dd5- pm session final (1) handout
TRANSCRIPT
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Pharmaceutical Calculations
FTY Leads
FTY 2021/2022 | Development day 5: PM session
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Aim• To provide practice opportunities for the
range of calculation types encountered within the CRA, namely:–dilutions– infusion rates–displacement values–displacement volumes
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Learning outcomesHaving completed this session, you will be able to:üDevelop strategies to answer the range of different
calculation question types, namely:– dilutions– infusion rates– displacement values– displacement volumes
üRecognise the importance of accuracy when completing these calculation questions
üAppreciate the need to work efficiently to answer these question types within the CRA
üRecap on common errors with calculations
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Performance Standards
C1.5 Perform calculations correctly
10.2.3 Ensuring that safe and effective systems are in place to manage the risk inherent in the practice of pharmacy and the delivery of pharmaceutical services
• Use pharmaceutical calculations to verify the safety of doses and administration rate (High)
CRA Framework
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CRA:Approved calculators for Part 1
Casio MX 8B-WE / MX 8B
(in black or white)
Aurora HC133
Aurora DT210
*Unapproved calculator models are NOT permitted in the assessment
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Common mistakes –recap!
Not reading
the question properly
Using the wrong
units
Decimal point in
the wrong place
Rounding errors
Running
out of time
Illogical answers
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Pre-requisite worksheet
• 11 questions • Topics covered during DD1 PM session–Estimations of kidney function–Dose and dose regimens–Dosage and unit conversions–Concentrations–Molecular weight–Pharmacokinetics–Using provided formulae–Health economics–Quantity to supply
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1. Estimations of kidney function
You have been asked to calculate the creatinineclearance for a 34-year-old woman who weighs 57.1kg. Her most recent serum creatinine is 161 micromoles/L. Using the formula provided below, calculate the creatinine clearance, in L/hour, to one decimal place
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1. Estimations of kidney function
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2. Dose and dose regimens
A 6-year-old girl has been prescribed fluorometholone eye drops. The prescription contains the following directions: Instil one drop in the right eye every hour for the first 48 hours, including during the night, and then instil one drop four times a day thereafter.If there are 20 drops in 1 mL, how many full days will one bottle containing 5 mL ophthalmic solution last?
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2. Dose and dose regimens
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3. Dosage and unit conversions
Mrs G is a 64-year-old woman with stage IV lung cancer. She is currently using a 125 microgram/hour fentanyl patch which is to be switched to an equivalent dose of modified release oral morphine. Local palliative care guidelines show 125 microgram/hour fentanyl is equivalent to 300 mg per 24 hours of oral morphine.
The guidelines state that for the first 24 hours, half the calculated equivalent dose of oral opioid should be given since the transdermal opioid will take time to be cleared from the plasma and subcutaneous reservoir. After 24 hours, the dose can be increased to the calculated equivalent dose if clinically indicated by pain.
According to the local palliative care guideline described above, what is the total dose of morphine, in mg, which Mrs G will take in the first 72 hours of oral opioid therapy?
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3. Dosage and unit conversions
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4. Concentrations
A pharmacist is mixing 65 g of 0.025% w/w betamethasone with 85 g of 0.05% w/w betamethasone. What is the concentration, in % w/w, of betamethasone in the final mixture? Give your answer to two decimal places.
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4. Concentrations
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5. Molecular weight
How many grams of potassium chloride are needed to prepare 6.75 L of a solution containing 16 mmol of potassium ions per 20 mL? Give your answer to one decimal place. [atomic weight of potassium = 39; atomic weight of chlorine = 35.5]
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5. Molecular weight
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6. Pharmacokinetics
A drug is administered by IV infusion and immediately after administration, its plasma level is calculated to be 318mcg/mL. If the drug’s half-life is 9 hours, what will the plasma concentration be, in mcg/mL, after 45 hours? Give your answer to two decimal places.
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6. Pharmacokinetics
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7. Using provided formulaeA 7-year-old girl (31 kg) has been brought into A&E suffering from asthma, and a decision is made to initiate treatment with theophylline. The desired steady-state concentration is 15 µg/mL. The apparent volume of distribution (Vd) for theophylline is 0.5 L/kg.
Using the formula and information above, what would be the most appropriate intravenous loading dose, in mg? Give your answer to one decimal place.
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7. Using provided formulae
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8. Health economicsYou are reviewing the use and cost of venlafaxine XL capsules:
Venlalic® XL 75 mg Tablets £11.20 per 84 tablets Efexor® XL 75 mg Capsules £22.50 per 30 capsules
You have reviewed 14 patients who are prescribed Efexor® XL Capsules 75 mg OD and have identified that 9 of them can potentially switch to Venlalic® XL Tablets 75 mg OD. The practice repeat prescribing policy is for 56 days of treatment per prescription. Using the information above, what is the total saving for the practice for 4 repeats assuming all 9 suitable patients switch to using Venlalic® XL Tablets? Give your answer to the nearest pound.
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8. Health economics
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9. Health economics
According to local guidelines, apixaban has been shown to be a more effective medication than warfarin for stroke prevention. A local GP practice would now like to switch all patients on their disease register from warfarin to apixaban.
*NNT for drug of interest vsaspirin in stroke prevention
How many more patients will potentially gain the benefit of apixaban if all patients on the register are switched from warfarin to apixaban?
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9. Health economics
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10. Health economicsA practice with a list size of 20,000 has agreed to support the CCG initiative in switching some patients on quetiapine modified release tablets to quetiapine immediate release tablets. The average prices for a 2-month (60 day) supply are shown below:
Having completed a search, it is found that 1% of patients registered at the practice are prescribed quetiapine modified release tablets as a once daily dose. The practice pharmacist reviews these and finds that only 10% of these patients on quetiapine modified release are clinically stable to be switched to immediate release, at an equivalent twice daily dose. Calculate the saving, in £’s, which can be achieved over a 60-day period by completing the switch at the practice for all suitable patients.
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10. Health economics
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11. Quantity to supply
A new patient has been admitted into one of the care homes to which you supply medication. The home requires you to supply 30 days of his liquid medicines to cover his stay. He usually takes amantadine 100 mg twice daily. The syrup comes as 50 mg/5mL in a 150 mL bottle. What is the correct amount of amantadine syrup, in litres, to supply for 30 days treatment? Give your answer to the nearest 0.1 L.
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11. Quantity to supply
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CRA:Types of pharmaceutical
calculationsDoses and dose
regimensDosage and unit
conversionsEstimations of kidney function
Displacement volumes and
values
Concentrations (eg. expressed as w/v, % or 1 in X)
Dilutions Molecular weight Using provided formulae
Infusion rates Pharmacokinetics Health economics Quantities to supply
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Type of pharmaceutical calculations
There are 4 types of pharmaceutical calculation included within the CRA that we will consider during this webinar.
1. Dilutions2. Displacement Values3. Displacement Volumes4. Infusion Rates
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DilutionsDilution is the process of decreasing the concentration of a solute in solution, by adding a solvent such as water.
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Let’s have a look…
If 10 g of active ingredient was dispersed in 100 mL of liquid (i.e. 10% w/v) it would have a different concentration compared with 20 g of active ingredient being dispersed in 100 mL of liquid i.e. 20% w/v.
Dilutions
100mL
100mL
10g
10g
10g
10% w/v
20% w/v
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The dilution factorThe dilution factor is the ratio of:
Stock solutions are an example of concentrated solutions.
If 1mL of a concentrated solution is diluted with 9mL of solvent, it produces 10mL of dilute solution. The dilution factor would be 1:10 or 1 in 10. We could also say the concentrated solution had been diluted 10 times.
1mL conc. soln
9mL solvent
1:101 in 10
Diluted 10 times
vol of the conc soln: vol of the dilute soln
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Dilutions method (1)C1 X V1 = C2 X V2
In questions where you already have been provided with three of the four variables, and you are asked to calculate the missing volume or concentration, the above formula can be used.
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Dilutions method (1)C1 X V1 = C2 X V2
Let’s practice:
You have been asked to prepare a 10% v/v skin cleaning solution for Mrs W, a regular patient of yours.
How many mL of water must be added to 250 mL of 20% v/v solution in order to produce the 10% v/v solution?
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In this question, we are given two concentrations and one volume. We are then asked to find the missing volume. Let’s add the known values into the formula:
V2 = 250 mL x 20% = 500 mL 10%
The question asks how much water must be added to 250mL, therefore we must deduct that as shown below, to give us the final answer:
500 mL – 250 mL = 250mL
Dilutions method (1)
C1 X V1 = C2 X V220% X 250mL = 10% X V2
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Dilutions method (2)
Another method which you may find helpful is drawing flasks to help visualise the scenario in the question.For example: You are required to provide 500 mL of a Potassium Chloride solution such that when diluted 1 in 20 it produces a 1 in 500 solution. You have Potassium Chloride concentrate 25% w/v in stock.
What volume of concentrate, in mL, is required to produce your initial solution?
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Dilutions method (2)
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You have received a prescription for 250 mL of levothyroxine oral suspension for a patient in hospital. You have in stock are all the items required, except the levothyroxine 2% w/v, which you only have available as levothyroxine 3.75% w/v. The suspension is to be prepared according to the following formula:
§ Levothyroxine (2% w/v) 10 mL§ Citric acid monohydrate 2.5 g§ Poloxamer 188 0.2 g§ Potassium sorbate 0.3 g§ Propylene glycol 2.1 mL§ Purified water up to 20 mL
What volume of levothyrozine 3.75% w/v, in mL, will you need to prepare the prescription? Give your answer to one decimal place.
Dilutions – example 1
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Dilutions – example 1 answer
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In your pharmacy you have a stock solution of drug X with a concentration of 15.7% w/v. Drug X is used as a mouthwash at a concentration of 0.0125% w/v.
You are requested to supply 300 mL of a solution of intermediate strength, such that the patient will dilute this solution 1 in 15 to get the correct concentration immediately before use.
What is the concentration (% w/v) of the intermediate solution? Give your answer to two decimal places.
Dilutions – example 2
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Dilutions – example 2 answer
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Displacement values
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Displacement valuesThe displacement value (DV) is a measure of the amount of active substance that displaces 1g of base.This value is largely dependent on the density of the active ingredient and so will be different depending on the drug in question. • For example, a DV of 0.9 means that 0.9g of the drug
displaces 1g of base
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Displacement values method
The DV formula can be used to calculate the amount of suppository base required, as shown below:
Total base(g) = (no. of suppositories x mould size) – Total drug (g) DV
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Displacement values method
So, let’s have a look at how to use the DV formula.
You are preparing a batch of 40 suppositories, each weighing 1.5 g. The suppositories are each to contain 250mg active ingredient and the displacement value of the active ingredient is 1.9.
Calculate the total quantity of suppository base, in grams, required to prepare the 40 suppositories. Give your answer to one decimal place.
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Total base(g) = (no. of suppositories x mould size) – Total drug (g) DV
Total base (g) = (40 suppositories x 1.5g mould size) – 10g 1.9
Displacement values method
What information does the question give us?• No. of suppositories = 40 • Mould size = 1.5 g• Each suppository contains 250mg active
ingredient, therefore 40 x 250 mg = 10,000 mg (or 10g) active needed, total drug = 10g
• DV = 1.9 which means that 1.9 g of active ingredient displaces 1 g of base.
Total base (g) = (40 supps x 1.5 g) - 10g / 1.9 Total base (g) = 57g
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Displacement values –example 1
You receive a prescription for a 9-year-old child for 30 x 2.5 g suppositories, each containing codeine phosphate 30 mg. The prescriber would like you to preparethe suppositories extemporaneously. Youfind the displacement value of codeinephosphate is 2.1 and work out a formula tomake the 30 suppositories, plus a 30%overage, using Witepsol as the base.
What quantity of Witepsol, in grams, isrequired to make the full quantity ofsuppositories, including the overage? Giveyour answer to one decimal place.
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Displacement values –example 1 answer
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Displacement values – example 2
You have been asked to prepare 15 ibuprofen suppositories for a 2-year-old child. Each suppository should be prepared in a 1 g mould and contain 60 mg of ibuprofen. The displacement value of ibuprofen is 1.2 and the base to be used is hydrous polyethylene glycol. You plan to make a 20% overage to account for any losses during preparation.What weight of hydrous polyethylene glycol, in grams, will be required to prepare all suppositories, including the overage? Give your answer to one decimal place.
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Displacement values –example 2 answer
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Displacement volumes
The displacement volume is the amount of solvent displaced by a specified amount of a solid.
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Displacement volumes –method
The displacement volume for midazolam in water is 0.27 mL per 10 mg. This means that 10 mg of midazolam will displace 0.27mL of water.
It therefore follows that 100 mg of midazolam will displace 2.7mL of water (0.27mL x 10) and 1,000 mg (1 g) of midazolam will displace 27mL of water (0.27mL x 100). This means that 1g of midazolam has the same volume as 27mL of water.
100mL10mg
100.27mL
100mL1000mg
127mL
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Displacement volumes –example 1
A vial containing 150 mg hydrocortisone sodiumsuccinate powder for injection is to be reconstituted toproduce 2.25 mL of injection. The displacement volumeof hydrocortisone sodium succinate is 0.1 mL/25 mg.
How much water, in mL, should be added to thepowder? Give your answer to two decimal places.
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Displacement volumes –example 1 answer
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Displacement volumes – example 2
In order to produce 100 mL of a mixture containing 250mg of amoxicillin in each 5 mL dose, the pharmacist isrequired to add 74 mL of water to the antibiotic powdermix.
Calculate the displacement volume for a quantity ofpowder equivalent to 250 mg of amoxicillin. Give youranswer to one decimal place.
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Displacement volumes – example 2 answer
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Infusion rates
Infusions allow medication to be administered constantly for a set period of time. Infusions are set at a flow rate that gives the required dosage per hour or minute.
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Infusion rates –method
A 10-year-old boy is in A&E with accidental iron poisoning. Treatment with desferrioxamine mesilate infusion is prescribed at a dose of 20mg/kg/hour for the first 6-8hrs. The child weighs 30kg.
What is the maximum dose of desferrioxamine mesilate infusion, in grams, that can be administered over the first 360 minutes of treatment? Give your answer to two decimal places.
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1. Calculate the amount of drug required per hour:Dose of drug for the first 6-8 hours is 20mg/kg/hour. 20mg/hour x 30kg = 600mg/hour 2. Calculate the amount of drug which will be administered over the given time frame:The question asks how many grams will be given in 360 minutes = 6 hours (6 x 60 mins) 600mg/hour x 6 hrs = 3,600mg
Answer: 3,600mg = 3.6g = 3.60g to two decimal places
Infusion rates –method
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Infusion rates – example 1
Mr D is prescribed digoxin to be administered at adose of 12.5 mcg/kg/hr. Available in the dispensary isa 500 mL infusion bag containing 2,000 microgramsdigoxin. Mr D weighs 80 kg.
Calculate the drop rate to be given assuming 0.05 mLequals one drop. Give your answer in drops perminute to the nearest whole number.
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Infusion rates – example 1 answer
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Infusion rates – example 2
An 81-year-old woman has a percutaneous endoscopic gastrostomy (PEG) tube in situ. She requires 1,800 kcal per 24 hours from her enteral feed and has been instructed to use Ensure® Compact which contains 240 kcal per 100 mL. For convenience, she would like to feed for 9 hours overnight.
At what rate, in mL/hour, should the feed be delivered? Give your answer to the nearest 10 mL.
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Infusion rates – example 2 answer
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Practice and practise and keep on practising!
Checkyou answered the question that was asked.
you used the correct units and number of decimal places in your answer.
your answer makes sense in real life.
Don’t overcomplicate
the question or your method of calculating the answer.
and keep the process as simple as possible.
and use a method you are comfortable with and have practiced
Identify the numbers and other information which you need from the question.
Read every question very carefully - at least twice.
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Summaryü There are 4 types of pharmaceutical calculation questions
covered in this webinar:§ Dilutions § Displacement values§ Displacement volumes§ Infusion rates
ü Common errors when completing pharmaceutical calculationsinclude:§ Not reading the question properly§ Incorrect rounding§ Incorrect level of precision§ Incorrect units§ Time pressure§ Illogical answers
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• Development day 611th (G1) 12th (G2) 13th (G3) January 2022• Pre-requisites available on
the FTY hub from 21st
December 2021• Complete mandatory eLearning by
31st December 2021• Controlled drugs: striking
a balance (8 hours) • The responsible
pharmacist (3 hours)• The EU General Data
Protection Regulation (2 hours)
• Appraisal 2• Reflective Learning Cycles -
progress
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