# GPhC registration exam: infusion calculations ## How should you prepare for infusion calculation questions? Try our five worked examples

Do you struggle with infusion calculations? Having a good grip on infusion calculations will not only help you pass the General Pharmaceutical Council (GPhC) exams, but it is key to delivering safe pharmacy care in whatever sector you practise.

There are four main areas that you need to focus on. First is your conversion of units eg converting between gram (g), milligram (mg) and micrograms (mcg). This can be confusing, so draw up a table and practice converting up and converting down between units.

Second, you need to understand the concept of concentration expressed in different formats and be able to use and convert different concentration notations eg 1 in X, mg/mL, % (w/v) and mmol/L.

Third is understanding the concept of dilution and dilution factors, as most infusions are used in diluted form; for example, a certain volume of active drug may be diluted with sodium chloride 0.9% (w/v) solution in the infusion bag. For infusion drugs that are presented in powder form, you would also need to understand the displacement volume and how it affects concentration after dilution.

The fourth and last concept to understand is that of rate of infusion. Rate in simple terms is the amount drug administered per given time and it can be expressed in different units eg mg/min, mcg/hr, mL/hr and so forth.

The starting point in infusion calculations is therefore an understanding of the key concepts outlined above, so that you can work out what is required of you. It is important, as always, to practise with as many different questions as possible and identify areas which you struggle with to improve on them. Below, we have worked out five infusion questions demonstrating how you would apply your knowledge to the given situation. Please feel free to use a method you prefer and, as always, we are happy to receive your feedback.

You can find more practice calculation questions and tips on how to prepare for the GPhC exam and chat with our pre-registration leads on the C+D Community.

Question 1: Salbutamol 5mg/5mL infusion

A seven-year-old boy weighing 23kg is due to receive salbutamol infusion at a rate of 2mcg/kg/min in glucose 5% (w/v). The infusion is made up by adding 10mL of salbutamol ampoules 5mg/5mL to 40mL of glucose 5% (w/v). What flow rate in (mL/h) would you set the infusion to deliver the prescribed dose? Give your answer to one decimal place.

It is important to read the question carefully. Note any pertinent information that you will need and any unit conversions that will simplify your calculation and help you get to the answer quickly. Now, make a note of the following before you proceed:

1. The final answer requires units of mL/hr, but the rate is expressed as 2mcg/kg/min and this automatically tells you that you would need at some point to convert rate to mL/hr from mcg/kg/min.
2. The rate is given as mcg/kg/min so you would need to convert it to mcg/min (using the weight provided), then convert it to mcg/h (using your knowledge of conversion of units) and eventually to mL/hr to match your final units in the question.
3. 10mL of salbutamol is added to 40mL of glucose 5% (w/v) so this is a dilution, and your final volume is 50mL (from 10mL + 40mL).
4. You are required to round to one decimal place so your knowledge of rounding should be up to date.

So now we can execute the calculations as follows:

Method 1:

1. Dilution factor = (10mL + 40mL)/10mL = 50mL/10mL = 5 x dilution
2. Rate = (2mcg/kg/min) x 23kg x 60 min/hr = 2760mcg/hr = 2.76mg/hr
3. Initial salbutamol conc = 5mg/5mL or 1mg/1mL; final conc (1mg/mL) / 5 = 0.2mg/mL
4. If 0.2mg = 1mL; 2.76mg = X; X/2.76 = 1/0.2; X = 2.76/0.2 = 13.8mL/hr

Method 2:

1. Salbutamol ampoule is 5mg/5mL = 1mg/1mL = 1000mcg/1mL
2. We know 10mL of salbutamol were added so if 1mL = 1000mcg; 10mL = X; X/10 = 1000mcg/1; X = 10,000mcg
3. We know the final volume of the infusion is 50mL (from 10mL salbutamol + 40mL glucose 5%)
4. So final concentration = 10,000 mcg/50mL = 200mcg/1mL
5. Rate = (2mcg/kg/min) x 23kg x 60 min/hr = 2760mcg/hr
6. If 200mcg = 1mL; 2760mcg = X; X/2760 = 1/200
7. X = 2760/200 = 13.8mL
8. Rate = 13.8mL/hr to one decimal place

Question 2: Vancomycin infusion

A 60-year-old man is to receive a 250mL infusion containing 750mg of vancomycin at a dose of 10mg/minute. Calculate the rate at which this infusion should be set to deliver the prescribed dose in mL/h.

The two key pieces of information to calculating infusions is knowing the final concentration and rate. This is straight forward if you know what you are looking for.

1. Concentration of vancomycin in infusion bag = 750mg/250mL = 3mg/1mL
2. Rate = 10mg/min = 10mg x 60 min/hr = 600mg/hr
3. If 3mg = 1mL; 600mg = X
4. X/600 = 1/3; X = 600/2 = 20mL/hr

Question 3: Time to run immunoglobulin infusion

A 62-year-old woman weighing 65kg is prescribed immunoglobulin 10% (w/v) 500mg/kg as follows; 1mL/kg/hr for 15 mins; 2mL/kg/hr for 15 mins; 4mL/kg/hr for 15 mins and 6mL/kg/hr to complete the infusion. Calculate the total infusion duration in minutes. Give your answer to the nearest whole number.

This is one of the hardest infusion questions. Proceed systematically as follows:

1. Total dose of immunoglobulin = 500mg/kg x 65kg= 32,500mg
2. 10% (w/v) = 10g/100mL = 10,000mg/100mL = 100mg/mL
3. 100mg = 1mL; 32,500mg = X; X/32 500 = 1/100; X = 32500 x 10/100 = 325mL
4. Calculate volumes for each given time interval as follows:
5. 1 mL/kg/hr for 15 mins = 1 mL/kg x 65kg/hr x 0.25hr= 16.25mL
6. 2 mL/kg/hr for 15 mins= 2 mL/kg x 65kg/hr x 0.25hr = 32.5mL and
7. 4 mL/kg/hr for 15 mins = 4 mL/kg x 65kg/hr x 0.25hr = 65mL
8. 5.6 mL/kg/hr to complete the infusion can now be calculated as follows:
9. Remaining infusion = 325mL - 16.25mL - 32.5mL - 65mL = 211.25mL
10. Final infusion rate = 6mL/kg/hr = 6mL/kg x 65 kg/hr = 390mL/hr
11. 390mL = 1h; 211.25mL = X; X/211.25 = 1/390; X = 0.541666667hr = 0.541666667 x 60 min = 32.5min

Total time = 15+15+15+32.5 = 77.5 min = 78 min to nearest whole number

Question 4: Midazolam infusion

A child weighing 8kg is receiving midazolam infusion at a rate of 0.5mL/hr. The infusion was prepared by withdrawing 9.6mL of midazolam 10mg/2mL and adding to 40.4mL of normal saline 0.9% (w/v). Express the dose the child is receiving in micrograms/kg/min. Give your answer to the nearest whole number.

As before, the two key pieces of information to calculating infusions is knowing the final concentration and rate.

Method 1: Using dilution factor

1. Dilution factor = (40.4mL + 9.6mL)/9.6mL = 50/9.6 = 5.2
2. Initial conc is 10mg/2mL or 5mg/1mL so final conc after dilution (5mg/1mL) / DF = (5/50) x 9.6/1mg/mL = 0.96mg/1mL = 48mg/50mL
3. Rate = 0.5 mL/hr
4. From 2 above, 0.96mg = 1mL; 0.5mL = X
5. X/0.5 = 0.96/1
6. X = 0.5 x 0.96 = 0.48mg = 480mcg/hr = 480mcg/60min = 8mcg/min
7. For an 8kg child, rate in mcg/kg/min = 8/8 = 1mcg/kg/min

Method 2:

1. Amount of midazolam added to normal saline = 10mg/2mL x 9.6mL = 48mg
2. Final volume after dilution = 9.6mL + 40.4mL = 50mL
3. Conc = 48mg/50mL = 0.96mg/mL
4. Rate given = 0.5mL/hr
5. From 3, 0.96mg = 1mL; 0.5mL = X
6. X/0.5 = 0.96/1
7. X = 0.5 x 0.96 = 0.48mg = 480mcg/hr = 480mcg/60min = 8mcg/min
8. For an 8kg child, rate in mcg/kg/min = 8/8 = 1mcg/kg/min

Question 5: Heparin infusion

A 70-year-old man weighing 70kg is receiving a maintenance dose of heparin at a dose of 20 units/kg/hr. An ampoule containing heparin sodium 25,000 units is made up to 50mL with sodium chloride 0.9% (w/v).  At what rate should the pump be set to deliver the correct dose in mL/hr? Give your answer to one decimal place.

The two pieces of information required to do this calculation are your rate and concentration. You need to proceed as follows:

1. Rate = 20 units/kg/hr = 20 units/kg x 70kg/hr = 1400 units/hr
2. Heparin concentration is 25 000 units/50mL = 500 units/1mL
3. From 2 above, 500 units = 1mL; 1400 units = X
4. X /1400 = 1/500
5. X = 1400/500
6. X = 2.8
7. Rate = 2.8mL/hr

As you can see from these five examples, it is very important to understand the question fully. You need to be comfortable with converting different units, visualise the dilution process and manipulate and convert different concentrations. Observe any rounding rules stipulated and be systematic in your approach. Lastly, practise on a wide range of questions. We hope you will find these examples useful and a good starting point.

Good luck!

Authors:

Luso Kumwenda: MSc Community Pharmacy (Cardiff), B Pharm Hons (Zimbabwe), Independent Prescriber, MRPharms, Mentor at UKBPA & RPS

Prof David R. Katerere: PhD Pharmaceutical Science (Strathclyde), Tshwane University of Technology, Platform Research Chair – Pharmaceutical and Biotech Advancement and Development in Africa (PbADA)

Acknowledgements: The questions were kindly provided by: Focus Pre-Reg Revision

Disclaimer: The questions and explanations presented here are for educational purposes only and do not replace your training, knowledge and application of professional judgement as a pharmacist or pre-reg or prov-reg pharmacist. The infusion calculations depicted here cannot be viewed to reflect the infusion calculations in real practice. Please consult the relevant Summary of Product Characteristics (SmPC) and clinical guidelines to inform your infusion calculations in practice. The views in this article are our own and do not represent the views of any organisations we are associated with.  