## 3 Results
### Influence of Graft Materials  
Various graft materials were commercially available for the aortic arch repair. The role of the graft material properties on their von Mises stress distributions using the commonly adopted half-moon shape are illustrated in Figure 9. Generally, stresses on the grafts were larger than on the adjacent tissue, and stress concentrations were observed at the interface between the graft and the native tissue. A stiffer graft resulted in larger stress concentrations. The peak von Mises stresses for PTFE, CorMatrix, pulmonary, and native tissue equivalent grafts were 2.067 MPa, 0.638 MPa, 0.251 MPa, and 0.109 MPa, respectively. To further illustrate the stress-shielding effect of the graft, the von Mises stresses along two pathlines, representing the lower border of the graft or the native tissue with an offset of 13 mm from the superior border of the graft, are depicted in Figure 10. The peak von Mises stress for both pathlines was generally located around the proximal or distal borders of the graft. The stiffer graft shielded much more stress for the adjacent native tissue, leading to a much smaller stress on the native tissue. This could be explained by the larger load-sharing capacity of the stiffer graft. Specifically, the peak von Mises stresses at the lower border of the graft were 1.808 MPa, 0.637 MPa, 0.204 MPa, and 0.090 MPa in order of the PTFE, CorMatrix, pulmonary, and native tissue equivalent materials, respectively. The corresponding stresses at the native tissue pathline were 0.039 MPa, 0.047 MPa, 0.050 MPa, and, 0.051 MPa, respectively.  
Figure 9: Stress distributions at t = 0.4 s (peak systolic pressure): (**a**) PTFE graft = 1000 MPa, (**b**) Commatrix graft = 30 MPa, (**c**) pulmonary graft = 3 MPa, and (**d**) native tissue equivalent graft = 0.84 MPa.  
The graft material-induced blood flow dynamics had similar patterns as illustrated in Figure 6a,b. Reversed flow patterns were observed near the inner curvature of the aortic arch. The reversed flow region expanded with a softer graft material. The relation between graft compliance and the flow pulsation during one cardiac cycle is summarized in Table 3. It was obvious that the aortic cross-sectional areas increased with the softer graft materials. As the stiffness of the graft material reduced, the maximum velocity at systolic phase reduced, and the maximum velocity at diastolic phase increased. This implied that the flow pulsation during one cardiac cycle, represented by the maximum velocity difference between 0.4 s and 0.6 s, was increased with a stiffer graft.  
Various graft materials resulted in a similar percentage area of low TAWSS, high OSI, and high RRT, calculated over the graft region, as shown in Figure 8. Specifically, for the adopted four graft materials, the percentage areas of low TAWSS (<0.2 Pa), high OSI (>0.2), and high RRT (>10 Pa\({}^{-1}\)) were 0.363 \(\pm\) 0.015, 0.158 \(\pm\) 0.014, and 0.253 \(\pm\) 0.005, respectively. The corresponding relative standard deviations were 4.12%, 8.97%, and 1.89%, respectively. This implies that the pathological hemodynamic parameters were not sensitive to graft materials.