Understanding Angiography-Based Aneurysm Flow Fields through Comparison with Computational Fluid Dynamics

BACKGROUND AND PURPOSE: Hemodynamics is thought to be an important factor for aneurysm progression and rupture. Our aim was to evaluate whether flow fields reconstructed from dynamic angiography data can be used to realistically represent the main flow structures in intracranial aneurysms. MATERIALS AND METHODS: DSA-based flow reconstructions, obtained during interventional treatment, were compared qualitatively with flow fields obtained from patient-specific computational fluid dynamics models and quantitatively with projections of the computational fluid dynamics fields (by computing a directional similarity of the vector fields) in 15 cerebral aneurysms. RESULTS: The average similarity between the DSA and the projected computational fluid dynamics flow fields was 78% in the parent artery, while it was only 30% in the aneurysm region. Qualitatively, both the DSA and projected computational fluid dynamics flow fields captured the location of the inflow jet, the main vortex structure, the intrasaccular flow split, and the main rotation direction in approximately 60% of the cases. CONCLUSIONS: Several factors affect the reconstruction of 2D flow fields from dynamic angiography sequences. The most important factors are the 3-dimensionality of the intrasaccular flow patterns and inflow jets, the alignment of the main vortex structure with the line of sight, the overlapping of surrounding vessels, and possibly frame rate undersampling. Flow visualization with DSA from >1 projection is required for understanding of the 3D intrasaccular flow patterns. Although these DSA-based flow quantification techniques do not capture swirling or secondary flows in the parent artery, they still provide a good representation of the mean axial flow and the corresponding flow rate.

V isualization of in vivo aneurysmal flow structures and quantification of aneurysm hemodynamic characteristics is important in understanding the role of hemodynamics in the mechanisms responsible for wall degeneration and progression toward rupture or stabilization 1 as well as for evaluating endovascular procedures such as flow diversion. 2,3 Previous studies have used computational fluid dynamics (CFD) to characterize the hemodynamic environment of the aneurysm to study aneurysm evolution 4,5 and rupture. [6][7][8] Other studies have used CFD to evaluate flow-diverting devices and procedures. 9, 10 On the other hand, imaging researchers have investigated using phase-contrast MR imaging to depict the in vivo flow fields within cerebral aneurysms, 11 while others have developed flow-quantification methods from dynamic angiography. 12,13 Visualization and quantification of flow fields directly from angiography data are attractive because they can be performed directly in the angiography suite while imaging the aneurysm for diagnosis or treatment. Previous studies along this line have shown the potential clinical value of these techniques and have compared the results with those of Doppler sonography and synthetic angiography generated from CFD simulations. 14 The purpose of our study was to analyze the flow fields reconstructed from dynamic angiography data by comparing them with patient-specific CFD models; in particular, we investigated whether these fields can be used to realistically represent the main intra-aneurysmal flow structures and identify limitations and factors that affect the flow field reconstruction.

Angiography-Based Flow Quantification
Fifteen cerebral aneurysms with diameters of Ͼ5 mm, imaged with 3D rotational angiography and 2D digital subtraction angiography at 60 frames per second and a typical in-plane resolution of 0.29 mm, were studied. Because the dose per frame is relatively low, the dose-area product level is comparable with a standard 3-frames per second DSA acquisition (dose-area product ϭ 716 mGy ⅐ cm 2 /s for the 60-frames per second protocol versus 786 mGy ⅐ cm 2 /s for the 3-frames per second protocol). We acquired the 2D DSA sequences from 2 different viewpoints, trying to minimize the overlap between the aneurysm and the surrounding vessels. These sequences spanned approximately 7-12 cardiac cycles. In 2 patients, DSA sequences were acquired from a single projection, making a total of 28 sequences for all 15 patients.
2D flow fields in the aneurysms and surrounding vessels were reconstructed from the DSA sequences by using a previously developed technique based on an optical flow approach. 12 Visualizations of these DSA flow fields were created by using virtual particle tracing (ie, a visualization technique based on integration of the equation of motion of massless particles to visualize velocity vector fields). Measurements of the instantaneous flow rate in the parent artery were obtained by integration of the velocity profile in ROIs placed on the proximal parent artery. The mean aneurysm flow amplitude (MAFA) was calculated by averaging the velocity magnitude over an ROI delineating the aneurysm contour. 13

Computational Fluid Dynamics Modeling
Computational fluid dynamics models with patient-specific geometries were constructed from the 3D rotational angiography images by using previously described methods. 15 We performed pulsatile flow simulations by numerically solving the 3D incompressible Navier-Stokes equations, assuming rigid walls and Newtonian fluid. 16 These assumptions seem reasonable because aneurysm walls in general do not undergo large displacements, and shear thinning effects do not have enough time to develop in aneurysm flows. 16 The maximum element size was set to 0.02 cm, and a minimum of 10 points across any vessel cross-section was specified. The resulting number of elements ranged from 3 to 4 million tetrahedra. The time-dependent flow rate measurements obtained in the parent artery from the DSA sequences were used to prescribe patient-specific inflow boundary conditions. The simulations were performed for all cardiac cycles covered by the dynamic DSA sequences, by using 120 time-steps per cycle. To avoid possible imprecisions due to the initialization of the flow calculations, we discarded data from the first cardiac cycle. The resulting CFD fields were saved at 60 frames per cycle, coinciding with the time instants of the DSA sequences. The mean aneurysm velocity (VEL) was calculated as the average of the 3D velocity magnitude over the aneurysm region and over the cardiac cycles and compared with the MAFA.
For comparison, the CFD flow fields were projected to the same views used for the DSA acquisitions. This projection results in a 2D vector field on the imaging plane normal to the line of sight. Because the 3D rotational angiography images used to reconstruct the CFD models and the 2D DSA sequences were acquired relative to the same reference frame, this projection was straightforward (ie, it did not require any image coregistration). During the projection, the CFD velocity components along the line of sight were discarded. The remaining in-plane components were averaged along the line of sight. All CFD mesh points mapped to the same DSA pixels were averaged (for a MEAN or average projection), or the vector with the maximum magnitude was taken (for an MIP projection). The projected 2D CFD flow fields were visualized in a manner similar to the DSA fields by using virtual particle tracing.

Data Analysis
The 2D DSA and CFD flow fields were quantitatively compared by using a directional similarity measure s defined as where v i is the DSA velocity vector; u i , the projected CFD velocity vector; ROI, the region of interest (aneurysm or parent vessel); N, the number of pixels in the ROI; and the dot operator denotes the dot product. This quantity measures the similarity of the directions of the 2 vector fields over the ROI. A similarity of 100% means a perfect match, random input would yield a 0%, and op-  posing fields would give a Ϫ100%. Similarities of the 2D DSA and CFD fields were calculated for the aneurysm and parent artery regions separately and for both regions combined. The DSA flow fields and the 2D projected CFD fields were qualitatively compared with visualizations of the 3D flow fields obtained from the CFD models by using streamlines. These comparisons were performed to evaluate whether the DSA or the projected CFD fields were able to depict the location of the inflow jet, the main vortex structure within the aneurysm, the flow split within the aneurysm (if any), the direction of flow rotation within the aneurysm, and the swirling or secondary flows in the parent artery.

RESULTS
The directional similarity measures between the DSA and the projected CFD flow fields are presented in the Table for the aneurysm and vessel regions and for both regions combined. In the parent artery, the DSA and projected CFD flow fields are in good agreement with an average similarity of 78%. In contrast, the average agreement within the aneurysm region alone is quite poor with a mean similarity of only 30%.
To understand this discrepancy in the agreement of the DSA and CFD fields between the aneurysm and parent artery regions, we visually compared the 2D fields with visualizations of the 3D field. The results are presented in the On-line Table. This table  indicates whether the DSA or projected CFD fields capture differ-ent flow characteristics observed in the streamline visualizations of the 3D fields. As explained previously, the in-plane components of the projected CFD velocity were averaged along the line of sight. We denoted this field as MEAN. A second field was computed by keeping the in-plane vector with the largest magnitude, similar to a maximum intensity projection used for visualization of 3D images. We denoted this second field as MIP. The MIP field was introduced to highlight the effects of vessel overlaps and to better understand the effects of projection of 3D vector fields onto a 2D plane. The On-line Table includes results for both the MEAN and MIP fields. The results indicate that the DSA and MEAN CFD flow fields often fail to capture many of the flow features of interest (ie, they only provide reasonable representations in Ͻ60% of the cases). Furthermore, in many cases, certain features are captured by the DSA field but not by the MEAN CFD field or vice versa. Qualitatively, the MIP CFD fields give a better depiction of the intrasaccular flow structure and provide a direct visualization of vessel overlaps but cannot be used directly to quantify the similarity with the DSA fields because the MIP projection loses any depth information and vessel overlaps tend to distort the aneurysm fields as discussed below.
Linear regression analysis (Fig 1A) indicates that the mean aneurysm flow amplitude determined from 2D DSA is linearly correlated to the mean aneurysm velocity estimated from the CFD models after discarding views with noticeable overlaps of the an- eurysm and surrounding vessels (slope ϭ 7.92 Ϯ 1.00, R 2 ϭ 0.80, P Ͻ .001). Vessel overlap was determined by inspection of the DSA and the projected CFD model and flow fields. Eight of the 25 DSA views were discarded (32%). This correlation is in agreement with earlier work comparing the MAFA ratios generated by DSA and CFD simulations. 17 This suggests that the MAFA is a good surrogate measure for VEL but needs to be interpreted carefully because it provides an underestimation of the aneurysm mean velocity because it discards velocity components along the line of sight.  Finally, in cases in which the displacements of fluid particles in 1 timeframe are comparable with the dimensions of the aneurysm, an interesting effect can be observed in which particle traces seem to jump across streamlines instead of following them. This undersampling effect is illustrated in Fig 5. The arrows point to regions where this effect is thought to take place. Note that this affects the DSA flow reconstruction but not the CFD projections; therefore, it can lead to poor similarity between the DSA and projected CFD fields. Because this can also affect the MAFA quantification, the difference (ratio) between MAFA and VEL is plotted in Fig 1B as a function of mean aneurysm transit time or the number of frames required for fluid particles to traverse the aneurysm, estimated as Frames ϭ 60 ϫ Aneurysm Diameter / Mean Aneurysm Velocity. The difference decreases (the ratio becomes closer to 1) as the number of frames increases (the flow within the aneurysm is better resolved in time).

DISCUSSION
Most interesting, both the DSA and projected MEAN CFD flow fields neglect swirling or secondary flows in the parent artery but provide reasonable representations of the mean axial flow profile (which explains why the similarities are good in the vessel region). In the first example of Fig 2 (top row), the flow in the proximal parent artery has strong secondary flows shown by the streamline visualization and the MIP CFD projection, but not by the DSA or MEAN CFD fields. Similarly, in the first example of Fig 3 (top row), a strong swirling can be observed proximal to the internal carotid artery bifurcation in the streamline visualization, but the DSA or MEAN CFD fields give the impression of a perfect laminar parallel flow in this region.

CONCLUSIONS
Linear regression analysis suggests that the mean aneurysm flow amplitude determined from DSA is linearly correlated to the mean aneurysm velocity determined from CFD after discarding views with substantial vessel overlap.
While a good correspondence between the arterial flow fields detected in DSA and CFD reconstructions has been observed (directional similarity of 78% on average), the similarity fluctuated considerably for the aneurysm flow fields. Several factors affect the reconstruction of 2D aneurysm flow fields from angiography sequences. The most important factors are the 3-dimensionality of the intrasaccular flow patterns and inflow jets; the alignment of the main vortex structure with the line of sight; the overlapping of surrounding vessels, which many times is unavoidable; and possible frame-rate undersampling. Flow visualization with DSA from Ͼ1 projection is required for understanding the 3D intrasaccular flow patterns.
Although these DSA-based flow quantification techniques do not capture swirling or secondary flows in the parent artery, they still provide a good representation of the mean axial flow and the corresponding flow rate. This information is valuable for prescribing patient-specific flow conditions in CFD models of cerebral aneurysms used to understand mechanisms of aneurysm evolution and rupture and to evaluate endovascular procedures and devices.