# Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms
## 4 Discussion
This can be observed by the presence of wrapping and distortion effects seen in the distal descending aorta when deformations are at high boundary of the shape space (i.e., \(\pm 3\)\(\sigma\)). Based on these observations, the PCA method provided acceptable models with \(\pm 1.5\)\(\sigma\), as represented by a 6.68% chance to obtain the deformed aneurysm configuration. For high shape deviations, the resulting model can likely influence the computational flow stability because of mesh distortion and negative element volume associated with distorted geometries. For SSM with 2D shapes [44], the PCA method was demonstrated to generate unrealistic geometries when the Mode 1 was varied to three standard deviations above the mean shape. As reported by [PERSON] et al. [10], shape vectors for each patient with ATAA can be obtained from PCA and then used to assess the correlation between morphological features (i.e., aortic size and tortuosity) and biomechanical functional parameters (i.e., WSS). In this study, the SSM was adopted to generate a virtual patient cohort and assess the hemodynamic in borderline ATAA shapes. The current SSM method is also specific to develop computational flow modeling. In this study, the supra-aortic vessels were removed to avoid bias in the alignment of ATAA models and prevent the assessment of shape variations related to patient-to-patient differences in supra-aortic vessel geometries (i.e., the classic versus the bovine aortic arch). This assumption can likely change the resulting hemodynamic environment of the ascending aorta. There are also potential improvements in the proposed methodology with regards to the boundary conditions. For all shape modes, we used standards inflow and outflow profiles by neglecting the difference in the patient physiology. In a previous investigation, statistically significant correlations were found between shape modes and functional parameters collected from Doppler ultrasound [10]. Thus, established probabilistic methods can be adopted to estimate boundary conditions from probability distributions and thus tailor more realistic inflow and outflow profiles to each shape mode [44]. Moreover, the solution of the fluid-governing equations is time-consuming, so simulations were carried out for the first three shape modes (i.e., a total of 14 simulations). As a standard computational fluid dynamic approach was used, the aortic valve was assumed as rigid and segmented at fully opened shape from CT scan at systole. In future studies, for realistic flow simulation, fluid-solid interaction will be used to simulate the motion of the aortic valve during the cardiac beating. In a different way, the ATAA leads to stiffening of the aortic wall so that the assumption of a rigid aortic wall is reasonable, as reported in numerical comparison between computational fluid dynamic and fluid-solid interaction techniques [45, 46]. It is known in SSM that shape modes representing a relatively small percent of the total variation could have a large effect on the resulting biomechanics, though high modes are influenced by noise due to imaging and segmentation processes. Future studies can be undertaken to fully investigate the flow disturbances for high shape deformations and thus capture the influence of key anatomic features.