title: The role of counter-current exchange in preventing hypoxia in skeletal muscle.
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.
authors.affiliation: Department of Mathematics, Lafayette College, Easton, PA 18042, USA.
authors.forename: Miranda I
authors.initials: MI
authors.lastname: Teboh-Ewungkem
authors.forename: Eric P
authors.initials: EP
authors.lastname: Salathe
mesh_terms: D002196:Capillaries / Q000378:metabolism; D006801:Humans; D000860:Hypoxia / Q000097:blood / Q000378:metabolism*; D008954:Models, Biological; D018482:Muscle, Skeletal / Q000098:blood supply* / Q000378:metabolism*; D009211:Myoglobin / Q000502:physiology; D010100:Oxygen / Q000097:blood / Q000378:metabolism*; D012039:Regional Blood Flow / Q000502:physiology
chemical_list: D009211:Myoglobin; D010100:Oxygen