Analysis of the influences of bracket and force system in different directions on the moment to force ratio by finite element method

The human teeth face a variety of ways to move during orthodontic treatment. The types of orthodontic tooth movements have linked to the moment to force (M/F) ratio. This paper aims to determine the precise M/F ratios that generate different types of movements for the models with and without bracket, and the M/F ratios are compared between the force systems applied in buccal-lingual and distal-mesial direction for the mandible canine by using finite element method (FEM). A segment of mandible canine obtained from autopsy had been scanned with microcomputed tomography, and two finite element models with and without brackets were established. Each canine model was subjected to a force of 100 cN and varied M/F ratios from 0 ~ 12 in buccal-lingual and distal-mesial directions. We find that the model with a bracket required larger M/F ratio compared to the model without a bracket for the same tooth movement. For the different directions, the value of M/F ratio is larger in the buccal-lingual than in the distal-mesial direction. The geometry of the tooth and the PDL are gained from a regular patient. Therefore, the results are applicable to any canine, and the precise M/F values provide a theoretical basis for the orthodontist design optimal force system.