Solution of the FPE describing diffusion in Alveoli.

If the cross-sectional area A(x) of alveoli increases with exponential law the solution of the equation of the motion has an exponential shape, with an apparently dominant role of velocity v(x,t): the function c(x,t) crosses the ordinate axis at , and then tends toward a rapid increase with time. The mathematical model provided by the Fokker-Planck equation for alveolar diffusion provides a relationship between the diffusive lung capacity and the physical property of the alveoli (effective diffusity.). Boundary conditions given above seem play a major role on the diffusing capacity, and therefore, the measure of this parameter (by means of the single breath test) is enough to detect diffusion abnormalities, but yet not suitable to distinguish different causes of respiratory diseases.