Distribution of oxygen partial pressure in a two-dimensional tissue supplied by capillary meshes and concurrent and countercurrent systems

Abstract

For the calculations of oxygen partial pressure in a two-dimensional tissue model supplied by a capillary network (inhomogeneously perfused tissue), two differential equations are given that describe the process in the tissue and capillaries. The differential equations are coupled by the boundary conditions. Results obtained by using the method of successive displacements are given for the two-dimensional problem. This method exhibits a satisfactory convergence. The accuracy of the results is about ±5% based on the initial concentration. The results for the network model are compared with those for equivalent concurrent and countercurrent systems. Equivalence means in this connection that the area of tissue, the total length of capillaries, and the constants characterizing blood and tissue are the same. Our results for the two-dimensional models permit us to conclude that the differences between the lowest partial pressure in the tissue and the venous partial pressure are smallest in the countercurrent system and largest in the capillary network.