Finite element analysis of effectiveness of lever arm in lingual sliding mechanics

Objective: The aim of this study was to conduct three-dimensional finite element analysis of individual tooth displacement and stress distribution when a posterior retraction force of 200 g was applied at different positions of the retraction hook on the transpalatal arch (TPA) of a molar, and over different lengths of the lever arm on the maxillary anterior teeth in lingual orthodontics. Methods: A three-dimensional finite element model, including the entire upper dentition, periodontal ligaments, and alveolar bones, was constructed on the basis of a sample (Nissan Dental Product, Kyoto, Japan) survey of Asian adults. Individual movement of the incisal edge and root apex was estimated along the x-, y-, and z-coordinates to analyze tooth displacement and von Mises stress distribution. Results: When the length of the lever arm was 15 mm and 20 mm, the incisal edge and root apex of the anterior teeth was displaced lingually, with a maximum lingual displacement at the lever arm length of 20 mm. When the posterior retraction hook was on the root apex, the molars showed distal displacement. When the length of the lever arm was 20 mm, anterior extrusion was reduced and the crown of the canine displaced toward the buccal side, in which case, the retraction hook was on the edge, rather than at the center, of the TPA. Conclusions: The results of the analysis showed that when 6 anterior teeth were retracted posteriorly, lateral displacement of the canine and lingual displacement of the incisal edge and root apex of the anterior teeth occur without the extrusion of the anterior segment when the length of the lever arm is longer, and the posterior retraction hook is in the midpalatal area.