Nonlinear finite element analysis of the vibration characteristics of the maxillary central incisor related to periodontal attachment

The vibration characteristics of a maxillary central incisor were investigated by using the finite element method (FEM) according to nonlinear behavior of the human periodontal ligament (PDL). The effect of alveolar bone loss was also studied to obtain the relationship between the vibration property of the tooth in the periodontal system and the level of periodontal attachment for assessing the condition of periodontium. Three-dimensional (3D) finite element model of the tooth was constructed using CT image-reconstruction, and the elastic face foundation constraint was applied to the surface of the tooth root where the PDL was attached to. Modal analysis was performed by using FEM. The nonlinear behavior of the PDL was assigned and approached by the piecewise linearized method. The results indicated that the vibration of the maxillary central incisor in the periodontal system could be described by several modal frequencies and modes. The first four modes were dominant, which varied with the deformation of the PDL or the force applied on the tooth. The vibration frequency of the maxillary central incisor decreased with the losing of the alveolar bone, but the ratio of decrease had no significant correlation with the nonlinear behavior of the human PDL. The vibration frequency of the maxillary central incisor can be used to describe the loss of the alveolar bone and the level of periodontal attachment, under physiological short-term loading.