A Model of Oxygen Exchange Between an Arteriole or Venule and the Surrounding Tissue

[+] Author and Article Information
D. P. V. Weerappuli, A. S. Popel

Department of Biomedical Engineering, School of Medicine, The Johns Hopkins University, Baltimore, Md. 21205

J Biomech Eng 111(1), 24-31 (Feb 01, 1989) (8 pages) doi:10.1115/1.3168335 History: Received March 30, 1988; Revised November 07, 1988; Online June 12, 2009


A mathematical model is developed to study the effect of capillary convection on oxygen transport around segments of arterioles and venules that are surrounded by capillaries. These capillaries carry unidirectional flow perpendicular to the vessel. The discrete capillary structure is distributed in a manner determined by the capillary blood flow and capillary density. A nonlinear oxyhemoglobin dissociation curve described by the Hill equation is used in the analysis. Oxygen flux from the vessel is expressed as a relationship between Sherwood and Peclet numbers, as well as other dimensionless combinations involving parameters of the capillary bed. A numerical solution is obtained with a finite difference method. The numerical results obtained within the physiological range of parameters allow the prediction of longitudinal gradients of hemoglobin-oxygen saturation along the arterioles and venules.

Copyright © 1989 by ASME
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