## 4 Discussion  
In this study, we analyzed the tooth movement forces and moments during CA treatment for maxillary midline diastema closure with and without enhanced structure and intrusive movement. Although CAs are widely used due to their esthetics and convenience, it is known that the accuracy and predictability of tooth movement are limited due to the low stiffness of the appliance [12, 13, 15]. In particular, the thermoplastic material of CAs exhibits viscoelastic behavior, which has elastic and plastic properties [15], which can lead to difficulties in achieving the intended tooth movement. However, implementing structural modifications that increase the thickness of certain areas of the CAs, as in this study, may help to achieve the planned tooth movement. [PERSON] et al. reported that the forces and moments generated during tooth movement can be controlled by changing the design of CAs using 3D printing [17]. Although this study used CAs fabricated by thermoforming, the addition of enhanced structures changed the distribution of forces and moments during tooth movement. Recently, the materials for CAs have diversified, and direct 3D-printed CAs made from materials such as TC-85 (Graphy Inc., Seoul, Republic of Korea) have been commercialized. However, the most commonly used CAs in clinical practice are still thermoplastic materials, typically 0.75 mm thick. Although different manufacturers use slightly different materials, common compositions include polyurethane, polymethyl methacrylate (PMMA), and polyethylene terephthalate glycol (PETG). In this study, we used PETG, a thermoplastic material with a thickness of 0.75 mm, which is representative of the most commonly used clinical CAs. Thus, the experimental setup used in this study is likely to reflect the physical properties of CAs commonly used in clinical practice, which has meaningful implications for clinical application. Future studies should consider evaluating different thicknesses and material properties to provide a more comprehensive comparison. The increasing interest in CA treatment is evident in bibliometric analyses that highlight research trends in removable orthodontic appliances, biomechanics, and predictability of tooth movement [18]. These studies emphasize the importance of experimental validation, particularly in force and moment analysis, which is consistent with the focus of our study. Our findings contribute to this growing field of knowledge by providing experimental evidence for the biomechanical efficiency of structural modifications in diastema closure. The results of the simulation of the mesial movement of maxillary central incisors with four groups of CAs showed that the largest mesiodistal force (Fy), which is most related to the direction of tooth movement for diastema closure, was generated in Group 3 with the enhanced structure. This is consistent with previous studies that have shown a strong correlation between the thickness of the CAs and the force transmitted [12; 13]. In particular, the enhanced structure generated greater forces with increasing thickness of the interproximal area, which [PERSON] et al. reported [19], the thicker the CAs, the less deformation of the appliance, and the stronger the adjustment force for the same size of deformation, resulting in a more uniform distribution of forces on the PDL surface. For the vertical force (Fz), Groups 1 and 3, which were not subjected to an intrusive force, generated an extrusive force, which is similar to what is commonly observed with conventional fixed appliances. Previous studies have reported that in treatment with fixed appliances, mesial tipping can result in inclination movement, which can result in a wedge effect in the occlusion due to the application of an occlusal force [20]. However, in the present study, intrusive forces were observed in Groups 2 and 4, which were given 0.1 mm of intrusive movement, and greater intrusive forces occurred in Group 4, where both enhanced structure and intrusive forces were applied.