Interaction between secondary velocities, flow pulsation and vessel morphology in the common carotid artery

Abstract

The common carotid artery (CCA), one of the vessels more frequently investigated by ultrasound (US), is often modeled as a straight tube in quasi-laminar flow regimens. Experimental investigations based on a prototype multigate system show that blood velocity profiles are parabolic during diastole and early systole, and flat during the systolic peak. However, during late systole/beginning of diastole, they have an “M” shape, where the velocity near the walls is higher than in the vessel center. Moreover, the profile shape changes when the sound beam direction is moved over a given cross-section; thus, suggesting a nonaxisymmetrical velocity distribution, which contradicts the straight tube assumption. The purpose of this paper was twofold. First, the actual velocity distribution in “normal” CCAs was reconstructed. The analysis of several velocity profiles confirms that the velocity distribution is markedly asymmetrical, especially during the deceleration phase following the systolic peak. Second, a tentative explanation for such behavior is given by correlating it with the growth of secondary flows caused by the slight vessel curvature and viscous effects. This explanation is supported by the comparison between in vitro results and numerical solution of the Navier–Stokes equations in laminar pulsed-flow regimens.

Introduction

Carotid arteries, the main suppliers of blood to the brain, are among the vessels more often investigated by ultrasound (US). However, their hemodynamics are still not totally known, due to the uncertainties in the fluid flow structure.

The common carotid artery (CCA) has been typically modeled as a straight tube. For example, under the assumptions of infinitely stiff walls and Newtonian fluid, application of the Womerseley theory leads to the estimation of quasi-parabolic velocity profiles for most of the cardiac cycle Evans and McDicken 2000, Jensen 1996. By adding the hypothesis of elastic walls, the only consequence is that the profile turns out to be more flat, as shown by Perktold and Rappitsch (1995) in the straight duct portion of their computer simulation of the CA bifurcation.

However, a set of experimental investigations has indicated that the blood velocity distribution can have a considerably different behavior Keller et al 1976, Brands et al 1995, Bardelli et al 1995. In such experiments, the expected parabolic and plug-shaped velocity profiles were evident during late diastole and the systolic acceleration phase, respectively, but, during the deceleration phase, the largest velocities frequently appeared in proximity to the walls. Keller et al (1976), after observing such (“saddle-like”) behavior by using a 14-gate Doppler system, erroneously considered it as predictable by the Womersley theory for particular values of α coefficient.

Brands et al (1995), in a series of Doppler multigate measurements in the CCA, identified some flow structures with evident asymmetries at the end of the systolic and beginning of diastolic phases. However, no explanation of such behavior was suggested.

A similar phenomenon was observed by Bardelli et al (1995), who employed a cross-correlation-based multigate system. The (“camel’s hump”) profile was, in this case, attributed to the combination of the longitudinal pressure gradient, with the transverse pressure gradient related to the arterial wall movements.

Caro et al (1992) investigated CCA morphology and hemodynamics through magnetic resonance (MR) angiography. In particular, they found an asymmetrical velocity distribution during systolic deceleration. They also observed that the CCA under investigation was characterized by a δ = 1:20 curvature ratio, and that the flow asymmetry tended to disappear when the neck was stretched in such a way that this curvature was completely avoided. Hence, they hypothesized that such behavior could be attributed to the presence of secondary flow components Bovendeerd et al 1987, Krams et al 1999, van Langenhove et al. 2000).

The justification of the complex velocity profile in the CCA environment is worth further investigation. In this view, the purpose of this study was twofold. First, by exploiting the processing capabilities of a recently developed multigate spectral Doppler system (Tortoli et al 1997), the velocity distribution in normal CCAs was reconstructed. The analysis of velocity profiles from 20 volunteers confirmed that such distribution is markedly asymmetrical during the phase following the systolic peak, and the deceleration in the center of the artery turns out to be faster than in regions close to the walls. Second, a tentative explanation for such behavior is given by correlating it to the existence of secondary flows caused by the slight vessel curvature.

To support such hypotheses, accurate in vitro investigations were made by using a dedicated flow test rig. Vessel curvatures comparable to the CCA curvature were carefully analyzed to identify their effects in terms of deviation from the parabolic velocity profile.

Finally, the in vitro measurements have been compared with the results of a finite-volume computer simulation carried out by a commercial code solving the Navier–Stokes equations for incompressible fluids in steady and unsteady flow regimens. The integration between in vitro measurements and computer simulation is proved to enhance the understanding of the flow field.