## 2 Materials and Methods  
The left coronary artery bifurcation models were reconstructed based on a reverse engineering (RE) technique by scanning two different shapes of artificial medical-trained coronary artery models by Nextengine (Nextengine Inc., Santa Monica, CA, USA). Each RE-based model was further transferred into a software of Geomagic Essentials (Geomagic Inc., Morrisville, NC, USA) for a surfacing process to generate a solid model of the basic coronary bifurcation artery. Two basic solid coronary artery bifurcation models (called artery A and artery B) with different shapes were generated with green color models, as shown in Figure 1. The left coronary artery bifurcation model in this study was composed of the left main coronary artery (LMCA), left anterior descending artery (LAD), and left circumflex artery (LCX), as shown in Figure 1. One of the two coronary artery models was larger in diameter and straighter in both the LCX and LAD side branches. Another model was smaller in diameter and more curved in the LCX side branch. These two types of the arterial models could reflect the majority of patients in a group of stenting stenosis in a clinic, not just presenting with the idealized model. The average diameters of LMCA, LAD, and LCX of the artery A are 4.4 mm, 3.9 mm, and 3.8 mm, respectively, and the original bifurcation angle of the artery A is 113\({}^{\circ}\). The average diameters of LMCA, LAD, and LCX of the artery B are 3.5 mm, 2.9 mm, and 2.5 mm, respectively, and the original bifurcation angle of the artery B is 142\({}^{\circ}\). Previous studies have pointed out that the bifurcation angles of the left coronary artery were different for each patient [26; 27]. In order to investigate the restenosis effects of the coronary artery bifurcation angles, this study defines three ranges for the coronary artery bifurcation angles: (a) small angle--the bifurcation angle was less than 90\({}^{\circ}\); (b) medium angle--the bifurcation angle was between 90\({}^{\circ}\) and 120\({}^{\circ}\); (c) large angle--the bifurcation angle was more than 120\({}^{\circ}\). Hence, three types of bifurcation angles of the arteries A and B in the small, medium, and large angles were remodelied in 80, 113, and 142\({}^{\circ}\), respectively. The variations of the bifurcation angles were mainly changed between the LAD and LCX arteries by a computer-aided procedure (SolidWorks 2010, SolidWorks Corp, Concord, MA, USA) to generate new models with different bifurcation angles. Three bifurcation angle models in the arteries A and B are also showed in Figure 1. The coronary artery models of this study were reconstructed from a human anatomical-based silicon model of the left coronary artery by reverse engineering scanning. The two silicon models of the left coronary artery have precise geometry to reflect the artery's contour, surface feature, and inlet and outlet diameters. The two models are mainly to replicate two types of left coronary arteries in size and shape of the human subjects. The two models are not reconstructed through a CAD procedure. The CAD arterial model has uniformity in the artery shape for each artery branch, particularly in the bifurcation region, and also reflects non-reality geometry. Hence, the two anatomically based models of this study can provide a reliable artery size and shape to investigate the stenting stenosis problem, but are not idealized models. Figure 1: The models of the left coronary bifurcation arteries. Two types of basic reverse engineering-based coronary bifurcation arteries (green color models) from different types of the artificial medical-trained artery, which was originally included in medium and large angles in the arteries A and B, respectively. Three angle types of solid models with small, medium, and large angles of the coronary bifurcation arteries were redesigned and changed by CAD modifying around the bifurcation region of the arteries A (upper row) and B (lower row).