The minimization of muscular energy expenditure during inspiration in linear models of the respiratory system

Abstract

The consequences of requiring a general linear model of respiratory mechanics to inspire a fixed volume in a fixed time in a way that minimizes various measures of muscular energy expenditure are examined. For such a model no volume profile minimizes the time-integral of the applied pressure developed by the respiratory muscles, although this integral is not independent of the profile. Minimizing the mechanical work done by the respiratory muscles, on the other hand, requires that the inspiratory flow be constant. These results support the hypothesis that neither the pressure integral nor the mechanical work are individually minimized over an inspiration by an animal or man at rest. Minimization of a weighted sum of the pressure integral and the work done may be a more physiologically reasonable criterion by which the respiratory muscles direct inspiration. This combined cost function predicts a non-constant optimum velocity profile.