# Hemodynamic Analysis on the Anastomosis Angle in Arteriovenous Graft Using Multiphase Blood Model
## 1 Introduction  
A lasting functioning vascular access is essential for renal function replacement therapy by hemodialysis. Surgical vascular access creation, including arteriovenous fistula (AVF) and arteriovenouson graft (AVG), are the preferred options for long-term dialysis compared to central venous catheters [1]. Although the dialysis access creation technique is widely used in clinical practice, long-term patency remains an unsolved major clinical problem for chronic hemodialysis treatment and a leading cause of morbidity and hospitalization in these patients [2]. The patency of vascular access for hemodialysis is mostly limited by growing stenoses that lead to decreased flow rate, thromboses, and, finally, access failure. Several risk factors are related to the patency of dialysis access, including sex, vessel size or distensibility, surgical technique, hypoxia, and an underlying uremic condition, but no clear pathophysiology has been elucidated yet [3, 4, 5]. Intimal hyperplasia is central to the pathology of hemodialysis access stenosis and occlusion [6]. Intimal hyperplasia has been widely studied in various vascular bypass surgeries, not limited to vascular access creation [7, 8]. In arterial bypass grafts, simulation or animal studies have reported that disturbed flow regions are seen at the heel, the toe, and at the floor of the distal end-to-side anastomosis, which corresponds to the disturbed flow regions [9]. Similarly, in vascular access for hemodialysis, wall shear stress (WSS) from the localized fluid pattern is believed to be one of the most important factors in developing intimal hyperplasia [5]. Endothelial cells probably play a key role in the change of wall properties and altered WSS, as endothelial cells are in direct contact with the flowing blood and can translate the physical stimuli of shear stress to a biological effect [10]. The WSS is suggested as an index for the prediction of stenosis resulting from intimal hyperplasia [11]. [PERSON] et al. found that low shear stress occurred where the stenosis progressed; it was also mentioned that this low wall shear stress causes damage to endothelial cells [12]. [PERSON] et al. found that high WSS and reverse flow could cause dysfunction of theAVF [13; 14]. [PERSON] et al. showed that AVF was associated with extremely high shear rates, also supporting the hypothesis that low and oscillating shear stress is the pathogenesis of the disease [15; 16]. The anastomotic angle has a significant impact on the local disturbed flow patterns in both types of vascular access and is a factor that can be altered by the surgeon [17; 18; 19]. Most studies were conducted on AVFs, and conflicting results on the recommended anastomotic angle associated with low-flow disturbance were observed [17; 19; 20]. Usually, the sites and types of hemodialysis access are primarily determined on the basis of the diameter and condition of the outflow vein and inflow artery [21]. In the case of AVF, there is little room for morphologic variation created by the surgeon because the configuration of the AVF is primarily determined by the patient's venous anatomy once the anastomosis is made. However, in the case of the AVG, the configuration may vary depending on the surgeon's experience and preferences, especially for the prosthetic brachial-antecubital forearm loop access. In most cases, a superficial vein located in the antecubital fossa is selected as the outflow vein. However, the basilic vein right above the elbow joint can also be utilized to save the upper arm veins when the forearm veins are unsuitable, as shown in Figure 1. When comparing with the antecubital veins as the outflow, the basilic vein above the elbow joint provides an almost parallel course to the graft with a more acute anastomotic angle. In practice, the anastomotic angle is not simply determined by the angle at which the end of the vessel was cut for the anastomosis on a three-dimensional plane.