PMID: 11339327May 8, 2001Paper

Modeling advection and diffusion of oxygen in complex vascular networks

Annals of Biomedical Engineering
Daniel A Beard, James B Bassingthwaighte

Abstract

A realistic geometric model for the three-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 are 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 fl...Continue Reading

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Citations

Aug 22, 2007·Biomechanics and Modeling in Mechanobiology·K K CeelenF P T Baaijens
Jun 16, 2006·Annals of Biomedical Engineering·Ranjan K Dash, James B Bassingthwaighte
Apr 7, 2006·Annals of Biomedical Engineering·Renat A Krasnoperov, Dietrich Stoyan
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Aug 24, 2012·Annals of Biomedical Engineering·James B BassingthwaighteKalyan Vinnakota
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