Data-driven modelling of drug tissue trapping using anomalous kinetics

This work revisits the pharmacokinetic models derived from classical differential equations and proposes an extension to fractional differential equations to account for tissue trapping, which modifies the predicted drug concentration profiles. Unlike monotonic decay profiles, an oscillatory behaviour is often observed. The phenomenon may be the result of the recirculation of trapped drug molecules due to the heterogeneity of the tissue combined with the local action of the liver or other organs in depositing part of the drug for later release. The proposed model alleviates this limitation in data fitting profiles, without violating mass balance principles and physiological states. The paper also points to new concepts and techniques in modelling drug pharmacokinetic dynamics to account for short- and long-time recirculation effects. As such, it provides a better characterisation of unexplained secondary effects in patients undergoing treatment. It also establishes a link to unbounded drug accumulation models.