Effect of Non-Newtonian Behaviour of Blood on Pulsatile Flows in Stenotic Arteries

Authors: Somkid Amornsamankul, Benchawan Wiwatanapataphee, Yong Hong Wu, Yongwimon Lenbury

Abstract:

In this paper, we study the pulsatile flow of blood through stenotic arteries. The inner layer of arterial walls is modeled as a porous medium and human blood is assumed as an incompressible fluid. A numerical algorithm based on the finite element method is developed to simulate the blood flow through both the lumen region and the porous wall. The algorithm is then applied to study the flow behaviour and to investigate the significance of the non-Newtonian effect.

Keywords: Stenotic artery, finite element, porous arterial wall, non-Newtonian model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084738

References:

[1] F. Migliavacca, R. Yates, G. Pennati, G. Dubini, R. Fumero, and M. R. de Leval, “Calculating blood flow from doppler measurements in the systemic-to-pulmonary artery shunt after the norwood operation: a method based on computational fluid dynamics," Ultrasound in Medicine and Biology, vol. 26, pp. 209-219, 2000.
[2] F. Migliavacca, G. Dubini, G. Pennati, R. Pietrabissa, R. Fumero, T.-Y. Hsia, and M. R. de Leval, “Computational model of the fluid dynamics in systemic-to-pulmonary shunts," Journal of Biomechanics, vol. 33, pp. 549-557, 2000.
[3] F. Migliavacca, L. Petrini, M. Colombo, F. Auricchio, and R. Pietrabissa, “Mechanical behavior of coronary stents investigated through the finite element method," Journal of Biomechanics, vol. 35, pp. 803-811, 2002.
[4] M. Oshima, R. Torii, T. Kobayashi, N. Taniguchi, and K. Tukagi, “Finite element simulation of blood blow in the cerebral artery," Computer methods in applied mechanics and engineering, vol. 191, pp. 661-671, 2001.
[5] A. Redaelli, F. Boschetti, and F. Inzoli, “The assignment of velocity profiles in finite element simulations of pulsatile flow in arteries," Computers in Biology and Medicine, vol. 27, pp. 233-247, 1997.
[6] C. A. Taylor, T. J. Hughes, and C. K. Zarins, “Finite element modeling of blood flow in arteries," Computer methods in applied mechanics and engineering, vol. 158, pp. 155-196, 1998.
[7] K. Lee and X. Xu, “Modelling of flow and wall behaviour in a mindly stenosed tube," Medical Engineering and Physics, vol. 24, pp. 575-586, 2002.
[8] B. Liu and D. Tang, “A numerical simulation of viscous flows in collapsible tubes with stenose," Applied Numerical Mathematics, vol. 32, pp. 87-101, 2000.
[9] H. Jung, J. W. Choi, and C. G. Park, “Asymmetric flows of nonnewtonian fluids in symmetric stenosed artery," Korea-Australia Rheology Journal, vol. 16, pp. 101-108, 2004.
[10] H. Hoogstraten, J. Kootstra, B. Hillen, J. Krijger, and P. Wensing, “Numerical simulation of blood flow in an artery with two successive bends," Journal of Biomechanics, vol. 29, pp. 1075-1083, 1996.
[11] T. Ishikawa, L. F. Guimaraes, S. Oshima, and R. Yamane, “Effect of non-Newtonian property of blood on flow through a stenosed tube," Fluid Dynamics Research, vol. 22, pp. 251-264, 1998.
[12] C. Tu and M. Deville, “Pulsatile flow of non-newtonian fluids through arterial stenoses," Journal of Biomechanics, vol. 29, pp. 899-908, 1996.
[13] M. Bonert, J. G. Myers, S. Fremes, J. Williams, and C. R. Ethier, “A Numerical Study of Blood Flow in Coronary Artery Bypass Graft Sideto- Side Anastomoses," in Annals of Biomedical Engineering, vol. 30, 2002, pp. 599-611.
[14] D.-Y. Fei, J. D. Thomas, and S. E. Rittgers, “The Effect of Angle and Flow Rate Upon Hemodynamics in Distal Vascular Graft Anatomoses: a Numerical Model Study," Journal of Biomechanical Engineering, vol. 116, pp. 331-336, 1994.
[15] M.-H. Song, M. Sato, and Y. Ueda, “Three-Dimensional Simulation of Coronary Artery Bypass Grafting with the Use of Computational Fluid Dynamics," Surgery Today, vol. 30, pp. 993-998, 2000.