## 2 Materials and Methods  
The geometry of the mandibular bone was obtained from the computed tomographic images of the Sawbone 1337-3 model (Sawbone; Pacific Research Laboratories Inc., Vashon Island, WA, USA) at 0.625 mm intervals and digitized into the DICOM format. The geometry of the miniplates and screws was obtained from the manufacturer-provided information of the commercially available product for plates (10-51204 four-hole plate, thickness, 1.0 mm; bar, 12 mm straight gold; MONDEAL MEDICAL SYSTEM GMBH, Muhlheim a. d. Donau, Germany) and screws (10-82009 CF Screw; \(\upmu\), 2.0 mm; length, 9 mm, gold; MONDEAL MEDICAL SYSTEM GMBH, Muhlheim a. d. Donau, Germany). Three-dimensional solid models of different miniplate fixations on the mandible bone were reconstructed and assembled using a commercial software application (SolidWorks 2008; Dassault Systemes SolidWorks Corporation, Waltham, MA, USA). The integratedmodel was imported into the finite element (FE) package (ANSYS 19.0, ANSYS Inc., Canonsburg, PA, USA) and meshed using a 3D 10-node tetrahedral structure with an element size of 1.4 mm after the convergence of the FE model was calculated. Since the objective of this study was focused on the configuration of fixation, the interface between each component was assumed to be bonded and the friction between each component was ignored for saving calculation time. A 1 mm gap was created in the midline of the mandibular symphysis to simulate a fracture line. Three groups of fixation were studied (Table 1.). The first group is single four-hole plate group (S4 HP). We fixed a single centrally extended four-hole plate (S4 HP) on the anterior lower border of the mandible, 5 mm below the mental foramen. The second group is the perpendicular four-hole and two-hole plate group (Per4H2 HP). A two-hole plate (2 HP) was added on the inferior border of the S4 HP group in a perpendicular orientation. The 2 HP was fabricated with a six-hole plate, which was cut in half to form a pair of three-hole plates. The central hole of the plate acted as the central extension, and two lateral holes were used for fixation. The third group is the perpendicular double two-hole plate group (PerD2 HP). A pair of 2 HPs were fixed on the anterior lower border and inferior border of the mandible. The mandible bone and miniplate system in the FEA model were both assumed to be composed of homogeneous, isotropic, and linear elastic materials. The mechanical properties, including the Young's modulus (E) and Poisson's ratio (\(\
u\)) of the cortical bone (E = 14,000 MPa, \(\
u\) = 0.3), cancellous bone (E = 1500 MPa, \(\
u\) = 0.3), and minipilates and screws (E = 115,000 MPa, \(\
u\) = 0.35) were used in this study [27]. The interfaces between the bone, plate, and screws were all assumed to be bonded; however, the bone surface of the fracture incision site was set in contact. Because the stress around the fixation system was the major concern in this study, the interior structure of the teeth was not modelled and the mechanical properties were assumed as the cortical bone. After the mesh models were generated, the acting muscles and their vectors (force and direction) were applied according to the study by [PERSON] et al. (Table 2 and Figure 1) [28]. All surface nodes were fixed in the mandibular condyle region. The maximum von Mises stress (MaxVMS) of the plates, screws, and screw holes were evaluated to study the stress originally generated in S4 HP group, the shifting of stress after adding a perpendicularly oriented 2 HP in Per4H2 HP group, and the effects on stress when the plate holes on the anterior lower border of the plate were reduced in the PerD2 HP group. The MaxVMS of the plates and screws were compared with the yield strength of the plate at 830 MPa, and the MaxVMS of the screw holes was compared with the tensile strength of the mandible bone at 85 MPa [29]. The stability of the fixation was evaluated by measuring the displacement of the inferior border of the mandibular fracture site.