School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, 710119, People's Republic of China.
School of Science, Shanghai Maritime University, Shanghai, 201306, People's Republic of China.
Bull Math Biol. 2023 Jun 9;85(7):65. doi: 10.1007/s11538-023-01173-0.
Poor drug adherence is considered one of major barriers to achieving the clinical and public health benefits of many pharmacotherapies. In the current paper, we aim to investigate the impact of dose omission on the plasma concentrations of two-compartment pharmacokinetic models with two typical routes of drug administration, namely the intravenous bolus and extravascular first-order absorption. First, we reformulate the classical two-compartment pharmacokinetic models with a new stochastic feature, where a binomial random model of dose intake is integrated. Then, we formalize the explicit expressions of expectation and variance for trough concentrations and limit concentrations, with the latter proved of the existence and uniqueness for steady-state distribution. Moreover, we mathematically demonstrate the strict stationarity and ergodicity of trough concentrations as a Markov chain. In addition, we numerically simulate the impact of drug non-adherence to different extents on the variability and regularity of drug concentration and compare the drug pharmacokinetic preference between one and two compartment pharmacokinetic models. The results of sensitivity analysis also suggest the drug non-adherence as one of the most sensitive model parameters to the expectation of limit concentration. Our modelling and analytical approach can be integrated into the chronic disease models to estimate or quantitatively predict the therapy efficacy with drug pharmacokinetics presumably affected by random dose omissions.
药物依从性差被认为是许多药物治疗无法实现临床和公共卫生效益的主要障碍之一。在本文中，我们旨在研究剂量遗漏对两种典型给药途径（即静脉推注和血管外一级吸收）的两室药代动力学模型的血浆浓度的影响。首先，我们用新的随机特征重新构建经典的两室药代动力学模型，其中整合了一种二项式随机剂量摄入模型。然后，我们正式确定了谷底浓度和极限浓度的期望和方差的显式表达式，后者证明了稳态分布的存在性和唯一性。此外，我们从数学上证明了谷底浓度作为马尔可夫链的严格平稳性和遍历性。此外，我们还数值模拟了药物不依从性对药物浓度变异性和规律性的不同程度的影响，并比较了一室和两室药代动力学模型之间的药物药代动力学偏好。敏感性分析的结果还表明，药物不依从性是极限浓度期望值最敏感的模型参数之一。我们的建模和分析方法可以整合到慢性病模型中，以估计或定量预测药物治疗效果，因为药物药代动力学可能受到随机剂量遗漏的影响。
