Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, People's Republic of China.
Faculté de pharmacie, Université de Montréal, Montréal, QC, H3C 3J7, Canada.
J Pharmacokinet Pharmacodyn. 2018 Oct;45(5):693-705. doi: 10.1007/s10928-018-9599-4. Epub 2018 Jul 9.
Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis-Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.
具有内源性来源的药物通常表现出一级和米氏消除的同时作用，在药代动力学建模中变得越来越常见。在本文中，我们研究了单剂量静脉推注的一室模型情况。基于先前引入的超越函数，我们能够对该模型的浓度时间过程进行分析，并对其成分进行药代动力学解释。使用校正浓度的概念，还给出了浓度时间曲线下部分和总面积（AUC）的数学表达式。讨论了校正浓度和 AUC 的影响，以及在外源部分存在内源性产生时的外源性部分的相对贡献。本研究从理论上阐明了所考虑的药物化合物的几个药代动力学问题，并为合理估计其药代动力学参数提供了指导。
