Time Scale Calculus: a new approach to multi-dose pharmacokinetic modeling.

IF 2.2 4区 医学 Q3 PHARMACOLOGY & PHARMACY Journal of Pharmacokinetics and Pharmacodynamics Pub Date : 2024-12-01 Epub Date: 2024-07-25 DOI:10.1007/s10928-024-09920-z
José Ricardo Arteaga-Bejarano, Santiago Torres
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Abstract

In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete processes. This characteristic makes TSC particularly suited for multi-dose pharmacokinetic problems, which inherently feature a blend of continuous processes (such as absorption, metabolization, and elimination) and discrete events (drug intake). We use this toolkit to derive analytical expressions for blood concentration trajectories under various multi-dose regimens across several flagship pharmacokinetic models. We demonstrate that this mathematical framework furnishes an alternative and simplified way to model and retrieve analytical solutions for multi-dose dynamics. For instance, it enables the study of blood concentration responses to arbitrary dose regimens and facilitates the characterization of the long-term behavior of the solutions, such as their steady state.

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时标计算:多剂量药代动力学建模的新方法。
在本文中,我们使用时间尺度微积分(TSC)来建立和求解探索多剂量动态的药代动力学模型。时间尺度微积分是一种数学框架,可对由连续和离散过程组成的动态系统进行建模。这一特点使得 TSC 特别适合多剂量药代动力学问题,因为这些问题本身就具有连续过程(如吸收、代谢和消除)和离散事件(药物摄入)的混合特征。我们利用这一工具包推导出了几种旗舰药代动力学模型中各种多剂量方案下的血药浓度轨迹分析表达式。我们证明,这一数学框架为多剂量动力学建模和检索分析解决方案提供了另一种简化方法。例如,它可以研究任意剂量方案下的血药浓度反应,并有助于描述解的长期行为,如稳态。
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来源期刊
CiteScore
4.90
自引率
4.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Broadly speaking, the Journal of Pharmacokinetics and Pharmacodynamics covers the area of pharmacometrics. The journal is devoted to illustrating the importance of pharmacokinetics, pharmacodynamics, and pharmacometrics in drug development, clinical care, and the understanding of drug action. The journal publishes on a variety of topics related to pharmacometrics, including, but not limited to, clinical, experimental, and theoretical papers examining the kinetics of drug disposition and effects of drug action in humans, animals, in vitro, or in silico; modeling and simulation methodology, including optimal design; precision medicine; systems pharmacology; and mathematical pharmacology (including computational biology, bioengineering, and biophysics related to pharmacology, pharmacokinetics, orpharmacodynamics). Clinical papers that include population pharmacokinetic-pharmacodynamic relationships are welcome. The journal actively invites and promotes up-and-coming areas of pharmacometric research, such as real-world evidence, quality of life analyses, and artificial intelligence. The Journal of Pharmacokinetics and Pharmacodynamics is an official journal of the International Society of Pharmacometrics.
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