Numerical analysis of pulmonary indicator gas wash-in

Mathematical modelling of gas transport in the human lung yields a diffusion-convection problem. Transport is described by a second-order parabolic partial differential equation with variable coefficients and initial and boundary conditions. A new numerical approach for the solution of these governing equations is proposed in which the convection term is dealt with exactly. This method combines integration along characteristics and the finite difference method. The results obtained are in agreement with those of other investigators but are based on less stringent assumptions. To judge the merit of various finite difference schemes, the results are compared with analytical solutions for a special case in which the lung is modelled as a uniform cylinder. Laplace transform techniques and expansion into Fourier series are used to obtain the analytical solutions.