Pharmaceutical Calculations and Techniques PDF

PHARMACEUTICAL CALCULATIONS AND TECHNIQUES RICHIE G. BAYURAN, RPh, SMRIPh, MSPharm, PhDc Dean, School of Pharmacy Director, Institutional Research and Development Office OIC, Innov...

PHARMACEUTICAL CALCULATIONS AND TECHNIQUES RICHIE G. BAYURAN, RPh, SMRIPh, MSPharm, PhDc Dean, School of Pharmacy Director, Institutional Research and Development Office OIC, Innovation and Intellectual Property Management Office Certified Pharmacy Services NCIII Trainer, Technical Vocational Education SAINT GABRIEL COLLEGE PRESCRIPTION  Phone: 621-4454 DEA# AC-1273525 DEA Number Juan Dela Cruz Andagao, Kalibo, Prescriber Information Aklan Patient Information Name: Richie Bayuran Age: 37 Date: Address: Old Buswang, Kalibo, Aklan 5/3/2918 Date Rx was written Rx Phenobarbital. 0.015 Simethicone. 0.080 Superscription Magnesium CO3. 0.050 Inscription Ft #8 caps (Prescribed Medicines) Sig. 1 capsule bid Subscription (Direction to Pharmacist) Signa/Transcription Refill: …………. (Direction to Patient) Prescription should be handled with Special Instruction confidentiality Prescriber’s Signature Dispense as Written  PHARMACEUTICAL CALCULATIONS OBJECTIVES: After this module, PA’s should be able to: 1. Compute appropriate quantity of medicine to verify prescribed regimen of the doctor. 2. Refer incorrect quantities based on calculations to the pharmacist 3. Explain where necessary amount and dosage and name of drugs in prescription to customer. 18 EX 109g  Myrg 15 PET 12 TER 0.0109 9 GIGA 6 MEG 4 MYR 3 KILO 2 HEC 1 DEKA --BASE- (g/L/m) -1 DECI -2 CEN -3 MIL -6 MIC -9 NA -12 PIC -15 FEM -18 AT  RATIO AND PROPORTION Ratio and Proportion methodology can be used in solving most calculation problem in the pharmacy setting. A ratio states the relative size relationship between two quantities expressed as the quotient of one divided by the other. --------------------------------------- For example, if there are 5 g of dextrose in 100 mL of sterile water, you express the ratio as 5/100, or 5:100. A ratio is a mathematical expression that indicates a relationship of one part of a quantity to the whole.  RATIO AND PROPORTION A proportion expresses the relationship between two equal ratios. For example, a proportion may be expressed as two equal fractions: This expression would be spoken as “5 is to 10 as 15 is to 30.” The two inside terms in a proportion are called the means. The two outside terms in a proportion are called the extremes.  RATIO AND PROPORTION In the previous example, 5 and 30 are the extremes, and 10 and 15 are the means. In a proportion, the product of the means is equal to the product of the extremes. In the same example, 5 × 30 = 10 × 15 = 150 The usefulness of a proportion lies in the fact that if you know three of the four terms in a proportion, you can calculate the unknown fourth term. Proportion will be the single most useful tool that you will use for pharmaceutical calculations.  Solving Problems by the Ratio and Proportion Method The ratio and proportion method is an accurate and simple way to solve some problems. In order to use this method, you should learn how to arrange the terms correctly, and you must know how to multiply and divide. “Term #1 is to Term #2 as Term #3 is to Term #4.” Term #1 and Term #4 are the extremes and Term #2 and Term#3 are the means. By cross multiplying Term #1 with Term #4 and Term #2 with Term #3, the proportion can now be written as: Solving Problems by the Ratio and Proportion Method If you know any three of these terms, you can use this equation to solve for the unknown fourth term. A good way to set up your proportion is to always write what information you have (your first ratio) equal to what information you want (your second ratio). have = want  Sample problem How many grams of dextrose are in 10 mL of a solution containing 50 g dextrose in 100 mL of water?  Solution Set-up the proportion: have = want Cross multiply to get this equation: (parentheses indicate multiplication) Solve for x by dividing both sides by 100 mL:  Let us look at this one again and see the steps one by one: SOLUTION 50 : 150 : : 25 : 75 50 25 ---- = ---- 150 75  MEASURING SYSTEMS AND CONVERSIONS In order to safely prepare and accurately dispense the prescribed amount of medications to patients, you must be familiar with dosage calculations. A knowledge of the weights and measures used in the prescription and administration of medications is necessary. The systems of weights and measures used by health professionals, is mainly the metric system of measurement. There are other systems used in the pharmacy setting as well, such as the apothecary and household systems.  THE METRIC SYSTEM The metric system (also known as the International System of Units, or SI) is the most widely used system of measurement in the world. The accuracy and simplicity of the metric system lies in the fact that it is based on the decimal system, in which everything is measured in multiples or fractions of ten.  HOUSEHOLD SYSTEM OF MEASUREMENT Though inaccurate, the use of the household system of measurement is on the rise because of an increased home health care delivery. In this system, the patients use household measuring devices such as the teaspoon, dessertspoon, tablespoon, wine-glass, coffee cup, etc. HOUSEHOLD SYSTEM OF MEASUREMENT Common household measurement:  Sample Problem # 1 A Cefuroxime suspension contains 100mg/5mL of the drug. If the patient takes one teaspoonful of the suspension twice daily for ten day, how many grams of the drug does the patient consume? 5mlx2x10 = 100mL total dose 100mg/5mL 100mg mg --------- =----------- 5mL 100mL 2000mg --> 2g  Sample Problem #2 If a teaspoonful of Lagundi syrup is to be given three times daily for five days, how many bottles of 30mL should be dispense? one teaspoon is equal to 5ml hence, 5ml x 3 = 15mL daily And for 5 days, 15mL x 5 = 75mL was needed, Then, 75ml / 30mL (unit amount per bottle) = 2.5 or 3 bottles should be dispensed. Conversions and Equivalencies between Systems Conversions, or the changing of one unit of measure to another unit of measure such that they are equal, can easily be solved using ratios and proportions. SENIOR CITIZEN  SENIOR CITIZEN AND PWD DISCOUNT COMPUTATION STEPS IN COMPUTING AMOUNT BILLABLE TO SENIOR CITIZEN 1. Determine the amount of VAT Exempt Sale A senior citizen is exempted from paying Value-Added Tax (VAT). As such, you need to deduct the amount of VAT from the selling price. Here’s how to compute the VAT Exempt Sales to senior citizen: Selling Price: P1,000.00 VAT Rate: 12% Formula: VAT Exempt Sales = Selling Price ÷ 1.12 Computation: P1,000.00 ÷ 1.12 = P892.86 Note: This applies only if you’re company is VAT-registered. If you are NON-VAT registered, you can skip this step. The whole selling price will be considered VAT exempt sale. SENIOR CITIZEN AND PWD DISCOUNT COMPUTATION Deduct the 20% discount The 20% senior citizen discount will be computed from the VAT Exempt Sale. Here’s how to compute for the discount: Formula: Senior Citizen Discount = VAT Exempt Sale x 20% Computation: P892.86 x 0.20 = P178.57  SENIOR CITIZEN AND PWD DISCOUNT COMPUTATION Compute the billable amount Once you’ve figured the VAT Exempt Sale and the senior citizen discount, you may now compute the amount billable or collectible to senior citizen. Here’s how: Formula: Amount Collectible = VAT Exempt Sale – Senior Citizen Discount Computation: P892.86 – P178.57 = P714.29 PWD (Person with disability), by virtue of RA 10754 & RA 9442 with corresponding IRR’s implementing also imposes same discount.  SENIOR CITIZEN AND PWD DISCOUNT COMPUTATION Step 1. Compute for the VAT-exempted price Step 2. Perform discount on the VAT-exempted price SHORT CUT CONVERSION Ratio to % 2:450  % 2: 450  1:225 2 ------ x 100 = 0.44% 450 0.44%  ratio 100 ------ = 227.27 --> 1:227 0.44 1:3500  (1/3500)x 100 = 0.028%  ratio 100/0.028 = 3571 % mg% (x1000) 5% means 5g in 100mL  mg% 5x1000  5000mg%  g in 100 (%) 5000mg g mg%% (/1000) 5000mg%/1000mg= 5% %mg/mL (x10) 2.5%  mg/mL 2.5%x10 = 25mg/mL mg/mL% (/10) 25mg/ml divide 10 = 2.5% Ppm = parts per million Ppb = parts per billion 200ppm means 200g in 1,000,000  Ppm% (/10,000) (200/1,000,000) x 100 = 0.02%  DOSAGE CALCULATIONS Formula: X = (D/H) x Q Where: * X = unknown quantity of drug * D = desired dose * H = strength on hand * Q = quantity of solution/preparation/form’n Sample 1: Sample 2: A doctor prescribed 10mg Atorvastatin tablet to patients with hypertension which to be taken 3 times a day for 1 month. How many tablets should be dispensed? Desired dose (D) = 3 x 30days x 10mg = 900mg Quantity of preparation (Q) = 1 tablet Strength on hand (H) = 10mg Unknown quantity of drug (X) = ? Solution: X = (900mg / 10mg) x 1 = 90 tablets Sample 3: A prescription calls for 125mg/5mL Clarithromycin, with a dose of 125mg 3 times a day for 1 week. If the available preparation in the drugstore is 250mg/5mL in 50 mL bottle, how many bottles will you dispense? Solution: X=? D = 125 mg x 3 x 7days = 2,625 mg H = 250 mg Q = 5 mL X = (2,625mg / 250 mg) x 5 mL = 52.5 mL Since the available preparation of 250mg/5mL is in 50mL bottle, dispense 2 bottles, totally consume the 1st bottle and consume only 2.5mL of the second bottle. The rest will be discarded after 7 days if non-refrigerated and after 14 days if refrigerated. Seek the help from the pharmacist for proper disposal advice. 1.If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per hour, how many milligrams of medication are delivered per minute? 2.The biotechnology drug filgrastim (NEUPOGEN) is available in vials containing 480 micrograms (mcg) of filgrastim per 0.8 mL. How many micrograms of the drug would be administered by each 0.5 mL injection? 3.A prescription drug cost the pharmacist $42.00 for a bottle of 100 tablets. What would be the cost for 24 tablets? 1.If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per hour, how many milligrams of medication are delivered per minute? 15mg xmg ------- = ------- = 0.25mg 60mins 1min 1.The biotechnology drug filgrastim (NEUPOGEN) is available in vials containing 480 micrograms (mcg) of filgrastim per 0.8 mL. How many micrograms of the drug would be administered by each 0.5 mL injection? 480ug Xug -------- = --------- = 300ug 0.8mL 0.5mL 1.A prescription drug cost the pharmacist $42.00 for a bottle of 100 tablets. What would be the cost for 24 tablets? $42 X$ ----- = ------ = 10.08$ 100. 24  SUBMINIMUM DOSE MINIMUM DOSE OPTIMUM DOSE (AVERAGE DOSE) MAXIMUM DOSE TOXIC DOSE LETHAL (FATAL DOSE)  200mg  0.2g 10g/0.2g = 50 doses 180mL/5mL = 36tsp/18doses = 2tsp 2 x 2 x 15ml x 8days =480mL Rules (Child’s Dose) A(YR) BSA (PATIENT) YOUNG = ------------ X BSAR = ------------------------ AD x AD 12 1.73 sq. mtr A(YR)+1 COWLING= ------------ X AD 24 A (MONTH) FRIED = -------------- x AD 150 WT (lb) CLARK = ----------------- x  Patient Data: 17months FR = ---------------- x 250mg/kg = 28.33 Name: Alex Yu mg/kg Age: 1yr and 5months 150 44lbs Weight: 20kg  44lbs CkR = ---------------- x 250mg/kg = Height: 1’ 11” 73.33 mg/kg Adult Dose of Amox is 150 250mg/kg 58.42cm x 20kg Solve the Child’s Dose BSA = ----------------------- = 0.57 sqmt 1.41 3600 YR = -------- x 250mg/kg = 29.38mg/kg 12 0.57 1.41 + 1 BSAR = ---------------- x 250mg/kg = CR = -------------- x 250mg/kg = 82.37 mg/kg 25.1mg/kg 1.73 sqmt 24  1ft and 11 inch = 23inches 12 inches = 1ft 2.54cm = 1 inch 2.54cm 23 inches x ---------- = 58.42cm 1inch ‘ = foot “ = inch Seatwork Patient Profile: Name: Angela Tan Age: 3yrs and 4 months Height: 2’ 3” Weight: 35.5kg Adult Dose: Cefalexin 200mg/kg Solve the Child’s Dose using Young, Clark, Fried, Cowling and BSA’s Rule DILUTION  How much 10% w/w (in grams) ammonia solution can be made from 1800 g of 28% w/w strong ammonia solution? 1800 x 28 Q1 x C1 = Q2 x C2 ------------- = 5040mL 1800g x 28% = ? 10 X 10% How much (in milliliters) of a 1 : 5000 w/v solution of phenylmercuric acetate can be made from 125 mL of a 0.2% solution? 1/5000 x 100 = 0.02 = 1250mL 125mL x 0.2% = ? X 0.02 ISOTONICITY  Rx Sol.Silver Nitrate 0.5%  decimal (E=0.33) Make isotonic Solution. 15 ml Sig for eyes How many grams of NaCl should be used to make the prescription isotonic? S1: 0.005 x 15 = 0.075 x 0.33 = 0.0248g S2: 15 x 0.009 = 0.135g S3: (s2-s1) 0.135-0.0248 = 0.1103g  Rx Sol.Silver Nitrate 0.5% (E=0.33) Make isotonic Solution. 15 ml Sig for eyes How many grams of pottasium nitrate (E0.58) should be used to make the prescription isotonic? S1: 0.005 x 15 = 0.075 x 0.33 = 0.0248g S2: 15 x 0.009 = 0.135g S3: 0.135-0.0248 = 0.1103g S4: 0.1103 / 0.58 = 0.19g BODY MASS INDEX Additional Topic: Body Mass Index BMI = (182/5184) x 703 = 24.68 Calculate the BMI for a person weighing 182 lb and standing 72 inches in height. wtinlb BMI= -------------------- x703= (htininches)2  The adult dose of a drug is 250 mg. What would be the approximate dose for a 6 year old child weighing 60 lb? (Use Young’s Rule) PD = (6/6+12) x 250 = 83.33mg Acyclovir (zovirax) is administered in a dose of 15 mg/kg/day. How many milligrams of the drug must be administered daily to a 175 lb adult? 15mg. x ------- = ---------- = 1193.25mg 2.2 lb. 175lb  ALLIGATION MEDIAL ALLIGATION ALTERNATE Additional topic: (Alligation Medial) What is the final concentration of glucose solution obtained by mixing 100 ml of 5% w/v with 200 ml of 4% and 300 ml of 30% w/v? Q1 x C1 = Q2 x C2 100ml x 5 % = 500 ml-% 200ml x 4 % = 800 ml-% 300ml x 30 % = 9000 mL-% -------- --------------- 600ml 10,300ml-% 10,300ml-% / 600ml = 17.16% Additional topic: (Alligation Alternate) You are to mix 20% and 40% of zinc oxide ointment. To what proportion can these be mixed to obtain a 30% concentration 20 10 30 40 10 10 : 10 = 1:1 How much 5%, 50g of ZnO ointment and 25% ZnO, 40g ointment is needed to make 20% of ZnO ointment? 5 x 50 = 20 5% 5 parts of 5% (50g) x? = 12.5g from 20 5% 15 x 40 = 20 x ? 25% 15 parts of 25% (40g) = 30g from 25% 20 parts What is the final concentration of alcohol solution obtained by mixing 150 ml of 50% alcohol with 200 ml of 40% alcohol, 250 ml 70% alcohol, and 300 ml of 30% sugar solution? 150 X 50 33,000/900 = 36.67% 7500 200 X 40 8000 250 X 70 17500 300 X 0 0 ----- --------- PRESCRIPTION  In acute hypersensitivity reactions, 0.5 mL of a 1:1000 (w/v) epinephrine solution may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given. 1:1000 = (1/1000) x 100 = 0.1% 0.1g x ------ = --------- = 0.0005g x 1000 = 0.5mg 100ml. 0.5mL  In acute hypersensitivity reactions, 0.5 mL of a 1:1000 (w/v) epinephrine solution may be administered subcutaneously or intramuscularly. Calculate the milligrams of epinephrine given. 1:1000 = (1/1000) x 100 = 0.1% x 1000 = 100mg % 100mg x ---------- = --------- = 0.5mg 100ml 0.5mL What is the percentage strength (v/v) if 250 g of a liquid with a specific gravity of 0.8 is added to enough water to make 2 liters of the solution? 250/0.8 = 312.5 (312.5ml / 2000mL) x 100 = 15.625% PROOF GALLONS How many proof gallons are contained in 500 g of wine gallon of Diluted alcohol NF that contain 49 % (v/v) of pure alcohol? Proof= %x2 180proof/2 = 90% % = Proof/2 PG = (500WG x 49%) / 50 = 490proof gal MILLIEQUIVALENCE How many millilitres of a 10% KCL (MWt. 74.6) solution contain 5mEq of K+? 10% means 10g in 100 mL mEq = (mg x valence) / AW 10g = 10000mg mEq = (10000 x 1) / 74.6 = 134.05mEq/100ml 134.05 mEq in 100mL 5mEq 134.05 mEq -------- x. ----------------- = 3.73 mL ?mL 100 mL How many mL contains 2mEq of Ca++ if the bottle is labeled 1:20 CaCl2 in 50mL (MW:111g/mole) 1:20 = 5% in 50mL  5g  500mg mEq= (5000mg x 2) / 111 = 90.09mEq in 50mL 90.09 2 ------- = ------ = 1.11mL 50 x ADD-ON PROBLEMS A 44 kg child has been ordered to receive a dose of cortisone acetate. If the adult dose is 150 mg, what will the child’s dose be? (use Clark’s Rule) 44kg x 2.2lb = 96.8 (96.8 / 150) x 150 = 96.8 The concentration of mercury in a water sample is reported as 5 ppm. Express this concentration as a percentage. (5/1,000,000,000) x 100 = 0.0005% THERMOMETRY Wool fat is stated as having a melting point range of 36 to 42 degrees Celsius. Express this range in Fahrenheit. oF  oC (F – 32)/1.8 oC oF (C x 1.8) + 32 KoC K-273 oCK C+273 ADD-ON PROBLEMS What is the ratio strength of a trituration containing 120 mg of a hyoscine with 2.28 g of lactose? 120mg = 0.120g (solute) 2.28 g + 0.120 g = 2.4 g (solution) % = (0.12/2.4) x 100 = 5%  100/5 = 20  1:20 A 3 yr old child weighing 15 kg requires furosemide at a dose of 2 mg/kg daily. The only available preparation is an oral solution containing 10mg/ml of furosemide. What volume of the oral solution should be dispensed so the child has sufficient 28 days? 2mg x 28 days = 56mg 15 kg needs: 56mg x 15 = 840mg 840mg 10mg --------- x ------- = 84ml mL 1ml A syrup contains 7.5 % of potassium chloride (MWt.=74.5) How many millimoles of K+ are contained in 1 ml of this syrup? 7.5 g in 100 ml No. of moles = 7.5g / 74.5 g-mole = 0.1007 moles 0.1007m moles ----------- x ------------ = 0.001007 moles x 1000 100 mL 1mL =1.007mmoles Calculate the Body Mass Index (BMI) for a person measuring 1.7 meters in height and weighing 87 kilograms. 1.7 x 1.7 = 2.89 87/2.89  Density = Spgr. D=g/mL Spgr = unitless Convert 2.5g to mL; spgr of 0.985 Given = Needed 2.5g g --> mL / spgr mL -------------- = 2.54mL g 0.985 g/mL ----- g/mL 2.54mL  g 2.54mL x 0.985g/mL = mL  g x spgr g 2.5g mL x g/mL  SOLUTION AND CONCENTRATION  Solution Solute Solvent (being dissolved) (dissolves solute) %w/w = (wt of solute in g / wt of solution in g) (100) %w/v = (wt of solute in g / vol of solution in mL) (100) %v/v = (vol of solute in mL / vol of solution in mL) (100) Concentration: 1. What is the concentration in %w/v if 205g of NaCl is mixed with 350mL of distilled water. (NaCl Spgr = 1.95) Given: wt of solute NaCl = 205g vol of solvent = 350mL ml of solution=? %w/v = (wt of solute in g / vol of solution in mL) x 100 350ml water solvent 205g NaCl solute mL g-->mL 205g/1.95 = 105.13mL solute Solution: solute + solvent (105.13mL + 350mL) = 455.13mL %w/v = (205g / 455.13mL ) x 100 = 45.04%w/v 2. What is the amount of KCl needed if the formula calls for 5%w/v in 250mL of solution? wt of solute in g %w/v = ------------------------------ x 100 vol of solution in mL x 5% = ---------- x 100 5% --> dec = 0.05 x 250 250ml 12.5g KCl 3. Given the data: Weight of KOH = 35g Spgr 1.85 Volume of water = 95mL Spgr 1.00 Solve the concentration in %w/w, %w/v and %v/v Unit solute solvent solution g 35g 95g 130g mL 35g/1.85 = 95ml 113.92mL 18.92mL %w/w = (35g / 130g ) x 100 = 26.92%w/w %w/v = (35g / 113.92mL) x 100 = 30.72% w/v %v/v = (18.92mL / 113.92mL) x 100 = 16.61%v/v