# Numerical Investigation of the Relationship between
## 1 Introduction
However, one issue in the multiple studies performed by their team is they only optimized the graft design based on the assumption that higher WSS leads to better graft performance. They did not consider that higher WSS may also lead to detrimental biological effects. Nonetheless, it has been shown that the induction of spiral flow can be achieved through the modification of conventional bypass graft geometry, and evidence suggests its effectiveness compared to traditional counterparts. Of particular interest are the ridged bypass grafts. Their simple geometry is attractive from a manufacturing perspective, and preliminary results show promising performance. However, existing studies have not taken into consideration the effect of the anastomosis angle in their performance. In the literature it is well-documented that the angle between the bypass graft and host artery largely influences the flow field within the anastomosis region, making it a useful design criterion for optimizing the hemodynamic performance of bypass grafts. [PERSON] et al. have shown, using CFD and particle image velocimetry, that the anastomosis angle in coronary artery bypass grafts has a positive correlation with local flow field disturbances. As the anastomosis angle increases, the number and extent of recirculation areas subsequently increase, indicating how inappropriate anastomosis angles may cause complications in treated vessels [26]. [PERSON] et al. correlated anastomosis angles with real-world patient images of arteriovenous grafts. Patient-specific models of bypass grafts plagued with stenotic lesions were numerically observed. Their findings show that flow disturbances were observed directly in areas affected by the stenotic lesions and the extent of these disturbances was dependent on the anastomosis angle. This study brings forth real-world evidence of the role of the anastomosis angle in vascular pathogenesis [27]. [PERSON] et al. attempted to minimize pathological flow fields in arteriovenous grafts through the optimization of the anastomosis angle. CFD revealed that intermediate values are the most suitable for bypass grafts since smaller anastomosis angles caused a substantial increase in pathologically low WSS while larger anastomosis angles caused an increase in pathologically high wall shear stress. Their study implies that the optimization of the anastomosis angle is an effective strategy for ensuring endothelial homeostasis in bypass grafting [28]. These studies show the huge impact of the anastomosis angle on the local hemodynamics of the anastomosis region, highlighting the importance of optimizing it to create more favorable blood flow conditions to prevent bypass graft failure [29,30]. However, these studies only use traditional bypass graft designs, and the effect of the anastomosis angle on spiral flow bypass grafts is yet to be explored in the literature. In summary, we have seen from our literature review that although bypass grafting is already an established medical intervention for atherosclerosis, there is still a need for improving the technology because of the high failure rate observed for bypass grafts. These failures are linked to disturbed hemodynamics in affected areas which can effectively be controlled by altering the bypass graft geometry. The use of ridged spiral flow bypass grafts has been gaining attention in academia due to their stabilizing effects on the hemodynamics of the anastomosis region. However, there is still no study focusing on how the performance of ridged spiral flow bypass grafts is affected by the anastomosis angle. The anastomosis angle by itself is a useful tool for reducing hemodynamic disturbances within the anastomosis region due to its influence on local flow fields. The effects of anastomosis angle and spirality in blood flow must therefore be looked into since the combined effects of these two may provide a means to address the problems associated with bypass grafting.