## 4 Discussion
Therefore, instead of using the methods attempted in previous studies, the design of the edentulous area, i.e., morphometric change (distal cervical area), was modified in this study to increase the contact area between the CA and the canine while simultaneously changing the elasticity and stiffness of the material in the localized area of the CA to control the forces and moments generated on the canine [38; 39]. When there was a posterior extraction space, Group 1 grasped the three sides of the canines the most, followed by Group 4 with the beam structure, and then by Groups 3 and 2. However, these contact areas refer to when the CA is mounted passively on the dentition; hence, the contact area between the tooth and the CA is different for active aligners that are set to allow 0.25 mmbodily movement of the maxillary canines, as in this study. Groups 2 and 3, which had similar morphologies, were more similar than Groups 1 and 4, which had different force and moment values. However, for the buccolingual tilting moment (My) value, Group 3 showed a larger lingual tilting moment than that of Group 2. This is probably due to the increased stiffness in the pontic region of Group 3 due to the difference in the pontic space of the edentulous area between the groups. According to [PERSON] et al. [29], there is a correlation between the CA thickness and the forces transmitted by the CA. As the thickness of the CA increases in the interproximal space, the tensile stresses generated in these regions are enhanced [40]. Similarly, in Group 3, because the pontic was one-half the width of the maxillary first premolar, the closeness between the buccolingual CA and the cervical region may have increased the stiffness, similar to increasing the thickness. Therefore, it is assumed that Group 3 transmitted a stronger force to the cervical region than did Group 2, resulting in an increased lingual tilting moment. Although distal tipping moments occurred regardless of the edentulous area design, they were not substantial (range, 0.22-7.66 Nmm). Notably, the distal tipping moment and lingual tilting moment tended to increase with the distal surface contact area between the CA and the canine, being the largest in Group 1, followed by Groups 4, 3, and 2. This is probably due to a wider contact area, such as in Group 4, where the point of action of the force is not only on the proximal surface of the canine, but also on the distal cervical area, and the opposite direction of the force is easily transmitted, resulting in a large rotational moment while wearing the CA. Group 4 showed adequate intrusive force and significantly larger distal force than the other groups, and it is considered the most appropriate design for the edentulous area when attempting distal bodily movements of the canine. This study has several limitations. Because we measured and compared the initial forces and moments generated by the CA on the teeth, we could only describe the initial effect when analyzing the force system of the orthodontic appliance and could not determine the changes in the orthodontic forces over time. Moreover, the biomechanical effects of the attachment position on the tooth were not evaluated; the shape of the attachment and the attachment position on the tooth surface can affect the forces and moments. Finally, as the forces and moments of only a single tooth were examined, they did not accurately reflect the actual orthodontic treatment scenarios, wherein multiple teeth move simultaneously, nor did they consider the effects of masticatory movements and occlusal forces following the use of CAs. Therefore, complementary preclinical evaluation studies and biomechanical studies are warranted to investigate the efficacy during actual orthodontic treatment.