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 (C_max), time to achieve C_max (or T_max), 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 T_max or C_max may be used for assessing the rate of absorption. But estimation of the rate of absorption with T_max or C_max is not always feasible, as explicit solutions relating T_max and C_max to the absorption (k_a) and elimination rate (k) constants exist only for the one and not multicompartmental oral model. Therefore, the determination of T_max or C_max 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 T_max and C_max 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 (k_a < β) models. Simulations showed that the C_max and T_max 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 T_max and C_max.