## 2 Materials and Methods
### Construction of the Geometric Model  
The aim of constructing a geometric model was to produce a mathematical model, which represented the biological properties of the teeth and the periodontium. This was represented in terms of points (grids), lines, surfaces (patterns), and volume (hyper patches). A 3D cone beam computed tomography (CBCT) scan of six anterior teeth of the maxilla was taken. An average 0.25 mm thickness periodontal ligament was considered to generate the model around the root as the periodontal ligament is consistent in all areas. The normal apical-gingival height of the alveolar bone was considered to be 14 mm. Analysis system (ANSYS) software was used for geometric modeling (Figure 1).  
A Finite Element Model Construction from the Geometric Models  
A finite model was generated from the constructed geometric models explained in step 1, which represent the finite number of nodes and elements. This process is called discretization. The main idea behind discretization is to improve the accuracy of the results. These finite elements might be tetrahedrons, rectangular points, or hexahedrons (Figure 2). These elements are considered interconnected at joints which are called nodes or nodal points. The corner nodes are called primary external nodes. The additional nodes which occur on the sides of the elements are called secondary external nodes. The secondary nodes have fewer displacements than corner nodes. The number of finite elements and nodes used is presented in Table 1.  
Material Property Data Representation  
The alveolar bone along with maxillary teeth are the main structures that are included in this study. Each of these structures consists of different material properties. This study used the material property from [PERSON] et al. (2019) and [PERSON] et al. (2019). The average values for the material property are stated in the literature shown in Table 2.  
_Defining the Boundary Condition_  
A controlled model was imitated in order to avoid the free-body motions of the models, which are known as boundary conditions. The outer surface of the bones is attached to the nodes and fixed around the tooth to prevent the free body movement of the tooth.  
_Looding Configuration and Evaluation of Stress Distribution_  
At these steps, forces were applied at two different points. Therefore, two different models were prepared:  
1. Group 1: The maxillary teeth model consists of bonded brackets to a stainless-steel arch wire of 0.019 \(\times\) 0.025 dimension. The power arm was placed between the lateral incisor and canine at a height of 4 mm. The titanium mini screw implant of 1.3 \(\times\) 8 mm dimension was placed between the second premolar and first molar at a height of 9 mm. A NiTi coil spring of 9 mm length was attached from the mini screw implant to the power arm, which generated a force of 250 gm/side (Figure 3).
2. Group 2: The maxillary teeth model consists of bonded brackets to a stainless-steel arch wire of 0.019 \(\times\) 0.025 dimension. The power arm was placed between the lateral incisor and canine at a height of 8 mm. The titanium mini screw implant of 1.3 \(\times\) 8 mm dimension was placed between the second premolar and first molar at a height of 9 mm. A NiTi coil spring of 9 mm length was attached from the mini screw implant to the power arm, which generated a force of 250 gm/side (Figure 3).