Stress-related molar responses to the transpalatal arch: a finite element analysis

The finite element method of analysis (FEM) was used to analyze theoretically the effects of a transpalatal arch (TPA) on periodontal stresses of molars that were subjected to typical retraction forces. The purposes of this investigation were (1) to construct an appropriate finite element model, (2) to subject the model to orthodontic forces and determine resultant stress patterns and displacements with and without the presence of a TPA, and (3) to note any differences in stress patterns and displacements between models with and without a TPA. Because anchorage is stress-dependent, a TPA must be able to modify periodontal stresses as a prerequisite for increasing orthodontic anchorage. A finite element model, consisting of two maxillary first molars, their associated periodontal ligaments and alveolar bone segments, and a TPA, was constructed. The model was subjected to simulated orthodontic forces (2 N per molar) with and without the presence of the TPA. Resultant stress patterns at the root surface, periodontal ligament, and alveolar bone, as well as displacements with and without a TPA, were calculated. Analysis of the results revealed minute differences of less than 1% of the stress range in stress values with respect to the presence of a TPA. Modification of bone properties to allow for increased displacement levels confirmed the ability of the TPA to control molar rotations; however, no effect on tipping was noted. Results suggested that the presence of a TPA has no effect on molar tipping, decreases molar rotations, and affects periodontal stress magnitudes by less than 1%. The final results suggest an inability of the TPA to modify orthodontic anchorage through modification of periodontal stresses.