Time to Steady State — FRCA Primary MCQ

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ModeratePharmacology - General PrinciplesTime to Steady StateFRCA Primary

A constant-rate continuous intravenous infusion is started in a patient with no drug initially present. The drug follows linear, one-compartment pharmacokinetics with first-order elimination. Approximately how many elimination half-lives are required for the plasma concentration to reach 97% of its steady-state value?

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Reveal the answer and explanation

Correct answer: D — 5

Explanation lettering: E = shown as D · D = shown as E

The correct answer is E: 5 half-lives. During a constant-rate infusion with first-order elimination, concentration approaches steady state exponentially. The fraction attained after n half-lives is 1 - (1/2)^n. Thus, after five half-lives the concentration is 1 - 1/32 = 96.875%, approximately 97%. One, two and three half-lives produce 50%, 75% and 87.5%, respectively, so options D, A and C are too early. Seven half-lives would produce about 99.2%, making B unnecessarily late. The time required to reach a specified fraction of steady state depends on the relevant elimination half-life, not the infusion rate; however, the infusion rate determines the absolute steady-state concentration because at steady state the infusion rate equals the elimination rate.

Reference: Electronic Medicines Compendium. Empliciti 300 mg and 400 mg powder for concentrate for solution for infusion, Summary of Product Characteristics, section 5.2 Pharmacokinetic properties; last updated 30 January 2025. https://www.medicines.org.uk/emc/product/7722/smpc