Hemodynamic Conditions that Favor Bleb Formation in Cerebral Aneurysms

Abstract

Background

Although it is generally believed that blebs represent weaker spots in the walls of intracranial aneurysms (IAs), it is largely unknown which aneurysm characteristics favor their development.

Methods

A total of 270 IAs in 199 patients selected for surgical clipping were studied. Blebs were visually identified and interactively marked on patient-specific vascular models constructed from pre-surgical images. Blebs were then deleted from the vascular reconstruction to approximate the aneurysm before bleb formation. Computational fluid dynamics studies were performed in these models as well as cases without blebs. Hemodynamic and geometric characteristics of aneurysms with and without blebs were compared.

Results

A total of 173 aneurysms had no blebs, while 97 aneurysms had a total of 122 blebs. Aneurysms favoring bleb formation had stronger (p<0.0001) and more concentrated inflow jets (p<0.0001), higher flow velocity (p=0.0061), more complex (p<0.0001) and unstable (p=0.0157) flow patterns, larger maximum wall shear stress (WSS) (p<0.0001), more concentrated (p=0.0005) and oscillatory (p=0.0004) WSS distribution, and a more heterogeneous WSS field (p<0.0001), than aneurysms without blebs. They were also larger (p<0.0001), more elongated (p<0.0001), had wider necks (p=0.0002), and more distorted and irregular shapes (p<0.0001).

Conclusions

Strong and concentrated inflow jets, high speed, complex and unstable flow patterns, and concentrated, oscillatory, and heterogeneous WSS patterns favor the formation of blebs in IAs. Blebs are more likely to form in large, elongated, and irregularly shaped aneurysms. These adverse characteristics could be considered signs of aneurysm instability when evaluating aneurysms for conservative observation or treatment.

Introduction

The presence of blebs or secondary focalized bulging of the wall has been included as a risk factor in scoring scales used to assess the risk of rupture of intracranial aneurysms (IAs),^1,2 and have been shown to be risk indicators independent from aneurysm size and location.³ Although, it is generally believed that blebs represent weaker spots in the aneurysm wall that are vulnerable to failure, it is largely unknown which patient and aneurysm characteristics favor the development of blebs. Identifying and understanding these characteristics, which could be considered biomarkers for aneurysm instability, is extremely valuable for improving current aneurysm evaluation and treatment recommendations.

The progressive weakening of the aneurysm wall is thought to be strongly related to flow-induced degenerative remodeling of the wall through inflammatory processes,^4,5 among other multi-factorial processes.⁶ Many studies have investigated associations between abnormal flow conditions to aneurysm rupture and instability.⁷ Similar associations with aneurysm size and shape characteristics have also been analyzed,⁸ since geometric characteristics are thought to influence not only the hemodynamic environment but also the biomechanical stresses within the aneurysm wall, and many of them are relatively simple to measure or calculate from medical images. Therefore, it is logical to investigate possible associations between aneurysm hemodynamic and geometric characteristics to the development of blebs in intracranial aneurysms, which is the objective of the current study.

Methods

Aneurysm Data and Bleb Identification

A total of 270 intracranial aneurysms in 199 patients selected for surgical clipping and previously used for studying associations of patient and clinical characteristics with presence of blebs were further analyzed.⁹ Deidentified aneurysm vascular geometries were obtained from our database.

The overall methodology for identifying the bleb region in the aneurysm sac is illustrated in Figure 1(a–d) and Supplementary Figure I. Using previously described methods,¹⁰ patient-specific vascular models were constructed from rotational angiography (3DRA) or computed tomographic angiography (CTA) images acquired prior to surgery. In these aneurysms, blebs were identified by visual inspection of corresponding volume rendered 3D images (Fig. 1a), reconstructed vascular models (Fig. 1b), and aneurysm Gaussian curvature maps (Fig. 1c), and interactively marked on the vascular models (Fig. 1d), using a tool called ChePen3D, as detailed in.⁹ An illustration of the use of the curvature map for guidance in the definition and marking of blebs is presented in Supplementary Figure I.

Figure 1.

Vascular modeling: a) volume rendering of 3DRA image, b) patient-specific vascular model, c) curvature map highlighting bleb (red=positive Gaussian curvature, blue=negative Gaussian curvature), d) marking of bleb using ChePen3D tool, e) bleb removal, f) closure of bleb orifice, g) meshing. Hemodynamics visualization at peak systole after bleb removal (surrogate for aneurysm prior to bleb formation): h) inflow jet, i) wall shear stress magnitude, j) oscillatory shear index, k) flow streamlines, l) vortex corelines, m) swirling flow around vortex corelines.

Hemodynamic Modeling

In order to approximate the hemodynamic conditions and geometry prevalent prior to bleb formation, new vascular models were automatically created by virtually deleting the blebs in aneurysms with identified blebs as shown in Figure 1(e–g). Briefly, the mesh elements labeled as belonging to the blebs were deleted from the vascular model triangulation (Fig. 1e), and the hole corresponding to the bleb neck was automatically closed with a surface triangulation algorithm that preserves surface curvature at the edges¹¹ (Fig. 1f). Finally, a volumetric grid of tetrahedral elements was generated inside this new vascular model for subsequent CFD analysis (Fig. 1g). In aneurysms without blebs, the CFD meshes were generated directly from the original vascular model. Mesh resolution was set to a minimum of 0.02 cm, resulting in grids ranging from approximately 2–7 million elements.

Hemodynamic simulations were then performed on both sets of aneurysms: aneurysms with their blebs removed, and aneurysms without blebs. In these simulations, blood was approximated as a Newtonian incompressible fluid, and the unsteady Navier-Stokes equations were numerically solved with a finite element code.¹² Vascular walls were approximated as rigid. Pulsatile inflow conditions were imposed by scaling a representative flow waveform with an empirical law relating flow rate and cross-sectional area in internal carotid and vertebral arteries.¹³ Outflow conditions were imposed by splitting flows consistent with Murray’s law. Simulations were run for two cardiac cycles and data from the second cycle was used to characterize the hemodynamic conditions in the aneurysm. Example flow visualizations are shown in Fig. 1(h–m).

Data Analysis

The aneurysm hemodynamics was characterized by computing flow variables that measure different properties of the intra-aneurysmal flow,¹⁴ including: strength (Q) and concentration (ICI) of the inflow jet, speed (VE), viscous dissipation (VD), complexity (corelen) and stability (podent) of the flow pattern, and strength (WSSmean, WSSmax), concentration (SCI) and spread (LSA), and oscillation (OSImean, OSImax) of the wall shear stress (WSS). The mean and maximum WSS normalized with the mean WSS value over the near (<1 cm away from the neck) parent artery were also computed as measures of the strength of the WSS relative to the WSS in the parent artery.

In addition, critical points in the WSS vector field were detected, counted, and averaged over the cardiac cycle. A critical point is mathematically defined as a location on the aneurysm sac where the shear stress vector is zero (stationary point). Different kinds of critical points such as saddle points, node sources or sinks, focus sources or sinks, are distinguished by the local derivatives around the stationary point.¹⁵ Critical points are valuable for characterizing the local WSS field, which can presumably affect the endothelial function. For example, the point on the aneurysm surface associated with the end of a vortex core-line is a critical point. The mean number of critical points (nCrPoints) is thus a variable that measures the total number of regions with “insult” to the endothelium by the abnormal WSS field during the cardiac cycle.

Similarly, the geometry of the aneurysm was characterized by computing variables that capture different aspects of the aneurysm geometry,¹⁶ including: aneurysm sac size (Asize, SR, GAA), aneurysm neck size (Nsize), aneurysm elongation (AR, VOR, BF), and aneurysm shape distortion relative to a spherical shape (NSI, CR) and surface irregularity (UI). More details are presented in Supplementary Table I.

The hemodynamic and geometric characteristics of aneurysms that developed blebs (with their blebs removed to approximate their characteristics before bleb formation) were compared to those of aneurysms without blebs. Specifically, the mean values of variables were statistically compared between these two groups using the two-sample Mann-Whitney U test coded into R scripts. The p-values were then adjusted for multiple testing using the Benjamini & Hochberg (BH) method available in R. Differences were considered statistically significant if p<0.05 after adjustment.

Results

A total of 173 aneurysms in 121 patients were classified as having no blebs. Blebs were identified in the remaining 97 aneurysms in 78 patients, for a total of 122 blebs. Comparisons of the patient and clinical characteristics between aneurysms with and without blebs are reported in a separate paper.⁹ Hemodynamic and geometric differences between aneurysms with blebs (removed) and aneurysms without blebs are presented in Table 1. As shown in this table, most of the hemodynamic and geometric variables were significantly different between the two groups of aneurysms, even after adjustment for multiple testing.

Table 1.

Hemodynamic and geometric characteristics of aneurysms with blebs (after bleb removal, mimicking conditions before bleb formation) and aneurysms without blebs. Statistically significant differences are indicated with a “*”. See Supplementary Table I for more details on the hemodynamic and geometric variables.

Characteristic	Variable	Aneurysms with deleted blebs	Aneurysms without blebs	p-value	Adjusted p-value
		Mean ± SD	Mean ± SD
Hemodynamics
Inflow jet	Q (ml/s)	0.95 ± 0.79	0.64 ± 0.94	<0.0001*	<0.0001*
	ICI	1.04 ± 0.75	0.70 ± 0.77	<0.0001*	<0.0001*
Flow pattern	VE (cm/s)	10.3 ± 6.99	8.16 ± 6.44	0.0046*	0.0061*
	VD	1170 ± 1930	1000 ± 1890	0.2300	0.2343
	corelen (mm)	22.3 ± 22.1	11.7 ± 13.7	<0.0001*	<0.0001*
	podent	0.27 ± 0.22	0.21 ± 0.16	0.0126*	0.0157*
Wall shear stress pattern	WSSmax (dyn/cm2)	334 ± 349	204 ± 170	<0.0001*	<0.0001*
	WSSmean (dyn/cm2)	21.3 ± 18.2	17.5 ± 16.1	0.0801	0.0953
	MaxWSSnorm	7.06 ± 5.77	5.28 ± 2.71	0.0003*	0.0005*
	WSSnorm	0.44 ± 0.28	0.46 ± 0.35	0.9300	0.9300
	LSA (%)	48.2 ± 31.8	52.7 ± 34.6	0.1830	0.2079
	SCI	7 ± 7.71	5.05 ± 12.3	0.0003*	0.0005*
	OSImax	0.34 ± 0.11	0.28 ± 0.13	0.0002*	0.0004*
	OSImean	0.02 ± 0.01	0.02 ± 0.01	0.2180	0.2343
	nCrPoints	2.28 ± 0.87	1.60 ± 0.99	<0.0001*	<0.0001*
Geometry
Size	Asize (mm)	8.5 ± 3.2	6.7 ± 4.5	<0.0001*	<0.0001*
	Nsize (mm)	5.6 ± 2.1	4.8 ± 2.6	0.00012*	0.0002*
	SR	2.63 ± 1.02	2.18 ± 1.54	<0.0001*	<0.0001*
	GAA (cm−1)	7.64 ± 5.60	17.8 ± 23.2	<0.0001*	<0.0001*
Elongation	AR	1.14 ± 0.48	0.93 ± 0.63	<0.0001*	<0.0001*
	VOR (mm)	9.8 ± 9.5	5.7 ± 9.5	<0.0001*	<0.0001*
	BF	1.37 ± 0.38	1.16 ± 0.37	<0.0001*	<0.0001*
Shape distortion	NSI	0.21 ± 0.04	0.19 ± 0.05	<0.0001*	<0.0001*
	CR	0.83 ± 0.11	0.78 ± 0.13	0.0012*	0.0016*
Irregularity	UI	0.17 ± 0.11	0.22 ± 0.13	0.0012*	0.0016*

Hemodynamically, aneurysms with blebs (with their blebs deleted) had stronger (Q, p<0.0001) and more concentrated inflow jets (ICI, p<0.0001), higher intra-aneurysmal flow velocity (VE, p=0.0061), more complex (corelen, p<0.0001) and unstable (podent, p=0.0157) flow patterns than aneurysms without blebs. In addition, they also had larger maximum wall shear stress (WSSmax, p<0.0001; MaxWSSnorm, p=0.0005), more concentrated (SCI, p=0.0005) and oscillatory (OSImax, p=0.0004) WSS distribution, and a larger number of critical points of the wall shear stress field (nCrPoints, p<0.0001).

Geometrically, aneurysms that developed blebs were larger (Asize, p<0.0001; SR, p<0.0001; GAA, p<0.0001), more elongated (AR, p<0.0001; VOR, p<0.0001; BF, p<0.0001), had wider necks (Nsize, p=0.0002), and more shape distortion (CR, p=0.0016, NSI, p<0.0001) and more surface irregularity (UI, p=0.0016) than aneurysms without blebs.

Discussion

Aneurysm shape irregularity and, in particular, the presence of blebs has been considered a risk factor for rupture of cerebral aneurysms.^1–3 However, little is known about the conditions that predispose aneurysms to develop blebs and place them at immediate risk of rupture. As such, the focus of this work was to investigate what flow conditions and aneurysm geometries could favor bleb formation, which would subsequently predispose the wall for failure and aneurysm rupture. For this purpose, a series of aneurysms with and without blebs were compared. The geometry and hemodynamics of the aneurysms with blebs were analyzed by first virtually removing the bleb from the vascular model in order to approximate the conditions prior to bleb formation, which were then compared to those of aneurysms without blebs. In this manner, the comparison is essentially between those aneurysms that are prone to develop blebs and those that are unlikely to develop blebs. There are two underlying assumptions in this approach. First, is the assumption that the aneurysm shape and hemodynamics before the blebs were formed are reasonably approximated by deleting the blebs from vascular models reconstructed from 3D images obtained after the blebs were formed. This, in turn, presupposes that blebs develop and grow more rapidly than the rest of the aneurysm, which is not unreasonable since longitudinal studies have suggested two modes of growth, one associated with overall enlargement of the aneurysm and another associated with focalized growth and bleb development.¹⁷ However, there may be other modes of aneurysm growth and bleb development, for example early bleb formation followed by aneurysm enlargement, or progressive growth of the aneurysm and simultaneous bleb development. Although it is unknown how frequently these growth modes occur in the aneurysm population, previous studies have shown in a few cases rapid development of blebs without major enlargement of the rest of the aneurysm sac in longitudinal images,^18,19suggesting that our assumption is reasonable. The second underlying assumption is that aneurysms without blebs at the time of imaging have had a lower likelihood of developing blebs than those that have already developed a bleb. This conjecture seems reasonable, but it is not known if some of these aneurysms would develop blebs in the future. In spite of these limitations, the findings of this study are intriguing as further discussed below.

The methodology used for defining blebs in cerebral aneurysms involves the manual step of visually identifying the blebs and interactively marking them on the vascular models, with guidance from volume rendered 3D angiographic images and aneurysm surface curvature maps. It has previously been shown that this approach is quite consistent between different operators.⁹ Furthermore, all the subsequent steps (bleb removal, hole triangulation, meshing, flow simulation, and hemodynamic and geometric characterization) are fully automatic, thus making the entire process quite objective and reproducible.

Our results suggest that in general aneurysm flow conditions characterized by high and concentrated inflow jets, high speed, complex and unstable flow patterns with an associated concentrated, complex, and oscillatory wall shear stress distribution seem more favorable for the development of blebs in intracranial aneurysms. Furthermore, blebs seem to be in general more likely to develop in larger, more elongated, and more irregular aneurysms. To illustrate these differences, examples of flow visualizations in two aneurysms at the middle cerebral artery (MCA) bifurcation are presented in Figure 2, one without bleb (left) and another with a bleb (right, in this case flow simulation corresponds to the aneurysm prior to bleb formation, i.e. with the bleb virtually deleted). Further examples are presented in Supplementary Figures II, III, IV, and V for aneurysms at the posterior communicating artery (PCOM), anterior communicating artery (ACOM), M1 segment of the MCA, and MCA bifurcation, respectively. These visualizations show, in general, stronger inflow jets and impingement regions, higher and more heterogeneous wall shear stress, and more complex flow patterns in aneurysms that developed blebs compared to those without blebs.

Figure 2.

Examples of hemodynamics (at peak systole) for MCA aneurysms with and without blebs. Left panel – aneurysm with bleb removed (surrogate for IA prior to bleb formation): a) geometry of MCA aneurysm after removal of one bleb (insert shows marked bleb in red), b) inflow jet (iso-velocity surface), c) WSS magnitude, d) flow pattern (streamlines), e) vortex corelines. Right panel – representative MCA aneurysm that presented without bleb: f) geometry of MCA aneurysm without bleb, g) inflow jet, h) WSS magnitude, i) flow pattern, and j) vortex corelines.

Since treatment decisions are more difficult for small aneurysms, the analysis was repeated for aneurysms smaller than 7mm. The results are presented in Supplementary Table II. It can be seen that most differences remained significant for this subset. Interestingly, viscous dissipation became significantly different between small aneurysms with and without blebs, while measures of flow instability (podent) and oscillation (OSI) became not significantly different. Similarly, neck size and measures of aneurysm shape distortion (NSI, CR, UI) were no longer significantly different in this subset. This suggests that flow instabilities and shape irregularity are less important factors for bleb formation in small aneurysms compared to measures of flow strength and WSS heterogeneity.

Similar hemodynamic and geometric characteristics have been previously associated to aneurysm rupture,²⁰ as well as aneurysm growth and instability,²¹ and have been used in aneurysm rupture probability models.²² However, other studies have suggested connections between low and oscillatory wall shear stress to aneurysm rupture.^23,24 In those studies, the aneurysm WSS was normalized with the average WSS in the parent artery. In the current study, the normalized mean WSS tended to be lower in aneurysms that developed blebs compared to aneurysms without blebs, but this difference did not reach statistical significance. In contrast, the maximum normalized WSS was significantly larger. Note that these differences cannot in general be explained by the difference in aneurysm size. In addition, high flow conditions and irregular aneurysm shapes have also been related to increased aneurysm wall inflammation²⁵ and decreased aneurysm wall strength.²⁶ Bleb formation seems to be a highly localized phenomenon, and the flow conditions identified here as favorable for bleb formation are characterized by strong and concentrated flow characteristics (inflow jet, WSS distribution, critical points). Therefore, it seems reasonable to propose that these adverse flow and geometric characteristics may be signs of aneurysm instability and could be used to better understand which aneurysms are more likely to develop blebs and progress to a more fragile and rupture-prone status. Moreover, once the blebs are formed, they become high risk features that could increase local wall stress²⁷ and permeability leading to inflammation which has been linked to wall enhancement in MR vessel wall imaging.²⁸

Conclusions

Hemodynamic conditions characterized by strong and concentrated inflow jets, high speed, complex and unstable flow patterns, and concentrated, oscillatory and heterogeneous wall shear stress patterns favor the formation of blebs in cerebral aneurysms. Similarly, blebs are more likely to form in large, elongated and irregularly shaped aneurysms. These adverse characteristics could be considered signs of vulnerability to aneurysm instability when evaluating aneurysms for conservative observation or treatment.