A porous medium model of alveolar gas diffusion

A mathematical model based on the volume-averaging technique is derived for simulating the diffusion process within the alveolar region of the lung. The derivation of this macroscopic model leads to a lung effective diffusivity that depends on the diffusivity and on the interface geometry of each alveolar constituent. Unfortunately, describing the internal geometry of the alveolar region for estimating the lung effective diffusivity is impractical. We found, however, that the steady-state solution of the macroscopic model can be used to obtain the lung effective diffusivity once the lung diffusing capacity is known. A preliminary investigation considering a hypothetical cubic domain representing the alveolar region of the lung is undertaken for demonstrating the applicability of the method. Using characteristic values of capillary red blood cell density, alveolar volume, and lung diffusing capacity, the representative lung effective diffusivity is computed and satisfactorily compared with the molecular diffusivity of each constituent of the alveolar region.