# Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms
## 3 Results  
The trend of shape probability as a function of \(\sigma\) appears to follow a Gaussian distribution, as shown by Figure 1A. Specifically, the shape probability represents the chance that the specific deformed shape will occur for a given value of the shape boundary. This curve evinces that, for shape deviations of 0.5 \(\sigma\), 1 \(\sigma\), 1.5 \(\sigma\), 2 \(\sigma\), 2.5 \(\sigma\), and 3 \(\sigma\), the deformed shape probability is 30.85%, 15.87%, 6.68%, 2.28%, 0.62%, and 0.14%, respectively. Figure 1B shows the scree plot with the cumulative variance described by each SSM for either TAV ATAA or BAV ATAA. For the ATAA patient population here investigated, the PCA demonstrates that 90% of the overall shape variability can be captured by the first seven modes for BAV ATAAs and eight modes for TAV ATAAs. Figure 1: (**A**) Shape probability curve as a function of standard deviation; (**B**) scree plot of PCA-related shape modes for BAV ATAA and TAV ATAA. Each shape mode was correlated to distinct morphological features of the aneurysm and aortic valve type using visual assessment. Figure 2 highlights that Mode 1 accounts for nearly 50% of the overall shape variability and is mainly associated with a proportional aneurysm size change (scale factor) and slightly by aortic arch unfolding. Videos S1 and S2 display an animation of Mode 1 for BAV ATAA and TAV ATAA, respectively. For high values of the shape space, the template deformation shows a long and unfolded geometry of the dilated aorta. In a different way, low values of \(\sigma\) lead to small and unfolded ascending aortic geometries. The aortic valve shows clockwise rotations for TAV ATAAs while BAV ATAAs have high values of the orifice area for low standard deviations and small values for high standard deviations. Figures 3 and 4 evince the first eight shape modes for both BAV ATAA and TAV ATAA. For both aortic valve morphologies, Mode 2 manifests changes in the aortic aneurysm curvature from highly tortuous aortic shapes to straight aortic segments. Mode 3 indicates variations in the aortic valve phenotypes and accounts for nearly 10% of aneurysm shape variability. The remaining shape modes are associated with the aortic valve rotation and inclination with respect to sagittal and coronal planes, as well as changes in the aortic valve geometry. Figure 2: Graphic representation of ATAA and its valve for Mode 1 at different values of \(\sigma\) for both BAV ATAA and TAV ATAA. Figure 3: Dominant shape modes shown by deforming the mean TAV ATAA template (grey color) from low (\(-1.5\)\(\sigma\)) to high (\(+1.5\)\(\sigma\)) shape boundaries (red color). Figure 5 illustrates flow parameters for the mean template as obtained by computational flow analyses. For BAV ATAAs, the peak systolic flow velocity has a helical flow pattern characterized by high velocities in the aortic wall periphery and a slow moving flow in the aneurysm centerline. In a different way, the mean template of TAV ATAAs has an uniform flow field distribution at systole. Indeed, flow patterns highlight the effect of different modalities of aortic wall flow impingements, resulting in local changes in the flow patterns. Figure 4: Dominant shape modes shown by deforming the mean BAV ATAA template (grey color) from low (\(-1.5\)\(\sigma\)) to high (\(+1.5\)\(\sigma\)) shape boundaries (red color). blood pressure and shear forces. Maxima of time-averaged blood pressure are found in the major curvature of the aortic wall for the mean template of TAV ATAAs and near the anterior side of the mean aortic wall template of BAV ATAAs. WSSs are highest in the region between the sinotubular junction and mid-ascending aorta. Figures 6-8 show hemodynamic parameters of BAV ATAA and TAV ATAA atlases from Mode 1 to 3.