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Nonlinear mathematical analysis for blood flow in a constricted artery under periodic body acceleration. (English) Zbl 1219.92014

Summary: This study analyses the pulsatile flow of blood through mild stenosed narrow arteries, treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. A perturbation method is employed to solve the resulting coupled implicit system of nonlinear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and longitudinal impedance to flow are obtained. The effects of pulsatility, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow increase as the yield stress and stenosis depth increase and they decrease with the increase of the body acceleration, pressure gradient, width of the peripheral layer thickness.
It is observed that the plug flow velocity and flow rate increase with the increase of the pulsatile Reynolds number, body acceleration, pressure gradient and the width of the peripheral layer thickness and the reverse behavior is found when the yield stress, stenosis depth and lead angle increase. It is also recorded that the wall shear stress and longitudinal impedance to flow are considerably lower for the two-fluid Casson model than that of the single-fluid Casson model. It is found that the presence of body acceleration and peripheral layer influences the mean flow rate and mean velocity by increasing their magnitude significantly in the arteries.

MSC:

92C35 Physiological flow
35B20 Perturbations in context of PDEs
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
35Q92 PDEs in connection with biology, chemistry and other natural sciences
76Z05 Physiological flows
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[1] Sud, V. K.; Sekhon, G. S., Arterial flow under periodic body acceleration, B Math Biol, 47, 35-52 (1985) · Zbl 0553.92008
[2] Srivastava, L. M.; Edemeka, U. E.; Srivastava, V. P., Effects of external body accelerations on blood flow, Jpn J Appl Phys, 33, 3648-3655 (1994)
[3] Belardinelli, E.; Ursino, E.; Lemmi, E., A preliminary theoretical study of arterial pressure distribution under shock acceleration, ASME J Biomech Eng, 111, 233-240 (1989)
[4] Elshahewey, E. F.; Elbarbary, E. N.E.; Elsayed, M. E.; Afifi, N. A.S.; El-Shahed, M., Pulsatile flow of blood through a porous medium under periodic body acceleration, Int J Theor Phys, 39, 183-188 (2000) · Zbl 0982.76100
[5] Misra, J. C.; Pal, B., A. mathematical model for the study of the pulsatile flow of blood under externally imposed body acceleration, Math Comput Model, 29, 89-106 (1999) · Zbl 1098.76655
[6] Chaturani, P.; Ponnalagar Samy, R., A study of non-Newtonian aspects of blood flow through stenosed arteries and its applications in arterial diseases, Biorheology, 22, 521-531 (1985)
[7] Davies, M. J.; Thomas, A. C., Plaque fissuring – the cause of acute myocardial infarction, sudden ischaemic death and crescendo angia, British Heart J, 53, 363-373 (1985)
[8] Davies, M. J., Stability and instability: two faces of coronary atherosclerosis, Circulation, 94, 2013-2020 (1996)
[9] Glagov, S.; Weisenberd, E.; Zarins, C.; Stankunavicius, R.; Kolettis, G., Compensatory enlargement of human atherosclerotic coronary arteries, New Engl J Med, 316, 1371-1375 (1987)
[10] Mandal, P. K.; Chakravarty, S.; Mandal, A., Numerical study of the unsteady flow of non-Newtonian fluid through differently shaped arterial stenoses, Int J Comput Math, 84, 1059-1077 (2007) · Zbl 1196.76018
[11] Berger, S. A.; Jou, L. D., Flows in stenotic vessels, Ann Rev Fluid Mech, 32, 347-382 (2000) · Zbl 0989.76096
[12] Chaturani, P.; Ponnalagar Samy, R., Pulsatile flow of Casson fluid through stenosed arteries with applications to blood flow, Biorheology, 23, 499-511 (1986)
[13] MacDonald, D. A., On steady flow through modeled vascular stenosis, J Biomech, 12, 13-20 (1979)
[14] Young, D. F., Fluid mechanics of arterial stenosis, J Biomech Eng (Trans. ASME), 101, 157-175 (1979)
[15] Long, Q.; Ku, X. Y.; Ramnarine, K. V.; Hoskins, P., Numerical investigations of physiologically realistic pulsatile flow through arterial stenosis, J Biomech, 34, 1229-1242 (2001)
[16] Liu, G. T.; Wang, X. J.; Ai, B. Q.; Liu, L. G., Numerical study of pulsating flow through a tapered artery with stenosis, Chinese J Phys, 42, 401-409 (2004)
[17] Tu, C.; Deville, M., Pulsatile flow of non-Newtonian fluids through arterial stenosis, J Biomech, 29, 899-908 (1996)
[18] Charavarthy, S.; Sarifuddin, S.; Mandal, P. K., Unsteady flow of a two-layer blood stream past a tapered flexible artery under stenotic conditions, Comput Models Appl Math, 4, 391-409 (2004) · Zbl 1060.35145
[19] Sankar, D. S.; Hemalatha, K., Pulsatile flow of Herschel-Bulkey fluid through stenosed arteries-A mathematical model, Int J Non-Linear Mech, 41, 979-990 (2006) · Zbl 1160.76446
[20] Mandal, P. K., An Unsteady analysis of non-Newtonian blood flow through tapered arteries with a stenosis, Int J Non-Linear Mech, 40, 151-164 (2005) · Zbl 1349.76943
[21] Mann, J. M.; Davies, M. J., Vulnerable plaque – relation of characteristics to degree of stenosis in human coronary arteries, Circulation, 94, 928-931 (1996)
[22] Shukla, J. B.; Parihar, R. S.; Gupta, S. P., Effects of peripheral layer viscosity on blood flow through the artery with mild stenosis, B Math Biol, 43, 797-805 (1980) · Zbl 0446.92002
[23] Misra, J. C.; Pandey, S. K., Peristaltic transport of blood in small vessels: study of a mathematical model, Comput Math Appl, 43, 1183-1193 (2002) · Zbl 1045.92015
[24] Srivastava, V. P.; Saxena, M., Two-layered model of Casson fluid flow through stenotic blood vessels: applications to the cardiovascular system, J Biomech, 27, 921-928 (1994)
[25] Sankar, D. S.; Lee, U., Two-phase non-linear model for the flow through stenosed blood vessels, J Mech Sci Technol, 21, 678-689 (2007)
[26] Sankar, D. S.; Joan, Goh; Ismail, A. I.M., FDM analysis for blood flow through stenosed tapered arteries, Boundary Value Problems (2010), Article ID: 917067 · Zbl 1425.76326
[27] Nagarani, P.; Sarojamma, G., Effect of body acceleration on pulsatile flow of Casson fluid through a mild stenosed artery, Korea-Australia Rheol J, 20, 189-196 (2008)
[28] Siddiqui, S. U.; Verma, N. K.; Mishra, S.; Gupta, R. S., Mathematical modeling of pulsatile flow of Casson’s fluid in arterial stenosis, Appl Math Comput, 210, 1-10 (2009) · Zbl 1159.92012
[29] Biswas, D.; Chakraborty, U. S., Pulsatile flow of blood in a constricted artery with body acceleration, Appl Appl Math, 4, 329-342 (2009) · Zbl 1178.76390
[30] Srivastava, V. P., Particle – fluid suspension model of blood flow through stenotic vessels with applications, Int J Bio-Med Comput, 38, 141-154 (1995)
[31] Chaturani, P.; Isaac, A. S.A. W., Blood flow with body acceleration forces, Int J Eng Sci, 33, 1807-1820 (1995) · Zbl 0901.92014
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