Inverse kinematic modeling for simulation of initial tooth displacement responding to orthodontic forces

Rate of tooth displacement under orthodontic loads has proven to be independent of force magnitudes. No finite element model (FEM) has been able to explain the underlying process of this phenomenon. The aim of this study was to analytically describe the initial response of periodontal ligament (PDL) by means of inverse kinematic modeling. The model was developed with reference to the experimental data for tooth translation along a straight line. The reaction of the PDL was assumed to derive from viscoelastic and complementary elements. The reaction force of the complementary element was calculated by solving the inverse kinematic problem. 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 reasonable consistency with the measured data. The initial response of orthodontic retraction between the premolar and molar teeth was also simulated. The molar displacement was 91% of that of the premolar displacement. The results demonstrate that the inverse kinematic model is capable of analytical documentation of tooth displacement that is independent of the force magnitude.