A Digital Model for Determining Oxygen Consumption in Tissue
Tissue oxygenation models based on the Krogh cylinder geometry have often been used to determine oxygen distribution in various tissues, especially brain and muscle. Often, the quantity of interest is the partial pressure of oxygen (pO2) at the point in the tissue farthest from the arterial end of the capillary. This point is designated the “lethal corner” since it corresponds to the least oxygenated point in the tissue and is therefore theoretically at the greatest risk of becoming anoxic. Generally, assumptions are made regarding the dynamics of oxygen transport within such a geometry and appropriate partial differential equations are written to describe the system. Given a set of values, including tissue cylinder radius, length of capillary, metabolic rate and others, a solution can be obtained by programming the equations on a digital and/or analog computer. The solution to the equations is the pO2 at any point in the tissue or capillary cylinder.
KeywordsOxygen Metabolism Capillary Radius Estimation Program Tissue Cylinder Terminal Section
Unable to display preview. Download preview PDF.
- 1.Reneau, D.D., D.F. Bruley and M.H. Knisely, “A Mathematical Simulation of Oxygen Release, Diffusion and Consumption in the Capillaries and Tissue of the Human Brain,” in Chemical Engineering in Medicine and Biology, Plenum Press (1967)Google Scholar
- 2.Blum, J.J.: Concentration Profiles in and around Capillaries. Amer. J. Physiology 198, 991 (1960).Google Scholar
- 3.Radtke, R.R., D.F. Bruley, unpublished, (1975).Google Scholar
- 4.Advanced Continuous Simulation Language (ACSL) Users Guide Reference Manual, 3rd edition, Mitchell and Gauthier, Associates, (1981) .Google Scholar
- 5.James, M.L., G.M. Smith, J.C. Wolford, Applied Numerical Methods for Digital Computation, Harper and Row, Inc. (1977).Google Scholar
- 6.Meade, J., Prediction of Oxygen Metabolism in the Brain During Interjctai Eqpileptlform Activity by Means of a Dynamic Deter-ministic Mathematical Model. M.S. Thesis, Tulane University (1978).Google Scholar