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# Mathematical Aspects of Intravenous Therapy

Mathematical Aspects of Intravenous Therapy. Simon Shah Pharmacy Department. General Points. Use S.I. units at all times Grams (g) Milligrams (mg) Micrograms Nanograms Litres (l) Millilitres (ml). Units. 1kg contains 1000g 1g contains 1000mg 1mg contains 1000 micrograms

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## Mathematical Aspects of Intravenous Therapy

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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 1000 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. 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!

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