Automated solutions of breathing pattern optimizations

Abstract

A numerical procedure which allows the convenient exploration of various optimization hypotheses of breathing pattern regulation is described. The method is based on the calculus of variations and uses a novel technique for the automatic evaluation of all required derivatives. Advantages of this approach include: exact calculation of all derivatives, parsimonious computer code, and speed of execution. By eliminating the need for hand calculation of derivatives, a major reduction was made in the tedium involved in exploring various optimization strategies. Examples are presented of determining the optimal breathing pattern characteristics for minimum work or force (pressure) required for breathing, based on linear and nonlinear models of respiratory mechanics. The developed procedure can be used to predict the optimal volume-time trajectory and breathing frequency which minimizes a criterion function subject to constraints.