Patsatzis Dimitris G, Maris Dimitris T, Goussis Dimitris A
Department of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 157 73, Athens, Greece.
Bull Math Biol. 2016 Jun;78(6):1121-61. doi: 10.1007/s11538-016-0176-y. Epub 2016 Jun 8.
A detailed analysis is reported on a multiscale pharmacokinetic model, simulating the interaction of a drug with its target, the binding of the compounds and the outcome of their interaction. The analysis is based on the algorithmic computational singular perturbation (CSP) methodology. Among others, the analysis concludes that the partial equilibrium approximation and the quasi-steady-state approximation (PEA and QSSA) are valid in two distinct stages in the evolution of the process. Similar conclusions are reached from the algorithmic criteria for the validity of the QSSA and PEA. The reactions in the pharmacokinetic model that (i) generate the fast time scales, (ii) generate the constraints in which the system evolves and (iii) drive the system at various phases are identified, with the use of algorithmic CSP tools. These identifications are very important for the improvement of the model and for the identification of ways to control the evolution of the process. Regarding the qualitative understanding of the process, the present analysis systematises the findings in the literature and provides some new insights.
本文报道了对一个多尺度药代动力学模型的详细分析，该模型模拟了药物与其靶点的相互作用、化合物的结合以及它们相互作用的结果。该分析基于算法计算奇异摄动（CSP）方法。分析得出的结论包括，部分平衡近似和准稳态近似（PEA和QSSA）在过程演化的两个不同阶段是有效的。从QSSA和PEA有效性的算法标准也得出了类似的结论。利用算法CSP工具，确定了药代动力学模型中（i）产生快速时间尺度、（ii）产生系统演化所受约束以及（iii）在不同阶段驱动系统的反应。这些识别对于改进模型以及确定控制过程演化的方法非常重要。关于对该过程的定性理解，本分析系统化了文献中的研究结果并提供了一些新的见解。
