A method of solution for a non-linear diffusion model and for computing the parameters in the model

摘要

The diffusion of a drug through a skin-like membrane which tends to partially absorb the drug, was modelled by means of a system of strongly coupled nonlinear parabolic differential equations. We present a method of computing the parameters in the model characterizing a particular drug and membrane by an optimization procedure. This method consists of minimizing a quantity measuring the correspondence between the predictions of the model and experimental data, as a function of the parameters. In the method the solution of the differential equations for different sets of parameters is used repeatedly. The equations are solved by an implicit finite difference method employing an iterative procedure at every time step.