## 4 Discussion  
This study analyzed the biomechanical differences between power arms and lever jigs for mandibular canine retraction using FEA. While the power arm facilitates en-masse retraction of the anterior segment, the lever jig is designed for isolated canine retraction. Nevertheless, comparing the lever jig with the commonly used power arm provides insight into their biomechanical differences.  
Recent studies have demonstrated that increasing the length of the power arm to approximate the center of resistance of the tooth can reduce the tendency for distal tipping [11]. However, this approach was insufficient in preventing extrusion. In contrast, the application of a lever jig has been shown to effectively control both distal tipping and extrusion. These results indicate that the lever jig provides a more controlled force application, improved bodily movement, and a more balanced stress distribution compared to the power arm. Notably, the lever jig effectively suppressed extrusion despite a similar posterior-superior force vector, suggesting its potential advantages in controlling vertical displacement. This observation can be made from Figure 5d. The irregular pattern of the graph can be attributed to the fact that the lever jig is not directly affixed to either the bracket or the archwire, resulting in interactions with the main archwire or the bracket. Specifically, the hook, which is wrapped around the posterior of the canine bracket, makes contact with the main archwire, generating a hook contact force. This interaction leads to the irregular redistribution of force, as evidenced in the graph.  
A key biomechanical difference was how force was transmitted to the bracket and tooth. Increasing power arm length shifted the force vector posterior-superiorly, leading to extrusion and distal tipping, consistent with previous studies [2; 3; 4; 5]. However, this  
Figure 8: Compressive stress in the PDL when using a power arm (**a**) and a lever jig (**b**).  
effect plateaued beyond 8-10 mm, reducing efficiency. In contrast, the lever jig redirected force downward and backward by pressing against the bracket, minimizing extrusion and promoting bodily movement. This mechanism highlights its potential for torque and root control during space closure.  
Stress distribution analysis further supported these findings. The power arm concentrated tensile and compressive stress in localized PDL regions, increasing the risk of undesirable rotation. Conversely, the lever jig maintained a broader, evenly distributed stress pattern, particularly in the apical and meso-buccal areas, potentially reducing unwanted side effects like root resorption.  
Despite its strengths, this study has limitations. The PDL was modeled as a linear elastic material, though in reality, it exhibits nonlinear and viscoelastic properties. Additionally, only initial displacement was analyzed, limiting insights into progressive tooth movement. Future studies should incorporate nonlinear modeling and longitudinal assessments to validate these findings in vivo. A further limitation is that the model was derived from the CBCT data of a single individual, and thus the initial tooth alignment may not have been ideal for precise bracket and archive placement. To reduce potential discrepancies, bracket heights were uniformly standardized, and controlled movement of the main archive was allowed under consistent conditions.  
Clinically, the lever jig may offer advantages in reducing tipping and extrusion while improving root control, making it a valuable tool for orthodontic space closure. Further clinical studies are necessary to confirm its long-term effects on root resorption, periodontal health, and progressive tooth movement under continuous force application.