Modeling drug retention as memory effects in obese patients using fractional and augmented models

Lipophilic anesthetic drugs accumulate in adipose tissue, leading to delayed release and prolonged effects, particularly in obese patients. This study proposes two novel physiologically motivated pharmacokinetic (PK) models to address these dynamics. The first is an augmented model with a trap compartment to simulate retention, and the second is a fractional-order model using Partial-Caputo derivatives to capture memory effects. By applying a discrete-time Euler method to the augmented model, we reveal an inherent fading memory behavior, where the current drug release depends on a weighted influence of past drug concentrations in fat. Both models are integrated into a PK/PD framework. Their behavior is first explored in a single-input single-output (SISO) case using simulated Bispectral Index (BIS) responses under three common dosing protocols: single bolus, repeated boluses, and continuous infusion. Evaluation against real clinical data is then performed in a multiple-input single-output (MISO) case, where the simulated BIS responses are compared to recorded BIS measurements from a representative obese patient under total intravenous anesthesia (TIVA). During the awakening phase, both the augmented and fractional-order models reduce BIS prediction error compared to the classical model. The augmented model lowers RMSE by 22.5% (from 10.38 to 8.04), while the fractional model achieves a 21.4% reduction (to 8.16) (based on one obese patient case). Sensitivity analysis confirms the impact of the fractional-order parameter () on long-term BIS dynamics. These results and proposed models illustrate the potential role of memory-aware PK models for advanced patient-specific digital twin systems in healthcare.