An implicit finite difference scheme for analyzing the effect of body acceleration on pulsatile blood flow through a stenosed artery

Subject Areas : Partial differential equations

A. Haghighi ¹ (Department of Mathematics, Faculty of shahid beheshti, Urmia Branch Technical and Vocational University(TVU), Tehran, Iran)
N. Aliashrafi ² (Department of Mathematics, Urmia University of Thechnology, Urmia, Iran)
N. Asghary ³ (Department of Mathematics, Islamic azad university, Central Tehran Branch, Tehran, Iran)

Received: 2017-06-20 Accepted : 2017-09-10 Published : 2017-04-01

Keywords:

References:

[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.