# Hemodynamic Analysis on the Anastomosis Angle in Arteriovenous Graft Using Multiphase Blood Model
## 4 Results and Discussion
### Effect of the Anastomosis Angle  
Vascular responses to high blood flow and WSS, and to low blood flow and WSS, are known to be endothelial cell-dependent [24]. The response to WSS varies between the autogenous AVF and the prosthetic AVG. For autogenous vein fistulas, intimal thickening was reported to correlate with low blood velocity and resulting low WSS [25, 26]. On the contrary, on the venous side of AVG, higher blood flow leads to flow disturbances and intima-media thickening [27]. Figure 8: Velocity w contour at the surface of Line (E), hematocrit is 58%, anastomosis angle of (**a–c**) are 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), respectively. Figure 9: Velocity, w, distribution according to the hematocrit at Line (E), anastomosis angle of (**a–c**) are 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), respectively. In our numerical study, a low WSS of \(<\) 0.2 Pa region was not observed. Therefore, we took higher WSS into consideration, which corresponds to the higher endothelial damage and resultant intimal hyperplasia. Figure 10 represents the WSS contour at the upper surface of the vein divided by the Y-Z plane (x = 0) ((a) Case 1: \(\theta\)g = 15\({}^{\circ}\), (b) Case 2: \(\theta\)g = 30\({}^{\circ}\), and (c) Case 3: \(\theta\)g = 45\({}^{\circ}\), hematocrit of injection needle is 58%). The WSS after the anastomosis (z = 0) showed over 3 Pa on the whole wall of the vein in Case 1, while the WSS of Cases 2 and 3 was \(<\)3 Pa, which corresponds to the shear stress of the normal limit of the vein. The lowest WSS value was 0.311 Pa at the upper surface of z-1. The WSS near the anastomosis was associated with the flow characteristics, which depends on the angle of anastomosis. The reason WSS was lower than 3 Pa in Cases 2 and 3 is that the flow velocity change near the wall is relatively low, as shown in Figure 9b,c. In particular, in Case 3, the very low WSS region occurs relatively broadly, as can be seen in Figure 9c, because the flow near the wall causes the recirculation flow in the opposite direction to the main flow, which flows from the graft to the vein anastomosis. In addition, high WSS, \(>\)11 Pa, occurs on both \(Y\)-axis walls. In particular, as the anastomosis angle increases, the high WSS area of both walls increases because the high flow velocity range is formed relatively close in the direction of both walls, as shown in Figure 8c. If the gradient of the flow velocity near the wall is large, the shear rate increases and the WSS also increases. Excessively high or low WSS is known to cause problems, such as intimal hyperplasia. Therefore, in terms of high WSS, Case 2 and Case 3 are advantageous in the vicinity of the anastomosis (Z \(<\) 10 mm), but there is a disadvantage in that the high WSS region is widened in the Z direction. Low WSS regions occur locally only below the anastomosis area (Z \(<\) 10 mm). Figure 11 shows the high WSS area over 11 Pa. The variation of the high WSS area is up to about 38%, depending on the anastomotic angle. However, as described in Figure 10 above, at a low anastomosis angle, a high WSS area occurs near the anastomotic site, and at a high anastomosis angle, a high WSS area occurs at a location away from the anastomosis site. In this study, the shape was simplified as much as possible for a parameter study on the effect of WSS with hematocrit. Therefore, it is difficult to conclude which anastomosis angle is appropriate considering the actual shape of vein anastomosis and the characteristics, such as vasodilation and intimal hyperplasia. Therefore, it is necessary to examine which angle is advantageous in terms of intimal proliferation and more diverse viewpoints. Additionally, there is a limitation in size, similar to the diameter of the vessels applied in the study. If the blood vessel is excessively dilated or has an excessively different shape, additional considerations for the flow are required.