Investigation of Fractional Compartmental Models with Application to Amiodarone Drug Diffusion in Pharmacokinetics

Abstract

This paper presents three fractional models formulated from a classical Pharmacokinetics compartmental system: commensurable, non-commensurable, and implicit non-commensurable models. Their distinguishing characteristics are further examined comprehensively. Because analytic solutions for such models are typically challenging to obtain, we study the application of the Fractional Finite Difference Method (FFDM) to simulate approximate solutions. The characteristic of the non-commensurable model is shown to be incompatible with the concept of mass balance. However, it appeared to outlast fractional calculus theory when simulating anomalous kinetics. We proved this by fitting the proposed fractional and classical models to an experimental data set (amiodarone) and estimated the parameters using the least-square approach. The classical model diverged, but the non-commensurable model predicted a fit comparable to the other two fractional models. The fractional models described anomalous diffusion better than classical theories. The numerical results showed that the proposed numerical method is equally efficient in solving any complex compartmental models, as they performed well in simulations for the classic example of the model.