Modeling advection and diffusion of oxygen in complex vascular networks

A realistic geometric model for the threec dimensional capillary network ge ometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to t he available morphometric statistics and is supplied by a single arterial s ource and drains into a pair of venular sinks, We explore steady-state oxyg en transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of disso lved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissol ved and protein-bound oxygen, and Michaelis-Menten consumption in the paren chymal tissue, The advection velocity field is found by solving the hemodyn amic problem for flow throughout the network. The resulting system is descr ibed by a set of coupled nonlinear elliptic equations, which an solved usin g a finite-difference numerical approximation. We find that coupled advecti on and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially dist ributed models, and that no "lethal corner," or oxygen-deprived region occu rs for physiologically reasonable values for flow and consumption. Concentr ations 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 loca l oxygen consumption rates are close to those of delivery by flow and myogl obin-facilitated diffusion, a fairly narrow range. (C) 2001 Biomedical Engi neering Society.