Vortex formation and associated aneurysmogenic transverse rotational shear stress near the apex of wide-angle cerebral bifurcations

2021 ◽  
pp. 1-12
Author(s):  
Adel M. Malek ◽  
James E. Hippelheuser ◽  
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.

BMC Neurology ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Mikołaj Zimny ◽  
Edyta Kawlewska ◽  
Anna Hebda ◽  
Wojciech Wolański ◽  
Piotr Ładziński ◽  
...  

Abstract Background Previously published computational fluid dynamics (CFD) studies regarding intracranial aneurysm (IA) formation present conflicting results. Our study analysed the involvement of the combination of high wall shear stress (WSS) and a positive WSS gradient (WSSG) in IA formation. Methods We designed a case-control study with a selection of 38 patients with an unruptured middle cerebral artery (MCA) aneurysm and 39 non-aneurysmal controls to determine the involvement of WSS, oscillatory shear index (OSI), the WSSG and its absolute value (absWSSG) in aneurysm formation based on patient-specific CFD simulations using velocity profiles obtained from transcranial colour-coded sonography. Results Among the analysed parameters, only the WSSG had significantly higher values compared to the controls (11.05 vs − 14.76 [Pa/mm], P = 0.020). The WSS, absWSSG and OSI values were not significantly different between the analysed groups. Logistic regression analysis identified WSS and WSSG as significant co-predictors for MCA aneurysm formation, but only the WSSG turned out to be a significant independent prognosticator (OR: 1.009; 95% CI: 1.001–1.017; P = 0.025). Significantly more patients (23/38) in the case group had haemodynamic regions of high WSS combined with a positive WSSG near the bifurcation apex, while in the control group, high WSS was usually accompanied by a negative WSSG (14/39). From the analysis of the ROC curve for WSSG, the area under the curve (AUC) was 0.654, with the optimal cut-off value −0.37 Pa/mm. The largest AUC was recognised for combined WSS and WSSG (AUC = 0.671). Our data confirmed that aneurysms tend to form near the bifurcation apices in regions of high WSS values accompanied by positive WSSG. Conclusions The development of IAs is determined by an independent effect of haemodynamic factors. High WSS impacts MCA aneurysm formation, while a positive WSSG mainly promotes this process.


2019 ◽  
Vol 131 (2) ◽  
pp. 442-452 ◽  
Author(s):  
Alexandra Lauric ◽  
James E. Hippelheuser ◽  
Adel M. Malek

OBJECTIVEEndothelium 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.METHODSComputational 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.RESULTSNarrow 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.CONCLUSIONSApical 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.


Author(s):  
Navid Freidoonimehr ◽  
Rey Chin ◽  
Anthony C. Zander ◽  
Maziar Arjomandi

Abstract Temporal variations of the coronary arteries during a cardiac cycle are defined as the superposition of the changes in the position, curvature, and torsion of the coronary artery axis markers and the variations in the lumen cross-sectional shape due to the distensible wall motion induced by the pulse pressure and contraction of the myocardium in a cardiac cycle. This review discusses whether the modelling the temporal variations of the coronary arteries is needed for the investigation of the hemodynamics specifically in time critical applications such as a clinical environment. The numerical modellings in the literature which model or disregard the temporal variations of the coronary arteries on the hemodynamic parameters are discussed. The results in the literature show that neglecting the effects of temporal geometric variations is expected to result in about 5\% deviation of the time-averaged pressure drop and wall shear stress values and also about 20\% deviation of the temporal variations of hemodynamic parameters, such as time-dependent wall shear stress and oscillatory shear index. This review study can be considered as a guide for the future studies to outline the conditions in which temporal variations of the coronary arteries can be neglected, while providing a reliable estimation of hemodynamic parameters.


2010 ◽  
Vol 112 (4) ◽  
pp. 306-313 ◽  
Author(s):  
Pankaj K. Singh ◽  
Alberto Marzo ◽  
Bethany Howard ◽  
Daniel A. Rufenacht ◽  
Philippe Bijlenga ◽  
...  

2016 ◽  
Vol 43 (1) ◽  
pp. 99-115 ◽  
Author(s):  
Khairuzzaman Mamun ◽  
Most. Akhter ◽  
Mohammad Ali

A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity is given. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Determination of the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k ? w model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole. In general, the velocities at throat regions are highest at all-time phase. However, at pick systole higher velocities are observed at post-stenotic region. Downstream flow of all models creates some recirculation regions at diastole.


1978 ◽  
Vol 85 (1) ◽  
pp. 57-83 ◽  
Author(s):  
A. M. M. Aly ◽  
A. C. Trupp ◽  
A. D. Gerrard

Fully developed air-flows through an equilateral triangular duct of 12·7 cm sides were investigated over a Reynolds number range of 53 000 to 107 000. Based on equivalent hydraulic diameter, friction factors were found to be about 6% lower than for pipe flow. Mean axial velocity distributions near the wall were describable by the inner law of the wall (when based on local wall shear stress) but the constants differ slightly from those for pipe flow. As expected, the secondary flow pattern was found to consist of six counter-rotating cells bounded by the corner bisectors. Maximum secondary velocities of about 1 ½% of the bulk velocity were observed. The effects of secondary currents were evident in the cross-sectional distributions of mean axial velocity, wall shear stress and Reynolds stresses, and very prominent in the turbulent kinetic energy distribution. For the flow prediction, the vorticity production terms were expressed by modelling the Reynolds stresses in the plane of the cross-section in terms of gradients in the mean axial velocity and a geometrically calculated turbulence length scale. The experimental and predicted characteristics of the flow are shown to be in good agreement.


Neurosurgery ◽  
2013 ◽  
Vol 72 (5) ◽  
pp. 739-748 ◽  
Author(s):  
Bulang Gao ◽  
Merih I. Baharoglu ◽  
Adel M. Malek

Abstract BACKGROUND: Self-expanding intracranial stent-assisted coiling of bifurcation aneurysms has recently been shown to straighten target cerebral vessels, a phenomenon with unknown hemodynamic effect. OBJECTIVE: To investigate the impact of angular remodeling in aneurysms treated with single stent-assisted coiling with the use of computational fluid dynamic techniques. METHODS: Fourteen patients (7 women, mean age 55) who underwent stent coiling of 14 wide-necked bifurcation aneurysms were included based on the availability of high-resolution 3-dimensional rotational angiography. Pretreatment data sets underwent virtual aneurysm removal to isolate the effect of stenting. Wall shear stress and pressure profiles obtained from constant flow input computational fluid dynamic analysis were analyzed for apical hemodynamic changes. RESULTS: Stenting increased the bifurcation angle with significant straightening immediately after treatment and at follow-up (107.3° vs 144.9°, P &lt; .001). The increased stented angle at follow-up led to decreased pressure drop at the bifurcation apex (12.2 vs 9.9 Pa, P &lt; .003) and migration of the flow impingement zone (FIZ) toward the contralateral nonstented daughter branch by a mean of 1.48 ± 0.2 mm. Stent-induced angular remodeling decreased FIZ width separating peak apical wall shear stress (3.4 vs 2.5 mm, P &lt; .004). Analysis of FIZ distance measured from the parent vessel centerline showed it to be linearly (r = .58, P &lt; .002) and FIZ width inversely correlated (r = .46, P &lt; .02) to vessel bifurcation angle. CONCLUSION: Stent-induced angular remodeling significantly altered bifurcation apex hemodynamics in a favorable direction by blunting apical pressure and inducing the narrowing and migration of the FIZ, a novel response to intracranial stenting that should be added to intimal hyperplasia and flow diversion.


2014 ◽  
Vol 553 ◽  
pp. 316-321
Author(s):  
Ashkan Javadzadegan ◽  
Babak Fakhim ◽  
Rahman T. Nakkas ◽  
Masud Behnia

This study was to investigate the effect of the bifurcation angle asymmetry on recirculation flow, pressure drop and wall shear stress (WSS) in an atherosclerotic model of a left coronary artery with left anterior descending (LAD) and left circumflex (LCX) branches. The linear regression analysis results showed that there is a positive correlation between WSS and bifurcation angle asymmetry. However, small increase in the WSS magnitude due to the increase in bifurcation angle asymmetry revealed the angle asymmetry does not seem to have a profound effect on the WSS. The results also showed that the bifurcation angle asymmetry play a prominent role in determining the pressure drop and recirculation area, while having relatively unnoticeable effects on the wall shear stress (WSS).


2018 ◽  
Vol 128 (3) ◽  
pp. 723-730 ◽  
Author(s):  
Sherif Rashad ◽  
Shin-ichiro Sugiyama ◽  
Kuniyasu Niizuma ◽  
Kenichi Sato ◽  
Hidenori Endo ◽  
...  

OBJECTIVERisk factors for aneurysm rupture have been extensively studied, with several factors showing significant correlations with rupture status. Several studies have shown that aneurysm shape and hemodynamics change after rupture. In the present study the authors investigated a static factor, the bifurcation angle, which does not change after rupture, to understand its effect on aneurysm rupture risk and hemodynamics.METHODSA hospital database was retrospectively reviewed to identify patients with cerebral aneurysms treated surgically or endovascularly in the period between 2008 and 2015. After acquiring 3D rotational angiographic data, 3D stereolithography models were created and computational fluid dynamic analysis was performed using commercially available software. Patient data (age and sex), morphometric factors (aneurysm volume and maximum height, aspect ratio, bifurcation angle, bottleneck ratio, and neck/parent artery ratio), and hemodynamic factors (inflow coefficient and wall shear stress) were statistically compared between ruptured and unruptured groups.RESULTSSeventy-one basilar tip aneurysms were included in this study, 22 ruptured and 49 unruptured. Univariate analysis showed aspect ratio, bifurcation angle, bottleneck ratio, and inflow coefficient were significantly correlated with a ruptured status. Logistic regression analysis showed that aspect ratio and bifurcation angle were significant predictors of a ruptured status. Bifurcation angle was inversely correlated with inflow coefficient (p < 0.0005), which in turn correlated directly with mean (p = 0.028) and maximum (p = 0.014) wall shear stress (WSS) using Pearson's correlation coefficient, whereas aspect ratio was inversely correlated with mean (0.012) and minimum (p = 0.018) WSS.CONCLUSIONSBifurcation angle and aspect ratio are independent predictors for aneurysm rupture. Bifurcation angle, which does not change after rupture, is correlated with hemodynamic factors including inflow coefficient and WSS, as well as rupture status. Aneurysms with the hands-up bifurcation configuration are more prone to rupture than aneurysms with other bifurcation configurations.


Author(s):  
Ian C. Campbell ◽  
William W. Sprague ◽  
Marina Piccinelli ◽  
Alessandro Veneziani ◽  
John N. Oshinski

The link between hemodynamic forces, notably wall shear stress (WSS), and atherogenesis is well established. Patient-specific computational fluid dynamics (CFD) modeling of human vasculature has attracted recent attention because it allows investigators to determine areas at risk for plaque formation and subsequent rupture [1]. Non-invasive in vivo imaging methods such as magnetic resonance (MR) angiography allow acquisition of vascular geometry and cross-sectional velocity such that a CFD model can determine the spatial distribution of WSS. WSS may then be correlated with phenomena such as wall thickening.


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