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A Mathematical Analysis Predicting Cerebral Tissue Reoxygenation Time as a Function of the Rate of Change of Effective Cerebral Blood Flow

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Blood Oxygenation

Abstract

In vivo experimental investigations in the cortex of cat brains with the new, ultramicro oxygen electrode (2), (3) have produced surprising results that need to be correlated with adequate convectiondiffusion theory for proper analysis and future predictions. Transient changes (Figure 1) forced on arterial oxygen partial pressure (oxygen tension) of healthy cats produced tissue responses similar to that shown in Figures 2 and 3. On returning to normal conditions, oxygen tension was observed to “overshoot” normal values before leveling out at the previously recorded normal level. Identical experiments performed on the same animals when under conditions of intravascular red cell aggregation (sludge), hemorrhage, or hemorrhage combined with aggregation produced tissue responses similar to that shown in Figure 4. In these latter cases of pathologic physiology the “reoxygenation time” was greatly extended, and no overshoot was recorded.

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Bibliography

  1. Ananthakrishnan, V., W.N. Gill, and A.J. Barduhn: Laminar Dispersion in Capillaries, A.I.Ch. E. Journal, 11, No. 6, 1063–1072 (1965).

    CAS  Google Scholar 

  2. Bicher, H.I. and M.H. Knisely: Brain Tissue Reoxygenation Time Demonstrated with the New Untramicro Oxygen Microelectrode, J. App. Physiol. (In press).

    Google Scholar 

  3. Bicher, H.I., D.D. Reneau, and M.H. Knisely: The Effect of Intravascular Red Cell Aggregation (Sludge) and Hemorrhage on Blood and Tissue Oxygenation as Determined with a New, Ultramicro Oxygen Electrode, Proceedings of the ISBO (In press).

    Google Scholar 

  4. Bruce, G.H., D.W. Peaceman, H.H. Rackford, and J.D. Rice: Trans., A.I.M.E., 198, 79 (1953).

    Google Scholar 

  5. Bruley, D.F. and M.H. Knisely: Hybrid Simulation-Oxygen Transport in the Microcirculation, Chem. Engr. Symp. Ser. (In Press).

    Google Scholar 

  6. Kety, S.S.: The Cerebral Circulation in “Handbook of Physiology, Neutrophysiology III”, ed. by W.F. Hamilton and P. Dow, Chapter 71, 1751–1760, Williams and Wilkins, Baltimore, Md., 1960.

    Google Scholar 

  7. Kety, S.S., and C.F. Schmidt: The Effects of Altered Arterial Tensions of Carbon Dioxide and Oxygen on Cerebral Blood Flow and Cerebral Oxygen Consumption of Normal Young Men, J. Clin. Invest., 27, 484–492 (1948).

    Article  CAS  Google Scholar 

  8. Knisely, M.H.: Intravascular Erythrocyte Aggregation (Blood Sludge), in “Handbook of Physiology, Circulation III,” ed. by W.F. Hamilton and P. Dow, Chapter 63, pp. 2249–2292. Williams and Wilkins, Baltimore, 1965.

    Google Scholar 

  9. Knisely, M.H., D.D. Reneau and D.F. Bruley: The Development and Use of Equations for Predicting the Limits on the Rates of Oxygen Supply to the Cells of Living Tissues and Organs, Angiology (In Press).

    Google Scholar 

  10. Krogh, A.: “The Anatomy and Physiology of Capillaries,” Yale University Press, New Haven, Conn., 1922, 1 ed.

    Google Scholar 

  11. 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, 126–260 (1950).

    Article  Google Scholar 

  12. Peaceman, D.W., and H.H. Rachford, Jr.; The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Indust. Appl. Math., 3, No. 1, 28–41 (1955).

    Article  Google Scholar 

  13. 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, pp. 135–241, Plenum Press (1967).

    Google Scholar 

  14. Reneau, D.D., D.F. Bruley, and M.H. Knisely: A Digital Simulation of Oxygen Transport in Capillary-Tissue Systems (Cerebral Gray Matter), A.I.Ch.E. Journal (In Press).

    Google Scholar 

  15. Reneau, D.D., D.F. Bruley and M.H. Knisely: A Computer Simulation Showing Multiple Minute Hypoxie Areas in Cerebral Tissue as a Result of Sludged Blood, 5th Europ. Conf. Microcirculation, Gothenburg, 1968, Bibl. Anat., 10, Karger, Basel/New York (1969).

    Google Scholar 

  16. Reneau, D,D., D.F. Bruley and M.H. Knisely: A Computer Simulation for Prediction of Oxygen Limitations in Cerebral Gray Matter, JAAMI (In Press).

    Google Scholar 

  17. Reneau, D.D,, and M.H. Knisely: A Mathematical Simulation of Oxygen Transport in the Human Brain Under Conditions of Countercurrent Capillary Blood Flow, 62nd Annual Meeting A.I.Ch.E., Gas Exchange in Biological Systems, Symposium, Paper 66c, Washington, D.C. (1969).

    Google Scholar 

  18. Reneau, D.D. and M.H. Knisely: A Mathematical Simulation of Glucose Diffusion and Consumption in Brain, Proceedings of the 21st Annual Conference on Engineering in Medicine and Biology, 10, p. 29.2, 1968.

    Google Scholar 

  19. Schmidt, C.F., Central Nervous System Circulation, Fluids and Barriers-Introduction, in “Handbook of Physiology, Neuroohysiology III“, ed. by W.P. Hamilton and P. Dow, Chapter 70, 1745–1750, Williams and. Wilkins, Baltimore, Md., 1960.

    Google Scholar 

  20. Sokoloff, L. and S.S. Kety: Regulation of Cerebral Circulation, Physiol. Rev., 40, 38–49 (1960).

    Google Scholar 

  21. Thews, G.: Oxygen Diffusion in the Brain. A Contribution to the Question of the Oxygen Supply of the Organs, Pflugers Archiv, 271, 197–226 (1960).

    Article  CAS  Google Scholar 

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© 1970 Plenum Press, New York

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Reneau, D.D., Bicher, H.I., Bruley, D.F., Knisely, M.H. (1970). A Mathematical Analysis Predicting Cerebral Tissue Reoxygenation Time as a Function of the Rate of Change of Effective Cerebral Blood Flow. In: Hershey, D. (eds) Blood Oxygenation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1857-6_9

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  • DOI: https://doi.org/10.1007/978-1-4684-1857-6_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1859-0

  • Online ISBN: 978-1-4684-1857-6

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