Vortical Structures Promote Atheroprotective Wall Shear Stress Distributions in a Carotid Artery Bifurcation Model

Abstract

Carotid artery diseases, such as atherosclerosis, are a major cause of death in the United States. Wall shear stresses are known to prompt plaque formation, but there is limited understanding of the complex flow structures underlying these stresses and how they differ in a pre-disposed high-risk patient cohort. A 'healthy' and a novel 'pre-disposed' carotid artery bifurcation model was determined based on patient-averaged clinical data, where the 'pre-disposed' model represents a pathological anatomy. Computational fluid dynamic simulations were performed using a physiological flow based on healthy human subjects. A main hairpin vortical structure in the internal carotid artery sinus was observed, which locally increased instantaneous wall shear stress. In the pre-disposed geometry, this vortical structure starts at an earlier instance in the cardiac flow cycle and persists over a much shorter period, where the second half of the cardiac cycle is dominated by perturbed secondary flow structures and vortices. This coincides with weaker favorable axial pressure gradient peaks over the sinus for the 'pre-disposed' geometry. The findings reveal a strong correlation between vortical structures and wall shear stress and imply that an intact internal carotid artery sinus hairpin vortical structure has a physiologically beneficial role by increasing local wall shear stresses. The deterioration of this beneficial vortical structure is expected to play a significant role in atherosclerotic plaque formation.

Keywords: cardiovascular disease; healthy and pre-disposed geometry; physiological pulsatile flow; vortical structures; wall shear stresses.

Figure 1

Examples of vortical structures: (a) vortex ring front (i) and side (ii) view [33]; (b) schematic of a Dean (D) vortex pair viewed from upstream in a curved pipe; clockwise and counter-clockwise rotation of the secondary flow is indicated by the arrows [34].

Figure 2

‘Healthy’ (a, left) and ‘pre-disposed’ (b, right) model geometry of the carotid artery bifurcation: (a) symmetric total branching angle with 30° ICA branching angle, characteristic of a ‘healthy’ geometry; (b) asymmetric total branching angle with 45° ICA branching angle, characteristic of a ‘pre-disposed’ geometry. Regions of interest are highlighted.

Figure 3

Physiological pulsatile inflow into the common carotid artery inlet over one cardiac cycle. The diagram represents the time dependence of the total inflow velocity magnitude at the inlet boundary. Waveform is the patient-averaged CCA flow of a healthy patient population [56].

Figure 4

Wall shear stress distribution and the underlying three-dimensional vortices. The wall shear stress distribution is shown as slightly transparent (color bar on the bottom), and vortices in the vessel volume are shown in gray using a ${\lambda }_2$ threshold. The ‘healthy’ geometry is shown in the left column (famed in blue), and the ‘pre-disposed’ geometry is shown in the right column (framed in red). The middle column insets show an instant in the cycle for the ‘healthy’ and ‘pre-disposed’ geometry with a blue and red dot on the pulsatile inflow waveform, respectively.

Figure 5

Secondary velocities in the ICA sinus over the cardiac cycle. ‘Healthy’ geometry is on the left (a,c,e,g), and ‘pre-disposed’ geometry is on the right (b,d,f,h). The middle insets show the analyzed instant in time, which is highlighted with an orange diamond on the pulsatile inflow waveform. The axial inflow in the CAB just upstream of the bifurcation is indicated with black axial velocity vectors. Velocity results are presented on 6 planes perpendicular to the ICA center axis; planes are labeled 1-6 where 1 is most upstream near the CCA and 6 is the most downstream (labeled in a). Nondimensionalized secondary velocity magnitude (u/U) (secondary velocity magnitude divided by U = U (t/T = 0.27), where U is the mean velocity magnitude at the CCA inlet) is defined with the color bar, and streamlines are added in black. Three-dimensional vortical structures are determined using a constant ${\lambda }_2$ criterion over all time instances t/T and shown in gray.

Figure 6

The life span (wall attachment) of the main hairpin vortical structure is shown on the pulsatile inflow waveform (black) for the ‘healthy’ geometry in blue and for the ‘pre-disposed’ geometry in red. The hairpin vortical structure is observed earlier for the ‘pre-disposed’ case and also stops to be detected significantly earlier.

Figure 7

Axial pressure gradient over the ICA sinus through the cardiac cycle. ‘Healthy’ geometry is in blue, and ‘pre-disposed’ is illustrated in red. The indicated moments in time are shown with dashed lines: t/T = 0.165 (magenta), t/T = 0.22 (cyan), t/T = 0.325 (yellow), t/T = 0.43 (green), and t/T = 0.50 (black). Lines indicating favorable pressure gradients are marked with dash dots, and lines indicating adverse pressure gradients are solid. Large differences in the favorable pressure gradient are observed, which are higher for the ‘healthy’ geometry (highlighted with the arrows). Smaller differences are evident in the case of an adverse pressure gradient.

Figure 8

Nondimensionalized static pressure on artery wall (transparent, color bar) with underlying three-dimensional vortical structure using ${\lambda }_2$ vortex identification. Pressure is nondimensionalized by dividing by P0, where P0 = P(t/T = 0.191) at the CCA inlet center for the entire cardiac cycle. The illustrated instantaneous moment is t/T = 0.325. The pressure minimum on the sinus side wall shows the position of the vortical structure core of the main hairpin vortical structure: (a) blue shows the ‘healthy’ geometry; (b) red indicates the ‘pre-disposed’ geometry.

Figure 9

Vortical structure motion over the cardiac cycle. ‘Healthy’ geometry is in blue, and ‘pre-disposed’ is shown in red: (a) location of vortex core along axial ICA direction; (b) velocity of vortex core. The indicated moments in time are shown with the dashed lines: t/T = 0.165 (magenta), t/T = 0.22 (cyan), t/T = 0.325 (yellow), t/T = 0.43 (green), and t/T = 0.50 (black).