  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.
