A numerical simulation of tooth movement by wire bending

Introduction: In orthodontic treatment, wires are bent and attached to teeth to move them via elastic recovery. To predict how a tooth will move, the initial force system produced from the wire is calculated. However, the initial force system changes as the tooth moves and may not be used to predict the final tooth position. The purpose of this study was to develop a comprehensive mechanical, 3-dimensional, numerical model for predicting tooth movement. Methods: Tooth movements produced by wire bending were simulated numerically. The teeth moved as a result of bone remodeling, which occurs in proportion to stress in the periodontal ligament. Results: With an off-center bend, a tooth near the bending position was subjected to a large moment and tipped more noticeably than the other teeth. Also, a tooth far from the bending position moved slightly in the mesial or the distal direction. With the center V-bend, when the second molar was added as an anchor tooth, the tipping angle and the intrusion of the canine increased, and movement of the first molar was prevented. When a wire with an inverse curve of Spee was placed in the mandibular arch, the calculated tendency of vertical tooth movements was the same as the measured result. In these tooth movements, the initial force system changed as the teeth moved. Tooth movement was influenced by the size of the root surface area. Conclusions: Tooth movements produced by wire bending could be estimated. It was difficult to predict final tooth positions from the initial force system.