A theoretical model of absorption of gases by the bronchial wall

The pattern of dispersion and uptake of an inhaled slug of tissue-soluble gas is examined within a branching model of the bronchial airways of the human lung, considered as an assembly of segments from infinitely long, straight rigid tubes with absorbing walls of finite thickness. The model is based on the first three (time-dependent) spatial moments of the solute distribution in such tubes, determined by the Aris method of moments. Poiseuille flow in each airway is assumed, and the solute distribution is taken to be initially zero in the tissue and radially uniform in the gas. First, the time dependence of axial velocity and mixing coefficient of the advancing solute in infinitely long tubes is shown and the mechanisms responsible are discussed. Transit times, uptake, uptake efficiency and mixing coefficient predicted from the model are then shown for different flow rates and solubilities, as functions of the generation of branching. As is expected, greater penetration is found for lower-solubility gases. However, of greater interest is the model prediction that uptake decreases with increasing flow rate whereas uptake efficiency increases, a result consistent with experimental indications. Finally, the mixing coefficient is shown to fall, with distance into the lung, to a value which may be much smaller than the molecular diffusivity, depending on the solubility.