Torque differences according to tooth morphology and bracket placement: a finite element study

Torque of the maxillary incisors is essential in esthetics and proper occlusion, while torque expression is influenced by many factors. The aim of this finite element study was to assess the relative effect of tooth morphology, bracket prescription, and bracket positioning on tooth displacement and developed stresses/strains after torque application.A three-dimensional upper right central incisor with its periodontal ligament (PDL) and alveolus was modelled. The tooth varied in the crown-root angle (CRA) between 156°, 170°, and 184°. An 0.018-inch slot discovery® (Dentaurum, Ispringen, Germany) bracket with a rectangular 0.018 × 0.025-inch β-titanium wire was modelled. Bracket torque prescription varied between 0°, 12°, and 22°, with bracket placement at the centre of the middle, gingival or incisal third of the crown. A total of 27 models were generated and a buccal root torque of 30° was applied. Afterwards, crown and apex displacement, strains in the PDL, and stresses in the bracket were calculated and analysed statistically.The palatal crown displacement was significantly affected by bracket positioning (up to 94 per cent), while the buccal apex displacement was significantly affected by bracket prescription (up to 42 per cent) and bracket positioning (up to 23 per cent). Strains in the PDL were affected mainly by CRA (up to 54 per cent), followed by bracket positioning (up to 45 per cent). Finally, bracket prescription considerably affected the stresses in the bracket (up to 144 per cent).These in silico results need to be validated in vivo before they can be clinically extrapolated.Tooth anatomy and the characteristics of the orthodontic appliance should be considered during torque application.