Pharmacy Calculations Workshop

Yuxin Qian090422

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)”

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

pH = logSalt

AcidpKa

pH = logSalt

BasepKa

• 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)

• MANON SHROFF CALCULATIONS

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

Acid at the bottom

pH = logSalt

AcidpKa

pH = logSalt

BasepKa

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

t1/2 =0.693 Vd

CltEstimating drug clearance (Cl):

For linear pharmacokinetic drug clearance and normal renal function

Provided Formulas

Multiple dose: Accumulation Rate

Fraction remaining in the bodyafter a dosage interval

f = e kT

R = e kT

IV infusion

DL = DM

1

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)

Fried's rule for infants

Ideal Gas: PV = nRT P1V1 / T1 = P2V2 / T2

Dose for child =Weight in pound x adult dose

150 lb (avg wt of adult)

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

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

t1/2 =0.693 Vd

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] << Km;

The Michaelis-Menten equation will appear zero order when Km << [S].

This is the basis for most single-substrate enzyme kinetics.

The Michaelis constant Km is defined as the concentration at which the rate of the enzyme

reaction is half Vmax.

Basic Pharcokinetics

One-compartment model

• Intravenous bolus injection:

– complete absorption; elimination : both followed first-order

• Single oral dose:

– absorption and elimination : first-order; T max depends on kA

and k

• Intravenous infusion:

– zero-order absorption; first-order elimination;

• Css steady-state concentration;

– esp useful for drugs with narrow therapeutic range.

Basic Pharcokinetics

One-compartment model

• Loading dose:

– DL = Css Vd or R/k ( R: the infusion rate; k: elimination rate constant)

• Some oral controlled-release drug:

– zero-order systemic absorption;

• Intermittent intravenous infusions:

– aminoglycoside (gentamicin), no Css

• Multiple doses:

– Dosing rate: D0 / τ (τ: interval between doses, or the frequency of

dosing)

– Certain antibiotics are given by multiple rapid intravenous bolus injections.

Cockcroft-Gault formula

Estimated GFR for Children using Schwartz formula

• ( Height in cm, SCr in mg /dL)

• K: constant that depends on muscle mass varies with a child's age;

• In first year of life, for pre-term babies K=0.33; for full-term infants K=0.45

• For children between ages of 1 and 12 y, K=0.55

• Estimated creatinine clearance rate (eCcr)

• What is the rate of infusion of phenytoin in a patient that requires steady state plasma concentration of 20 mcg/mL? The elimination half-life of phenytoin is 4 hours and an apparent volume of distribution is 15 L.

The rate of infusion can be calculated by the following formula:

• MANON SHROFF CALCULATIONS

Multiple IV bolus injections

Linear Plot of Cp Versus Time Showing Doses Every Six Hours

Linear Plot of drug concentration Versus Time

Provided Formulas

Accumulation Rate

Fraction remaining in the bodyafter a dosage interval

f = e kT

R = e kT

Cpmax and Cpmin

Multiple IV bolus injections

• An example: t1/2 = 4 hr; IV dose 100 mg every 6 hours; V = 10 liter; What

are the Cpmax and Cpmin values when the plateau values are reached?

• Cp fluctuate between 15.5 and 5.4 mg/liter

during each dosing interval when the plateau

is reached.

• A suitable DL: Cpmax • V = 15.5 x 10 = 155

mg as a bolus would give Cp = 15.5 mg/liter

• Followed by 100 mg every 6 hours to maintain

the Cpmax and Cpmin values at 15.5 and 5.5

mg/liter, respectively.

• A subject in whom the renal clearacne of inulin is 120 mL/min is given a drug, the clearance of which is 18 mL/min. If the drug is 40% plasma protein bound, what percentage of filtered drug must be reabsorted in the renal tubules?

A. 10% B. 12.5% C. 25% D. 50% E. 75%

• MANON SHROFF CALCULATIONS

Pharmacy financial assessment

• Inventory turnover,

• Gross Margin,

• Net Profit Margin;

• Price Markup and Elasticity

Reference Guide for Foreign Pharmacy Licensing Exam Questions and Answers, by Manan H. Shroff, R. Ph, Krisman (1000 Qs)

Efficiency: Inventory Turnover

IN TOR Inventory turnover rate; calculated by dividing the cost of the goods sold by the average

of beginning and ending inventroy. >6

NS:IN net sales to inventory: calculated by dividing the net sales by the inventory; >8

NS:NWCnet sales to net working capital: calculated by dividing the net sales by net working

capital(current assets minus current liabilities); 4 to 8

NS:NWnet sales to net worth: calculated by dividing the net sales by net worth(total assets total

liabilities); 3 to 8

A/R CTaccounts receivable collection time; calculated by dividing year end accounts receivable by

mean credit sales per day. It is a direct measure of efficient credit management. 30 days

A/R RTaccounts payable remitance time: calculated by year end accounts receivable devided by

mean purchases per day. 21 days

Gross profit margin

• Gross profit margin is a financial ratio used to assess the profitability of a

firm's core activities, excluding fixed costs.

• The general calculation is

• The gross profit margin is related to the net profit margin, which assesses

the profitability of an organization after including fixed costs.

• Indicates the relationship between net sales revenue and the cost of goods

sold. A high gross profit margin indicates that a business can make a

reasonable profit on sales, as long as it keeps overhead costs in control.

Liquidity and solvency

Acid test ratio

also known as Qucik test ratio; calculated by dividing the sum of cash and accounts

receivable by the current liabilities;

Acid test ratio = (Current assets －－－－

see above)

1:1 ratio represents a successful pharmacy; Current assets

Current ratio

CA:CL

The current ratio: dividing current assets by current liabilities; minimum standard value

would be 2

Inventory to Net working

capital

IN:NWC

dividing mean inventory (average of the beginning and ending inventory) by net working capital (unencumbered portion of current assets);

The higher the value, the lower the liquidity; normall value: 80-100%

Current assets Including Cash, accounts receivable, inventory

profitability:

"net profit"

net profit to net worth ratio is the best indicator;

the acceptable ratio for a 10 year old pharmacy : 15%, target value: 20%

NP:NSnet profit to net sales; the acceptable ratio: 5-7%

NP:NW

Return on investment

net profit to net worth; For a new pharmacies: 40%; 15% would be acceptable for old pharmcies

NP:TAReturn on asset investment

net profit to total assets; It is generally useful for a new pharmacies: 10-20%;

NP:INnet profit to inventory; It is generally useful for a new pharmacies: 10-20%; It is also a good indicator for efficiency of the pharmacy.

Profitability

Price Markup and Elasticity

• Elasticity: coefficient of elasticity E = Q / P

– Q: % of sales quantities change;

– P: % of price change).

• Pricing: – Rx: professional fee + cost price

– OTC: retail price = markup + cost price

– markup on cost or markup on retail price;

– Maintained markup = gross margin - cash discounts from suppliers;

Statistics

• Mean / Median / Mode

• Degree of freedom

• Range

( Chapter 2 CPR )

• What is the median of the following values?

120, 135, 140, 118, 175, 105, 115, 190

• Median: a middle value of an experiment;

• If the number of values are even, then the average of middle values should be considered

• So the first step: arrange the data in order

105, 115, 118, 120, 135, 140, 175, 190

The answer is 127.5

• What is the degree of freedom in a 4 X 3

contingency table in a Chi-square test?

• Equation: (R-1) X (C-1) = 3 X 2 = 6

Statistics

• Standard deviation (SD)

• Relative standard deviation (RSD, precision)

• Standard error of the mean (SEM)

• p value

• Confidence interval and Confidence region

• About 68% of values drawn from a normal distribution are within one

standard deviation σ > 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."

A plot of a normal distribution (or bell curve). Each colored band has a width of one standard deviation.

First Aid for the USMLE Step 1 2008

First Aid for the USMLE Step 1 2008

First Aid for the USMLE Step 1 2008

↓

Specificity

↓

Sensitivity

→ Negative predictive valueTrue NegativeFalse Negative

(Type II error)Negative

→ Positive predictive valueFalse Positive

(Type I error, P-value)True PositivePositive

Test

outcome

NegativePositive

Condition

(as determined by "Gold standard")

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

yuxinqian@hotmail.com