Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
How are most medication doses for children calculated?
A patient on long-term lithium passes large amounts of dilute urine and is always thirsty. What is the most likely explanation?
A vial contains 2 g of powder. The label says: add 7.4 mL of water for injection to give a total volume of 8 mL. The prescription is 100 mg. What volume V of the reconstituted solution do you give?
The prescription is 930 micrograms. The ampoule contains 1 mg/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 200 mg of tobramycin. The level back-extrapolated to time zero is 8 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 58-year-old man weighs 78 kg and has a serum creatinine of 2.4 mg/dL (212 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual gentamicin regimen is 80 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.
Answer: D · By body weight in kilograms, or sometimes body surface area
Children's doses are usually weight-based, sometimes using body surface area, and must not exceed the adult maximum. Accurate, recent weight in kilograms is essential.
Answer: D · Lithium blocks the kidney's response to ADH (nephrogenic diabetes insipidus)
Lithium interferes with ADH action in the collecting duct, causing polyuria and polydipsia. Dehydration from this can raise lithium levels further, so fluid balance matters.
Answer: V = 0.4 mL
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: V = 0.93 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.
Answer: CL = 6.931 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: τ = 25.9 h
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.
In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.
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