Formation and destruction of the erythrocytes clots in the vessel with local expansion
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 3-15.

Voir la notice de l'article provenant de la source Math-Net.Ru

A mathematical model of aggregation and destruction of erythrocytes clots in the shear flow is constructed. Calculations show the influence of shear stress realized in a blood shear flow on the average size of clots. It is also shown that the bosoms of aneurysms create conditions for formation of the large agglomerates, which can result to the thrombosis of a considered part of blood vessel.
@article{MM_2008_20_1_a0,
     author = {S. E. Kornelik and E. K. Borzenko and A. N. Grishin and M. A. Bubenchikov and V. I. Stoliyarov},
     title = {Formation and destruction of the erythrocytes clots in the vessel with local expansion},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--15},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_1_a0/}
}
TY  - JOUR
AU  - S. E. Kornelik
AU  - E. K. Borzenko
AU  - A. N. Grishin
AU  - M. A. Bubenchikov
AU  - V. I. Stoliyarov
TI  - Formation and destruction of the erythrocytes clots in the vessel with local expansion
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 3
EP  - 15
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_1_a0/
LA  - ru
ID  - MM_2008_20_1_a0
ER  - 
%0 Journal Article
%A S. E. Kornelik
%A E. K. Borzenko
%A A. N. Grishin
%A M. A. Bubenchikov
%A V. I. Stoliyarov
%T Formation and destruction of the erythrocytes clots in the vessel with local expansion
%J Matematičeskoe modelirovanie
%D 2008
%P 3-15
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_1_a0/
%G ru
%F MM_2008_20_1_a0
S. E. Kornelik; E. K. Borzenko; A. N. Grishin; M. A. Bubenchikov; V. I. Stoliyarov. Formation and destruction of the erythrocytes clots in the vessel with local expansion. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a0/

[1] Lou Z., Yang W. J., “A Computer Simulation of the Blood Flow in the Aortic Bifurcation with Flexible Walls”, Mechanics Computing in 1990's and Beyond, v. 1, eds. Adeli H., and Sierakowski R., ASCE, New York, 544–548

[2] Ferguson G. G., “Physical Factors in the Initiation, Growth and Rupture of Human Intracranial Saccular Aneurysms”, J. Neursurg, 37 (1972), 666–676 | DOI

[3] Stehbens W. E., “Flow Disturbances in Glass Models of Aneurysms at Low Reynolds Numbers”, Q. J. Exp. Physiology, 59 (1974), 167–174

[4] Steiger H. J., “Pathophysiology of Development and Rupture of Cerebral Aneurysms”, Acta Neurochir, 48 (1990), 11–23

[5] Kayembe K. N. T., Sasahara M., Nazama F., “Cerebral Aneurysms and Variations of the Circle of Willis”, Stroke, 15 (1984), 846–850

[6] Stenbens W. E., “Etiology of Intracranial Berry Aneurysm”, J. Neurosurg, 70 (1989), 823–831 | DOI

[7] Ahmed S., Giddens D. P., “Pulsatile Poststenotic Flow Studies with Laser Doppler Anemometry”, J. of Biomechanics, 17 (1984), 695 | DOI

[8] Ojha M., Cobbold R. S., Johnston K. W., Hummel R. L., “Pulsatile Flow Through Constricted Tubes: An Experimental Investigation Using Photochromic Tracer Methods”, J. Fluid Mech, 203 (1989), 173–197 | DOI

[9] Ojha M., Cobbold R. S., Johnston K. W. Hummel R. L., “Detailed Visualization of Pulsatile Flow Fields Produced by Modelled Arterial Stenoses”, J. Biomed. Eng., 12 (1990), 463–469 | DOI

[10] Chien S., “Physiological and Pathological Significance of Hemorheology”, Clinical Hemorheology, eds. S. Chien, Martinus Nijhoff, Dordrecht, 1987, 125–164

[11] Chien S., Luse S. A., Jan K. M., Usami S., Miller L. H., and Fremount H., “Effects of Macromolecules on the Rheology and Ultrastructure of Red Cells Suspensions”, 6th Europ. Conf. Microcirculation (Proc.) (Aalborg, 1970), eds. J. Ditzel and D. H. Lewis, S. Karger, Basel, 29–34

[12] Chien S., “Clumping (reversible aggregation and irreversible agglutination) of Blood Cellular Elements”, Thromb. Res., 8, Suppl. II (1976), 189–202 | DOI

[13] Chien S., “Electrochemical Interaction and Energy Balance in Red Blood Cell Aggregation”, Topics in Bioelectricity and Bioenergetics, vol. 4, eds. G. Milazzo, Wiley, New York, 1981, 73–112

[14] Gast A. P., Leibler L., “Interaction of Sterically Stabilized Particles Suspended in a Polymer Solution”, J. Macromolecules, 19 (1986), 686–691 | DOI

[15] Joanny J. F., Leibler L., De Gennes P. G., “Effects of Polymer Solutions on Colloid Stability”, J. of Polymer Sci., 17 (1979), 1030–1084

[16] Chien S., “Biophysical Behavior of Red Cells in Suspentions”, The Red Blood Cell, eds. D. M. Surgenor, Academic Press, New York, 1975, 1031–1133

[17] Elimelech M., Gregory J., Jia X., Williams R. A., “Particle Deposition and Aggregation”, Measurement, Modeling and Simulation, Ch. 6, Butterworth-Heinemann, Oxford, 1995, 157–202

[18] Shamlou P. A., Titchener-Hooker N., “Turbulent Aggregation and Breakup of Particles in Liquids in Stirred Vessels”, Processing of Solid-Liquid Suspensions, eds. P. A. Shamlou, Butterworth-Heinemann, Oxford, 1993, 1–25

[19] Muhle K., “Floc Stability in Laminar and Turbulent Flow”, Coagulation and Flocculation, Theory and Applications, eds. B. Dobias, M. Dekker, New York, 1993, 355–390

[20] Shortland A. P., Black R. A., Jarvis J. C., Henry F. S., Iudicello F., Collins M. W., Salmons S., “Formation and Travel of Vortices in Model Ventricles: Application to the Design of Skeletal Muscle Ventricles”, J. of Biorheology, 29:4 (1996), 501–511

[21] Hasegawa M., “Rheological Properties and Wall Structures of Large Veins”, J. of Biorheology, 20 (1983), 531–545

[22] Lim B., Bascom P. J., Cobbold R. S. C., “Simulation of Red Cell Aggregation in Shear Flow”, J. of Biorheology, 34:6 (1997), 425–441

[23] Yuan Y. W., Shung K. K., “Echoicity of Whole Blood”, J. Ultrasound Med., 8 (1989), 425–434

[24] Mo L. Y. L., Cobbold R. S. C., Gutt C., Joy M., Santyr G., Shung K. K., “Non-Newtonian Behavior of Whole Blood in a Large Diameter Tube”, J. of Biorheology, 28 (1991), 421–427

[25] Shehada R. E. N., Cobbold R. S. C., Mo L. Y. L., “Aggregation Effects in Whole Blood: Influence of Time and Shear Rate Measurement Using Ultrasound”, J. of Biorheology, 31 (1994), 115–135

[26] Murata T., Secomb T. W., “Effects of Shear Rate on Rouleau Formation in Simple Shear Flow”, J. of Biorheology, 25 (1988), 113–122

[27] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971, 552 pp. | MR | Zbl

[28] Kolb M., Jullien R., “Chemically Limited Versus Diffusion Limited Aggregation”, J. Physique Lett., 45 (1984), 977–981 | DOI

[29] Mills P., “Non-Newtonian Behavior of Flucculated Suspensions”, J. Physique Lett., 46 (1985), 301–309 | DOI

[30] Snabre P., Bitbol M., Mills P., “Cell Disaggregation Behavior in Shear Flow”, J. Biophysics, 51 (1987), 795–807 | DOI

[31] Meakin P., “Fractal Aggregates and Their Fractal Measures”, Phase Transitions and Critical Phenomena, 12, eds. C. Domb, and J. L. Lebowitz, Academic Press, London, 1988 | MR

[32] Fabry T., “Mechanism of Erythrocyte Aggregation and Sedimentation”, J. of Blood, 70 (1987), 1572–1576

[33] Cloutier G., Qin Z., Durand L. G., Teh B. G., “Power Doppler Ultrasound Evaluation of the Shear Rate and Shear Stress Dependencies of Red Blood Cell Aggregation”, IEEE Trans. Biomed. Eng., 43 (1996), 441–450 | DOI

[34] Copley A. L., King R. G., Huang C. R., “Erythrocyte Sedimentation of Human Blood at Varying Shear Rates”, Microcirculation, Grayson and Zingg, Plenum Press, New York, 1976, 133–134

[35] Schmid-Schonberg H., Gaehtgens P., Hirsch H., “On the Shear Rate Dependence of Red Cell Aggregation in Vitro”, J. Clin. Invest., 47 (1968), 1447–1454 | DOI

[36] Cho Y. I., Kensey K. R., “Effects of the Non-Newtonian Viscosity of the Blood on Flows in a Diseased Arterial Vessel. Part 1: Steady Flows”, J. of Biorheology, 28 (1991), 241–262