Finite element analysis of torque control efficiency of a homemade four ⁃ curved auxiliary arch for anterior teeth

Abstract

Objective To analyze the initial displacement of the upper central incisor and stress distribution of periodontal ligament under different torque values of upper incisors under the action of a four⁃curved auxiliary arch to provide a reliable basis for the safety of clinical application of four⁃curved auxiliary arches. Methods A three⁃dimen⁃ sional finite element model for torque control of upper anterior teeth with a homemade quadrilateral auxiliary arch was established. Four different states were analyzed: molar ligation without extraction space (group A), microimplant ligation without extraction space (group B), molar recovery with extraction space closure (group C) (the adductive traction force was set at 115 g) and microimplant recovery with extraction space closure (group D) (the adductive traction force was set at 115 g). When four types of torque (0.5 N, 1.0 N, 1.5 N, and 2.0 N) were applied. The initial displacement of upper central incisors and the stress distribution of periodontal ligament in 16 groups (A1⁃A4, B1⁃B4, C1⁃C4, D1⁃D4) were ob⁃ served. Results Under different conditions, as the strength of the four⁃curve auxiliary arch increases, the maxillary an⁃ terior teeth has crown labial inclination and a root lingual inclination. The displacement of the incisor tip increases with the increase in the loading force of the torque auxiliary arch, and the displacement of the incisor root apex increases as the force increases. The difference in incisor⁃apex displacement distance in A1⁃A4, B1⁃B4, C1⁃C4, D2 and D4 groups increased as the torque force increases, while the difference between the D3 group and D1 and D2 groups decreased slightly. The stress of the cervical periodontal ligament of the upper central incisor did not exceed the stress of the peri⁃ odontal ligament in the following groups: A1, A2, B1, B2, B3, C1, C2, D1, and D2. The stress of the lip side of the up⁃ per central incisor did exceed the stress of the periodontal ligament in the following groups: A3, A4, B4, C3, C4, D3, and D4. In other words, when using the four⁃curved auxiliary arch as an implant anchorage, the force applied in the ab⁃ sence of extraction space should not exceed 1.5 N, and the force applied in the adduction of extraction space should not exceed 1.0 N. When using the nonimplant anchorage, the force applied in the absence of extraction space and the ad⁃ duction of extraction space should not exceed 1.0 N. In addition, the range of force should not exceed the maximum stress of the periodontal ligament in the cervical region such that the effective and safe torque movement can be achieved. Under other stress conditions, the stress of the labial and cervical periodontal ligament of the upper central in⁃ cisor exceeded the stress value (2.6 × 10 ⁃ 2 MPa). The stress value of periodontal ligament was 2.6 × 10 ⁃ 2 MPa in all groups. Conclusion A four⁃curved auxiliary arch has a significant effect on the upper anterior teeth, and the use of mi⁃ croimplants can better control root movement such that the crown of upper central incisors cannot be excessively lip in⁃ clined.

Keywords

• Four⁃curved auxiliary bow，
• Anterior teeth，
• Torque force，
• Three⁃dimensional finite element，
• Peri⁃ odontium，
• Malocclusion，
• Implant anchorage，
• Stress analysis，