Modeling advection and diffusion of oxygen in complex vascular networks

A realistic geometric model for the threec dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks, We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis-Menten consumption in the parenchymal tissue, The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which an solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no "lethal corner," or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0,5-1.0 myoglobin facilitate the transport of oxygen and thereby protect the;issue from hypoxia at levels near its p(50), that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range. (C) 2001 Biomedical Engineering Society.