Mathematical Aspects of Intravenous Therapy
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Transcript 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
1 microgram contains 1000 nanograms
1l contains 1000ml
Concentrations
Different ways of expressing
concentration:
Weight in volume
Units in volume
Percentages
Molar
Ratios
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
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
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
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
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
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
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
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
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
Infusions
Giving IV drugs by infusion requires
two separate stages:
Preparation
Administration
Infusions - Doses
Dose of a drug given will depend on two
factors:
1. Concentration of infusion (mg/ml)
2. Rate of administration (ml/hr)
BOTH must be known for the dose to be
calculated.
e.g. 2ml/hr on a prescription means
nothing.
Infusion Preparation
Two main methods:
Amount of drug added individualised to
patient
2. Standardised solutions
1.
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?
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
Standard Solution Infusions
AMINOPHYLLINE INFUSIONStandardised 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
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
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
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)
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)
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
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
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?
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!