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Transient oxygen transport in hemoglobin layers under conditions of the microcirculation

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Abstract

In mathematical simulation of oxygen transport the diffusion problem is often simplified by several assumptions including that of local chemical equilibrium and of negligible augmentation of oxygen transport by oxyhemoglobin diffusion. In the present work the applicability of the various assumptions is investigated by numerical solution of the equations governing transient diffusion and reaction in hemoglobin layers. The fluxes, and space and time scales are chosen to cover the range of interest in the microcirculation. The results show that significant improvements in accuracy are possible by treatment of a more complete system of equations, and show the relative importance of the various simplifying assumptions.

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References

  1. Douglas, J. The application of stability analysis in the numerical solution of quasilinear parabolic differential equations.Trans. Am. Math. Soc. 89:484–518, 1958.

    Google Scholar 

  2. Fletcher, J.E. A model describing the unsteady transport of substrate to tissue from the microcirculation. SIAMJ. Appl. Math. 29:449–480, 1975.

    Article  Google Scholar 

  3. Gaehtgens, P. and H. Schmid-Schonbein. Red cell rheology and flow. Abstract from Second World Congress for Microculation: La Jolla, CA, July 1979.

  4. Garred, L.J. Aspects of mass transport in biological systems. Ph.D. thesis, University of Minnesota, Minneapolis, 1975.

    Google Scholar 

  5. Gijsbers, G.H. and J.J. Van Ouwerkerk. Boundary layer resistance of steady-state oxygen diffusion facilitated by a four-step chemical reaction with hemoglobin in solution.Pflugers Arch. 365:231–241, 1976.

    Article  CAS  PubMed  Google Scholar 

  6. Gonzalez-Fernandez, J.M. and S.E. Atta. Transport and consumption of oxygen in capillary-tissue structures.Math. Biosci. 2:225–262, 1968.

    Article  Google Scholar 

  7. Hellums, J.D. The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue.Microvasc. Res. 13:131–136, 1977.

    Article  CAS  PubMed  Google Scholar 

  8. Kutchai, H. Numerical study of oxygen uptake by layers of hemoglobin solution.Resp. Physiol. 10:273–284, 1970.

    CAS  Google Scholar 

  9. Leonard E.F. and S.B. Jørgensen. The analysis of convection and diffusion in capillary beds.Ann. Rev. Biophys. and Bioeng., 293–339, 1974.

  10. Lightfoot, E.N., Jr.Transport Phenomena and Living Systems. New York: John Wiley and Sons, 1974, pp. 334–343.

    Google Scholar 

  11. Lih, M.M.Transport Phenomena in Medicine and Biology. New York: John Wiley and Sons, 1975, pp. 415–427.

    Google Scholar 

  12. Middleman, S.Transport Phenomena in the Cardiovascular Systems. New York: John Wiley and Sons, 1972, pp. 116–140.

    Google Scholar 

  13. Moll, W. The influence of hemoglobin diffusion on oxygen uptake and release by red cell.Resp. Physiol. 6:1–15, 1969.

    Google Scholar 

  14. Nicolson, P. and F.J.W. Roughton. A theoretical study of the influence of diffusion and chemical reaction velocity on the rate of exchange of carbon monoxide and oxygen between the red blood corpuscle and the surrounding fluid.Proc. Roy. Soc. London, Ser. B. 140:203–229, 1952.

    Google Scholar 

  15. Reneau, D.D., D.F. Bruley, and M.H. Knisley. 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, edited by D. Hershey. New York: Plenum Press, 1967, pp. 135–241.

    Google Scholar 

  16. Reneau, D.D., D.F. Bruley, and M.H. Knisley. A digital simulation of transient oxygen transport in capillary tissue systems (cerebral grey matter).AICHE J. 15:916–925, 1969.

    Article  CAS  Google Scholar 

  17. Roughton, F.J.W. Diffusion and chemical reaction velocity in cylindrical and spherical systems of physiological interest.Proc. Roy. Soc. London, Ser. B. 138:241–264, 1951.

    Google Scholar 

  18. Sheth, B.V. Oxygen transport in hemoglobin solution-applications in the microcirculation, M.S. thesis in chemical engineering, Rice University, 1979.

  19. Spaan, A.E., F. Kreuzer, and L. Hoofd. A theoretical analysis of nonsteady-state oxygen transfer in layers of hemoglobin solution.Pflugers Arch. 384:231–239, 1980.

    CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Biomedical Engineering Laboratory, Rice University, 77001, Houston, Texas

    B. V. Sheth & J. D. Hellums

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  1. B. V. Sheth
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  2. J. D. Hellums
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This work was supported by the National Institutes of Health under Grant 2R 01 HL18584.

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Sheth, B.V., Hellums, J.D. Transient oxygen transport in hemoglobin layers under conditions of the microcirculation. Ann Biomed Eng 8, 183–196 (1980). https://doi.org/10.1007/BF02364475

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