Coordinating bracket torque and incisor inclination : Part 3: Validity of bracket torque values in achieving norm inclinations.

PURPOSE: To analyze common values of bracket torque (Andrews, Roth, MBT, Ricketts) for their validity in achieving incisor inclinations that are considered normal by different cephalometric standards. METHODS: Using the equations developed in part 1 (eU1(BOP) = 90° - BT(U1) - TCA(U1) + α1 - α2 and eL1(BOP) = 90° - BT(L1) - TCA(L1) + ß1 - ß2) (abbreviations see part 1) and the mean values (± SD) obtained as statistical measures in parts 1 and 2 of the study (α1 and ß1 [1.7° ± 0.7°], α2 [3.6° ± 0.3°], ß2 [3.2° ± 0.4°], TCA(U1) [24.6° ± 3.6°] and TCA(L1) [22.9° ± 4.3°]) expected (= theoretically anticipated) values were calculated for upper and lower incisors (U1 and L1) and compared to targeted (= cephalometric norm) values. RESULTS: For U1, there was no overlapping between the ranges of expected and targeted values, as the lowest targeted value of (58.3°; Ricketts) was higher than the highest expected value (56.5°; Andrews) relative to the bisected occlusal plane (BOP). Thus all of these torque systems will aim for flatter inclinations than prescribed by any of the norm values. Depending on target values, the various bracket systems fell short by 1.8-5.5° (Andrews), 6.8-10.5° (Roth), 11.8-15.5° (MBT), or 16.8-20.5° (Ricketts). For L1, there was good agreement of the MBT system with the Ricketts and Björk target values (Δ0.1° and Δ-0.8°, respectively), and both the Roth and Ricketts systems came close to the Bergen target value (both Δ2.3°). Depending on target values, the ranges of deviation for L1 were 6.3-13.2° for Andrews (Class II prescription), 2.3°-9.2° for Roth, -3.7 to -3.2° for MBT, and 2.3-9.2° for Ricketts. CONCLUSIONS: Common values of upper incisor bracket torque do not have acceptable validity in achieving normal incisor inclinations. A careful selection of lower bracket torque may provide satisfactory matching with some of the targeted norm values.

Coordinating bracket torque and incisor inclination : Part 1: The development of widely applicable equations.

PURPOSE: The objective of this investigation was to develop equations to describe the geometric relations among "targeted incisor inclinations" (tU1, tL1) accommodating different cephalometric norms (Ricketts, Bergen, etc.) with the "expected inclinations" (eU1, eL1), as they can be generated by bracket torque values according to Andrews, Roth, Ricketts, and MBT. METHODS: In its key parts, the present study is a theoretical work in which structural relationships are described using standard mathematical and geometric methodologies. RESULTS: The "targeted norm-inclinations" (tU1, tL1) were calculated relative to a single reference plane (BOP according to Downs), thus, allowing for a direct comparison of different cephalometric values. Referring to the "expected inclinations" (eU1, eL1), it was found that in addition to bracket torque (BT) morphological and structural parameters also have to be taken into account. These are the "torque coordination angle" (TCA) representing the variation in dental morphology and, the correction angles between BOP and the upper (uOP) (α1) or the lower (lOP) occlusal plane (ß1). Moreover, the angles α2 between an upper (uBPP) and ß2 between a lower bracket positioning plane (lBPP) and the occlusal planes (uOP, lOP) have to be considered. As a consequence, suitable equations were developed (eU1(BOP) = 90°â€¯- BT(U1) - TCA(U1) + α1 - α2, and eL1(BOP) = 90°â€¯- BT(L1) - TCA(L1) + ß1 - ß2), allowing the calculation of expected torque-dependent inclinations (eU1, eL1) and representing the prerequisite for a comparison with the cephalometric targeted values (tU1, tL1). CONCLUSIONS: By developing suitable equations, it became possible to name and quantify those parameters that are responsible for incisor inclinations and enable a comparison with targeted cephalometric values.