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.

中文翻译：

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拐点：用于在上颌中切牙的surface表面曲率上将舌托架定位的扭矩参考。

背景技术与口腔正畸相反，舌状正畸没有参考上颌中切牙上的垂直托槽定位。这项研究的目的是为上颌中切牙的surface表面曲率（PSC）上的舌托定位提供与扭矩有关的参考点。方法将50个来自牙科放射中心存档的右上颌中切牙的锥形束计算机断层摄影（CBCT）射线照片转移到Photoshop，在其中使用钢笔工具追踪其PSC。在Excel中，使用立方聚贝塞尔曲线以0.5 mm的增量并在PSC的拐点处计算了切牙的PSC扭矩角值。然后计算增量的扭矩角值和50个切牙的拐点的描述统计量。单向方差分析用于检测增量之间的系统差异，事后使用Tukey检验。结果对于所有切牙，切牙至拐点的增量均显示扭矩角值从第一个计算的增量到拐点逐渐减小，而子宫颈至拐点的增量则显示从拐点至最后计算的增量逐渐增大。所有增量和拐点的平均扭矩角值显示出高标准偏差和宽范围的值。单向方差分析具有高度统计学意义（p <0.0001），并且使用Tukey检验对增量的大多数成对比较均具有显着性。结论拐点可用作在PSC上支架放置的参考。垂直托槽位置的颈椎定向移位会导致子宫颈顶唇/根pa运动向拐点移动，而切牙的顶冠/根唇运动也将其切向。还提供了针对上颌中切牙PSC上定制的支架扭矩处方的科学数学依据。