{"title":"时标计算:多剂量药代动力学建模的新方法。","authors":"José Ricardo Arteaga-Bejarano, Santiago Torres","doi":"10.1007/s10928-024-09920-z","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":16851,"journal":{"name":"Journal of Pharmacokinetics and Pharmacodynamics","volume":" ","pages":"825-839"},"PeriodicalIF":2.2000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11579191/pdf/","citationCount":"0","resultStr":"{\"title\":\"Time Scale Calculus: a new approach to multi-dose pharmacokinetic modeling.\",\"authors\":\"José Ricardo Arteaga-Bejarano, Santiago Torres\",\"doi\":\"10.1007/s10928-024-09920-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>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.</p>\",\"PeriodicalId\":16851,\"journal\":{\"name\":\"Journal of Pharmacokinetics and Pharmacodynamics\",\"volume\":\" \",\"pages\":\"825-839\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11579191/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pharmacokinetics and Pharmacodynamics\",\"FirstCategoryId\":\"3\",\"ListUrlMain\":\"https://doi.org/10.1007/s10928-024-09920-z\",\"RegionNum\":4,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/7/25 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"PHARMACOLOGY & PHARMACY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pharmacokinetics and Pharmacodynamics","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1007/s10928-024-09920-z","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/25 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"PHARMACOLOGY & PHARMACY","Score":null,"Total":0}
Time Scale Calculus: a new approach to multi-dose pharmacokinetic modeling.
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.
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.