# Atlas-Based Evaluation of Hemodynamic in Ascending Thoracic Aortic Aneurysms
## 2 Materials and Methods
### Computation Flow Analysis  
Once the SSM for both TAV ATAA and BAV ATAA groups was developed, the first three shape modes were deformed with respect to the mean shape in order to quantify the aneurysm-related hemodynamic by computational flow analysis [28; 29]. To avoid excessive distortion and ensure computational stability, we deformed the mean shape upon a shape boundary of \(\pm 1.5\)\(\sigma\) for the first three modes. We decided to include the first three modes to assess the impact of 80% shape variability on the resulting flow dynamic. After deformation of the mean template, the resulting shape was used to generate several models, each representing a few borderline aneurysm case scenarios. The model was meshed  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Patient Characteristics** & **BAV ATAA** & **TAV ATAA** & \(p\)**-Value** \\ \hline Age (years) & \(58\pm 1\) & \(65\pm 1\) & 0.390 \\ Male (\%) & \(85.0\) & \(63.9\) & 0.234 \\ BSA (m\({}^{2}\)) & \(3.5\pm 6.2\) & \(2.4\pm 3.5\) & 0.078 \\ HR (ppm) & \(72.9\pm 10.8\) & \(72.8\pm 13.0\) & 0.769 \\ MAP (mmHg) & \(93.4\pm 9.5\) & \(91.9\pm 8.1\) & 0.107 \\ SV (mL) & \(77.7\pm 30.8\) & \(77.1\pm 26.9\) & 0.455 \\ CO (L/min) & \(5.5\pm 2.2\) & \(5.5\pm 2.5\) & 0.952 \\ Hypertension (\%) & \(51.5\) & \(60.2\) & 0.987 \\ \hline \hline \end{tabular} Note: BSA = body surface area; HR = heart rate; MAP = mean arterial pressure; SV = stroke volume; CO = cardiac output.  
\end{table}
Table 1: Clinical and demographic characteristics of patient study population. Mann–Whitney test with \(\alpha\) = 0.05.  
with unstructured tetrahedral elements and element size near the aortic wall of 0.4 mm, approximately.  
Unsteady transient simulations were carried out assuming the blood as a laminar non-Newtonian flow with viscosity portrayed by the Carreau model and density of 1060 kg/m\({}^{3}\)[30]. The blood flow was assumed to be laminar as this usually occurs in large vessels due to the low mean flow velocity. For the BAV ATAA template model, we found an average Reynolds number of 1434 at mid-height of the ascending aorta. Though the Reynolds number is low, the composition of the fluid could lead to different flow regimes such as the laminar-turbulent and the fully developed transitional regimes. In the areas of changes in the fluid flow direction, the acceleration field could lead to the separation of the dense part of the blood by modifying the velocity profile. The Navier-Stokes equations governing fluid motion were solved with an implicit algorithm in FLUENT v21 (ANSYS Inc., Canonsburg, PA, USA), using the SIMPLE pressure-velocity coupling algorithm and second-order pressure interpolation method. Numerical solution was assumed to converge with the residual of the continuity equation set at \(10^{-7}\) at all-time steps. The optimal time step was 0.0025 s as determined by time independency assessment. For the inflow, all models were set with a representative parabolic flow profile with fundamental frequency of 1 Hz and peak velocity of 1.2 m/s, as described previously [31]. For the descending aorta, the outflow boundary condition was imposed using a three-element Windkessel model with population-average values of the vascular resistance and compliance. Both inlet and outlet were extended three diameters normal to the aorta cross section to ensure a stable flow in the ATAA model. Flow simulations were run for three consecutive cardiac cycles, with result analysis carried out for the last cardiac cycle. Postprocessing was performed using EnSight (v21, ANSYS Inc., Canonsburg, PA, USA) to compute the following flow parameters: (a) flow streamlines at systole, (b) time-averaged blood pressure over one cardiac cycle, and (c) peak systolic wall shear stress (WSS).