Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.
How long does it take, approximately, for a drug given at regular intervals to reach a steady state?
Which strategy is most effective at preventing errors with IV insulin infusions?
A dose of 1000 mg is needed from a 20% (w/v) solution. What volume V contains this dose?
A patient is 111 cm tall and weighs 30 kg. The prescription is 25 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.
Practice exercise (made-up values, not clinical guidance). A patient receives an IV bolus of 230 mg of gentamicin. The level back-extrapolated to time zero is 12 mg/L and the half-life is 2 h. Find the volume of distribution Vd.
Practice exercise (made-up values, not clinical guidance). A 49-year-old woman weighs 62 kg and has a serum creatinine of 3.3 mg/dL (292 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 tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 100 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: C · 4 to 5 half-lives
With repeated dosing, the level approaches steady state after about 4–5 half-lives, whatever the dose. A loading dose can be used to reach it faster.
Answer: B · An independent double check and a smart pump with a drug library
Independent double checks, standard concentrations and smart pumps with dose limits reduce insulin errors. "U" for units is avoided because it can be misread as a zero.
Answer: V = 5 mL
Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.
Answer: D = 24.04 mg
Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).
Answer: Vd = 19.17 L
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 = 39.6 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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