Thesis & Dissertations

The palatal surface curvature of the maxillary central incisor which resembles an s-shaped curve is the most complex curvature in the human dentition. As of this, the torque expression in lingual orthodontics will be affected by the vertical bracket position due to the difference in the slot inclination between bracket sites. The palatal curvatures of the maxillary central incisors in the transition plateau and the cingulum convexity regions have not been mathematically described for an accurate torque angle (TA) calculation. This study aims to accurately describe the palatal curvatures of the maxillary central incisors in the cingulum convexity and the transition plateau with polynomial equations via non-linear regression analysis. It also aims to calculate their TA values at 0.5 mm increments. Cone beam computed tomography (CBCT) radiograms for 100 maxillary central incisors were obtained for that reason. These radiograms were then opened as Tiff images in Adobe Photoshop CC where the pen tool was used to trace the cingulum convexity and the transition plateau parts of the palatal surface of each maxillary central incisor. The coordinates of the traced parts were transferred from Photoshop to Microsoft Excel 2013, where non-linear regression was done using 4 polynomial regression models: 2nd order polynomial (2OP), 3rd order polynomial (3OP), piecewise 2nd order polynomial (P2OP) and piecewise 3rd order polynomial (P3OP). Graphpad prism version 6 was used to find the regression model with the best curve fit to the traced palatal incisor surface. Bland-Altman (BA) analysis was performed to check the agreement between the regression models. GraphPad prism revealed that P2OP is the most accurate regression model when a close fit exists between P2OP and the traced palatal incisor surface. The BA analysis showed wide limits of agreement between the regression models, except for P3OP against P2OP. The small limits of agreement between P3OP and P2OP allows the interchangeable use between P3OP and P2OP without clinical complications. The 3OP model was only successful in describing slight palatal curvatures, while the 2OP model was never successful in describing the palatal curvatures. The wide standard deviations of the mean TA values at the 0.5 mm increments calls for individualized 3rd order bracket prescription, while the large variety in the morphology of the palatal surfaces calls for bracket base customization.