Pharmaceutical Calculations Introduction Pharmaceutical calculations dealing with: Expressions of concentration Master formulae to working quantities Changing concentrations Small quantities ( trituration) Solubility Calculations related to doses Reconstitution and rates of infusion
How to minimize errors Write out the calculation clearly. Double check when transferring data from reference. Write down every step. Don t make short cuts. Try not to be totally dependent on your calculator. Double check your calculation. Expressions of concentrations - The metric system is the International System of Units (SI Units) for weight, volume and length. The basic unit for weight is kilogram (kg), for volume is liter (L) and for length is meter (m). - The avoirdupois (Imperial) {pound, grain, ounces, pints and fluid ounce & gallons). - The apothecary system: grain, scurple, drachm, minim, fluid drachm, fluid ounce. 1 kilogram (Kg)= 2.2 pounds (lb) 1 grain ( Avoir. Or Apoth.) = 64.8 mg 1 teaspoonful (tsp)= 5ml 1 table spoonful = 15 ml (3 teaspoonfuls) 1 pint (pt) = 473 ml 1 gallon (gal) = 3785 ml 1 fluid ounce (oz) = 29.57 ml ( 30ml) 1 fluid ounce ( oz) = 480 minims Example: A prescription is received for a dose of 10 grains of a drug. How many grams is the dose?
Expressions of concentration Expressions of strength: Ratio: is the relative magnitude of two like quantities thus 1: 10 = 1 part in 10 parts or 1g in 10g. Ratio strength: is the expression of a concentration by means ofa ratio, e.g 1:10. Percentage strength: is a ratio of parts per hundred, e.g. 10% Percentage weight in weight (w/w) Percentage weight in volume (w/v) Percentage volume in volume (v/v) Other expressions of concentration: Moles & molarity Molality. Normality. Expression Molarity Normality Molality Mole fraction Mole percent Percent by weight Percent by volume Percent weight-involume Milligram percent Symbol M N m X, N % w/w % v/v % w/v - Definition Moles (gram molecular weights) of solute in 1 liter of solution. Gram equivalent weights of solute in 1 liter of solution. Moles of solute in 1000 g of solvent. Ratio of the moles of one constituent (e.g. the solute) of a solution to the total moles of all constituents (solute and solvent). Moles of one constituent in 100 moles of the solution. Mole percent is obtained by multiplying the mole fraction by 100. Grams of solute in 100 g of solution. Milliliters of solute in 100 ml of solution. Grams of solute in 100 ml of solution. Milligrams of solute in 100 ml of solution.
Examples: Express 0.1% w/w as a ratio strength. Express 1:2500 as a percentage strength. How many grams of a drug should be used to prepare 240 grams of a 5% w/w solution. If 5 g of iodine is in 250 ml of iodine tincture, calculate the percentage of iodine in the tincture. If 20 ml of ethanol is mixed with water to make 40 ml of solution, what is the percentage of ethanol in the solution? What is the percentage of magnesium carbonate in the following syrup? Magnesium carbonate 10g Sucrose 820g Water, q.s. ad 1000 ml Compute the percentage of the ingredients in the following ointment: Liquid parafin 14 g Soft parafin 38 g Hard parafin 12 g
Calculating quantities from a master formula Quantities provided by the master formula have to be scaled up or down, depending on the quantity of the product required. Using proportion or a multiplying factor. BA-FP-JU-C 6/28/2015 Calculating quantities from a master formula When a combination of weights and volumes is used without indicating the exact final volume or weight of the preparation: An excess quantity is normally calculated for and the required amount is then measured.
Calculations involving parts: The no. of parts is added up and the quantity of each ingredient calculated by proportion or multiplying factor to provide the correct amount. BA-FP-JU-C 6/28/2015 Calculations involving percentages Conventions which apply when dealing with formulae which include percentages: A solid in a formula where the final quantity is stated as a weight is calculated as weight in weight (w/w). A solid in a formula where the final quantity is stated as a volume is calculated as weight in volume (w/v). A liquid in a formula where the final quantity is stated as a volume is calculated as volume in volume (v/v). A liquid in a formula where the final quantity is stated as a weight is calculated as weight in weight (w/w).
some situations where the standard conventions do not apply: I. Syrup BP is a liquid-a solution of sucrose and water. If the normal convention applied it would be w/v, i.e. certain weight of sucrose in a final volume of syrup -However, in the BP formula the concentration of sucrose is quoted as w/w. Therefore Syrup BP is: Sucrose 66.7% w/w, Water to 100% 2. A gas in a solution is always calculated as w/w, unless specified otherwise. Formaldehyde Solution BP is a solution of 34-38% w/w formaldehyde in water.
Changing concentrations Increase or decrease the concentration by the addition of more drug or more diluent. The dilution equation: C 1 V 1 = C 2 V 2 e.g.1 What is the final concentration if 120 ml of a 12% w/v chlorhexidine solution is diluted to 240 ml with water? e.g.2 What percentage of atropine is produced when 200 mg of atropine powder is made up to 50 g with lactose as a diluent? Alligation A method for solving the no. of parts of two or more components of known concentration to be mixed when the final desired concentration is known. Calculate the amount of a 2% w/w metronidazole cream and of metronidazole powder required to produce 150 g of 6% w/wmetronidazolecream ( to 2 decimal places). Thioridazine suspension is available as 25mg/5ml ( 0.5% w/v) and 100 mg/5ml (2% w/v). Calculate the quantities to use to prepare 100ml of 40mg/5ml(0.8% w/v.) suspension
Calculations where quantity of ingredients is too small to weigh or measure accurately Small quantities in powder: Trituration: when a measurable quantity of active ingredient is diluted with an inert diluent. Normally a 1 in 10 or 1 in 100 dilution is used. Example: Calculate the quantities required to make 10 powders each containing 200 micrograms of digoxin. Assume that the balance available has a minimum weighable quantity of 100 mg. The convenient weight of each divided powder is 120 mg. Answer: The convenient weight of each divided powder is 120 mg. The total weight of powder mixture required will be 10 x 120 =1200 mg= 1.2g. Quantities for l0 powders: Digoxin2 mg, lactose 1198 mg, Total 1200 mg A 1 in l0 dilution is produced. Trituration A Digoxin100 mg, lactose 900 mg, Total 1000 mg Each 100 mg of this mixture (A) contains l0 mg of digoxin. Trituration B Mixture A 100 mg (= 10 mg digoxin), lactose 900 mg, Total 1000mg Each 100 mg of this mixture (B) contains 1 mg of digoxin. This amount of digoxinis less than the required amount, so mixture B can be used to give the required quantity. 200 mg of mixture B provides the 2 mg digoxinrequired. Final trituration(c) Mixture B 200 mg (= 2 mg digoxin) lactose (1200-200) = 1000 mg, Total 1200 mg Each 120 mg of this mixture (C) will contain 200 micrograms(0.2 mg) of digoxin.
Calculations where quantity of ingredients is too small to weigh or measure accurately Small quantities in Liquids: Normally a 1 in 10 or 1 in 100 dilution is used. Example: Calculate the quantities required to prepare 100 ml of a solution containing 2.5 mg morphine hydrochloride/5 ml. Assume that the balance available has a minimum weighable quantity of 100 mg. The solubility of morphine hydrochloride is 1 in 24 of water. Quantities for 100 ml: Morphine hydrochloride 50 mg Chloroform water to 100 ml. The minimum quantity of 100 mg of morphine hydrochloride is weighed and made up to 10 ml with chloroform water (this weight of morphine hydrochloride will dissolve in 2.4 ml). 5 ml of this solution (A) provides the 50 mg of morphine hydrochloride required. Take 5 ml of solution A and make up to 100 ml with chloroform 6/28/2015water. BA-FP-JU-C Calculating doses: Calculations involving doses e.g.1 The doctor prescribes levodopacapsules, 1000 mg to be taken every 8 hours for 28 days. Levodopa is available as 500 mg capsules. How many capsules should be supplied? e.g.2 The following prescription is received: Sodium valproate oral solution:100 mg to be given twice daily for 2 weeks. Note: Sodium valproate oral solution contains sodium valproate 200 mg/5ml.
Calculations involving doses Latin recipe mitte signa Ad aqua bis bis die bisin die terin die terde die quarter die quarter in die quantum sufficiat Abbreviation R x mitt. sig. ad aq. b. b.d. b.i.d. t.i.d. t.d.d. q.d. q.i.d. q.s. English name take send label to water twice Twice daily Twice daily Three times daily Three times daily Four times daily Four times daily sufficient Calculations involving doses Possibility of misinterpreting the data!!! Variation in terminology + lack of awareness serious consequences!!!!! The following prescription is received: Verapamil tablets 160 milligrams, Send 56, Take two tablets twice daily There are a variety of doses quoted for verapamil in the BNF depending on the condition being treated. They are as follows for oral administration. Supraventricular arrhythmias, 40-120 mg t.i.d. Angina, 80-120 mg t.i.d. Hypertension, 240-480 mg daily in 2-3 divided 6/28/2015 doses. BA-FP-JU-C
Calculations involving doses Different doses for children, an estimation of doses. Estimation of doses is best carried out using body weigh, but where this is not available, there are three formulas which relate the child's dose to the adult dose. Fried's rule for infants: age (months) x adult dose/150 = dose for infant. Clark's rule: weight (in kg) x adult dose/75 = dose for child. Body surface area method (BSA): BSA of child (m 2 ) x adult dose/l.73 m 2 BSA) = approximate child's dose. (average adult The BNF also gives a percentage method for calculating paediatric doses of drugs which have a wide therapeutic window, i.e. where accuracy is less critical. Calculation of doses by weight and surface area Using body weight: the dose will be expressed as mg/kg. The total dose required is then obtained by multiplying the weight of the patient by the dose per kilogram. Body surface area is a more accurate method when extreme accuracy is required for narrow range of plasma concentration between the desired therapeutic effect and severe toxicity, e.g. anticancer drugs. The body surface area can be calculated from body weight and height using the equation Body surface area (m 2 ) = Weight (kg) 0.425 x Height (cm) 0.725 x 0.007184
Reconstitution What dose of antibiotic will be contained in a 5 ml spoonful when a bottle containing 5g of penicillin V is reconstituted to give 200 ml of syrup? We have an ampicillin product for reconstitution. It contains 2.5g of ampicillin to be made up to 100 ml. To what volume should it be made to give 100 mg per 5 ml dose? Reconstitution A child weighing 60 lb requires a dose of 8 mg/kg of ampicillin. Given that a 5 ml dose is to be given, what volume of water must be added when the powder is reconstituted? Instructions on the label indicate that dilution to 150 ml (by adding 111 ml) gives 250 mg ampicillinper 5 ml. Conversion of weight to kg: 60/2.2 = 27.27 kg Calculation of amount of ampicillin required: 27.27 x 8 = 218 mg Calculation of amount of ampicillin in container: 250 mg/y mg = 5 ml/150 ml, therefore y= 7500 mg = 7.5 g Calculation of amount of water to add to give 218 mg per 5 ml: 218 mg/7500 mg = 5 ml/ x ml, therefore x= 172 ml Volume occupied by powder: 150 ml -111 ml = 39 ml 6/28/2015 Therefore, volume to be added: BA-FP-JU-C 172 ml-39 ml = 133 ml.
Calculation of infusion rates How much drug solution to be added? How fast the infusion should be administered (rate of infusion)? In terms of ml/min or drops per minute. An ampoule of flucloxacillin contains 250 mg of powder with instructions to dissolve it in 5 ml of water for infusion. What volume of this solution should be added to 500 ml of saline infusion to provide a dose of 175 mg? answer 3.5ml. 100 mg of methoxamine hydrochloride are added to 500 ml of saline infusion. What should be the rate of infusion to give a dose of 1 mg per minute? How long will the infusion take?
A doctor requires an infusion of 1000 ml of 5% dextrose to be administered over an 8-hour period. Using an IV giving set which delivers 10 drops/ml, how many drops per minute should be delivered to the patient? 20 ml of a drug solution is added to a 500 ml infusion solution. It has to be administered to the patient over a 5-hour period using a set giving 15 drops per millilitre, how many drops per minute are required?