Annals of Biomedical Engineering

, Volume 35, Issue 5, pp 755–765 | Cite as

Two-Dimensional Simulation of Red Blood Cell Deformation and Lateral Migration in Microvessels

  • Timothy W. Secomb
  • Beata Styp-Rekowska
  • Axel R. Pries


A theoretical method is used to simulate the motion and deformation of mammalian red blood cells (RBCs) in microvessels, based on knowledge of the mechanical characteristics of RBCs. Each RBC is represented as a set of interconnected viscoelastic elements in two dimensions. The motion and deformation of the cell and the motion of the surrounding fluid are computed using a finite-element numerical method. Simulations of RBC motion in simple shear flow of a high-viscosity fluid show “tank-treading’’ motion of the membrane around the cell perimeter, as observed experimentally. With appropriate choice of the parameters representing RBC mechanical properties, the tank-treading frequency and cell elongation agree closely with observations over a range of shear rates. In simulations of RBC motion in capillary-sized channels, initially circular cell shapes rapidly approach shapes typical of those seen experimentally in capillaries, convex in front and concave at the rear. An isolated RBC entering an 8-μm capillary close to the wall is predicted to migrate in the lateral direction as it traverses the capillary, achieving a position near the center-line after traveling a distance of about 60 μm. Cell trajectories agree closely with those observed in microvessels of the rat mesentery.


Erythrocyte mechanics Capillary flow Shear flow Tank-treading 



Supported by NIH Grant HL034555.


  1. 1.
    Burton A. C. (1972) Physiology and Biophysics of the Circulation. Chicago: Year Book Medical PublishersGoogle Scholar
  2. 2.
    Debruijn R. A. Tipstreaming of drops in simple shear flows. Chem. Eng. Sci. 48:277–284, (1993)CrossRefGoogle Scholar
  3. 3.
    Dzwinel W., Boryczko K., Yuen D. A. (2003) A discrete-particle model of blood dynamics in capillary vessels. J. Colloid Interface Sci. 258:163–173PubMedCrossRefGoogle Scholar
  4. 4.
    Eggleton C. D., Popel A. S. (1998) Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10:1834–1845CrossRefGoogle Scholar
  5. 5.
    Evans E. A. Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests. Biophys. J. 43:27–30, (1983)PubMedGoogle Scholar
  6. 6.
    Fischer T. M. (1980) On the energy dissipation in a tank-treading human red blood cell. Biophys. J. 32:863–868PubMedGoogle Scholar
  7. 7.
    Fischer, T. M., M. Stöhr, and H. Schmid-Schönbein. Red blood cell (rbc) microrheology: Comparison of the behavior of single rbc and liquid droplets in shear flow. AIChE Symp. Ser. No. 182, 74:38–45, 1978Google Scholar
  8. 8.
    Fischer T. M., Stöhr-Lissen M., Schmid-Schönbein H. (1978) The red cell as a fluid droplet: Tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202:894–896PubMedCrossRefGoogle Scholar
  9. 9.
    Gaehtgens P., Schmid-Schönbein H. (1982) Mechanisms of dynamic flow adaptation of mammalian erythrocytes. Naturwissenschaften 69:294–296PubMedCrossRefGoogle Scholar
  10. 10.
    Goldsmith H. L., Cokelet G. R., Gaehtgens P. (1989) Robin Fahraeus: Evolution of his concepts in cardiovascular physiology. Am. J. Physiol. 257:H1005–H1015PubMedGoogle Scholar
  11. 11.
    Hochmuth R. M., Waugh R. E. (1987) Erythrocyte membrane elasticity and viscosity. Annu. Rev. Physiol. 49:209–219PubMedCrossRefGoogle Scholar
  12. 12.
    Hsu R., Secomb T. W. (1989) Motion of nonaxisymmetric red blood cells in cylindrical capillaries. J. Biomech. Eng. 111:147–151PubMedCrossRefGoogle Scholar
  13. 13.
    Keller S. R., Skalak R. (1982) Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120:27–47CrossRefGoogle Scholar
  14. 14.
    Olla P. Simplified model for red cell dynamics in small blood vessels. Phys. Rev. Lett. 82:453–456, (1999)CrossRefGoogle Scholar
  15. 15.
    Pozrikidis C. (2003) Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Eng. 31:1194–1205PubMedCrossRefGoogle Scholar
  16. 16.
    Pries A. R., Ley K., Claassen M., Gaehtgens P. (1989) Red cell distribution at microvascular bifurcations. Microvasc. Res. 38:81–101PubMedCrossRefGoogle Scholar
  17. 17.
    Secomb T. W. Flow-dependent rheological properties of blood in capillaries. Microvasc. Res. 34:46–58, (1987)PubMedCrossRefGoogle Scholar
  18. 18.
    Secomb T. W. (1995) Mechanics of blood flow in the microcirculation. Symp. Soc. Exp. Biol. 49:305–321PubMedGoogle Scholar
  19. 19.
    Secomb, T. W. Mechanics of red blood cells and blood flow in narrow tubes. In Pozrikidis, C. (ed.) Hydrodynamics of Capsules and Cells. Chapman & Hall/CRC Boca Raton, Florida: 163–196, 2003Google Scholar
  20. 20.
    Secomb T. W., Hsu R. (1993) Non-axisymmetrical motion of rigid closely fitting particles in fluid-filled tubes. J. Fluid Mech. 257:403–420CrossRefGoogle Scholar
  21. 21.
    Secomb T. W., Hsu R. (1996) Motion of red blood cells in capillaries with variable cross-sections. J. Biomech. Eng. 118:538–544PubMedGoogle Scholar
  22. 22.
    Secomb T. W., Skalak R. (1982) A two-dimensional model for capillary flow of an asymmetric cell. Microvasc. Res. 24:194–203PubMedCrossRefGoogle Scholar
  23. 23.
    Secomb T. W., Skalak R., Ozkaya N., Gross J. F. (1986) Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163:405–423CrossRefGoogle Scholar
  24. 24.
    Sugihara-Seki M., Secomb T. W., Skalak R. (1990) Two-dimensional analysis of two-file flow of red cells along capillaries. Microvasc. Res. 40:379–393PubMedCrossRefGoogle Scholar
  25. 25.
    Sun C., Munn L. L. (2005) Particulate nature of blood determines macroscopic rheology: A 2-D lattice Boltzmann analysis. Biophys. J. 88:1635–1645PubMedCrossRefGoogle Scholar
  26. 26.
    Tran-Son-Tay R., Sutera S. P., Rao P. R. (1984) Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion. Biophys. J. 46:65–72PubMedCrossRefGoogle Scholar
  27. 27.
    Zhou H., Pozrikidis C. (1993) The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255:103–127CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2007

Authors and Affiliations

  • Timothy W. Secomb
    • 1
  • Beata Styp-Rekowska
    • 2
  • Axel R. Pries
    • 2
    • 3
  1. 1.Department of PhysiologyUniversity of ArizonaTucsonUSA
  2. 2.Department of PhysiologyCharité – Universitätsmedizin Berlin, Campus Benjamin FranklinBerlinGermany
  3. 3.Deutsches Herzzentrum BerlinBerlinGermany

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