The Effect of Stenotic Geometry and Non-newtonian Property of Blood Flow through Arterial Stenosis

Author(s): Somchai Sriyab*

Journal Name: Cardiovascular & Hematological Disorders-Drug Targets
Formerly Current Drug Targets - Cardiovascular & Hematological Disorders

Volume 20 , Issue 1 , 2020

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Graphical Abstract:


Background: A mathematical model of blood flow is a way to study the blood flow behavior. In this research work, a mathematical model of non-Newtonian blood flow through different stenosis, namely bell shape and cosine shape, is considered. The physiologically important flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as resistance to flow, skin friction and blood flow rate.

Methods: Mathematical methods are used to analyze a mathematical model of blood flow through stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate while the skin friction is the friction at the artery membrane.

Resutls: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and skin friction decrease but the blood flow rate increases.

Conclusion: The stenosed artery geometry, the stenosis length, stenosis depth and the power law index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed artery. This work provides some potential aspects to further study the causes and development of cardiovascular diseases.

Keywords: Stenotic geometry, arterial stenosis, non-newtonian fluid, skin friction, cardiovascular diseases.

Young, D.F. Fluid mechanics of arterial stenosis. J. Biomech. Engng. Trans. ASME, 1979, 101, 157-175.
Moayeri, M.S.; Zendehbudi, G.R. Effects of elastic property of the wall on flow characteristics through arterial stenoses. J. Biomech., 2003, 36(4), 525-535.
[] [PMID: 12600343]
Mustapha, N.; Mandel, P.K.; Johnson, P.R.; Amin, N. A Numerical Simulation of Unsteady Blood Flow Though Multi-Irregular Arterial Stenoses. Appl. Math. Model., 2010, 34, 1559-1573.
Chakravarty, S.; Mandel, P.K. Two-dimensional blood flow through tapered arteries under stenotic conditions. Int. J. Nonlinear Mech., 2000, 35(5), 779-793.
Rathod, V.P.; Tanveer, S. Pulsatile flow of couple stress fluid through a porous medium with periodic body acceleration and magnetic field. Bull. Math. Sci., 2009, 32, 245-259.
Jagannath, M. Biofluid Mechanics, 2nd ed; World Scientific: Australia, 1992.
Fournier, R.L. Basic Transport Phenomena in Biomedical Engineering., 4th Ed.; CRC, UK 2007.
Ishikawa, T.; Guimaraes, L.F.R.; Oshima, S.; Yamone, R. Effect of non-newtonian property of blood on flow through a stenosed tube. Fluid Dyn. Res., 1998, 22, 251-264.
Mandal, P.K. An unsteady analysis of non-newtonian blood flow through tapered arteries with a stenosis. Int. J. Non-linear Mech., 2005, 40, 151-164.
Ismail, Z.; Abdullah, I.; Mustapha, N.; Amin, N. A Power-law Model of Blood Flow Through a Tapered Overlapping Stenosed Artery. Appl. Math. Comput., 2008, 195, 669-680.
Prakash, J.; Ogulu, A. A study of pulsatile blood flow modeled as a power law fluid in a constricted tube. Int. Commun. Heat Mass Transf., 2007, 34(6), 762-768.
Nadeem, S.; Akbar, N.S.; Hendi, A.A.; Hayat, T. Power law fluid model for blood flow through a tapered artery with a stenosis. Appl. Math. Comput., 2011, 7108-7116.
Mandel, P.K. An unsteady analysis of non-Newtonian blood flow through tapered arteried with a stenosis; Intern. J. Non-Lin Mach, 2005, pp. 151-164.
Siddiqui, S.; Verma, N.; Mishra, S.; Gupta, R. Mathematical modelling of pulsatile flow of Casson’s fluid in arterial stenosis. App. Math. Conput, 2009, 210(1), 1-10.
Venkatesan, J.; Sankar, D.; Hemalatha, K.; Yatim, Y. Mathematical analysis of casson fluid model for blood rheology in stenosed narrow arteries; J. App. Math, 2013, p. 11.
Sriyab, S. Mathematical analysis of non-Newtonian blood flow in stenosis narrow arteries. Comput. Math. Methods Med., 2014.479152
Gauthier, P. Mathematics in atmospheric sciences: An overview, discrete geometry for computer imagery. Intern. Conf. Discrete Geo. Comput. Imag., 2009, 22-23.
Misra, J.; Shit, G. Blood flow through arteries in a pathological state: A theoretical study. Intern. J. Engin. Sci, 2006, 44(10), 662-671.
Easthope, P.L.; Brooks, D.E. A comparison of rheological constitutive functions for whole human blood. Biorheology, 1980, 17(3), 235-247.
[PMID: 7213990]

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Article Details

Year: 2020
Page: [16 - 30]
Pages: 15
DOI: 10.2174/1871529X19666190509111336

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