A drug with a volume of distribution of 42 L is administered as an intravenous bolus. Its plasma clearance is 70 mL/min. The steady-state plasma concentration (Css) during a continuous infusion at 14 mg/hr is closest to:

• A 3.3 mcg/mL ✓
• B 6.6 mcg/mL
• C 1.7 mcg/mL
• D 0.83 mcg/mL

Explanation

At steady state, the rate of drug input equals the rate of elimination. Css = Infusion rate / Clearance. CL = 70 mL/min = 4200 mL/hr = 4.2 L/hr. Infusion rate = 14 mg/hr. Css = 14 mg/hr / 4.2 L/hr = 3.33 mg/L = 3.33 mcg/mL, approximately 3.3 mcg/mL. This formula applies when steady state is reached (after approximately 4-5 half-lives); volume of distribution determines the time to reach steady state (t½ = 0.693 × 42 / 4.2 = 6.93 hr, so ~35 hours to steady state).

Reference: KD Tripathi, Essentials of Medical Pharmacology, 8th ed.

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