## 3 Results
### Influence of Graft Shapes
The maximum velocity of the crescent graft was 24.1% higher than that of the half-moon one due to the smaller area and relatively larger mass flow rate. It is interesting to observe that during diastolic phase (0.6 s), the maximum velocity of the half-moon graft was 22.7% higher than that of the crescent one although the cross-sectional area of the half-moon graft was 30.1% larger than that of the crescent one. This could be explained by the vena contracta effect [35]. The positive flow area (PFA), as illustrated in Figure 7, is the area with only forward flow. The PFA at the cross-section B-B\({}^{\prime}\) at 0.6 s for the half-moon and crescent grafts was 364.8 mm\({}^{2}\) and 344.3 mm\({}^{2}\), respectively. The PFA at the cross-section B-B\({}^{\prime}\) at 0.6 s in the half-moon graft was 31% smaller than the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Area (mm\({}^{2}\))** & **Area (mm\({}^{2}\))** & **V\({}_{max}\) (m/s)** & **V\({}_{max}\) (m/s)** & \(\dot{m}\) (kg/s) at & \(\dot{m}\) (kg/s) at \\  & **at 0.4 s** & **at 0.6 s** & **at 0.4 s** & **at 0.6 s** & **0.4 s** & **0.6 s** \\ \hline
**Half-moon** & & & & & & \\
**(A-A\({}^{\prime}\))** & 454.8 & 437.7 & 0.236 & 0.073 & 0.08592 & 0.01905 \\
**Crescent** & & & & & & \\
**(A-A\({}^{\prime}\))** & 480.4 & 464.4 & 0.237 & 0.070 & 0.09555 & 0.02070 \\
**Half-moon** & 484.1 & 461.0 & 0.170 & 0.092 & 0.04926 & 0.01735 \\
**Crescent** & & & & & & \\
**(B-B\({}^{\prime}\))** & 367.0 & 354.4 & 0.224 & 0.075 & 0.05090 & 0.01771 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cross-sectional areas, maximum velocities and mass flow rates of A-A\({}^{\prime}\) and B-B\({}^{\prime}\) at both 0.4 s and 0.6 s.  
Figure 6: Velocity distributions with y-direction velocity vectors without any projection at two different time points (0.4 s and 0.6 s) and two different cross-sections (A-A\({}^{\prime}\) and B-B\({}^{\prime}\)) in the half-moon and crescent pulmonary grafts: (**a**) half-moon graft at 0.4 s, (**b**) half-moon graft at 0.6 s, (**c**) crescent graft at 0.4 s, and (**d**) crescent graft at 0.6 s.  
total cross-sectional area, while the difference in the crescent one was minimal (i.e., 2.9%). Moreover, the mass flow rate in the PFA of the half-moon graft was 8.4% higher than that of the crescent graft. Therefore, the maximum velocity in the half-moon graft was higher than that in the crescent graft. The percentage areas of low TAWSS, high OSI and high RRT, viewed from the bottom of the aortic arch, are shown in Figure 8. The crescent graft, compared with the half-moon one, demonstrated a smaller percentage area of low TAWSS, high OSI and high RRT, which was calculated over the graft region. Specifically, the percentage areas of low TAWSS (i.e., less than 0.2 Pa) were 0.360 and 0.046 for the half-moon and crescent graft, respectively; the corresponding high OSIs, (i.e., larger than 0.2) were 0.161 and 0.030, respectively; the high RRTs (i.e., larger than 10 Pa\({}^{-1}\)) were 0.260 and 0.028, respectively. These were associated with the potential clinical outcomes. Figure 8: Distributions of TAWSS (\(<\) 0.2 Pa), OSI (\(>\) 0.2) and RRT (\(>\) 10 Pa\({}^{-1}\)) for the half-moon-shaped (**a**) and crescent-shaped (**b**) pulmonary grafts: views from the bottom of the aortic arch. Figure 7: Area enclosed by the boundary line and shaded positive flow area (PFA) at the cross-section B-B\({}^{\prime}\) at 0.6 s: (**a**) half-moon graft and (**b**) crescent graft.