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The effects of parent artery motion on the hemodynamics of basilar tip saccular aneurysms and its potential effect on aneurysm rupture were studied.
The aneurysm and parent artery motions in two patients were determined from cine loops of dynamic angiographies. The oscillatory motion amplitude was quantified by registering the frames. Patient-specific computational fluid dynamics (CFD) models of both aneurysms were constructed from 3D rotational angiography images. Two CFD calculations were performed for each patient, corresponding to static and moving models. The motion estimated from the dynamic images was used to move the surface grid points in the moving model. Visualizations from the simulations were compared for wall shear stress (WSS), velocity profiles, and streamlines.
In both patients a rigid oscillation of the aneurysm and basilar artery in the anterio-posterior direction was observed and measured. The distribution of WSS was nearly identical between the models of each patient, as well as major intra-aneurysmal flow structures, inflow jets, and regions of impingement.
The motion observed in pulsating intracranial vasculature does not have a major impact on intra-aneurysmal hemodynamic variables. Parent artery motion is unlikely to be a risk factor for increased risk of aneurysmal rupture.
The pathogenesis, progression and rupture of cerebral aneurysms are multi-factorial mechanisms that involve arterial hemodynamics, wall biomechanics, wall mechano-transduction or mechano-biology, and peri-aneurysmal environmental effects . Although the relative importance and interaction of these factors is not entirely understood, hemodynamics is thought to play a fundamental role in these processes. Early studies of the hemodynamics in cerebral aneurysms were carried out on idealized geometries using both experimental  and computational models . Subsequently, realistic experimental and computational models that replicate the patient-specific geometry have been created from medical images and analyzed using particle-image velocimetry and laser Doppler velocimetry , and computational fluid dynamics [5-7] techniques. These studies have identified variables of intraaneurysmal hemodynamics that have been associated with previous aneurismal rupture including concentration of the inflow jet and impaction zone, and elevations in the maximum WSS .
As with all computational studies a number of assumptions are made to facilitate the computations. These assumptions are approximations or simplifications of the in vitro conditions that have the potential to impair the accuracy of the computational representation leading some to question whether the CFD can be relied on in the evaluation of aneurysm hemodynamics. Many of these assumptions have been studied to determine the relative sensitivity of small changes in the physiologic range on the CFD results. Because the majority of the previous studies have been performed under the assumption of rigid vessel walls and only a few studies including the radial pulsation of the arterial walls [8,9], the effect of motion of the oscillation of the efferent and afferent arteries remains unknown.
The purpose of this work is to study the effect of arterial oscillation on the intraaneurysmal hemodynamics by applying observed arterial oscillatory motions to our simulations. Specifically, the effects on the previously identified features which have been associated with the history of previous rupture will be analyzed in two basilar tip aneurysms. In these aneurysms, the motion of the arterial walls has been studied using dynamic imaging techniques based on multi-slice computed tomography angiography (4D CTA) and high frame rate X-ray digital subtraction angiography (DSA) [9,10].
Two patients with intracranial aneurysms imaged with dynamic DSA and 3D rotational angiography (3DRA) were selected from our database. Patient 1 was a 48 years old female with a 12.9 mm ruptured basilar tip aneurysm, while patient 2 was a 69 years old female with a 10.3 mm unruptured basilar tip aneurysm. These aneurysms were selected because they had the largest motion of the parent artery observed in a previous study of approximately 30 intracranial aneurysms . Thus, the selected aneurysms represent the most extreme arterial wall motions observed in vivo using dynamic DSA. Both patients underwent conventional transfemoral catheterization and cerebral angiography using a Philips Integris Biplane angiography unit. Biplanar dynamic angiograms at 7.5Hz were acquired during a six-second contrast injection. In addition, an expert neuroradiologist (CP) measured the aneurysm maximum height and width on these projection views. This information was then used to establish the pixel size and to quantify the vascular wall excursion. The rotational angiography images were obtained during a 180 degree rotation and imaging at 15 frames per second for a total of 8 seconds. The corresponding 120 projection images were reconstructed into a 3D dataset of 256 × 256 × 256 voxels covering a field of view of 54.02 mm on a dedicated Phillips workstation. The imaging protocol was approved by the institutional review board and informed consent was obtained from all patients.
The motion of the aneurysms and parent arteries were determined from cine loops of dynamic biplane angiography images as an oscillatory rotation on the median plane (there is no perceptible movement on the coronal plane). The amplitude and center of the rotation were quantified using a manual rigid registration, as follows. All frames were examined to find the frames showing maximum displacement in the anterior/posterior directions. After these two frames were selected, both images were loaded in an image processing program as layers . On each image the contour of the aneurysm and the parent basilar artery were manually delineated using different colors. Then one image was made partially transparent and the two images were superposed. One of the images was rotated until the two delineations visually matched and the amplitude and the center of rotation were determined. The procedure was repeated to obtain a rough estimation of the error in the amplitude of the oscillatory motion. It was verified that the motion was well described by a rigid rotation in the anterior-posterior plane by visually checking that the arterial delineations in different angiography frames coincided after rotating one of the images. Figure 1 shows DSA images of both aneurysms in an anterior-posterior view (left column) and on the medial plane (right column). The vessel contours showing the maximum vessel wall displacements are shown on the medial planes. The green dots indicate the location of the center of rotation of each aneurysm.
Patient-specific computational fluid dynamics (CFD) models of the two aneurysms were constructed from the 3DRA images using a previously developed modeling pipeline . Segmentation was performed with a seeded region growing algorithm to reconstruct the topology of the vascular network followed by an iso-surface deformable model to adjust the geometry to the vessel boundaries. The vascular model was then smoothed with a non-shrinking algorithm and vessels were truncated perpendicularly to their axis. Volumetric grids composed of tetrahedral elements were generated using an advancing front method with a resolution of 0.015 cm, resulting in approximately 2.6 and 1.0 million elements for patients 1 and 2, respectively. Previous studies have shown that this resolution is sufficient for clinically meaningful solutions [13-15]. Blood flow was considered an incompressible Newtonian fluid (with density ρ=1.0 g/cm3 and viscosity μ=0.04 Poise) and modeled by the unsteady Navier-Stokes equations in 3D. The diameters of the parent arteries of patients 1 and 2 were approximately 3 mm and 3.5 mm, and the Reynolds numbers based on these diameters varied from approximately 100 to 400. The governing equations were numerically solved using an implicit arbitrary Lagrangian-Eulerian (ALE) finite element formulation on dynamic unstructured grids [16,17]. The time-integration scheme can be written as a steady-state problem in pseudo-time τ:
where v is the velocity, w is the mesh velocity, p the pressure, η the kinematic viscosity, vn denotes the velocity at the previous timestep and vθ=(1-θ) un + θ un+1. The parameter θ selects the numerical scheme: first order implicit Euler scheme (θ=1), first order explicit Euler scheme (θ=0) and second order Crank-Nicholson scheme (θ=1/2). These equations solved using a pressure-projection method and the spatial discretization is carried out using an edge-based upwind finite element method . The discretized momentum equation is solved using a Generalized Minimal Residuals (GMRES) method and the discretized pressure Poisson equation is solved using a deflated preconditioned conjugate gradients method .
Since patient-specific flow conditions were not available, pulsatile physiologic flow rates derived from phase-contrast magnetic resonance measurements on normal subjects were prescribed at the inlet boundary using the fully developed Womersley profile [20,21]. This is a reasonable approximation since the parent arteries did not have significant stenoses or evidence of other vascular diseases. The flow division from the parent artery to the outflow vessels was determined from their area ratio and corresponding pressure boundary conditions were applied at the model outlets.
Two CFD calculations were performed for each of the two patients, corresponding to static and rigid oscillating models, respectively. The moving and static models of each aneurysm used the same computational grid, except that the grid point coordinates varied during the cardiac cycle in the moving models. The vascular wall motion observed in the dynamic DSA images was used to move the surface grid points. This was done by applying a time-dependent rigid rotation derived from the DSA images to the surface points. The interior mesh points were then updated using a non-linear velocity smoothing algorithm . The basic idea of this algorithm is to solve an equation of the form:
where k(d) is a function of the distance to the wall (d), and w is the mesh velocity. Since the velocity on the surface is known, Dirichlet boundary conditions are used to compute the mesh velocity at the interior mesh points:
with w0 the surface mesh velocity. Subsequently the mesh point coordinates are updated from:
Since the dynamic DSA images were acquired with no cardiac gating or cardiac monitoring, there was no information available to synchronize the flow and wall motion waveforms. Therefore, it was first assumed that these waveforms were in phase, i.e. that the maximum wall displacement occurs at peak systole. Secondly, it was assumed that the maximum wall displacement occurs in the diastolic phase, which corresponds to a phase shift of about 20% between the corresponding waveforms. CFD simulations with moving walls under these two conditions were carried out.
A total of three cardiac cycles were computed using 100 timesteps per cycle, and it was verified that the results of the second and third cycles coincided. Results are therefore presented for the second cycle.
The motion of the basilar artery and the aneurysm observed in the DSA images of both patients could be well represented by an oscillatory rigid rotation around a center of rotation located close to the basilar tip in the medial plane near the anterior wall of the aneurysm and midway between the neck and the fundus of the aneurysm. No motion was observed in the perpendicular (anterior-posterior) view. The amplitude and time dependence were similar on both patients. The amplitude of the rotational motions were 1.16 ± 0.16 deg and 1.11 ± 0.12 deg for patients 1 and 2, respectively.
Visualizations of the velocity fields, flow patterns and wall shear stress distributions at peak systole for the static and oscillating models are presented in Figures 2 and and33 for patients 1 and 2, respectively. These figures show velocity contours on the medial plane (top left) and on a plane through the aneurysm neck (top right), streamlines (bottom left), and wall shear stress (WSS) contours on the aneurysm surface (bottom right). The blue lines correspond to the static models while the red lines correspond to the oscillating models. These visualizations show that although the motion of the basilar arteries were among the largest observed in a series of intracranial aneurysms imaged with dynamic DSA, little differences in the velocity fields and WSS distributions can be observed between the static and moving models. Therefore, the hemodynamics of the static and moving models is qualitatively in very good agreement for both patients. Adding a 20% phase shift between the flow and wall motion waveforms did not substantially modify these results.
Graphs of the WSS magnitudes obtained with both models for each patient are presented in Figure 4 (top row). In these plots, the x-axis corresponds to the WSS computed by the static model and the y-axis the WSS computed with the moving model, at the same grid points. It can be clearly seen that both models are in close agreement, for both patients. The relative difference in the local values of the WSS magnitude between the static and moving models is below 5%. Linear regressions of the WSS values obtained with the static and moving models of each aneurysm indicate no relative over or under estimation of the WSS magnitude between these models (slopes values were 0.9912 and 0.9990 for patients 1 and 2, with R2=0.999918 and 0.999947, respectively). The corresponding visualizations of the distributions of WSS magnitudes at peak systole for both patients are also presented in Figure 4 (bottom row).
Computational approaches to the study of cerebral aneurysms and the interaction with the intra-aneurysmal hemodynamics have yielded several interesting associations that influence our thinking about the mechanisms responsible for aneurysm formation, growth, and ultimate rupture. Cebral et al showed using patient-specific models that aneurysms with a previous history of rupture were associated with focus inflow jets, small impaction zones, and complex intra-aneurysmal flow patterns . Other studies have pointed to either elevation or depression of WSS measures in ruptured aneurysms [7,22].
All previous works using computational techniques have in common the use of assumptions which are approximations of the in vitro conditions. Typically, CFD simulations use a simplification of the conditions because of either a lack of specific information regarding the condition or as a means of simplifying or facilitating the computations. Implicitly the investigator is making a judgment that the assumptions are close enough to the in vitro condition that they will not significantly affect the computation result.
In the study of aneurismal pathophysiology in relation to intra-aneurysmal hemodynamics the investigator has a difficult problem. In order to determine whether an assumption is appropriate the investigator must know what outcome parameters are important. Because methods of measurement of intra-aneurysmal flow conditions are just now being developed, the investigator has had to rely largely on computational methods. Now that the important parameters which affect aneurismal pathophysiology are becoming known it is critical that the assumptions be carefully tested so that any distortions of the CFD results can be minimized and understood.
Previous works have studied different aspects of basilar aneurysms using computational fluid dynamics, such as how flow patterns are influenced by the parent-artery angle [23,24] and surgical intervention , and comparison of CFD results to in vivo MRI measurements . Furthermore, the motion of arterial and aneurysms walls have been observed, described and simulated [9-11,27], but to the best knowledge of the authors this the first work to simulate the observed motion of the parent artery.
We have observed using dynamic high frame rate angiography that the basilar artery has a small motion that could be well represented by an oscillatory rigid rotation around a center of rotation located close to the basilar tip in the medial plane near the anterior wall of the aneurysm and midway between the neck and the fundus of the aneurysm. A priori one could think that the observed arterial motion could concentrate, spread or deviate the aneurysm inflow jets, or substantially change the flow impaction zones or regions of low or elevated wall shear stress, and therefore could be a major factor in the rupture risk assessment of aneurysms at this location. However, this study suggests that the motion of the parent artery has little effect on the aneurysm hemodynamics. The effect is likely minimized by the only small displacement of the artery as well as the rigidity of the rotation. This apparently rigid displacement maintains the relative angles of the arteries and the aneurysm and consequently minimizes the effect. Finally, the velocity of the arterial wall in the displacement is very small when compared to the velocity of the blood flow. So, distortion of the developed flow stream is minimal.
This study does not address other potential effects of parent artery motions. Parent artery motion could still have an important effect on the arterial wall stresses and/or accentuate the interactions between the aneurysm and surrounding environment. These questions will require more detailed study.
The current study has other limitations that should be considered when assessing the results of this work. The accuracy of the wall motion estimation from dynamic DSA images is limited by the image spatial and temporal resolution. The aneurysms selected for this study were among the ones with the largest parent artery motions observed. In these cases, the wall displacement is substantially larger than the image resolution. The motion of the parent artery was approximated as a rigid rotation of the medial plane around a point near the basilar tip. No pulsatile motion of the vessel wall was included. The motion of the vessel wall observed in the dynamic DSA images could be well represented by this rigid rotation with no pulsation. Previous studies of the influence of pulsatile motion of the vessel wall on aneurysmal hemodynamics suggested that rigid models could slightly over estimate the WSS with respect to pulsating models . No patient-specific flow conditions were available. Nevertheless, the static and moving wall models were in very close agreement during the entire cardiac cycle. In the moving wall models, the vessel wall displacement was synchronized with the peak of the pulsatile flow waveform used as the inflow condition. Adding a phase difference of about 20% between the flow and displacement waveforms did not substantially alter the results. Only two aneurysms were included in this study. Although the motions of the basilar arteries of these patients were quite large, the conclusion of no change in the hemodynamics cannot be generalized to the entire population. This result should have to be tested with a larger sample. Despite these limitations, these models can help us better understand the influence and importance of the motion of the parent artery on the intraaneurysmal hemodynamics.
Although the basilar artery can exhibit a significant oscillatory motion, it has little effect on the hemodynamics of basilar tip aneurysms. Thus, CFD models with a static proximal artery provide a good approximation of the in vivo hemodynamic conditions in aneurysms at this location. Studies of aneurysm pathophysiology using image-based computational fluid dynamics methods to represent the intra-aneurysmal flow characteristics and wall shear stress distributions can be carried out without incorporating the parent artery oscillatory motion.
We thank the American Heart Association (Grant # 0655413U) and Philips Medical Systems for financial support.