Subject-Specific Modeling of Intracranial Aneurysms

Juan R. Cebral*a, Monica Henandezb, Alejandro Frangib, Christopher Putmanc, Richard Pergolesic, James Burgessc

aSchool of Computational Sciences, George Mason University, Fairfax, VA 22030 bAragon Institute of Engineering Research, University of Zaragoza, 50015 Zaragoza, Spain

cInova Fairfax Hospital, Falls Church, VA 22042

ABSTRACT Characterization of the blood flow patterns in cerebral aneurysms is important to explore possible correlations between the hemodynamics conditions and the morphology, location, type and risk of rupture of intracranial aneurysms. For this purpose, realistic patient-specific models are constructed from computed tomography angiography and 3D rotational angiography image data. Visualizations of the distribution of hemodynamics forces on the aneurysm walls as well as the intra-aneurysmal flow patterns are presented for a number of cerebral aneurysms of different sizes, types and locations. The numerical models indicate that there are different classes of intra-aneurysmal flow patterns, that may carry different risks of rupture. Keywords: cerebral aneurysm, hemodynamics, computational fluid dynamics, CT angiography, 3D rotational

angiography

1. INTRODUCTION Intracranial aneurysms are pathological dilatations of cerebral arteries. They tend to occur at or near arterial bifurcations, mostly in the circle of Willis [1]. They can be roughly classified into terminal, lateral or bifurcation aneurysms depending on their relation to the parent vessel. The most serious complication happens when the aneurysm breaks, since this has fatal consequences in 2.6 - 9.8% of the patients and serious consequences in 10.9% of the patients due to intra cranial bruise, subsequent recurrent bleeding, hydrocephaly and spasms in brain vessels [2,3,4]. The reasons for genesis, growth and rupture of saccular aneurysms are not clear. However, hemodynamic factors, such as wall shear stress, pressure, residence time and flow impingent, are thought to play a role in the pathogenesis of aneurysms and thrombosis [5]. Since measuring hemodynamic quantities in vivo is difficult, various modeling approaches have been considered in the past [6]. In vitro studies allow very detailed measurement of hemodynamic variables, but cannot be used in a straight manner for clinical evaluation of individual cases. In vivo image-based computational models have only since recently been attempted with promising results [7, 8]. In this paper, a methodology for realistic patient-specific modeling of the hemodynamics in cerebral aneurysms is described. Using this methodology, the flow dynamics in several models constructed from computed tomography angiography and 3D rotational angiography images are analyzed.

2. METHODS Subject-specific models of cerebral aneurysms are constructed from 3D anatomical image data obtained with computed tomography angiography (CTA) and 3D rotational angiography (3DRA). Each of these imaging modalities has some advantages and disadvantages. For instance CTA images contain bright bone structures that in some cases are difficult to separate from the vasculature. In 3DRA images this problem is greatly reduced by the use of intra-arterial contrast. However, aneurysms located in the anterior communicating artery require special attention

since a single injection of contrast, e.g. in one of the internal carotid arteries, will fail to properly image all the connected vessels (the contralateral side). Due to the different structure and resolution of the CTA and 3DRA images, different model construction techniques are used for each of these imaging modalities. A level set approach is used on CTA images, while a deformable model is used on 3DRA images. These methodologies are described in more detail in what follows. In addition to proper anatomical representation of the aneurysms, computational fluid dynamics modeling requires proper representation of the connected vessels. Reconstruction techniques that work for aneurysms may not work for vessels and vice versa. In these cases, a component-based modeling approach is used, in which the aneurysm and the connected vessels are reconstructed independently using different techniques. Vessels are reconstructed using tubular deformable models [9]. Then, the final model is obtained by merging of the reconstructed components using an adaptive volumetric technique [10]. 2.1 Aneurysm reconstruction from CT angiography CTA images of intracranial aneurysms were obtained using a Helical Elscint CT Twin scanner (Marconi, Haifa, Israel) with intravenous injection of a non-ionic contrast agent. The reconstructed images contained 512x512 pixels with a square FOV of 20.8 cm and a resolution of 0.4 mm between planes. Aneurysms are segmented using a two-stage segmentation algorithm. In the first stage, a fast and rough segmentation is obtained by means of a fast marching method [11]. The speed used for the evolution of the surface is based on a vessel enhancement filter [12]. In the second stage, this pre-segmentation is used as initialization for a geodesic active region model [13] as follows. The pre-segmentation defines a partition of the image domain into regions corresponding to vessel and background. The histogram of the gray values for each of these regions is modeled by a Gaussian distribution. A propagation speed based on these descriptors is used in the equation of the surface evolution. The level set algorithm is used to track the motion of the embedding function. The final segmentation is the zero level set of the embedding function. The geometrical model is obtained by extraction of the zero-level iso-surface of the distance map associated with the level set method. More details of this approach can be found in [8]. 2.2 Aneurysm reconstruction from 3D rotational angiography The 3D rotational angiography data consists in a series of 120 images that are obtained over 180o during intra-arterial injection of radio-opaque material. These images are sent to a workstation (Philips Integris3DRA) where a 3D volume is reconstructed with isotropic voxels. Typically these volumes consist in 128x128x128 voxels of 0.422 mm. The reconstruction of cerebral aneurysms from 3DRA images is based on a deformable model technique [14]. In order to obtain a proper initial surface for the deformable model, the image is processed as follows. The image is smoothed by convolution with a Gaussian kernel of 3x3x3 pixels. The voxel intensities are then sharpened. Note that the Gaussian blurring operation tends to expand the anatomical structures, while the sharpening operator tends to shrink them. The application of blurring followed by sharpening operations tends to smooth the images without shrinking or expansion of the anatomical structures. In fact, this combination acts as a low pass filter. This algorithm was inspired by a non-shrinking surface smoothing technique based on the application of a shrinking followed by an expanding operator [15]. The initial reconstruction is then obtained by a region growing segmentation followed by iso-surface extraction [16]. The selection of the intensity values for these algorithms is done on a trial and error basis. This surface is then allowed to deform under the action of internal smoothing forces between the connected nodes and external forces computed from the energy gradient of the original (unprocessed) image. This operation tends to place the surface nodes on the edges of the vascular structures, thus achieving sub-voxel accuracy. 2.3 Grid generation Unstructured grid generation requires a water tight definition of the computational domain. Therefore, the reconstructed surface model needs further processing before volumetric grid generation. As mentioned earlier, if the aneurysm and the connected vessels were reconstructed independently, a single surface is created by merging the

individual components [10]. In some cases there may be vessels running very close to the aneurysm sac which the reconstruction algorithms fail to separate. In such cases, the vessel and the aneurysm are separated by manual edition of the surface. This requires interactive deletion of elements, closing of holes and creation of new elements and points. The geometrical model is then smoothed using a non-shrinking algorithm [15] in order to eliminate high frequency noise in the triangulation. The element quality is then optimized by edge collapsing and diagonal swapping [16]. Finally, the vessels are cut at the proximal and distal ends perpendicularly to their axis and the boundaries are extruded in order to minimize the effects of the boundary conditions on the region of the aneurysm. Finite element grids are generated in two steps using the reconstructed model as a support surface to define the geometry of the domain to be meshed. First, the surface is re-triangulated using an advancing front technique that places newly created points on the original surface using linear or quadratic interpolation [17]. Then, the volume enclosed by this surface is filled with tetrahedral elements using an advancing front method [18]. The resolution of the finite element grid can is prescribed by the user. If required, adaptive background grids and sources are used to increase the mesh resolution in regions of high surface curvature or in small vessels [19]. The mesh resolution used in the models presented in this paper ranges from 0.1 mm to 0.2 mm, and the finite element grids contained between 1 and 2.5 million elements. Note that this approach does not require any analytical representation of the computational domain and at the same time geometric features present in the original triangulation are automatically detected and preserved in the final grid. 2.4 Blood flow analysis Blood flow is modeled by the incompressible Navier-Stokes equations for a Newtonian fluid [20]:

0=⋅∇ v (1)

vvvv 2∇µ+−∇=∇⋅+

∂

∂ρ

pt

, (2)

where v is the velocity, p the pressure µ the viscocity and ρ the density. For blood ρ=1.0 g/cm3 and µ=0.04 Poise. Non-Newtonian effects in large arteries are usually regarded as second order and neglected. However, in regions of low flow this approximation is not entirely justified and further investigation is required. For simplicity vessel wall compliance was also neglected. Fluid-structure interaction calculations accounting for wall compliance would require data on the material properties of the vessel wall, such as elasticity and wall thickness, which is difficult to obtain in vivo. No slip boundary conditions were prescribed at the vessel walls. Since no flow measurements were performed on these patients, realistic pulsatile flow conditions are imposed from flow measurements acquired in the same arteries of different subjects using phase-contrast magnetic resonance techniques [19]. Fully developed pulsatile velocity profiles were prescribed at the entrance of the feeding vessel using a Fourier decomposition into Womersley modes [21]. Traction free boundary conditions were imposed on all other connected vessels. The governing equations are solved numerically using an implicit finite element formulation [22]. Since this scheme allows for arbitrary timestep sizes, 100 steps were performed in each cardiac cycle. The heart rate was 70 bpm. A generalized minimum residual (GMRES) solver is used for the discretized momentum equation while a diagonal preconditioned conjugate gradient solver for the pressure equation. An in-house developed flow solver (FEFLO) has been used, which has been extensively validated [23]. The numerical results are post-processed in order to compute hemodynamic quantities such as the time average of the wall shear stress magnitude and the oscillatory shear index [20].

3. RESULTS 3.1 Models from CT angiography Five models of cerebral aneurysms constructed from CTA images are presented in this section. The CTA images were cropped in the region of the aneurysm prior to segmentation. Figure 1 shows volume renderings of the cropped CTA images (top row) and the corresponding reconstructed anatomical models (bottom row). This figure shows,

from left to right, an anterior communicating artery aneurysm, a bifurcation aneurysm, two lateral aneurysms, and a complex aneurysm with multiple sacs. We denote the models shown in figure 1, from left to right, ct1 to ct5. Pulsatile flow calculations were carried out for all these models, and the mean (time average over a cardiac cycle) of the wall shear stress (WSS) and oscillatory shear index (OSI) were computed. The finite element grids contained between 0.9 to 1.6 million elements, and the numerical solutions were obtained over night on a Linux cluster with 12 nodes of dual 2.8 GHz Xeon processors and 2.0 GB of RAM at the University of Zaragoza, Spain. Visualizations of the WSS and OSI are presented in figure 2. The top row shows the mean wall shear stress magnitude while the bottom row shows the oscillatory shear index. These visualizations indicate that, for these particular patients, the WSS in the aneurysm sac is low compared to the WSS in the connected vessels. However, there is an increase in WSS at the aneurysm neck. High OSI indicate regions of significant change in the direction of the wall shear stress vector during the cardiac cycle. The visualizations presented in figure 2 (bottom row) show increased OSI in different regions of the dome of the aneurysm and its neck. This indicates intra-aneurysmal flow patterns of different characteristics, i.e. different vortex structures. Complex distributions of high OSI in the aneurysm sac are indicative of disturbed flow patterns (ct1, ct3 and ct4), while more stable flow patterns have an associated distribution of OSI which is simpler and tends to localize high OSI in the region of the neck (ct4). 3.2 Models from 3D rotational angiography In this section, twelve cerebral aneurysm models constructed from 3DRA image data are presented. Figure 3 shows volume rendering of the 3DRA images. We denote these cases, from left to right and top to bottom, as ra1 to ra12. These aneurysms can be roughly classified as follows: ra1-3 are terminal aneurysms in the middle cerebral artery, ra4-6 are lateral aneurysms in the cavernous internal carotid artery, ra7-9 are bifurcation aneurysms in the basilar artery, and ra10-12 are big or giant aneurysms. The reconstructed models corresponding to the aneurysms of figure 3 are shown in figure 4. Note that case ra7 contains a clip previously implanted surgically to treat a previous basilar aneurysm. The clip, that appears brighter than the intra-arterial contrast under X-rays, was manually segmented out from the 3DRA images before aneurysm reconstruction. Finite element grids for each of these models were generated. These grids contained between 1.4 and 2.5 million elements. Computational fluid dynamics simulations were performed for each of these models over night on Linux boxes with 3.2 GHz Pentium4 processors and 2.0 GB of RAM at George Mason University, Virginia. Visualizations of the mean WSS magnitude are presented in figure 5. These visualizations show that for some aneurysms the mean WSS may be comparable or even larger in some regions of the aneurysm dome compared to the connected vessels, e.g. ra1, ra2, ra5, ra6, ra7, ra10 and ra12. On the other hand, other aneurysms exhibit WSS magnitudes lower in the sac than in the connected vessels, e.g. ra3, ra4, ra8, ra9 and ra11. Since the wall thickness is greatly reduced in the aneurysm dome, values of the WSS magnitude in the sac that are comparable or larger than those encountered in the connected vessels may indicate aneurysms at higher risk of rupture. Distributions of OSI are presented in figure 6. Again, these visualizations show different distributions of OSI for different aneurysms, even between aneurysms of the same type. This is consistent with the fact that the flow dynamics strongly depends on the geometry of the aneurysm. As previously mentioned, the distribution of OSI may be indicative of disturbed vs. simpler flow patterns within the aneurysms. The pressure distribution at peak systole in the aneurysm dome and the connected vessels are shown in figure 7. In most of the cases, the pressure in the dome is similar to that in the connected vessels. However, in some cases in which the flow impinges into the aneurysm sac, a region of increased pressure can be observed (e.g. ra1, ra6, ra7 ar10 and ra12). Finally, visualizations of the intra-aneurysmal flow patterns are presented in figure 8. The instantaneous velocity magnitude at peak systole is shown on a planar cut through the aneurysm sac, for a selected subset of CTA and 3DRA models. The pictures of figure 8 correspond, from left to right and top to bottom, to ct4, ra4, ra8, ra7 ra11,

ct2, ra1, ra9, ra10 and ra12. These visualizations display different types of flow patterns, ranging from flows containing only a single vortex that changes magnitude but remains roughly in the same position during the cardiac cycle (e.g. ct4, ct2, ra4, ra1), to disturbed non-stationary flow structures (e.g. ra10, ra11, ra12). An exact objective characterization and classification of the flow patterns is still under investigation.

4. DISCUSSION AND CONCLUSIONS Several patient-specific, image-based numerical models of the hemodynamics in cerebral aneurysms have been presented. Different image segmentation methods have been applied to reconstruct anatomical models from CTA and 3DRA image data. A component-based modeling approach allows for independent reconstruction of the aneurysm and the connected vessels, using the best suited technique for each anatomical structure. The finite element method used to solve the fluid equations has been previously validated and is general enough to deal with the complex geometries typical of intracranial aneurysms. The methodology described in this paper has several limitations. Reconstruction from CTA images is problematic when the aneurysm is close to bone structures. The segmentation algorithms need improvement to deal with these cases. The image data obtained with 3D rotational angiography of aneurysms with more than one feeding vessel, such as those in the anterior communicating artery, may be incomplete since the contrast agent is injected into only one of the feeding arteries. Thus, the connected vasculature may not be imaged completely. This problem may be overcome by taking more images with injections in each the feeding vessels and using a component-based approach for the construction of the model. However this type of imaging is not typically done in routine clinical practice. CTA images do not suffer from this limitation and may be used to complement the 3DRA images. Another complication that affects both CTA and 3DRA images is the proximity of vessels to the aneurysm sac. In these cases, the image resolution may not be sufficient and the reconstruction algorithms may yield models with vessels intercepting the aneurysm. As mentioned earlier, such models are manually edited to remove the intersections. The reconstruction algorithms need improvement to properly handle these situations. Specification of the correct physiologic flow conditions for each individual patient is important. Flow conditions may be obtained non-invasively using phase-contrast magnetic resonance techniques and in some cases transcranial Doppler. Although for the present study this information was not available, pulsatile flow conditions measured in the same arteries of a different (normal) subject were used. Ideally, the flow rates in all the connected vessels should be measured. However, it remains to be studied how sensitive the flow patterns are to changes in the flow boundary conditions. Another important assumption of these models is that of rigid vessel walls. Incorporating wall compliance into the models using fluid-structure interaction algorithms require extra information about the elasticity and thickness of the vessel wall as well as the intra-arterial pressure waveform that drives the deformation process. Obtaining this information in vivo is problematic, and in general other approximations will be required. Non-Newtonian rheological behavior of blood inside the aneurysms, where the flow is low, may be important. Future studies will investigate the importance of wall compliance, non-Newtonian effects, and the pulsatile flow conditions. Despite these limitations, the methodology has been successfully applied to study the blood flow dynamics in several cerebral aneurysms from CTA and 3DRA images. These models provide information otherwise inexistent on the hemodynamics conditions that are involved in the development, growth and rupture of aneurysms. The numerical results indicate that there are different classes of intra-aneurysmal flow patterns. Although, an exact and objective characterization of the flow patterns has not been attempted in the present study, the different classes of flows observed may carry different risks of rupture. It has been suggested that unstable or disturbed flow patterns induce oscillations in the aneurysm wall that may eventually lead to its rupture. The significance of this work is that these models can be used to study possible correlations between the intra-aneurysmal flow patterns and the morphology of the aneurysm and eventually with the risk of rupture. Future work will focus on validation of the numerical models using in vitro and in vivo data, extending our database of aneurysm models, characterization of the flow patterns and exploring correlations to the morphology, location, type and rupture of aneurysms.

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Figure 1: Aneurysm models from CTA images. Top row: volume renderings of cropped CTA images. Bottom row: corresponding reconstructed models. Figure 2: Distribution of mean wall shear stress magnitude (top row) and oscillatory shear index (bottom row) in the aneurysms of figure 1. Figure 3: Volume renderings of the 3D rotational angiography images of 12 intracranial aneurysms.

Figure 4: Aneurysm models reconstructed from the 3D rotational angiography images of figure 3. Figure 5: Visualizations of the distribution of mean wall shear stress magnitude in the aneurysm models reconstructed from 3D rotational angiography images. Figure 6: Visualizations of the distribution of oscillatory shear index in the aneurysm models reconstructed from 3D rotational angiography images.

Figure 7: Visualizations of the peak pressure distribution in the aneurysm models reconstructed from 3D rotational angiography images. Figure 8: Visualizations of intra-aneurysmal flow patterns in selected CTA and 3DRA models. Instantaneous velocity magnitude at peak systole are visualized on planar cuts through the aneurysm sacs.