Muscle kinematics for minimal work of breathing

A mathematical model was analyzed to obtain a quantitative and testable rep resentation of the long-standing hypothesis that the respiratory muscles dr ive 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). T he 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 corresp onding kinematics of muscle shortening is simple: active inspiratory muscle s shorten more during active inflation than during passive inflation, and t he 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 du ring active inflation to work required for passive inflation is the same as the ratio of active to passive muscle shortening. The minimal-work hypothe sis was tested by measurement of the passive and active shortening of the i nternal intercostal muscles in the parasternal region of two interspaces in five supine anesthetized dogs. Fractional changes in muscle length were me asured by sonomicrometry during passive inflation, during quiet breathing, and during forceful inspiratory efforts against a closed airway. Active mus cle shortening during quiet breathing was, on average, 70% greater than pas sive shortening, but it was only weakly correlated with passive shortening. Active shortening inferred from the data for more forceful inspiratory eff orts was similar to 40% greater than passive shortening and was highly corr elated with passive shortening. These data support the hypothesis that, dur ing forceful inspiratory efforts, muscle activation is coordinated so as to expand the chest wall with minimal work.