# Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms
## 4 Discussion
In this study, Mode 1 was found to be the main shape contributor of both the aneurysm diameter and aortic size, thereby impacting the resulting WSS and blood pressure distributions exerted on the weaken aortic wall. For BAV ATAAs, the small aortic model (\(-\)1.5 \(\sigma\)) had a 2.5-fold increase in the blood pressure and a 21.4-fold fold increase in the WSS magnitude with respect to those of the large ATAA model (+1.5 \(\sigma\)). Indeed, the shear stress parameter was the variable that exhibited the largest differences among shape boundaries for all investigated shape modes. Similar changes in the distribution of WSS and blood pressure magnitudes were found for TAV ATAAs, suggesting that valve morphologies do not significantly impact aneurysm hemodynamic across different aneurysm dimensions. These relationships between aneurysm size and flow parameters can explain recent clinical findings demonstrating that the ascending aortic length is a valuable prognostic indicator together with aneurysm size for the stratification of the aortic dissection risk. In a large patient study group, [PERSON] and collaborators [42] estimated an odds ratio of 12.4-fold greater in ATAAs with aortic length \(\geq\)13 cm (as computed from the aortic annulus to the origin of the innominate artery) compared with ATAAs with length of <9 cm. They concluded that ascending aortic length and aneurysm size, taken together, are more powerful predictors than the aortic diameter alone. It can be observed that these two morphological parameters are indeed representative of Mode 1 shape variations here modeled by the SSM. For both BAV ATAA and TAV ATAA, Mode 2 reflected variations in the tortuosity of the ascending aneurysmal aorta, being more curved with low deformations of the mean template than high mean-template deformations. The less tortuous ATAA had both blood pressure and WSS with more uniform distributions on the major curvature of the aortic wall as compared to those locally focused on the tortuous ATAA wall. This is likely due to differences in the flow jet impingement between shape boundaries as shown by velocity streamlines. As a consequence, the aneurysmal aorta can manifest local bulging of the ascending aorta, as commonly seen in the clinical practice of ATAA surgery. In a different way, Mode 3 was representative of the aortic-valve cusp fusion imparting different distributions on WSS forces and flow velocities. Computational flow studies [19,33] and 4D flow MRI [32] have widely shown that a right-left fusion pattern can result in a flow jet locally directed towards the right anterior aortic wall. This can result in a nested helical flow with low velocity in the aneurysm axis and high velocity in the ATAA wall periphery (see Figure 8). Our computational flow analysis performed for Mode 3 with +1.5 \(\sigma\) estimated a flow jet towards the posterior aorta, with increased shear stress values at the right posterior side of the aorta as compared to those resulting from the flow impingement on the anterior aorta (i.e., shape space of \(-1.5\)\(\sigma\)). These alterations in the spatial distribution of flow parameters are a consequence of changes in the valve orientation, as depicted by Mode 3, and likely determine differences in aneurysm progression and, ultimately, patient outcome. Though the mechanistic link between WSS and vascular weakening has been demonstrated in ATAAs [23, 36], the correlation of ascending aortic dilatation rates with BAV phenotypes has not been fully addressed. Propagation patterns of BAV-induced hemodynamic disturbances are still not uniform in patients with BAV with the same valve cusp fusions, and this could be in part due to patient selection criteria and the effect of confounding clinical and demographic variables [43]. Though the proposed SSM method was developed to be used for population-based computational flow analyses, there are several limitations. The PCA method used in this investigation has limitations for accurately capturing shape variations with excessive rotation and bending.