Combined clinical and computational information in complex cerebral aneurysms: application to mirror cerebral aneurysms

Alessandro G. Radaelli*a, Teresa Sola Martínezc, Elio Vivas Díazc, Xavier Melladoa,

Marcelo A. Castrob, Christopher M. Putmand, Leopoldo Guimaraensc, Juan R. Cebralb, Alejandro F. Frangia

aComputational Imaging Lab, Department of Technology, Pompeu Fabra University, Pg. Circumval·lació 8, 08003 Barcelona, Spain

bLaboratory for Computational Fluid Dynamics Fluids and Materials Program, School of Computational Sciences, George Mason University , 4400 University Drive, MSN 4C7, Fairfax, Virginia 22030, USA

cNeuroangiografia Terapèutica J.J.Merland, Hospital General de Catalunya, 08190 San Cugat del Valles, Barcelona, Spain

dInterventional Neuroradiology, Inova Fairfax Hospital, Falls Church, VA 22042, USA

ABSTRACT

Although the incidence of ruptured cerebral aneurysms is relatively small, when rupture occurs, morbidity and mortality are exceptionally high. The understanding of the pathological and physiological forces driving aneurysmal pathogenesis and progression is crucial. In this paper we analyze the occurrence of mirror cerebral aneurysms in 8 patients and speculate on the effect of haemodynamics on the localization and course of the disease. By mirror cerebral aneurysms we indicate two aneurysms in the same patient and at the same location in the cerebral vasculature but symmetrically with respect to a sagittal plane. In particular we focus on cases of mirror cerebral aneurysms where only one of the two aneurysms presented subarachnoid hemorrhage (SAH). Anatomical information is extracted from 3D rotational angiography (3DRA) images and haemodynamic information is obtained through blood flow simulation in patient-specific anatomical models. The distribution of Wall Shear Stress (WSS) and the flow patterns through the vessels and inside the aneurysms are reported. By combining clinical observations on asymmetry of the cerebral vasculature and aneurysmal shape and size with computed information on blood flow patterns we explore the causes behind a specific localization and a different outcome of disease progression. Keywords: cerebral aneurysm, mirror cerebral aneurysms, haemodynamics, image-based modeling

1. INTRODUCTION

Cerebral aneurysm disease has been reported to affect around 1-5% of the population [1]. Although the majority of cerebral aneurysms are unruptured, the catastrophic consequences of subarachnoid hemorrhage (SAH) following rupture of cerebral aneurysms makes optimal treatment of patients with unruptured aneurysms subject of important debates. The understanding of the pathological and physiological forces driving aneurysmal progression is crucial in determining whether to treat or not a patient. In this decisional process high morbidity and mortality rates of patients with ruptured cerebral aneurysms have to be balanced with possible neurological deficits and complications during surgery and costly and prolonged care after endovascular embolization.

Rather difficult scenarios are presented by patients with two or more cerebral aneurysms. The treatment strategy for these patients may be very challenging. Multiple aneurysms are discovered in approximately 20-30% of patients with cerebral aneurysms. Female sex and age ≥ 50 years have been associated with high risk of SAH occurrence in patients affected by multiple cerebral aneurysms [2-4]. Among SAH patients, higher rates of neurological deficits and post-treatment complications have been reported in patients with multiple cerebral aneurysms when compared with patients *alessandro.radaelli@upf.edu, phone: +34 935 421447, fax: +34 935 422517, www.cilab.upf.edu

affected by a single cerebral aneurysm [2]. Known risk factors of multiple cerebral aneurysm incidence are limited to cigarette smoking and high blood pressure and Anterior Communicating Artery (ACoA) aneurysms have shown to be the most prone to hemorrhage [2,4]. An interesting subgroup of multiple cerebral aneurysms is constituted by the mirror or twin cerebral aneurysms, which affect corresponding arteries symmetrically with respect to a sagittal plane. Mirror cerebral aneurysms are approximately 20-30% of all multiple cerebral aneurysms and a distinct occurrence in female subjects has been reported (70% of patients) [5]. Although the age of disease presentation (mean age is 50 years) and the rates of SAH occurrence (70-80% of patients) in patients with mirror cerebral aneurysms are similar to patients with non-mirror multiple cerebral aneurysms, early rupture with no extrinsic risk factors in patients with mirror cerebral aneurysms has lead to support the role of congenital predisposition over degenerative causes [5]. The nature of congenital predisposition is however not clear. The occurrence of mirror cerebral aneurysms is typically synchronous, with high incidence at the M1-M2 bifurcation of the Middle Cerebral Artery (MCA) and in the region of the Posterior Communicating Artery (PCoA) [3]. Casimiro et al. in [5] report that hereditary connective tissue disease and familial history are normally associated to a higher risk of aneurysm formation, but this does not hold for mirror cerebral aneurysms. Campos et al. [6] suggest that embryological endothelial defects may lead to dysfunctional symmetrical vessel abnormalities and repeated and long-lasting triggers such as haemodynamic forces may initiate aneurysmal development and progression. The concept of “defected” arterial segments initiated by haemodynamic triggers is further developed by Baccin et al. in [7]. The authors explain that the apparent homogenous cerebral arterial system is divided into segments conserving an embryological identity throughout life. Defects during vasculogenesis may occur at specific locations and bilaterally in corresponding segments and specific triggers such as haemodynamic forces may lead to aneurysm formation.

If the localization of mirror aneurysms in specific sites can be explained with a defined role of congenital abnormalities, limited information is however available in the literature on possible mechanisms behind a different progression of the two mirror cerebral aneurysms. Mirror cerebral aneurysms have been reported to occur simultaneously, but progression can be exquisitely different. This is a difficult scenario for clinical professionals as the decision-making on the treatment of the unruptured mirror aneurysm may be biased by the occurrence of SAH in an aneurysms in the same location and in the same patient, although often very different in morphology and size and possibly in blood flow patterns. Asymmetries in the vascular anatomy of the circle of Willis have been indicated to have a role in aneurysmal disease [8]. Although with controversial results, aneurysmal size and aspect ratio are also commonly evaluated in clinical practice. Novel insight is believed to be provided by understanding the action of haemodynamic forces on aneurysmal wall. Interactions between haemodynamic forces and arterial wall biology are believed to play an important role not only in triggering aneurysm formation, but also in the growth and rupture of cerebral aneurysms. Measurement of blood flow in cerebral arteries is possible through modern Time-resolved Phase-Contrast Magnetic Resonance Angiography (4D PC MRA) techniques, but detailed information on haemodynamic variables are impaired by limited resolution and the effectiveness of the methodology is still unproven in cerebral aneurysms. In addition, SAH patients are typically received in critical conditions in intensive care units and time for a pre-operative PC MRA session would be seldom allowed. Image-based Computational Fluid Dynamics (CFD) offers the ability of reconstructing patient-specific blood flow and detailed information on haemodynamic variables in all possible aneurysmal configurations from a wide range of imaging modalities. Efforts in the validation of the information provided by CFD analysis [9-13] are being accompanied by important insight that CFD studies are providing in the association between computed haemodynamic variables and aneurysmal growth and rupture [14,15].

Mirror aneurysms constitute an interesting scenario for understanding cerebral aneurysms. Although haemorrhagic stroke is a complex and multi-factorial process, mirror cerebral aneurysms, as a disease model, offer the potentials of an environment where most of other factors are controlled and where the combination of clinical observations on vascular anatomy and computed information such as blood flow patterns may give fresh insight. In this paper we combine clinical observations and an image-based blood flow modelling method previously illustrated in [9] to describe differences in vascular anatomy and computed haemodynamic variables in 8 patients presenting mirror cerebral aneurysms, one of which has typically ruptured, and speculate on their possible associations with a different outcome of disease progression.

2. METHODS

2.1. Patient clinical and image data

The patient population is composed of 8 subjects, divided in 7 women and 1 man. Table 1 summarises data on patient demographics, presence of known risk factors (S = smoking, Hyp = Hypertension, St = Stimulants, D = Diabetes), symptoms (World Federation of Neurological Surgeons (WFNS) scale), SAH extension (Fisher scale), location of the mirror aneurysms and side of the ruptured aneurysm. Seven patients were symptomatic and hospitalized with a suspect of SAH, while in 1 case the patient did not present rupture, but was hospitalized due to clear symptoms. Location and extension of the hemorrhage together with the rupture site were determined by experienced neuroradiologists considering clinical and radiological information, obtained either locally or at a centre of primary care. All patients then underwent endovascular treatment in a neuroradiological interventional suite. At the Hospital General de Catalunya (HGC) all unruptured aneurysms were not treated and were selected for surveillance.

Table 1: Patient clinical data and mirror aneurysms information

Two pre-treatment images depicting the mirror cerebral aneurysms and connected vessels were acquired via 3D Rotational Angiography (3DRA) by two injections of contrast material in both internal carotid arteries (ICA’s). In particular, case 1 was imaged at the Department of Radiology of the Academic Medical Centre (AMC), Amsterdam, The Netherlands, cases 2 and 3 at the Department of Interventional Neuroradiology of the Inova Fairfax Hospital (IFH), Fairfax, USA and cases 4 to 8 at the Department of Therapeutic Neuroangiography JJ Merland of the Hospital General de Catalunya, Barcelona, Spain. All centres possess Philips Integris Systems (Philips Medical Systems, Best, The Netherlands). The 3DRA images at AMC and HGC were obtained during a 240 degree rotation for a duration of 8 s and 6s respectively to obtain a total of 100 projection images. The 3DRA images at IFH were obtained during a 180 degree rotation and imaging at 15 frames per second for 8 s to obtain a total of 120 projection images. In all centres the projection images were transferred to a dedicated workstation where they were reconstructed into a 3D volume dataset. At AMC, the projection images were reconstructed into a 3D dataset of 128 x 128 x 128 voxels covering a field of view of 59.81 mm. At IFH, the projection images were reconstructed into a 3D dataset of 256 x 256 x 256 voxels covering a field of view of 62.58 mm. At HGC, the projection images were reconstructed into a 3D dataset of 256 x 256 x 256 voxels covering a field of view of 96.40 mm.

Number and location of the mirror aneurysms were verified during intervention. In 4 cases the mirror aneurysms were identified at the M1-M2 bifurcation of the MCA (MCA M1-M2), in 2 cases at the level of the PCoA and in 2 cases on the ICA at the level of the Ophthalmic Artery (ICA-OphA). In case 3 an additional cerebral aneurysm was detected on the ACoA, in case 6 on the right A1 segment of the Anterior Cerebral Artery (ACA) and in case 4 on the left ICA at the level of the OphA. In this last case an initiating mirror dilatation harbouring in the right side was interestingly noticed. Measurements of aneurysmal size and evaluation of its shape (saccular/fusiform, regular/irregular, blebs/dilatations) were reported during intervention to strategize the endovascular treatment or later to guide decisions on the treatment of the unruptured aneurysms. These measures included the aneurysmal sac height from the neck to the dome, sac width (frontal nominal diameter), sac depth (lateral nominal diameter) and the neck width. The aneurysmal volume was

Cases Sex Age Risk factors WFNS Fisher Aneurysms location Rupture side 1 F 46 n/a n/a n/a MCA M1-M2 Right 2 F 46 n/a n/a n/a PCoA Left 3 M 36 n/a n/a n/a MCA M1-M2 Left 4 F 43 S V 4 MCA M1-M2 Left 5 F 61 S II - ICA-OphA - 6 F 65 S II 3 MCA M1-M2 Left 7 F 32 St I 1 ICA-OphA Left 8 F 76 Hyp, D II 3 PCoA Right

calculated as the half product of the first three measures and the aspect ratio as the ratio between aneurysmal sac height and neck width.

2.2. Vascular modelling

The 3DRA image datasets were exported to a PC for vascular modelling. We followed a modelling methodology based on the one already illustrated in detail in [9] and that we here summarize. The images were cropped to capture only the vessels of interest. Anatomical models were extracted using a Geodesic Active Regions approach [16] or a region-growing algorithm where image quality allowed it. A surface representation was obtained applying a Marching Tetrahedra algorithm [9] to the segmentation results, which are typically represented by a volumetric distance transform whose zero-level set is the vascular boundary. The obtained surface triangulation was then smoothed and vessel branches were truncated. A correct depiction of all vascular features was constantly verified overlapping the anatomical models to 3D renderings of the medical images. Due to the presence of regions of low image quality, especially in case of aneurysm located in narrow bifurcations, topological and geometrical correction was applied to the surface triangulations using the freeware package Remesh [22], (Remesh v.1.2, IMATI-GE/CNR, Genova, Italy). In case 3, the patient had another aneurysm in the ACoA, thus the right and left anatomical models were fused using the surface merging approach illustrated in [17] in order to create a single model for the entire anterior portion of the circle of Willis. Smaller vessels were then extruded along the vessel axis as a strategy for a correct imposition of the flow boundary conditions. The 16 anatomical models are shown in Figure 1. All anatomical models were finally examined by experienced neuroradiologists.

Figure 1: Anatomical models of mirror cerebral aneurysms. The case numbering is reported at each pair of models; the letter “a” and “b” denote the ruptured and unruptured side respectively, case 5 excluded.

The anatomical models were then imported into a commercial package (GAMBIT v.2.2, Fluent Inc., Lebanon, NH, USA) for the generation of high quality volumetric finite element (FE) grids composed of tetrahedral elements. For cases 2 and 3 the advancing front technique illustrated in [18-20] was instead applied. The mesh resolution was set for all models to a minimum of 0.18mm resulting in volumetric FE grids containing between 1.5 and 2 millions elements. For case 3 a grid of more than 2 millions elements was generated, while for case 5a flow simulation in the giant aneurysm was not performed due to low image quality (the OphA was hardily detectable for the low amount of contrast flowing into it and the extension of the aneurysm resulted in a diffuse masking of several vessels in the native projections) and to a difference in growth mechanisms that are believed to affect giant aneurysms. Strikingly, this aneurysm did not rupture.

2.3. Blood flow simulation

Blood flow simulation was performed using a commercially available FE solver (FLUENT v.6.2, Fluent Inc., Lebanon, NH, USA) solving the Navier-Stokes equations in 3D. Blood was modeled as an incompressible Newtonian fluid with density ρ = 1.0x103 Kg/m3 and viscosity μ = 4.0x10-3 N/m2. Vessel walls were assumed rigid with no-slip condition. A steady flow rate with uniform velocity profile was imposed at the inflow of each anatomical model, typically at the level of the petrous or cavernous segments of the ICA’s. A nominal inflow condition of 4.81x10-3 L/s was derived from the

mean flow rate of a pulsatile flow waveform obtained via PC MRA measurements in a healthy subject. Using Poiseuille’s formula the inflow rate magnitude for each model was then scaled with the ICA radius to obtain a wall shear stress of approximately τ = 1.5 Pa [21]. The same flow condition was then deduced for each pair of mirror aneurysms as an average of the relative scaled flow rates. For cases 2 and 3 blood flow simulation was performed using a fully implicit finite element formulation reported in [9]. In these cases, the unsteady Navier-Stokes equations were solved by imposing the pulsatile flow condition previously mentioned and equivalently scaling the waveform amplitude with the ICA radius to obtain a mean wall shear stress of <τ> = 1.5 Pa, where <> represents the time average. Fully developed pulsatile profiles were prescribed using the Womersley solution.

Wall shear stress (WSS) distribution was visualized and streamlines colored according to flow velocity magnitude were additionally extracted. The same color scales were selected for each pair of mirror aneurysms for both WSS and streamlines visualizations. In cases 2 and 3 the time-average of the WSS distribution and the velocity field corresponding to the mean inflow rate were used.

3. RESULTS

3.1. Clinical results

Although the database is quite limited, a large prevalence of mirror aneurysm in female subjects was reported and ruptured aneurysms occurred mainly on the left side of the cerebral vasculature (5 cases out of 7). In case 5 the giant aneurysm was also located on the left side. In 6 cases both mirror aneurysms were classified as terminal. In case 7 both aneurysms were located distal to the OphA and were classified as lateral, while the aneurysm in case 5b was classified as terminal. Most of aneurysms were saccular with a regular shape, although blebs were present only in ruptured cases (cases 2a and 7a). Multilobular shape appeared in both the ruptured and the unruptured groups. For example, the mirror aneurysms in case 4 presented the same bi-lobular shape. Aneurysmal dimensions and aspect ratio of all anatomical models are reported in Table 2. We performed statistical t-test analysis with 95% confidence to report on the significance of differences in aspect ratio and volume between ruptured and unruptured aneurysms both as independent groups and pairing them by patient. Both anatomical models of case 5 were excluded in the analyses between pairs of mirror aneurysms and included in the unruptured group otherwise. The effect of case 5a on the unruptured group was also analyzed. No significant differences in aspect ratio were found both between pairs of mirror aneurysms (p=0.19) and between the ruptured and the unruptured groups (p=0.22 including case 5a, p=0.17 excluding it). Aneurysmal volume did not significantly differ between the ruptured and unruptured groups (p=0.55 including case 5a, p=0.11 excluding it), while the difference in aneurysmal volume between pairs of ruptured and unruptured mirror aneurysms was statistically significant (p<0.05), with larger volumes for the aneurysms on the side where rupture occurred.

Table 2: Aneurysmal dimensions and aspect ratio of all anatomical models.

More qualitative results were obtained from the observation of symmetry of vascular anatomy. All cases were distinctly asymmetric. For mirror aneurysms located at the M1-M2 bifurcation of the MCA (cases 1, 3, 4 and 6), a longer M1 segment corresponded to the ruptured side in 3 cases out of 4. For the remaining mirror aneurysms located on the ICA either at the PCoA or at the level of the OphA, the curvature of the segment of the ICA proximal to the OphA was noticeably different between pairs of mirror aneurysms. Including case 5, sharper turns corresponded to the larger aneurysms, while, excluding it, to the ruptured aneurysms.

3.2. Blood flow simulation results

Blood flow simulation was carried out in 15 anatomical models. Except case 5, all cases were composed of two aneurysms placed bilaterally at the same site in the circle of Willis, although only one had ruptured. Distribution of WSS and streamlines depicting the flow structure in the anatomical models were extracted. The differences between pairs of mirror aneurysms are reported in the following and extrapolated to differences between the ruptured and the unruptured groups when appropriate.

The distribution of WSS in the 15 models is shown in Figure 2. All anatomical models showed locally higher WSS in the region between the aneurysm and contiguous vessels. In all cases higher WSS occurred at the neck of the aneurysm, either in contiguity with the major branching vessel or, for terminal aneurysms, in a more extended area of the bifurcation. In 5 models out of 15 high WSS was also found in the parent vessel distally to the aneurysm due to vessel narrowing. The extension of the region of high WSS is however different between pairs of aneurysms. A more irregular aneurysmal WSS distribution was observed in 5 cases out of 7 in the ruptured side. Although locally low WSS was a common feature for all cases, peaks of WSS inside the aneurysm sac occurred in 6 cases out 7 in the ruptured side, while a more uniform distribution was found among the unruptured group.

Cases Neck width [mm]

Sac height [mm]

Sac width [mm]

Sac depth [mm]

Volume [mm3] Aspect Ratio

1a 3.21 7.06 4.60 4.61 74.86 2.20 1b 2.14 3.80 3.76 6.40 45.76 1.78 2a 4.68 6.20 15.30 8.61 408.56 1.32 2b 4.35 10.24 7.28 7.97 297.26 2.35 3a 4.39 7.85 5.81 6.92 157.86 1.79 3b 2.75 1.99 2.33 2.53 5.89 0.73 4 a 3.11 5.60 5.73 4.34 69.63 1.80 4 b 2.32 3.71 4.65 3.22 27.82 1.60 5 a 7.74 17.36 20.36 20.32 3592.05 2.24 5 b 4.54 4.46 4.73 4.40 46.36 0.98 6 a 3.81 5.44 6.24 7.89 133.83 1.43 6 b 1.76 1.79 1.31 1.35 1.58 1.01 7 a 3.78 9.26 8.47 8.58 336.62 2.45 7 b 2.03 2.39 1.53 2.28 4.15 1.17 8 a 3.50 4.29 3.63 3.06 23.90 1.23 8 b 4.28 2.58 2.71 2.45 8.57 0.60

Figure 2: Wall Shear Stress (WSS) distribution in the aneurysmal region. The contour colours are scaled with the WSS magnitude and the same scale is used for pairs of mirror cerebral aneurysms. The case numbering is reported at each pair of models; the letter “a” and “b” denote the ruptured and unruptured side respectively. In case 5 only one side was simulated.

The flow structure in the 15 anatomical models is depicted by streamline visualization in Figure 3. In all cases, flow entered more directly the ruptured aneurysm when compared to the corresponding unruptured mirror aneurysm. Although qualitatively, we also observed that the relative fraction of the flow from the parent vessel entering the aneurysm sac with the flow from the parent vessel directed to the side branches is greater in the ruptured group. The analysis of flow patterns was simplified when considering pairs of aneurysms occurring at the same location and the anatomical asymmetries between the two groups. For ruptured aneurysms occurring at the M1-M2 bifurcation of the MCA (cases 1, 3, 4, 6), a longer parent vessel and wider bifurcation angles were among the geometrical parameters leading to a larger fraction of flow entering the aneurysmal sac. The impingement jets were small when scaled to the aneurysm size and flow in the smaller side branches was fed directly from the aneurysm in all ruptured aneurysms and only in 1 unruptured aneurysm (case 1b). In the unruptured models instead, the jet appeared slower or more diffuse (case 1b) and a larger fraction of flow from the parent artery fed directly the side branches. For aneurysms occurring at the PCoA (cases 2 and 8), the bifurcation between PCoA and ICA was distinctly different between ruptured and unruptured aneurysms. In cases 2a and 8a the bifurcation was rather planar and the PCoA and the ICA stemmed nearly opposite forming a wide bifurcation angle. Lower bifurcation angles and non-planarity were instead observed in cases 2b and 8b. In ruptured aneurysms flow entered directly the aneurysmal sac in a larger proportion and an important fraction of the flow from the parent vessel entered first the aneurysm before feeding the ICA and the PCoA. In the unruptured aneurysm instead the ICA distal to the aneurysm was fed directly from the ICA proximal to the aneurysm.

The effect of anatomical differences on blood flow patterns is also conspicuous in case 7. In the ruptured side a sharper turn of the ICA proximally to the OphA resulted in a greater momentum-driven aneurysmal inflow and a greater impaction zone, while in the unruptured side the ICA presented a smoother curvature variation and aneurysmal inflow was lower.

Figure 3: Visualization of flow patterns using streamlines coloured by velocity magnitude. The same colour scale is used for pairs of mirror cerebral aneurysms. The case numbering is reported at each pair of models; the letter “a” and “b” denote the ruptured and unruptured side respectively. In case 5 only one side was simulated.

4. DISCUSSION

Although the size of the population is rather small, no significant difference in aneurysmal volume can be reported between ruptured and unruptured groups, although for all cases the ruptured aneurysm presented a larger volume when compared to the mirror unruptured pair. Aspect ratio did not help to differentiate both between pairs of mirror aneurysms and between the ruptured and unruptured groups. These findings suggest that aneurysmal size and aspect ratio may have a limited impact on decisions of aneurysmal treatment and that better descriptors of aneurysmal morphology should be pursued.

Interestingly, rupture occurred mainly on the left side. This appears common for patients treated at our clinical centres and it may be due to differences in vascular anatomy that start as far as the aortic arch. The left carotid artery stems directly from the aortic arch while the right carotid artery is a bifurcation of the brachiocephalic trunk, which stems

from the aortic arch. This may lead to different flow conditions and to an asymmetric development of the cerebral vasculature, which may be more pronounced in certain subjects or be determining of a different disease progression in subjects with congenital abnormalities. Bifurcation angles, length, size and curvature of the parent vessel proximal to the aneurysms did differ between the two sides and greatly affected differences in flow conditions. The patient database however is rather small and a larger population study might give more relevance to the role of these geometrical parameters.

Image-based CFD has shown to be a valuable tool providing more insight to clinical observations in a defined population such as mirror cerebral aneurysms. A marked difference in WSS distribution and flow patterns between mirror aneurysms is among the most interesting findings of this work. Some of the findings could also be extended to differences between the ruptured and the unruptured groups. The distribution of aneurysmal WSS was spatially more irregular in the ruptured side and local aneurysmal WSS maxima appeared mainly in the ruptured side. These findings well correlate with what reported on a population of 20 MCA aneurysms in [15]. The proximity of high and low WSS on a small region of the aneurysmal sac might enhance the degeneration of the aneurysmal wall leading to growth and, possibly, to rupture. Differences in flow patterns found common patterns within the ruptured and the unruptured groups especially when aneurysmal location was considered. The importance of the size of the impingement jet into the aneurysmal sac has already been analysed by Cebral et al. in [14] and smaller and faster impingement jets when compared to the aneurysmal dimensions were associated to aneurysms that ruptured. In addition we have observed that the relative fraction of the flow from the parent vessel entering the aneurysm sac with the flow from the parent vessel directed to the side branches is greater in the ruptured group. Similar findings have been reported by Castro et al. [23] who recently described four flow types in ACoA aneurysms and their association with rupture. The generalization of these concepts to a larger portion of terminal aneurysms is work in progress.

Our modelling method involves several approximations to reconstruct physiological blood flow. Blood flow is a non-Newtonian fluid that circulates in vessel with distensible walls and in a patient-specific pulsatile regime. The numerical approach and the mesh size may also lead to inconsistencies. However CFD simulations have shown to be first-degree dependent on the definition of the geometry [9,11,13]. Consequently our main efforts have been allocated in the reconstruction of accurate anatomical models and in the generation of high quality FE grids. In addition we are here considering macroscopic characteristic such as WSS distribution and flow patterns, which are likely not to be affected significantly by these approximations. Although two of the simulations were performed under pulsatile regime, blood flow simulation with pulsatile flow conditions for all cases is granted so as to provide additional insight also in differences in flow time changes in mirror cerebral aneurysms.

5. CONCLUSIONS

In this paper 8 cases of mirror cerebral aneurysms were analysed through the combination of clinical observations and computed information on blood flow. The patients’ population was composed of 7 women and 1 man, between 32 and 76 years of age. In 7 cases rupture occurred in one side, while in one case both aneurysms were unruptured. Although the size of the population was rather small, aneurysmal size and aspect ratio did not differ significantly between the ruptured and the unruptured groups. Asymmetry between the two sides of both the circle of Willis and intracranial segments of the ICA were notable. The length and the curvature of the vessel proximal to the aneurysm and the angle and the planarity of the bifurcation involving the aneurysm presented a correlation with the ruptured side and had an impact in the differentiation in blood flow patterns and derived quantities. Pairs of mirror aneurysms presented differences both in WSS distribution around the aneurysm, intra-aneurysmal flow patterns and in the parent vessel flow division between side branches and aneurysm sac. Observations could be also extended to speculate on differences between ruptured and unruptured groups. Irregular aneurysmal WSS distribution, small impingement jets when compared to the aneurysmal dimensions and a large fraction of flow from the parent vessel entering directly into the aneurysmal sac were observed in the ruptured aneurysms when compared to the mirror unruptured aneurysms.

Image-based CFD modelling has shown in this work its potentials in providing fresh insight as a clinical tool for the analysis of flow patterns in realistic anatomical models of cerebral aneurysms. Mirror cerebral aneurysms as a disease model has the potential to provide an effective test bed for the verification of clinical questions and for speculations on the association between computed information and aneurysmal rupture.

ACKNOLEDGMENTS The authors would like to thank Dr. Charles B. Majoie and Mr. Hugo Gratama van Andel from the Academic Medical Centre, Amsterdam, The Netherlands, for providing the imaging data of case 1 and for the enthusiastic contribution to this work. This work was partially generated within the framework of the Integrated Project @neurIST (IST-2005-027703), which is co-financed by the European Commission, and also partially supported by MEC TEC2006-03617, ISCIII FIS2004/40676, and CDTI CENIT-CDTEAM grants. The work of AFF is supported by the Spanish Ministry of Education & Science under a Ramón y Cajal Research Fellowship. The CILab is part of the ISCIII CIBER-BBN (CB06/01/0061).

REFERENCES 1. J. M. Wardlaw and P. M. White, “The detection and management of unruptured intracranial aneurysms”, Brain

123:205–221, 2000. 2. M. Kaminogo, M. Yonekura and S. Shibata, “Incidence and outcome of multiple intracranial aneurysms in a

defined population”, Stroke, 2003 Jan;34(1):16-21. 3. S. Juvela, “Risk factors for multiple intracranial aneurysms”, Stroke, 2000 Feb;31(2):392-7. 4. S. Vega-Basulto, S. Silva-Adán and R. Peñones-Montero, “Aneurismas intracraneales múltiples en Camagüey,

Cuba”, Revista de Neurologia, 2003, 37(2):112-117. 5. M. V. Casimiro, A. W. McEvoy, L. D. Watkins and N. D. Kitchen, “A comparison of risk factors in the etiology of

mirror and nonmirror multiple intracranial aneurysms”, Surg Neurol. 2004 Jun; 61(6):541-5. 6. C. Campos, A. Churojana, G. Rodesch, H. Alvarez and P. Lasjaunias, “Multiple intracranial arterial aneurysms: a

congenital metameric disease?”, Interv. Neuroradiol, 1998, 4:293-299. 7. C. E. Baccin, T. Krings, H. Alvarez, A. Ozanne and P Lasjaunias, “Multiple mirror-like intracranial aneurysms.

Report of a case and review of the literature”, Acta Neurochir (Wien), 2006 Oct;148(10):1091-5. 8. B. Weir, “Aneurysms affecting the nervous system”, Baltimore: Williams & Wilkins, 1987. 9. J. R. Cebral, M. A. Castro, S. Appanaboyina, C. Putman, R. D. Millan, and A .F. Frangi. “Efficient pipeline for

image-based patient-specific analysis of cerebral aneurysm haemodynamics: technique and sensitivity.” IEEE Trans on Medical Imag, 2005, 24(4):457-467.

10. L. Dempere-Marcos, E. Oubel, M. A. Castro, C. M. Putman, A. F. Frangi, J. R. Cebral, “CFD analysis incorporating the influence of wall motion: application to intracranial aneurysms", Medical Image Computing and Computer Assisted Interventions (MICCAI), Copenhagen, Denmark, October 1-6, 2006.

11. M. A. Castro, C. M. Putman, and J.R. Cebral, “Computational fluid dynamics modeling of intracranial aneurysms: effects of parent artery segmentation on intra-aneurysmal hemodynamcis”, AJNR American Journal of Neuroradiology, 2006, 27: 1703-1709.

12. D. A. Steinman, J. S. Milner, C. J. Norley, S. P. Lownie and D. W. Holdsworth, “Image-based computational simulation of flow dynamics in a giant intracranial aneurysm”, AJNR American Journal of Neuroradiology, 2003 Apr; 24(4): 559-566.

13. K. R. Moyle, L. Antiga and D. A. Steinman, “Inlet conditions for image-based CFD models of the carotid bifurcation: Is it reasonable to assume fully-developed flow?”, J Biomech Eng 2006 Jun;128(3):371-9.

14. J. R. Cebral, M. A. Castro, J. E. Burgess, R. Pergolizzi, M. J. Sheridan and C.M. Putman, “Characterization of cerebral aneurysm for assessing risk of rupture using patient-specific computational hemodynamics models”, AJNR American Journal of Neuroradiology, 2005, 26: 2550-2559.

15. M. Shojima, M. Oshima, K. Takagi, R. Torii, M. Hayakawa, K. Katada, A. Morita and T. Kirino, “Magnitude and Role of Wall Shear Stress on Cerebral Aneurysm: Computational Fluid Dynamic Study of 20 Middle Cerebral Artery Aneurysms”, Stroke, 2004;35:2500-2505.

16. M. Hernandez and A. F. Frangi, “Geodesic Active Regions Using Non-parametric Statistical Regional Description and Their Application to Aneurysm Segmentation from CTA”, MIAR 2004: 94-102.

17. J. R. Cebral, R. Löhner, P.L. Choyke and P.J. Yim, “Merging of intersecting triangulations for finite element modeling. Journal of Biomechanics”, 2001, 34: 815-819.

18. R. Löhner, “Automatic unstructured grid generators”, Finite Elements in Analysis and Design, 1997, 25: 111-134.

19. R. Löhner, “Extensions and improvements of the advancing front grid generation technique”, Computer Methods in Applied Mechanics and Engineering, 1996, 5: 119-132.

20. R. Löhner, “Regridding surface triangulations”, Journal of Computational Physics, 1996, 126: 1-10. 21. R. S. Reneman, T. Arts and A. P. G. Hoeks, “Wall Shear Stress - an important determination of endothelial cell

function and structure - in arterial system in vivo”, Journal of Vascular Research, 2006, 43: 251-269. 22. M. Attene and B. Falcidieno, "ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes". In

Proceedings of Shape Modeling International (SMI'06), IEEE Computer Society Press, pp. 271-276, 2006. 23. M.A. Castro, C. M. Putman and J. R. Cebral, “Patient-Specific Computational Fluid Dynamics Modeling of

Anterior Communicating Artery Aneurysms: A Study of the Sensitivity of Intra-Aneurysmal Flow Patterns to Flow Conditions in the Carotid Arteries”, AJNR American Journal of Neuroradiology , 2006 in press.