Pharmacokinetics and Drug Calculations Flashcards

A drug has a half-life of 6 hours. How long does it take to reach 93.75% of steady-state concentration?

Answer: 24 hours (4 half-lives)

Steady state is reached in 4–5 half-lives. After each half-life: 50% → 75% → 87.5% → 93.75%. Four half-lives = 4 × 6 hours = 24 hours reaches 93.75% of steady state. Five half-lives reach 96.875% (approximately 97%). This principle applies regardless of the drug or dosing frequency.

A drug follows first-order kinetics. If the plasma concentration is 100 mg/L and the half-life is 4 hours, what is the concentration after 12 hours?

Answer: 12.5 mg/L

After 4 hours (1 t½): 100 → 50 mg/L. After 8 hours (2 t½): 50 → 25 mg/L. After 12 hours (3 t½): 25 → 12.5 mg/L. In first-order kinetics, the concentration halves with each half-life. Three half-lives = 100 × (0.5)³ = 100 × 0.125 = 12.5 mg/L.

What is the clearance (CL) of a drug if the volume of distribution is 42 L and the elimination rate constant (ke) is 0.1 h-1?

Answer: 4.2 L/hr

CL = Vd × ke = 42 L × 0.1 h⁻¹ = 4.2 L/hr. Alternatively, CL = 0.693 × Vd / t½ (since ke = 0.693/t½). Clearance describes the volume of plasma completely cleared of drug per unit time and is used to calculate maintenance dose.

A drug's oral bioavailability is 25%. If the IV dose required to produce a therapeutic effect is 100 mg, what oral dose provides the same systemic exposure?

Answer: 400 mg

Oral dose = IV dose / bioavailability = 100 mg / 0.25 = 400 mg. Bioavailability (F) represents the fraction of administered dose reaching systemic circulation. An F of 25% means only 1/4 of the oral dose reaches circulation, so 4 times more is needed orally compared to IV.

What does a high plasma protein binding (e.g., 99%) of a drug imply about its pharmacokinetics?

Answer: Only 1% is free (active) drug; small changes in protein binding have large effects on free fraction; displaced drug can cause toxicity

Highly protein-bound drugs have only a small free fraction available for pharmacological action. A small percentage change in protein binding (e.g., from 99% to 98%) doubles the free fraction (from 1% to 2%), potentially doubling activity/toxicity. This is especially important with narrow TI drugs like warfarin (99% protein bound).

A patient is given 500 mg of drug X intravenously. The initial plasma concentration measured immediately after injection is 10 mg/L. What is the volume of distribution?

Answer: 50 L

Vd = Dose / C₀ = 500 mg / 10 mg/L = 50 L. This is the apparent volume in which the drug is distributed at the initial concentration. A Vd of 50 L (approximately 0.7 L/kg for a 70 kg person) represents moderate tissue distribution beyond plasma (plasma volume = ~3 L, blood volume = ~5 L).