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ORIGINAL ARTICLE Torque expression of self-ligating brackets Hisham M. Badawi,a Roger W. Toogood,b Jason P. R. Carey,c Giseon Heo,d and Paul W. Majore Edmonton, Alberta, Canada Introduction: The labiolingual inclination of maxillary and mandibular incisors is considered by many orthodontists to be an important determinant of pleasing dental esthetics and ideal stable occlusion. In contemporary fixed appliances, attaching a rectangular orthodontic archwire to a bracket with a rectangular slot makes third-order control possible. The purpose of this study was to measure the difference in third-order moments that can be delivered by engaging 0.019 ⫻ 0.025-in stainless steel archwires to 2 active self-ligating brackets (In-Ovation, GAC, Bohemia, NY; Speed, Strite Industries, Cambridge, Ontario, Canada) and 2 passive self-ligating brackets (Damon2, Ormco, Orange, Calif; Smart Clip, 3M Unitek, Monrovia, Calif). Methods: A bracket/wire assembly torsion device was developed. This novel apparatus can apply torsion to the wire while maintaining perfect vertical and horizontal alignment between the wire and the bracket. A multi-axis force/torque transducer was used to measure the moment of the couple (torque), and a digital inclinometer was used to measure the torsion angle. Fifty maxillary right central incisor brackets from each of the 4 manufacturers were tested. Results: There was a significant difference in the engagement angle between the 2 types of brackets; on average, torque started to be expressed at 7.5° of torsion for the active self-ligating brackets and at 15° of torsion for the passive self-ligating brackets. The torque expression was higher for the active self-ligating brackets up to 35° of torsion. Torsion of the wire past this point resulted in a linear increase of the measured torque for the Damon2, the Smart Clip, and the In-Ovation brackets. The torque was relatively constant past 35° of torsion for the Speed bracket. Conclusions: We conclude that active self-ligating brackets are more effective in torque expression than passive self-ligating brackets. (Am J Orthod Dentofacial Orthop 2008;133:721-8) C orrect buccolingual inclination of anterior teeth is considered essential to providing good occlusal relationships in orthodontic treatment. Inclination of the maxillary anterior teeth is particularly critical in establishing an esthetic smile line, proper anterior guidance, and a Class I canine and molar relationship. Undertorqued maxillary anterior teeth affect the arch length and the space requirements. It has been shown that for every 5° of anterior inclination, about 1 mm of arch length is generated.1 Undertorqued posterior teeth have a constricting effect on the maxillary arch, since they do not allow appropriate cusp-tofossa relationships between the maxillary and mandibular teeth.2 Torque expression can be achieved by filling the bracket slot and gradually increasing the archwire dimensions during treatment. However, the dimensions From the University of Alberta, Edmonton, Alberta, Canada. a Resident, Orthodontic Graduate Program, Faculty of Medicine and Dentistry. b Associate professor, Department of Mechanical Engineering. c Assistant professor, Department of Mechanical Engineering. d Assistant professor, Orthodontic Graduate Program, Faculty of Medicine and Dentistry. e Professor and director, Orthodontic Graduate Program, Faculty of Medicine and Dentistry. Reprint requests to: Paul W. Major, Orthodontic Graduate Program, Faculty of Medicine and Dentistry, 4051B Dentistry/Pharmacy Centre, Edmonton, Alberta, Canada, T6G 2N8; e-mail, [email protected]. Submitted, October 2005; revised and accepted, January 2006. 0889-5406/$34.00 Copyright © 2008 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2006.01.051 of the final working archwire never reach the full dimensions of the bracket slot; therefore, a percentage of the torque built into the bracket is lost because of the play between the archwire and the bracket slot. This amount of play has been theoretically calculated and experimentally measured.3-17 Theoretical third-order moments can be calculated from the nominal dimensions of archwires and brackets from the manufacturers. It has been shown that there is a considerable discrepancy between the theoretical and the measured bracket/archwire play.8 This play often extends to 100% of the prescribed torque; this is equivalent to using round wires.2 Deviations from those calculations can be attributed to intrinsic variations in archwire cross-sectional diameters,3,11,13 bracket slot dimensions,7,8,13 archwire edge beveling,8,10 and bracket deformations.4,18 Other factors also have an impact on third-order moments, including bracket placement errors19 and irregularities in tooth morphology.20,21 Therefore, due to these variations in torque expression resulting from variations in brackets and archwires, accurate calculation of thirdorder moments with the manufacturer’s archwire and bracket dimensions is impossible. Self-ligating orthodontic brackets are gaining popularity because of their advantages in reducing friction and treatment time in orthodontic mechanotherapy.22 However, no studies have investigated the torque expression of self-ligating orthodontic brackets. In our 721 722 Badawi et al American Journal of Orthodontics and Dentofacial Orthopedics May 2008 Fig 2. Bracket alignment assembly. Fig 1. Orthodontic torque measurement device. a, Inclinometer, b, wire support substructure; c, conical wire support and alignment component; d, bracket wire assembly area; e, dual turn table alignment system; f, work gear-based torsion system; g, load cell; h, springs; i, bushings; j, height adjustment system; k, guide rails; l, base support. study, we developed a comprehensive experimental technique to measure the torque expressed from orthodontic brackets. This technique was used to test the torque expression of 2 passive and 2 active commercially available self-ligating brackets. MATERIAL AND METHODS An experimental device was designed to measure the torque expression of orthodontic brackets as accurately as possible. The orthodontic torque measurement device (Fig 1) was developed with the collaboration of members from the Departments of Dentistry and Mechanical Engineering at the University of Alberta, Edmonton, Alberta, Canada. This novel apparatus has the unmatched capability to apply known torsion to an orthodontic wire while maintaining perfect vertical and horizontal alignment between the wire and the bracket. The design uses a multi-axis force/torque transducer that can measure forces and moments in 3 dimensions. The use of the multi-axis force transducer facilitated isolating and recording the moment generated by thirdorder wire activations (torsion), and it allowed us to Fig 3. Schematic of the torsion application system. measure the forces and moments in all other planes to ensure that they are as close to zero as possible. As a result, we could generate and measure pure orthodontic torque. The device consists of a digital inclinometer. The inclinometer (model T2-7200-1N; US Digital, Vancouver, Wash) (Fig 1, a) was used to measure the torsional rotation of the wire. The inclinometer has a 360° rotation range with a 0.05° resolution (manufacturer’s specification). The wire support substructure, which includes the conical wire support and alignment dies, holds the wire and is designed to ensure near-perfect rotation of the wire around its long axis. The torsion device has an alignment assembly (Fig 2) that guarantees perfect alignment between the archwire and the bracket slot. This assembly is made of a base turntable and a secondary turntable (the stainless steel cylinders). Rotation of the base turntable adjusts the position of the bracket slot perpendicular to the wire. Rotation of the secondary turntable adjusts the rotational alignment of the bracket slot to the wire to achieve a perfect parallel relationship between the archwire and the bracket slot. Badawi et al 723 American Journal of Orthodontics and Dentofacial Orthopedics Volume 133, Number 5 A worm gear-based torsion system (Fig 1, f ) with the inclinometer allowed us to place well-controlled torsion of known degrees onto the brackets. The wire substructure (Fig 3), a rigid assembly, is fully rotated by the worm gear (Fig 1, f ), thus imposing the same rotation at both ends of the structure. Therefore, both worm gear and inclinometer undergo the same torsional rotation. The gear ratio of the gear system is 1:120. In other words, a full turn of the handle results in a 3° of rotation of the torsional assembly. The ATI Industrial Automation Nano 17 MultiAxis force/torque transducer (Apex, NC) was used to measure the 3 force and 3 moment components of the applied load. The load cell is a silicon strain gauge. Based on the manufacturer’s specifications, it is rated for maximum loads of 25 N of transverse forces (Fx, Fy), 35 N axial force (Fz), and 0.25 Nm moments in all 3 axes. The resolutions of the measurements are 1/1280 and 1/256 for forces and moments, respectively. The error of measurement of the force/torque transducer was 1.5%. The load cell was used in conjunction with a data acquisition card (DAQ 16-Bit E series NI PCI-6033E; National Instruments, Austin, Tex) recommended by the manufacturer. The transducer signal was imported to a personal computer via the data acquisition card with 16 bits of input resolution. LabView data acquisition software (National Instruments, Austin, Tex) was used to acquire the signal from the transducer and log it to file. Fifty maxillary right central incisor brackets of each of 4 types of brackets (total, 200 brackets) were included in the study (In-Ovation, GAC, Bohemia, NY; Speed, Strite Industries, Cambridge, Ontario, Canada; Damon2, Ormco, Orange, Calif; Smart Clip, 3M Unitek, Monrovia, Calif) and mounted on stainless steel cylinders (secondary turntable, Fig 2). Epoxy adhesive (Loctite, E-20HP, Hysol; Henkel, Rocky Hill, Conn) was used to bond the brackets to the cylinders after treating the surfaces with methyl ethyl ketone. A bracket mounting jig was used for bonding all brackets. The epoxy was allowed to fully cure before testing the brackets. The brackets’ torque prescription did not affect our method, since the true zero torque position was used as a baseline reference for all brackets. RESULTS A pilot study was conducted with 7 Speed brackets and 10 Damon2 brackets. For detecting a difference between the brackets ⱖ5 Nmm with ␣ ⫽ 0.05,  ⫽ 0.1, the sample sizes were calculated to be 81, 40, 19, and 54 for angles 12°, 24°, 36°, and 48°, respectively. Those calculations were averaged, and a sample size of 50 was determined to be adequate for this study. Table I. Bracket 1 Bracket 2 Bracket 3 Bracket 4 Bracket 5 Coefficient of variation (CV) of error analysis Angle Mean SD CV 36 48 36 48 36 48 36 48 36 48 12.703 28.809 8.703 23.863 3.0745 23.184 9.644 24.443 6.638 28.398 0.207 0.162 0.317 0.107 0.2417 0.239 0.438 0.311 0.347 0.203 1.63 0.56 3.64 0.45 7.86 1.03 4.54 1.27 5.23 0.72 Error analysis was conducted to assess the variability in our measurements after controlling for the variation resulting from the brackets and the wires. Five wire/bracket combinations were tested (0.019 ⫻ 0.025-in stainless steel with Damon2 brackets). For each bracket/wire combination, the test was repeated 10 times, recording torque measurements for 4 angles (12°, 24°, 36°, and 48°). Greater variability in data is usually expected when the mean increases; therefore, the coefficient of variation was used to evaluate the standard deviation of the data as a percentage of the mean (Table I). The coefficient of variation for angle 48° was 0.45% to 1.27%. The average coefficient of variation was 2.7%. During the error analysis, care was taken to avoid plastic deformation of the wires or the brackets. Figure 4 shows that there was no decrease in the moments as repeated measurements were made with the same bracket/wire combination. The measurement error of the force/torque transducer was 1.5% (manufacturer’s specification). The Kolmogorov-Smirnov test was used to evaluate the data statistically to confirm normal distribution. The data were distributed normally among all the groups except for the Speed bracket at angle 12°. The mean moment of couple (torque) for the 4 self-ligating brackets was compared at 4 angles (12°, 24°, 36°, and 48°). Repeated measures analysis of variance (ANOVA) and multivariate ANOVA were conducted with a statistical package (version 13; SPSS, Chicago, Ill) to identify any significant differences between the brackets (Table II). Descriptive statistics for the 4 bracket types are given in Table III. There was considerable variation among the torque measurements in each type of bracket. For the Speed brackets, this variation was 1.97 to 11 Nmm; for the In-Ovation brackets, it was 3.7 to 16.7 Nmm; for the Damon2 brackets, it was 1.4 to 11.2 Nmm; and for the Smart Clip brackets, it was 2.8 to 14.2 Nmm. This variation was small for small torsion angles and increased as the torsion angle increased (Fig 5). 724 Badawi et al American Journal of Orthodontics and Dentofacial Orthopedics May 2008 Fig 4. Moments measured for error analysis showing no plastic deformation of wire or bracket. Table II. Repeated measures ANOVA (pairwise comparison) 95% CI for mean Angle 12° 24° 36° 48° Bracket comparisons Damon2 In-Ovation Smart Speed In-Ovation Smart Speed Smart Clip Speed Damon2 In-Ovation Smart Speed In-Ovation Smart Speed Smart Clip Speed Damon2 In-Ovation Smart Speed In-Ovation Smart Speed Smart Clip Speed Damon2 In-Ovation Smart Speed In-Ovation Smart Speed Smart Clip Speed Mean difference Significance Lower bound Upper bound ⫺2.36036 .07858 ⫺1.54796 .001 1.000 .000 ⫺3.89228 ⫺1.12382 ⫺2.48965 ⫺.82844 1.28098 ⫺.60627 2.43894 .81240 .002 .685 .67954 ⫺.79206 4.19834 2.41686 ⫺1.62654 .007 ⫺2.92264 ⫺.33044 ⫺6.90882 ⫺.99844 ⫺6.34030 .000 .874 .000 ⫺9.94213 ⫺3.53284 ⫺8.82384 ⫺3.87551 1.53596 ⫺3.85676 5.91038 .56852 .000 .998 2.57153 ⫺2.73360 9.24923 3.87064 ⫺5.34186 .000 ⫺8.19997 ⫺2.48375 ⫺4.53588 2.23154 .88280 .240 .816 .996 ⫺10.53013 ⫺2.90407 ⫺3.58141 1.45837 7.36715 5.34701 6.76742 5.41868 .018 .049 .80477 .00833 12.73007 10.82903 ⫺1.34874 .959 ⫺5.76834 3.07086 1.09862 8.09258 27.47506 .999 .012 .000 ⫺6.55311 1.22711 21.51632 8.75035 14.95805 33.43380 6.99396 26.37644 .147 .000 ⫺1.32748 18.75947 15.31540 33.99341 19.38248 .000 12.55642 26.20854 Badawi et al 725 American Journal of Orthodontics and Dentofacial Orthopedics Volume 133, Number 5 Table III. Angle 12° 24° 36° 48° Descriptive statistics Bracket Mean SD n Damon2 In-Ovation Smart Speed Damon2 In-Ovation Smart Speed Damon2 In-Ovation Smart Speed Damon2 In-Ovation Smart Speed .45336 2.81372 .37478 2.00132 5.52642 12.43524 6.52486 11.86672 23.23314 27.76902 21.00160 22.35034 55.83124 54.73262 47.73866 28.35618 1.488591 3.702820 2.772042 1.978374 3.894859 6.922984 5.402589 5.239754 9.632597 12.478563 9.492177 6.686943 11.181229 16.690271 14.180880 11.008746 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 Clinically effective torque has been suggested to be 5 to 20 Nmm.9,23,24 The angles of torsion at which the lower limit of that range (5 Nmm) is achieved were 15° for the active self-ligating brackets and 22.5° for the passive self-ligating brackets. For the active self-ligating brackets, the angle of torsion at which the upper limit of that range (20 Nmm) was achieved was 31°, but it was 34.5° for the passive self-ligating brackets (Fig 6). The active self-ligating brackets produced higher levels of torque (moment) up to 35° of torsion. Any torsion beyond this point resulted in a linear increase in the moments generated by the Damon2, Smart Clip, and In-Ovation brackets. As for the Speed bracket, a further increase in torsion beyond this point did not result in increases in the moments generated at the same rate as the other 3 brackets. The moment generated by the Speed bracket reached a plateau at which the increase in torsion did not result in increases in the moments generated (Fig 6). At 12° of torque, there were no significant differences between Damon2 and Smart Clip brackets, or between Speed and In-Ovation brackets. There were, however, statistically significant differences between Damon2 and both Speed and In-Ovation, and between Smart Clip and both Speed and In-Ovation (Table II). At 24° of torque, again there were no significant differences between Damon2 and Smart Clip brackets, or between Speed and In-Ovation brackets. However, there were statistically significant differences between Damon2 and both Speed and In-Ovation, and between Smart Clip and both Speed and In-Ovation. Speed and In-Ovation brackets delivered statistically significant higher torque than did Damon2 and Smart Clip brackets at angles 12° and 24° (Table II). At 36° of torque, the only statistically significant difference was between In-Ovation and both Speed and Smart Clip brackets. At 48° of torque, the most significant difference was between Speed and the other brackets. Speed delivered significantly less torque than the other brackets. There was also a significant difference between Damon2 and Smart Clip brackets (Table II). DISCUSSION Fig 5. Variation in the torque measurement increases as angle of torsion increases. On average, the angle of engagement (the angle at which torque was first expressed) for both Speed and In-Ovation brackets was at 7.5° of torsion. The same angle of engagement for Damon2 and Smart Clip brackets was at 15° of torsion (Fig 6). The applied load in this study delivered a torsional moment of a couple directly to the bracket to simulate orthodontic torque application. This load was measured for 4 commercially available self-ligating bracket systems. We found no statistically significant difference in torque expression between Damon2 and Smart Clip brackets at angles 12°, 24°, and 36°. There was, however, a statistically significant difference between the 2 brackets at angle 48°. There was no statistically significant difference between In-Ovation and Speed 726 Badawi et al American Journal of Orthodontics and Dentofacial Orthopedics May 2008 Fig 6. Torque expression of the 4 brackets. brackets at angles 12° and 24°, but there was a statistically significant difference between the 2 brackets at angles 36° and 48° (Table I). The torque expression of Damon2 and Smart Clip brackets followed a similar pattern, characteristic of passive self-ligating brackets. Torque started to be expressed at an angle of 15° of torsion compared with an angle of 7.5° for Speed and In-Ovation brackets, characteristic of active self-ligating brackets. For Damon2 and Smart Clip brackets, the value of the deviation angle (the amount of this axial rotation that the wire is permitted to undergo before contact with the slot walls) was found to be greater than that of the theoretically calculated one based on the nominal archwire and bracket slot sizes. This is consistent with previous research on torque expression of conventional brackets.2,17 For the Speed and the In-Ovation brackets, the actual deviation angles were less than the theoretically calculated ones. This can only be explained by the active ligating mechanism that seems to reduce the amount of archwire play in the bracket slot. Clinically effective torque has been suggested to be 5 to 20 Nmm.9,23,24 This range of torque was expressed at 15° to 31° of torsion for the active self-ligating brackets, and at 22.5° to 34.5° of torsion for the passive self-ligating brackets. To standardize the experiment, we used rigid clamps to hold the wire on either side of the tested brackets. In a clinical situation, the wire is held by brackets on either side, and there would be some play. Therefore, 2 clinically useful conclusions can be drawn based on this finding. First, the range of clinically useful torsion by using active self-ligating brackets is likely to be larger than that for the passive self-ligating brackets (16° for the active self-ligating brackets and 12° for the passive self-ligating brackets). Second, in vivo, meaningful torque control can only be achieved if torsion in the wire is higher than 15° and 22.5° for active self-ligating brackets and passive self-ligating brackets, respectively. This amount of torque is much higher than most torque prescriptions available commercially. Future research might need to investigate ways to use brackets instead of rigid clamps on either side of the tested brackets, without compromising the experimental technique. The difference between the load deflection curves of the Speed and In-Ovation brackets seems to be due to the material from which the clip mechanism is made. The Speed clip is made of nickel-titanium alloy, and the load deflection curve of the Speed bracket was consistent with what would be expected of a nickel-titanium alloy (Fig 6). The In-Ovation bracket clip is made of stainless steel, and the load deflection curve of the In-Ovation bracket was consistent with what would be expected of a stainless steel alloy. The In-Ovation bracket followed a similar load deflection curve as the Damon2 and the Smart Clip brackets; however, the torque expression for the In-Ovation bracket started much earlier than the other 2. In the data for these 4 brackets, the amounts of variation were considerable. For the Speed brackets, this variation was between 1.97 and 11 Nmm; for the In-Ovation brackets, it was 3.7 to 16.7 Nmm; for the Damon2 brackets, it was 1.4 to 11.2 Nmm, and for the Smart Clip brackets, it was 2.8 to 14.2 Nmm (Table III). This variation was small for small torsion angles and increased as the torsion angle increased. This variation can be attributed to the bracket, the wire, or the experimental technique. Testing of the wires is underway as a part of another study focusing on orthodontic wire characteristics. The preliminary results show that the 0.019 ⫻ 0.025-in stainless steel wires are consistent. The error analysis showed that this Badawi et al 727 American Journal of Orthodontics and Dentofacial Orthopedics Volume 133, Number 5 experimental technique was reliable and consistent; the measurement error of the transducer was 1.5%, and the average coefficient of variation (standard deviation as a percentage of the mean) was 2.7% (Table I). Repeated measurements of the same bracket and wire showed a small amount of variation. Figure 4 confirms that, during data collection for the error analysis, the wires and the brackets were not permanently distorted, and the graph shows no pattern of decrease in the loads as the measurements were made. We concluded that the significant amount of variation in measurements resulted from structural variation in the brackets, specifically the archwire slot size. As with any other product, the manufacturing process of brackets results in some variation in sizes and characteristics, including dimensional accuracy and torque prescription consistency.2 Various bracket manufacturing processes such as injection-molding, casting, and milling can affect the accuracy of the prescribed torque values, and this has been reported to be about 5% to 10%.2 Cash et al17 investigated slot size of orthodontic brackets and found that all brackets tested were oversized— between 5% and 17%. Investigators who evaluated thirdorder moments generated by specific bracket/archwire combinations concluded that there is considerable variation in the tolerances of orthodontic appliances, and that these variances are clinically unacceptable because they reduce the amount of third-order control that otherwise should be present with those wire/bracket combinations.10,11,25 CONCLUSIONS 1. The active self-ligating brackets seem to have better torque control, a direct result of their active clip forcing the wire into the bracket slot. 2. The amount of archwire bracket slop was considerably less for active self-ligating brackets than passive self-ligating brackets. 3. The active self-ligating brackets expressed higher torque values than the passive self-ligating brackets at clinically usable torsion angles (0°-35°). 4. The passive self-ligating brackets produced lower moments at low torsion angles and started producing higher moments at high torsion that cannot be used clinically. 5. The clinically applicable range of torque activation was greater for the active self-ligating brackets than for the passive self-ligating brackets. 6. All the brackets showed significant variations in the torque expressed; this seemed to be attributed to the variation in bracket slot dimensions. Damon2 and Speed brackets were relatively more consistent than Smart Clip and In-Ovation brackets. 7. Based on our findings, future research should investigate torque expression on all maxillary anterior teeth simultaneously. 8. This research warrants a closer look at the usefulness of multiple bracket prescriptions because of the wide variations in torque expression and the high degrees of bracket archwire slop in passive self-ligating bracket systems. REFERENCES 1. O’Higgins EA, Kirschen RH, Lee RT. The influence of maxillary incisor inclination on arch length. Br J Orthod 1999;26:97-102. 2. Gioka C, Eliades T. Materials-induced variation in the torque expression of preadjusted appliances. 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