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.

翻译：本文提出了三种基于经典药代动力学房室系统构建的分数阶模型：可公度模型、非公度模型及隐式非公度模型，并对其区分特征进行了全面深入分析。由于此类模型的解析解通常难以获得，我们研究了分数阶有限差分法（FFDM）在模拟近似解中的应用。研究表明，非公度模型的特征与质量守恒概念不相容，但在模拟反常动力学时表现出超越分数阶微积分理论的特性。我们通过将所提出的分数阶模型及经典模型拟合至实验数据集（胺碘酮）验证了这一点，并采用最小二乘法估计参数。经典模型发散，而非公度模型预测的拟合效果与其他两种分数阶模型相当。分数阶模型在描述反常扩散方面优于经典理论。数值结果表明，所提出的数值方法在求解任何复杂房室模型时同样高效，因为其在对经典模型例子的模拟中表现良好。