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.