Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory.

中文翻译：

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分形药代动力学。

传统上，药代动力学（PK）是在同质性假设下处理的。但是，如今，生物系统已被全面理解为固有的分形。具体而言，药物分子与膜界面，代谢酶或药理学受体相互作用的微环境被一致认为是未搅拌的，空间受限的，异质的和几何形的。因此，必须重新考虑经典的Fickean扩散和作为均匀动力学空间的隔室概念。分形空间中的扩散已经进行了很长时间的研究，它利用分数演算并扩展了维数的概念。将这种新范式与描述和解释实验数据的需求相结合，可以定义具有特征分形指数的随时间变化的速率常数。在单室简化模式下，此策略非常简单。但是，正是由于基础生物学的异质性，通常至少需要一个两室模型来处理宏观数据，例如药物浓度。这种简单的建模步骤意味着显着的分析和数值复杂性。但是，有几种方法可以使原始的石屑成为可能。实际上，通过探索各种参数可能性并查看不同的药物和各自的生物浓度，可以得出结论，所有PK建模方法的确是分形PK理论的特殊情况。通常至少需要两室模型来处理宏观数据，例如药物浓度。这种简单的建模步骤意味着显着的分析和数值复杂性。但是，有几种方法可以使原始的石屑成为可能。实际上，通过探索各种参数可能性并查看不同的药物和各自的生物浓度，可以得出结论，所有PK建模方法的确是分形PK理论的特殊情况。通常至少需要两室模型来处理宏观数据，例如药物浓度。这种简单的建模步骤意味着显着的分析和数值复杂性。但是，有几种方法可以使原始的石屑成为可能。实际上，通过探索各种参数可能性并查看不同的药物和各自的生物浓度，可以得出结论，所有PK建模方法的确是分形PK理论的特殊情况。