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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2310.19984 |
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| _version_ | 1866909163442929664 |
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| author | Paz, Santiago Torres Bejarano, Jose Ricardo Arteaga |
| author_facet | Paz, Santiago Torres Bejarano, Jose Ricardo Arteaga |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19984 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Time Scale Calculus: A New Approach to Multi-Dose Pharmacokinetic Modeling Paz, Santiago Torres Bejarano, Jose Ricardo Arteaga Dynamical Systems 26E70, 34N05, 39A60 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. |
| title | Time Scale Calculus: A New Approach to Multi-Dose Pharmacokinetic Modeling |
| topic | Dynamical Systems 26E70, 34N05, 39A60 |
| url | https://arxiv.org/abs/2310.19984 |