Finite Element Analysis of Orthodontic Relapse in Different Maxillary Arch Form

Background: Orthodontic relapse is fairly common; however, the mechanisms between relapse and the dental arch form remain unclear. The purpose of our study was to establish three-dimensional (3D) finite element models of different dental arch forms after orthodontic treatment and to analyze the states of different arches applied with various sagittal forces.Methods: By calculating the equations of different dental arch forms and combining them with a full maxillary arch (14 teeth), 3D finite element models of square, oval, and tapered dental arches were established; they were designed to be subjected to anterior lingual, posterior mesial, and combined forces, respectively.Results: The von Mises stress and displacement of teeth under different forces were calculated for each loading scenario. Under the different forcing scenarios, all incisors had irregularity trends, and the inclination and intrusion of the canines were increased, and the premolars had a tendency to buccal or lingual crown tipping or even intrusion in our study. The tapered arch was the most stable and had the smallest displacement and von Mises stress, followed by the ovoid arch; the most unstable arch was the square arch.Conclusions: To achieve a stable orthodontic effect, a tapered or ovoid arch, rather than a square arch, should be chosen as the final outcome of treatment.