Aneurysm Inflow-Angle as a Discriminant for Rupture in Sidewall Cerebral Aneurysms
Morphometric and Computational Fluid Dynamic Analysis
Background and Purpose— The ability to discriminate between ruptured and unruptured cerebral aneurysms on a morphological basis may be useful in clinical risk stratification. The objective was to evaluate the importance of inflow-angle (IA), the angle separating parent vessel and aneurysm dome main axes.
Methods— IA, maximal dimension, height–width ratio, and dome–neck aspect ratio were evaluated in sidewall-type aneurysms with respect to rupture status in a cohort of 116 aneurysms in 102 patients. Computational fluid dynamic analysis was performed in an idealized model with variational analysis of the effect of IA on intra-aneurysmal hemodynamics.
Results— Univariate analysis identified IA as significantly more obtuse in the ruptured subset (124.9°±26.5° versus 105.8°±18.5°, P=0.0001); similarly, maximal dimension, height–width ratio, and dome–neck aspect ratio were significantly greater in the ruptured subset; multivariate logistic regression identified only IA (P=0.0158) and height–width ratio (P=0.0017), but not maximal dimension or dome–neck aspect ratio, as independent discriminants of rupture status. Computational fluid dynamic analysis showed increasing IA leading to deeper migration of the flow recirculation zone into the aneurysm with higher peak flow velocities and a greater transmission of kinetic energy into the distal portion of the dome. Increasing IA resulted in higher inflow velocity and greater wall shear stress magnitude and spatial gradients in both the inflow zone and dome.
Conclusions— Inflow-angle is a significant discriminant of rupture status in sidewall-type aneurysms and is associated with higher energy transmission to the dome. These results support inclusion of IA in future prospective aneurysm rupture risk assessment trials.
Improvements in vascular imaging methods have led to increased detection of incidental unruptured intracranial aneurysms.1 In contrast to earlier data, which reported an annual rupture rate of approximately 1% to 2% for unruptured aneurysms,2,3 recent studies estimate a significantly lower annual rupture risk of 0.1% to 0.2%.4,5 Although aneurysmal subarachnoid hemorrhage carries a mortality rate of 40% to 50% and a morbidity rate of 10% to 20%,6,7 preventive surgical or endovascular treatment carries an age-dependent risk of complication. Thus, the decision to treat incidental unruptured aneurysms has to be balanced against the risk of rupture.
Predicting rupture risk for a given incidental aneurysm would be of great clinical value. The quest for such predictors has focused mainly on aneurysm size,2–5,8,9 location,4,5,8 and shape.10–12 Aneurysm aspect ratio (AR)12 and height–width ratio (H/W)13 were both found to be higher in ruptured aneurysms. These studies bundled all aneurysm subtypes without segregation between sidewall (SW) and bifurcation-type aneurysms (Figure 1A), a potential confounding factor given computational fluid dynamic (CFD) analysis by Hassan et al14 suggesting a dichotomy between these subtypes.
CFD analysis of rupture risk has centered on wall shear stress (WSS) and its spatial gradient (WSSG) with studies relating low WSS to aneurysm growth and rupture,15,16 whereas others find greater WSS14 and more direct inflow patterns in ruptured aneurysms.16,17 Greater interest has also been accorded to the morphological relationship between aneurysm and parent vessel because of it influencing intra-aneurysmal flow.17–20
The current objective is to evaluate distinguishing morphometric features between ruptured and unruptured SW cerebral aneurysms with special attention to the relationship between parent vessel and aneurysm dome, specifically the inflow-angle (IA) between flow in the parent vessel and the aneurysm dome axis.
Materials and Methods
Patient Selection and Demographics
All patients with cerebral aneurysms were included in the period spanning September 2001 to April 2009. SW aneurysms were defined as lesions emanating off the side of the parent vessel either without or with a very small vascular branch. A total of 463 aneurysms in 401 patients was selected based on 3-dimensional angiographic availability. After excluding mycotic, peripheral, fusiform, and extradural lesions, based on the latter’s different natural history and lower rupture risk,21 330 aneurysms remained, of which 116 were SW-type. Clinical information was retrieved from a prospectively maintained database.
Aneurysm Morphology Measurement
Three-dimensional cerebral angiograms were obtained from either Philips Integris (Bothel, Wash) or Siemens Artis (Malvern, Pa) biplane systems and reconstructed using their respective clinical software packages. Volumetric data sets, including aneurysm and parent vessel, were analyzed in Amira Version 4.1 (Mercury Computer Systems, Chelmsford, Mass) to measure in 3-dimensional space (Figure 1B): maximal dome dimension (Dmax); longest dimension from neck to dome tip (height: H); dome width perpendicular to height (W); and neck width (N). AR was computed by dividing height by neck width12 and H/W by aneurysm width.13 IA was measured as the angle between axis of flow in the parent vessel at the level of the aneurysm neck and the aneurysm’s main axis from the center of the neck to the tip of the dome (Figure 1C).
JMP Version 5 (SAS Institute, Cary, NC) was used for statistical analysis with significance assumed for P<0.05. Characteristics were evaluated independently using Student t test assuming unequal variances and with multivariate logistic regression to analyze interdependence. Receiver operating characteristic curve analysis was used to determine sensitivity and specificity.
Computational Fluid Dynamics
Aneurysm Model and Computational Method
Aneurysm models were constructed with Solidworks (Concord, Mass) measuring 8×4 mm off a 4-mm diameter vessel with IA between 60° and 140° in 10° increments. This parametric design included a spherical neck connector ensuring constant neck and aneurysm dimensions irrespective of IA. The neck was >5 diameters downstream from the inflow, enabling fully developed flow.22 A second model was constructed on the outer bend of a circular curved geometry with varying IA in plane with parent vessel curvature.23
High-resolution polyhedral meshes with prismatic boundary layer enrichment were generated with Star-CCM+ Version 4.02 (CD-Adapco, Melville, NY) at a count of approximately 1 000 000 cells. For comparison and validation of grid size independence,24 hybrid hexahedral meshes (approximately 450 000 cells) were generated with Harpoon Version 3.4 (Sharc Ltd, Manchester, UK). Finite-volume solution used Fluent Version 6.3.26 (Ansys, Lebanon, NH) in the laminar double-precision unsteady regime,24 assuming rigid nonslip wall conditions, blood viscosity of 3.5 cP, and density of 1070 kg/m3. A 1000-timestep pulse was derived from Ford et al25 with time-average inlet velocity of 0.25 m/s with Re=371 and Womersley number22 of 3.3.23,26
Postprocessing and Data Analysis
Postprocessing was performed in Ensight Version 9 (CEI, Apex, NC).24 The net-flow and kinetic energy crossing an orthogonal cut plane halfway toward the dome tip was computed by integrating unidirectional normal velocities and energies. Shear jet zone size was defined as the height from the neck to the 50th percentile of the WSS contour. Velocity jet distance to tip was measured from the 50th percentile velocity contour to the dome tip on a midlongitudinal cut plane.
Demographics and Aneurysm Location
One hundred sixteen SW aneurysms in 102 patients, mean age 56 years (range, 28 to 89 years), were analyzed. Eighty-four patients (82%) were female and 24 aneurysms (21%) had ruptured. Lesion location was 51 paraclinoid internal carotid, 27 posterior communicating, 23 carotid ophthalmic, 7 anterior choroidal, 4 vertebral, 2 posterior cerebral, 1 basilar, and 1 anterior cerebral artery.
Univariate Statistical Analysis
Aneurysms were divided into ruptured and unruptured subsets. IA was significantly higher for the ruptured group at 124.9°±26.5° compared with 105.8°±18.5° for the unruptured (P=0.0001). Dmax, H/W, and AR also showed significantly greater values in the ruptured subset (Table; Figure 2A). Receiver operating characteristic analysis showed H/W to have the largest area under the curve (0.76) followed by Dmax (0.75), AR (0.73), and IA (0.71; Figure 2B).
Multivariate Logistic Regression
The multivariate logistic regression model using Dmax, IA, H/W, and AR showed only IA (P=0.0158) and H/W (P=0.0017) to be statistically significant morphological discriminants of previous aneurysm rupture (Table). No dependence of IA or H/W on age or gender was observed.
Computational Fluid Dynamic Analysis
Inflow Velocity Pattern With Respect to IA
Increasing IA, holding all other parameters and dimensions constant (Figure 3A), led to an increase in the size of the shear jet zone at the base of the aneurysm. This was accompanied by a progressively and comparatively greater and deeper migration of the velocity jet into the dome as measured by distance between jet zone and dome tip (Figure 3B–C).
IA Effect on Net Flow and Kinetic Energy Halfway to the Aneurysm Dome Tip
Analysis of flow parameters through an orthogonal cut plane at 50% from the neck to dome tip revealed significant higher peak flow velocity with higher IA increasing 80-fold from 0.004 m/s at 60° to 0.32 m/s at 140° (Figure 4A–C). Net directional flow traveling across the cut plane increased significantly by 223% (0.0065 mL/s to 0.021 mL/s) from 60° to 120° IA with gentle falloff beyond that point (Figure 4D). In contrast, peak kinetic energy transmission through the cut plane toward the dome tip increased 20-fold from 9.2×10−9 J at 60° to 1.8×10−7 J at 140° IA (Figure 4E).
Aneurysm Dome WSS Dependence on IA
WSS magnitude measured along a longitudinal cut plane inside the parent vessel and aneurysm dome (Figure 5A) exhibited the expected drop in value within the dome. There was little WSS and WSSG variation at the neck inflow and outflow owing to the design of the model, which kept a constant neck area. Consistent with increasing IA leading to higher flow velocities deeper in the dome, higher IA led to a 7.2-fold WSS increase (6.28×10−5 Pa to 4.5×10−4 Pa) in the minimum value at the dome with WSSG increasing 5.6-fold (0.014 Pa/m to 0.079 Pa/m; Figure 5B, D). This increase was persistent independent of dynamic phenomena during the cardiac cycle and was observed in both straight and curved parent vessel models (data not shown).
IA as a Morphological Discriminant
The current study, based on high-resolution 3-dimensional rotational angiographic data, supplemented by parametric CFD modeling, identifies aneurysmal IA as an independent discriminant of rupture status in SW aneurysms, which appears to be statistically more robust than aneurysm size. This finding is consistent with prior descriptive observations by investigators reporting more direct flow into the aneurysm dome16,18 and more often a parallel axis of the aneurysm relative to the parent vessel17 in ruptured aneurysms. Although most aneurysm rupture-risk morphological analyses8,10 such as AR12 and nonsphericity10 consider the aneurysm dome as a separate entity detaching it from the neck up, our analysis of IA incorporates the relation of the aneurysm dome to the parent vessel. This spatial relationship has been shown to be an important determinant of flow patterns inside the aneurysm dome19,23 and may influence rupture risk, consistent with our idealized CFD model findings. A recent study by Dhar et al27 evaluated the angle of inclination between the aneurysm dome and its neck plane; although significantly different in their ruptured subset, the angle of inclination between the aneurysm dome and its neck plane was not found to be an independent discriminant in a multivariate analysis. This may highlight the greater importance of the relative direction of flow in parent vessel with the dome itself rather than the inflow zone at the neck.
Inflow Jet Velocity and Kinetic Energy
We opted not to use patient-derived angiographic data for CFD modeling, but instead elected to define parametric models allowing us to vary IA independently of the multitude of other morphometric features, at the same time keeping specific variables, including neck size, dome height, and width, constant. This approach enables the independent isolation of the hemodynamic effect of varying IA without including confounding variables such as neck inclination angle, neck surface area, or lateral angle with respect to parent vessel curvature.23 The constant neck parameters in our model enable us to attribute hemodynamic differences purely to changes in IA. This reductionist approach uncovered important effects with increasing IA, including inward migration of the flow recirculation core into the aneurysm dome and significantly higher peak velocities and kinetic energy transmission into the distal dome. Although the current analysis assumes a rigid wall, such increased focal velocity and energy impact is likely to result in greater focal wall tension in a more physiological viscoelastic model of the aneurysm wall, a phenomenon demonstrated recently in a fluid–structure interaction model.28 Although beyond the scope of the current study, such an approach, especially accounting for nonuniform anisotropic viscoelasticity and aneurysm wall thickness, may be valuable in furthering our understanding of aneurysm rupture despite its high computational demand.
WSS and Spatial Gradient
Previous studies16 have linked low WSS to aneurysm rupture through focal endothelial dysfunction.29 Other investigations have postulated a higher average WSS in ruptured aneurysms16 and in rupture areas.14 Although our data showed higher WSS in the dome of aneurysms with greater IA, these values remain significantly lower than in the parent vessel (by >3 orders of magnitude at the dome tip). The levels of WSS in the majority of the dome for all IA values in this study is lower than 0.1 Pa, a value at which aortic endothelial cells in vitro do not express the flow-sensitive phenotype.30,31 In fact, flow-mediated endothelin-1 and endothelial nitric oxide synthase shear-induced expression is not activated by shear values <0.4 Pa.31 High spatiotemporal WSSG are known to induce endothelial cell migration away from the high WSS area29 both in vitro and in animal models. Meng et al32 showed that a high product of WSS and WSSG can lead to destructive remodeling of the endothelial layer and subjacent vessel wall; such combination of high WSS and WSSG was found at the neck inflow zone in our model but was largely unaffected by IA variation owing to the design of the model with fixed neck region parameters. Evaluation of the product of WSS and WSSG in the dome of our model aneurysm reveals it to be much too low to be affected by the phenomena described by Tardy29 and Meng.32
Putative Aneurysm Rupture Mechanism
The WSS values at all IA tested for the model used here are very low in the dome; accordingly at the dome tip, both high and low IA models would be characterized by varying but similar degrees of endothelial dysfunction because of the low focal hemodynamic WSS, resulting in the expression of the static deleterious endothelial phenotype.30,31 In that context, we hypothesize that higher peak velocity and transmitted energy of the flow-jet hitting the dome with increasing IA (increasing by approximately 1 order of magnitude between IAs of 60° and 140°) is likely the driving force behind further tensile strain and deflection of the degenerated focal wall in the region of the dysfunctional endothelium. We propose that rupture may be the result of 2 pathological mechanisms: first, focal degenerative changes driven by endothelial dysfunction in regions of low WSS16 (such as blebs and daughter components), and second, coincident elevated wall tension and strain resulting from high velocity and kinetic energy influx on such a degenerative weakened wall region,32 leading to supramaximal wall deflection and aneurysm rupture.
We limited our analysis to SW aneurysms on a straight segment and on a curved segment model IA in-plane with parent vessel curvature; it is possible that results may differ for other lateral angles as described by Liou et al.23 In contrast to SW lesions, bifurcation aneurysm hemodynamics are dependent on the relative size and the multiple relative angles of the daughter vessels, introducing significant complexities to the analysis. Paradoxically, in a symmetrical bifurcation, an inline IA of 180° would result in an area of stasis and low flow in the dome, leading to lower velocity, kinetic energy, and WSS compared with a lower IA (data not shown).
Shape analysis to differentiate between ruptured and unruptured aneurysms assumes that the process of rupture itself does not alter aneurysm shape, a hypothesis that has not yet been conclusively ruled out.
Our data are retrospective in nature and, although we identified a parameter whose importance was further validated by CFD analysis, will need additional prospective testing of their predictive potential.
Our CFD approach assumes rigid walls and does not take into account the viscoelasticity of the vessel wall and the focal anisotropic degenerative changes usually observed in vivo in the aneurysm.
Finally, aneurysm rupture is likely precipitated by several aneurysm characteristics. Mathematical models predicting aneurysm rupture status have been proposed before8,27 and work on such a model incorporating IA is currently underway and could be further refined by addition of multicenter data.
The current study has identified IA as an independent and robust rupture status differentiator in SW intracranial intradural aneurysms. Although Dmax, AR, and H/W were separately significantly higher in the ruptured subset, only IA and H/W were independent discriminants and were more important than maximal aneurysm size, the more conventional morphological feature that has been relied on in clinical risk stratification.5 Future prospective analyses may benefit from inclusion of higher-order shape descriptors and parent vessel–aneurysm relationship analysis such as IA.
- Received October 18, 2009.
- Revision received February 12, 2010.
- Accepted March 9, 2010.
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