enables to link empirical and theoretical approaches and

to make them comparable. Special emphasis has been put on the definition of the ACD in order to avoid later confusions.

REFERENCES 1. Sanders DR, Retzlaff J, Kraff MC, “Development of the SRK/ T intraocular lens implant power calculation formula”, J Cataract Refract Surg 1990;16:333-40. 2. Holladay JT, Prager TC, Chandler TY, et al. “A three-part system for refining intraocular lens power calculations”. J Cataract refract Surg 1988;14:17-24.

Review of IOL Power Calculation 3. Holladay JT. “International intraocular lens and implant registry 2002”. J Cataract Refract Surg 2002;28:152-74. 4. Retzlaff J. “A new intraocular lens calculation formula”, Am Intra-Ocular Implant Soc J 1980;6:148-52. 5. Sanders DR, Kraff MC. “Improvement of intraocular lens power calculation using empirical data”. Am Intra-Ocular Implant Soc J 1980;6:263-67, Erratum 1981;7:82. 6. Sanders DR, Retzlaff J, Kraff MC. “Comparison of the accuracy of the Binkhorst, Colenbrander and SRKTM implant power predication formulas”. Am Intra-Ocular Implant Soc J 1981;7:337-40. 7. Sanders DR, Retzlaff J, Kraff MC. “Comparison of the SRK IITM and other second generation formulas”. J Cataract Refract Surg 1988;14:136-41. 8. Donzis PB, Kalst PR, Gordon RA. “An intraocular lens formula for short, normal and long eyes”. CLAO J 1985; 11:95-98. 9. Thompson JT, Maumenee AE, Baker CC. “A new posterior chamber intraocular lens formula for axial myopes”. Ophthalmology 1984;91:484-88. 10. Zalvidar R, Shultz MC, Davidorf JM, Holladay J. “Intraocular lens power calculations in patients with extreme myopia”. J Cataract Refract Surg 2000;26:668-74. 11. Clarke GP, Burmeister J. “Comparison of intraocular lens computation using a neural network versus the Holladay formula”. J Cataract Refract Surg 1997;23:1585-89. 12. Preussner PR, Wahl J, Lahdo H, Dick B, Findl O. “Ray tracing for intraocular lens calculation”. J Cataract Refract Surg 2002; 28:1412-19. 13. Binkhorst RD. “The optical design of intraocular lens implants”. Ophtalmic Surg 1975;6:17-31. 14. Holladay JT, Maverick KJ. “Relationship of the actual thick intraocular lens optic to the thin lens equivalent”. Am J Ophthalmol 1998;126:339-47. 15. Holladay JT. “Standardizing constant for ultrasonic biometry, keratometry, and intraocular lens power calculation”. J Cataract Refract Surg 1997;23:1356-70. 16. Elkington AR, Frank HJ, Greaney MJ. Clinical optics, Blackwell Scien 1999, ISBN 0-632-04989-8. 17. Thijssen JM, Boerrigter RMM. “Ultrasonic biometry for the lens implantation : analysis of systematic error”, Ophtalmic Echography ISBN 0-89838-873-2, KC Ossoinig editor 1987;35-41.

18. Hosny M, Aliò JL, Claramonte P et al. “Relationship between anterior chamber depth, refractive state, corneal diameter, and axial length”. J Cataract Refract Surg 2000;16:336-40. 19. OlsenT, Thim K, Corydon L. “Accuracy of the newer generation intraocular lens power calculation formulas in long and short eyes”. J Cataract Refract Surg 1991;17:18793. 20. Olsen T, Olesen H, Thim K, Corydon L. “Prediction of the pseudophakic anterior chamber depth with the newer calculation formulas”. J Cataract Refract Surg 1992;18:28085. 21. Olsen Th, Corydon L, Gimbel H. “Intraocular lens power calculation with an improved anterior chamber depth prediction algorithm”. J Cataract refract Surg 1995;21:31319. 22. Shammas HJ. Intraocular lens power calculations, Sclack Incorporated 2004, ISBN 1-55645-652-6. 23. Hoffer KJ. “The Hoffer Q formula : a comparison of theoretic and regression formulas”. J Cataract refract Surg 1993;19:700-712. 24. Haigis W, Lege B, Miller N, Schneider B. “Comparison of immersion ultrasound biometry and partial coherence interferometry for the IOL calculation to Haigis”,Graefes Arch Clin Exp Ophthalmol 2000;238:765-73. 25. Hoffer KJ. “Biometry of 7500 cataractous eyes”. Am J Ophthalmol 1980;90:360-68. 26. http://www.augenklinik.uni-wuerzburg.de/eulib/ const.htm. 27. Kriechbaum K, Findl O, Preussner PR, Koppl C, Wahl J, Drexler W. “Determining postoperative anterior chamber depth”. J Cataract Refract Surg 2003;29:2122-26. 28. Hill WE. “Choosing the right formula”, http://www.doctorhill.com/formulas.htm, Last accessed 2004-10-11. 29. http://www.augenklinik.uni-wuerzburg.de/ulib/c1.htm. 30. Shammas HJF. “The fudged formula for intraocular lens power calculations”. Am Intra-Ocular Implant Soc J 1982;8:350-52. 31. Jenkins F, Harvey WE. Fundamentals of optics (fourth edition), Chapter 5 “Thick lenses”, 78-97, Dover Publication Inc, New York, 1981, ISBN 0-486-68328-1. 32. Barrett GD. “Improved universal theoretical formula intraocular lens power prediction”, J Cataract Refract Surg 1993;19:713-20. 33. Erratum Hoffer Q. J Cararact Refract Surg 1994;20:677.

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IOL Power Calculation for Cornea Triple and Penetrating Keratoplasty with IOL Exchange

INTRODUCTION Introduction of micro-surgical techniques, improved quality viscoelastic substances, newer suturing techniques and availability of quality donor corneas have significantly improved the anatomical success following penetrating keratoplasty. In addition the newer methods of control of allograft reaction, post penetrating keratoplasty astigmatism and management of post penetrating keratoplasty glaucoma have improved the functional outcome of corneal grafts. Due to the recent advancements, cornea triple i.e. combined penetrating keratoplasty, cataract extraction and posterior chamber intraocular lens implantation is the choice procedure for patients having corneal opacity and cataract. In pseudophakic patients with unstable ACIOLs, iris supported IOLs and dislocated PCIOLs, IOL exchange may be required. Patients with aphakic corneal edema may need secondary IOL implantation. In all these indications of penetrating keratoplasty accurate biometry is a pre-requisite to select IOL of appropriate power (Table 55.1). Intraocular lens implant power calculation prior to penetrating keratoplasty is challenging due to unpredictable post keratoplasty keratometry. Complete ophthalmic examination including slit lamp biomicroscopy should be performed and type of surgical procedure should be carefully planned. Anterior segment examination with widely dilated pupil makes the examination of post capsule easier and assists the surgeon to determine, whether secondary PCIOL implantation is possible. In case, it is not possible to as certain adequacy of posterior capsule preoperatively it is better to plan for scleral fixated PCIOL implantation. If during surgery surgeon finds that the posterior capsular support is

Table 55.1: Indications for biometry prior to corneal transplant surgery 1. 2. 3. 4.

Single Step, Corneal triple (PKP + ECCE+ PCIOL) Single step, PKP + IOL exchange Single step, PKP + Trans scleral fixation of PCIOL Single step, Cornea Triple (DSAEK + Phacoemulsification + PCIOL) 5. Multi step, PKP + cataract extraction followed by IOL implantation 6. Multi step, PKP + IOL explantation following by IOL Implantation 7. Multi step, DALK / LK followed by Phaco / ECCE + PCIOL implantation

adequate, PCIOL implantation should be performed. One should perform anterior segment ultrasound biomicroscopy in those cases in which anterior segment details are not visible on slit lamp biomicroscopy. Patients with grossly deformed anterior segment, those with more than 180° peripheral anterior synechia and with gross fibrous ingrowth are better left aphakic and may be visually rehabilitated using contact lenses. Patients should also undergo B scan ultrasonography to rule out any localized posterior segment problem. Presence of post staphyloma will alter the prognosis as well as power of the intraocular lens implant. Accurate refraction of the other eye should be performed and the refraction in the eye to be operated should be aimed to provide binocular single vision to the patient. The most difficult part in biometry in patients undergoing combined penetrating keratoplasty with cataract extraction is to obtain accurate keratometry value (Table 55.2). Even if we get keratometry values preoperatively these may be abnormal. In such cases standard

IOL Power Calculation for Cornea Triple and Penetrating Keratoplasty with IOL Exchange Table 55.2: Various methods for obtaining accurate keratometry 1. 2. 3. 4. 5.

Preoperative keratometry (41-47D) Standard constant keratometry (42.5D) Surgeon’s Average Post PKP keratometry Keratometry of the other eye Corneal topographic index

constant keratometry may be used.1-3 In a study the accuracy of the use of standard constant keratometry values in eyes undergoing cornea triple procedure has been evaluated.4 A standard constant keratometry value (42.5 D) was applied in biometry of the eyes undergoing triple procedure with preoperative keratometry abnormal values (either < 41 D or > 47 D) The spherical equivalent of postoperative refraction and expected values were compared after mean follow-up of 25 months. Patients achieved spherical equivalent within +/– 2 D of expected value in 9 to 18 eyes (50%) in which a standard keratometry value of 42.5 D was used, 3 of 17 eyes (18%) in keratometry values out of normal range were applied (p = 0.004) and eight of 18 eyes (45%) in which preoperative keratometry values within normal range were applied (p=0.862). Authors have advocated the use of standard constant keratometry value of 42.50 D for intraocular lens power calculation in triple procedure in case preoperative keratometry is abnormal.4 In most of the patients keratometry reading is not at al possible due to corneal surface irregularity. These cases may also the standard constant keratometry value (42.5D) can be used to determine the power of the intraocular lens implant. Several surgeons have advocated the use of keratometry value obtained in the other eye to calculate IOL power. In several studies the average keratometry of the patients operated by the surgeon himself has been used to calculate IOL power. Some authors have found that the use of surgeon’s average post keratoplasty keratometry gives accurate biometry. In this study surgeon’s average postkeratoplasty values were used in 21 consecutive eyes. Eighty two percent eyes were with +/-2D and 100% within +/– 3D of targeted refractive error.5 We have calculated the mean as 43D and routinely use 43D keratometry for IOL power calculation for cornea triple in our patients. In case there is significant difference between surgeon’s average postoperative keratometry value and the keratometry value in fellow eye, the keratometry value 2D greater that the value in the fellow eye should be used. This is to compensate for the induced steepness due to oversized grafts.6

In our experience the same protocol work for patients who are to undergo penetrating keratoplasty with transsclerally fixated PCIOLs. In one of the studies the refractive results of combined penetrating keratoplasty/ transsclerally sutured posterior chamber lens implantation and cornea triple procedures were compared.7 The biometry was found equally reliable in both the procedures. The mean postoperative deviation from predicted refractive error was 1.79 D for the triple group and 1.81 D for PKP/ TS-SPCL group (p =0.95). Sixty three percent of cornea triple and 67% of PKP/TS-SPCL patients were within +/ – 2D of predicted refractive error.7 In patients who are to undergo IOL replacement during penetrating keratoplasty may be benefited by the power of the original intraocular lens. In case the patient has dislocated posterior chamber IOL the same power PCIOL lens may be used. In case we have to perform scleral fixation PCIOL implantation and penetrating keratoplasty single stage procedure we use the IOL of power equivalent to the posterior chamber IOL. Patients who have ACIOL and need replacement of IOL, surgeon should take ACIOL power of the original lens and subtract 1.5 diopters. This is because oversized graft (0.25 mm) will lead to the steeping ranging from 1 to 2 diopters postoperatively. In case the IOL in the eye to be operated is iris supported then one should subtract 2.5 diopters from the power of the lens in the eye.8

MULTI STEP PROCEDURE A multistep procedure has been advocated by several authors. The multistep procedure involves IOL removal and PK prior to the definite IOL replacement.9-11 The advantage of multistep approach are that the post operative keratometry and astigmatism can be accurately assessed and may be included in SRK calculations. This will improve unaided visual acuity and accuracy of post operative refraction by reducing astigmatism and anisosmetropia. In one of the studies the refractive outcome following cornea triple versus non-simultaneous procedures have been compared compared. The study comprised of 82 eyes; 53 eyes underwent triple procedure and 29 eyes underwent non-simultaneous procedures.4 Statistically significantly higher number of eyes in nonsimultaneous procedures group had postoperative refractive error within 2 D diopters of predicted refraction.4 The authors have advocated that if possible non-simultaneous procedure should be preferred.4 Most of the surgeons prefer single step surgery as multiple step procedure increases the risk of cystoid macular edema. Some surgeons feel very comfortable in placing PCIOL when using the open sky technique (Table 55.3).

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Mastering the Techniques of Intraocular Lens Power Calculations Table 55.3: Comparison of single step vs multi step procedure Biometry accuracy +++ ++++ +++ ++++ Refractive outcome Unaided VA ++ +++ Procedure Single Multiple Time for visual rehabilitation Less More Expenses Less More CME -ve +ve Endothelial cell lose Less More Most surgeons prefer single stage surgery.

In the recent studies posterior lamellar procedure, endothelial keratoplasty has been recommended for patients suffering from Fuch’s dystrophy or corneal edema. Surgical procedures including posterior lamellar keratoplasty and more recently Descement’s Stripping Automated Endothelial Keratoplasty (DSAEK) has been found safe and effective. For patients requiring cataract surgery and endothelial keratoplasty, a triple procedure combined DSAEK with phacoemulsification and IOL implantation is preferred over multi stage approach. In these cases same principles of biometry may be applied. In case the accurate preoperative keratometry reading is possible it should be used in biometry, as the curvature of the recipient cornea remains unaltered in DSAEK in contrast to penetrating keratoplasty. In case it is not possible to obtain reliable preoperative keratometry, keratometry value from the other eye or standard constant keratometry (42.50D) may be used to calculate IOL power. The above methods of biometry are applicable to the standard corneal transplant procedure i.e. recipient trephination 7.5 mm / 8.0 mm over sized graft with host donor disparity 0.25 mm, suturing technique (interrupted, continuous or combination) as perform by the surgeon. In case over sizing is increased, induced corneal steepening should be taken into the account. In case same size graft is used then induce corneal flattening should be taken into account and appropriate adjustment with lens should be done. In most of studies repeated in the literature SRK II formula has been used to calculate power IOL power before cornea triple. In a study role of choice of IOL power formula and effect of personalized constants within IOL power formula in improving refractive prediction after combined penetrating keratoplasty, cataract extraction and IOL

implantation were evaluated.12 The records of the patients undergoing cornea triple procedure were evaluated using SRK II, SRK/T, Holladay and Hoffer formulas to predict the post operative spherical equivalent refractions for implanted lens power. Calculations were carried out with and without personalized constants.12 The predictive power of the each formula was assessed by comparing the actual postoperative spherical equivalent of refractive error with that predicted by the formulas. The findings suggested that the choice of IOL power formula does not affect IOL power predictions in corneal triple procedure, however, personalized constants within a formula has been found a critical factor in improving postoperative refractive predictions.12

REFERENCES 1. Waring GO III. Management of pseudophakic corneal edema with reconstruction of the anterior ocular segment, Arch Ophthalmol 1987;105:709-15. 2. Holland EJ, Daya SM, Evangelista A, et al. Penetrating keratoplalsty and transscleral fixation of posterior chamber lens, Am J Ophthalmol 1992;114:182-87. 3. Davis RM, Best D, Gilbert GE. Comparison of intraocular lens fixation techniques performed during penetrating keratoplasty Am J Ophthalmol 1991;111:743-49. 4. Gruenauer-Kloevekorn C, Kloevekom-Norgall K, Habermann A. Refractive error after triple and non-simultaneous procedures: It the application of standard constant keratometry value in IOL power calculation advisable? Acta Ophthalmologica Scand 2006;87:679-83. 5. Mattax JB MC Culley JP. The effect of standardized keratoplasty technique on IOL power calculation for triple procedure. Acta Opthalmol Suppl 1989;192:24-9. 6. Probst E, Holland EJ. Penetrating keratoplasty and IOL exchange. In Brightbill PS (Ed). Cornea Surgery of the cornea and conjunctiva Mosby 1997;1602-26. 7. Djalilan AR, George JE, Doughman DJ Holland EJ. Comparison between the refractive results of combined penetrating keratoplasty/transclerally sutured posterior chamber lens implantation and the triple procedure. Cornea 1997;16:319-21. 8. Lass JH. Lens replacement in pseudophakic bullous keratopathy. Anterior chamber intraocular lenses. In Brightbill FS (Ed): Corneal surgery. Theory, technique and tissue, ed 2. St Louis: Mosby 1994;163-67. 9. Hoffer KJ. Triple procedure for intraocular lens exchange, Arch Ophthalmol 1987;105:609. 10. Binder PS. Intraocular lens implantation during or after corneal transplantation. Am J Ophthalmol 1985;99:515-20. 11. Binder PS. Intraocular lens implantation after penetrating keratoplasty. Refract Corneal Surg 1989;5:224-30. 12. Flowers CE, Mc Loed SD, Mc Donell PJ, Irvine JA, Smith RE. Evaluation of lens power calculation formulas in the triple procedure. J Cataract Refract Surg 1996;22:116-22.

Barun K Nayak, Sunil Moreker (India)

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IOL Power Calculations in Eyes with Irregular Corneas

INTRODUCTION Intraocular lens power calculation has always been a challenge in abnormal eyes. Many surgeons used various methods in vain with postoperative surprises always proving that each method had its fallacy. The attention worldwide has been focussed on this problem in a bigger way after the advent of refractive surgery. The various challenging conditions other than IOL calculation in eyes postrefractive surgery are: 1. Post-traumatic corneal scars 2. Pterygia (operated as well as non-operated) 3. Postkeratoplasty 4. Peripheral degenerative corneal conditions –Mooren’s and Terrien’s 5. Irregular astigmatism.

CORNEAL POWER CALCULATION Corneal power estimation is the main challenge. All keratometers and topography machines measure the steeper peripheral curvature missing the flatter central curvature leading to over-calculation of corneal power and underestimation of IOL power and a hypermetropic correction or measuring the flatter peripheral curvature missing the steeper central curvature leading to undercalculation of corneal power and overestimation of IOL power and a myopic correction.

KERATOMETRY PROBLEMS Manual Keratometry This takes into consideration four points on a cornea approximately 3 mm apart from each other. The flatter the corneal curvature, the longer the radius, the larger the

image mire and the lower the power. The steeper the corneal curvature, the shorter the radius, the smaller the image mire and the higher the power. Myopic eyes may have steeper corneal curvatures, while hypermetropic eyes may have flatter corneal curvatures. The curvatures may vary from point to point in an irregular cornea. A manual keratometer assumes that a cornea has a prolate shape (steeper centrally) and extrapolates information based on a normal curvature relationship. One problem with manual keratometry is that many patients who have corneal irregularity have a resulting oblate corneal shape (flatter centrally) or a prolate shape depending on the site of opacity. Thus, manual keratometry tends to overestimate central keratometry if oblate or underestimate if more prolate. It extrapolates approximately the central 4.5 mm of surface power in the flatter corneas. While this information is consistent, it’s consistently wrong. The average postoperative outcome if clinicians use such keratometric readings to determine IOL power can be approximately + 3.00D to + 5.00D of relative undercorrection in oblate corneas and the other way in steeper corneas.

Automated Keratometry Automated keratometers are usually more accurate than manual keratometers in corneas with small clear optical zone because automated keratometers sample a smaller central area of the cornea (nominally 2.6 mm). In addition, the automated instruments often have additional eccentric fixation targets that provide more information about the paracentral cornea. Portable automated keratometry is a simple keratometric technique that appeared to be as accurate as

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but with less variability than manual keratometry in determining corneal power for cataract surgery.1

Alternatives A brief review of various methods used for the same still shows the lacunae.

Refractive History Method The clinical history method as proposed by Holladay et al and refined by Hoffer et al in to a formula is the most simple method wherein the estimated corneal power is the sum of preoperative average K reading and preoperative spherical equivalent refractive error from the sum of which is deducted the postoperative spherical equivalent refractive error keeping in mind the fact that all figures are algebraically added.Vertex correction was advocated but later proved to lead to a hypermetropic correction by Odenthal et al.2

Assumption This assumes that the refractive change results from the change in pre- and postinjury or keratoplasty keratometry. Thus one can determine the effective keratometry for IOL calculations based on the amount of refractive change.

Limitations 1. If one cannot obtain or if one receives unreliable preoperative data. 2. The developing cataract can influence the postkeratoplasty surgery refraction.

Contact Lens Over-refraction Method The contact lens method was more refined. First proposed by Ridley et al. Principle: The method uses a known curve to determine an unknown curve. A contact lens of a known base curve and power is placed on a patient’s postoperative eye and an overrefraction performed. One can then calculate the true power that the cornea had before refractive surgery. The patient’s refraction without the contact lens is compared to the contact lens over-refraction. Then the amount of difference between the manifest refraction without the contact lens and the contact lens overrefraction (plano lens) is algebraically added to the known base curve of the contact lens.

For example: Manifest refraction without CL = 5.00 + 2.00 × 170 4.00 (Spherical equivalent) Contact lens over-refraction = 8.00 8.00 (Spherical equivalent) Contact Lens Base Curve = 38.00 diopters Difference: 4.00 to 8.00 = 4.00 38.00 + (– 4.00) = 34.00 Using this method, the average central keratometry of the postkeratoplasty cornea is 34 diopters in curvature. It’s important to note the direction of the change in the refraction compared to the over-refraction when making this calculation. For example: Manifest refraction without CL = 5.00 +2.00 × 170 4.00 (Spherical equivalent) Contact lens over-refraction = +1.00 +1.00 (Spherical equivalent) Contact Lens Base Curve = 38.00 diopters Difference: 4.00 to +1.00 = +5.00 38.00 + (+ 5.00) = 43.00 Using this method, the average central keratometry of the postkeratoplasty cornea is 43 diopters in curvature. Therefore, it is easy to use 43.00 as the average keratometry measurement along with the axial length measurement in calculating the IOL power. It is worthy to note that researchers have determined that vertex distance calculations are not necessary when using the contact lens over-refraction method. When using this method, it is suggested that one uses large (10.8 mm) diameter lenses in plano power manufactured from PMMA plastic. Contact lens over-refraction may be a viable alternative to refractive history and videokeratography for estimating true corneal power in patients with surgically altered or irregular corneas.3

Refraction-derived Keratometric Values The refractive error of IOL power calculation in postoperative eyes significantly reduces when refractionderived keratometric values are used for IOL power calculation though persistent residual hyperopia still occurs in some cases. Refractive results appear more accurate and predictable when the Holladay II or Binkhorst II formulas are used for IOL power calculation. Hyperopic error after cataract surgery in post-LASIK eyes was significantly reduced by using refraction-derived keratometric values for IOL power calculation. The same may be used for postkeratoplasty eyes. Persistent hyperopic error can be corrected by hyperopic LASIK.4

IOL Power Calculations in Eyes with Irregular Corneas Double K Method5 The SRK/T formula was modified by Aramberri et al to use the prerefractive surgery K-value (Kpre) for the effective lens position calculation and the postrefractive surgery K-value (Kpost) for IOL power calculation by the vergence formula. The Kpre value was obtained by keratometry or topography and the Kpost, by the clinical history method. Double-K modification of the SRK/T formula improved the accuracy of IOL power calculation after LASIK and PRK. In our practice the same if used with caution also works in post-keratoplasty eyes and eyes with irregularcorneas.

Corneal Topography The standard keratometer is useless in cases in which the mires appear irregular or incomplete. In such cases, computer-assisted corneal topography can be used successfully. Recently, a new corneal topography index has been developed, the average corneal power, which is a measure of the average corneal power within the entrance pupil. One paper currently evaluated the use of average corneal power to assist in the calculation of IOL powers. (J Refract Surg 1996;12:S309-S311). Current corneal topography units measure more than 5000 points over the entire cornea and more than 1000 points within the central 3 mm. This additional information provides greater accuracy in determining the power of corneas with irregular astigmatism compared to keratometers.

Advantage The computer in topography units allows the measurement to account for the Stiles-Crawford effect, actual pupil size, etc. These algorithms allow an accurate determination of the anterior surface of the cornea.

Disadvantage The algorithms provide no information, however, about the posterior surface of the cornea. To accurately determine the total power of the cornea, the power of both surfaces must be known. This has been already pointed out in relation to postkeratoplasty cataract surgery and IOL power calculation.6

Solution?

Consideration of the Orbscan measurement of posterior corneal surface toricity may improve the prediction of the magnitude of refractive astigmatism.8

Evidence of Use of Systems Various systems have been used. They include. 1. EyeSys Laboratories’ Corneal Analysis System 2. Topographic Modeling System (TMS-1) from Computed Anatomy, Inc are two systems recently in vogue. Both were recently used to evaluate eyes with abnormal corneas including keratoconus, corneal scars, and residual postoperative astigmatism following refractive surgery to compare the ease of operation, the accuracy of corneal readings, and the usefulness of generated data.9 Three millimeter zone (Corneal Analysis System) and Simulated Keratometry (TMS-1) are comparable to standard keratometric readings. Neither system works ideally for severely irregular surfaces but does make matters a little better. 3. The Zeiss 10 SL/O keratometer: The Zeiss 10 SL/O keratometer and the TMS-1 videokeratoscope when compared showed poor measurement agreement for irregular corneal surfaces, despite good correlation previously shown between keratometry and videokeratography in calibrated spheres and regular corneas. The TMS-1 usually shows a systematic bias, measuring a greater power in the steeper meridian than the Zeiss 10 SL/O keratometer.10 4. The total axial power map (Orbscan(R), Bausch and Lomb), total optical power map (Orbscan), and contact lens over-refraction method provided the most accurate estimates of central corneal power in these patients. Computerized scanning-slit videokeratography, which analyzes the anterior and posterior surfaces of the cornea, and the contact lens overrefraction method give good estimations of corneal power in patients with irregular corneal astigmatism. This type of analysis may improve the accuracy of IOL calculation in patients with corneal pathology and irregular astigmatism.11 “To reduce their percentage of ametropic outcomes in this population, surgeons must take each patient as an individual and reconstruct the optics.”

Orbscan

Toric IOL Calculations

In normal eyes, data on posterior corneal curvature from the Orbscan II can be used to calculate corneal power in close agreement with the standard keratometric method.7

The ophthalmic community is looking at implanting nontoric IOLs but one paper suggests IOL power calculation for toric IOLs.12

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The method used by them was based on a schematic model eye with spherocylindric surfaces. Two alternative notations were used for description of vergences or prescriptions: 1. Standard notation (refraction in both cardinal meridians and axis) 2. Component notation (spherical equivalent and cylindric component in 0 degree and 45 degrees. Refractive surfaces were added to the vergence in component notation, whereas the transformation of the vergence through media was performed in the standard notation for both cardinal meridians. This mathematical concept for computation of toric IOLs or prediction of the refractive outcome with a toric implant in place may substitute for empirical methods of determining toric IOL implants.

FUTURE Estimation of the corneal power and the corneal visual acuity could be linked to each other. In a seminal study Ucakhan et al13 evaluated each subject eye using ray tracing analysis with the Technomed C-scan color ellipsoid topometer, using basic software (Technomed GmbH, Baesweiler, Germany). They found that predicted corneal visual acuity as determined by ray tracing analysis is useful for estimating best spectacle-corrected VA in normal corneas and the effect of irregular corneal astigmatism on VA in eyes with mild to moderate keratoconus. Further studies are required to evaluate the efficacy of ray tracing in evaluation of aberrations of the optical system of the eye and it needs to be seen how much these evaluations help in minimizing refractive surprises.

REFERENCES 1. Manning CA, Kloess PM. Comparison of portable automated keratometry and manual keratometry for IOL calculation. J Cataract Refract Surg 1997;23(8):1213-16. 2. Odenthal MT, et al. Intraocular lens power calculation in cataract surgery after photorefractive keratectomy.Arch Ophthalmol 2003:121:1071. 3. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standard keratometry for measuring corneal curvature in eyes with lenticular opacity.J Cataract Refract Surg 1999;25(7):898-903. 4. Gimbel HV, Sun R. Accuracy and predictability of intraocular lens power calculation after laser in situ keratomileusis. J Cataract Refract Surg 2001;27(4):571-76. 5. Aramberri J. Intraocular lens power calculation after corneal refractive surgery: Double-K method. J Cataract Refract Surg 2003;29(11):2063-68. 6. Seitz B, Langenbucher A, Beyer A, Kus MM, Behrens A. Posterior corneal curvature after penetrating keratoplasty before and after suture removal. Klin Monatsbl Augenheilkd 2000;217(3):137-43. 7. Leyland M. Validation of Orbscan II posterior corneal curvature measurement for intraocular lens power calculation. Eye 2004;18(4):357-60. 8. Prisant O, Hoang-Xuan T, Proano C, Hernandez E, Awwad ST, Azar DT. Vector summation of anterior and posterior corneal topographical astigmatism. J Cataract Refract Surg 2002;28(9):1636-43. 9. Antalis JJ, Lembach RG, Carney LG. A comparison of the TMS-1 and the corneal analysis system for the evaluation of abnormal corneas. CLAO J 1993;19(1):58-63. 10. Karabatsas CH, Cook SD, Powell K, Sparrow JM. Comparison of keratometry and videokeratography after penetrating keratoplasty. J Refract Surg 1998;14(4):420-26. 11. Cua IY, Qazi MA, Lee SF, Pepose JS. Intraocular lens calculations in patients with corneal scarring and irregular astigmatism. J Cataract Refract Surg 2003;29(7):1352-57. 12. Langenbucher A, Seitz B. Computerized calculation scheme for toric intraocular lenses. Acta Ophthalmol Scand 2004;82(3 Pt 1):270-76. 13. Ucakhan OO. Predicted corneal visual acuity in keratoconus as determined by ray tracing. Acta Ophthalmol Scand 2003;81(3):264-70.

Index

A Accommodating IOLs 106 basic principles dual-optics IOL 108 single-optics IOL 106 single-optics IOL 108 categories of AIOL 106 optimal IOL design 111 three-optics system (in phakia) 110 Accommodative IOL 95 three-optics formulas 97 both optics mobile 98 mobile back-optics case 98 mobile front-optics case 97 two-optics formulas 97 Age dependent IOL power calculations 136 customized IOL power 138 adjusted factors 139 adjusted IOL-power 139 Lin’s double-rate 138 pseudophakic eye 137 refraction power of aphakic 136 age 0 to 3 137 age 3 and up 136 Anterior chamber depth 26 methods to measure 26 pitfalls in ACD measurement 27 various methods 26 A-scan in difficult situations 292 adjusting intraocular lens power for sulcus fixation 296 axial length measurement and asteroid hyalosis 301 bilateral microcornea and unilateral macrophthalmia 302 changes in keratometric corneal power and refractive error after laser thermal keratoplasty 298 hard contact lens method 295 intraocular lens power calculation after macular hole surgery 301

intraocular lens power calculation for lens exchange 397 intraocular lens power calculations in patients with extreme myopia 297 keratometry in corneal scarring/ lacerations 292 methods of estimating corneal refractive power after hyperopic laser in situ keratomileusis 298 postrefractive surgery IOL calculation 294 refractive changes in pediatric pseudophakia 298 refractive history method 296 Aspherical IOL 265 applications 271 central ablation depth 268 comparison of central ablation depths 272 comparison of theory and measurements 272 effective zone size 269 IOL profile 265 positive cylinder for mixed astigmatism 268 prediction of corneal asphericity 266 surface aberration 270 Axial length dependence of IOL constants material and methods 31 clinical data 32 model calculations 31 results 32 clinical results 33 model calculations 32 Axial length measurement 5

B Biometry for refractive lens surgery 244 axial length measurements 245

keratometry after keratorefractive surgery 246 surgical outcomes assessment 245

C Cataract surgery 17 astigmatism decreased 18 astigmatism increased 18 basic rule 18 extracapsular cataract extraction 17 foldable IOL 17 non-foldable IOL 19 phakonit 20 unique case 19 Cataract surgery after previous refractive surgery 164 case report clinical outcomes 170 follow-up and secondary procedures 171 piggyback IOL 171 delay of cataract surgery after previous refractive corneal surgery 164 IOP power calculation 167 patient’s age at time of cataract surgery 165 prevalence of cataract in myopia and manifestation of cataract in myopia 165 decision to perform cataract surgery 166 excimer laser surgery cause cataract formation 166 IOL choice 167 prevalence of cataract in myopia 166 surgical considerations of cataract surgery excimer laser 167 radial keratotomy 167 type of cataract after refractive surgery 164

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Classical vs modern formulas for estimated lens position aphakic versus phakic IOL 70 estimated lens position (ELP) 72 nonlinear Gaussian-formula 72 classical formula 72 Lin formula 73 nonlinear optimization 73 triple optimization 73 Computerized videokeratography 11 Consistent IOL calculation in normal and odd eyes with the raytracing program 285 clinical results after corneal surgery 289 normal eyes 289 corneal radii 288 currently available IOL types 287 axial eye lengths 287 IOL position 288 principle raytracing 285 Contact lens-induced warpage 13 Conversion function 93 conversion to spectacle power 94 IOL-power (P) vs spectacle power 94 Cornea 10 Corneal diseases 12 Corneal refractive surgery 142 clinical history method 143 hyperopic treatments 143 myopic treatments 142 Customization of IOL formulas 121 constants 122 IOL power calculation formulas 122 postoperative period 123 preoperative planning 121 special situations 123

D Design of aspherical IOLs 99 Dual-optics accommodating IOL 259 accommodating rate both optics mobile 261 mobile back-optics case 260 derivation of Lin’s M-formula 263 performance and configurations maximal accommodation 261 source aberration 262

E Error analysis of IOL power calculations 101 axial length error 104 corneal-power errors 102 IOL position error 103 Mis-labeling error 104 notations 102

I Immersion ultrasound biometry 41 Intraocular lens calculation after prior refractive surgery biphakic eyes phakic 337 corneal refractive eyes 337 formula error 338 index of refraction error 337 instrument error 337 history of solutions 338 adjusted refractive index methods 339 methods to adjust/calculate the target intraocular lens power 341 methods to estimate true postoperative corneal power 338 how to handle problems and errors? 343 important things to keep in mind 342 what formula to use? 342 Intraocular lens power calculation after advanced surface ablations 225 aphakic refraction technique 228 contact lens over-refraction 227 corrected refractive index of refraction 227 Feiz-Mannis formula 226 Gaussian optics 228 proposed methods 226 Intraocular lens power calculation in bimanual microphacoemulsification 159 axial length measurements 160 IOL constant optimization 160 keratometry 159 patients and methods 160 surgical technique 160, 161 Intraocular lens power calculations for high myopia 153 intraocular lens power calculation formulas 153 preoperative biometry 155 refractive index of cornea and Aconstant 157 satisfactory postoperative refractive status 156 Intraocular lens power calculations in phaco and microphaco 146 a scan biometry applanation 146 immersion 146 immersion vector A/B scan biometry 147

IOL master 147 technique 147 accuracy of IOL power calculation 151 formulas for calculating IOL power regression formulas 148 theoretical formulas 148 intraocular lens power calculation after corneal refractive surgery 150 Intraocular lens power selection for children 127 core message biometry 127 formulas 127 implanting a fixed power of IOL in a growing eye 128 IOL power selection method axial length and keratometry 128 desired immediate postoperative refraction 129 IOL power calculation formulas 129 our current approach age at cataract surgery 130 expected compliance 131 IOL power 131 parents’ refractive error 131 refractive surprizes 132 special situations 132 status of fellow eye 130 visual acuity 131 Intraoperative IOL power calculation 320 fundoscopy 323 intraoperative factors 322 NO AL-NO KM’S 321 optical and physical basis 320 refractive methods 322 special cases eyes with silicone oil 324 keratoconus 325 piggy back implantations 324 post cornea refractive surgery 324 IOL calculation 114 axial length dependence of prediction error 117 IOL power formulas 116 long and short eyes 114 long eyes 115 short eyes 114 IOL calculation in hyperopes material and methods 281 results 282 IOL calculations in eyes with central corneal scars 277

Index computerized videokeratography 278 examination and surgical planning 279 rigid contact lens over-refraction 278 IOL for pediatric eyes 90 IOL formula 6, 28 Binkhorst formula 6 modern theoretical formulas 29 regression formula 6, 29 Sanders-Retzlaff-Kraff (SRK) formula 7 theoretical formula 6, 28 IOL formula to use after refractive surgery 221 consensus-K technique from JB Randleman 223 estimate true corneal power without history CL method 223 estimate true corneal power without history Koch/ Maloney TOPO central 223 fudge the target IOL power without history mackool secondary IOL 223 history derived method 222 modified Hoffer Q formula 223 IOL master 24 inference 25 limitations 25 technique ideal axial length recording 24 IOL master physics 36 limitations 37 principle 36 IOL power calculation 8 factors affecting accuracy axial length correction factor 8 axial length measurement 8 density of the cataract 8 IOL tilt and decentration 8 karatometry 8 orientation of planoconvex implants 8 postoperative change in corneal curvature 8 site of loop implantation 8 IOL power calculation after incisional and photoablatine refractive surgery 184 Camellin-Calossi formula 199 clinical data 200 incisional refractive surgery 199 laser ablative refractive surgery 200

corneal power after keratorefractive surgery change of corneal asphericity 184 change of ratio between anterior and posterior corneal surfaces 186 Gulstrand’s schematic 186 keratometric refractive index after laser ablative refractive surgery 191 effective lens position 193 intraocular lens power calculation after refractive corneal surgery 194 aphakic intraoperative refraction techniques 198 clinical history methods 194 consideration of posterior corneal curvature 195 contact lens method 195 correlation between actual corneal curvature and corneal power correcting factor 197 correlation between axial eye length and a theoretical variable keratometric refractive index 196 correlation between axial eye length and corneal radius correcting 196 empirical method 194 modifying the final value of the IOL as a function of the SIRC 197 refraction-derived method 198 topographic data 195 IOL power calculation after LASIK surgery errors 46 methods to improve the prediction of intraocular power 48 adjusted effective refractive power 49 clinical history methods 48 contact lens overrefraction 49 Feiz-Mannis method 49 IOL formulas 49 Maloney methods 49 single-K versus double-K method 49 methods to measure keratometric diopters keratometry 47 optical coherence tomography 48

377 topography access 47 IOL power calculation formulae 37 3rd generation theoretical formulae 38 applications of various formulae 40 comparison in efficacy of formulae 40 fallacies of newer formulae 41 axial length measurement 38 Binkhorst formula 37 constant of IOL formulae 39 Donzis Kastle Gordon formula 38 Haigis formula 38 Hoffer Q formula 39 Holladay formula 39 modified Binkhorst formula 37 regression (empirical) formulae 38 SRK formula 38 theoretical formulae 37 IOL power calculation in posthyperopic presby lasik cataract 180 IOL power calculation in the high myopic eye 314 axial length measurement A-scan and B-scan ultrasonography 315 IOL-master 315 formulas of IOL power calculation first regression formula 314 second-generation formulas 315 third generation formulas 315 IOL power calculations axial length 75 axial length instruments 76 biphakic eyes 79 immersion technique 77 optional CALF method 78 retinal thickness factor 79 ultrasound velocities 78 biometry 75 clinical variables 86 corneal power 79 astigmatism 80 corneal scar eyes 82 corneal transplant eyes 82 instrumentation 79 keratoconus eyes 80 previous refractive surgery 80 formulas generations 83 methodology 84 personalization 86 refraction formula 84 usage 84

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Mastering the Techniques of Intraocular Lens Power Calculations IOL position 83 problems and errors 88 prevention of common errors 90 special circumstances monocular cataract in bilateral high ametrope 87 pediatric eyes 87 piggyback lenses 87 silicone oil refractive effect 87 IOL power calculations after corneal refractive surgery 205, 316 back calculated IOL power 208 corneal topography 209 corrected keratometry 208 corrected refractive index method 209 DBR method 207 double K method 208 Gaussian optics formula 211 hard contact lens method 210 history method 207 intraoperative retinoscopy 210 modified keratometry method 208 nomogram based adjustment of IOL power 209 regression derived clinical method 210 theoretical formula 2004 208 theoretical variable refractive index method 211 using corneal topography 207 IOL power calculation for cornea triple and penetrating keratoplasty 368 multi step procedure 369 IOL power calculations in eyes with irregular corneas corneal power calculation 371 keratometry problem automated keratometry 371 contact lens over-refraction method 372 corneal topography 373 evidence of use of systems 373 manual keratometry 371 orbscan 373 refraction-derived keratometric values 372 refractive history method 372 toric IOL calculations 373 IOL power calculations in phakic IOLs clinical rules 252 PRL power calculation 252 IOL power calculations: a topographic method 175 examples for topographic method 177

after LASIK 178 after RK radial keratometry 177 formulas for IOL calculation 176 post corneal surgery shape 175 topographic method 176 IOL power formulas 51 accommodating IOL 59 accuracy of IOL power calculation 54 IOL power in aphakic eye 56 IOL power in phakia and piggyback- IOL 57 new generation formulas 54 Haigis formula 55 Hoffer Q formula 55 Holladay formulas 55 Lin’s S-formula 56 Olson formula 55 SRK formula 54 regression formulas axial length measurement 53 corneal power 53 preoperative anterior chamber depth 53 the estimated IOL position (ELP) 53 theoretical formulas 51 basic theoretical formulas 52 modified theoretical formulas 52 the modern formulas 52 IOL power in aphakia (2-optics) 92 IOL power in case of anisometropia 345 defining a patient’s refractive balance 345 postoperative aniseikonia 350 preoperative anisometropia 350 theoretical aniseikonia 348 to measure aniseikonia and normal aniseikonia 346 type of anisometropia 346 IOL power in cataract with silicone oil eyes 318

K Keratometric measurements 5 Keratometry 10, 11, 47

L Lasik 14 complications of lasik central islands 16 decentered ablation 16 hyperopia 14 astigmatism 15 myopia 14 regression after lasik hyperopia 15 myopia 15 re-lasik 16

Latkany regression formula for intraocular lens calculations 213 after hyperopic refractive surgery 218 Feiz-Mannis nomogram 219 after myopic refractive surgery 213 intraocular lens power calculation 216 prospective analysis 216

M Mathematics of LASIK 231 asphericity comparison 233 bifocal (presby-lasik) 232 lasik ablation nomogram aspherical surface 234 asphericity control 235 spherical surface 234 lasik ablation rate 232 mixed astigmatism 233 refraction power 231 refractive error (D) 231 surface aberration 236

N New IOL formulas based on Gaussian optics 62 comparison of 2 and 3-optics 66 conversion function clinical application 64 IOL power in aphakia 63 piggyback IOL-power 65 revised Z2 formulas 65 three-optics IOL system 65 spectacle power and Holladay formula 67 two optics formulas (aphakic eye) 63 unified effective formula 66 error analysis 67 Normal cornea 11

O Optical coherence biometry 42 Optical coherence tomography 48 technology for the anterior chamber 238 AC OCT and the study of accommodation endothelium safety distance 239 measurement of the anterior chamber’s internal diameter 239 possibility of contact crystalline lens 240

Index Optical corneal tomography 21 Optics of the thin plus lens 28

P Partial coherence interferometry 41 Piggyback IOL power 57 Problems of IOL power calculation in pediatric cataract surgery normal eye development 331 postoperative refractive goal in children 333 practical guidelines in IOL calculation in children 333 choice of IOL calculation formula 334 factors influencing predicted IOL power values 335 keratometry 334 measurement of axial length 333 performance of measurements 333 rate of undercorrection of IOL calculation results 334 refractive changes of the eye after lens removal and IOL implantation 332 Pseudophakic lasik 9

R Radial keratotomy 14 Raytracing analysis of accommodating IOL 254 methods of accommodation 254 summary of analysis 256 Reading a corneal topography 12 Refractive surprises after cataract surgery 305 case reports 310 corneal refractive surgery 309 intraocular lens exchange 306 piggyback lens exchange 308 secondary piggyback intraocular lens implantation 308 Review of IOL power calculation 356 definitions based on the Binkhorst formula 357 derivation of the Binkhorst formula 364 equivalence of the first generation formulas 365 printing errors found in original articles 366

S Schematic eye 3 Donder’s reduced eye 4 eye of Gullstrand 4

379 Gauss’s theorem 3 Listing’s eye 4 refraction by combination of lenses 3 Slit-scanning videokeratography 48

T Targeting IOL postoperative refraction binocular correction 7 monocular correction 7 The two-lens system 28 Three-optic IOL system 94 conversion function 95 phakic-IOL 94 piggyback IOL 94 Topography 10

Z Zemax raytracing method for accommodative IOL 327 accommodating rate mobile back-optic case 327 mobile front-optics case 328 derivation of Lin’s M-formula back optics mobile 329 front optics mobile 330 ZEMAX raytracing method 328