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 contains cefuroxime 750 mg as a powder. The practice label says to add 7.2 mL of sterile water; the powder adds 0.3 mL to the volume. What is the concentration C in mg/mL after reconstitution?
A vial holds 2000 mg of powder. You add 4.5 mL of diluent, and the powder adds 0.5 mL of volume. The prescription is 240 mg. Draw up the dose: what volume V do you give?
A child weighing 12 kg is prescribed 4 mg/kg of a drug. The stock solution contains 10 mg/mL. Draw up the dose: what volume V do you give?
The prescription is 4300 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 6 mg/L at 2 h and 1.5 mg/L at 7 h. Assume first-order elimination. Find the half-life t½.
Practice exercise (made-up values, not clinical guidance). A 95 kg patient takes oral aminophylline (S = 0.8, F = 1) every 12 h. The theophylline clearance is 0.05 L/kg/h. Each dose is 500 mg of aminophylline. Find the average steady-state level Css,avg.
Answer: C = 100 mg/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 = 0.6 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: V = 4.8 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 10 mL syringe every small line is 0.2 mL.
Answer: V = 0.43 mL
Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.
On this 1 mL syringe every small line is 0.01 mL.
Answer: t½ = 2.5 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 = 7.018 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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