Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
Practice exercise (made-up values, not clinical guidance). A vial of penicillin G contains 5 000 000 units. Its practice label gives three strengths (see the table). You add 8.2 mL of diluent. The prescribed dose is 1 200 000 units. What volume V do you draw up? Round to one decimal place.
A vial holds 1000 mg of powder. You add 4.4 mL of diluent, and the powder adds 0.6 mL of volume. The prescription is 880 mg. Draw up the dose: what volume V do you give?
A patient weighs 18 kg. The prescribed dose is 7.5 mg/kg per day, given in 4 equal doses. How many milligrams D are given per dose?
An infusion contains 20000 units of a drug in 500 mL. The prescription is 1250 units per hour. At what rate R do you set the pump, in mL/h?
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 180 mg of tobramycin. The level back-extrapolated to time zero is 9 mg/L and the half-life is 2.5 h. Find the clearance CL in L/h.
Practice exercise (made-up values, not clinical guidance). A 74 kg patient takes oral theophylline (F = 1) every 12 h. The clearance is 0.04 L/kg/h. Each dose is 250 mg of theophylline. Find the average steady-state level Css,avg.
Answer: V = 2.4 mL
Reconstitution: the powder takes up space, so the final volume is the diluent plus the powder volume. Concentration = drug in the vial/final volume, and the volume to give = dose/concentration. On a multi-strength label, use the concentration that belongs to the amount of diluent you actually added. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: V = 4.4 mL
Strength to volume: turn the strength into mg per mL first. A w/v percentage is grams per 100 mL, so x% = 10x mg/mL. A ratio strength 1:n is 1 g in n mL. After reconstitution the concentration is the powder's dose over the final volume (diluent + powder volume). Then volume = dose/concentration.
Answer: D = 33.75 mg
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: R = 31.25 mL/h
Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.
Answer: CL = 5.545 L/h
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Answer: Css,avg = 7.038 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
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