Vortex Analysis of Intra-Aneurismal Flow in Cerebral Aneurysms

Abstract

This study aims to develop an alternative vortex analysis method by measuring structure ofIntracranial aneurysm (IA) flow vortexes across the cardiac cycle, to quantify temporal stability of aneurismal flow. Hemodynamics were modeled in "patient-specific" geometries, using computational fluid dynamics (CFD) simulations. Modified versions of known λ₂ and Q-criterion methods identified vortex regions; then regions were segmented out using the classical marching cube algorithm. Temporal stability was measured by the degree of vortex overlap (DVO) at each step of a cardiac cycle against a cycle-averaged vortex and by the change in number of cores over the cycle. No statistical differences exist in DVO or number of vortex cores between 5 terminal IAs and 5 sidewall IAs. No strong correlation exists between vortex core characteristics and geometric or hemodynamic characteristics of IAs. Statistical independence suggests this proposed method may provide novel IA information. However, threshold values used to determine the vortex core regions and resolution of velocity data influenced analysis outcomes and have to be addressed in future studies. In conclusions, preliminary results show that the proposed methodology may help give novel insight toward aneurismal flow characteristic and help in future risk assessment given more developments.

Figure 1

Main steps in the generation and analysis of vortex core structures: (a) arterial geometry generated and segmented from a DSA scan; (b) volumetric mesh generation and CDF simulation on the segmented structure; (c) manual extraction of an aneurysm surface from the artery (gray denotes the area of an aneurysm and red denotes the parent artery); (d) extracted aneurysm surface masked over the simulated data to isolate aneurysm flow velocity and resampled at various voxel sizes (0.1–0.8 mm); (e) the λ ₂ and Q-criterion methods identify vortexes for 21 equally spaced data points over the cardiac cycle; (f) analysis of vortex: characteristics and DOV (stability) between each cardiac step's vortex core and the cycle-averaged vortex core. In (e), identified vortex core regions are segmented out using the classic marching cube algorithm. In (e), while the white color denotes streamlines of the aneurysmal flow, the black color is used to indicate vortex structures using the two above-mentioned methods—λ ₂ and Q-criterion methods.

Figure 2

Five sidewall aneurysms (SAs) and five terminal aneurysms (TAs) used in this study. All geometries were reconstructed from high-resolution 3D-Digital Subtraction Angiography (DSA). Arrows point to IAs.

Figure 3

Example of variations to vortex core structure across 5 data points along the cardiac cycle: marked waveforms represent a point in the cardiac cycle for each data point. The black structure is the extracted vortex core(s) while gray is an aneurysm. The top row is for SA2 which had a lower DVO (less stable) than the bottom row from TA2 which had a higher DVO (more stable). All cores were extracted using the [normalized] $\stackrel{̿}{Q}$-criterion method. The mean [normalized] $\stackrel{̿}{Q}$ threshold values were used to extract the vortex core and only vortex cores with a volume ≥ 0.5 mm³ were saved.

Figure 4

Plots representing variations of identified vortex volumes due to the selection of 5 different threshold values in (a) TA1 and (b) SA1. Threshold values were tested for four vortex extraction methods: standard Q-criterion, standard λ ₂ method, [normalized] $\stackrel{̿}{Q}$-criterion, and [normalized] $\stackrel{̿}{{\lambda }_2}$ method. Geometries of SA2 and TA1 are displayed in Figure 2. Selected threshold values were mean/4, mean/2, mean, mean ± (STD/2), and mean ± STD (positive sign for Q-criterion and [normalized] $\stackrel{̿}{Q}$-criterion methods and negative sign for λ ₂ and [normalized] $\stackrel{̿}{{\lambda }_2}$ methods).

Figure 5

Plots illustrating the impact on extracted vortex cores (i.e., the black surface in each plot) due to changes of isosurface threshold values. From left to right: mean/4, mean/2, mean, mean + (std/2), and mean + std. All images were from TA case 1, [normalized] $\stackrel{̿}{Q}$ with a voxel resolution of 0.2 mm. At increased threshold values (≥mean + std/2) a reduction of identified vortex core structures occurred, sometimes not identifying any areas of vortex. All images came from the [normalized] $\stackrel{̿}{Q}$-criterion methodology, case TA1 (see Figure 2), and cardiac cycle-averaged vorticity data.

Figure 6

Comparison of identified vortex cores from the four mentioned methods: (a) standard λ ₂, (b) [normalized] $\stackrel{̿}{{\lambda }_2}$, (c) standard Q-criterion, and (d) [normalized] $\stackrel{̿}{Q}$-criterion. Top row is from SA2 case, and bottom row is from the TA1 case. Velocity streamlines were added to represent simulated flow patterns. Geometries of SA2 and TA1 can be found in Figure 2. Threshold values for each case were the mean (for their representative value), and only extracted vortex cores with a volume > 0.5 mm³ are shown. Figures are from each method's vorticity averaged data.

Figure 7

Visual comparison of the impact of voxel size on extracted vortex core structures for case SA2. Voxel sizes: (a) 0.1 mm, (b) 0.2 mm, (c) 0.3 mm, (d) 0.4 mm, (e) 0.6 mm, and (f) 0.8 mm. All structures were extracted using the [normalized] $\stackrel{̿}{Q}$-criterion method, a threshold value of the mean [normalized] $\stackrel{̿}{Q}$ value per case, and only cores with a volume > 0.5 mm³ were saved. The marked waveform shows the data point in the cardiac cycle used for extracting the structures.

Figure 8

Alterations to vortex core characteristics over different voxel sizes ranged from 0.1 mm to 0.8 mm: (a) changes to the number of vortex cores and (b) changes to DVO. Error bars stand for ±one STD of respective measurements over a cardiac cycle.

Figure 9

Relative variation for the change in the number of cores over the cardiac cycle or all 10 IA cases.

Figure 10

Vortex cores identified from two (SA4 and TA2) ANSYS-FLUENT-simulated cases (a and c) and the same cases using the Siemens LBM-simulated velocity fields from the Siemens CFD solver (b and d) under the same boundary conditions. Visual inspection ensured that main vortex core structures occurred in the same generalized location while Siemens CFD solver (b and d) resulted in a smoother core surface. Both cases had cores extracted using the same parameters: [normalized] $\stackrel{̿}{Q}$-criterion; threshold is their mean of [normalized] $\stackrel{̿}{Q}$, and only vortex cores with a volume > 0.5 mm³ were saved. Each vortex core was extracted from the cycle-averaged vorticity data (per respective case).

Figure 11

Bland-Altman plots showing the relation between two CFD platform results: (a) a mean number of cores and (b) mean DVO. The directionality of the BA plots is the Siemens CFD values minus the ANSYS-FLUENT CFD values.