The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model
Introduction
From clinical practice it is known that specific sites in the arterial tree are sensitive to the development of atherosclerotic lesions. Local hemodynamics are believed to play an important role in the development of these lesions in the sinus of the carotid bifurcation (Caro et al., 1971; Friedman et al., 1981; Zarins et al., 1983; Nerem 1992). Local hemodynamics are not only governed by the pressure pulse, the geometry of the bifurcation and the properties of the arterial wall, but also by the rheological properties of blood. In this study, the influence of the non-Newtonian properties of blood on the velocity distribution in a rigid model of the carotid bifurcation under steady flow conditions is described.
The flow in a carotid bifurcation model (see Fig. 1) was studied by numerous authors (e.g. Bharadvaj et al., 1982a, Bharadvaj et al., 1982b; Perktold and Hilbert, 1986; Rindt et al., 1990; Rindt and van Steenhoven 1996; Palmen et al., 1997). In these studies, and many other investigations on flow in large arteries, blood was modeled as a Newtonian fluid. The viscoelasticity of blood was ignored, and using the argument that shear rates in large arteries are predominantly high, the viscosity of blood was taken equal to the high shear rate limit viscosity of blood (η∞=3.5×10−3 Pa s). Whether or not the assumption that blood can be modeled as a Newtonian fluid is admissible is under dispute. Several numerical studies indicate that the influence of shear thinning properties of blood are not significant for the flow in large arteries (Perktold et al., 1991; Cho and Kensey, 1991). Other studies do find significant influence (e.g. Rodkiewicz et al., 1990), or apply scaling procedures while comparing Newtonian and shear thinning fluid models (e.g. Baaijens et al., 1993; Ballyk et al., 1994). None of the above studies incorporated the viscoelastic behavior of blood. Experimental studies on non-Newtonian flow in large arteries are relatively sparse, but the ones available indicate a significant influence of the viscoelasticity of the blood analog fluids on the flow phenomena (e.g. Liepsch and Moravec, 1984; Ku and Liepsch, 1986).
This study consist of two parts. The first part deals with steady flow in a three-dimensional model of the carotid bifurcation. A blood analog fluid will be presented that can be used for LDA measurements in a Plexiglas model of the bifurcation. The measured axial velocity distribution will be compared to finite element simulations. In the finite element computations, the shear thinning properties of the blood analog fluid are taken into account. A comparison between the numerical and experimental results of Newtonian and non-Newtonian velocity field is presented. The second part of this study focuses on the unsteady flow in a 90° degree curved tube: not only the velocity distribution but also application of dimensionless parameters in non-Newtonian flow will be discussed in detail.
Section snippets
Blood analog fluid
The shear thinning and viscoelasticity of blood in viscometric flow (Chien et al., 1970; Thurston, 1973, Thurston, 1979) are closely related to its microscopic structure. The red blood cells determine the rheological behavior of blood; both shear thinning and viscoelasticity are related to aggregation, deformation and alignment of the red blood cells. A suitable blood analog fluid should include these non-Newtonian properties. Application of the blood analog fluid for LDA measurements in a
Newtonian fluid
The numerical modeling of incompressible and isothermal flow of a (generalized) Newtonian fluid requires the solution of the impulse or Navier–Stokes equations and the continuity equation. In combination with a constitutive equation, followed by a discretization using Galerkin’s finite element method (e.g. Cuvelier et al., 1986), the following set of non-linear differential equations is obtained:where and are columns containing the unknown velocity
Results
In Fig. 5 the axial velocity profile in the common carotid artery is given for the Newtonian and the non-Newtonian fluid. As the flow is fully developed, the axial velocity profile for the Newtonian fluid is parabolic. The velocity profile of the non-Newtonian fluid is flattened as expected for a shear thinning fluid. The flattened velocity profile is predicted well by the numerical method. The errors in the velocity signal can be attributed to the noise on the velocity signal and the presence
Discussion and conclusion
Laser Doppler anemometry and numerical analyses were applied to obtain detailed quantitative information on axial velocity distribution in a three-dimensional model of the carotid bifurcation for a Newtonian and non-Newtonian fluid under steady flow conditions. The distensibility of the vessel wall, pulsatility of the flow and the compliance of the arterial tree downstream of the bifurcation were not included in this study. Direct comparison of the results of this study with in-vivo velocity
Acknowledgements
The authors would like to thank Jasper Zuidervaart for doing the LDA experiments.
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