Role of fractional derivatives in pharmacokinetic/pharmacodynamic anesthesia model using BIS data

Abstract

In this paper, we investigate a pharmacokinetic/pharmacodynamic model for anesthesia to describe the effects of propofol and the impact of fractional derivatives. Using actual bispectral index data from surgical patients, we demonstrate how fractional-order models can more effectively capture the memory-dependent dynamics of anesthesia than traditional integer-order models. Model parameters are estimated using the trust region reflective algorithm, and numerical simulations employ the Adams-type predictor–corrector method. Comparative analysis across multiple patients reveals that the fractional-order model consistently provides a superior fit to bispectral index data, as indicated by lower prediction errors and reduced Akaike information criterion values. This study primarily aims to demonstrate the advantages of employing fractional derivatives for this specific data set, particularly in accounting for memory effects, which are crucial in capturing the prolonged effects of anesthetic agents. By incorporating actual bispectral index scale data and fractional derivatives, we significantly enhance the relevance and impact of this research, offering a more flexible and accurate model. Our findings highlight the superiority of fractional derivatives in capturing the complex, time-dependent dynamics of anesthetic drug effects, making it a more suitable modeling approach compared to traditional methods, with the potential for improved patient-specific anesthesia management.