For an oral drug with ka and ke, under what condition will tmax occur after oral administration?

• A. ka < ke
• B. ka = ke
• C. ka > ke and dC/dt = 0; tmax ≈ (ln(ka) - ln(ke)) / (ka - ke)
• D. tmax occurs at t = 0

Answer: (C)

When a drug is absorbed and eliminated by first-order processes, the peak plasma concentration occurs when the rate of absorption equals the rate of elimination. Mathematically, that happens when dC/dt = 0, which for this system leads to a finite tmax only if the absorption rate constant is greater than the elimination rate constant (ka > ke). In that case, the time to peak is approximately tmax = [ln(ka) − ln(ke)] / (ka − ke).

If ka ≤ ke, there is no finite peak time: with ka = ke the peak would occur at infinity, and with ka < ke the concentration rises without a true maximum. The tmax at t = 0 would imply an immediate peak, which doesn’t happen because absorption takes time.