Mathematical modeling of heat and water transport in human respiratory tract

Excessive heat and water losses from the airways are stimuli to asthma. To study heat and water vapor transport in the human respiratory tract, a time-dependent model, based on a single differential equation with an analytical solution, was developed that could predict the intra-airway temperatures and water vapor contents. The key feature is the dependence of the temperature and water vapor along the respiratory tract as a function of the air residence time at each location. The model assumes disturbed laminar flow leading to enhanced transport mechanisms and wall temperature profiles modeled according to experimental data (E. R. McFadden, Jr., B. M. Pichurko, H. F. Bowman, E. Ingenito, S. Burns, N. Dowling, and J. Soloway. J. Appl. Physiol. 58: 564-570, 1985). It predicts that 1) the air equilibrates with the wall before it reaches body conditions (37 degrees C, 99.5% relative humidity); 2) conditioning of the inspired air involves several generations, with the number depending on the respiratory conditions; and 3) the walls of the upper airways are unsaturated, although it is difficult to judge at this state the depth of the respiratory tract affected.