## 1 Introduction  
Mandibular symphysis fractures are the most common types of facial bone fractures [1, 2] and account for 13.8-27.5% of all mandible fractures [3, 4, 5, 6]. The purpose of treatment is adequate reduction with stable internal fixation to decrease the micromotion to less than 150 \(\upmu\)m to minimize nonunion [7, 8, 9], restore occlusion, and restore mastication. Currently, microplates, mulipulates, locking plates, reconstruction plates, compression plates [10], and lag screws are used for internal fixation. According to [PERSON] [11], double-plate fixation is more stable than single-plate fixation. [PERSON] et al. showed that double four-hole plate fixation has lower stress than a single four-hole plate, regardless of the location of biting force (inter-cuspal, incisal, and left unilateral molar) [12]. Therefore, the current popular approach is to use the parallel double four-hole plates (ParD4 HP) oriented along Champy's ideal osteosynthesis line on the mandibular anterior lower border (buccal side). The fracture pattern on the symphysis area is usually simple, but the forces acting on this region are complex. The ParD4 HP method was reported to be able to sustain the negative bending moments produced by the masseter and temporalis muscles [13], which contract to produce tension force on the lower margin of the mandible and compression force on the gingiva area [14]. It can also resist the light shear force [15] but high torsion moment [14, 16] on the mandibular symphysis area. The discussion about the best internal fixation method [17] has not been extensive because the number and orientation of plates seems straightforward, and experience is the key factor [18]. However, if mandibular symphysis fractures are accompanied by body, angle, or subcondylar fractures, parallel double-plate fixation on the anterior/buccal side alone cannot prevent the posterior/lingual side from separation, thus causing inadequate reduction, malocclusion, and widening of the inter-gonal distance [19; 20]. If subcondylar fractures are to be treated conservatively, fixation on the mandibular symphysis must be very stable to maintain the width of the mandible [21]. Owing to the advantages of increased calculation capacity of the computer, cost-efficiency and the consistency of the test protocol, finite element (FE) analysis has become a powerful approach for biomechanical research [22; 23; 24; 25; 26]. Despite irregular geometry and uncertain loading conditions, FE modeling can achieve a three-dimensional representation of the biomechanical response for the internal or external structure. In 2006, [PERSON] et al. used three-dimensional finite element analysis to study the effectiveness of perpendicular double four-hole plate (PerD4 HP) fixation on a mandibular symphysis fracture [18]. They found that PerD4 HP was more suitable and stable than ParD4 HP in the fixation of mandibular symphysis fractures. The maximal stress of screw holes was significantly lower in the PerD4 HP group than that in the ParD4 HP group, indicating the presence of a stable fixation [18]. However, plate-screw stress and displacement showed no significant differences. Because the strain and displacement on the lingual site of the mandibular symphysis fracture are higher than those on the buccal side [15], the gap on the margin of the fracture site is a direct indicator of stability [18]. The displacement of fracture sites by [PERSON] et al. was 171 \(\upmu\)m (range, 10-310 \(\upmu\)m), which is stable enough under usual conditions unless the maximal biting force is applied. The number of screws performed an important role in the stress sharing of the fixation plates. Traditionally, four-hole plate fixation with two holes on each side, with or without central extension, is the most popular method. [PERSON] et al. [18] and [PERSON] et al. [12] pointed out that the maximum von Mises stress was concentrated on the two central screws near the fracture site despite the single four-hole plate (S4 HP), ParD4 HP, or PerD4 HP. [PERSON] et al.