Yan Dingding, Wu Xiaotian, Tang Sanyi
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, People's Republic of China.
College of Arts and Sciences, Shanghai Maritime University, Shanghai, People's Republic of China.
J Pharmacokinet Pharmacodyn. 2022 Apr;49(2):209-225. doi: 10.1007/s10928-021-09794-5. Epub 2021 Oct 27.
Pharmacokinetics is a scientific branch of pharmacology that describes the time course of drug concentration within a living organism and helps the scientific decision-making of potential drug candidates. However, the classical pharmacokinetic models with the eliminations of zero-order, first-order and saturated Michaelis-Menten processes, assume that patients perfectly follow drug regimens during drug treatment, and the significant factor of patients' drug adherence is not taken into account. In this study, therefore, considering the random change of dosage at the fixed dosing time interval, we reformulate the classical deterministic one-compartment pharmacokinetic models to the framework of stochastic, and analyze their qualitative properties including the expectation and variance of the drug concentration, existence of limit drug distribution, and the stochastic properties such as transience and recurrence. In addition, we carry out sensitivity analysis of drug adherence-related parameters to the key values like expectation and variance, especially for the impact on the lowest and highest steady state drug concentrations (i.e. the therapeutic window). Our findings can provide an important theoretical guidance for the variability of drug concentration and help the optimal design of medication regimens. Moreover, The developed models in this paper can support for the potential study of the impact of drug adherence on long-term treatment for chronic diseases like HIV, by integrating disease models and the stochastic PK models.
药代动力学是药理学的一个科学分支，它描述了药物在生物体内的浓度随时间变化的过程，并有助于对潜在候选药物进行科学决策。然而，经典的药代动力学模型，包括零级、一级消除以及饱和米氏过程，假定患者在药物治疗期间能完美遵循给药方案，而未考虑患者药物依从性这一重要因素。因此，在本研究中，考虑到在固定给药时间间隔内剂量的随机变化，我们将经典的确定性单室药代动力学模型重新构建为随机框架，并分析其定性性质，包括药物浓度的期望和方差、极限药物分布的存在性以及诸如暂态和常返性等随机性质。此外，我们对与药物依从性相关的参数进行敏感性分析，以研究其对期望和方差等关键值的影响，特别是对最低和最高稳态药物浓度（即治疗窗）的影响。我们的研究结果可为药物浓度的变异性提供重要的理论指导，并有助于优化给药方案的设计。此外，本文所建立的模型通过整合疾病模型和随机药代动力学模型，可为研究药物依从性对如艾滋病等慢性疾病长期治疗的影响提供潜在支持。
