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Mathematical Aspects of Intravenous Therapy

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Mathematical Aspects of Intravenous Therapy. Simon Shah. Pharmacy ... pethidine 50mg/ml or 100mg/2ml. Units in Volume. Unit is a measure of biological activity ... – PowerPoint PPT presentation

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Title: Mathematical Aspects of Intravenous Therapy


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
  • 1w/v 1g in 100ml (1000mg in 100ml)
  • 5w/v 5g in 100ml (or 50g/l)
  • 0.9w/v 900mg in 100ml (or 9g/l)
  • Potassium Chloride
  • 15w/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 its in
    (ml)
  • the amount you have (mg)

23
Adrenaline 11000
  • 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 11000 (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. Dont 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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