## 4 Discussion  
In this study, the most important finding was the significant difference in displacement between the S4 HP and perpendicular plate fixation. There was even at the fracture site, and the displacement was 0.311 mm in the S4 HP group. When 2 HP was added to the mandibular inferior border (Per4H2 HP), the displacement was 0.034 mm (\(-\)89.06%), and there was no evasion at the fracture site. Furthermore, when the holes on the plate on the mandibular anterior lower border decreased from four (Per4H2 HP) to two (PerD2 HP), the displacement was 0.025 mm (\(-\)91.96%), and there was no evasion at the fracture site. The apparently lower displacement on the fracture site revealed that the PerD2 HP group was as stable as the Per4H2 HP group and more stable than the S4 HP group.  
In 1992, [PERSON] and [PERSON] proposed that the best way to fix the mandible fracture is to orient the plates on different axes [30]. However, the concept of perpendicular plate fixation has not been explored. [PERSON] et al. found that a high-tension force was present on the lower margin of the mandibular symphysis fracture and high compression force, on the gingiva area. In addition, the strain and deformity on the lingual side were larger than those on the buccal side [15], thus causing mandible version. To prevent this, thick plates or over-bent plates were used [31]. However, thick plates have a high strain and stress shielding effect, but widening the plate can decrease the strain and increase the force against fracture site version [15]. It is not easy to increase the width of the plate, but ParD4 HP can achieve this goal. Furthermore, PerD4 HP increased the distance between the plates along different axes, which might be better than the distance achieved with ParD4 HP.  
Figure 4: Stress distribution of PerD2 HP. (**a**) plate; (**b**) screws; (**c**) screw holes. (Unit: MPa).  
The first study on PerD4 HP in the fixation of a mandibular symphysis fracture was performed by [PERSON] et al. in 2006 using FEA in different computer models [18]. In 2010, [PERSON] et al. used FEA to show that the PerD4 HP technique is suitable for fixation of mandibular symphysis fractures [10]. In 2011, [PERSON] et al. studied a single four-hole plate (S4 HP), ParD4 HP, PerD4 HP, and lag screw technique for fixation of mandibular symphysis fracture using a polyurethane model [17]. [PERSON] et al. showed that both PerD4 HP and ParD4 HP had more stable fixation than the S4 HP due to significantly lower plate-screw strain, lower screw hole strain, and less displacement [18]. [PERSON] et al. found that the PerD4 HP and lag screw had equal stability to resist high displacement at 5 mm and 10 mm, but there was no difference between the ParD4 HP and PerD4 HP [17] in displacements less than 5 mm. [PERSON] et al. also proposed that PerD4 HP resisted more vertical biting force and limited horizontal displacement compared with ParD4 HP, thus favoring bone healing [10]. [PERSON] explained why PerD4 HP is more stable. When the force acts on the molar teeth, a shearing force and torsion force would cause the displacement to move inferiorly and laterally. The stress of the ParD4 HP was on the screw-plate junction, but the stress of the PerD4 HP was on the plate and thus resisted the lateral displacement [18]. Although there was no significant difference between ParD4 HP and PerD4 HP, the stress of the PerD4 HP screw holes was significantly lower than that of the ParD4 HP, indicating stable fixation.  
[PERSON] et al. found that the perpendicularly oriented double plates had a significantly smaller fracture site displacement than the single plate [18]. [PERSON] et al. proposed that perpendicularly oriented fixation of double plates in the tension zone is more stable than the fixation of a single plate [17]. By using a 2 HP on the mandibular anterior, stable fixation was achieved similar to that with a 4 HP in the perpendicular fixation method.