## 1 Introduction  
Aortic coarctation (CoA) (i.e., a narrowing in the aorta) is one of the common congenital heart defects [1]. Its severity is associated with an elevated pressure gradient and blood velocity [2]. Common treatment techniques adopted by cardiothoracic surgeons include end-to-end anastomosis, balloon angioplasty and graft repair [3]. Specifically, the graft repair is preferred for diffuse arch hypoplasia [4]. A clinical study of patients demonstrated the efficacy of graft repair [5]. The major complications include recoarctation and aneurysms at the graft site. These complications are well acknowledged to be associated with altered biomechanical environments (i.e., hemodynamics and solid wall mechanics at the graft zone) [6]. A stiff Dacron graft, adopted in 1952, resulted in early and late complications following the repair by material mismatch [7]. A relatively soft polytetrafluoroethylene (PTFE) graft mitigates the material mismatch with the native tissue and exhibits a better clinical outcome [8; 9]. The autologous graft, homograft, or heterograft further reduces the material mismatch with the native tissue. For example, the pulmonary artery homograft, compared with the PTFE, has a stiffness closer to the native tissue [10]. CorMatrix extracellular matrix, a heterograft made from the decellularized porcine small intestinal submuc [11], is commonly used in aortic reconstruction due to its commercial availability. Regardless of the diminished variation between graft materials and native tissue, the surgical repair of the aortic arch is still suboptimal in terms of late complications such as recoarctation [12]. The geometric feature may significantly affect the blood flow dynamics [13]. Specifically, the aortic arch shape (i.e., the arch angle, curvature, and cross section dimensions) has been associated with a disturbed flow [14], which in turn causes late aortic remodeling [15]. It has been shown that flow disturbance and recirculation contributes to endothelial dysfunction, localization of atherosclerosis, and arterial thickening by upregulating endothelial cell genes, leukocyte adhesion, permeability, and so on [16; 17]. From the perspective of mechanics, the graft geometry that deviates from the native arch causes suboptimal hemodynamics immediately after the surgical repair, and thus results in early and late clinical complications. However, there is scant data on the role of graft shapes on the reconstructed mechanical environments of the aortic arch. In addition, the documented clinical studies of aortic arch repair generally ignore the specification or description of graft shapes [18]. The graft shape adopted by our clinical coauthors was considered as the baseline of this work. It looked like a half-moon from its anterior view, and therefore it was referred to as the half-moon shaped graft. The goal of this work was to quantitatively depict the underlying mechanism of aortic arch repair. The impacts of graft shapes and materials on the hemodynamics and wall mechanics of the aortic arch following surgical repair were characterized. The three-dimensional aortic arch model was reconstructed from magnetic resonance images (MRIs). Three commonly used graft materials (i.e., PTFE, CorMatrix, and pulmonary homograft) were studied. A crescent graft was proposed to better resemble the curvature of the aortic arch in comparison to the half-moon shaped graft as illustrated in Figure 1. Both grafts were named by their anterior view. There were a total of five model configurations in terms of graft materials and shapes. Their roles in the hemodynamics and solid wall mechanics were quantified through numerical fluid-structure interaction (FSI) analysis. The wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT), and von Mises stress distributions on the aortic wall were obtained and compared among the five choices. These mechanical indices have been associated with clinical outcomes. Results were expected to provide a mechanistic understanding of the optimum surgical repair.