What is the accumulation factor (R) for multiple dosing, and how is it calculated?

• A. R = e^(−kτ)
• B. R = kτ
• C. R = 1 / (1 − e^(−kτ))
• D. R = 1 − e^(−kτ)

Answer: (C)

The accumulation factor in multiple dosing measures how much drug builds up in the body when doses are given repeatedly before the drug is fully cleared. With first-order elimination, each dose leaves a portion that survives to the next dosing time, shrinking by e^(−kτ) each interval, where k is the elimination rate constant and τ is the dosing interval. If you add up the contributions from all previous doses, you get a geometric series: 1 + e^(−kτ) + e^(−2kτ) + …, which sums to 1 / (1 − e^(−kτ)). This is the accumulation factor. It tells you how much higher the steady-state concentration (or amount) is compared with the concentration after a single dose.

Interpreting the formula, R increases when the drug clears slowly (small k) or when dosing is frequent (small τ), leading to greater buildup. Conversely, as the dosing interval gets long relative to clearance, accumulation diminishes and R approaches 1. The terms e^(−kτ) and 1 − e^(−kτ) describe, respectively, the fraction remaining after each interval and the fraction eliminated between doses, not the total built-up amount from all prior doses, which is why they don’t represent the accumulation factor.