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The Role of Counter-Current Exchange in Preventing Hypoxia in Skeletal Muscle

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Abstract

Mathematical models that describe oxygen transport from a single capillary into a region of surrounding tissue often predict that the tissue is hypoxic, whereas in reality diffusion from more richly perfused nearby capillaries prevents hypoxia from forming in the tissue. In this manuscript, a mathematical model of oxygen transport is presented that is applicable to vascular beds consisting of a large number of non-uniformly perfused parallel capillaries arranged in a manner characteristic of skeletal muscle. The model is used to examine conditions under which counter-current flow and myoglobin-facilitated diffusion provides sufficient oxygen to poorly perfused regions to prevent the occurrence of hypoxia. The method developed here leads to a coupled system of nonlinear ordinary differential equations for the oxygen concentration in the capillaries, and is easy to apply even for vascular beds containing a large number of capillaries.

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Authors and Affiliations

  1. Department of Mathematics, Lafayette College, Easton, PA, 18042, USA

    Miranda I. Teboh-Ewungkem

  2. Department of Mathematics, Institute for Biomedical Engineering and Mathematical Biology, Lehigh University, 14 East Packer Avenue, Bethlehem, PA, 18015-3174, USA

    Eric P. Salathe

Authors
  1. Miranda I. Teboh-Ewungkem
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  2. Eric P. Salathe
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Correspondence to Eric P. Salathe.

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Teboh-Ewungkem, M.I., Salathe, E.P. The Role of Counter-Current Exchange in Preventing Hypoxia in Skeletal Muscle. Bull. Math. Biol. 68, 2191–2204 (2006). https://doi.org/10.1007/s11538-006-9102-z

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  • DOI: https://doi.org/10.1007/s11538-006-9102-z

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