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Original research
Wall shear stress association with rupture status in volume matched sidewall aneurysms
  1. Alexandra Lauric,
  2. James Hippelheuser,
  3. Alex D Cohen,
  4. Laith M Kadasi,
  5. Adel M Malek
  1. Cerebrovascular and Endovascular Division, Department of Neurosurgery, Tufts Medical Center, and Tufts University School of Medicine, Boston, Massachusetts, USA
  1. Correspondence to Dr A M Malek, Cerebrovascular and Endovascular Division, Department of Neurosurgery, Tufts Medical Center, 800 Washington Street, Boston, MA 02111, USA; amalek{at}


Objective Flow induced tangential wall shear stress (WSS) is thought to be involved in aneurysm formation, growth, and rupture. Low WSS was previously associated with rupture, but definitive quantitative analyses remain scant as larger aneurysms are associated with lower WSS regardless of rupture status, and ruptured aneurysms are larger than unruptured aneurysms. Here, the intra-dome WSS was evaluated on 18 internal carotid artery aneurysms, volume matched as ruptured/unruptured pairs in order to remove the confounding effect of size dependence.

Methods Computational fluid dynamic simulations were performed and WSS was evaluated at peak systole, end diastole, and as time averaged over the cardiac cycle. WSS logarithmic scaling was applied to refine value discrimination at extrema. Ruptured/unruptured lesions were statistically evaluated using pairwise t test analysis. The effect of size on WSS was evaluated in parametric models.

Results In parametric data, there was a statistically significant negative correlation between volume and WSS values. In patient data, mean WSS was not statistically significant but low range WSS values were significantly lower for ruptured aneurysms, regardless of WSS evaluation (time averaged, peak systole, end diastole). Statistically, logarithmic WSS performed better than WSS, with minimum logarithmic WSS at end diastole being the best rupture status discriminator (p=0.001, area under the curve=0.98). Higher range and maximal WSS were not significantly significant.

Conclusions Aneurysm size is a confounding factor to WSS rupture discrimination, and volume matched analysis is necessary for unbiased evaluation. While these results lend support to the hypothesis that lower WSS induces wall changes which may be associated with rupture, it raises questions regarding the extent of this association, which requires further exploration.

  • Aneurysm
  • Subarachnoid
  • Angiography

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The factors leading to cerebral aneurysm rupture remain elusive. Increasingly, research has implicated the hemodynamic microenvironment in aneurysm formation and rupture, and has served as a target of study and consideration in risk analysis. Wall shear stress (WSS), the frictional force exerted by blood flow on the vessel wall, has been determined to be a critical mediator of gene expression regulation via endothelial mechanoreceptors, resulting in changes in cellular cytoskeleton organization and ion channel activation, featuring the mitogen activated protein kinase cascade and transcription factor nuclear factor κB.1–4 In both animal and human studies, low WSS from focal stasis has been associated with an elevated oxidant state with increased apoptosis and cell turnover5–8 and a degenerative gene expression pattern, with higher expression of proinflammatory products.9 ,10

Previous studies have revealed aneurysm size, shape, and location as independent predictors of rupture risk.11 ,12 For sidewall variants, not only are larger aneurysms more likely to rupture13 but aneurysm size was shown to be negatively correlated with WSS, with large aneurysms being characterized by low WSS, independent of other risk factors, such as aneurysm shape.14 Consequently, studies exploring the importance of WSS in aneurysm rupture that do not compensate for dome size disregard their confounding contributions. Analysis on aneurysmal datasets with large ruptured aneurysms are likely to report low WSS significance which does not reflect the rupture risk of small aneurysms, thus introducing bias against smaller ruptured aneurysms. Conversely, analysis on aneurysmal datasets with larger unruptured aneurysms, such as giant internal carotid artery aneurysms, may fail to report the statistical significance of WSS features or may even find WSS values being larger for ruptured compared with unruptured aneurysms.

The current study seeks to remove the confounding effect of aneurysm size on the hemodynamic simulations, and especially on WSS distributions, as they pertain to discriminating rupture status. Here, WSS parameters were evaluated on a dataset of size matched as well as location matched, ruptured and unruptured cerebral aneurysms, thus resulting in a size independent analysis.

Materials and methods

Patient selection and demographics

Consecutive high resolution three-dimensional angiographic data of patients with saccular intradural aneurysms were examined for this study. Dissecting, fusiform, blood blister-type, traumatic, and mycotic aneurysms were excluded. Similar to other studies,15 only cases in which the rotational angiographic images were of sufficient quality for accurate segmentation and reconstruction were included. All aneurysms originating off the internal carotid artery were evaluated for size and volume using a prospectively maintained aneurysm database previously described.16 Each ruptured aneurysm was subsequently paired with size matched controls of unruptured aneurysms at similar locations. A total of 16 ruptured aneurysms met these criteria. On analysis, seven pairs were then excluded because of volume differences greater than 25% with the available unruptured matched counterparts. Consequently, analysis was performed on nine ruptured (mean volume 134.9±148.3 mm3) and nine unruptured (mean volume 132.3±135.5 mm3) volume matched aneurysms. Mean age of the ruptured set was 61.4 years (eight women, age range 38–77 years) whereas mean age of the unruptured set was 58.4 years (seven women, age range 34–77 years), which also resulted in statistical age matched analysis. All angiographic imaging within the ruptured set were obtained in urgent fashion within less than 24–48 h from the onset of rupture, prior to onset of vasospasm.

The temporal aneurysm shape evolution and clinical symptomatology were not followed clinically over a period of time, and were not available prior to rupture. Clinical information, including rupture status, was retrieved from a prospectively maintained database.

Cerebral angiography and data processing

Three-dimensional catheter based cerebral angiograms were obtained using a Philips Integris (Bothell, Wash) calibrated biplane system, with volume reconstruction using the available clinical software package, to yield a three-dimensional volumetric dataset (figure 1A). Volumetric datasets, including aneurysm and parent vessel, were analyzed in Amira V.5.3 (Mercury Computer Systems, Chelmsford, Massachusetts, USA) for segmentation in three-dimensional space (figure 1B).

Figure 1

Segmentation and isolation of data. (A) Original three-dimensional angiographic data. (B) Segmented vessels are represented by a curvature based non-uniform polyhedral mesh. The aneurysm dome is separated from its parent vessel. The blue band on the inflow vessel shows the area used for flow normalization. (C) Four parametric models of different volumes with radii of 3, 4, 5, and 6 mm.

Patient derived models

The segmented surfaces were used to create polyhedral meshes of approximately 250 000 cells with a boundary layer enhancement. The final mesh was created with a vessel entrance length several times the diameter of the parent vessel using Star-CCM+ (CD-Adapco, Melville, New York, USA).

Computational fluid dynamic simulations were performed using Ansys Fluent 12.0 (Ansys Inc, Labanon, New Hampshire, USA) by modeling laminar transient flow with a Carreau non-Newtonian profile to better approximate viscosity and flow of blood.17 In order to account for variability in size, shape, and length of the parent vessel, flow scaling factors were determined for each model to ensure ideal parent vessel WSS conditions of approximately 1.5 Pa at the proximity of the aneurysm neck. Subsequently, scaled pulsatile flow was applied at the inlet for three complete cardiac cycles to allow flow to develop adequately and the third cycle was used for analysis. Each cycle period was T=1 s and had a time step of t=0.002 s, with the peak systole at t=0.16 s. This resulted in an average Reynolds number of 67±18.5 and an average Wormersley number (α) of 2.4±0.4.18 At the outlets, gauge pressure was set to zero Pascal.18

All post-processing analysis was performed using EnSight V.10.0 (Computational Engineering International, Apex, North Carolina, USA). For each model, the aneurysm dome was separated from the parent vessel, and WSS statistics were evaluated on the dome (figure 1B).

Parametric models

In order to evaluate the effect of aneurysm volume on WSS, synthetic models of carotid ophthalmic aneurysms were constructed using SolidWorks (Concord, Massachusetts, USA). The models were created by extrusion of a circle (5 mm diameter) perpendicular over a centerline path. The initial model consisted of a proximal horizontal arm of 25 mm, followed by a bend over a curve representing a semicircle with a radius of curvature of 3 mm (curvature along the bend=0.33) and ending with a distal horizontal arm of 25 mm. An initial aneurysm, modeled as a sphere with a radius of 3 mm and a neck radius of 2.5 mm, was positioned 22.5 mm from the outlet plane. Three additional models were created by increasing the aneurysm radius to 4, 5, and 6 mm (resulting in a volume increase of 165%, 97.9%, and 74.1% between each model, respectively), while maintaining parent vessel, aneurysm location, and neck size constant (figure 1C).

Wall shear stress

Time averaged WSS was evaluated at each mesh point as the mean magnitude of the instantaneous shear stress vectors over the duration of the cardiac cycle. Spatial means were computed for the peak systole WSS, end diastole WSS, and time averaged WSS as area weighted integrations over the entire aneurysmal surface.

Given the wide non-linear range of WSS values characterizing the aneurysm dome, logarithmic transformation was proposed in order to evaluate WSS distributions and statistics, and enable finer discrimination across a wide range of shear values.

Additional analysis was focused on the aneurysmal area covering the low WSS distribution range. The 5% lowest WSS area was identified on the aneurysm dome using custom processing software code (Matlab V.7.10, MathWorks, Natick, Massachusetts, USA). The size of the evaluated area was increased in steps of 5% until up to 95%. WSS statistical performance was evaluated for the resulting areas.

Statistical analysis

JMP statistical software (V.9.0.2, SAS Institute, Cary, North Carolina, USA) was used to evaluate the performance of all parameters in discriminating between ruptured and unruptured aneurysms. Statistical significance was assumed for p<0.05. All variables were tested independently using the pairwise t test analysis. Receiver operating characteristics curve analysis was employed, and area under the curve (AUC) index was evaluated for each variable. Bivariate analysis was used to quantify statistical correlation, as quantified by the square of the correlation coefficient (R2).


Effect of aneurysm volume on WSS distribution

Analysis performed on aneurysm models of increasing volume showed a strong negative correlation between WSS values and volume. A statistically significant fit was observed in reciprocal transformations between aneurysmal volume and average WSS (R2=0.96) as well as minimum WSS (R2=0.95) (figure 2B). A strong negative linear correlation was observed between volume and maximum WSS (R2=0.97). Histogram analysis showed the entire WSS distribution shifting towards lower values with increased volume (figure 2A). Aneurysm volume has the potential of acting as a confounding factor in WSS discrimination performance.

Figure 2

(A) Time averaged wall shear stress (WSS) distributions and histograms for parametric models of increasing volume, corresponding to radii of (A) 3 mm, (B) 4 mm, (C) 5 mm, and (D) 6 mm. Increase in volume results in a larger aneurysmal area covered by lower WSS and increased flow stagnation near the models walls. The histograms show a visible distribution shift towards the lower end of the WSS distribution. (B) Reciprocal transformation between aneurysm volume and dome time averaged WSS (TAWSS) (correlation R2=0.96). An increase in volume is correlated with a decrease in TAWSS.

WSS analysis in volume matched ruptured/unruptured aneurysms pairs

Pairwise analysis showed that at end diastole, ruptured aneurysms are characterized by significantly lower dome averaged mean WSS compared with unruptured aneurysms (p=0.03, AUC=0.75). Time averaged WSS, as well as peak systole WSS, did not distinguish rupture status (table 1). Minimum WSS values were significantly lower for ruptured compared with unruptured aneurysms, regardless of whether WSS was evaluated at peak systole (p=0.04, AUC=0.86) at end diastole (p=0.03, AUC=0.98), or as a time averaged mean (p=0.03, AUC=0.96). Spatial mean WSS in areas of low WSS were statistically lower for ruptured compared with unruptured aneurysms for percentage areas up to 50% (from 5% area p=0.01, to 50% area p=0.04).

Table 1

Pairwise statistical analysis of wall shear stress rupture discrimination performance

Logarithmic statistics were found to perform better in rupture status discrimination compared with their non-logarithmic correspondents. Mean dome averaged logarithmic WSS was significant not only at end diastole (p=0.004, AUC=0.89) but also at peak systole (p=0.03, AUC=0.83), as well as time averaged WSS (p=0.01, AUC=0.84) (table 1). Minimum values of the dome averaged logarithmic WSS were also strong rupture status discriminators: minimum logarithmic WSS at peak systole (p=0.01, AUC=0.86), at end diastole (p=0.001, AUC=0.98), and as time averaged (p=0.002, AUC=0.96). No statistically significant difference was found for maximum WSS values, regardless of how WSS was evaluated, and regardless of the use of a logarithmic scale. WSS statistics at end diastole were better statistical performers compared with time averaged and peak systole WSS statistics.

Figure 3 shows the time average WSS distributions on the surface of the 18 aneurysms evaluated in this study. Here, the aneurysms are grouped as volume matched pairs and are shown sorted by their volume. Histogram details are provided for three of the ruptured/unruptured aneurysm pairs in figure 4. The first row represents the pair having the smallest volume from the dataset (ruptured 19.9 mm3, unruptured 17.8 mm3). It is evident from the corresponding histograms that, even with a volume small enough to not usually be associated with a high risk of rupture, the ruptured aneurysm is characterized by lower WSS compared with its unruptured matched counterpart. The second row represents a pair of aneurysms in which both aneurysms have irregular surfaces. Although the two histograms have somewhat similar shapes, the ruptured aneurysm is characterized by lower minimum and mean WSS values, as well as by a larger area covered by a lower WSS. The third row of the figure shows the largest pair of aneurysms in our dataset (ruptured 513 mm3, unruptured 479 mm3). The ruptured aneurysm is characterized by lower WSS values, as evident from the individual histograms.

Figure 3

Time averaged wall shear stress (WSS) distributions on the surface of the nine volume matched aneurysmal pairs. The pairs are sorted by volume from top to bottom. Left column represents ruptured aneurysms; right column represents the corresponding unruptured aneurysms.

Figure 4

Time averaged wall shear stress (WSS) distributions and histograms for three ruptured/unruptured volume matched aneurysmal pairs. The volume of the aneurysms increases from pair 1 to pair 3. Pair 1 represents the smallest aneurysms in the dataset. None of the aneurysms have blebs. Pair 2 represents a ruptured aneurysm with a bleb and an unruptured aneurysm which also has a bleb. Pair 3 represents the largest aneurysms in the dataset. The ruptured aneurysm has a bleb and the unruptured aneurysm has no blebs. Regardless of bleb presence, the ruptured aneurysms are characterized by lower WSS values.

Figure 5 shows the cumulative ruptured/unruptured WSS histograms accounting for all nine pairs (both WSS and logarithmic WSS distributions). First, it is evident that using a logarithmic scale for WSS representation results in the expansion of the lower WSS values over a larger range, permitting a more detailed analysis of this distribution aspect. Second, the figure shows that, even in these cumulated ruptured/unruptured set comparisons, the ruptured aneurysms are characterized by a wider range of lower WSS values. Third, cumulative ruptured/unruptured histograms are more similar in shape compared with paired ruptured/unruptured histograms in which the difference is more striking (see figure 4). This is an additional argument for volume matched pair analysis being more accurate for WSS evaluation.

Figure 5

Cumulative time averaged wall shear stress (WSS) histograms for the ruptured (top row) and unruptured (bottom row) sets. WSS histograms are shown in the first column, and the corresponding logarithmic transformation is shown in the second column. Use of the logarithmic scale expands the lower range of WSS values and makes evident the changes between ruptured and unruptured distributions. The insert shows the lower range of the logarithmic WSS (smaller than −8) magnified by an order of 10 for visualization purposes.

Effect of bleb presence

In the current dataset of 18 aneurysms, seven aneurysms harbored blebs (four ruptured) and 11 aneurysms did not (five ruptured). Statistically, bleb presence was not found to correlate with rupture status (p=0.63, by Pearson's correlation test). Moreover, WSS values, evaluated as mean, minimum, and maximum values at peak systole, end diastole, and time averaged, were not found to be statistically different between aneurysms with blebs compared with aneurysms without blebs (table 2). Using a logarithmic scale did not improve these statistics.

Table 2

Statistical analysis of wall shear stress distribution for aneurysms with and without blebs

Overall, given that both ruptured and unruptured aneurysms presented with blebs, the bleb effect on WSS statistics did not appear to be strong enough to explain, by itself, the significantly lower WSS values which characterized ruptured aneurysms.


It is well established that different hemodynamic properties play a role in the development and growth of aneurysms19 but to the best of our knowledge this is the first study to evaluate WSS characteristics using pairwise statistical analysis on a population of volume matched ruptured/unruptured aneurysms at similar locations. Volume matched analysis removes the risk of aneurysm volume and size acting as confounding factors to WSS discriminative performance. In addition to being controlled for volume, the aneurysms evaluated here were all sidewall aneurysms originating from the internal carotid artery. This adds an additional degree of data homogeneity, as the hemodynamic and morphological differences between sidewall and bifurcation aneurysms were previously documented.11 ,13

Several studies have recently associated low WSS with a higher risk of aneurysmal rupture20–22 but the results presented here suggest that methodologies which do not control for volume disregard the aneurysm size as a confounding factor of low WSS. Ruptured aneurysms tend to be larger compared with unruptured aneurysms, and this is particularly true for sidewall aneurysms originating off the internal carotid artery.13 It was previously shown that larger aneurysms are characterized by low WSS, independent of rupture status.14 Here, analysis on parametric models of aneurysms of increasing volume resulted in decreasing WSS, regardless of evaluation as minimum, maximum, or mean values. The results suggest that low WSS previously reported may be, at least in part, the effect of size differences between ruptured/unruptured subsets rather than being related to the underlying pathophysiology leading to the likelihood of rupture.

Even if low WSS is in fact associated with aneurysmal rupture, methodologies which do not compensate for volume may be biased against smaller ruptured aneurysms. While ruptured sidewall aneurysms tend to be larger compared with unruptured aneurysms, many small aneurysms do rupture. The management of small aneurysms is often difficult as these aneurysms are associated with a larger volume of subarachnoid hemorrhage23 and more frequent intraprocedural complications.24 Understanding of the rupture phenomenon in these aneurysms is critical. However, analysis on aneurysmal datasets which do not compensate for differences in aneurysmal size is very likely to report low WSS thresholds which are not sensitive to small ruptured aneurysms and thus not useful for clinical rupture prediction purposes; they could also be misleading in the characterization of the role of WSS in aneurysmal rupture.

This pairwise analysis on volume matched aneurysms did not find that the spatial mean time averaged WSS was associated with rupture. Instead, only the lower range of WSS was statistically lower for ruptured versus unruptured aneurysms. The use of a logarithmic scale to narrow the very sparse WSS distribution, and thus increase the distribution weight of the lower WSS values, resulted in significant statistical improvement for ruptured status discrimination.

The findings of our study bring to light another question—that of causation. Due to the natural history of aneurysms, there tend to be more aneurysms discovered after becoming symptomatic and in many cases after rupture. It is extremely challenging to determine if low WSS is a causal factor for rupture or if the low WSS is a post-rupture phenomenon. Recent analysis on a set of 16 unruptured aneurysms suggested that low WSS regions co-localize with thin wall regions on the aneurysmal surface.25 Focally degenerated arterial wall was previously associated with bleb formation,26 and a significant portion of aneurysms develop blebs prior to rupture,25 and blebs have further been shown to be characterized by lower WSS.26 ,27 In this population, four of the ruptured and three of the unruptured aneurysms presented with blebs. Given the fact that blebs are present in both ruptured and unruptured aneurysms, we believe blebs were not likely to have an overall effect on the results presented here. While the exact mechanism of aneurysmal rupture remains elusive and needs further exploration, this study suggests that, in certain conditions, whole aneurysm hemodynamic analysis could be misleading, and analysis of regions with low WSS may be more accurate.

Study limitations

The current analysis is retrospective in character and thus can only imply prediction of previously determined rupture status. The conclusions of this study will require validation in prospective randomized studies before their performance can be validated and applied in risk assessment of incidentally found unruptured aneurysm in clinical practice.

Moreover, the results of the study apply to sidewall aneurysms originating off of the internal carotid artery. The differences between sidewall and bifurcation aneurysms have been previously documented13 and thus bifurcation aneurysms, as well as aneurysms at other locations, may behave differently and require future investigation.

Analysis dependent on aneurysm shape depends on the hypothesis that aneurysm shape does not change after rupture. Were shape to dramatically change after rupture, the current class of analysis would not be helpful. Even though prior evidence indicates that such a change does not occur,28 ,29 consistent with intraoperative findings, conclusive data on this subject remain to be found.


Aneurysms size acts as confounding factor to WSS discriminative performance, as larger aneurysms have lower WSS values. In sidewall aneurysms, volume and location matched analysis revealed that only the lower range of WSS distribution was associated with rupture status, whereas mean and maximum WSS was not. Using a logarithmic scale to evaluate WSS statistics resulted in significantly improved statistical performance. While these results lend support to the hypothesis that lower WSS induces wall changes which may be associated with rupture, it raises questions regarding the extent of this association which requires further exploration.



  • Contributors All authors are justifiably credited with authorship, according to the authorship criteria. AL: analysis and interpretation of the data, drafting of the manuscript, and final approval. JH: acquisition of the data, and analysis and interpretation of the data. ADC: acquisition of the data, and analysis and interpretation of the data. LMK: acquisition of the data. AMM: conception, design, analysis and interpretation of the data, critical revision of the manuscript, and final approval.

  • Funding This work was supported by a grant from the National Institutes of Health (NIH-R21HL102685).

  • Competing interests AMM has received unrestricted research funding from Codman Neurovascular, Stryker Neurovascular, Microvention Inc, and Siemens Inc for research that is unrelated to the submitted work here.

  • Ethics approval This research was approved by Tufts Health Sciences Campus institutional review board.

  • Provenance and peer review Not commissioned; externally peer reviewed.