An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

TL;DR

This paper presents an analytical solution for the time-optimal control problem during anesthesia induction, demonstrating its effectiveness and advantages over traditional numerical methods like shooting, within a pharmacokinetic/pharmacodynamic model.

Contribution

The authors develop a novel analytical approach to determine the optimal induction time, reducing dependence on initial conditions compared to existing numerical methods.

Findings

Analytical solution aligns with shooting method results.

Optimal infusion rate and transition time are consistent across methods.

The new method is independent of unknown initial adjoint conditions.

Abstract

We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic/pharmacodynamic (PK/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables.