A Stochastic Model for the Transport of Oxygen to Brain Tissue

  • Duane F. Bruley
  • Lynn J. Groome
  • Haim Bicher
  • Melvin H. Knisely
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 75)


Material balances around a small, but finite volume element have formed the basis for previous mathematical models describing the transport of oxygen in the brain microcirculation. Seeking a model which would be both simple and versatile, a stochastic model was proposed based on the assumption that oxygenation of the brain can be described quantitatively by simulating the activity of only one erythrocyte and the oxygen molecules surrounding it. Compared with existing deterministic models, the capillary space-average oxygen partial pressure profiles were in close agreement. Tissue tensions were decidedly different.


Stochastic Model Oxygen Partial Pressure Deterministic Model Oxygen Molecule Fractional Saturation 
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Literature Cited

  1. 1.
    Bugliarello, G., and G. C. Hsiao, “Numerical Simulation of Three-Dimensional Flow in the Axial Plasmatic Gaps of Capillaries”, Digest of the Seventh International Conference on Medical and Biological Engineering (1967).Google Scholar
  2. 2.
    Davis, E. J., D. O. Cooney and R. Chang, “Mass Transfer Between Capillary Blood and Tissues”, to be published.Google Scholar
  3. 3.
    Groome, L. J., “The Random Walk as Applied to Stochastic Modeling of the Brain Microcirculation”, unpublished Masters Thesis, Clemson University, Clemson, South Carolina, 1974.Google Scholar
  4. 4.
    Halberg, M. R., Bruley, D. F., and M. H. Knisely, “Simulation of Oxygen Transport in the Brain by Monte Carlo Methods”, Simulation, Vol. 15, No. 5, pp. 206–212, November 1970.CrossRefGoogle Scholar
  5. 5.
    Hoel, P. G., S. C. Port, and C. J. Stone, Introduction to Stochastic Processes, Houghton Mifflin Company, Boston, 1971.Google Scholar
  6. 6.
    Hunt, D. H., D. F. Bruley, H. I. Bicher and M. H. Knisely, “Oxygen Transport In the Brain Microcirculation by A Hybrid Computer Nonlinear Monte Carlo Method”, Proceedings of Summer Computer Simulation Conferences, Montreal, Canada, July 1973.Google Scholar
  7. 7.
    Langely, L. L., I. R. Telford and J. B. Christenson, Dynamic Anatomy and Physiology, McGraw-Hill Book Company, 1969.Google Scholar
  8. 8.
    McCracken, T. A., Bruley, D. F. and M. H. Knisely, “A Systems Analysis for the Transport of Oxygen and the Simultaneous Transport of Oxygen, Carbon Dioxide and Glucose in the Capillaries and Tissues of the Human Brain” Proceedings of First Pacific Chemical Engineering Congress, Kyoto, Japan, pp. 137–143, October, 1972.Google Scholar
  9. 9.
    Opitz, E., and M. Schneider, “The Oxygen Supply of the Brain and the Mechanism of Deficiency Effects”, Ergebnisse der Physiologie, biologischem, Chemie, und experimentallen Pharmakologie, 46, 126 (1950).CrossRefGoogle Scholar
  10. 10.
    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, ed., by D. Hershey, Plenum Press, N. Y., 1967.Google Scholar
  11. 11.
    Reneau, D. D., D. F. Bruley, and M. H. Knisely, “A Digital Simulation of Transient Oxygen Transport in Capillary-Tissue Systems (Cerebral Grey Matter),” AIChE Journal, 15, 916, November, 1969.CrossRefGoogle Scholar
  12. 12.
    Wyman, C. E., “Numerical Solution of Multidimensional and Nonlinear Diffusion Problems”, unpublished Ph.D. Dissertation, Princeton University, Princeton, New Jersey, 1971.Google Scholar
  13. 13.
    Wyman, C. E., and M. D. Kosten, “Stochastic Green’s Function Method for Calculating the Concentration Profile of a Chemically Reactive Species”, Chemical Engineering Computing, November (1971).Google Scholar
  14. 14.
    Grote, Jurgen. “Biological Problems of Gas Exchange in Human Organism” unpublished paper, Physiologisches Institute, Johannes Gutenberg — Universitat, Mainz, West Germany, April, 1968.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • Duane F. Bruley
    • 1
  • Lynn J. Groome
    • 2
  • Haim Bicher
    • 3
  • Melvin H. Knisely
    • 4
  1. 1.Dept. of ChETulane Univ.New OrleansUSA
  2. 2.Dept. of ChEClemson Univ.ClemsonUSA
  3. 3.Dept. of PharmacologyMed. School of ArkansasLittle RockUSA
  4. 4.Dept. of AnatomyMed. Univ. of S.C.CharlestonUSA

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