Shielding Calculation for LINAC

Therapy Shielding Calculations Melissa C. Martin, M.S., FACR, FACMP American College of Medical Physics 21st Annual Meeting & Workshops Scottsdale, AZ June 13, 2004

Therapy Shielding Design Traditionally Relies on NCRP Reports ■

NCRP Report 49 – Primary and secondary barrier calculation methodology – Applicable up to 60Cobalt and linacs up to 10 MV

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NCRP Report 51 – Extended NCRP 49 methodology up to 100 MV – Empirical shielding requirements for maze doors

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NCRP Report 79 – Improved neutron shielding methodology

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NCRP Report 144 – Update of NCRP 51 primarily aimed at non-medical facilities

Reports Reportsreflect reflectprogress progressin inlinac linacdesign designand andshielding shieldingresearch research

Revised NCRP Report in Drafting Stage by AAPM Task Group 57, NCRP SC 46-13 ■

Design of Facilities for Medical Radiation Therapy – 4 MV - 50 MV (including 60Co)

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Calculation scheme generally follows NCRP 49

■

All shielding data (TVLs) reviewed and updated

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Updated for intensity modulated radiation therapy (IMRT)

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Improved accuracy of entrance requirements – Both with and without the use of maze

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Laminated barriers for high energy x-rays – Photoneutron generation due to metal in primary barrier

Goal: Goal:Improved Improvedaccuracy accuracy

Linear Accelerator Energy and Workload ■

BJR #11 megavoltage (MV) definition used here – British Journal of Radiology (BJR) Supplement No. 11

■

Comparison of BJR #11 and BJR #17 MV definitions

BJR #11 MV BJR #17 MV ■

4 4

6 6

10 10

15 16

18 23

20 25

24 30

Workload assumptions typically used for shielding design – Workload identified by symbol “W” in calculations – For MV ≤ 10 MV: W = 1000 Gy/wk at 1 meter from the target » Based on NCRP 49 Appendix C Table 2 – For MV > 10: W = 500 Gy/wk » Based on NCRP 51 Appendix B Table 5

Radiation Protection Limits for People ■

Structural shielding is designed to limit exposure to people – Exposure must not exceed a specific dose equivalent limit – Limiting exposure to unoccupied locations is not the goal

■

NCRP 116 design dose limit (P) – 0.10 mSv/week for occupational exposure – 0.02 mSv/week for the general public

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Typical international design dose limits – 0.12 mSv/week for controlled areas – 0.004 mSv/week for uncontrolled areas

NCRP NCRP116 116dose doselimit limitis isaafactor factorof of55lower lowerthan thanNCRP NCRP49 49value value

Radiation Protection Limits for Locations ■

Permissible dose outside vault depends on occupancy

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Occupancy factor (T): Fraction of time a particular location may be occupied

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Maximum shielded dose (Smax) at protected location

S max =

P T

– Assuming occupancy factor T for protected location

Maximum Maximumshielded shieldeddose doseis istraditionally traditionallyreferred referredto tosimply simplyas asP/T P/T

Occupancy Values from NCRP 49 ■

Full occupancy for controlled areas by convention (T=1)

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Full occupancy uncontrolled areas (T=1) – Offices, laboratories, shops, wards, nurses stations, living quarters, children’s play areas, and occupied space in nearby buildings

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Partial occupancy for uncontrolled areas (T=1/4) – Corridors, rest rooms, elevators with operators, unattended parking lots

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Occasional for uncontrolled areas (T=1/16) – Waiting rooms, toilets, stairways, unattended elevators, janitor’s closets, outside areas used only for pedestrian or vehicular traffic

Hourly Limit for Uncontrolled Areas ■

0.02 mSv hourly limit for uncontrolled areas

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20 Gy/hr common assumption for calculation

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Implies a lower limit for occupancy factor – T ≥ 20 / ( U W ) – T ≥ 0.16 for higher energy accelerators (500 Gy / wk workload) – T ≥ 0.08 for lower energy accelerators (1000 Gy wk workload)

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Not applied to low occupancy locations with no public access – e.g., unoccupied roof, machinery room

TT==1/10 1/10rather ratherthan than1/16 1/16typically typicallyused usedfor forexterior exteriorwalls walls

NCRP 134 Impact on Linac Shielding ■

NCRP 134 distinguishes general employees from public – NCRP 134 maintains NCRP 116 limit of 0.02 mSv/wk for both – Limit 25% of 0.02 mSv/wk from individual facility for general public

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Occupancy assumptions proposed for general public – T=1/40 for occasional occupancy

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Equivalent to T=1/10 occasional for general employees – Similar to P/T required by hourly limit for primary barriers – Slightly increase from T = 1/16 used for secondary barriers – T=1/16 still appropriate for locations with no public occupancy » e.g., machine rooms, unoccupied roofs, etc.

Impact Impactincreases increasesififhigher higheroccupancy occupancythan thanT=1/40 T=1/40adopted adopted

Basic Primary Barrier Calculation Unchanged from NCRP 49 ■

Unshielded dose calculation

S pri ■

WU 2 d pri

T a rg e t R o ta tio n a l P la n e D'

 S pri  log10   P / T

Barrier thickness (tc) calculation

tC =

TVL1 + (n −1) TVLe

D

A'

A

Door

Attenuation in tenth-value layers

n = ■

=

*

M aze

d

C'

T arget Is o c e n te r

p ri

tC

C 1 ft

Margin Marginin inprimary primarybarrier barrierthickness thicknessis isrecommended recommendedto to compensate compensatefor forpotential potentialconcrete concretedensity densityvariation variation

B

Primary Barrier Photon Tenth-Value Layers (mm) Come from a Variety of Sources MV 0.2 0.25 0.3 0.4 0.5 1 2 4 6 10 15 18 20 24

Lead TVL1 TVLe 1.7 1.7 2.9 2.9 4.8 4.8 8.3 8.3 11.9 11.9 26 26 42 42 53 53 56 56 56 56 56 56 56 56 56 56 56 56

NCRP 49

NCRP 51

Concrete TVL1 TVLe 84 84 94 94 104 104 109 109 117 117 147 147 210 210 292 292 367 323 410 377 445 416 462 432 470 442 483 457

Steel TVL1 TVLe 15 15 19 19 22 22 29 29 33 33 54 51 76 69 91 91 100 100 104 104 108 108 109 109 110 110 110 110

Nelson & LaRiviere

Earth TVL1 TVLe 135 135 151 151 167 167 175 175 188 188 236 236 336 336 468 468 572 572 648 648 720 720 740 740 752 752 773 773

McGinley

Borated Poly TVL1 TVLe 84 84 94 94 104 104 109 109 117 117 147 147 210 210 292 292 343 343 379 379 379 379 379 379 390 390 401 401

Estimated from Concrete

Anticipate Anticipateupcoming upcomingNCRP NCRPreport reportto toreview reviewand andupdate updateTVL TVLdata data

Primary Barrier Width ■

0.3 meter margin on each side of beam rotated 45 degrees – Barrier width required assuming 40 cm x 40 cm field size

wC = ■

0.4 2 d C ' + 1.0 ft

Field typically not perfectly square (corners are clipped) – 35 cm x 35 cm field size typically used to account for this

T a r g e t to N a r r o w P o in t D is t a n c e ( d C ')

*

T a rg e t Is o c e n te r

T a r g e t to N a r r o w P o in t D is t a n c e ( d C ')

*

T a rg e t Is o c e n te r

1 ft

w C

C' 1 ft

C

C' 1 ft

1 ft

w C

C

T a r g e t to N a r r o w P o in t D is t a n c e ( d C ')

*

T a rg e t Is o c e n te r

1 ft

1 ft M e ta l

w

C

Slant Factor and Obliquity Factor ■

Slant Factor – Path from target to protected location diagonally through barrier » Incident angle θ of line with respect to perpendicular – Required barrier thickness reduced by cos(θ ) » Same total distance through barrier to protected location

■

Scatter causes slant factor to underestimate exit dose – Multiplying thickness by obliquity factor compensates for this Angle 0 30 45 60 70

4 MV 1.00 1.03 1.07 1.21 1.44

Lead 10 MV 1.00 1.02 1.07 1.21 1.47

18 MV 1.00 1.03 1.10 1.22 1.52

Concrete 4 MV 10 MV 1.00 1.00 1.02 1.00 1.07 1.04 1.20 1.14 1.47 1.28

18 MV 1.00 1.00 1.04 1.08 1.22

4 MV 1.00 1.02 1.07 1.20 1.48

Steel 10 MV 1.00 1.02 1.07 1.17 1.42

18 MV 1.00 1.04 1.08 1.20 1.45

Photoneutron Generation Due to Metal in Primary Barrier (Linacs ≥ 10 MV) ■

Dose-equivalent 0.3 m beyond barrier (McGinley) WU NF −t / TVL −t / TVL 1 P = SN 10 10 3 N t2 + t + 0.305 3 2 – N is neutron production constant (Sv neutron per Gy workload) » 1.9 x 10-3 for lead, 1.7 x 10-4 for steel at 18 MV (from McGinley) ■

Recent safety survey indicated somewhat higher 3.8 x 10-4 value for steel at 18 MV is appropriate

» N adjusted versus MV based on neutron leakage fraction vs MV – F is field size (conventionally 0.16 m2), t2 is metal thickness (m) – X-Ray attenuation prior to metal layer: 10^(-t1 / TVLp) – Neutron attenuation after metal layer: 10^(-t3 / TVLN)

Patient Photonuclear Dose Due to Metal in Primary Barrier for MV > 10 ■

Metal in primary barrier can increase patient total body dose if MV > 10 – Lead inside layer approximately doubles patient total body dose – Increases risk of secondary cancer

■

Concrete or borated polyethylene inside metal in primary barrier is recommended if MV >10 – Each inch of borated poly decreases patient dose from metal barrier photoneutron by approximately factor of 2

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Impact of IMRT on patient photonuclear dose is addressed later Avoid Avoidmetal metalas asinside insidelayer layerof ofprimary primarybarrier barrierififMV MV>> 10 10

Secondary Barrier ■

Patient scatter unshielded dose

Sp

=

a W ( F / 400) 2 2 d sca d sec

T a rg e t R o ta tio n a l D' P la n e

– F is field size in cm2 » typically 1600 –

■

a

= scatter fraction for 20 x 20 cm beam

D

d

M aze

sca

*

SL

=

W 10 2 d sec

−3

T a rg e t Is o c e n te r

d

B

sec

tB 1 ft

Leakage unshielded dose – Assumes 0.1% leakage fraction

A'

A

Door

C'

C

Leakage Photon Tenth-Value Layers (mm) Also Come from a Variety of Sources

MV 4 6 10 15 18 20 24

Lead TVL1 TVLe 53 53 56 56 56 56 56 56 56 56 56 56 56 56

NCRP 49

Concrete TVL1 TVLe 292 292 341 284 351 320 361 338 363 343 366 345 371 351

Nelson & LaRiviere

Steel TVL1 TVLe 91 91 96 96 96 96 96 96 96 96 96 96 96 96

Earth TVL1 TVLe 468 468 546 455 562 512 578 541 581 549 586 552 594 562

Kleck & Varian Average

Borated Poly TVL1 TVLe 292 292 341 284 351 320 361 338 363 343 366 345 371 351

Estimated from Concrete

Neutron Leakage ■

Same form as photon leakage calculation

■

Based on dose-equivalent neutron leakage fraction vs MV – 0.002%, 0.04%, 0.10%, 0.15% and 0.20% for 10, 15, 18, 20 and 24 MV – Based on Varian and Siemens neutron leakage data » Assumes quality factor of 10 for absorbed dose

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Shielded dose equivalent based on leakage neutron TVLs – 211 mm for concrete – 96 mm for borated polyethylene

Intensity Modulated Radiation Therapy (IMRT) ■

IMRT requires increased monitor units per cGy at isocenter – Typical IMRT ratio is 5 MU per cGy, as high as 10 for some systems

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Percent workload with IMRT impacts shielding – 50% typically assumed; 100% if vault is dedicated to IMRT

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Account for IMRT by multiplying x-ray leakage by IMRT factor – IMRT Factor = % IMRT x IMRT ratio + (1 - % IMRT) – 3 is typical IMRT factor (50% workload with IMRT ratio of 5)

■

IMRT factor lower for neutrons if machine is dual energy – e.g., 1.5 if dual energy linac with 50% of treatments below 10 MV » Pessimistic since most IMRT is performed at 6 MV (next chart)

IMRT above 10 MV Significantly Increases Patient Photonuclear Dose ■

Neutrons dominate patient total body dose for high energy linacs – Neutron dose equivalent as high as ten times photon dose » Potentially 1% of workload vs 0.1% photon leakage ■

0.05% required absorbed neutron dose x 20 quality factor

– Typical neutron dose equivalent is lower than requirement » 0.1 to 0.2% of workload ■

IMRT factor of 5 increases patient incidental dose 5X – Results in typical neutron total body exposure of 0.5 to 1.0% of WL – Significantly increases risk of secondary cancer

Most MostIMRT IMRTis isperformed performedat at66MV MVto tomitigate mitigateincreased increasedsecondary secondary cancer cancerrisk riskfrom fromphotoneutrons photoneutrons

Patient Scatter Significant Adjacent to Primary Barrier ■

Scatter traditionally neglected for lateral barriers – Generally a good assumption – 90 degree scatter has low energy

■

Scatter is significant adjacent to primary barrier – Calculations indicate comparable to leakage – Slant thickness through barrier compensates for the increase in unshielded dose due to scatter » Barrier thickness comparable to lateral is adequate for same P/T

T a rg e t R o ta tio n a l P la n e D'

D

d

M aze

*

sca

θ S la n t t h ic k n e s s u s e d t o c a lc u l a t e a tte n u a tio n

d

C 1 ft

T a rg e t Is o c e n te r S c a tte r A n g le

sec

C' A c tu a l b a r r ie r t h ic k n e s s

A'

A

Door

B

Patient Scatter Fraction for 400 cm2 Field ■

Based on recent simulation work by Taylor et.al.

■

Scatter fraction increases as angle decreases

■

Scatter fraction vs MV may increase or decrease – Tends to increase with MV at small scatter angles – Decreases with increasing MV at large scatter angles MV 4 6 10 15 18 20 24

10 1.04E-02 1.04E-02 1.66E-02 1.51E-02 1.42E-02 1.52E-02 1.73E-02

20 6.73E-03 6.73E-03 5.79E-03 5.54E-03 5.39E-03 5.66E-03 6.19E-03

30 2.77E-03 2.77E-03 3.18E-03 2.77E-03 2.53E-03 2.59E-03 2.71E-03

Angle (degrees) 45 60 2.09E-03 1.24E-03 1.39E-03 8.24E-04 1.35E-03 7.46E-04 1.05E-03 5.45E-04 8.64E-04 4.24E-04 8.54E-04 4.13E-04 8.35E-04 3.91E-04

90 6.39E-04 4.26E-04 3.81E-04 2.61E-04 1.89E-04 1.85E-04 1.76E-04

135 4.50E-04 3.00E-04 3.02E-04 1.91E-04 1.24E-04 1.23E-04 1.21E-04

150 4.31E-04 2.87E-04 2.74E-04 1.78E-04 1.20E-04 1.18E-04 1.14E-04

Patient Scatter Energy ■

Mean Scatter Energy MV 6 10 18 24

■

0 1.7 2.8 5.0 5.7

Scatter Angle (degrees) 20 45 1.2 0.6 1.4 0.6 2.2 0.7 2.7 0.9

90 0.25 0.25 0.3 0.3

No standardized scatter Tenth-Value Layer – Primary MV rating based on peak MV in spectrum, not mean energy – Primary TVL at slightly higher MV (e.g, 50%) appears reasonable » % increase little more than wild guess; more research is needed

Ambiguity Ambiguityremains remainsas asto toTVL TVLto touse usefor forscatter scatter

Maze Calculation Likely Revised in Upcoming NCRP Report ■

New method identifies and evaluates specific mechanisms – Patient Scatter, Wall Scatter, Leakage scatter – Direct leakage – Neutrons, capture gammas

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Mechanisms calculated at most stressing orientation – Scatter calculations multiplied by 2/3 to compensate for this

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Scatter energy relatively low at maze door – Primary 0.3 MV TVLs used for patient and wall scatter (2 bounces) – Primary 0.5 MV TVLs used for leakage scatter (1 bounce) – Scatter is significant typically only for low energy linacs

Goal: Goal:More-precise More-precisecalculation calculationavoiding avoidingover overor orunder-shielding under-shielding

Maze: Patient Scatter ■

Unshielded dose

a W ( F / 400) α 0.5 AC d P21 d P2 2 d P2 3

Sp = ■

where –

T a rg e t R o ta tio n a l P la n e D'

D

d

d P3

α0.5 is 0.5 MV scatter fraction

d

» Second bounce fraction » 0.02 per m2 typically used – Other constants as before, e.g., » a = patient scatter fraction » F = field size in cm^2 » h = room height

A w

A'

A

Door

C

C

= w

C

h

P1

*

P2

C

T arg et Is o c e n te r

B

Maze: Wall Scatter ■

Unshielded dose

SS

=

f W α1 A1 α 0.5 AM d S21 d S22 d S23

d

where

S3

T a rg e t R o ta tio n a l P la n e D'

D

–

f = patient transmission

–

α1 = first reflection coefficient » 0.005 per m2 for 6 MV » 0.004 per m2 for ≥ 10 MV

–

A1 = beam area (m2) at wall

–

AM = Maze cross section (m2) » dM x room height

d d

A'

A

Door

d

*

S1

S2

M

C

T arg et Is o c e n te r

Maze: Leakage Scatter ■

Unshielded dose

S LS

=

W 10 3 α1 AC d L21 d L22 −

where

D' D

d

T a rg e t R o ta tio n a l P la n e

L2

– Constants as previously defined

d

A w

A'

A

D oor

C

C

= w

C

h

*

L1

C

T arget Is o c e n te r

B

Maze: Direct Leakage ■

Unshielded dose

SL

=

−3

W 10 10 d L2

−t D ' / TVL

■

Same as standard secondary photon leakage calculation

■

Standard neutron leakage not typically used – Use only if it exceeds the maze neutron calculation » e.g., if maze wall not sufficiently thick

A

Door

tD '

θ

d D'

D

C'

L

* C

A' T a rg e t R o ta tio n a l P la n e

T a rg e t Is o c e n te r

B

Maze Neutron Calculation Based on Modified Kersey Method ■

Unshielded dose equivalent

H NT

=

W Ln [1+ ( d N 2 −3) / 5 ] 2 d N 1 10

where

A

D oor T a rg e t R o ta tio n a l P la n e D'

D

d

N2

– Ln is neutron leakage fraction

d

» Same as used for secondary neutron leakage calculation – Modification to Kersey is assuming first tenth-value distance is 3 m instead of 5 m

C'

*

A'

T arget Is o c e n te r

B

N1

C

Upcoming UpcomingNCRP NCRPreport reportmay mayrecommend recommendaamore-complex more-complexapproach approach than thanthis this

Maze Neutron Shielding ■

Modeled as 50% thermal neutrons and 50% fast neutrons

■

1 inch borated poly effectively eliminates all thermal neutrons

■

Fast neutron TVL is 2.4 inches for the first 4 inches

■

Fast neutron TVL is 3.6 inches beyond 4 inches thickness

Maze Capture Gammas from Concrete ■

Gamma rays generated by neutron capture in the maze – Very significant for high energy linacs

■

Unshielded dose is a factor of 0.2 to 0.5 of the neutron dose equivalent at the treatment room door – Use the conservative factor (0.5)

■

Capture gammas have moderate energy (3.6 MeV) – TVL of 61 mm for lead – Limited attenuation also provided by polyethylene (278 mm TVL)

Dominates DominatesX-Ray X-Raydose doseat atmaze mazeentrance entrancefor forhigh highenergy energylinacs linacs

Direct-Shielded Door ■

Neutron Door is simply a secondary barrier – Typically more layers and different materials than a wall » Lead to attenuate leakage photons » Borated polyethylene to attenuate leakage neutrons ■

Typically sandwiched between layers of lead

» Steel covers ■

Specialized shielding procedure adjacent to door – Compensates for relatively small slant thickness in this location – Vault entry toward isocenter similar to maze – Vault entry away from isocenter is secondary barrier » But with specialized geometry

Direct-Shielded Door: Far Side of Entrance ■

Extra material added to corner – Lead to entrance wall – Borated polyethylene or concrete beyond wall

■

■

Uses standard secondary barrier calculation Goal: provide same protection as wall or door for path through corner

P r o te c te d P o in t (1 ft b e y o n d d o o r e n c lo s u re ) I s o c e n te r to F a r S id e o f E n tr a n c e D i s ta n c e

Is o c e n te r to D o o r S e c o n d a ry D i s ta n c e

Is o c e n te r T a rg e t R o ta tio n a l P la n e

D o o r O v e r la p B e y o n d F a r S id e o f E n tr a n c e 7 .5 " O v e r la p T y p ic a l T y p ic a l Gap 0 .5 "

Direct-Shielded Door: Near Side of Entrance ■

Geometry similar to short maze – Maze calculation can be used but is likely pessimistic

■

T y p ic a l G ap 0 .5 "

Requires less material than far side of entrance – Lower unshielded dose – Lower energy

d

Is o c e n te r T arg et

*

7 .5 " T y p ic a l Door O v e r la p N1

T a rg e t R o ta tio n a l P la n e

d

N2

P ro te c te d P o in t (1 ft b e y o n d door e n c lo s u r e )

Shielding for Heating, Ventilation, and Air Conditioning (HVAC) Ducts ■

HVAC penetration is located at ceiling level in the vault – For vaults with maze, typically located immediately above door – For direct-shielded doors, located in a lateral wall as far away from isocenter as possible

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Ducts shielded with material similar to the door at entrance

■

Material thickness 1/2 to 1/3 that required of the door – Path through material is at a very oblique angle due to penetration location with slant factor between 2 and 3 – Factor of at least 5 reduction in dose at head level (the protected location) vs. at the HVAC duct opening

■

NCRP 49 recommends that shielding extend at least a factor of three times the width of the HVAC penetration

Photon Skyshine ■

Unshielded dose

S sky =

0.0249 W U Ω1.3 d Y21 d Y22

where –

Ω (steradians) = 0.122 » for 40 x 40 cm beam

Ω 2 m e te r s

d

Y1

h Is o c e n te r

■

Multiplying by additional factor of two is recommended

*

■

Primary TVLs used to calculate attenuation

F lo o r

T a rg e t

d

h Y2

New Newconstruction constructionseldom seldomshields shieldssolely solelyfor forskyshine skyshinedue dueto to vigilance vigilancerequired requiredto toprevent preventunauthorized unauthorizedroof roofaccess access

Neutron Skyshine ■

Unshielded dose

H sky =

5.4 × 10

−4

H pri Ω

2π

where –

Ω = 2.71 (steradians) typical (target above isocenter)

– Hpri is neutron dose-eq in beam (0.00013, 0.002, 0.0039, 0.0043, and 0.014 times W for 10, 15, 18, 20, and 24 MV, respectively) ■

Use factor is not applied since neutrons in all orientations

■

Multiplying by additional factor of two is recommended

Ω

*

T arg et Is o c e n te r

F lo o r U p to 2 0 m e te r s la te r a l d is ta n c e

Primary Goal of Upcoming NCRP Report is Improved Shielding Calculation Accuracy ■

Very little impact for low energy accelerators – Primary and secondary barrier calculation method unchanged – Very little impact to calculated shielding for given protection limit

■

Improved accuracy for high-energy accelerators – Avoids extra cost of over design due to pessimistic calculations – Avoid extra cost of retrofitting if inaccurate calculations underestimate required shielding

References ■

Biggs, Peter J. “Obliquity factors for 60Co and 4, 10, 18 MV X rays for concrete, steel, and lead and angles of incidence between 0º and 70º,” Health Physics. Vol. 70, No 4, 527-536, 1996.

■

British Journal of Radiology (BJR) Supplement No. 11. Central axis depth dose data for use in radiotherapy, 1972.

■

Chibani, Omar and C.C. Ma. “Photonuclear dose calculations for high-energy beams from Siemens and Varian linacs,” Medical Physics, Vol 30, No. 8:1990-2000, August 2003.

■

Kleck, J. “Radiation therapy facility shielding design.” 1998 AAPM Annual Meeting

References (Continued) ■

McGinley, P.H. Shielding Techniques for Radiation Oncology Facilities, 2nd ed. Madison, WI: Medical Physics Publishing, 2002.

■

National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for medical use of x-ray and gamma rays of energies up to 10 MeV. Washington, DC: NCRP, NCRP Report 49, 1976.

■

National Council on Radiation Protection and Measurements. Radiation protection design guidelines for 0.1-100 MeV particle accelerator facilities. Washington, DC: NCRP, NCRP Report 51, 1977.

References (Continued) ■

National Council on Radiation Protection and Measurements. Neutron Contamination from Medical Accelerators. Bethesda, MD: NCRP, NCRP Report 79, 1984.

■

Nelson, W.R., and P.D. LaRiviere. “Primary and leakage radiation calculations at 6, 10, and 25 MeV,” Health Physics. Vol. 47, No. 6: 811-818, 1984.

■

Rodgers, James E. “IMRT Shielding Symposium” AAPM Annual Meeting, 2001.

■

Shobe, J., J.E. Rodgers, and P.L. Taylor. “Scattered fractions of dose from 6, 10, 18, and 25 MV linear accelerator X rays in radiotherapy facilities,” Health Physics, Vol. 76, No. 1, 27-35, 1999.

References (Continued) ■

Taylor, P.L., J.E. Rodgers, and J. Shobe. “Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV," Medical Physics, Vol. 26, No. 8, 1442-46, 1999.