Advertisement

Microcirculatory Mass Transfer

  • E. N. Lightfoot
  • A. M. Lenhoff
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 180)

Abstract

The dynamics of Krogh tissue cylinders and related structures are critically reviewed to determine the roles of underlying transport and reaction processes, and the interactions between them. Emphasis is put on the gaining of insight through efficient scaling procedures, and discussion is organized about the time constants characteristic of these structures and the processes occurring in them.

The basis of discussion is a new analytic solution technique which provides a formal description of indefinitely large arrays of parallel interacting elements and which includes both axial diffusion and uniform convection as well as first or zero order reaction within each element. The solution has the form of an expansion in the eigenfunctions of a non-self-adjoint differential operator.

Comparison of model predictions with previously available results identifies the useful parameter ranges of analytic approximations and determines the accuracy of existing numerical procedures.

Keywords

Peclet Number Axial Diffusion Full Solution Convective Mass Transfer Zero Order Reaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bassingthwaighte, J. B., 1974, A concurrent flow model for extraction during transcapillary passage, Circ. Res., 35:483.PubMedCrossRefGoogle Scholar
  2. Bassingthwaighte, J. B., and C. A. Goresky, 1983, Modelling in the analysis of solute and water exchange in the microvasculature, in: “Handbook of Physiology,” Sec. II, “The Cardiovascular System,” Vol. 3, “The microcirculation,” American Physiological Society, Bethesda.Google Scholar
  3. Bassingthwaighte, J. B., T. J. Knopp and J. B. Hazelrig, 1970, A concurrent flow model for capillary-tissue exchanges, in: “Capillary Permeability” (Alfred Benzon Symp. II), C. Crone and N. A. Lassen, eds., Munksgaard, Copenhagen.Google Scholar
  4. Bassingthwaighte, J. B., and B. Winkler, 1982, Kinetics of blood to cell uptake of ratio tracers, in: “Biological Transport of Radio Tracers,” L. G. Columbetti, ed., CRC Press Inc.Google Scholar
  5. Bastian, W. C., and L. Lapidus, 1956, Longitudinal diffusion in ion exchange and chromatographic columns: finite column, J. Phys. Chem., 60:816.CrossRefGoogle Scholar
  6. Bohr, C., 1909, Uber die spezifische Tatigkeit der Lungen bei der respiratorischen Gasaufnahme und ihr Verhalten zu der durch die Alveolarwand stattfindenden Gasdiffusion, Skand. Arch. f. Physiol., 22:221.CrossRefGoogle Scholar
  7. Brenner, H., 1962, The diffusion model of longitudinal mixing in beds of finite length: numerical values, Chem. Eng. Sci., 17:229.CrossRefGoogle Scholar
  8. Bronikowski, T. A., J. H. Linehan and C. A. Dawson, 1980, A mathematical analysis of the influence of perfusion heterogeneity on indicator extraction, Math. Biosci., 52:27.CrossRefGoogle Scholar
  9. Goresky, C. A., and C. P. Rose, 1977, Blood-tissue exchange in liver and heart: the influence of heterogeneity of capillary transit times, Fed. Proc., 36:2629.PubMedGoogle Scholar
  10. Goresky, C. A., W. H. Ziegler and G. G. Bach, 1970, Capillary exchange modeling: barrier-limited and flow-limited distribution, Circ. Res., 27:739.PubMedCrossRefGoogle Scholar
  11. Homer, L. D., and P. K. Weathersby, 1980, The variance of the distribution of traversal times in a capillary bed, J. Theor. Biol., 87:349.PubMedCrossRefGoogle Scholar
  12. Kety, S. S., 1951, Theory and applications of the exchange of inert gas at the lungs and tissues, Pharmacol. Rev., 3:1.PubMedGoogle Scholar
  13. Lenhoff, A. M., and E. N. Lightfoot, 1982, The effects of axial diffusion and permeability barriers on the transient response of tissue cylinders: I. Solution in transform space, J. Theor. Biol., 97:663.PubMedCrossRefGoogle Scholar
  14. Lenhoff, A. M., and E. N. Lightfoot, 1983, The effects of axial diffusion and permeability barriers on the transient response of tissue cylinders: I. Solution in transform space, J. Theor. Biol., in press.Google Scholar
  15. Lenhoff, A. M., and E. N. Lightfoot, 1983, Use of non-self-adjoint operators for describing convective mass transfer, To be presented at AIChE Annual Meeting, Washington, D.C.Google Scholar
  16. Levitt, D. G., 1970, Evaluation of the early extraction method of determining capillary permeability by theoretical capillary and organ models, Cire. Res., 27:81.CrossRefGoogle Scholar
  17. Levitt, D. G., 1971, Theoretical model of capillary exchange incorporating interactions between capillaries, Am. J. Physiol., 220:250.PubMedGoogle Scholar
  18. Lightfoot, E. N., A. M. Lenhoff and R. L. Rodriguez, 1982, Use of moments to characterize mass transport in steady flows of arbitrary complexity, Chem. Eng. Sci., 37:954.CrossRefGoogle Scholar
  19. Martin, P., and D. Yudilevich, 1964, A theory for the quantification of transcapillary exchange by tracerdilution curves, Am. J. Physiol., 207:162.PubMedGoogle Scholar
  20. Perl, W., and F. P. Chinard, 1968, Convection-diffusion model of indicator transport through an organ, Circ. Res., 22:273.PubMedCrossRefGoogle Scholar
  21. Rose, C. P., and C. A. Goresky, 1976, Vasomotor control of capillary transit time heterogeneity in the canine coronary circulation, Circ. Res., 39:541.PubMedCrossRefGoogle Scholar
  22. Stakgold, I., 1979, “Green’s Functions and Boundary-Value Problems,” Wiley-Interscience, New York.Google Scholar
  23. Tepper, R. S., H. L. Lee and E. N. Lightfoot, 1978, Transient convective mass transfer in Krogh tissue cylinders, Ann. Biomed. Eng., 6:506.PubMedCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • E. N. Lightfoot
    • 1
  • A. M. Lenhoff
    • 1
  1. 1.Department of Chemical EngineeringUniversity of WisconsinMadisonUSA

Personalised recommendations