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 ampicillin 500 mg as a powder. The practice label says to add 1.8 mL of sterile water; the powder adds 0.2 mL to the volume. What is the concentration C in mg/mL after reconstitution?
A vial holds 2000 mg of powder. You add 4.2 mL of diluent, and the powder adds 0.8 mL of volume. The prescription is 1240 mg. Draw up the dose: what volume V do you give?
A patient weighs 60 kg. The prescribed dose is 7.5 mg/kg per day, given in 2 equal doses. How many milligrams D are given per dose?
An infusion contains 20000 units of a drug in 250 mL. The prescription is 1200 units per hour. At what rate R do you set the pump, in mL/h?
Practice exercise (made-up values, not clinical guidance). A 56 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 15 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.
Practice exercise (made-up values, not clinical guidance). A 43-year-old man weighs 89 kg and has a serum creatinine of 1.6 mg/dL (141 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 dose is 120 mg every 8 h for a creatinine clearance of 120 mL/min. Keeping the interval, the dose is reduced in proportion to the creatinine clearance. Find the adjusted dose D. Round to the nearest whole number.
Answer: C = 250 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 = 3.1 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 = 225 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 = 15 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: LD = 639.1 mg
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.
In practice the dose is rounded to a convenient amount.
Answer: D = 75 mg
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 dose is rounded to a convenient amount and checked against the product information.
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