Diffusional Coupling in a Hemoglobin-Free Perfused Capillary-Tissue Structure

  • J. E. Fletcher
  • R. W. Schubert
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 169)


The theoretical prediction of substrate levels in tissue from a mathematical model has been an intensely investigated topic since Krogh initiated the concept in the period 1918 to 1929 (Krogh, 1919). Oxygen has been the most widely investigated substrate because of its obvious necessity for cell viability. However, attempts to study this viability, both experimentally and by means of a mathematical model, have been frustrated by the presence of the blood hemoglobins. The hemoglobin has the effect of a nonlinear buffer which complicates the description by mathematical model and introduces experimental difficulties in measuring actual oxygen levels in perfused tissues. Schubert (1976) had attempted to circumvent these difficulties by using an oxygen saturated modified Krebs-Henseleit perfusate.


DIFFUSIONAL Coupling Axial Diffusion Lower Pressure Range Substrate Distribution Capillary Entrance 
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  1. Blum, J., 1960, Concentration profiles in and around capillaries, Am, J, Physiol., 198: 991–998.Google Scholar
  2. Fletcher, J., 1978, Mathematical modelling of the microcirculation, Math. Biosci., 38: 159–202.CrossRefGoogle Scholar
  3. Fletcher, J., and Schubert, R., 1982a, On the computation of substrate levels in perfused tissues, Math. Biosci., in press.Google Scholar
  4. Fletcher, J., and Schubert, R., 1982b, Diffusional coupling in perfused capillary-tissue structures, in press.Google Scholar
  5. Krogh, A., 1919, The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue, J. Physiol., 52: 409–415.PubMedGoogle Scholar
  6. Olver, F.W.J., 1964, Bessel functions of integer order, in.: “Handbook of Mathematical Functions”, M. Abramowitz, I. Stegun, eds., AMS 55, NBS, U.S. Dept. of Commerce, Washington D.C., pp. 374–429.Google Scholar
  7. Schubert, R., 1976, A physiological and mathematical study of oxygen distribution in the autoregulating isolated heart, PhD thesis, Case Western University, Cleveland, Ohio.Google Scholar
  8. Schubert, R., and Whalen, W., 1976, A mass transport model for predicting O2 distribution in the autoregulating heart, Micro-vasc. Res., 11: 127.Google Scholar
  9. Schubert, R., Whalen, W., and Nair, P., 1978, Myocardial Po2 distribution: relationship to coronary autoregulation, Am. J. Physiol., 234(4): H361-H370Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • J. E. Fletcher
    • 1
  • R. W. Schubert
    • 2
  1. 1.Division of Computer Research and Technology, N.I.H.Laboratory of Applied StudiesBethesdaUSA
  2. 2.Department of Biomedical EngineeringLouisiana Tech. UniversityRustonUSA

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