# Numerical Investigation of the Relationship between
## 4 Discussion
### Comparison of Spiral-Flow-Inducing Graft Design vs. Conventional Graft Design  
To assess whether the inducement of spiral flow was beneficial to graft performance, a subsequent transient simulation was performed to compare the performance of the 30\({}^{\circ}\) graft with and without an internal ridge. The TAWSS was used as a basis for comparison between the two configurations. TAWSS is the temporal average of WSS in a single cardiac cycle [51]. Figure 14 shows the TAWSS contours of the host artery that has been grafted at a 30\({}^{\circ}\) anastomosis angle using non-spiral and spiral configurations. A qualitative analysis of the two models shows two prominent differences between the non-spiral and spiral flow. First, it can be seen that a conventional, non-spiral graft resulted in a symmetric TAWSS profile that extended distally from the anastomosis toe, whereas a ridged, spiral-flow-inducing graft resulted in an asymmetric one. This agreed with the findings of [PERSON] et al. [24; 25], showing that a ridged graft design resulted in an asymmetric TAWSS contour due to the bulk swirling motion in the host artery. Another noticeable difference lies in the region where the blood flow from the graft directly impinged the artery bed. In the non-spiral configuration of the graft, the said region was characterized by low TAWSS. Figure 13: Comparison of hemodynamic performance resulting from bypass grafts of varying anastomosis angles. Meanwhile, in the spiral graft configuration, elevated TAWSS was observed on the region, extending proximally from the anastomosis toe toward the occlusion. Closer inspection also shows higher TAWSS along the suture line of the anastomosis. This may also be explained by the fluid dynamics within bends where the change in fluid direction causes the fluid to shift toward the extrados due to inertial centrifugal forces. As such, the blood flow shifts toward the host artery bed where the bulk fluid motion and secondary flow components caused the generation of higher shear stresses. Quantitatively speaking, the spiral configuration resulted in higher TAWSS. Table 3 compares the maximum and area average values of TAWSS. The values were averaged across the entire length of the host artery. The non-spiral graft yielded a higher maximum TAWSS value, but its difference from the maximum value of the spiral configuration was practically negligible. On the contrary, the spiral configuration resulted in a higher TAWSS area average than that of its counterpart. In support of this, Figure 15 shows the percentage count of elements in the model according to the TAWSS value. As can be seen, a larger area of the artery was covered with elevated TAWSS when the spiral graft configuration was used. Conversely, at lower TAWSS, the non-spiral graft configuration had higher counts. Low TAWSS is associated with the development and progression of intimal hyperplasia. [PERSON] et al. performed a longitudinal study to observe hemodynamic values on implanted femoral bypass grafts. Through combined ultrasound imaging and CFD processes, they correlated regions of stenosis with low TAWSS [52]. Similarly, [PERSON] et al. linked low values of computed TAWSS to increased intimal thickening on lower limb venous bypass grafts measured through ultrasound imaging [53]. As previously described, low shear stresses acting on endothelial cells prevent the inhibitory effects of the nitric oxide signaling pathway against smooth muscle cells and increase the presence of low-density lipoproteins, macrophages, and adhesion molecules in affected areas. These reasons may explain why low TAWSS causes graft stenosis [3,41]. The use of the internal ridge to induce spiral flow in the blood may therefore enhance graft patency and longevity by raising TAWSS. The ability of spiral-flow-inducing grafts to raise TAWSS has been documented by several computational studies [23,25,54,55]. A study by [PERSON] et al. further confirmed the effectiveness of spiral flow in increasing the patency rates of arteriovenous grafts in vivo [18].