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

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Abstract

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.

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References

  1. Burton A. C. (1972) Physiology and Biophysics of the Circulation. Chicago: Year Book Medical Publishers

    Google Scholar 

  2. Debruijn R. A. Tipstreaming of drops in simple shear flows. Chem. Eng. Sci. 48:277–284, (1993)

    Article  Google Scholar 

  3. Dzwinel W., Boryczko K., Yuen D. A. (2003) A discrete-particle model of blood dynamics in capillary vessels. J. Colloid Interface Sci. 258:163–173

    Article  PubMed  CAS  Google Scholar 

  4. Eggleton C. D., Popel A. S. (1998) Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10:1834–1845

    Article  CAS  Google Scholar 

  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)

    PubMed  CAS  Google Scholar 

  6. Fischer T. M. (1980) On the energy dissipation in a tank-treading human red blood cell. Biophys. J. 32:863–868

    PubMed  CAS  Google Scholar 

  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, 1978

  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 202:894–896

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  10. Goldsmith H. L., Cokelet G. R., Gaehtgens P. (1989) Robin Fahraeus: Evolution of his concepts in cardiovascular physiology. Am. J. Physiol. 257:H1005–H1015

    PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  12. Hsu R., Secomb T. W. (1989) Motion of nonaxisymmetric red blood cells in cylindrical capillaries. J. Biomech. Eng. 111:147–151

    Article  PubMed  CAS  Google Scholar 

  13. Keller S. R., Skalak R. (1982) Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120:27–47

    Article  Google Scholar 

  14. Olla P. Simplified model for red cell dynamics in small blood vessels. Phys. Rev. Lett. 82:453–456, (1999)

    Article  CAS  Google Scholar 

  15. Pozrikidis C. (2003) Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Eng. 31:1194–1205

    Article  PubMed  CAS  Google Scholar 

  16. Pries A. R., Ley K., Claassen M., Gaehtgens P. (1989) Red cell distribution at microvascular bifurcations. Microvasc. Res. 38:81–101

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  18. Secomb T. W. (1995) Mechanics of blood flow in the microcirculation. Symp. Soc. Exp. Biol. 49:305–321

    PubMed  CAS  Google Scholar 

  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, 2003

    Google Scholar 

  20. Secomb T. W., Hsu R. (1993) Non-axisymmetrical motion of rigid closely fitting particles in fluid-filled tubes. J. Fluid Mech. 257:403–420

    Article  Google Scholar 

  21. Secomb T. W., Hsu R. (1996) Motion of red blood cells in capillaries with variable cross-sections. J. Biomech. Eng. 118:538–544

    PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  25. Sun C., Munn L. L. (2005) Particulate nature of blood determines macroscopic rheology: A 2-D lattice Boltzmann analysis. Biophys. J. 88:1635–1645

    Article  PubMed  CAS  Google Scholar 

  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. 46:65–72

    Article  PubMed  CAS  Google Scholar 

  27. Zhou H., Pozrikidis C. (1993) The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255:103–127

    Article  CAS  Google Scholar 

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Acknowledgments

Supported by NIH Grant HL034555.

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Authors and Affiliations

  1. Department of Physiology, University of Arizona, Tucson, AZ, 85724-5051, USA

    Timothy W. Secomb

  2. Department of Physiology, Charité – Universitätsmedizin Berlin, Campus Benjamin Franklin, Arnimallee 22, 14195, Berlin, Germany

    Beata Styp-Rekowska & Axel R. Pries

  3. Deutsches Herzzentrum Berlin, Augustenburger Platz 1, 13353, Berlin, Germany

    Axel R. Pries

Authors
  1. Timothy W. Secomb
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  2. Beata Styp-Rekowska
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  3. Axel R. Pries
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Correspondence to Timothy W. Secomb.

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Secomb, T.W., Styp-Rekowska, B. & Pries, A.R. Two-Dimensional Simulation of Red Blood Cell Deformation and Lateral Migration in Microvessels. Ann Biomed Eng 35, 755–765 (2007). https://doi.org/10.1007/s10439-007-9275-0

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  • DOI: https://doi.org/10.1007/s10439-007-9275-0

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