The origin of the allometric scaling of lung ventilation in mammals

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.

Propagation of an idealized infection in an airway tree, consequences of the inflammation on the oxygen transfer to blood

“…Non inflamed lung. The model of the human lung used in this work is the same as in [29][30][31]. The model is based on the assembly of self-similar trees that mimic the functional regions of the lung.…”

“…The model is based on the assembly of self-similar trees that mimic the functional regions of the lung. Self-similar trees have been thoroughly used in the literature to model the mammalian lungs and have allowed to uncover many interesting behaviors of the lung [29][30][31][32][33][34]. The lung is modelled as a tree of bifurcating cylindrical airways.…”

“…for generations i ∈ G, N . To mimic the exchange surface with blood in the acini, the airways in our model of acini are layered with "virtual" alveoli represented by the exchange surface area per unit of airway wall surface area, ρ s [30].…”

“…Hence, air and respiratory gas will go through a tree potentially with asymmetric bifurcations. To the contrary of the model in [30], where airways could be studied only through their generation index, here, each airway of the tree could have its own behavior. Consequently, the airways have to be indexed independently.…”

“…Hence, we used a more specific, but also more complex model [28] that describes not only the immune response in the tissue and blood, but also the tissue inflammation. This last model is then linked to the gas transport model introduced in [29,30] to simulate the propagation of an infection in an idealized lung and to simulate inflammation bronchi per bronchi. Our model is generic, it does not focus on one pathogen only.…”