A mathematical model for simultaneous determination of vascular and extravascular permebilities within the microcirculation

Abstract

The diffusive transport process of macromolecules across the capillary wall and into the extravasculature is mathematically modelled by Fick's diffusion equation in the cylindrical co-ordinate system. No ad hoc assumptions are made. A closed-form time-dependent solution is obtained employing inverse Laplace transform methods. The vascular and extravascular diffusion constants are determined simultaneously by solving a system of non-linear equations. This mathematical model provides the theoretical basis for the further understanding of the diffusion process in the microcirculation. In addition, an algorithm for extracting three dimensional data from two dimensional experimental data is developed. In addition to modelling endothelial wall, the mathematical technique developed in this study has been applied successfully to heat transfer and microwave transmission problems. It can also be used to study the diffusion process of electrons and holes within the semiconductor material. The applicability of these techniques should be found in many other cylindrical diffusion problems. All the mathematical procedures are coded in computer programs using Fortran language. These computer programs are interactive and easy to use. Furthermore, these computer programs are modular in design so that to make an improvement in one program will not affect the other programs.