Finding T max and C max in Multicompartmental Models.

Drug absorption data are critical in bioequivalence comparisons, and factors such as the maximum drug concentration (Cmax ), time to achieve Cmax (or Tmax ), as well as the area under the curve (AUC) are important metrics. It is generally accepted that the AUC is a meaningful estimate of the extent of absorption, and Tmax or Cmax may be used for assessing the rate of absorption. But estimation of the rate of absorption with Tmax or Cmax is not always feasible, as explicit solutions relating Tmax and Cmax to the absorption (ka ) and elimination rate (k) constants exist only for the one and not multicompartmental oral model. Therefore, the determination of Tmax or Cmax for multicompartmental models is uncertain. Here, we propose an alternate, numerical approach that uses the point-slope method for the first and second derivative(s) of the concentration-versus-time profiles and the Newton-Raphson iteration method for the determination of Tmax and Cmax We show that the method holds for multicompartmental oral dosing under single or steady-state conditions in the absence of known microconstants, even for flip-flop (ka < β ) models. Simulations showed that the Cmax and Tmax estimates obtained with the Newton-Raphson method were more accurate than those based on the noncompartmental, observation-based method recommended by the US Food and Drug Administration. The %Bias attributable to sampling frequency and assay error were less than those determined by the noncompartmental method, showing that the Newton-Raphson method is viable for the estimation of Tmax and Cmax .