Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-29T07:58:12.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation of the Three-Dimensional Flow of Blood Using aShear-Thinning Viscoelastic Fluid Model

Published online by Cambridge University Press:  10 August 2011

T. Bodnár ,
K.R. Rajagopal  and
A. Sequeira
T. Bodnár
Affiliation:
Department of Technical Mathematics, Faculty of Mechanical Engineering Czech Technical University, Náměstí 13, 121 35 Prague 2, Czech Republic
K.R. Rajagopal
Affiliation:
Department of Mechanical Engineering, Texas A & M University College Station, TX 77843-3123, USA
A. Sequeira*
Affiliation:
Department of Mathematics and CEMAT/IST, Instituto Superior Técnico Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
*
⋆ Corresponding author. E-mail: [email protected]
Get access

Abstract

This paper is concerned with the numerical simulation of a thermodynamically compatibleviscoelastic shear-thinning fluid model, particularly well suited to describe therheological response of blood, under physiological conditions. Numerical simulations areperformed in two idealized three-dimensional geometries, a stenosis and a curved vessel,to investigate the combined effects of flow inertia, viscosity and viscoelasticity inthese geometries. The aim of this work is to provide new insights into the modeling andsimulation of homogeneous rheological models for blood and a basis for furtherdevelopments in modeling and prediction.

Keywords

blood rheologyviscoelasticitystenosiscurved vesselsecondary flows
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 1 - 24
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anand, M., Rajagopal, K.R.. A shear-thinning viscoelastic fluid model for describing the flow of blood. Int. J. of Cardiovascular Medicine and Science, 4, 2 (2004), 59–68. Google Scholar
Anand, M., Rajagopal, K.R.. A mathematical model to describe the change in the constitutive character of blood due to platelet activation. C. R. Méchanique, 330 (2002), 557–562. CrossRefGoogle Scholar
Anand, M., Rajagopal, K., Rajagopal, K.R.. A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J. of Theoretical Medicine, 5, 3–4 (2003), 183–218. CrossRefGoogle Scholar
Anand, M., Rajagopal, K., Rajagopal, K.R.. A model for the formation and lysis of blood clots. Pathophysiology Haemostasis Thrombosis, 34 (2005), 109-120. CrossRefGoogle ScholarPubMed
Anand, M., Rajagopal, K., Rajagopal, K.R.. A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J. of Theoretical Biology, 253 (2008), 725–738. CrossRefGoogle ScholarPubMed
N. Arada, M. Pires, A. Sequeira. Viscosity effects on flows of generalized Newtonian fluids through curved pipes. Computers and Mathematics with Applications, 53 (2007), pp. 625-646.
N. Arada, M. Pires, A. Sequeira. Numerical simulations of shear-thinning Oldroyd-B fluids in curved pipes. IASME Transactions, Issue 6, 2 (2005), pp. 948-959.
Bailyk, P.D., Steinman, D.A., Ethier, C.R.. Simulation of non-Newtonian blood flow in an end-to-side anastomosis. Biorheology, 31 (5) (1994) 565-586. Google Scholar
Berger, A.A., Talbot, L., Yao, L.-S.. Flow in curved pipes. Annu. Rev. Fluid Mech., 15 (1983) 461512. CrossRefGoogle Scholar
T. Bodnár, A. Sequeira. Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel. In: Advances in Mathematical Fluid Mechanics (edited by R. Rannacher & A. Sequeira), pp. 83–104. Springer Verlag (2010).
Bodnár, T., Příhoda, J.. Numerical simulation of turbulent free-surface flow in curved channel. Journal of Flow, Turbulence and Combustion, 76 (4) (2006) 429–442. Google Scholar
Bodnár, T., Sequeira, A.. Numerical simulation of the coagulation dynamics of blood. Computational and Mathematical Methods in Medicine, 9 (2) (2008) 83–104. CrossRefGoogle Scholar
T. Bodnár, A. Sequeira, L. Pirkl. Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd - B Model In: Numerical Analysis and Applied Mathematics, Vols 1 and 2. Melville, New York: American Institute of Physics, (2009), vol. 2, pp. 645–648.
Bodnár, T., Sequeira, A., Prosi, M.. On the Shear-Thinning and Viscoelastic Effects of Blood Flow under Various Flow Rates. Applied Mathematics and Computation, 217 (2011), 5055–5067. CrossRefGoogle Scholar
Charm, S.E., Kurland, G.S.. Viscometry of human blood for shear rates of 0-100,000 sec-1. Nature, 206 (1965), 617–618. CrossRefGoogle ScholarPubMed
Chien, S., Usami, S., Taylor, H.M., Lundberg, J.L., Gregersen, M.I.. Effect of hematocrit and plasma proteins on human blood rheology at low shear rates. Journal of Applied Physiology, 21, 1 (1966), 81–87. Google Scholar
Chien, S., Usami, S., Dellenback, R.J., Gregersen, M.I..Blood viscosity: Influence of erythrocyte aggregation. Science, 157, 3790 (1967), 829–831. CrossRefGoogle ScholarPubMed
Chien, S., Usami, S., Dellenback, R.J., Gregersen, M.I.. Blood viscosity: Influence of erythrocyte deformation. Science, 157, 3790 (1967), 827–829. CrossRefGoogle ScholarPubMed
Chien, S., Usami, S., Dellenback, R. J., Gregersen, M.I.. Shear-dependent deformation of erythrocytes in rheology of human blood. American Journal of Physiology, 219 (1970), 136–142. Google ScholarPubMed
Chien, S., Sung, K.L.P., Skalak, R., Usami, S., Tozeren, A.L.. Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophysical Journal, 24, 2 (1978), 463–487. CrossRefGoogle ScholarPubMed
Evans, E.A., Hochmuth, R.M.. Membrane viscoelasticity. Biophysical Journal, 16, 1 (1976), 1–11. CrossRefGoogle ScholarPubMed
Fan, Y., Tanner, R.I., Phan-Thien, N.. Fully developed viscous and viscoelastic flows in curved pipes. J. Fluid Mech., 440 (2001), 327-357. CrossRefGoogle Scholar
Gijsen, F., van de Vosse, F., Janssen, J.. The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. Journal of Biomechanics, 32 (1999), 601-608. CrossRefGoogle Scholar
Hron, J., Málek, J., Turek, S.. A numerical investigation of flows of shear-thinning fluids with applications to blood rheology. Int. J. Numer. Meth. Fluids, 32 (2000), 863-879. 3.0.CO;2-P>CrossRefGoogle Scholar
A. Jameson, W.Schmidt, E. Turkel. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping scheme. In: AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto (1981), AIAA paper 81-1259.
Leuprecht, A., Perktold, K.. Computer simulation of non-Newtonian effects of blood flow in large arteries. Comp. Methods in Biomech. and Biomech. Eng., 4 (2001), 149–163. CrossRefGoogle ScholarPubMed
Quemada, D.. Rheology of concentrated disperse systems III. General features of the proposed non-Newtonian model. Comparison with experimental data. Rheol. Acta, 17 (1978), 643–653. CrossRefGoogle Scholar
Rajagopal, K.R., Srinivasa, A.R.. A thermodynamic frame work for rate type fluid models. Journal of Non-Newtonian Fluid Mechanics, 80 (2000), 207–227. CrossRefGoogle Scholar
Rajagopal, K.R., Srinivasa, A.R.. A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials. Proc. R. Soc. A, 467 (2011), 39–58. CrossRefGoogle Scholar
Thurston, G.B.. Viscoelasticity of human blood. Biophysical Journal, 12 (1972), 1205–1217. CrossRefGoogle ScholarPubMed
Thurston, G.B.. Frequency and shear rate dependence of viscoelasticity of blood. Biorheology, 10, 3 (1973), 375–381. Google Scholar
Thurston, G.B.. Non-Newtonian viscosity of human blood: Flow induced changes in microstructure. Biorheology, 31(2), (1994), 179–192. Google ScholarPubMed
Vierendeels, J., Riemslagh, K., Dick, E.. A multi-grid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids. J. Comput. Phys., 154 (1999), 310–344. CrossRefGoogle Scholar