A Green's function method for analysis of oxygen delivery to tissue by microvascular networks.

A theoretical model is formulated for analyzing oxygen delivery from an arbitrary network configuration of cylindrical microvessels to a finite region of tissue. In contrast to models based on the classical Krogh cylinder approach, this model requires no a priori assumptions concerning the extent of the tissue region supplied with oxygen by each vessel segment. Steady-state conditions are assumed, and oxygen consumption in the tissue is assumed to be uniform. The nonlinear dissociation characteristics of oxyhemoglobin are taken into account. A computationally efficient Green's function approach is used, in which the tissue oxygen field is expressed in terms of the distribution of source strengths along each segment. The utility of the model is illustrated by analyses of oxygen delivery to a cuboidal tissue region by a single segment and by a six-segment network. It is found that the fractional contribution of the proximal segments to total oxygen delivery increases with decreasing flow rate and metabolic rate.