Abstract
This work presents a new mathematical model of the heat and water exchanges in the human lungs (newborn to adult). This model is based on a local description of the water and energy transports in both the lumen and the surrounding tissues, and is presented in a comprehensive, dimensionless framework with explicitly stated assumptions and a strong physiological background. The model is first used to analyze and quantify the key phenomena and dimensionless numbers governing these heat and water exchanges and then it is applied to an adult in various situations (varying atmospheric conditions, exercising…). The results highlight several interesting physiological elements. They show that the bronchial region of the lungs is able to condition the air in all the considered situations even if, sometimes, for instance when exercising, distal generations have to be involved. The model also shows that these distal generations are super-conditioners. Moreover, the results quantify the key role of the submucosal glands in mucus hydration. They also show that, during expiration, a significant cooling of the air and condensation of water occur along the respiratory tract as the vascularization of the tissues surrounding the airways is not able to maintain these tissues at body temperature during inspiration. Due to the interaction between several phenomena, it appears that the ratio of the amount of water returned to the mucosa during expiration to the amount extracted during inspiration is almost independent of the breathing conditions (around 33%). The results also show that, in acute situations, such as suffering from a pathology with airway dysfunction, when being intubated or when exercising above an intensity threshold, the heat and water exchanges in the lungs may be critical regarding mucus hydration. In proximal generations, the evaporation may overwhelm the ability of the submucosal glands to replenish the airway surface liquid with water. In some situations, the cooling of the mucosa may be very important; it can even become colder than the inspired air, due to evaporative cooling. Finally, the results show that breathing cold air can significantly increase the exchanges between the lungs and the environment, which can be critical regarding disease transmission.