Michalaki Lida I, Goussis Dimitris A
School of Chemical Engineering, National Technical University of Athens, 157 73, Athens, Greece.
School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 157 73, Athens, Greece.
J Math Biol. 2018 Sep;77(3):821-855. doi: 10.1007/s00285-018-1234-x. Epub 2018 Apr 19.
The multi-scale dynamics of a two-compartment with first order absorption Target-Mediated Drug Disposition (TMDD) pharmacokinetics model is analysed, using the Computational Singular Perturbation (CSP) algorithm. It is shown that the process evolves along two Slow Invariant Manifolds (SIMs), on which the most intense components of the model are equilibrated, so that the less intensive are the driving ones. The CSP tools allow for the identification of the components of the TMDD model that (i) constrain the evolution of the process on the SIMs, (ii) drive the system along the SIMs and (iii) generate the fast time scales. Among others, such diagnostics identify (i) the factors that determine the start and the duration of the period in which the ligand-receptor complex acts and (ii) the processes that determine its degradation rate. The counterintuitive influence of the process that transfers the ligand from the tissue to the main compartment, as it is manifested during the final stage of the process, is studied in detail.
利用计算奇异摄动（CSP）算法分析了具有一级吸收的双室靶介导药物处置（TMDD）药代动力学模型的多尺度动力学。结果表明，该过程沿着两个慢不变流形（SIMs）演化，模型中最强烈的组分在这些流形上达到平衡，从而使强度较小的组分成为驱动因素。CSP工具能够识别TMDD模型中的组分，这些组分：（i）在慢不变流形上约束过程的演化；（ii）沿着慢不变流形驱动系统；（iii）产生快速时间尺度。除此之外，此类诊断还能识别：（i）决定配体-受体复合物起作用时期的开始和持续时间的因素；（ii）决定其降解速率的过程。详细研究了在过程的最后阶段表现出的将配体从组织转移到主室的过程的反直觉影响。
