Speaker
Description
Fractional-order compartmental models have been increasingly adopted in pharmacokinetics to capture anomalous drug diffusion, memory effects, and non-exponential elimination patterns that classical integer-order models cannot adequately describe. However, the numerical treatment of these models remains challenging because of nonlocal operators, memory dependence, and mass-balance inconsistencies.
In this work, we build upon the Radial Basis Function-Enhanced Fractional Physics-Informed Neural Networks (RBF-fPINN) framework to investigate fractional pharmacokinetics compartmental models. We consider three classes of fractional pharmacokinetics models formulated from a classical two-compartment system: (i) commensurable fractional models with a uniform fractional order, (ii) non-commensurable models with distinct fractional orders across compartments, and (iii) implicit non-commensurable models that fractionalize transport processes while preserving mass balance. The RBF-fPINN methodology is adapted to each model class, enabling a unified comparison of accuracy and computational efficiency.
Numerical experiments demonstrate that our recently proposed method accurately captures the slow, non-exponential drug dynamics and outperforms classical numerical schemes, particularly for implicit non-commensurable models. Furthermore, the framework enables simultaneous state estimation and parameter identification, making it very useful for data-driven pharmacokinetics applications.
Bibliography
\bibitem{PK} Borkor, Reindorf Nartey, et al. “Investigation of Fractional Compartmental Models in Pharmacokinetics with Application to Amiodarone Drug Diffusion.” Scientific African, vol. 28, June 2025, p. e02700. DOI.org (Crossref), https://doi.org/10.1016/j.sciaf.2025.e02 700.
\bibitem{RBF-fPINNs} Mohammadi, Maryam, et al. “RBF-fPINNs: Radial Basis Function-Enhanced Fractional Physics-Informed Neural Networks.” Engineering with Computers, vol. 42, no. 1, February 2026, p. 42. DOI.org (Crossref), https://doi.org/10.1007/s00366-025-02258-1.
\bibitem{citekey} Qiao, Yanli, et al. “Numerical Simulation of a Two‐compartmental Fractional Model in Pharmacokinetics and Parameters Estimation.” Mathematical Methods in the Applied Sciences, vol. 44, no. 14, September 2021, pp. 11526-36. DOI.org (Crossref), https://doi.org/10.1002/mma.7511.
