Evaluation of orthodontic loads and wire–bracket contact configurations in a three-bracket setup: Comparison of in-vitro experiments with numerical simulations

So far, no practicable procedure exists to quantify the orthodontic loads applied to teeth in vivo. Dentists therefore rely on experience and simplified mechanical in-vitro experiments comprising deflection of orthodontic wires. Predicting the mechanical behaviour of orthodontic wires during clinical therapy requires understanding of the different contact states at multi-bracket–wire interfaces. This study experimentally investigates the effect of different bracket–wire contact configurations in a three-bracket setup and uses two numerical approaches to analyse and complement the experimental data. Commonly used round stainless-steel wires (diameter: 0.012″ and 0.016″) and titanium–molybdenum alloy wires (diameter: 0.016″ and 0.018″) were tested. All six force–moment components were measured separately for each of the three brackets. The results indicate that a specific sequence of distinct bracket–wire contact configurations occurs. Several transitions between configurations caused substantial changes of effective wire stiffness (EWS), which were consistent among experimental and numerical methods. The lowest EWS was observed for the configuration in which the wire touched only one wing of the lateral brackets. Taking this stiffness as 100%, the transition to a configuration in which the wire touched two opposing wings of the lateral brackets resulted in an increase of EWS of 300% ± 10%. This increase was independent of the wire type. Additional contacts resulted in further increases of stiffness beyond 400%. The results of this combined experimental and numerical study are important for providing a fundamental understanding of multi-bracket–wire contact configurations and have important implications for clinical therapy.