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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 units/ml 5000 units/ml 5000 units/0.2ml

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**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

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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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**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)

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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)

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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. 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?

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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!

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