Water and heat exchanges in mammalian lungs

Abstract

AbstractA secondary function of the respiratory system of the mammals is, during inspiration, to heat the air to body temperature and to saturate it with water before it reaches the alveoli. Relying on a mathematical model, we propose a comprehensive analysis of this function, considering all the terrestrial mammals (spanning six orders of magnitude of the body mass, M) and focusing on the sole contribution of the lungs to this air conditioning. The results highlight significant differences between the small and the large mammals, as well as between rest and effort, regarding the spatial distribution of heat and water exchanges in the lungs, and also in terms of regime of mass transfer taking place in the lumen of the airways. Interestingly, the results show that the mammalian lungs appear to be designed just right to fully condition the air at maximal effort (and clearly over-designed at rest, except for the smallest mammals): all generations of the bronchial region of the lungs are mobilized for this purpose, with calculated values of the local evaporation rate of water from the bronchial mucosa that can be very close to the maximal ability of the serous cells to replenish this mucosa with water. For mammals with a mass above a certain threshold ($$\simeq 5$$ ≃ 5 kg at rest and $$\simeq 50$$ ≃ 50 g at maximal effort), it appears that the maximal value of this evaporation rate scales as $$M^{-1/8}$$ M - 1 / 8 at rest and $$M^{-1/16}$$ M - 1 / 16 at maximal effort and that around 40% (at rest) or 50% (at maximal effort) of the water/heat extracted from the lungs during inspiration is returned to the bronchial mucosa during expiration, independently of the mass, due to a subtle coupling between different phenomena. This last result implies that, above these thresholds, the amounts of water and heat extracted from the lungs by the ventilation scale with the mass such as the ventilation rate does (i.e. as $$M^{3/4}$$ M 3 / 4 at rest and $$M^{7/8}$$ M 7 / 8 at maximal effort). Finally, it is worth to mention that these amounts appear to remain limited, but not negligible, when compared to relevant global quantities, even at maximal effort (4–6%).