## 3 Results
### Transvalvular Hemodynamic Indices
In Figure 13, the variations in kinetic energy in the Valsalva sinus and ascending aorta for different degrees of aortic calcification are illustrated under reduced flow conditions, which correspond to the role of severe aortic stenosis. In our computational simulations, kinetic energy was calculated in the volumes of the Valsalva sinus and the ascending aorta. We observed an unexpected decrease in kinetic energy as the severity of aortic calcification increased. These findings are best understood within the context of our specific simulation parameters. Our model utilized a reduced flow rate to mimic the diminished cardiac output commonly associated with severe aortic stenosis. This reduction directly impacts kinetic energy, as \(1/2\,\rho V^{2}\), leading to lower kinetic energy values, especially in areas distant from the stenotic orifice. Notably, the Valsalva sinus and ascending aorta are areas where kinetic energy could inherently be lower due to factors like the sinus's expansion and the more disturbed flow in the ascending aorta. These regions may also experience further reductions in kinetic energy due to flow disturbances induced by calcification, except in Grade 3, which shows a sudden jump at the diastole phase due to severe asymmetry at a single leaflet in uniform flow. The same jump in Grade 3 is not visible in the case of helical flow, as seen in Figure 13.  
Figures 14 and 15 show the variations in the energy dissipation rate and the magnitude of vorticity in aortic valves with varying calcifications under uniform and helical flow conditions, respectively, over a cardiac cycle. The trends for both metrics are similar,  
Figure 12: Maximum fluid velocities through the orifice area in uncalcified and calcified conditions, under uniform and helical inflow regimes. Velocities measured at 0.068 cm from the inlet. Figure 13: Variation in kinetic energy in the Valsalva sinus and ascending aorta across different calcification severities for uniform and helical inflow. suggesting that increased calcification in aortic valves contributes to the formation of more intense vortices and a corresponding rise in energy loss. For the non-calcified case, these metrics generally exhibit the lowest values, owing to the least resistance to blood flow. However, a slight increase in both the energy dissipation rate and vorticity magnitude was observed under helical flow conditions. Interestingly, the energy dissipation among the calcified leaflets does not follow a straightforward increase with the grade of calcification. Here, the influence of localized calcifications and their asymmetrical form with helical flow patterns becomes apparent. For example, Grade 3, which has only one calcified leaflet, shows a spike in both vorticity and energy dissipation during peak systole and backflow periods, likely due to intense fluttering of the free leaflets due to strong pattern asymmetry. Under uniform inflow, a second peak in these metrics is noticeable for all calcified cases during the valve-closure phase. However, this is not the case under helical flow for Grades 5 and 6, which show a more regular pattern. Grades 3 and 4, however, still exhibit a second peak, indicating that asymmetric calcification can have a negative impact on the vortical structures and consequent energy dissipation.