## Abstract

### Background

Contrary to buccal orthodontics, lingual orthodontics has no reference for vertical bracket positioning on the maxillary central incisor. The aim of this study was to provide a reference point in relation to torque for lingual bracket positioning on the palatal surface curvature (PSC) of the maxillary central incisor.

### Methods

Cone beam computed tomography (CBCT) radiographs of 50 right maxillary central incisors from archives of a dental radiographic center were transferred to Photoshop, where their PSC was traced using pen-tool. The PSC torque angle values of the incisors were calculated in Excel using cubic poly-Bezier curves at 0.5-mm increments and at the inflection point of PSC. Descriptive statistics for the torque angle values of the increments and for the inflection point for the 50 incisors were then calculated. One-way ANOVA test was used to detect systematic differences between the increments, and Tukey test was used post-hoc.

### Results

For all incisors, increments incisal to inflection point exhibited progressive decrease in torque angle values from the first-calculated increment to inflection point while increments cervical to inflection point exhibited progressive increase from inflection point to last-calculated increment. Mean torque angle values of all the increments and inflection point showed high standard deviations and vast range of values. One-way ANOVA test was highly statistically significant (*p* < 0.0001) and most pairwise comparisons of the increments using Tukey test were significant.

### Conclusions

Inflection point can be used as a reference for bracket positioning on PSC. Cervically oriented shifts in vertical bracket position cause crown labial/root palatal movement cervical to inflection point and crown palatal/root labial movement incisal to it. A scientific mathematical justification for customized bracket torque prescriptions on PSC of maxillary central incisor was also provided.