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<p>To gain deeper insight into the distribution of drugs within the human body through various routes of administration, this paper develops multi-compartmental mathematical models. Two models are built using diffusion principles, employing Fickian diffusion and mass-action kinetics. The rate constants related to mass-action kinetics are estimated based on the drug’s effectiveness across different biological sites. The resulting ordinary differential equations, which model concentration variations across compartments, are solved using the Laplace transform technique, and the extended Mittag-Leffler function is used to express the general solution for drug concentration. The Laplace Transform Decomposition Method is applied to solve the fractional models. Numerical simulations compute drug concentrations across compartments, and the results are visualized through MATLAB-generated graphs that depict a decreasing pharmacological level in the first section and steady rises in subsequent ones. Furthermore, qualitative analysis is conducted-sensitivity analysis, including the Morris screening method, examines the influence of parameter variation; stability analysis confirms the system’s behavior under perturbations; and the existence and uniqueness of solutions are ensured through mathematical validation. The fractional model provides valuable insights and offers potential for advancing understanding in the medical field. </p>

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A mathematical approach to multi-route drug distribution via compartmental models

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Mehak Jan,
  • Khadija Tul Kubra,
  • Sameer Hassan Farooqi,
  • Aiman Asghar

摘要

To gain deeper insight into the distribution of drugs within the human body through various routes of administration, this paper develops multi-compartmental mathematical models. Two models are built using diffusion principles, employing Fickian diffusion and mass-action kinetics. The rate constants related to mass-action kinetics are estimated based on the drug’s effectiveness across different biological sites. The resulting ordinary differential equations, which model concentration variations across compartments, are solved using the Laplace transform technique, and the extended Mittag-Leffler function is used to express the general solution for drug concentration. The Laplace Transform Decomposition Method is applied to solve the fractional models. Numerical simulations compute drug concentrations across compartments, and the results are visualized through MATLAB-generated graphs that depict a decreasing pharmacological level in the first section and steady rises in subsequent ones. Furthermore, qualitative analysis is conducted-sensitivity analysis, including the Morris screening method, examines the influence of parameter variation; stability analysis confirms the system’s behavior under perturbations; and the existence and uniqueness of solutions are ensured through mathematical validation. The fractional model provides valuable insights and offers potential for advancing understanding in the medical field.