On the Validation of a Fractional Order Model for Pharmacokinetics Using Clinical Data

This study aims to validate the hypothesis that the pharmacokinetics of certain drug regimes are better captured using fractional order differential equations rather than ordinary differential equations. To support this research, two numerical methods, the Grunwald–Letnikov and the L1 approximation, were implemented for the two-compartment model with Michaelis–Menten clearance kinetics for oral and intravenous administration of the drug. The efficacy of the numerical methods is verified through the use of the method of manufactured solutions due to the absence of an analytic solution to the proposed model. The model is derived from a phenomenological process leading to a dimensionally consistent and physically meaningful model. Using clinical data, the model is validated, and it is shown that the optimal model parameters select a fractional order for the clearance dynamic for certain drug regimes. These findings support the hypothesis that fractional differential equations better describe some pharmacokinetics.