Hemodynamics in the carotid artery bifurcation:: a comparison between numerical simulations and in vitro MRI measurements
Introduction
The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry (Nerem et al., 1980; Friedman et al., 1983; Caro, 1994). The carotid bifurcation, the coronary arteries, the infrarenal aorta and the vessels supplying the lower extremities may be markedly diseased while other vessels are rather spared. Due to these findings local hemodynamics is considered to play an important role in the initiation and development of atherosclerosis. Studies on postmortem human arteries (Zarins et al., 1983; Ku et al., 1985) and on the experimental animal (Sawchuk et al., 1994) showed positive correlation between plaque thickness and the presence of low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Comparison between flow velocity measurements and plaque distributions in human carotid artery specimens revealed that at the outer wall of the carotid sinus, where wall shear stress and flow velocities are low, plaque thickness is maximal whereas at the flow divider wall, where wall shear stress and velocities are high, plaque thickness is minimal (Zarins et al., 1983). At the side walls, where circumferential flow velocities (secondary flow) are present plaque thickness is medium.
Various flow quantification techniques such as laser Doppler anemometry (LDA) (Liepsch et al., 1984; Ku et al., 1987; Steiger, 1990), ultrasound Doppler (US) (Hatle et al., 1985; Steinke et al., 1989; Sugawara et al., 1989) or magnetic resonance imaging (MRI) (Nayler et al., 1986; Boesiger et al., 1992; Kilner et al., 1993) are commonly used to study arterial hemodynamics. The choice of one of these techniques depends on the specific application and the demand on spatial and temporal resolution. An alternative and complementary approach to study arterial hemodynamics uses numerical simulations (Perktold et al., 1995a, Perktold et al., 1995b, Perktold et al., 1995c, Perktold et al., 1998; Reuderink, 1991; Rindt et al., 1990). The development of efficient numerical methods and new computer generations allows the calculation of local flow behavior under physiologic and anatomically realistic conditions. This approach may be very useful for detailed quantitative studies of the influence of various local vessel geometries on specific vessel pathologies.
The aim of this study was to verify that numerical simulations and flow velocity measurements such as MRI lead to same flow patterns if the computational geometric vessel model is an exact copy of the experimental bifurcation and if the same flow conditions are used.
Section snippets
Mathematical model
The local fluid dynamics was described using the three-dimensional time-dependent Navier–Stokes equations for incompressible Newtonian fluids:with the velocity vector field and the pressure p.ν=μ/ρ represents the kinematic viscosity, ρ and μ stand for the constant fluid density and the dynamic viscosity, respectively.
For the numerical solution of the flow problem the finite element method was applied: The approximation applies eight-node isoparametric
Results
As expected flow in the carotid sinus proofed to be highly complex. Axial and circumferential (secondary) flow velocities were measured and calculated at the midsinus (C) and the endsinus (D) level of the internal carotid bifurcation (Fig. 3) during early systole (t/tp=0.075), mid-systole (t/tp=0.15), late systole (t/tp=0.25) and end-systole (t/tp=0.325). High spatial and temporal flow variations were observed for both approaches leading to high mainly axial directed flow velocities at the flow
Discussion
Velocity measurements performed in a anatomically realistic carotid bifurcation model with nearly rigid walls and simulations performed on the corresponding computational geometric model with rigid walls (for differences in the flow patterns for rigid and compliant walls see Perktold et al., 1995c) show that numerically calculated axial flow velocity patterns lead to similar results as MRI flow velocity measurements provided that both are performed for exactly the same vessel geometry and under
Acknowledgements
The study was supported by the Austrian Science Foundation, Project No. P 11 982-TEC, Vienna, by EUREKA Project No.EU 1353, and by the Swiss Commission for Technology and Innovation KTI, Project No. 3030.2.
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