How mammals adapt their breath to body activity – and how this depends on body size

Abstract

A model of optimal control of ventilation recently developed for humans has suggested that the localization of the transition between a convective and a diffusive transport of the respiratory gas determines how ventilation should be controlled to minimize its energetic cost at any metabolic regime. We generalized this model to any mammal, based on the core morphometric characteristics shared by all mammals' lungs and on their allometric scaling from the literature.Since the main energetic costs of ventilation are related to the convective transport, we prove that, for all mammals, the localization of the shift from an convective transport into a diffusive transport plays a critical role on keeping that cost low while fulfilling the lung's function. Our model predicts for the first time where this transition zone should occur in order to minimize the energetic cost of ventilation, depending on the mammals' mass and on the metabolic regime. From that optimal localization, we are able to derive predicted allometric scaling laws for both tidal volumes and breathing rates, at any metabolic regime. We ran our model for the three common metabolic rates -basal, field and maximal- and showed that our predictions accurately reproduce the experimental data available in the literature. Our analysis supports the hypothesis that the mammals' allometric scaling laws of tidal volumes and breathing rates are driven by a few core geometrical characteristics shared by the mammals' lungs, the physical processes of respiratory gas transport and the metabolic needs.