A NUMERICAL METHOD TO DETERMINE THE OPTIMAL INDUCTION PHASE OF ANESTHESIA

Abstract

This research paper, titled "A Numerical Method to Determine the Optimal Induction Phase of Anesthesia," explores the use of mathematical modeling and optimal control to enhance the anesthesia process. The study is based on a pharmacokinetic/pharmacodynamic (PK/PD) model for propofol and applies Pontryagin’s Maximum Principle for optimal control to determine the best drug infusion rate and the minimum time required to transition from an awake to an anesthetized state. The methodology employs the shooting method alongside a novel analytical approach that avoids dependency on initial guesses. Numerical simulations in MATLAB confirmed the consistency of both methods in computing the optimal induction time and infusion rate. The study highlights the significance of these techniques in improving the safety and efficacy of anesthesia, particularly for high-risk patients, with potential applications to other PK/PD models in the future.