A Mesh-Based Model for Prediction of Initial Tooth Movement

Orthodontics is making an evolution from a highly experience based treatment towards a computer assisted patient specific therapy. The development of models that can predict tooth movement therefore is a critical research topic. Many existing models, FEM as well as analytical, simplify the calculations by assuming that the tooth root can be approximated by a paraboloïd or an elliptical paraboloïd. Other studies state that these approximations are only allowed within a certain range for tipping movements. But when it comes to bodily movement the real root and the approximation can give very different FEM results. This paper presents a model that is based on an analytical approach using paraboloïds. The analytical approach is chosen to avoid FEM analysis and to limit calculation time. The developed model expands the applicability so that it can do the calculations for a mesh representation of the root. As a validation a set of elliptical paraboloïds is constructed and the results for the analytic and the mesh-based procedure are compared. This is done by comparing the forces necessary to cause a certain displacement or rotation of the root. Both methods produced the same results except for small deviations that can be assigned to the mesh accuracy and the accuracy of thenumerical integration that is used within the analyticalapproach. This makes the presented model an interesting toolfor the evaluation of the correctness of an approximatingparaboloïd. It is also suitable for the calculation of initial tooth movement as part of a model for the simulation of orthodontic tooth movement.

Publication year:2009