# Three-Dimensional Force Characterizations in Maximly Molar Distalization: A Finite Element Study
## 2 Materials and Methods  
A 3D model containing the mandible and maxilla was reconstructed from CBCT scanning images, which were obtained from a volunteer with consent. The premolar was absent in the image. Otherwise, no other periodontal conditions were observed from CBCT scanning or mentioned when consulting with the volunteer. The model reconstruction was implemented with open-source software, 3D Slicer (3D Slicer, version 5.0.3, open-source, Boston, MA, USA) [39]. The model reconstruction procedure is shown in Figure 1 and briefly described here. The maxilla, mandible, and teeth were segmented based on the gray value of each pixel with a built-in algorithm: region-growing segmentation. A smoothing operation was adopted to obtain a smooth geometry. Based on the interest of our study, only a half side of the segmented model, containing the maxilla, mandible, and teeth, was kept and exported as Standard Triangle Language (STL) files for FEA simulation, shown in Figure 1a. The 3D model of the JVB was from the manufacturer. The 3D models of the CM3D and CM3D Clear were built with open-source software, Onshape (Onshape, Education 1.16, Boston, MA, USA), based on the real model from our collaborator. The length of the appliance was about 28.5 mm and 30.1 mm for the JVB and both CM3 Ds, respectively. Of note, the CM3D (middle) and CM3D Clear (bottom) have similar bar lengths and hook location, shown in Figure 1b, which suggests that any force induced may cause the comparable reaction force and moment. All MSD models were in Standard for the Exchange of Product Data (STEP) format. The mandibular and maxillary models and each of the MSDs were assembled in Ansys SpaceClaim (Ansys(r) SpaceClaim, release 2022R1, Canonsburg, PA, USA), shown in Figure 1c. In this work, the MSDs were implemented on the canine and second molar, inspired by the clinical example [19], while the MSD connection between the canine and the first molar was also frequently applied clinically. The MSDs were connected on the upper left (UL) 3 and UL7, which are maxillary canine and molar teeth. The mechanical properties of the maxilla, the tooth, and all MSDs are shown in Table 1. All materials in the FEA were assumed homogeneous, isotropic, and linear elastic materials. The teeth were assumed as homogeneous materials, with a Young's modulus of 19.6 GPa and Poisson's ratio of 0.3 [22]. The material of the JVB and CM3D is stainless steel, which has a Young's modulus of 200 GPa and Poisson's ratio of 0.3 [33]. The material of the  
Figure 1: Process of producing FEA model from CBCT image. (**a**) Segmentation of CBCT in 3D slicer, including transverse, sagittal, and coronal view of CBCT, and segmented model; (**b**) model of JVB, CM3D, and CM3D Clear; (**c**) assembly of JVB with maxilla and teeth in SpaceClaim. CM3D Clear is medical-grade polystyrene, which has a Young's modulus of 3 GPa and Poisson's ratio of 0.33 [40]. Due to the much softer material, the arm of the CM3D Clear was thicker than the normal CM3D to keep the structural strength, as shown in Figure 1b. In our simulation, the deformation of the maxilla is not the focus of this study. This work focused on the 3D characterization of the reaction force directly induced by MSDs, so a rigid body behavior (i.e., a significantly higher Young's modulus of 1000 GPa than that of a tooth) was assigned to the maxilla to minimize the load sharing with neighbor teeth [41]. The maxilla, mandible, dentition, and MSDs were imported into Ansys Workbench 2022 R1 software (Ansys Static Structural analysis software, release 2022R1, Ansys(r) Inc., Canonsburg, PA, USA) to define the contact relation before performing FEA. Both the JVB and CM3D were bonded with a maxillary canine and molar, as shown in Figure 1c. In our simulation, a concentrated force was applied on the hook of the MSDs based on the observation that the force was induced by the ortho elastic connecting the hook and mandibular molar.