The tomographic dataset was acquired with a 320-detector scanner (Toshiba Aquilon One, Toshiba, Japan). The ECG-gated cardiac CT scans were performed in one cardiac cycle, a total of 10 ECG-gated phases were acquired. The chosen phases were taken within the ECG R-R interval with a fixed time step of 78 ms. In this way, it was possible to sample the aortic phases with a 10% resolution. The segmentation process was performed with the functions provided by the VMTK package (Vascular Modeling Toolkit, www.vmtk.org). In particular, a threshold algorithm with the same threshold level was imposed for all the phases. Three-dimensional geometrical models of ascending aorta, arch, and supra-aortic vessels were generated for each cardiac phase. The segmented models were exported as stereolithography (STL) file format for accomplishing the numerical simulation setup.

In numerical simulations workflows, the boundaries of the fluid geometry are modeled as smooth, however, the raw geometry obtained directly from medical imaging does not produce the required level of smoothness, and hence, it has to be pre-processed. The main cause is given by low resolution and artifacts, as already discussed in the previous section. Currently, different strategies are available to achieve smooth 3D patient-specific reconstructions. Given this wide variety of approaches, it is difficult to assess if the filtering process causes uncertainties. To account for this source of errors, a preliminary investigation was performed on a geometry with three different levels of smoothness (S_L, S_M, and S_H) as depicted in Figure 2. This investigation was set to define the most suitable smoothing level to use for the computational models. In particular, this process was carried out by applying a shape-preserving Taubin smoothing filter with a weighting factor (w) of 0.5 and the maximum number of iterations (n) of 15 (53). To achieve different levels of smoothness, the same filter was applied multiple times according to a smoothing strategy summarized in three main steps (refer to Figure 3). Also, the presence of calcifications was considered, given their expected effect on the numerical results (54):

The Taubin filter (55) was applied by using the implemented routine from the VMTK package. The presence of calcification artifacts within the ascending aorta region was individuated with the support of a skilled clinician. All the 3D segmented models included the ascending aorta, the aortic arch, the descending aorta (Desc), and the apico-aortic branches (brachiocephalic artery (BCA), left common carotid artery (LCC), and left subclavian artery (LSUB), as shown in Figure 2A). The evaluation of the smoothing effect was carried out exclusively on the CFD approach at the p₀ phase.

After defining the clinical images processing method, the different computational techniques adopted in the study are reported. In particular, three different approaches are investigated and compared:

In this subsection, we describe the common and specific settings for each approach.

For the fluid dynamics calculations, the same computational setup was assumed for all models. The pulsatile flow behaviors were analyzed by solving the 3D incompressible Navier-Stokes equation system:

where ρ is the density of the fluid, v is the blood velocity, and σ is the Cauchy stress. Blood was modelled as an incompressible Newtonian fluid, with constant values of density 1,060 kg·m³ and dynamic viscosity 0.0035 kg(m·s)⁻¹. Blood flow was assumed laminar, as the Reynolds number estimated from the worst configuration at the systolic peak was equal to 3,534. The proposed laminar hypothesis is in line with previous literature studies (40, 56–58).

For all the simulations, the fluid domain was partitioned in tetrahedral elements using Ansa (BetaCAE) with four boundary layers of triangular prisms. Ansys Fluent (ANSYS Inc. Canonsburg, PA, USA) was used as the solver. A mesh sensitivity analysis was carried out on the given aortic case. In particular, the mesh size was reduced and the average value of WSS in the ascending aorta region was monitored. The mesh size was chosen after reaching a WSS variation below 0.1%. After the analysis, the models were discretized with a tetrahedral mesh with a mean element size of 1 mm. Prism elements were added to the vessel wall by implementing 4-layers inflation for a total thickness of 1.2 mm and a growth-rate equal to 1.5.

For the CFD simulations, two geometries were considered to assess the variability linked with phase segmentation. In particular, the geometries were taken from two phases of the cardiac cycle: one at diastole (p₀) and one at the systolic peak (p₄) (refer to Figure 1).

For the CFD_RBF, the simulation scheme was implemented according to previous studies (47, 48). Briefly, the method imposes patient-specific aortic wall motion during the cardiac cycle without re-meshing using a morphing approach. It is worth pointing out that for this method all the phases from the segmentation were considered to calculate the radial basis function solution. Additionally, no material property estimation was required, as the method only relies on the knowledge of wall displacement at the different phases.

At last, for the FSI simulation, a fully-coupled partitioned approach was implemented. In particular, the FSI coupling used an Arbitrary Lagrangian-Eulerian method to transmit the wall displacement and the pressure between the fluid and the structural domains of the simulation (59). An isotropic linear elastic material behavior was assumed for the aortic wall, with the hypothesis of small deformations in the cardiac cycle (39). In order to guarantee a comparable wall displacement between the FSI and CT-gated results, the Young modulus (E) was estimated according to Laplace's law for the calculation of stresses within a pressurized membrane and the strain estimation from the normalized variation of vessel diameter between systole (p₄) and diastole phase (p₀). The wall thickness (t) was set equal to 2 mm (32) and the resulting E was equal to 0.5 MPa.

All the post-processing analyses carried out to extract the WSS-based descriptors focused on the luminal wall of the ascending portion of the aorta. The TAWSS was also calculated for all the investigated cases. The TAWSS magnitude was measured in the last cardiac cycles by integrating each nodal WSS magnitude over the cardiac cycle as:

To quantify the implemented smoothing range, the distances between the geometries obtained at different smoothing levels are reported. Figure 4 depicts the surface distance in the worst configuration: between the geometries with the lowest and highest smoothing level. The geodesic distance was carried out according to Dijkstra algorithm (61), implemented in the VMTK toolkit. Areas at maximum distances are observed as a consequence of calcium artifacts removal in the localized region of the vessel.

Figure 5 summarizes the WSS maps at the systolic peak for the aortic case with the three different levels of smoothing. The comparison in terms of CFD simulations was assessed for the phase p₀ in the ascending aorta region. The box plots of Figures 5D,H,N describe the WSS element distribution in the area of interest for the three cases. The corresponding TAWSS analysis is instead reported in Figure 6. For both the systolic WSS and the TAWSS parameters, the reported range was comparable regardless of the smoothing level adopted, with peaks of 11 Pa and 5.4 Pa, respectively.

Concerning the boundary conditions, the R_p, R_d, and the C computed according to 3WKM total, and to 3WKM tuning approaches for each outlet are reported in Table 1.

The results from the CFD at p₄ are now compared with those of CFD at p₀ with the S_M smoothing level. The contour maps from the p₄ geometry are, instead, reported in terms of systolic WSS and TAWSS in Figures 7, 8, respectively. The box plots of peak systolic WSS are represented in Figures 7D,H. For the sake of comparison, the results of WSS and TAWSS at p₀ with the S_M smoothing level were re-included in both figures.

Figure 9 depicts the different maps in terms of WSS at systolic peak for the CFD_RBF and FSI simulations. The corresponding box plots for the distributions are depicted in Figures 9D,H. Additionally, for the sake of comparison, the maps of the unfolded surface of the ascending aorta surface are presented in Figure 10, for the CFD at both segmentation phases, the CFD_RBF and FSI cases.

As a first step, the effect of surface smoothing after segmentation was defined. The distances between the S_L and S_H geometries are reported in Figure 4. The results of Figure 4 highlighted and quantified the effect of the implemented smoothing strategy, with maximum distances of 1.9 mm. It is worth stressing that the maximum values occurred in regions that required a local correction due to the presence of calcium artifacts. On the other hand, the global smoothing effects produced geodesic maximum distance differences less than 1 mm.

The results from Figures 5, 6 report the effect of the smoothing process in terms of WSS and TAWSS at the levels S_L, S_M, and S_H. Beyond the map distributions, the box plot representation from Figures 5D,H,N allows for a comparison. From the mechanobiological point of view, the WSS is a patho-physiological stimulus at the basis of extra-cellular matrix disruption and elastic fiber degeneration (65). A link between low/oscillatory WSS and localized lesions of the vascular tissue and early disruption of endothelial cells was proven (66, 67). For this reason, WSS can be considered as a numerical predictor for tissue damage/pathology. Although the shear stress range is maintained in all three cases of Figure 5, it appears clear that the S_L case produces higher and more dispersed WSS values. On the contrary, no significant differences appear in terms of WSS distribution between the S_M and S_H levels. It is interesting to observe that the WSS trend changed as the calcification artifact removal was imposed. The presence of thrombi and calcifications are a common diseases affecting the abdominal district. The effect of calcifications presence was already underlined as an issue to be resolved to prepare a suitable geometry for numerical simulations (54). According to Ladich et al. (68), this pathology also exists in the thoracic aorta. In particular, both micro calcifications or extensive circumferential calcifications of the ascending aorta or aortic arch can be observed. While calcifications are associated with chronic systemic inflammatory diseases, their presence also affects the surface morphology and consequently the WSS. Similar results also were found for intracranial aneurysm (69) and more recently for the aorta in Perinajová et al. (56). In this last study, the importance of the smoothing applied in the segmentation step has been stressed out on CFD simulations. Given the WSS distribution stabilization after calcification removal, the level S_M was chosen as the minimum level of surface smoothing to allow a stable estimation of WSS and it was adopted for all the following numerical simulations. Additionally, it is worth noting that, while discrepancies in the local distribution exist, the higher values of stress were reported within the inner curvature of the ascending aorta for all levels S_L, S_M, and S_H. These findings are important and give rise to reflection from a clinical perspective, for instance in patients affected by aortitis or porcelain aortas.

Concerning the results of the CFD from the systolic segmented phase p₄, the distribution of WSS and TAWSS can be analyzed from Figures 7, 8 and from the unfolded maps of Figures 10A,B. The box plot in Figures 7D,H displays results of WSS in accordance with the previous simulations segmented from phase p₀. Nevertheless, the distribution from Figures 10A,B reveals a different mapping between the CFD at the two phases. This aspect underlines again the effect of geometry on the WSS behavior within the aortic domain.

The implementation of numerical methods was investigated as well. Beyond the rigid wall CFD results, already presented, the CFD_RBF and FSI approach produced the WSS distributions of Figure 9. The box plots from Figures 9D,H allowed for distribution comparison. Except for the presence of peak areas, it appears that the distribution presents the same average and range for both modalities. No significant difference emerged from the comparison of distributions of Figures 9D,H. The same trend is confirmed by the unfolded maps of Figure 10, in which appears a difference in terms of WSS between both CFD_RBF and FSI approaches and the CFDs. The reported shear stress ranges appear to match, nevertheless, the CFD_RBF produced peaks, especially in the inner curvature zone of the ascending aorta. As an overall consideration, the investigation of the CFDs box plot in Figures 7, 9 shows the differences arising from the wall motion assumption. From Figure 10, it appears that the introduction of wall motion within the model produced a shift toward higher WSS values, regardless of the method used to implement it. This aspect corroborates the necessity to include a realistic wall motion model within the simulation of the aorta, as it significantly affects the result. Comparisons in terms of rigid and moving wall numerical simulations for the aorta were reported already in the state of the art (46). The presented results highlighted the presence of a WSS difference according to the numerical technique adopted, however, the discrepancy is expected to diminish as long as the tissue is rigid. An additional point to underline is that the FSI approach requires the estimation step of material properties. While the FSI and CFD_RBF manifested no significant difference in terms of WSS distribution, the CFD_RBF method did not require any hypothesis on the material constitutive model. For this reason, no strong assumption and indirect in vivo measures was introduced (27, 28). The CFD_RBF method was computed exclusively on the basis of the segmentation of the cardiac phases. Consequently, the CFD_RBF approach presented the advantage of an a-priori exclusion of the intrinsic uncertainties given by material characterization and modeling, which were demonstrated to be responsible for inaccuracies (70, 71). Recent studies proposed this approach to study the effect of aortic flow by imposing valve kinematics (72, 73).

The current study presents several points of development for the future. The effects of smoothing levels and different phase segmentation were carried out on a single patient-specific case. Nevertheless, the analyses of WSS distributions produced differences in terms of map distribution for given levels of smoothness and confirmed the influence of geometrical/morphological factors on the WSS, while the less evident map distribution differences were found for TAWSS.

The choice of different image phases for reconstruction implied differences in hemodynamic results. This demonstrates that the sources of morphological uncertainties are not only the segmentation technique and smoothing approach but also the different possible geometries that can be defined for the same patient-specific case. As the number of cases recruited is increased, a similar trend is expected. An additional point of development for the future is to adopt the CFD_RBF approach to account for the aortic root movement. It was demonstrated that the aortic root and left ventricle kinematics might have an influence on the numerical modeling of the aorta (74). The CFD_RBF method was demonstrated to be a potential tool to integrate the patient-specific displacement-based imaging data with numerical simulations. For this reason, it appears as a suitable way to include rigid motions like the ones occurring in the ventricle and aortic root. The results presented within the current study were focused on computational methods. Nevertheless, an interesting point of development would be the inclusion of experimental methods of validation like the adoption of mock circulatory loops (75, 76). In the in silico scenario, optical techniques like particle image velocimetry (77) could be adopted for velocity profiles comparison.