The Green's function for the convection-diffusion equation in an analytic lung model

The method of Green's functions is applied to the convection-diffusion equation describing gas transport in the human lung. Explicit analytic solutions are found for the zero^th approximation to the value of steady state alveolar oxygen concentration, given the frequency of breathing, tidal volume, oxygen consumption, alveolar volume, volume of the bronchial tree, and two modelling parameters describing the geometry. The results of the calculation are compared favorably with some experimental data.