# Numerical Investigation of the Relationship between
## 1 Introduction  
Atherosclerosis is one of the most prevalent types of and precursor to cardiovascular diseases. It is characterized by the narrowing or complete occlusion of the arterial lumen due to the deposition of different substances such as fat or cholesterol onto the artery walls. These plaque-obstructed arteries reduce blood flow in affected tissues or organs, resulting in reduced oxygen and nutrient supply that can cause other cardiovascular conditions [1]. Bypass grafting is a common procedure used to restore normal blood flow in areas affected by atherosclerosis. Bypass grafting can be carried out using either autologous or synthetic grafts. However, both autologous and synthetic bypass grafts face significant failure rates. They commonly fail due to intimal hyperplasia, atherosclerosis, and thrombosis. These failures are often linked to disturbed hemodynamics in affected areas [2]. Disturbances in normal, physiologic hemodynamics are often linked to the development and progression of common vascular diseases. In particular, wall shear stress (WSS)has been a useful hemodynamic indicator of vascular pathogenesis. Low WSS is associated with smooth muscle cell proliferation linked to intimal thickening and an increase in adhesion molecules and low-density lipoprotein deposition linked to atherosclerosis [3]. Meanwhile, high WSS is associated with endothelial cell damage linked to thrombosis and the formation of lesions [4; 5; 6]. Increased synthesis of vascular endothelial growth factors at higher WSS has also been linked to intimal hyperplasia [7]. This lack of consensus as to the optimal WSS value highlights the need for caution when selecting WSS thresholds for optimization purposes. A safer approach would be to consider that normal, physiological WSS levels range from 0.1 Pa to 7 Pa [8; 9]. Due to the association of disturbed hemodynamics with cardiovascular diseases, some studies have capitalized on the relationship between hemodynamics and endothelial homeostasis to manage vascular diseases. Pharmacological studies have utilized the irregular hemodynamics in diseased vessels to create shear-activated drug delivery systems. [PERSON] et al., for example, looked into the possibility of using the high shear stress associated with thrombosis in delivering treatment to affected areas. Using numerical analysis, they studied how different types of drug delivery agglomerates respond to fluid dynamic stresses and what conditions are needed to optimally form these drug delivery systems. Physiologic shear conditions retain the structure of these nanoparticles while the high shear caused by clots fragments these structures and causes the release of lysing agents necessary to remove lumen occlusion [10; 11]. These studies indicate great promise for using mechanical-responsive drug delivery systems in vascular diseases, but the technology is yet to be practically useful as current research is still limited [12]. Meanwhile, to prolong graft patency, the minimization of hemodynamic disturbances has become one of the most important guidelines in modern bypass graft designs. One particular line of research in bypass graft studies looks into the utility of spiral flow in improving bypass graft hemodynamics. Spiral flow is believed to be an indicator of a healthy vascular system, and it is observed to have potentially beneficial effects in bypass graft hemodynamics [13; 14]. [PERSON] et al. determined how spiral flow affects the washout characteristics in regions prone to atheorth thrombosis. They used a spiral-flow-inducing mechanism to supply straight and spiral flow into 3D-printed angled conduits and used ultrasound visualization to qualitatively describe spiral flow in pipe bends which are predictable stasis zones. The authors then used CFD to analyze the impacts of spirality on these thrombosis-prone regions. The spiral flow was determined to have decreased areas of low velocity, imparted more uniform mixing, improved flow near the walls, and reduced retrograde flow [15].