A 50-year-old woman is admitted to the cardiac intensive care unit for management of recur… — USMLE Step 3

A 50-year-old woman is admitted to the cardiac intensive care unit for management of recurrent, hemodynamically stable ventricular tachycardia. The medical team initiates a continuous intravenous infusion of a novel antiarrhythmic medication. The pharmacology profile of this new drug indicates a volume of distribution ( $V_d$ ) of $100$ L and a systemic clearance ( $CL$ ) of $10$ L/hr. The drug follows first-order elimination kinetics. Assuming no loading dose is administered, approximately how long will it take for the drug to reach $94\%$ of its steady-state plasma concentration?

A
7 hours
B
14 hours
C
21 hours
28 hoursAnswer
E
40 hours

Answer

28 hours

The time required to reach a steady-state plasma concentration during a continuous intravenous infusion is determined exclusively by the drug's elimination half-life (

t_{1/2}

). First, calculate the half-life using the pharmacokinetic formula

t_{1/2} = \frac{0.7 \times V_d}{CL}

. Substituting the given values yields

t_{1/2} = \frac{0.7 \times 100}{10} = 7

hours. Under first-order kinetics, drug accumulation is exponential: it takes one half-life to reach

50\%

of steady state, two to reach

75\%

, three to reach

87.5\%

, and four to reach

93.75\%

(which rounds to

94\%

). Therefore, it requires

4 \times 7 = 28

hours to achieve the target concentration.

Step-by-Step Solution

Calculate the elimination half-life of the drug.

t_{1/2} = \frac{0.7 \times 100 \text{ L}}{10 \text{ L/hr}} = 7 \text{ hours}

The time to reach steady state is dependent entirely on the drug's half-life.

Determine the number of half-lives required to reach approximately 94% of steady state.

4 half-lives

The approach to steady state follows an exponential curve: 1 half-life = 50%, 2 = 75%, 3 = 87.5%, 4 = 93.75% (approximately 94%).

Calculate the total time required.

4 \times 7 \text{ hours} = 28 \text{ hours}

Multiply the calculated half-life by the number of half-lives required to reach the target concentration.

Key Concept

The time to reach steady-state plasma concentration depends solely on the drug's elimination half-life (

t_{1/2}

). It reliably takes 4 to 5 half-lives to reach a clinically relevant steady state (

\geq 94\%

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