## 3 Results
### WSS-Based Hemodynamic Indices  
Since we use a Newtonian blood flow model, it is worth mentioning that non-Newtonian flow models appear at low strain rates; whereas aortic flow mostly generates mid- and high-strain rates where Newtonian blood flow treatment is considered to be a reasonable approximation. Therefore, we assume that the Newtonian flow model predicts WSS-based index values with an acceptable level of accuracy. TAWSS represents the  
Figure 14: Energy dissipation rate in aortic valves with varying calcification under uniform and helical inflow conditions over a cardiac cycle. Figure 15: Vorticity magnitude in aortic valves with different calcification levels under uniform and helical inflow during a cardiac cycle. cyclic average of the magnitudes of instantaneous WSS vectors. This index is presented in Figure 16 and shows significant variations with increasing calcification severity and different flow patterns. For instance, the tips of the leaflets are exposed to elevated TAWSS values due to greater fluttering, particularly when compared to the belly and root regions. As calcification becomes more severe, the increase in the TAWSS extends towards the belly region and mid-sections of leaflets. The presence of helical flow also slightly elevates TAWSS values and enriches the observed distribution patterns. The effect of calcification on the TAWSS also depends on the distribution, i.e., symmetry patterns of deposits. In Grades 3 and 4, where only one or two leaflets are calcified, the unoccupied leaflets demonstrate larger TAWSS values, possibly due to more intense contact and fluttering. Conversely, in Grades 5 and 6, all leaflets are calcified, resulting in a uniform TAWSS distribution across the leaflets. Figure 16: Distribution of TAWSS [Pa] on aortic valve leaflets, comparing varying degrees of calcification under uniform and helical inflow conditions. We believe that one potential erroneous contribution to the asymmetric TAWSS contours in the no-calcification case resulted from placing the fluid domain's staggered grid, with its 90-degree box shape, alongside the aortic valve and housing's inherent 120-degree symmetry. This mismatch in grid symmetries led to asymmetry in the TAWSS for one leaflet, where normally, we would expect a similar distribution pattern with the other leaflets. The OSI in Figure 17 serves as an indicator of the degree of reversing direction of the WSS within a cardiac cycle [49]. Thus, the OSI expresses the size of the changes in the direction and magnitude of the WSS. While the OSI reveals whether the WSS contains oscillatory components, it does not differentiate between unidirectional stress with varying magnitude and stress that changes in both magnitude and direction. A high OSI value, approaching 0.5, signifies an unsteady flow and is associated with a heightened risk of endothelial dysfunction and atherosclerosis in humans [45]. Figure 17: OSI contours on aortic and ventricle sides for varying grades of calcification and inflow patterns (uniform and helical). Unit is dimensionless. Generally, the OSI tends to inversely correlate with the TAWSS. In the case without calcification, the leaflets' high and unrestricted flutter leads to OSI values close to 0.5, except in areas experiencing a high TAWSS at the tips. Calcification restricts leaflet movements, resulting in lower OSI values where the most heavily calcified Grade 6 leaflets exhibit the larger calcified areas with smaller OSI values. As expected, OSI values are generally lower on the ventricle side due to its exposure to more consistent unidirectional flow compared to the aortic side, which experiences more oscillatory flow due to vortex formation and retrograde flow. For helical flow, a slight but negligible change in OSI values was observed on both the aortic and ventricle sides. This suggests that the impact of helical flow on the OSI is minimal, at least within the scope of the conditions examined in this study.