# Numerical Investigation of the Relationship between
## 1 Introduction
In a study by [PERSON] et al., they determined the effect of spiral blood flow on the WSS in a stenosed model of the left main coronary artery. They assessed the WSS according to varying take-off angles, stenosis severity, and eccentricity using CFD. The results of their study indicate that spiral blood flow may be atheoprotective as it reduces the maximum WSS in the stenosis region and the post-stenoic regions affected by low WSS [16]. [PERSON] et al. showed in their study that spiral blood flow through a stenosed arterial region is beneficial. Using CFD, they observed that for an axisymmetric stenosis, swirling flow has the beneficial effect of reducing the turbulent kinetic energy in the post-stenosis region of the artery. They argued that the turbulent kinetic energy may damage blood cell materials and activate blood platelets, which may result in the development of diseases. Despite this beneficial effect, they also showed that spiral flow may induce detrimental effects on the vascular network as it may induce the development of oscillatory WSS and recirculation zones which may cause endothelial damage and thrombosis, respectively [17]. [PERSON] et al. studied the use of spiral-flow-inducing grafts for arteriovenous (AV) channels. They used the spiral flow AV graft on patients with no available surficial veins for access sites in the upper arm, forearm, and chest wall. After one year of observations, they showed that the use of spiral flow grafts has patency rates superior to historic data from expanded polytetrafluoroethylene (ePTFE) grafts and heparin-bonded grafts. The results show minimal complications in subjects. This in vivo study showcases the practical use of spiral flow grafts and their effectiveness [18]. Inshort, these studies indicate that inducing spiral flow for the higher, atheroprotective shear stress generated by such flow is a possible strategy for improving bypass graft longevity. Further research on the application of spiral flow in bypass graft design must therefore be undertaken to capitalize on its stabilizing effects on hemodynamics. A few studies have recently attempted to capitalize on the benefits offered by spiral flow in bypass grafts by modifying conventional bypass graft designs to induce a swirling fluid motion. In modifying the design, a practical approach must be taken to ensure fast and inexpensive design verification. Numerical simulations have become an integral part of the design process across different industries [19; 20; 21; 22]. In bypass graft design, fluid flow simulations such as computational fluid dynamics (CFD) and fluid-structure interaction (FSI) analysis have been extremely useful. [PERSON] et al. utilized spiral folds in the inner walls of an artificial blood vessel to induce spiral flow. They performed FSI analysis and verified that such spiral folds can cause swirling flows with the three-dimensional bifurcation model. By increasing the pitch of the helix and the cross-sectional area of the artificial blood vessel, they were able to observe increased WSS and deformation [23]. In a particular in silico study, [PERSON] et al. tried to improve the patency of a bypass graft for the femoral artery. They optimized its design by incorporating an internal ridge within the graft and assessing the effect of different geometric properties such as the shape, orientation, and number of ridges on blood flow. They concluded that the shape and orientation of the ridge are critical in improving bypass graft performance [24]. In another study by the same team, they compared the results of flow in peripheral artery bypass grafts designed with straight, spiral, helical, and hybrid configurations through CFD. Based on the results, it has been shown that the incorporation of spirality and/or helicity results in better hemodynamic properties with increased secondary velocity, increased time-averaged wall shear stress (TAWSS), reduced oscillatory shear index, and reduced relative residence time [25].