The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model

Abstract

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent.

In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau–Yasuda model. The viscoelastic properties of the fluid were not included.

A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.

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.