Calculations Review for Evaluation Exam of pharmacist

Pharmacy Calculations Workshop Yuxin Qian 090422

Overview: • Formulas: provided and other important • Solutions, Compounding, and Dose related • Pharmacokinetics • Pharmacy financial assessment • Statistics

• “give us some examples of the formulas provided in PEBC information booklet( which are provided in the EE exam)”

pH = pKa

log

pH = pKa

log

Salt Acid Base Salt

Rule of nines: I pH – pKa I = 1 ---- 90 : 10 I pH – pKa I = 2 ---- 99 : 1 I pH – pKa I = 3 ---- 99.9 : 0.1

• What is the pH of the solution containing 0.5 moles of ephydrine and 0.05 moles of ephedrine HCl per liter of solution? (pKb = 4.56)

pH = pKa

log

pH = pKa

log

Salt Acid Base Salt

Base is not in the Basement (bottom) --- it is on the top; Acid at the bottom

• MANON SHROFF CALCULATIONS

Provided Formulas

•

The volume V of isotonic solution that can be prepared from W g of drug is obtained by solving this equation

• • •

W: the weight of the drug E: NaCl equivalent value 111.1 = 100/0.9

•

How much sodium chloride is required to render 100ml of a 1% solution of apomorphine hydrochloride isotonic with blood serum? ( Sodium Chloride Equivalent E = 0.14 ) 1. Weight of drug: 100 x 1% = 1.0 g 2. V = W x E x 111.1 = 1 x 0.14 x 111.1 = 15.55 ml 3. Dissolve 1g of apomorphone hydrocloride in 15.5 ml of water and make up this solution to 100ml with 0.9% sodium chloride solution.

Provided Formulas

• 1st order reaction

• 0 order reaction

Provided Formulas

Loading dose

0.693 Vd t1/2 = Estimating drug clearance (Cl):

Clt

For linear pharmacokinetic drug clearance and normal renal function

Provided Formulas

IV infusion Multiple dose: Accumulation Rate

1 e

kT

R = e

kT

f =

Fraction remaining in the body after a dosage interval

DL = DM 1

e

kT

If DM is given at a dosage interval equal to the elimination half-life of the drug: DL = 2 DM

Other Important Formulas Young's Rule (for children >2 years) dose

Clark's rule---weight (child aged 2-17) Weight in pound x adult dose Dose f or child = 150 lb (avg wt of adult)

Fried's rule for infants

Child’s dosage based on Body surface area (BSA)

Ideal Gas:

PV = nRT

P1V1 / T1 = P2V2 / T2

Calculations related to Solutions • Prepare Desired Concentrations; • Tonicity Solutions: – Freezing point – Sodium chloride equivalents:

• Molarity/Molality • mEq

Allegation Problems •

Example 1: A pharmacist has a 70% alcoholic elixir and a 20% alcoholic elixir. He needs a 30% alcoholic elixir to use as a vehicle for medications. In what proportion must the 70% elixir and the 20% elixir be combined to make a 30% elixir?

• How many grams of CaCl2 are required to prepare a 480 mL solution that contains 200 meq of Ca2+? (mw CaCl2 = 111 g/mole)

• MANON SHROFF CALCULATIONS

Normality (N) / Molarity (M) / Molality (m)

• Normality (N): the presence of number of gram equivalent weight of solute in 1000 ml or (1L) solution; – For example, in a salt such as MgCl2 (1 M), there are two moles of Cl- for every mole of Mg2+, so the concentration of Cl- is said to be 2 N (read: "two normal").

Molarity (M) vs Molality (m) • Molarity (M) or molar concentration: the presence of number of moles of solute in 1000 ml or (1L) of solution; – A 0.5 molar solution contains 0.5 moles of solute in 1.0 liter of solution. – This is not equivalent to 1.0 liter of solvent: either slightly more or slightly less than 1 liter of solvent

• Molality (m): the presence of number of moles of solute in 1000 gm of solvent – the number of moles of solute per kilogram of solvent (not solution). – For instance: adding 1.0 mole of solute to 2.0 kilograms of solvent constitutes a solution with a molality of 0.50 mol/kg.

Isotonic solutions • When 1 g mol wt (M-weight) of any nonelectrolyte is dissolved in 1000g of water, the freezing point of the solution is depressed by 1.86 ℃; • Freezing point depression of body fluids: - 0.52 ℃; • So, the amount needed for preparing isotonic solution: X = 0.52 × (M-weight) / 1.86 g

Isotonic solutions Sodium chloride equivalents • Dissociation values (i) considered as 80% dissociated in weak solutions: two ions (NaCl) 1.8; three ions (CaCl2) 2.6; four ions 3.4 • 0.9% NaCl is an isotonic fluid; – Calculated the mass of NaCl represented by all ingredients; – and the mass of NaCl required to prepare an equal volume of isotonic solution; – Based on the difference between those two masses, calculate the NaCl equivalent for the prescription component.

• How many mg of NaCl are required to prepare 250 mL of 1% boric acid solution to isotonic with eye tears? (The freezing point of boric acid is – 0.29 ℃; FP of 0.9% NaCl - 0.58 ℃; FP of body fluids: - 0.52 ℃)

• MANON SHROFF CALCULATIONS

Compounding and Dose • W/W • Parts • Displacement value: DV in suppositories • Dose related: – Abbreviations: tid, bid, qd; o.u., a.s. – Infusion rate:

How many grams of base are required to dispense 20 suppositories of boric acid each weighing 2 g and containing 500 mg of boric acid (Displacement value of boric acid = 1.5)

• MANON SHROFF CALCULATIONS

• Chloroquine can be used for prevention of malaria in areas where the parasite is still sensitive to this drug. Smith’s family (two adults and two 8 years old children) are going to central America for 8 weeks and they get a prescription of chloroquine: it should be used 2 week before exposure; continue weekly for 4 week after leaving the endemic area; 7-10 y (150mg base once/week); adults (300 mg base once/week). How many chloroquine needed for their trip (mg)? (Therapeutic choices p1456)

Ans: (2× ×300 + 2× ×150) ×(2 + 8 + 4) = 900 ×14 = 12600 mg

• 250 mg/500 mL Rocephine solution should be administered to a patient weighing 155 lbs. The recommended adult dose of drug is 1.5 mcg/kg/min. What would be rate of flow in mL/min?

• MANON SHROFF CALCULATIONS

Pharmacokinetics • Half-life: • Shelf-life: • K: constant rate • Estimated GFR • Clearance

• Loading Dose • Infustion rate • Css

Provided Formulas

Loading dose

For IV infusion

0.693 Vd t1/2 =

Clt

These formula can help us to solve most of the pharmacokinetic questions

• The initial concentration of a drug is 500 mg/mL, and turns into 50 mg/mL after 90 mins. What is the rate of constant if it is followed by first order kinetic?

• MANON SHROFF CALCULATIONS

• The initial concentration of a drug is 0.002M,. What is the half-life if it is followed by 2ed order kinetic? (rate of constant K = 7 liter/mole min)

• MANON SHROFF CALCULATIONS

Michaelis–Menten equation The Michaelis? enten equation describes how the reaction rate v depends on the position of the substrate-binding equilibrium and the rate constant k2. Michaelis and Menten showed when k2 is much less than k-1 (called the equilibrium assumption) they could derive the following equation: The Michaelis-Menten equation will appear first order when the substrate concentration [S] 0 away from the mean μ (dark blue) • 2 σ from the mean account for about 95% (medium and dark blue) • 3 σ account for about 99.7% (light, medium, and dark blue) • This is known as the "68-95-99.7 rule" or the "empirical rule."

First Aid for the USMLE Step 1 2008

First Aid for the USMLE Step 1 2008

Condition (as determined by "Gold standard") Positive

Negative

Positive

True Positive

False Positive (Type I error, P-value)

→ Positive predictive value

Negative

False Negative (Type II error)

True Negative

→ Negative predictive value

↓ Sensitivity

↓ Specificity

Test outcome

First Aid for the USMLE Step 1 2008

First Aid for the USMLE Step 1 2008

Calculator used in the exam

Units Transferring • • • • • • • •

1 gr = 65 mg ( avoir. = apoth.) 1 lb (pound) = 454 g (avoir.); 373 g (apoth.) 1kg = 2.2 lb (avoir.) 1 fluid dram = 1 teaspoonful = 5 ml 1 fluidounces = 30 ml 1 pint = 480 ml 1 cup = 240 ml = 8 fl. oz. 1 gallon = 3840 ml = 8 pt = 4 qt

Final Tips • Using The Provided Formulas to remember related Equations • Be Careful in calculation; • Unit transferring: L / hour to mL / min • Be prepared and take all the marks in this part !!!

References

•

MANON SHROFF CALCULATIONS

•

CPR chapter 2, 6, 36

•

Reference Guide for Foreign Pharmacy Licensing Exam Questions and Answers, by Manan H. Shroff, R. Ph, Krisman

Thanks

[email protected]