The development of anoxia following occlusion |
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Authors: | Eric P Salathé Tseng-Chan Wang |
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Institution: | (1) Center for the Application of Mathematics, Lehigh University, 18015 Bethlehem, PA, USA;(2) Department of Mathematics and Computer Sciences, The University of Nebraska at Omaha, 68101 Omaha, NB, USA |
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Abstract: | Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia
first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region
of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic,
is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral
equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary
problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range
of physiological conditions. |
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Keywords: | |
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