Simulation of initial tooth displacement by inverse kinematic modeling: Prediction of anchorage-loss for orthodontic tooth movement

The amount of tooth displacement under orthodontic loads has proven to be independent of force magnitudes. The underlying bio-physical process of this phenomenon remains uncertain. The aim of this study was to describe and simulate the initial response of periodontal ligament (PDL) by means of inverse kinematic modeling. The model was developed based on the experimental data for tooth translation along a straight line. The reaction of the PDL was assumed to derive from viscoelastic and complementary elements. An algorithm of putative poroelasticity allowed the number of elements that participate in the reaction to increase in proportion to the orthodontic force. The simulation outcomes showed consistency with the measured data. The orthodontic retraction between the premolar and two-molar segment was also simulated. The two-molar displacement was 85% of that of the premolar displacement. The results demonstrate that the inverse kinematic model is capable of predicting the tooth displacement that is independent of the force magnitude.