# Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms
## 1 Introduction  
Ascending thoracic aortic aneurysm (ATAA) is a permanent dilatation of the aortic wall, with risk stratification based on the maximum aortic diameter measured by diagnostic imaging [1]. Elective repair of ATAAs is carried out for aortic diameter \(\geq\) 50 mm, but aggressive management in case of predisposing risk factors as the bicuspid aortic valve (BAV) and hypertension is recommended [2]. If the aortic dilatation is not surgically treated, the risk of aneurysm rupture or dissection can be as high as 50% in patients with aortic diameter \(>\) 50 mm [3]. The estimated incidence of ATAAs is 5.0 per 100,000 individuals per year [4], and individuals with BAV have greater risk of aortic dilatation at young age than patients with the morphological normal tricuspid aortic valve (TAV) [2]. However, the maximum aortic diameter criterion is widely recognized as a poor prognostic biomarker of the likelihood of aneurysm complications as it fails to predict acute events in small-sized ATAAs. There is, therefore, a general consensus on the need for the development of new risk stratification strategies not only based on the aortic size, and this is a consequence of the awareness of aneurysm heterogeneity presenting different patterns of aortic dilatation (i.e., the aortic root phenotype, the tubular aorta, and the diffusive involvement of theaortic dilatation) and bicuspid phenotypes (i.e., the anterior-posterior cusp fusion or the right-left cusp fusion) [5].  
Population-based modeling has been adopted to meaningful effect in biomechanics by capturing the impact of the patient-to-patient anatomical variations on both cardiac [6; 7; 8] and vascular disease progression and development [9; 10; 11]. Statistical shape modeling (SSM) has the potential to address the challenging quantification of the complex nature of the aneurysm disease over time. The development of a computational atlas of image-based shapes allows a quantitative and qualitative evaluation of the anatomic variability as a descriptor of all geometrical shape information and its variations around a mean shape or template. The aortic shape variation is decomposed into a few key components using principal component analysis (PCA) to identify specific anatomic features for a given patient population. Once the shape atlas is built, the mean template can be virtually deformed from low \(-3\) standard deviation (\(\sigma\)) to high \(3\)\(\sigma\) values of each shape mode to visualize the anatomical shape boundaries. The understanding of the mechanistic link between the shape and function can reveal important insight not only on the aneurysm disease, but also for the development of novel risk metrics not based on the aortic size [12; 13]. According to Laplace's law, the large ATAA wall experiences a greater level of intramural stress than a nonaneurysmal aorta [14]. The intramural stress was demonstrated to provide better predictive capability than the aortic size [15; 16], even in the classic versus the bovine aortic arch [17]. Computational flow analyses have also evinced different patterns of fluid shear forces and eccentric flow in ATAAs with different morphological features [18; 19] and valve phenotypes [20]. In the setting of the aortic arch coartoaction, SSM was used to assess the link between shape features and biomechanical descriptors [9] as well as detect shape cluster of patients at high risk of complications [21].  
The overall goal of the present study is to carry out an atlas-based disease assessment of the computational flow dynamic of the dilated ascending aorta. An SSM was created to parametrize the aortic shape and its variability to consider different aneurysm patterns and aortic valve phenotype (i.e., the BAV ATAA versus the TAV ATAA). For each patient group, the mean shape was deformed upon the first three principal shape modes, and then the relationship between shape and computational flow parameters was investigated to quantify the hemodynamic in borderline aneurysm geometries.