Theoretical study on the constricted flow phenomena in arteries

S. Sen; S. Chakravarty

Korea-Australia Rheology Journal, Vol.24, No.4, 287-295, December, 2012

DOI10.1007/s13367-012-0035-9 Export Citation

Theoretical study on the constricted flow phenomena in arteries

S. Sen^†, and S. Chakravarty^{1, †}

Department of B. Ed., Kalna College, Burdwan, West Bengal, India
¹Department of Mathematics, Visva-Bharati, Santiniketan 731235, W.B., India

E-mail:,

The present study is dealt with the constricted flow characteristics of blood in arteries by making use of an appropriate mathematical model. The constricted artery experiences the generated wall shear stress due to flow disturbances in the presence of constriction. The disturbed flow in the stenosed arterial segment causes malfunction of the cardiovascular system leading to serious health problems in the form of heart attack and stroke. The flowing blood contained in the stenosed artery is considered to be non-Newtonian while the flow is treated to be two-dimensional. The present pursuit also accounts for the motion of the arterial wall and its effect on local fluid mechanics. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier-Stokes equations for non-Newtonian fluid representing blood. An extensive quantitative analysis presented at the end of the paper based on large scale numerical computations of the quantities of major physiological significance enables one to estimate the constricted flow characteristics in the arterial system under consideration which deviates significantly from that of normal physiological flow conditions.

Keywords:non-Newtonian fluid;wall shear stress;Navier-Stokes equation;atherosclerosis;hemodynamics

[References]

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Belardinelli ES, Cavalcanti, Comput. Biol. Med., 21, 1 (1991)
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Chakravarty S, Chowdhury AG, Rheol. Acta., 27, 418 (1988)
Chakravarty S, Sannigrahi A, Mathl.Comp. Modelling., 12, 1601 (1989)
Chakravarty S, Sen S, JMMB., 9, 377 (2009)
Deshpande M, Giddens D, Mabon R, J. Biomech., 9, 165 (1976)
Fischer GM, Swain ML, Cherian K, Blood Vessels., 17, 215 (1980)
Friedman MH, Hutchins GM, Bargeron CB, Deters OJ, Mark FF, Atherosclerosis., 39, 425 (1981)
Fry DL, Circulation Res., 22, 165 (1968)
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Hung T, Tsai TMC, JMMB., 4, 419 (2004)
Imaeda K, Goodman FO, J. Biomech., 13, 1007 (1980)
Ku DN, Giddens EDF, Zarins CK, Glagov S, Arteriosclerosis., 5, 293 (1985)
Ling SC, Atabek HB, J Fluid Mech., 55, 493 (1972)
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Mustapha N, Chakravarty S, Mandal PK, Amin N, JMMB., 8, 395 (2008)
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Srivastava VP, Saxena M, Math. Bioscs., 139, 79 (1997)
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[1] Baker M, Double-slit photometric measurement of velocity profiles for blood in microvessels and capillary tubes, Ph. D. Thesis, California Institute of Technology, Pasadena. (1972)

[2] Belardinelli ES, Cavalcanti, Comput. Biol. Med., 21, 1 (1991)

[3] Burton AC, Physiology and Biophysics of the Circulation: Introductory Text, Year Book Medical Publisher, Chicago. (1966)

[4] Chakravarty S, Chowdhury AG, Rheol. Acta., 27, 418 (1988)

[5] Chakravarty S, Sannigrahi A, Mathl.Comp. Modelling., 12, 1601 (1989)

[6] Chakravarty S, Sen S, JMMB., 9, 377 (2009)

[7] Deshpande M, Giddens D, Mabon R, J. Biomech., 9, 165 (1976)

[8] Fischer GM, Swain ML, Cherian K, Blood Vessels., 17, 215 (1980)

[9] Friedman MH, Hutchins GM, Bargeron CB, Deters OJ, Mark FF, Atherosclerosis., 39, 425 (1981)

[10] Fry DL, Circulation Res., 22, 165 (1968)

[11] Fry DL, Circulation Res., 24, 93 (1969)

[12] Hung T, Tsai TMC, JMMB., 4, 419 (2004)

[13] Imaeda K, Goodman FO, J. Biomech., 13, 1007 (1980)

[14] Ku DN, Giddens EDF, Zarins CK, Glagov S, Arteriosclerosis., 5, 293 (1985)

[15] Ling SC, Atabek HB, J Fluid Mech., 55, 493 (1972)

[16] Lou Z, Yang WJ, Critical Rev. Biomed. Engng., 19, 455 (1992)

[17] McDonald DA, J. Biomech., 12, 13 (1979)

[18] Milnor WR, Haemodynamics, Williams and Williams, Baltimore. (1982)

[19] Misra JC, Chakravarty S, J. Biomech., 19, 907 (1986)

[20] Misra JC, Patra MK, Misra SC, J. Biomech., 26, 1129 (1993)

[21] Mustapha N, Chakravarty S, Mandal PK, Amin N, JMMB., 8, 395 (2008)

[22] Ookawara S, Ogawa K, J. Chem. Eng. Jpn., 33(4), 582 (2000)

[23] Pedley TJ, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press, Cambridge. (1980)

[24] Pontrelli G, Math. Mod. & Meth. Appl. Sci., 10(2), 187 (2000)

[25] Pontrelli G, Proc. Instn. Mech. Engrs. Part H J. Eng. in Medicine., 215(1), 1 (2001)

[26] Pontrelli G, Med. Biol. Eng. Comput., 40, 550 (2002)

[27] Shaaban AM, Duerinckx AJ, AJR., 174, 1657 (2000)

[28] Srivastava VP, Saxena M, Math. Bioscs., 139, 79 (1997)

[29] Tu C, Deville M, Dheur L, Vanderschuren L, J. Biomech., 25, 1141 (1992)

[30] Wissler RW, Atherosclerosis., (Suppl.), 108, S3 (1994)

[31] Womersley JR, Phys. Med. Biol., 2, 178 (1957)