## 3 Results
### The Impacts of Valve Designs on Hemodynamic Characteristics
#### 3.3.2 Secondary Flow  
Figure 9 showed the velocity vector distributions of secondary flow in the ascending aorta (slice 1), aortic arch (slice 2) and descending aorta (slice 4) of all three cases at the acceleration peak (t\({}_{4}\)). The visualized results showed that different valve designs mainly affect the secondary flow distribution patterns in the ascending aorta (slice 1). \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Segment**} & \multicolumn{3}{c}{**SAWSS (Pa)**} \\ \cline{2-4}  & **SPAC Tubular** & **SPAC Molded** & **Conventional** \\ \hline AAo & 3.55 & 2.95 & 2.74 \\ \hline Aortic arch & 7.03 & 6.67 & 6.37 \\ \hline DAo & 5.49 & 5.44 & 5.53 \\ \hline \end{tabular} AAo: ascending aorta; DAo: descending aorta.  
\end{table} 
Table 4: The SAWSS magnitudes in different segments of aorta. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Time Point**} & \multicolumn{3}{c}{**SAWSS (Pa)**} & \multicolumn{3}{c}{**Low WSS Areas (cm2)**} \\ \cline{2-7}  & **SPAC Tubular** & **SPAC Molded** & **Conventional** & **SPAC Tubular** & **SPAC Molded** & **Conventional** \\ \hline t\({}_{1}\) & 0.18 & 0.19 & 0.19 & 102.57 & 101.08 & 100.8 \\ \hline t\({}_{2}\) & 0.20 & 0.20 & 0.25 & 100.31 & 100.11 & 98.35 \\ \hline t\({}_{3}\) & 0.52 & 0.50 & 0.50 & 48.90 & 68.49 & 61.49 \\ \hline t\({}_{4}\) & 5.03 & 4.82 & 4.74 & 0.85 & 1.99 & 2.38 \\ \hline t\({}_{5}\) & 0.35 & 0.34 & 0.31 & 65.22 & 84.12 & 73.81 \\ \hline \end{tabular}
\end{table} 
Table 3: The specific values of spatially averaged wall shear stress (SAWSS) and low WSS areas of all cases. Figure 9: The secondary flow velocity vector distributions of all three cases at t\({}_{4}\). The maximum and averaged secondary flow velocity in slices 1, 3 and 5 of the SPAC tubular valve, SPAC molded valve, and conventional valve are listed in Table 5. Obvious quantitative differences of both metrics in aorta were observed between the SPAC tubular valve case and the rest two valve designs. Figure 10 illustrates the strength of secondary flow in the aorta at the acceleration peak (t\({}_{4}\)). The secondary flow strength increased along the ascending aorta and the strongest secondary flow occurred near the aortic arch in all three cases. The specific values of the mean secondary velocity of all cases as well as the relative differences to the conventional case at t\({}_{4}\) are listed in Table 7. Although the mean secondary velocities in the aortic arch of both SPAC cases are around 10% higher than the conventional valve case, its magnitude in the AAo and DAo of the SPAC molded valve case is identical to that of the case of the conventional valve. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Slice**} & \multicolumn{3}{c}{**Percentage Difference in Averaged**} & \multicolumn{3}{c}{**Percentage Difference in Maximum**} \\  & \multicolumn{3}{c}{**Secondary Flow Velocity (\%)**} & \multicolumn{3}{c}{**Secondary Flow Velocity (\%)**} \\ \cline{2-7}  & **SPAC** & **SPAC** & **SPAC** & **SPAC** & **SPAC** & **Conventional** \\  & **Tubular** & **Molded** & **Tubular** & **Molded** & **Conventional** \\ \hline
1 & 27.75 & \(-\)0.21 & 0 & 157.26 & 0.57 & 0 \\ \hline
3 & 13.48 & 0.65 & 0 & \(-\)13.33 & \(-\)0.95 & 0 \\ \hline
5 & \(-\)15.44 & 0.01 & 0 & \(-\)26.42 & \(-\)1.65 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: The percentage differences of maximum and averaged secondary flow velocity of all designs at t\({}_{4}\). Figure 10: The mean secondary velocity of all three cases on five slices at t\({}_{4}\).