Moment-to-force ratio, center of rotation, and force level: A finite element study predicting their interdependency for simulated orthodontic loading regimens

Introduction: Changes in the stress/strain distribution in the periodontium after the application of orthodontic forces trigger remodeling processes that make tooth movement possible. The type of orthodontic tooth movement is linked to the force system applied to the bracket. By combining moments and forces, often expressed as the moment-to-force (M/F) ratio, it is possible to determine the prescribed type of tooth movement. According to classical theory, fixed values for M/F are associated with specific tooth movements. Methods: A segment of a mandible containing the canine and the first premolar obtained from autopsy was scanned with microcomputed tomography, and a finite element model was generated. In a series of finite element analyses simulating teeth subjected to various orthodontic loading regimens, the influences of the M/F ratio and the force magnitude were examined. Results: By applying a range of values of M/F, different types of tooth movement were generated, although the classic prescription of the M/F ratio suggested in the literature could not be confirmed. Due to the nonlinear behavior of the periodontal ligament, loading modes with a constant M/F ratio, yet varying the force magnitude, resulted in different types of tooth movement. Conclusions: The material properties of the periodontal ligament, the morphology of the root, and the alveolar bone are patient specific. Therefore, the M/F values generally advocated to obtain orthodontic tooth movement should be used only as guidelines. To be effective and accurate, the force system selected for a specific tooth movement must be monitored and the outcome compared with the predicted tooth movement.