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Red blood cell mechanics and capillary blood rheology

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Abstract

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessel walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic “tank-treading” motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.

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References

  1. Chien, S. (1975), Biophysical behavior of red cells in suspension,The Red Blood Cell, vol. 1, Surgenor, D. M., ed., Academic, New York, pp. 1031–1133.

    Google Scholar 

  2. Schmid-Schönbein, G. W., Sung, K. P., Tozeren, H., Skalak, R., and Chien, S. (1981), Passive mechanical properties of human leukocytes,Biophys. J. 36, 243–256.

    PubMed  Google Scholar 

  3. Lighthill, M. J. (1968), Pressure-forcing of tightly fitting pellets along fluidfilled elastic tubes,J. Fluid Mech. 34, 113–143.

    Article  Google Scholar 

  4. Barnard, A. C. L., Lopez, L., and Heliums, J. D. (1968), Basic theory of blood flow in capillaries,Microvasc. Res. 1, 23–34.

    Article  Google Scholar 

  5. Lin, K. L., Lopez, L., and Heliums, J. D. (1973), Blood flow in capillaries,Microvasc. Res. 5, 7–19.

    Article  PubMed  CAS  Google Scholar 

  6. Secomb, T. W. and Gross, J. F. (1983), Flow of red blood cells in narrow capillaries: role of membrane tension,Int. J. Microcirc. Clin. Exp. 2, 229–240.

    PubMed  CAS  Google Scholar 

  7. Secomb, T. W., Skalak, R., Özkaya, N., and Gross, J. F. (1986), Flow of axisymmetric red blood cells in narrow capillaries,J. Fluid Mech. 163, 405–423.

    Article  Google Scholar 

  8. Skalak, R. (1981), Blood rheology,Mathematical Aspects of Physiology (Lectures in Applied Mathematics, Vol 19). Hoppensteadt, F. C., ed. American Mathematical Society, Providence, RI, pp. 109–139.

    Google Scholar 

  9. Zarda, P. R., Chien, S., and Skalak, R. (1977), Interaction of viscous incompressible fluid with an elastic body,Computational Methods for Fluid-Solid Interaction Problems, Belytschko, T. and Geers, T. L., eds., American Society of Mechanical Engineers, New York, pp. 65–82.

    Google Scholar 

  10. Secomb, T. W. (1987), Flow-dependent rheological properties of blood in capillaries,Microvasc. Res. 34, 46–58.

    Article  PubMed  CAS  Google Scholar 

  11. Evans, E. A. and Skalak, R. (1980),Mechanics and Thermodynamics of Biomembranes, CRC., Boca Raton, FL, pp. 67–141.

    Google Scholar 

  12. Hochmuth, R. M. and Waugh, R. E. (1987), Erythrocyte membrane elasticity and viscosity,Ann. Rev. Physiol. 49, 209–219.

    Article  CAS  Google Scholar 

  13. Evans, E. A. (1983), Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests,Biophys. J. 43, 27–30.

    PubMed  CAS  Google Scholar 

  14. Chien, S., Sung, K.-L.P., Skalak, R., Usami, S., and Tözeren, A. (1978), Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,Biophys. J. 24, 463–487.

    PubMed  CAS  Google Scholar 

  15. Secomb, T. W. and Hsu, R. (1987), Effect of assumed stress-free configuration of red blood cell membrane on capillary blood rheology,Fed. Proc. 46, 1060.

    Google Scholar 

  16. Secomb, T. W. (1988), Interaction between bending and tension forces in bilayer membranes,Biophys. J. 54, 743–746.

    Article  PubMed  CAS  Google Scholar 

  17. Timoshenko, S. (1940),Theory of Plates and Shells, McGraw-Hill, New York.

    Google Scholar 

  18. Cameron, A. (1966),The Principles of Lubrication, Wiley, New York. p. 61.

    Google Scholar 

  19. Tözeren, H. and Skalak, R. (1978), The steady flow of closely fitting incompressible elastic spheres in a tube,J. Fluid Mech. 87, 1–16.

    Article  Google Scholar 

  20. Wang, H. and Skalak, R. (1969), Viscous flow in a cylindrical tube containing a line of spherical particles,J. Fluid Mech. 38, 75–96.

    Article  Google Scholar 

  21. Halpern, D. and Secomb, T. W. (1991), Viscous motion of disc-shaped particles through parallel-sided channels with near minimal widths,J. Fluid Mech. 231, 545–560.

    Article  Google Scholar 

  22. Dvinsky, A. S., and Popel, A. S. (1987), Motion of a rigid cylinder between parallel plates in Stokes flow: Poiseuille and Couette flow,Computers & Fluids 15, 405–419.

    Article  CAS  Google Scholar 

  23. Skalak, R. and Branemark, P.-I. (1969), Deformation of red blood cells in capillaries,Science 164, 717–719.

    Article  PubMed  CAS  Google Scholar 

  24. Gaehtgens, P., Dührssen, C., and Albrecht, K. H. (1980), Motion, deformation and interaction of blood cells and plasma during flow through narrow capillary tubes,Blood Cells,6, 799–812.

    PubMed  CAS  Google Scholar 

  25. Lingard, P. (1979), Capillary pore rheology of erythrocytes: The glass capillary array-effect of velocity and hematocrit in long bore tubes,Microvase. Res. 17, 272–289.

    Article  CAS  Google Scholar 

  26. Driessen, G. K., Fischer, T. M., Haest, C. W. M., Inhoffen, W., and Schmid-Schönbein, H. (1984), Flow behaviour of rigid red blood cells in the microcirculation,Int. J. Microcirc. Clin. Exp. 3, 197–210.

    PubMed  CAS  Google Scholar 

  27. Lee, J. S. and Fung, Y. C. (1969), Modeling experiments of a single red blood cell moving in a capillary blood vessel,Microvasc. Res. 1, 221–243.

    Article  PubMed  CAS  Google Scholar 

  28. Canham, P. B. and Burton, A. C. (1968), Distribution of size and shape in populations of normal human red blood cells,Circ. Res. 22, 405–422.

    PubMed  CAS  Google Scholar 

  29. Halpern, D. and Secomb, T. W. (1989), The squeezing of red blood cells through capillaries with near-minimal diameters,J. Fluid Mech. 203, 381–400.

    Article  Google Scholar 

  30. Gaehtgens, P. (1981), In vitro studies of blood rheology in microscopic tubes,The Rheology of Blood, Blood Vessels and Associated Tissues, Gross, D. R. and Hwang, N. H. C., eds., Sijthoff and Nordhoff, Alphen an den Rijn, The Netherlands, pp. 257–275.

    Google Scholar 

  31. Gaehtgens, P. and Schmid-Schönbein, H. (1982), Mechanisms of dynamic flow adaptation of mammalian erythrocytes,Naturwissenschaften 69, 294–296.

    Article  PubMed  CAS  Google Scholar 

  32. Secomb, T. W. and Skalak, R. (1982), A two-dimensional model for capillary flow of an asymmetric cell,Microvasc. Res. 24, 194–203.

    Article  PubMed  CAS  Google Scholar 

  33. Hsu, R. and Secomb, T. W. (1989), Motion of non-axisymmetric red blood cells in cylindrical capillaries,J. Biomechan. Eng. 111, 147–151.

    CAS  Google Scholar 

  34. Secomb, T. W. and Skalak, R. (1982), A two-dimensional model for capillary flow of an asymmetric cell,Microvasc. Res. 24, 194–203.

    Article  PubMed  CAS  Google Scholar 

  35. Fischer, T. M., Stöhr-Liesen, M., and Schmid-Schönbein, H. (1978), The red cell as a fluid droplet: Tank tread-like motion of the human erythrocyte membrane in shear flow,Science 202, 894–896.

    Article  PubMed  CAS  Google Scholar 

  36. Secomb, T. W. and Hsu, R. (1992), Non-symmetric motion of rigid closelyfitting particles in fluid-filled tubes,J. Fluid Mech. (submitted).

  37. Sugihara-Seki, M., Secomb, T. W., and Skalak, R. (1990), Two-dimensional analysis of two-file flow of red cells along capillaries,Microvasc. Res. 40, 379–393.

    Article  PubMed  CAS  Google Scholar 

  38. Lipowsky, H. H., Kovalcheck, S., and Zweifach, B. W. (1978), The distribution of blood rheological parameters in the microvasculature of cat mesentery,Circ. Res. 43, 738–749.

    PubMed  CAS  Google Scholar 

  39. Pries, A. R., Secomb, T. W., Gaehtgens, P., and Gross, J. F. (1990), Blood flow in microvascular networks-Experiments and simulation,Circ. Res,67, 826–834.

    PubMed  CAS  Google Scholar 

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Secomb, T.W. Red blood cell mechanics and capillary blood rheology. Cell Biophysics 18, 231–251 (1991). https://doi.org/10.1007/BF02989816

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  • DOI: https://doi.org/10.1007/BF02989816

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