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A Mathematical Simulation of Oxygen Release, Diffusion, and Consumption in the Capillaries and Tissue of the Human Brain

  • Daniel D. ReneauJr.
  • Duane F. Bruley
  • Melvin H. Knisely

Abstract

The purpose of this paper is to describe an attempt to obtain a better understanding of the oxygen supply to the cells of the brain by examining all phases of the release, diffusion, and consumption processes in a mathematical model. Since the original investigations of August Krogh in 1919, the mechanisms by which molecular oxygen is transported from red blood cells while they are carried in blood flowing longitudinally through capillaries, into plasma, thence radially out to and through the capillary wall into the surrounding tissues for tissue cell respiration, have been a topic of major interest. During maximal good health, and during several states of special physiology and disease states or pathologic conditions, what specific factors, or summation of factors, limit in the mathematical sense of the term the rates of oxygen supply to individual tissue cells located in individual geometric positions in the living organs? As examples, what are the effects of inhaling air containing low concentrations of oxygen, such as at high altitudes, on the individual nerve cells surrounding and all along the lengths of brain capillaries? What are the specific effects of forcibly reducing the linear rates of flow of blood through capillaries on nerve cells along the lengths of, and at various positions between, capillaries? What are the specific effects on nerve cells so located produced by the inhalation of air containing excessively high concentrations of oxygen, or of pure oxygen, perhaps under pressure such as during hyperbaric conditions?

Keywords

Oxygen Partial Pressure Oxygen Activity Mathematical Simulation Axial Diffusion Axial Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1967

Authors and Affiliations

  • Daniel D. ReneauJr.
    • 1
  • Duane F. Bruley
    • 1
  • Melvin H. Knisely
    • 2
  1. 1.Department of Chemical EngineeringClemson UniversityClemsonUSA
  2. 2.Department of AnatomyMedical College of South CarolinaCharlestonUSA

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