## 4 Discussion
Unfortunately, although this experiment attempted to reduce this effect using a rectangular attachment, it was difficult to reduce the overall intrusive force. In particular, Group 1,which utilized a shape that covers both the buccal and distal surfaces of the tooth, exhibited strong intrusive forces. [PERSON] et al. analyzed the forces and moments on the canine using the finite element method (FEM) after subjecting it to a distal bodily movement of 0.1 mm with the CA [23]. The results showed that most of the contact between the CA and the canine occurred on the mesial side of the canine. They also reported that distal forces and mesial tipping moments were generated on the canine, regardless of the presence and type of attachment. However, our study showed a contrasting result, with the distal tipping moment occurring in all groups, regardless of the design of the edentulous area. Additionally, the distal force applied to the canine in the previous study was approximately 370-390 cN [23], which was 12-30 times greater than the total force vector in our study (12.82-30.25 cN). This is a significant difference considering that the movement of the canines in our study was 0.25 mm and that in the FEM analysis was 0.1 mm. These differences could be attributed to the simulation in the FEM analysis. To activate the CA, the FEM analysis was performed by translating the canine 0.1 mm in the mesial direction while the canine and CA were passively mounted, storing the stresses generated by the CA and applying them to the movement of the canine to analyze the stresses on the canine. Because of this simulation method, the FEM study showed a slight extrusion force, and the majority of the contact force was generated on the proximal surface of the canine and the inferior surface of the attachment [23], which may have caused the distal force and mesial tipping moment of the canine. However, in our study, the CAs were actually inserted into and removed from the force/moment sensor apparatus; therefore, they were not initially passively mounted, resulting in an intrusive force rather than an extrusive force, and the distal tipping moment of the tooth occurred in all groups. Another possible reason for the inconsistency between the FEM analysis and this study is the material properties, i.e., the viscoelasticity of the material, thickness of the material, and experimental conditions [29]. The FEM analysis assumed the CA to be an isotropic, homogeneous, and linearly elastic material of constant thickness, which is not the case in actual practice. Moreover, since the CA is fabricated by vacuum thermoforming, it is difficult to have a uniform thickness on the tooth surface; moreover, the thickness is relatively thin in the cervical region [30], thus explaining the inconsistencies between the studies. The distribution and point of action of the forces generated by a CA on a tooth depend on the type of tooth movement, i.e., bodily movement or tipping movement. In particular, bodily movement requires a greater force to be applied at the cervical region than at the incisal region [31]. However, in thermoformed CA, the cervical region is the most vulnerable region due to deformation and irregularities [32; 33]; hence, it is challenging to apply a greater force at the cervical region than at the incisal region using a CA. To overcome these limitations, modifications in procedural protocols [34] and improvements in auxiliary tools and materials have been attempted [35; 36]. Treatment with auxiliary tools, such as attachments, power arms, and mini-implants, has been widely applied. However, the excessive use of auxiliary tools makes it difficult to insert and remove CAs, and the power arms are attached to the cervical region, resulting in a severe foreign body sensation and poor esthetics. Although improving the CA material to improve force transmission and reduce stress relaxation has achieved some success, it is limited by the difficulty of balancing stiffness and elasticity [36; 37].