title: Mathematical analysis of oxygen concentration in a two dimensional array of capillaries.
abstract: An approach is presented for modeling transport and exchange in skeletal muscle that can be used to analyze vascular beds consisting of a large number of interacting capillaries. First the oxygen concentration is determined in a functional unit consisting of a single capillary surrounded by a region of tissue in which a flux is prescribed on the outer boundary of the region. This flux, which is a result of the interaction among all of the capillaries comprising the vascular bed, is then found by matching the concentration along the borders between adjacent units. This leads to a system of ordinary differential equations for the oxygen concentration in the capillaries coupled with a system of algebraic equations for the fluxes. The method is illustrated by obtaining the oxygen concentration within an array of capillaries for the case when each capillary has a different initial concentration and for the case when each capillary has a different flow rate.
authors.affiliation: Department of Mathematics and Institute for Biomedical Engineering and Mathematical Biology, Lehigh University Bethlehem, PA 18015-317, USA. eps0@lehigh.edu
authors.forename: Eric P
authors.initials: EP
authors.lastname: Salathe
mesh_terms: D000818:Animals; D001160:Arterioles / Q000502:physiology; D001783:Blood Flow Velocity / Q000502:physiology; D002196:Capillaries / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D018485:Muscle Fibers, Skeletal / Q000378:metabolism; D018482:Muscle, Skeletal / Q000098:blood supply / Q000502:physiology; D010100:Oxygen / Q000097:blood*; D010101:Oxygen Consumption / Q000502:physiology; D010313:Partial Pressure; D012039:Regional Blood Flow / Q000502:physiology
chemical_list: D010100:Oxygen