Infusion Rate, Bag Count and a Protocol Cap
A 72-year-old patient weighing 84 kg is started on a continuous intravenous infusion of drug X at 15 micrograms/kg/min. The infusion is supplied as 400 mg of drug X in a 250 mL bag. Each bag costs £42. Bags are changed when empty or every 24 hours, whichever comes first; in practice this patient's bags empty well within 24 hours. Pharmacy stocks only 250 mL bags. Local protocol states that patients aged over 70 should receive no more than 12 micrograms/kg/min. The patient's renal function is stable and no other rate-altering factors apply.
1. Calculate the infusion rate in mL/hour at the prescribed dose.
Read the worked answer
Step 1 - dose per minute: 15 micrograms/kg/min × 84 kg = 1,260 micrograms/min.
Step 2 - convert to mg/hour: 1,260 × 60 = 75,600 micrograms/hour = 75.6 mg/hour.
Step 3 - concentration of the bag: 400 mg ÷ 250 mL = 1.6 mg/mL.
Step 4 - rate: 75.6 ÷ 1.6 = 47.25 mL/hour.
Check by proportion: 250 mL ÷ 1.6 mg/mL = 400 mg per bag; at 75.6 mg/hour a bag lasts 400 ÷ 75.6 = 5.29 hours.
2. How many bags are required for 7 days at this rate, and what is the drug cost?
Read the worked answer
Hours per bag: 250 mL ÷ 47.25 mL/hour = 5.291 hours.
Hours in 7 days: 7 × 24 = 168 hours.
Bags: 168 ÷ 5.291 = 31.75 → 32 bags (round up; a partly used bag cannot be carried over as a whole bag, and the 24-hour change rule is not reached).
Cost: 32 × £42 = £1,344.
Common error to avoid: rounding 31.75 down to 31 gives 31 × 5.291 = 164 hours and leaves the infusion short by four hours - a rounding error here becomes a missed dose, not just a wrong answer.
3. The prescription is corrected to the protocol maximum. Recalculate the rate and the 7-day bag count and cost, and state the percentage reduction in dose.
Read the worked answer
Rate at 12 micrograms/kg/min: 12 × 84 = 1,008 micrograms/min → × 60 = 60,480 micrograms/hour = 60.48 mg/hour → 60.48 ÷ 1.6 = 37.8 mL/hour.
Hours per bag: 250 ÷ 37.8 = 6.614 hours.
Bags in 168 hours: 168 ÷ 6.614 = 25.40 → 26 bags.
Cost: 26 × £42 = £1,092, a saving of £252 over 7 days.
Dose reduction: 12 ÷ 15 = 0.80, i.e. a 20% reduction in micrograms/kg/min - the same 20% applies to the mL/hour rate (47.25 → 37.8), because weight and concentration are unchanged.
Note the non-linear effect on bags: a 20% dose cut reduces bags by only about 19% (32 → 26), because each bag still has to be a whole bag.