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The development of anoxia following occlusion

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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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Authors and Affiliations

  1. Center for the Application of Mathematics, Lehigh University, 18015, Bethlehem, PA, USA

    Eric P. Salathé

  2. Department of Mathematics and Computer Sciences, The University of Nebraska at Omaha, 68101, Omaha, NB, USA

    Tseng-Chan Wang

Authors
  1. Eric P. Salathé
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  2. Tseng-Chan Wang
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Salathé, E.P., Wang, TC. The development of anoxia following occlusion. Bltn Mathcal Biology 44, 851–877 (1982). https://doi.org/10.1007/BF02465185

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  • DOI: https://doi.org/10.1007/BF02465185

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