Probabilistic modeling of oxygen transport in brain tissue

A three-dimensional model of a subregion of the microcirculation was developed. The model employed parallel probabilistic distributions of reaction and convection of oxygen. A Green's function solution to oxygen transport in this system was derived and applied in a series of dynamic solutions on a minicomputer. Results include the transient response of oxygen tension at grid points throughout the system and a correlation of the oxygen demand and surplus supply. Results clearly represent anticipated oxygen partial pressure behavior trends of a countercurrent flow system and in pertinent ways compared favorably with the results obtained by previous investigators. The technique is conservative and employs from 2,000 to 3,600 time steps to achieve precision of seven significant figures. Excellent stability was observed as well. The simulation provides a reliable means to represent the transient response of oxygen partial pressure in a three-dimensional system. Case studies show effects of changing arterial oxygen partial pressure as well as the importance in this system of the convection of dissolved oxygen. It is concluded that the system adequately simulates the anticipated broad profiles of a probabilistically distributed system and provides a rather original insight into neuronal viability through a correlation of oxygen supply and demand. Adaptation of such a complex, dynamic, three-dimensional stimulation to a minicomputer is a step toward simulation of more sophisticated geometries.