Analytical simulation of longitudinal gas mixing in the human central airways

In order to study gaseous mixing in the proximal respiratory airways during stationary breathing, a simple mathematical model with an analytical solution of the corresponding equation is presented. Calculations were carried out by solving the differential equation analytically according to the system response to a unit impulse combined with the convolution method. It seems that this analytical method gives similar results to those obtained by the numerical ones; however, our method is computationally simple and can provide a reasonable tool to study gas transport in the airways.