Induction of aneurysmogenic high positive wall shear stress gradient by wide angle at cerebral bifurcations, independent of flow rate

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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.

ABBREVIATIONS BA = basilar artery; CFD = computational fluid dynamics; EC = endothelial cell; MCA = middle cerebral artery; TAVel = time-averaged velocity; TAWSS = time-averaged wall shear stress; TAWSSG = TAWSS gradient; WSS = wall shear stress; WSSG = WSS gradient.

Article Information

Correspondence Adel M. Malek: Tufts Medical Center, Boston, MA. amalek@tuftsmedicalcenter.org.

INCLUDE WHEN CITING Published online August 10, 2018; DOI: 10.3171/2018.3.JNS173128.

DISCLOSURES Dr. Malek has received research funding from Stryker Neurovascular for research that is unrelated to the submitted work. He also has direct stock ownership in CereVasc LLC, and is a speaker for Microvention-Terump.

© AANS, except where prohibited by US copyright law.

Headings

Figures

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    A: Volumetric representations of 3D rotation angiography showing anatomical variations in the MCA bifurcations. B: Symmetrical parametric models (total bifurcation angles Φ1 + Φ2 = 60°, 80° (not shown), 85°, 120°, and 180°). C: Asymmetrical parametric models (fixed Φ1 = 30° angle, and varying Φ2 = 30°, 60°, and 90°). D: Curved parent vessel morphology with symmetrical bifurcation modeling (total bifurcation angles Φ1 + Φ2 = 60°, 80°, and 120°).

  • View in gallery

    CFD analysis on symmetrical models. A: TAWSS on 3D models. B: Time-averaged velocity (TAVel) shown on the longitudinal cut through the 3D volume. C: Plot of TAWSS on longitudinal 1D cut at the apex. D: Plot of TAWSSG on longitudinal 1D cut at the apex. Positive TAWSSG is detected starting from a bifurcation angle of 85°. Figure is available in color online only.

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    CFD analysis on asymmetrical models. A: TAWSS on 3D models. B: TAVel shown on the longitudinal cut through the 3D volume. C: Plot of TAWSS on longitudinal 1D cut at the apex. D: Plot of TAWSSG on longitudinal 1D cut at the apex. The side corresponding to the wider angle is characterized by positive TAWSSG. Figure is available in color online only.

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    CFD analysis on 3D curved models. A: TAWSS on 3D models. B: TAVel shown on the longitudinal cut through the 3D volume. C: Plot of TAWSS on longitudinal 1D cut at the apex. D: Plot of TAWSSG on longitudinal 1D cut at the apex. The side corresponding to the outer curve (the larger lateral angle) is characterized by positive TAWSSG. Figure is available in color online only.

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    Time-dependent analysis of WSS and WSSGs at peak systole (time step of t = 0.16). A: Symmetrical bifurcation. B: Asymmetrical bifurcation. C: Curved inlet and 60° bifurcation angle. D: Curved inlet and 80° bifurcation angle. E: Curved inlet and 120° bifurcation angle. Figure is available in color online only.

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    Simulation of increased flow rate. Analysis of WSS and WSSGs at peak systole (time step of t = 0.16). A: Symmetrical bifurcation. B: Asymmetrical bifurcation. C: Curved inlet and 60° bifurcation angle. D: Curved inlet and 80° bifurcation angle. E: Curved inlet and 120° bifurcation angle. Figure is available in color online only.

  • View in gallery

    CFD analysis of 3 patients with aneurysms at the MCA bifurcation. A: Patient-derived model prior to aneurysm removal using Laplacian smoothing. B: TAWSS. C: Plot of TAWSS on longitudinal 1D cut at the apex. D: Plot of TAWSSG on longitudinal 1D cut at the apex. Figure is available in color online only.

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