Investigation of fractional compartmental models in pharmacokinetics with application to amiodarone drug diffusion

This study offers and explores fractional models derived from a classical Pharmacokinetics (PK) compartmental system. The fractional models are essentially enlarged versions of the classical model, and their distinguishing characteristics are further examined comprehensively. Through numerical simulations using the Grunwald–Letnikov finite difference method, we demonstrate that fractional PK models provide a more realistic representation of drug dynamics compared to classical model. It is demonstrated that certain model features are incompatible with the idea of mass balance. However, they appeared to surpass classical calculus theory when simulating anomalous kinetics. We demonstrate this behaviour through stability analysis of the equilibrium point under conditions of different fractional orders as well as fitting the proposed models to an experimental data set (amiodarone), thereby estimating parameters using the least-square approach. The findings reveal that fractional pharmacokinetic models provide a more accurate and physically realistic representation of drug distribution, capturing memory effects and non-exponential drug elimination. This ensures better agreement with experimental observations compared to classical integer-order models.