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