Curvature effect on hemodynamic conditions at the inner bend of the carotid siphon and its relation to aneurysm formation

Abstract

Although high-impact hemodynamic forces are thought to lead to cerebral aneurysmal change, little is known about the aneurysm formation on the inner aspect of vascular bends such as the internal carotid artery (ICA) siphon where wall shear stress (WSS) is expected to be low. This study evaluates the effect of vessel curvature and hemodynamics on aneurysm formation along the inner carotid siphon. Catheter 3D-rotational angiographic volumes of 35 ICA (10 aneurysms, 25 controls) were evaluated in 3D for radius of curvature and peak curvature of the siphon bend, followed by univariate statistical analysis. Computational fluid dynamic (CFD) simulations were performed on patient-derived models after aneurysm removal and on synthetic variants of increasing curvature. Peak focal siphon curvature was significantly higher in aneurysm bearing ICAs (0.36 ± 0.045 vs. 0.30 ± 0.048 mm(-1), p=0.003), with no difference in global radius of curvature (p=0.36). In CFD simulations, increasing parametric curvature tightness (from 5 to 3mm radius) resulted in dramatic increase of WSS and WSS gradient magnitude (WSSG) on the inner wall of the bend. In patient-derived data, the location of aneurysms coincided with regions of low WSS (<4 Pa) flanked by high WSS and WSSG peaks. WSS peaks correlated with the aneurysm neck. In contrast, control siphon bends displayed low, almost constant, WSS and WSSG profiles with little spatial variation. High bend curvature induces dynamically fluctuating high proximal WSS and WSSG followed by regions of flow stasis and recirculation, leading to local conditions known to induce destructive vessel wall remodeling and aneurysmal initiation.

Keywords: Aneurysm formation; Internal carotid artery; Intracranial aneurysm; Vessel curvature.

Figure 1

Volumetric reconstruction of the 10 aneurysmal ICA models. All aneurysm originate from the inner wall of the proximal carotid siphon.

Figure 2

Centerline curvature computation of aneurysmal (top row) and control (bottom row) ICAs. The black arrows demonstrate the areas of greatest curvature which are proximal to the aneurysm in each case.

Figure 3

Two aneurysmal ICAs with wide global radius of curvature (4.4 mm and 3.96 mm respectively) describing a wider anterior bend, but with tight local radius of curvature (2.88 mm and 2.74 mm respectively) of the proximal elbow of the bend. Black arrows represent flow direction.

Figure 4

Synthetic models of the anterior bend of the carotid siphon are represented as tubular structures with a bend of variable radius of curvature. Shown are bends with radius of curvature of 5 mm, 4 mm, and 3 mm. Additional model (R5/R3) has an overall radius of curvature of 5 mm with a proximal peak curvature corresponding to a radius of curvature of 3 mm.

Figure 5

Digital removal of aneurysms. (A) Initial model with aneurysm in the inner bend of carotid siphon. (B) The aneurysm is digitally removed and (C) the vessel is reconstructed. The one dimensional curve where flow properties are evaluated during fluid dynamics postprocessing is shown in gray.

Figure 6

Hemodynamic results on synthetic models. All values are shown at peak systole (t= 2.275s). Black arrows point to the inflow direction. First column: wall shear stress (WSS). Second column: magnitude of WSS gradient (WSSG). Third column: Velocity shown on a longitudinal plane cutting through the middle of the model. Black rectangles highlight regions of flow stasis and recirculation.

Figure 7

WSS values plotted over a one dimensional (1D) curve cut positioned on the curved inner wall for multiple synthetic models (R5, R4, R3 and R5/R3). The length of the 1D curve is dependent on the radius of curvature of the bend. The cardiac cycle was sampled at 9 time points. The red curve is obtained at peak systole, whereas the gray curve is obtained at end diastole. First column: wall shear stress (WSS). Second column: magnitude of WSS gradient (WSSG).

Figure 8

The product of the wall shear stress and the magnitude of the wall shear stress gradient (WSS*WSSG). (A) Synthetic models. (B) Patient-derived models for two aneurysmal (red) and two control (black) ICAs.

Figure 9

Hemodynamic results on two aneurysmal patient-derived models. Red arrows point to the site of the aneurysm. Black arrows point to the site of the maximum peak curvature. First column: for each aneurysm, WSS and WSSG images were captured at peak systole (t= 2.275s). Second column: for each aneurysm, WSS and WSSG were plotted over a 1 dimensional curve cut positioned on the curved inner wall. The cardiac cycle was sampled at 9 time points. Red curve is obtained at peak systole. Gray curve is obtained at end diastole. The horizontal line represents the width of the aneurysm neck.

Figure 10

Hemodynamic results on control patient-derived models. Black arrows point to the site of the maximum peak curvature. First column: for each control WSS and WSSG images are captured at peak systole (t= 2.275s). Second column: for each control, WSS and WSSG were plotted over a one dimensional curve cut positioned on the curved inner wall. The cardiac cycle was sampled at 9 time points. Red curve is obtained at peak systole. Gray curve is obtained at end diastole.