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Updated: May 6, 2026

A Finite Element Approach for Locating the Center of Resistance of Maxillary Teeth
Published on: April 8, 2020
The effect of canine lingual attachments during maxillary arch distalization with clear aligner: a 4D finite element
Bochun Mao1, Yajing Tian2, Hanzhang Zhou1
1Department of Orthodontics, Peking University School and Hospital of Stomatology, National Center for Stomatology, National Clinical Research Center for Oral Diseases, National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing Key Laboratory of Digital Stomatology, Research Center of Engineering and Technology for Computerized Dentistry Ministry of Health, Beijing, 10081, China.
Objective:
During the maxillary premolar distalization process in clear aligner (CA) therapy, anterior aligner misfit and mesial displacement of the molars are two common challenges. This study aims to propose a novel attachment design to address these issues and to investigate the biomechanical effects of varying canine tipping angles during treatment.
Method:
A dual-methodological approach was employed: 1) A four-dimensional finite element model (4D FEM) incorporating automated staging simulation was developed, utilizing iterative computations for long-term tooth movement prediction and thermal expansion algorithms for CA morphology adaptation; 2) An electromechanical orthodontic simulator (OSIM) was implemented for in vitro validation. The study analyzed three canine inclination groups in FEM simulations versus eleven groups in OSIM experiments, with particular focus on lingual attachment biomechanics. The A t-test was used to compare the forces and moments of each tooth between the groups with the same canine tipping angle.
Results:
The findings from the 4D FEM analysis demonstrated that distally inclined canines provided greater anchorage during premolar distalization (0.27 mm mesial movement for the first molar in -10° group), while mesially inclined canines contributed to more pronounced anchorage loss (0.34 mm mesial movement for the first molar in 10° group). The use of lingual attachments on canines improved the average distalization efficacy of premolars by 1%, 6%, and 7% in the -10°, 0°, and 10° canine tipping groups, respectively. Similarly, the in vitro orthodontic simulator (OSIM) experiment showed a comparable trend in force and moment variations.
Conclusion:
Both the 4D FEM and OSIM analyses indicted that during the distalization process of premolars, canine lingual attachment significantly reduces the mesial displacement of molars by alleviating the unfitness of CA at anterior teeth area to enhance anterior anchorage. The efficiency of the attachment increased with the greater mesial tipping of canine. Based on the results of this study, it is clinically recommended to place lingual attachments during premolar distalization when the canine mesially tipped more than 4°.
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