The time to reach Css is about how many half-lives?

The time to reach Css is about how many half-lives?

• A. 3
• B. 4
• C. 6
• D. 5

Answer: (D)

When a drug is given by a constant-rate infusion and elimination follows first-order kinetics, the concentration in the body climbs toward the steady-state level (Css) in an exponential fashion. The time needed to get close to Css is tied to the drug’s half-life, because each half-life cuts the remaining gap in half. After n half-lives, the fraction of Css actually reached is 1 − (1/2)^n. So after five half-lives, you’re at about 1 − 1/32 = 31/32 ≈ 96.9% of Css, which is essentially at steady state. After four half-lives you’re at about 93.75%, which is close but not as close. Therefore the time to reach Css is about five half-lives.

When a drug is given by a constant-rate infusion and elimination follows first-order kinetics, the concentration in the body climbs toward the steady-state level (Css) in an exponential fashion. The time needed to get close to Css is tied to the drug’s half-life, because each half-life cuts the remaining gap in half. After n half-lives, the fraction of Css actually reached is 1 − (1/2)^n. So after five half-lives, you’re at about 1 − 1/32 = 31/32 ≈ 96.9% of Css, which is essentially at steady state. After four half-lives you’re at about 93.75%, which is close but not as close. Therefore the time to reach Css is about five half-lives.