Finite element-based force/moment-driven simulation of orthodontic tooth movement

Abstract

The objectives of this study were to develop a numerically controlled experimental set-up to predict the movement caused by the force systems of orthodontic devices and to experimentally verify this system. The presented experimental set-up incorporated an artificial tooth fixed via a 3D force/moment sensor to a parallel kinematics robot. An algorithm determining the initial movement of the tooth in its elastic embedding controlled the set-up. The initial tooth movement was described by constant compliances. The constants were obtained prior to the experiment in a parameterised finite element (FE) study on the basis of a validated FE model of a human molar. The long-term tooth movement was assembled by adding up a multiple of incremental steps of initial tooth movements. A pure translational movement of the tooth of about 8 mm resulted for a moment to force ratio of − 8.85 mm, corresponding to the distance between the bracket and the centre of resistance. The correct behaviour of this linear elastic model in its symmetry plane allows for simulating single tooth movement induced by orthodontic devices.

Keywords::

• force/moment-driven
• orthodontic tooth movement
• centre of resistance
• parallel kinematics robot
• finite element method
• bone remodelling

Acknowledgements

The author gratefully acknowledges the review and suggestions by Bernd Lapatki (Department of Orthodontics, University Dental Clinic of Ulm) and Uwe Wolfram (Institute of Orthopaedic Research and Biomechanics, University of Ulm). He also recognises the software support and service offered by Juergen Salk and Heinz Steil (Communication and Information Center of the University of Ulm). Generous support for the HEXAPOD robot hardware and software was provided by Physik Instrumente, Karlsruhe, Germany.