1. Mathematical Aspects of Intravenous Therapy
Simon Shah
Pharmacy Department

2. General Points Use S.I. units at all times Grams (g) Milligrams (mg)
Micrograms
Nanograms
Litres (l)
Millilitres (ml)

3. Units 1kg contains 1000g 1g contains 1000mg
1mg contains 1000 micrograms
1 microgram contains 1000 nanograms
1l contains 1000ml

4. Concentrations Different ways of expressing concentration:
Weight in volume
Units in volume
Percentages
Molar
Ratios

5. Weight in Volume Expressed as - grams/litre (g/l) mg/ml
e.g. dobutamine 250mg/5ml
digoxin 0.5mg/2ml
morphine 10mg/ml
pethidine 50mg/ml or 100mg/2ml

6. Units in Volume Unit is a measure of biological activity
i.e. 1 unit heparin is not equal to 1 unit of insulin.
Insulin 100 units/ml
Heparin units/ml
5000 units/ml
5000 units/0.2ml

7. Percentages 1%w/v = 1g in 100ml (1000mg in 100ml)
5%w/v = 5g in 100ml (or 50g/l)
0.9%w/v = 900mg in 100ml (or 9g/l)
Potassium Chloride
15%w/v = 15g/100ml = 1.5g/10ml
10ml also contains 20mmol

8. Molar Rarely used 1 molar = 1mole/litre
1 mole contains a certain number of molecules, electrolytes etc.
1 molar solution = 1000mmol/l
Often used by Biochemistry to report results e.g. Na 139 mmol/l

9. Ratio
Concentrations expressed as 1 in..... means 1g in however many mls
1 : 1 solution contains 1g/ml
1 : 1000 is 1/1000th of this
Adrenaline
1 : 1000 = 1g/1000ml or 1mg/ml
1 : 10,000 = 1g/10,000ml or 1mg/10ml
Exception –Tuberculin -ratio based on units

10. Other points Always make sure decimal points are preceded by a number
e.g. 0.5mg not .5mg
Always think carefully about calculations
Always get a check on calculations

11. Calculations - Volumes
Volume required is based on proportions.
What you want (Dose) x Volume you have(ml)
What you have (Amount in vial)
e.g. morphine 10mg/ml. Dose required = 15mg
Volume required = 15mg x 1ml = 1.5ml
10mg

12. Gentamicin 80mg in 2ml Dose prescribed is 140mg
What volume do you need?
You want 140mg x It is in 2mls
You have 80mg
= 3.5ml

13. Aminophylline 250mg in 10ml Dose prescribed is 210mg
What volume is required?
You want 210mg x it is in 10ml
You have 250mg
= 8.4ml

14. Infusions Giving IV drugs by infusion requires two separate stages:
Preparation
Administration

15. Infusions - Doses Dose of a drug given will depend on two factors:
Concentration of infusion (mg/ml)
Rate of administration (ml/hr)
BOTH must be known for the dose to be calculated.
e.g. 2ml/hr on a prescription means nothing.

16. Infusion Preparation Two main methods:
Amount of drug added individualised to patient
Standardised solutions

17. Individualised Infusions
AMINOPHYLLINE INFUSION
(Vials available as 250mg/10ml)
A 60kg patient is to receive an aminophylline infusion at a rate of 0.5mg/kg/hr for 24 hours
How much aminophylline injection (250mg/10ml) would you add to 1L of fluid and what rate would you set the pump at?

18. 0.5mg/kg/hr = 30mg/hr = 720mg in 24 hrs
720 x 10 = 28.8ml
250
Add 28.8ml to 1L infusion fluid
1 litre over 24 hours = 42ml/hr

19. Standard Solution Infusions
AMINOPHYLLINE INFUSION-
Standardised solution.
e.g. 500mg in 500ml, i.e. 1mg/ml
Dose is 30mg/hr therefore rate is 30ml/hr
Easier to adjust rate if dose changes
Standardisation of preparation between nurses

20. Dobutamine 250mg in 5ml
A 60kg patient is currently receiving dobutamine at a rate of
8 micrograms/kg/min...
How would you prepare the solution
at what rate would you set the syringe pump?
Use a standard solution = 250mg/50ml

21. Standard solution preparation 250mg/50ml
Dose
= 60 x 8 = 480 micrograms/minute
= 480 x 60 = 28,800 micrograms/hour
= 28,800/1000mg/hour
= 28.8mg/hr

22. Infusion Concentration = 250mg in 50ml
Dose = 28.8mg/hour
Infusion Concentration = 250mg in 50ml
Rate = 28.8mg/hour x 50ml = 5.8ml/hr
250mg
i.e. the rate you want (mg/hr) x volume it’s in (ml)
the amount you have (mg)

23. Adrenaline 1:1000
How would you prepare a 50ml infusion of adrenaline 0.2mg/ml
it needs to be added to a 50ml syringe
Amount = Concentration x Volume
= 0.2mg/ml x 50ml = 10mg in 50ml
= 10ml of 1:1000 (1mg/ml)

24. Glyceryl Trinitrate 50mg/10ml
How would you prepare a 0.1mg/ml infusion of GTN?
needs to be added to a 500ml polyfusor
Amount = Concentration x Volume
= 0.1mg/ml x 500ml
= 50mg in 500ml polyfusor
= 1 x 10ml ampoule

25. Heparin Heparin is to be given at a dose of 30,000 units/day
How would you prepare the solution and what rate would you use?
Use a 1000unit/ml solution e.g. Pump-Hep

26. Use a 1000unit/ml solution
Draw up 30ml into syringe. Don’t dilute.
30,000 units/24 hours = 1250 units/hour
1250 units = 1.25ml therefore rate = 1.25 or 1.3ml/hr
What if the dose is increased to
40,000 units/day?

27. Summary Different units may be used Different uses of same calculation
Doses depend on concentration and rate
Use standard solutions if possible
Calculate carefully
Get a check - redo calculation
If not sure - Ask!