Document Type: Research Paper
Authors
- A. Haghighi ^{} ^{1}
- N. Aliashrafi ^{2}
- N. Asghary ^{3}
^{1} Department of Mathematics, Faculty of shahid beheshti, Urmia Branch Technical and Vocational University(TVU), Tehran, Iran
^{2} Department of Mathematics, Urmia University of Thechnology, Urmia, Iran
^{3} Department of Mathematics, Islamic azad university, Central Tehran Branch, Tehran, Iran
Abstract
With an aim to investigate the effect of externally imposed body acceleration on two dimensional,pulsatile blood flow through a stenosed artery is under consideration in this article. The blood flow has been assumed to be non-linear, incompressible and fully developed. The artery is assumed to be an elastic cylindrical tube and the geometry of the stenosis considered as time dependent, and a comparison has been made with the rigid ones. The shape of the stenosis in the arterial lumen is chosen to be axially non-symmetric but radially symmetric in order to improve resemblance to the in-vivo situations. The resulting system of non-linear partial differential equations is numerically solved using the Crank-Nicolson scheme by exploiting the suitably prescribed conditions. The blood flow characteristics such as the velocity profile, the volumetric flow rate and the resistance to flow are obtained and effects of the severity of the stenosis, the body acceleration on these flow characteristics are discussed. The present results are compared with literature and found to be in agreement.
Keywords
Main Subjects
[1] N. Ali, A. Zaman, M. Sajid, Unsteady blood flow through a tapered stenotic artery using Sisko model, Comput Fluids. 101 (2014), 42-49.
[2] E. Belardinelli, S. Cavalcanti, A new nonlinear two-dimensional model of blood motion in tapered and elastic vessels, Computers in Biology and Medicine. 21 (1991), 1-13.
[3] S. Chakravarty, P. K. Mandal, Two-dimensional blood flow through tapered arteries under stenotic conditions, International Journal of Non-Linear Mechanics. 35 (5) (2000), 779-793.
[4] M. Deshpande, D. Giddens, F. Mabon, Steady laminar flow through modelled vascular stenoses, J. Biomech. 9 (1976), 165-174.
[5] A. R. Haghighi, S. A. Chalak, Mathematical modeling of blood flow through a stenosed artery under body acceleration, Journal of the Brazilian Society of Mechanical Sciences and Engineering. 39 (7) (2017), 2487-
2494.
[6] A. R. Haghighi, M.S. Asl, Mathematical modeling of micropolar fluid flow through an overlapping arterial
stenosis, International Journal of Biomathematics. (8) (4) (2015), —.
[7] A. R. Haghighi, M. S. Asl, and M. Kiyasatfar, Mathematical modeling of unsteady blood flow through elastic tapered artery with overlapping stenosed, Journal of the Braziliam Society of Mechanical Sciences and Engineering. (2014) .
[8] H. A. Hogan, M. Henriksen, An evaluation of a micropolar model for blood flow through an idealized stenosis, J Biomech. 22 (3) (1989) 21-218
[9] M. Ikbal, S. Chakravarty, K. Wong, J. Mazumdar, P. Mandal, Unsteady response of Non-Newtonian blood flow through a stenosed artery in magnetic field, Journal of Computational and Applied Mathematics. 230 (1) (2009), 243-259.
[10] M. Ikbal, S. Chakravarty, P. Mandal, Two-layered micropolar fluid flow through stenosed artery: effect of peripheral layer thickness, Computers andt Mathematics with Applications. 58 (7) (2009), 1328-1339.
[11] Z. Ismail, I. Abdullah, N. Mustapha, A. Amin, A power-law model of blood flow through a tapered overlapping stenosed artery, Appl Math Comput. 195 (2013), 669-680.
[12] G. Liu, X. Wang, B. Ai, L. Liu, numerical study of pulsating flow through a tapered artery with stenosis, Chin J Phys. 42 (2012), 401-409.
[13] P. Mandal, S. Chakravarty, A. Mandal, A. Amin, Effect of body acceleration on unsteady pulsatile flow of non-Newtonian fluid through a stenosed artery, Applied Mathematics and Computation. 189 (2007), 766-779.
[14] P. F. Marques, M. E. C. Oliveira, A. S. Franca, M. Pinotti, Modeling and simulation of pulsatile blood flow with a physiologic wave pattern, Artif Organs. 27 (5) (2003), 458-478.
[15] C. D. Mathers, and D. Loncar, Projections of global mortality and burden of disease from 2002 to 2030, PLoS Med. 3 (11) e442 (2006).
[16] J.C. Misra, and G. C. Shit, Flow of a biomagnetic viscoelastic fluid in a channel with stretching walls, Journal of Applied Mechanics. 76 (6) (2009), 061006.
[17] S. Mukhopadhyay, and G. Layek, Numerical modeling of a stenosed artery using mathematical model of variable shape, AAM Intern. 3(6) (2008) 308-328.
[18] N. Mustapha, N. Amin, S. Chakravarty, P. Mandal, Unsteady magnetohydrodynamic blood flow through irregular multi-stenosed arteries, Computers in Biology and Medicine. 39 (2009), 896-906.
[19] R. Ponalagusamy, R. Tamil Selvi, A study on two-layered model (Casson-Newtonian) for blood flow through an arterial stenosis: axially variable slip velocity at the wall, Journal of the Franklin Institute. 348 (9) (2011), 2308-2321.
[20] J. Prakash, and A. Ogulu, A study of pulsatile blood flow modeled as a power law fluid in a constricted tube, Int Commun Heat Mass. 34 (2007), 762-768.
[21] D. Sankar, U. Lee, FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries, J. Mech. Sci. Technol. 25 (10) (2001), 2573-2581.
[22] D. Sankar, U. Lee, Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries, Communications in Nonlinear Science and Numerical Simulation. 14 (7) (2009), 2971-2981.
[23] S. Shaw, P. Murthy, S. Pradhan, P. Mandal, The effect of body acceleration on two dimensional flow of Casson fluid through an artery with asymmetric stenosis, The Open Transport Phenomena Journal. 2 (2010), 55-68.
[24] D.S. Shankar, U. Lee, Nonlinear mathematical analysis for blood flow in a constricted artery under periodic body acceleration, Communications in Nonlinear Science and Numerical Simulation. 16 (11) (2011), 4390- 4402.
[25] G. C. Shit, M. Roy, Pulsatile flow and heat transfer of a magneto-micropolar fluid through a stenosed artery under the influence of body acceleration, Journal of Mechanics in Medicine and Biology. 11 (03) (2011), 643-661.
[26] G. C. Shit, S. Majee, Pulsatile flow of blood and heat transfer with variable viscosity under magnetic and vibration environment, Journal of Magnetism and Magnetic Material. 388 (2015), 106-115.
[27] S. Siddiqui, N. Verma, S. Mishra, R. Gupta, Mathematical modelling of pulsatile flow of Cassons fluid in arterial stenosis, Appl Math Comput. 210 (1) (2009), 1-10.
[28] S. Singh, Numerical modeling of two-layered micropolar fluid through an normal and stenosed artery, IJE- Transactions A: Basics. 24 (2) (2011), 177.
[29] N. Srivastava, The Casson fluid model for blood flow through an inclined tapered artery of an accelerated body in the presence of magnetic field, Int. J. Biomedical Engineering and Technology. 15 (3) (2014), 70-91.
[30] G. Zendehbudi, M. Moayeri, Comparison of physiological and simple pulsatile flows through stenosed arteries, J Biomech. 32 (1999), 959-965.