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Hospital pharmacists often need to prepare complex drug montages to ensure accurate medication delivery to patients. Calculating these montages requires understanding drug concentrations, infusion rates, and patient-specific factors. Below are practical examples illustrating common calculation methods used in hospital pharmacy settings.
Example 1: Calculating an Aminoglycoside Infusion
A patient requires gentamicin at a dose of 5 mg/kg/day, administered intravenously in divided doses. The patient weighs 70 kg. The pharmacy prepares a 20 mg/mL stock solution. The goal is to prepare an infusion of 120 mg over 24 hours.
Step 1: Determine total daily dose
5 mg/kg/day × 70 kg = 350 mg/day
Step 2: Calculate infusion rate
To administer 350 mg over 24 hours: 350 mg ÷ 24 hours ≈ 14.58 mg/hour
Step 3: Prepare the infusion solution
Using a stock solution of 20 mg/mL: 14.58 mg/hour ÷ 20 mg/mL = 0.729 mL/hour
To prepare a 24-hour infusion: 0.729 mL/hour × 24 hours ≈ 17.5 mL
Example 2: Preparing a Vancomycin Loading Dose
A patient with a suspected severe infection needs a vancomycin loading dose of 25 mg/kg. The patient weighs 80 kg. The pharmacy has vancomycin powder with a concentration of 500 mg/20 mL when reconstituted.
Step 1: Calculate total dose
25 mg/kg × 80 kg = 2000 mg
Step 2: Prepare the solution
Reconstitute 500 mg vials according to manufacturer instructions. To obtain 2000 mg: 2000 mg ÷ 500 mg per vial = 4 vials.
Each vial contains 20 mL, so total volume: 4 vials × 20 mL = 80 mL.
Example 3: Continuous Infusion of Dopamine
A patient requires dopamine infusion at 5 μg/kg/min. The patient weighs 65 kg. The pharmacy prepares a solution with a concentration of 400 mg in 250 mL of Dextrose 5%.
Step 1: Calculate total dose per minute
5 μg/kg/min × 65 kg = 325 μg/min
Step 2: Convert to mg per minute
325 μg = 0.325 mg
Step 3: Determine infusion rate
In 1 hour: 0.325 mg/min × 60 min = 19.5 mg/hour
Concentration of solution: 400 mg / 250 mL = 1.6 mg/mL
Flow rate: 19.5 mg/hour ÷ 1.6 mg/mL ≈ 12.19 mL/hour
Conclusion
Calculating drug montages accurately is vital for safe and effective patient care. These examples demonstrate essential steps in determining infusion rates and preparing appropriate solutions. Always verify calculations and follow institutional protocols for medication preparation.