@article {Handmd.118.082636, author = {Yi Rang Han and Ping I. Lee and K. Sandy Pang}, title = {A Commentary: Finding Tmax and Cmax in Multi-Compartmental Models}, elocation-id = {dmd.118.082636}, year = {2018}, doi = {10.1124/dmd.118.082636}, publisher = {American Society for Pharmacology and Experimental Therapeutics}, abstract = {Drug absorption data are critical in bioequivalence comparisons, and factors such as the maximum concentration (Cmax), the 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 the 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 multi-compartment oral model. Therefore, the determination of Tmax or Cmax 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 Tmax and Cmax. 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 Cmax and Tmax{\textquoteleft} 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 Tmax and Cmax.}, issn = {0090-9556}, URL = {https://dmd.aspetjournals.org/content/early/2018/08/22/dmd.118.082636}, eprint = {https://dmd.aspetjournals.org/content/early/2018/08/22/dmd.118.082636.full.pdf}, journal = {Drug Metabolism and Disposition} }