The Theoretical Prediction of Substrate Levels and Their Histograms in Cell Free Perfused Tissues

  • John E. Fletcher
  • Roy W. Schubert
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 159)


The development of experimental techniques to study substrate levels in the isolated perfused heart and brain have renewed interest in the mathematical modelling of perfused capillary-tissue structures. We have reconsidered an analytic representation of the Krogh cylinder model for capillary-tissue structures and relate this mathematical model to experimental data through histograms of the oxygen (PO2) distribution. Model histograms are computed for experimental parameters of interest and changes in the histogram associated with changes in model parameters, especially diffusion constants, are demonstrated.


Series Solution Radial Diffusion Substrate Level Axial Diffusion Perfuse Heart 


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  1. 1.
    Krogh, A. 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, 1919.PubMedGoogle Scholar
  2. 2.
    Schubert, R., Whalen, W. and Nair, P. Myocardial P02 distribution: relationship to coronary autoregulation, Am. J. Physiol. 234 (4), H361 - H370, 1978.Google Scholar
  3. 3.
    Blum, J. Concentration profiles in and around capillaries. Amer. J. Physiol. 198, 991–998, 1960.Google Scholar
  4. 4.
    Fletcher, J. Mathematical modelling of the microcirculation. Math. Biosciences. 38, 159–202, 1978.CrossRefGoogle Scholar
  5. 5.
    Schubert, R. A physiological and mathematical study of oxygen distribution in the autoregulating isolated heart, PhD thesis, Case Western Reserve University, Cleveland, Ohio, 1976.Google Scholar
  6. 6.
    Salathé, E., and Wang, T., Substrate concentrations in tissue surronding single capillaries, Math. Biosciences, Vol. 49: 235–247, 1980.CrossRefGoogle Scholar
  7. 7.
    Olver, F. Bessel functions of integer order, in Handbook of Mathematical Functions, Abramowitz and Stegun eds., NBS AMS Nc. 55, Nov. 1964, p. 374–379.Google Scholar
  8. 8.
    Fletcher, J. and Schubert, R. On the computation of substrate levels in perfused tissues, 1981, submitted for publication.Google Scholar
  9. 9.
    Schubert, R. and Reneau, D. Assembling and comparing histograms of micro circulation data, Micro Vasc. 17 (3), P. S172, 1979.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • John E. Fletcher
    • 1
    • 2
  • Roy W. Schubert
    • 1
    • 2
  1. 1.Laboratory of Applied StudiesDivision of Computer Research and Technology, N.I.H.BethesdaUSA
  2. 2.Department of Biomedical EngineeringLouisiana Tech UniversityRustonUSA

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