Abstract: BACKGROUND: In orthodontic treatment, patients with deep overbite and gummy smile often use micro-screw implants to depress the upper anterior teeth to open the bite. However, this method is prone to causing labial inclination of the anterior teeth. The torque auxiliary arch has a unique mechanical function in orthodontics. Whether it can improve the labial inclination of the anterior teeth and enhance the treatment efficiency is worthy of in-depth study.
OBJECTIVE: To simulate the scene of lowering anterior teeth with the finite element method, and explore the effects of different lip inclinations of anterior teeth and torque-assisted arch on tooth movement.
METHODS: Maxillary models with different labial inclinations of central incisors and lateral incisors (105°, 112°, and 120°) were constructed based on oral cone beam CT images of healthy adults. Micro-implants were implanted between the bilateral maxillary central incisors and lateral incisors in each group of models, and a tensile force of 60 g was applied. For each model, torque auxiliary arches were set to apply forces of 0.5, 1.0, and 1.5 N, and no auxiliary arch was set. Initial displacement of teeth, the maximum principal stress of the periodontal ligament, and the Von Mises equivalent stress were analyzed. 
RESULTS AND CONCLUSION: (1) After applying the torque auxiliary arch, as the torque value increased, the movement directions of the tooth crown and root changed. The tooth crown changed from labial movement to lingual movement, and the root changed from lingual movement to labial movement. Moreover, the displacement difference between them gradually increased. Simultaneously, the amount of depression of the tooth root and the amount of elongation of the tooth crown both showed an increasing trend. At the same torque value, as the labial inclination of the tooth increased, the displacement of the tooth root and crown in all directions gradually decreased. (2) The maximum equivalent stress distribution of each group of models was mainly concentrated in the two areas of the cervical edge and the root apex, and the stress values were within the normal range. With the increase of the torque value, the Von Mises equivalent stress gradually increased. With the increase of the labial inclination, the Von Mises equivalent stress did not change significantly. (3) The maximum principal stress-tensile stress was mainly concentrated in the labial gingival margin of the periodontal membrane, and the compressive stress was mainly concentrated in the root apex. With the increase of the torque value, the compressive stress and tensile stress of the periodontal membrane increased. With the increase of the labial inclination, the stress change of the periodontal membrane was not significant, where torque values exceeding 1 N might damage the health of the apical periodontal tissues. (4) The results show that the torque auxiliary arch can not only improve the efficiency of anterior tooth depression, but also correct the overly labially-inclined anterior teeth and effectively control the tooth torque. However, to prevent root resorption, it is advisable to choose a force of less than 1 N for the auxiliary arch.

Key words: torque auxiliary arch, anterior teeth depression, deep overbite, micro-screw implant, torque, labial inclination, gummy smile, engineered oral material