Mathematical Aspects of Intravenous Therapy

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Mathematical Aspects of Intravenous Therapy

• Simon Shah
• Pharmacy Department

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General Points

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

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Units

• 1kg contains 1000g
• 1g contains 1000mg
• 1mg contains 1000 micrograms
• 1 microgram contains 1000 nanograms
• 1l contains 1000ml

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Concentrations

• Different ways of expressing concentration
• Weight in volume
• Units in volume
• Percentages
• Molar
• Ratios

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Infusions

• Giving IV drugs by infusion requires two
  separate stages
• Preparation
• Administration

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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.

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Infusion Preparation

• Two main methods
• Amount of drug added individualised to patient
• Standardised solutions

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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?

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• 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

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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

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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

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• 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

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• 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)

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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)

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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

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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

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• 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?

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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!