NUMERICAL STUDY OF THE NON-NEWTONIAN BLOOD FLOW IN A STENOSED ARTERY USING TWO RHEOLOGICAL MODELS

Abstract

The numerical simulation of blood flow in arteries using non-Newtonian viscosity model, presents two major difficulties; the first one is the choice of an appropriate constitutive equation, because no one model is universally accepted as a reflection of the true behavior of blood viscosity until now. Another difficulty lies in the numerical convergence of the complex scheme solving the highly non-linear set of equations governing the blood motion. In this paper, the pulsatile blood flow through an arterial stenosis has been numerically modeled to evaluate the flow characteristics and the wall shear stress under physiological conditions. The Navier-Stokes equations governing the fluid motion are solved using the finite element method in unsteady two-dimensional case. The behavior of blood is considered as the Generalized Power-law (Gpl) and Cross models, where the shear-thinning characteristics of the streaming blood are taken into account. Constants in the constitutive equations of previous models have been obtained by fitting experimental viscosity data. The numerical simulations are performed for a wide range of apparent shear rates (10 s-1-750 s-1) with good convergence of the iterative scheme. Results from the blood flow simulations indicate that non-Newtonian behavior has considerable effects on instantaneous flow patterns. However, it seems that the Gpl model will be slightly better for describing the non-Newtonian characteristics of blood than the Cross model.

Dates

  • Submission Date2013-02-27
  • Revision Date2013-11-11
  • Acceptance Date2013-11-14
  • Online Date2013-12-22

DOI Reference

10.2298/TSCI130227161A

References

  1. Lee, J.S., Fung, Y.C., Flow in locally constricted tubes at low Reynolds numbers, Journal of Applied Mechanical, 37 (1970), pp. 9-16
  2. Deshpande, M.D., Giddens, D.P., Mabon, R.F., Steady laminar flow through modelled vascular stenosis, Journal of Biomechanics, 9 (1976), pp. 165-174
  3. Liepsch, D., Singh, M., Lee, M., Experimental analysis of the influence of stenotic geometry on steady flow, Biorheology, 29 (1992), pp. 419-431
  4. Huang, H., Modi, V.J., Seymour, B.R., Fluid Mechanics of stenosed arteries, International Journal of Engineering Science, 33 (1995), pp. 815-828
  5. Despotisa, G.K., Tsangarisa, S., A fractional step method for unsteady incompressible flows on unstructured meshes, International Jou. of Compu. Fluid Dynamics, 8 (1997), 1, pp. 11-29
  6. Bertolotti, C., Deplano, V., Three-dimensional numerical simulations of flow through a stenosed coronary bypass, Journal of Biomechanics, 33 (2000), pp. 1011-1022
  7. Berger, S., Jou, L., Flows in stenotic vessels, Annual Review of Fluid Mechanics, 32 (2000), pp. 347-382
  8. Rodkiewicz, C.M., Sinha, P., Kennedy, J.S., On the application of a constitutive equation for whole human blood, Transactions of the ASME, Journal of Biomechanical Engineering, 112 (1990), pp. 198-206
  9. Gambaruto, A.M., Janela, J., Moura, A., Sequeira, A., Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology, Mathematical Biosciences and Engineering, 8 (2011), 2, pp. 409-423
  10. Achab, L., Benhadid, S., Application d'une loi constitutive dans l'étude numérique de l'écoulement sanguin à travers une artère sténosée, Rhéologie, 7 (2005), pp. 28-34
  11. Sankar, D.S., A two-fluid models for pulsatile flow in catheterized blood vessels, International Journal of Non-Linear Mechanics, 44 (2009), pp. 337-351
  12. Chakravarty, S., Datta, A., Pulsatile blood flow in a porous stenotic artery, Mathematical and Computer Modelling,16 (1992), 2, pp. 35-54
  13. Jung, H., Choi, J., Park, G., Asymmetric flows of non-Newtonian fluids in symmetric stenosed artery, Korea-Australia Rheology Journal, 16, (2004), 2, pp.101-108
  14. Goubergrits, L., Wellnhofer, E., Kertzscher, U., Impact and choice of a non-Newtonian blood model for wall shear stress profiling of coronary arteries, Proceedings, 14th Biomedical Engineering and Medical Physics Conf., Riga, Latvian, 2008, Vol.20, pp. 111-114
  15. Akbar, N. S., Hayat, T., Nadeem, S. , Hendi, A., Influence of mixed convection on blood flow of Jeffrey fluid through a tapered stenosed artery, Thermal Science, 17, (2013), 2, pp. 533-546
  16. Neofytou, P., Comparison of blood rheological models for physiological flow simulation, Biorheology, 41 (2004), pp.693-714
  17. Tu, C., Deville, M., Pulsatile flow of non-Newtonian fluids through arterial stenoses, Journal of Biomechanics, 29 (1996), pp.899-908
  18. Buchanan, J.R, Kleinstreuer, C., Comer, J.K., Rheological effects on pulsatile hemodynamics in a stenosed tube, Computers and Fluids, 29 (2000), pp.695-724
  19. Modarres Razavi, M.R., Seyedein, H., Shahabi, P.B., Numerical Study of Hemodynamic Wall Parameters on Pulsatile Flow through Arterial Stenosis, IUST International Journal of Engineering Science, 17, (2006), 3-4, pp. 37-46
  20. Ballyk, P.D., Steinman, D.A., Ethier, C.R., Simulation of non-Newtonian blood flow in an end-to-end anastomosis, Biorheology, 31 (1994), 5, pp. 565-586
  21. Cross, M.M., Rheology of Non Newtonian Fluids: A New Flow Equation for Pseudoplastic Systems, Jou. Colloid Sci., 20 (1965), pp. 417-437
  22. Brooks, D.E., Goodwin, J.W., Seaman, G.V.F., Interactions among erythrocytes under shear, J. Appl. Physiol., 28 (1970), 2, pp.72-177
  23. Vigne J. Algorithmes numériques, analyse et mise en oeuvre. Equations et systèmes non-linéaires. Tome 2, Technip, Paris. 1980
  24. Young, D.F, Tsai, F.Y., Flow characteristics in models of arterial stenosis-I steady flow-, Journal of Biomechanic, 6 (1973), pp. 395-410
  25. Zienkiewicz, O.C, Taylor, R.L., The Finite Element method, Vol.3, Fluid Dynamics, Butterworth- Heinemann, Oxford, UK, 2000
  26. Dhatt, G., Touzot, G., Lefrançois, E., Méthode des éléments finis. Hermès, Lavoisier, 2005
  27. Womersley, J. R, Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known, Journal of Physiology, 127, (1955), pp. 553-563