Abstract

Drug absorption data are critical in bioequivalence comparisons, and factors such as the maximum concentration (C_max), the 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 Tmax or C_max may be used for assessing the rate of absorption. But the 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 multi-compartment oral model. Therefore, the determination of T_max or C_max for multi-compartment models is uncertain. Here, we propose an alternate, numerical approach that uses the point-slope method for the first/second derivatives of the concentration vs. time profiles and the Newton Raphson iteration method for the determination of T_max and C_max. We show that the method holds for multi-compartmental 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 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 FDA. The %Bias due 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.