Pharmaceutical Calculations Dr Kathy Burnett Senior Lecturer in Pharmacy Practice University of Ulster

Learning Outcomes After attending today’s workshop you should be able to: Understand the main types of calculations covered in the pre-registration exam Competently perform examples of pharmacy related calculations Appreciate the format of the calculations section of registration exam

Why calculations? At least 1.5 million Americans are injured annually as a result of medication errors 10-fold dosing errors are common Peppermint Water PJ 1 Feb 2003 Vol 270 Pg 172 “If you have no confidence in maths, or are just no good at it, you can kill a patient” [Dr C Hall, Nursing Standard, 2004]

Pre-registration examination Calculations must be passed OPEN BOOK paper 20 questions Currently 80% pass mark Potentially 100% No room for errors – patients can be killed! Reference sources are the CURRENT BNF edition 70 (September 2015 – March 2016) and BNFC 2015-16

Question format False / true answer Determine which variable you are going to prove or disprove

Exercise 1

Question 1 1.25 g of potassium permanganate is required to produce 1 L of a solution such that 10 mls of this solution diluted to 250 mls gives a 0.01% solution suitable for wound cleansing.  0.01% = 0.01 g in 100mls = 0.025 g in 250 mls   0.025 g in 250 mls comes from 10 mls so there is 0.025 g in the 10 mls A 0.025 x x = 1000 x 0.025 = 2.5 g vol 10 1000 10 FALSE

Question 2 If 300 mls of a 15% solution is added to 200 mls of a 45% solution the resulting mixture is a 27% solution. Solution 1 A 15 x x = 45 g Vol 100 300 Solution 2 A 45 y y = 90 g Final amount A = 45 + 90 = 135 g Vol 100 200 Final volume = 300 + 200 = 500 mls Product A 135 z z = 27% Vol 500 100 TRUE

Question 3 The formula for Ammonia and Ipecacuanha Mixture BP is: Ammonium bicarbonate 200 mg Liquorice liquid extract 0.5 ml Ipecacuanha tincture 0.3 ml Concentrated camphor water 0.1 ml Concentrated anise water 0.05 ml Double-strength chloroform water 5 ml Water to 10 ml   You have been asked to prepare 12 bottles each containing 60 mls of the mixture. You only have concentrated chloroform water to use. It is appropriate to use 18 mls concentrated chloroform water to fulfil the order.

Question 3 To make 12 bottles x 60 mls = 720 mls Need 5 mls DS chloroform water in 10 mls, so will need 360 mls DS chloroform water for 720 mls   SS 1:40 DS 1:20 Conc 1:1 Concentrated chloroform water is therefore 20 x stronger than DS, so need to divide amount by 20 360 mls / 20 = 18 mls concentrated chloroform water required. TRUE Give out chloroform water handout if required

Question 4 A prescription reads: Prednisolone tablets, 30 mg daily for 7 days, then reduce by 5 mg every three days to a maintenance dose of 5 mg daily. To be reviewed at outpatient clinic on 5th April. The prescription is dispensed on 12th March It would be appropriate to dispense 91 x 5 mg prednisolone tablets to last from the first dose on dispensing day to the last dose on the day of the clinic appointment.

Question 4 30 mg = 6 x 5 mg tablets, etc. 6 x 7 days = 42 tablets   6 x 7 days = 42 tablets 5 x 3 days = 15 tablets 4 x 3 days = 12 tablets 3 x 3 days = 9 tablets 2 x 3 days = 6 tablets = 19 days treatment 12 March – 5 April = 20 days in March and 5 days in April = 25 days in total 1 x 6 days = 6 tablets Total = 42+15+12+9+6+6 = 90 tablets FALSE

Question 5 30 g of Diprosalic® ointment contains 0.9 g salicylic acid and 0.15 g betamethasone diproprionate.   Diprosalic® ointment contains 3% salicylic acid and 0.05% betamethasone (BNF pg 1025) 3% = 3 g in 100 g = 0.9 g in 30 g 0.05% = 0.05 g in 100 g = 0.015 g in 30 g FALSE

Question 6 A 3 month baby weighing 5.2kg has been prescribed 0.78 mls of Augmentin-Duo® twice daily. It is appropriate for you to contact the prescriber as this is an underdose.  BNF for children Augmentin-Duo® 0.15 ml / kg twice daily = 0.15 x 5.2 = 0.78 mls twice daily    FALSE

Question 7 A patient has an Atrovent® inhaler and his directions are 20 -40 mcg three to four times a day. He is going on holiday for six weeks and it is appropriate for you to advise the patient that he should take two inhalers on holiday with him.  Atrovent® inhaler 20 mcg has 200 doses (BNF pg 218) If patient needs maximum dose = 2 puffs four times a day = 8 puffs a day 8 x 42 days = 336 doses Two inhalers required  TRUE  

Question 8 You have been asked to prepare 300 mls of Magnesium Trisilicate Mixture BP. You will be required to use 12 g of light magnesium carbonate.   BNF Magnesium Trisilicate Mixture BP contains 5% light magnesium carbonate (BNF pg 61) 5% = 5 g in 100 mls = 15 g in 300 mls  FALSE

Question 9 A patient is receiving Nutriflex Lipid plus® 2500 ml infusion. The prescriber wishes to increase the potassium content of the bag to 80 mmol. It would be appropriate for you to suggest that 10 mls of Potassium Chloride Concentrate is added to the bag.  Nutriflex Lipid plus® 2500 ml contains 28 mmol K+ per litre = 70 mmol K+ (BNF pg 875) Need to add 10 mmol K+ Potassium chloride concentrate contains 20 mmol K+ per 10 ml (BNF pg 863) Add 5 mls Potassium chloride concentrate  FALSE

Question 10 A pharmacist adds 59 mls water to an antibiotic powder to produce 100 ml of a 125 mg / 5 ml solution. The displacement volume of the antibiotic powder is 9 mls per 125 mg antibiotic.  A 125 x x = 100 x 125 = 2500 mg Vol 5 100 5   Amount water displaced = 100 – 59 = 41 mls DV 41 y y = 125 x 41 = 2.05 mls per 125 mg antibiotic A 2500 125 2500 FALSE

Question 11 9.17g base is required to produce 10 x 1 g suppositories each containing 125 mg paracetamol given that the displacement value of paracetamol is 1.5.  10 suppositories will need 10 x 125 mg = 1250 mg or 1.25 g paracetamol 10 x 1 g base = 10 g base  Displacement value = weight of drug that displaces 1 g base Displacement amount: Paracetamol 1.5 1.25 x=1 x 1.25 = 0.833 g base Base 1 x 1.5  Therefore amount of base required = (10 x 1) – 0.833 = 9.17 g base  TRUE

Question 12 Lithium carbonate (RMM 74 g) is a prescription-only medicine, but if it is in preparations intended for internal use with a maximum dose of 5 mg (calculated as base) and a maximum daily dose of 15 mg (calculated as base) the preparation is a P medicine. A tablet containing 20 mg of lithium carbonate to be taken three times a day can be sold over the counter. Lithium base has a RMM of 14 g.   Base 14 x x = 20 x 14 = 3.78 mg – less than 5 mg Salt 74 20 74 so single tablet okay One tablet 3 times a day = 3 x 3.78 mg = 11.35 mg so daily dose okay TRUE

Question 13 A syringe driver contain 5 mls of injection Y and has a length of 60 mm. Injection Y is a strength of 5 mg/ml. If a patient needs to receive 3 mg of drug Y per hour, the syringe driver should be set at a rate of 7.2 mm / hr. Injection Y is 5 mg / ml = 25 mg within 5 mls syringe driver  Inj 25 3 x = 3 x 5 = 0.6 mls Vol 5 x 25  Mm 60 y y = 60 x 0.6 = 7.2 mm / hr Ml 5 0.6 5 TRUE

Question 14 A patient is given an intravenous dose of gentamicin and his one-hour peak serum concentration is found to be 13.5 mg/litre. Given that 10 hours later his serum concentration is 1.6875 mcg/mL the elimination half-life of gentamicin in this patient is 2.5 hours. (You can assume that the distribution is complete and the elimination is described by a 1st order process)   Peak = 13.5 mg/L = 13500 mcg/L = 13.5 mcg/mL 13.5------6.75-----3.375------1.6875-----0.84375 mcg/mL t0 t2.5 t5 t7.5 t10 hrs FALSE

Question 15 A consultant wishes to prescribe rifabutin for an immunocompromised patient for the prophylaxis of Mycobacterium avium infection. The patient is 37 years old, weighs 56 kg and is 1.68 m tall. On his medical notes you notice that the serum creatinine is 0.13 micromol / ml. It is appropriate for you to recommend 300 mg once daily for prophylactic treatment.   Body surface area (m2) = √ [ {wt (kg) x ht (cm)} / 3600] Creatinine clearance mL/min = constant x (140-age) x ideal wt (kg) serum creatinine (micromole/L)

Question 15 Constant = 1.04 (for women); 1.23 (men) creatinine = 0.13 micromole/mL = 130 micromole/L wt = 56 kg  creatine clearance = 1.23 x (140-37) x 56 =54.57 mL/min 130  Body SA = √ [ {wt (kg) x ht (cm)} / 3600]  = √ [ {56 x 168} / 3600] = 1.62 m2   Creatinine clearance = 54.57 mL/min for 1.62 m2 = 58.27 mL/min/1.73 m2  BNF (pg 507) If creatinine clearance is less than 30 mL/min/1.73 should half normal dose so this dose is fine for this patient TRUE

Exercise 2

Exercise 2 Answers 1 6 11 2 7 12 3 8 13 4 9 14 5 10 15