Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal; Department of Mathematics, University of Djelfa, 17000 Djelfa, Algeria.
Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.
Comput Biol Med. 2023 Dec;167:107679. doi: 10.1016/j.compbiomed.2023.107679. Epub 2023 Nov 8.
We present a novel Pharmacokinetic/Pharmacodynamic (PK/PD) model for the induction phase of anesthesia, incorporating the ψ-Caputo fractional derivative. By employing the Picard iterative process, we derive a solution for a nonhomogeneous ψ-Caputo fractional system to characterize the dynamical behavior of the drugs distribution within a patient's body during the anesthesia process. To explore the dynamics of the fractional anesthesia model, we perform numerical analysis on solutions involving various functions of ψ and fractional orders. All numerical simulations are conducted using the MATLAB computing environment. Our results suggest that the ψ functions and the fractional order of differentiation have an important role in the modeling of individual-specific characteristics, taking into account the complex interplay between drug concentration and its effect on the human body. This innovative model serves to advance the understanding of personalized drug responses during anesthesia, paving the way for more precise and tailored approaches to anesthetic drug administration.
我们提出了一种新的麻醉诱导阶段的药代动力学/药效动力学（PK/PD）模型，其中包含 ψ-Caputo 分数导数。通过使用 Picard 迭代过程，我们推导出一个非齐次 ψ-Caputo 分数系统的解，以描述麻醉过程中药物在患者体内分布的动态行为。为了探索分数麻醉模型的动力学，我们对涉及各种 ψ 和分数阶函数的解进行数值分析。所有数值模拟都是在 MATLAB 计算环境中进行的。我们的结果表明，在考虑药物浓度与其对人体影响之间的复杂相互作用的情况下，ψ 函数和分数阶微分在个体特异性特征建模中具有重要作用。这个创新模型有助于提高对麻醉过程中个体药物反应的理解，为更精确和定制的麻醉药物管理方法铺平了道路。
