Advertisement

Formation and destruction of erythrocyte rouleau in a vessel with local bulge

  • S. E. Kornelik
  • E. K. Borzenko
  • A. N. Grishin
  • M. A. Bubenchikov
  • V. I. Stolyarov
Article

Abstract

A mathematical model of aggregation and destruction of erythrocyte clots in the shear flow is constructed. Calculations show the influence of shear stresses in a blood flow on the mean dimension of clots. It is also shown that the sinuses of aneurysms create conditions for formation of large agglomerates, which can result in thrombosis of a blood vessel under consideration.

Keywords

Shear Rate Deformation Rate Adhesion Force Fractal Dimensionality Erythrocyte Aggregation 
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.

References

  1. 1.
    Z. Lou and W. J. Yang, “A Computer Simulation of the Blood Flow in the Aortic Bifurcation with Flexible Walls,” in Proceedings of the ASCE Engineering Mechanics Speciality Conference “Mechanics Computing in 1990’s and Beyond”, Ohio, 1991, Ed. by H. Adeli and R. Sierakowski (ASCE, New York, 1991), vol. 1, pp. 544–548.Google Scholar
  2. 2.
    G. G. Ferguson, “Physical Factors in the Initiation, Growth and Rupture of Human Intracranial Saccular Aneurysms,” J. Neurosurg. 37, 666–676 (1972).Google Scholar
  3. 3.
    W. E. Stehbens, “Flow Disturbances in Glass Models of Aneurysms at Low Reynolds Numbers,” Q. J. Exp. Physiol. 59, 167–174 (1974).Google Scholar
  4. 4.
    H. J. Steiger, “Pathophysiology of Development and Rupture of Cerebral Aneurysms,” Acta Neurochir. 48, 11–23 (1990).Google Scholar
  5. 5.
    K. N. T. Kayembe, M. Sasahara, and F. Nazama, “Cerebral Aneurysms and Variations of the Circle of Willis,” Stroke 15, 846–850 (1984).Google Scholar
  6. 6.
    W. E. Stenbens, “Etiology of Intracranial Berry Aneurysm,” J. Neurosurg. 70, 823–831.Google Scholar
  7. 7.
    S. Ahmed and D. P. Giddens, “Pulsatile Poststenotic Flow Studies with Laser Doppler Anemometry,” J. Biomech. 17, 695 (1984).CrossRefGoogle Scholar
  8. 8.
    M. Ojha, R. S. Cobbold, K. W. Johnston, and R. L. Hummel, “Pulsatile Flow Through Constricted Tubes: An Experimental Investigation Using Photochromic Tracer Methods,” J. Fluid Mech. 203, 173 (1989).CrossRefGoogle Scholar
  9. 9.
    M. Ojha, R. S. Cobbold, K. W. Johnston, and R. L. Hummel, “Detailed Visualization of Pulsatile Flow Fields Produced by Modelled Arterial Stenoses,” J. Biomed. Eng. 12, 463–469 (1990).CrossRefGoogle Scholar
  10. 10.
    S. Chien, “Physiological and Pathological Significance of Hemorheology,” in Clinical Hemorheology, Ed. by S. Chien (Martinus Nijhoff, Dordrecht, 1987), pp. 125–164.Google Scholar
  11. 11.
    S. Chien, S. A. Luse, K. M. Jan, et al., “Effects of Macromolecules on the Rheology and Ultrastructure of Red Cells Suspensions,” in Proceedings of the 6th European Conference on Microcirculation, Aalborg, 1970, Ed. by J. Ditzel and D. H. Lewis (S. Karger, Basel), pp. 29–34.Google Scholar
  12. 12.
    S. Chien, “Clumping (Reversible Aggregation and Irreversible Agglutination) of Blood Cellular Elements,” Thromb. Res. 8(Suppl. II), 189–202 (1976).CrossRefGoogle Scholar
  13. 13.
    S. Chien, “Electrochemical Interaction and Energy Balance in Red Blood Cell Aggregation,” in Topics in Bioelectricity and Bioenergetics, Ed. By G. Milazzo (Wiley, New York, 1981), vol. 4, pp. 73–112.Google Scholar
  14. 14.
    A. P. Gast and L. Leibler, “Interaction of Sterically Stabilized Particles Suspended in a Polymer Solution,” J. Macromol. 19, 686–691 (1986).CrossRefGoogle Scholar
  15. 15.
    J. F. Joanny, L. Leibler, and P. G. De Gennes, “Effects of Polymer Solutions on Colloid Stability,” J. Polym. Sci. 17, 1030–1084 (1979).Google Scholar
  16. 16.
    S. Chien, “Biophysical Behavior of Red Cells in Suspensions,” in The Red Blood Cell, Ed. by D. M. Surgenor (Academic Press, New York, 1975), pp. 1031–1133.Google Scholar
  17. 17.
    M. Elimelech, J. Gregory, X. Jia, and R.A. Williams, Particle Deposition and Aggregation: Measurement, Modeling and Simulation (Butterworth-Heinemann, Oxford, 1995), chap. 6, pp. 157–202.CrossRefGoogle Scholar
  18. 18.
    P. A. Shamlou and N. Titchener-Hooker, “Turbulent Aggregation and Breakup of Particles in Liquids in Stirred Vessels,” in Processing of Solid-Liquid Suspensions, Ed. by P. A. Shamlou (Butterworth-Heinemann, Oxford, 1993), pp. 1–25.Google Scholar
  19. 19.
    K. Muhle, “Floc Stability in Laminar and Turbulent Flow,” in Coagulation and Flocculation, Theory and Applications, Ed. by B. Dobias (M. Dekker, New York, 1993), pp. 355–390.Google Scholar
  20. 20.
    A. P. Shortland, R. A. Black, J. C. Jarvis, et al., “Formation and Travel of Vortices in Model Ventricles: Application to the Design of Skeletal Muscle Ventricles,” J. Biorheol. 29(4), 501–511 (1996).Google Scholar
  21. 21.
    M. Hasegawa, “Rheological Properties and Wall Structures of Large Veins,” J. Biorheol. 20(5), 531–545 (1983).MathSciNetGoogle Scholar
  22. 22.
    B. Lim, P. J. Bascom, and R. S. C. Cobbold, “Simulation of Red Cell Aggregation in Shear Flow,” J. Biorheol. 34(6), 425–441 (1997).Google Scholar
  23. 23.
    Y. W. Yuan and K. K. Shung, “Echoicity of Whole Blood,” J. Ultrasound Med. 8, 425–434 (1989).Google Scholar
  24. 24.
    L. Y. L. Mo, R. S. C. Cobbold, C. Gutt, et al., “Non-Newtonian Behavior of Whole Blood in a Large Diameter Tube,” J. Biorheol. 28(5), 421–427 (1991).Google Scholar
  25. 25.
    R. E. N. Shehada, R. S. C. Cobbold, and L. Y. L. Mo, “Aggregation Effects in Whole Blood: Influence of Time and Shear Rate Measurement Using Ultrasound,” J. Biorheol. 31(1) 115–135 (1994).Google Scholar
  26. 26.
    T. Murata and T. W. Secomb, “Effects of Shear Rate on Rouleau Formation in Simple Shear Flow,” J. Biorheol. 25(1–2), 113–122 (1988).Google Scholar
  27. 27.
    A. A. Samarskii, An Introduction to the Theory of Difference Schemes (Nauka, Moscow, 1971) [in Russian].Google Scholar
  28. 28.
    M. Kolb and R. Jullien, “Chemically Limited Versus Diffusion Limited Aggregation,” J. Phys. Lett. 45, 977–981 (1984).CrossRefGoogle Scholar
  29. 29.
    P. Mills, “Non-Newtonian Behavior of Flucculated Suspensions,” J. Phys. Lett. 46, 301–309 (1985).CrossRefGoogle Scholar
  30. 30.
    P. Snabre, M. Bitbol, and P. Mills, “Cell Disaggregation Behavior in Shear Flow,” J. Biophys. 51, 795–807 (1987).CrossRefGoogle Scholar
  31. 31.
    P. Meakin, “Fractal Aggregates and Their Fractal Measures,” in Phase Transitions and Critical Phenomena, Ed. by -. Domb and J. L. Lebowitz (Academic Press, London, 1988), vol. 12.Google Scholar
  32. 32.
    T. Fabry, “Mechanism of Erythrocyte Aggregation and Sedimentation,” J. Blood 70, 1572–1576 (1987).Google Scholar
  33. 33.
    G. Cloutier, Z. Qin, L. G. Durand, and B. G. Teh, “Power Doppler Ultrasound Evaluation of the Shear Rate and Shear Stress Dependencies of Red Blood Cell Aggregation,” IEEE Trans. Biomed. Eng. 43, 441–450 (1996).CrossRefGoogle Scholar
  34. 34.
    A. L. Copley, R. G. King, and C. R. Huang, “Erythrocyte Sedimentation of Human Blood at Varying Shear Rates,” J. Microcirculation, Ed. By J. Grayson and W. Zingg (Plenum Press, New York), 133–134 (1976).Google Scholar
  35. 35.
    H. Schmid-Schonberg, P. Gaehtgens, and H. Hirsch, “On the Shear Rate Dependence of Red Cell Aggregation in Vitro,” J. Clin. Invest. 47, 1447–1454 (1968).CrossRefGoogle Scholar
  36. 36.
    Y. I. Cho and K.R. Kensey, “Effects of the Non-Newtonian Viscosity of the Blood on Flows in a Diseased Arterial Vessel. Part 1: Steady Flows,” J. Biorheol. 28(3–4), 241–262 (1991).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • S. E. Kornelik
    • 1
  • E. K. Borzenko
    • 1
  • A. N. Grishin
    • 1
  • M. A. Bubenchikov
    • 1
  • V. I. Stolyarov
    • 1
  1. 1.Faculty of Mechanics and MathematicsTomsk State UniversityTomskRussia

Personalised recommendations