2023/10/30 by Santiago Torres Paz, Paz, Santiago Torres, Jose Ricardo Arteaga Bejarano +1
Mathematics · Medicine · Pharmacology, Toxicology and Pharmaceutics · #26E70 #34N05 #39A60 #Cancer Treatment and Pharmacology #Dynamical Systems (math.DS) #FOS: Mathematics #Pharmacogenetics and Drug Metabolism #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2310.19984
openalex publication_date 2023/10/30 · openalex created_date 2023/11/02 · openalex updated_date 2026/07/28
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.