Analysis of Hemodynamics and Aneurysm Occlusion after Flow-Diverting Treatment in Rabbit Models

Animal Models and Imaging

Twenty-three elastase-induced aneurysms were created in New Zealand white rabbits, following the approach described in Altes et al.⁸ Four weeks after their creation, the aneurysms were treated with a FD device (Pipeline Embolization Device; Covidien, Irvine, California). Two days before treatment, the subjects were premedicated with aspirin (10 mg/kg by mouth) and clopidogrel (10 mg/kg by mouth) and were continued on these for 1 month after treatment. Immediately before treatment, 3D rotational angiography (3DRA) images were acquired, and velocities in the surrounding vessels were measured with Doppler sonography. Six animals were sacrificed before 1 week after treatment; all others, after 8 weeks. Immediately before sacrifice, 3DRA imaging was repeated. Some of the rabbits used in this study were part of another investigation in which we analyzed the mechanism of the endothelialization after flow diverter implantation. This article is entirely unrelated to the previous study.

Hemodynamics Modeling

Subject-specific computational fluid dynamics (CFD) models were constructed from pretreatment 3DRA images.⁹ Unstructured grids were generated with a resolution of 0.2 mm. Models of the FD devices used to treat the aneurysms were created and virtually deployed within the reconstructed vascular models.¹⁰ Blood flows were modeled by solving the unsteady 3D incompressible Navier-Stokes equations.¹¹ Physiologic flow conditions were derived from the Doppler sonography velocity measurements and imposed as boundary conditions in the computational models. Wall compliance was not included in the model. Blood attenuation was set to ρ = 1.0 g/cm³, and blood viscosity, to μ = 0.04 poise. The governing equations were numerically solved by using an efficient finite-element solver with a time-step of 0.01 seconds.¹² After deployment of the FD device, the mesh was adaptively refined to resolve the stent wires and a new CFD simulation was performed by using immersed grids.^13,14

Occlusion Modeling

Regions of the aneurysm that remained open or patent and regions that were occluded at the time of sacrifice were identified by constructing a second vascular model from the 3DRA image acquired before sacrifice. The pretreatment model and this premortem or follow-up model were manually aligned by using rigid registration. A new grid was generated filling the volume of the follow-up model. The aneurysm neck was interactively delineated on the pretreatment model by connecting selected points along the path of minimum geodesic distance.¹⁵ The aneurysm orifice defined by the delineated neck was triangulated, and grid points on each side of this surface were labeled as belonging to the aneurysm or the vessel.¹⁵ The bounding box of the aneurysm was found and voxelized with isotropic voxels of the same resolution as the 3DRA images. Mesh points in the aneurysm region were then labeled as “open” or “occluded,” depending on whether they were inside or outside the aligned follow-up model. The methodology is illustrated in Fig 1.

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Fig 1.

Imaging, modeling, and data analysis.

Global (per Aneurysm) Data Analysis

The degree of aneurysm occlusion at the time of sacrifice was quantified by the percentage of occluded voxels identified as described above. Aneurysms were then classified into 2 groups: 1) patent group: <80% of the voxels occluded at follow-up; 2) occluded group: >80% of the voxels occluded at follow-up. This 80% threshold was chosen because aneurysms with >80% occlusion of their volume looked almost completely closed on DSA images with perhaps a small “bump” in the parent artery—that is, they did not exhibit remnant necks of persistent filling of the sac.

Using the 3D meshes, we calculated geometric variables, including volume, maximum size, neck area, and maximum neck size for each aneurysm. Similarly, the following hemodynamic quantities were calculated over the aneurysm region and averaged over the cardiac cycle: mean aneurysm inflow rate <Q>, mean aneurysm velocity <v>, mean aneurysm wall shear stress <τ>, and mean aneurysm shear rate <γ̇>. These quantities were computed before and after treatment. Additionally, a new variable denoted “mean aneurysm transit time” (MATT) was defined as where V is the aneurysm volume, A is the neck area, and <v> is the mean aneurysm velocity. The rationale is that this variable, which has units of time, should do the following:

1. Increase with the aneurysm volume (ie, it takes longer to traverse a large aneurysm)

2. Decrease with the neck area (ie, a larger neck implies more chances of getting out of the aneurysm, while a smaller neck implies more chances of staying within the aneurysm and recirculating)

3. Decrease with the blood velocity (ie, slower velocities imply longer transit times).

The values of geometric and hemodynamic variables were then averaged over the patent and occluded groups. Cases belonging to the incompletely occluded group sacrificed before 1 week after treatment (between brackets in the Tables) were excluded from the statistical analysis. The Wilcoxon nonparametric test was used to test whether the means were statistically different between the occluded and patent groups.

Local (Voxel-by-Voxel) Data Analysis

Velocity (v), vorticity (ω), and shear rate (γ̇) were calculated on the CFD mesh and interpolated and averaged over each aneurysm voxel. The mean values of these quantities over open or occluded voxels of each aneurysm were calculated and compared.

Predictive statistical models of regional occlusion were then constructed. We defined 2 classes or outcomes: 1) occluded voxels (+1), and 2) open voxels (−1). Seven attributes or features were considered: 1) <v>_pre, 2) <ω>_pre, 3) <γ̇>_pre, 4) <v>_post, 5) <ω>_post, 6) <γ̇>_post, and 7) d = path distance to the neck. These values were calculated for each voxel from the pretreatment and posttreatment CFD simulations. A logistic regression model¹⁶ was trained by using a “leave-one-out” methodology. Specifically, it was trained with all open and occluded voxels from all aneurysms except 1. The aneurysm left out was then used to test the accuracy of the model. The probabilities of each voxel of this aneurysm belonging to each class were calculated, and the voxel was “predicted” to belong to the class of the highest probability. The accuracy of the prediction was calculated by counting the number of correctly and incorrectly classified voxels. The process was repeated by leaving each aneurysm out one at a time, and the total predictive accuracy of the model was computed.

Next, the voxels of each aneurysm were divided into 3 groups according to their distance to the aneurysm neck. Denoting by d the distance from a voxel to the neck and d_max the maximum distance from any voxel to the neck, we assigned voxels to the following 3 groups: a) dome if d/d_max > 2/3, b) body if 1/3 ≤ d/d_max ≤ 2/3, and c) neck if d/d_max < 1/3. The predictive statistical analysis described above by using the logistic regression model was repeated for voxels in each of these 3 regions. The corresponding predictive accuracies were calculated and compared.

Finally, we computed and compared the predictive power of the following statistical models typically used in machine-learning studies ¹⁷: 1) logistic regression, 2) neural network, and 3) support vector machine. Each of these models was trained with data from all aneurysms except 1 and was tested on the one left out. The process was repeated by leaving each aneurysm out in turn. The total predictive accuracy of each model was computed and compared.