## 2 Materials and Methods  
To analyze the stability of the implant and bone tissue based on bone quality and peri-implant bone loss, two bone models with different material properties (normal bone and low-quality bone) and six models with levels of bone loss (0, 1, 2, 3, 4, and 5 mm) were constructed. To reflect the anatomical structure of the bone, a three-dimensional (3D) model of the mandible was segmented from oral and maxillofacial computed tomography (CT) using medical image processing software (Mimics 26.0, Materialise Corporation, Leuven, Belgium). Using 3D modeling software (3-matic Research 18.0, Materialise Corporation, Leuven, Belgium), the mandibular region of the molar area was reconstructed by dividing it into cortical bone and cancellous bone, and then the implant fixture was implanted. The thickness and shape of the cortical and cancellous bone layers were configured based on actual anatomical proportions, with the cancellous bone positioned in the center and surrounded by a 2 mm thick cortical bone layer [28]. The implant is a type that is internally connected at the bone level and consists of a crown, cement, abutment, screw, and fixture model. The fixture was designed with a diameter of 4.0 mm and a length of 10.0 mm (Figure 1a). The peri-implant bone loss model implemented vertical bone loss based on a baseline model with standard bone height. By reducing the bone height in 1 mm increments, models with bone loss levels of 1, 2, 3, 4, and 5 mm were created (Figure 1b) [29; 30; 31]. The mesh consists of four-node tetrahedral elements, and the mesh convergence test was conducted by gradually reducing the mesh size according to previous studies [32]. Considering computational efficiency and result convergence, the mesh size was determined to be appropriate for FEA (Figure 2a). Table 1 lists the element size, number of nodes, and number of elements for each structure. Figure 1: Three-dimensional model: (**a**) composition of implants and bone; (**b**) peri-implant bone loss. Figure 2: Finite element model: (**a**) surface and volume mesh; (**b**) loading and boundary conditions. The finite element model with surface and volume meshes was transferred to the FEA software (Abaqus version 6.14-3, Dassault Systemes Simulia Corporation, Johnston, RI, USA) to perform static simulations. The implant components and bone tissue were assumed to be isotropic, homogeneous, and linearly elastic [33]. The normal bone model was set to have a general elastic modulus, and the low-quality bone model reflected a state of reduced bone strength, such as osteoporosis [34]. In the implant components, the crown type is all-ceramic, the cement type is temporary cement, and the abutment, screw, and fixture are selected as titanium [35; 36; 37]. The material properties assigned to the implant components and bone tissue are shown in Table 2.  
To implement the state where the surrounding tissues support the mandible, the cross-sections on both sides of the bone model were fixed in all directions to limit displacement. Each implant component and the implant-bone interface were set to a bonded condition. The implant-bone interface condition is assumed to be complete osseointegration. The loading condition was applied in two steps (Figure 2b). In the first step, the torque wrench was defined as the sum of the forces generated at the top and bottom of the screw during tightening. The torque wrench was set to 32 N\(\cdot\)cm, and an appropriate preload was applied to the top and bottom surfaces of the screw [38]. In the second step, a maximum occlusal force of 200 N was applied in the tooth axial direction to the occlusal surface of the crown [39; 40]. A total of 50 nodes were applied to six occlusal poin