Application of bone remodeling theories in the simulation of orthodontic tooth movements.

A numerical model that calculates bone apposition and resorption around a tooth root on the basis of bone remodeling theories was developed to simulate orthodontic tooth movements. The model was used to calculate different kinds of orthodontic tooth movements, that were then compared with the expected movements based on clinical experience. For simulation of the movements the root of a canine was modeled in an idealized way in the form of an elliptical paraboloid and was processed with a finite element program. The finite element model was loaded with defined force systems. Two model assumptions were used to calculate the bone remodeling process. The mechanical loads firstly in the periodontal ligament and secondly in the alveolar bone were taken to simulate the following tooth movements: 1. mesial tipping around the center of resistance (force system at the bracket: isolated torque MY = 5 Nmm), 2. rotation around the long axis of the tooth (MZ = 5 Nmm), 3. uncontrolled tipping around the root tip (FX = 1 N, MZ = 5 Nmm), 4. canine retraction (FX = 1 N, MY = -9.5 Nmm, MZ = 5 Nmm), 5. and 6. extrusion/intrusion (FZ = +/- 0.5 N, MX = +/- 2.5 Nmm). Comparison with clinical experience was performed by calculating the orthodontic tooth movements based on the assumption of a fixed position of the center of resistance. It could be demonstrated that the numerical model of orthodontic bone remodeling can be used to calculate orthodontic tooth movements. However, the results are strongly dependent on the model assumptions. The model simulating the bone remodeling on the basis of the loading of the periodontal ligament delivers results that are in very good accordance with the biomechanical assumptions of the position of the center of resistance. However, marked side effects occurred with the second model, especially in the simulations of uncontrolled tipping, translation and intrusion/extrusion. Clinically, these side effects cannot be observed.