Three-dimensional zone of the centers of resistance of the mandibular incisors and canines: A novel approach by finite element analysis

Objectives > The distribution and size of the zone of the centres of resistance (ZCR) are critical for accurate orthodontic treatments and minimizing unexpected tooth movements. However, this information remains unclear for mandibular incisors and canines. This study aims to address these gaps in knowledge. Methods > Finite element models of four incisors and canines from four individuals were created. Four centres of resistance (CRs) under four orthodontic directions (0 degrees similar to 45 degrees similar to 90 degrees similar to 135 degrees to the sagittal plane in the horizontal plane) were assessed by a novel method. The height of the CRs was normalized to a percentage of the long axis, and the offsets were expressed as a distance value after normalization. The ZCR was obtained by fitting a 90% confidence sphere of the CR distribution. Validation was conducted to find the perturbations when the positions out of the zone were applied. Results > The maximum variation of CR in the heights under four directions was 5.17% and 3.70% for the incisors and canines, respectively. The maximum offset between the CR and long axis was 0.14 mm in incisors and 0.99 mm in canines. The height of the zone in the incisor and canine was 57.75% and 59.72%, and the radius of the zone was 0.60 mm and 0.65 mm, respectively. The force-acting point outside the zone produced a large rotation, which was unexpected. Conclusions > The ZCR of mandibular incisors located slightly lower than that of canines, but they were almost the same size. The ZCR was recommended as the "gold reference" for orthodontics to reduce unexpected movement.