Finite element analysis of the convergence of the centers of resistance and rotation in extreme moment-to-force ratios

The aim of this study was to investigate how very high and very low M/F ratios affect the location of the center of rotation (CRo). A 3D model of a mesiodistal slice of the mandible was used for this purpose. The model comprised the lower right central incisor, its PDL, the spongy and cortical bone, and a bracket on the labial surface of the bracket. A couple of 1N was applied to the bracket slot to find the level of the center of resistance (Cre). In a second stage, we attempted to produce bodily movement by applying the appropriate M/F ratio. M/F ratios of ± 100, 200, 400, and 800 were applied to the last tenths of a millimeter of a pre-activated loop. Higher M/F ratios with positive or negative values, at constant force, increased both incisal and apical movements. The change in the tooth inclination before and after force application matched the difference produced by the different M/F ratios. It was found that a single center of rotation can be constructed for any tooth position. However, this single point does not act as the center of rotation during the entire movement.