Analytical determination of stress patterns in the periodontal ligament during orthodontic tooth movement

A dedicated software package that allows simulation of tooth movement can lead to shortening of the treatment program in orthodontics. A first step in the development of this software is the modelling of the movement of a single tooth. Forces applied to the crown of the tooth are transmitted to the alveolar bone through the periodontal ligament, stretching, and compressing the ligament, eventually resulting in tooth movement. This paper presents an analytical model that predicts stresses and strains inside this ligament by approximating the shape of the root as an elliptic paraboloid. The model input consists of 2 material parameters and 4 geometrical parameters. To assess the accuracy of the model a finite element model (FEM) was constructed to compare the results and the influence of the eccentricity of the root was studied. The results show that the model is able to successfully describe the global behavior of the PDL and, except at a region near the alveolar crest, the differences between analytical and FEM results are small. In contrast to FEM, the analytical model does not require setting up a 3D-model and creating a mesh, allowing for significantly lower computational times and reducing cost when implementing in clinical practice.