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