Three-dimensional finite element analysis of stress in the periodontal ligament of the maxillary first molar with simulated bone loss.

The purpose of the study was to use the finite element method to simulate the effect of alveolar bone loss on orthodontically induced stress in the periodontal ligament of the maxillary first molar. A 3-dimensional finite element model of a tooth with different levels of bone height was constructed to estimate the reduction in force and the increase in moment to force (M/F) ratio necessary to obtain evenly distributed stress in the periodontal ligament of a tooth with horizontal bone loss. The 3-dimensional finite model comprised a maxillary first molar, the periodontal ligament, and alveolar bone and consisted of 3097 nodes and 2521 elements. An anterior force of 300 g was applied at the center of the buccal crown surfaces of teeth with normal bone height and with bone loss that ranged from 2.0 to 6.0 mm. The results showed that force magnitude required lowering from 80% (2-mm bone loss) and gradually to 37% (6-mm bone loss) of the initial load applied to the tooth without bone loss. The countertipping moment (gram-millimeters) to force (gram) ratio should increase from 9 (no bone loss) to nearly 13 (6-mm bone loss) to maintain the same range of stress in the periodontal ligament as was obtained without bone loss. A linear relationship was observed between the amount of bone loss, the desired reduction in force magnitude, and the increase in M/F ratio. The results of this study indicate that a combination of force reduction and increased M/F ratio is required to achieve uniform stress in the periodontal ligament of a tooth with bone loss.

Analysis of stress in the periodontium of the maxillary first molar with a three-dimensional finite element model.

The aim of this study was to simulate the stress response in the periodontium of the maxillary first molar to different moment to force ratios, and to determine the moment to force ratio for translational movement of the tooth by means of the finite element method. The three-dimensional finite element model of the maxillary first molar consisted of 3097 nodes and 2521 isoparametric eight-node solid elements. The model was designed to dissect the periodontal ligament, root, and alveolar bone separately. The results demonstrate the sensitivity of the periodontium to load changes. The stress pattern in the periodontal ligament for a distalizing force without counterbalancing moments showed high concentration at the cervical level of the distobuccal root due to tipping and rotation of the tooth. After various counterrotation as well as countertipping moments were applied, an even distribution of low compression on the distal side of the periodontal ligament was obtained at a countertipping moment to force ratio of 9:1 and a counterrotation moment to force ratio of 5:1. This lower and uniform stress in the periodontal ligament implies that a translational tooth movement may be achieved. Furthermore, high stress concentration was observed on the root surface at the furcation level in contrast with anterior teeth reported to display high concentration at the apex. This result may suggest that the root morphology of the maxillary first molar makes it less susceptible to apical root resorption relative to anterior teeth during tooth movement. The stress patterns in the periodontal ligament corresponded with the load types; those on the root appeared to be highly affected by bending and the high stiffness of the root.