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Adel M. Malek, James E. Hippelheuser, and Alexandra Lauric

OBJECTIVE

Aneurysm formation preferentially occurs at the site of wide-angle cerebral arterial bifurcations, which were recently shown to have a high longitudinal positive wall shear stress (WSS) gradient that promotes aneurysm formation. The authors sought to explore the other components of the hemodynamic environment that are altered with increasing bifurcation angle in the apical region and the effects of these components on WSS patterns on the vessel wall that may modulate aneurysm genesis and progression.

METHODS

Parametric models of symmetrical and asymmetrical bifurcations were created with increasing bifurcation angles (45°–240°), and 3D rotational angiography models of 13 middle cerebral artery (MCA) bifurcations (7 aneurysmal, 6 controls) were analyzed using computational fluid dynamics. For aneurysmal bifurcations, the aneurysm was digitally removed to uncover hemodynamics at the apex. WSS vectors along cross-sectional planes distal to the bifurcation apex were decomposed as orthogonal projections to the cut plane into longitudinal and transverse (tangential to the cross-sectional plane) components. Transverse rotational WSS (TRWSS) and TRWSS gradients (TRWSSGs) were sampled and evaluated at the apex and immediately distal from the apex.

RESULTS

In parametric models, increased bifurcation angle was associated with transverse flow vortex formation with emergence of an associated apical high TRWSS with highly aneurysmogenic positive TRWSSGs. While TRWSS decayed rapidly away from the apex in narrow-angle bifurcations, it remained greatly elevated for many radii downstream in aneurysm-prone wider bifurcations. In asymmetrical bifurcations, TRWSS was higher on the aneurysm-prone daughter vessel associated with the wider angle. Patient-derived models with aneurysmal bifurcations had wider angles (149.33° ± 12.56° vs 98.17° ± 8.67°, p < 0.001), with significantly higher maximum TRWSS (1.37 ± 0.67 vs 0.48 ± 0.23 Pa, p = 0.01) and TRWSSG (1.78 ± 0.92 vs 0.76 ± 0.50 Pa/mm, p = 0.03) compared to control nonaneurysmal bifurcations.

CONCLUSIONS

Wider vascular bifurcations are associated with a novel and to the authors’ knowledge previously undescribed transverse component rotational wall shear stress associated with a positive (aneurysmogenic) spatial gradient. The resulting hemodynamic insult, demonstrated in both parametric models and patient-based anatomy, is noted to decay rapidly away from the protection of the medial pad in healthy narrow-angle bifurcations but remain elevated distally downstream of wide-angle aneurysm-prone bifurcations. This TRWSS serves as a new contribution to the hemodynamic environment favoring aneurysm formation and progression at wide cerebral bifurcations and may have clinical implications favoring interventions that reduce bifurcation angle.

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Alexandra Lauric, James E. Hippelheuser, and Adel M. Malek

OBJECTIVE

Endothelium adapts to wall shear stress (WSS) and is functionally sensitive to positive (aneurysmogenic) and negative (protective) spatial WSS gradients (WSSG) in regions of accelerating and decelerating flow, respectively. Positive WSSG causes endothelial migration, apoptosis, and aneurysmal extracellular remodeling. Given the association of wide branching angles with aneurysm presence, the authors evaluated the effect of bifurcation geometry on local apical hemodynamics.

METHODS

Computational fluid dynamics simulations were performed on parametric bifurcation models with increasing angles having: 1) symmetrical geometry (bifurcation angle 60°–180°), 2) asymmetrical geometry (daughter angles 30°/60° and 30°/90°), and 3) curved parent vessel (bifurcation angles 60°–120°), all at baseline and double flow rate. Time-dependent and time-averaged apical WSS and WSSG were analyzed. Results were validated on patient-derived models.

RESULTS

Narrow symmetrical bifurcations are characterized by protective negative apical WSSG, with a switch to aneurysmogenic WSSG occurring at angles ≥ 85°. Asymmetrical bifurcations develop positive WSSG on the more obtuse daughter branch. A curved parent vessel leads to positive apical WSSG on the side corresponding to the outer curve. All simulations revealed wider apical area coverage by higher WSS and positive WSSG magnitudes, with increased bifurcation angle and higher flow rate. Flow rate did not affect the angle threshold of 85°, past which positive WSSG occurs. In curved models, high flow displaced the impingement area away from the apex, in a dynamic fashion and in an angle-dependent manner.

CONCLUSIONS

Apical shear forces and spatial gradients are highly dependent on bifurcation and inflow vessel geometry. The development of aneurysmogenic positive WSSG as a function of angular geometry provides a mechanotransductive link for the association of wide bifurcations and aneurysm development. These results suggest therapeutic strategies aimed at altering underlying unfavorable geometry and deciphering the molecular endothelial response to shear gradients in a bid to disrupt the associated aneurysmal degeneration.