DIGITAL SIMULATION OF A SPATIAL DIFFUSION MODEL OF OXYGEN SUPPLY IN BIOLOGICAL TISSUE

A three-dimensional digital model was developed to enable the understanding of the oxygen pressure fields measured by means of Pt-needle electrodes and the supply conditions in the organism. Enlarging traditional conceptions this model permits for steady states the calculation of spatial oxygen pressure fields between asymmetric capillary structures. In the model first the pressure courses of the capillaries were checked with their supply areas, then the diffusion equation was solved interatively by transition to a difference equation. The iteration procedure was done by means of the Liebmann process in the form of overrelaxation. The supply areas and the minimum pressures in the oxygen pressure fields of three capillary structures are compared supposing conditions of normoxia and venous hypoxia in the grey substance of the human brain. Possibilities of subtilizing and enlarging the digital model are discussed. The program (ALGOL and FORTRAN) is in possession of the author. © 1969 Springer-Verlag.