Muscle kinematics for minimal work of breathing.

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Abstract
A mathematical model was analyzed to obtain a quantitative and testable representation of the long-standing hypothesis that the respiratory muscles drive the chest wall along the trajectory for which the work of breathing is minimal. The respiratory system was modeled as a linear elastic system that can be expanded either by pressure applied at the airway opening (passive inflation) or by active forces in respiratory muscles (active inflation). The work of active expansion was calculated, and the distribution of muscle forces that produces a given lung expansion with minimal work was computed. The calculated expression for muscle force is complicated, but the corresponding kinematics of muscle shortening is simple: active inspiratory muscles shorten more during active inflation than during passive inflation, and the ratio of active to passive shortening is the same for all active muscles. In addition, the ratio of the minimal work done by respiratory muscles during active inflation to work required for passive inflation is the same as the ratio of active to passive muscle shortening. The minimal-work hypothesis was tested by measurement of the passive and active shortening of the internal intercostal muscles in the parasternal region of two interspaces in five supine anesthetized dogs. Fractional changes in muscle length were measured by sonomicrometry during passive inflation, during quiet breathing, and during forceful inspiratory efforts against a closed airway. Active muscle shortening during quiet breathing was, on average, 70% greater than passive shortening, but it was only weakly correlated with passive shortening. Active shortening inferred from the data for more forceful inspiratory efforts was approximately 40% greater than passive shortening and was highly correlated with passive shortening. These data support the hypothesis that, during forceful inspiratory efforts, muscle activation is coordinated so as to expand the chest wall with minimal work.