# Hemodynamic Analysis on the Anastomosis Angle in Arteriovenous Graft Using Multiphase Blood Model
## 4 Results and Discussion  
### Hematocrit and Flow Analysis  
Figure 6 shows the hematocrit in Line (E) with a vein anastomosis angle of 45\({}^{\circ}\) and 5 mm away from the tip of the vein anastomosis site. The dimensionless radius of \(-1\) is the bottom surface of the vein, and dimensionless radius 1 is the top surface (x = 0). Blood with high hematocrit from the injection needle flows into the graft. Blood with high hematocrit mixes with blood flowing along the graft from the artery and flows into the vein anastomosis area. At the Line (E) position, the maximum hematocrit falls by about 2% from about 45% to 43% and from 58% to 56%. Because the graft length is short compared to the flow rate, blood flowing into the graft from the needle is concentrated in the center of the graft and flows into vein anastomosis. Due to this fluid characteristic, hematocrit is concentrated in the dimensionless radius 0.5 part. This hematocrit shows a high value at the bottom (dimensionless radius \(-1\)) at end-diastolic velocity (EDV), where the artery flow rate is relatively slower than peak systolic velocity (PSV) because when the flow rate into vein anastomosis is high, the hematocrit mixes less with the surrounding area.  
Figure 7 shows the viscosity at Line (E). The multiphase blood model has a characteristic of shear-thinning blood in which the viscosity decreases as the shear rate of the blood increases, and the viscosity increases as the hematocrit increases. The viscosity is generally low near the wall and high at the center of the flow because the shear rate is high near the wall. Viscosity varies according to hematocrit in areas with high hematocrit blood flow from the graft (dimensionless radius \(-1\) to 0). On the contrary, the viscosity does not change according to the hematocrit between dimensionless 0 and 1, where there is no change in hematocrit.  
Figure 5: Grid independence test at Line (D).  
Figure 8 is the contour of the X-Y plane for the velocity w component at the Line (E) location with hematocrit 58%. The anastomosis angles of Figure 8a-c are 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), respectively. As the anastomosis angle increases, the flow velocity from the graft to the vein anastomosis increases in an elliptical shape. On the contrary, the flow rate toward the upper surface decreases. The reason for the decrease in the flow velocity on the upper surface side is that recirculation flow occurs.  
Figure 6: Hematocrit distribution at Line (E), anastomosis angle is 45\({}^{\circ}\), the hematocrit is concentrated in a parabolic shape under the influence of flow from the graft.  
Figure 7: Viscosity distribution at Line (E), anastomosis angle is 45\({}^{\circ}\).  
Figure 9 is the velocity, w, distribution according to hematocrit. The higher the hematocrit, the higher the peak velocity, w, tends to increase slightly. In particular, in the case of 45\({}^{\circ}\), where the relatively high flow velocity range is concentrated in the center, the shear rate at the center is lowered, and as can be seen in Figure 2, the viscosity increases rapidly at the low shear rate range, so the change in the velocity, w, tends to increase.