Modal analysis of a tooth-PDL-bone complex

Previous studies have shown that applying external vibrational load of a certain frequency and intensity can accelerate the tooth movement, thus shorten orthodontic treatment time. It is believed that the optimal frequency is correlative to the modal mode of the target tooth-periodontal ligament (PDL)-bone complex (TPBC). This study aims to investigate modal mode, natural frequencies included, of the TPBC using finite element (FE) method. Methods: A three dimensional TPBC model of a maxillary central incisor were reconstructed from cone beam CT images. A FE model was then created in Ansys 14.5. The tooth, PDL, and bone were meshed with 10-node hexahedral elements (SOLID 187) with the numbers of the elements equaled to 17,803, 4,137, and 32,577, respectively. All parts were considered homogeneous and isotropic. The material properties (Young´s Module (Pa), Poisson´s ratio and Density (kg/m³) as: 2e10, 0.31 and 1.36e3 for tooth, 4.7e5, 0.4 and 1.1e3 for PDL, and 3.5e9, 0.33 and 1.4e3 for bone, respectively. Fixed constraint was set for the alveolar bone. PCG Lanczos method was used in the modal analysis. Six order modes were included in the computation. Result: The first six order modal mode of the TPBC were obtained. The corresponding natural frequencies were 702, 1049, 2713, 2805, 3026, and 3530 Hz, respectively. Different tooth movement patterns, including translation, rotation, extrusion/intrusion, were observed in these modal modes. Conclusion: The proposed method is able to obtain the natural frequencies and modal modes of a TPBC. The results can be used as reference for developing vibrational device to accelerate orthodontic tooth movement.