The effect of buccal lingual slot dimension size on third-order torque response

European Journal of Orthodontics, 2017, 209 214 doi:10.1093/ejo/cjw043 Advance Access publication 3 June 2016 Original Article The effect of buccal lingual slot dimension size on third-order torque response Dan L. Romanyk 1, Kenji Au 2, Darren Isfeld 1, Giseon Heo 1, Michael P. Major 1 and Paul W. Major 1 1 School of Dentistry, Faculty of Medicine and Dentistry and 2 Department of Mechanical Engineering, Faculty of Engineering, University of Alberta, Edmonton, Alberta, Canada Correspondence to: Paul W. Major, 5 478, Edmonton Clinic Health Academy (ECHA), University of Alberta, 11405 87 Avenue NW, Edmonton, AB, Canada T6G 1C9. E-mail: major@ualberta.ca Summary Introduction: The focus of the presented study was to investigate the effect of buccal lingual (B-L) orthodontic bracket slot dimension on third-order torque mechanics. Materials and methods: Three types of orthodontic brackets and two archwire sizes were considered. Ortho Classic H4 (0.026 B-L slot, passive), Ormco Damon Q (0.028 B-L slot, passive), and In-Ovation R (0.028 slot, active) brackets were tested using 0.017 0.025 and 0.019 0.025 beta-titanium archwires. An in vitro orthodontic torque simulator (OTS) was used to rotate archwires relative to a single bracket while recording forces and moments in three directions. For each bracket-archwire combination, a total of n = 47 samples were tested. Repeated measures analysis of variance between brackets was conducted for third-order torque values at 3 increments between 9 and 30 during loading and unloading for each archwire size. Results: Statistically significant differences between H4 and Q brackets were only found for 0.017 0.025 archwires during loading, and 0.019 0.025 archwires during unloading. Conversely, differences between H4 and R brackets were found for both archwires during loading and unloading phases. Finally, when using a 0.017 0.025 archwire the H4 brackets reached the 5 Nmm threshold before R and Q brackets; however, there was little difference found when using a 0.019 0.025 archwire. Conclusions: The concept of using a smaller B-L bracket slot dimension in orthodontic treatment showed it may theoretically allow for more options, primarily using smaller archwires to correct third-order rotational misalignments. However, it is suspected that bracket material limitations and added loading on the door currently prevent this from being clinically applicable. Introduction The study of third-order torque, referring to labial or lingual directed root torque, is an important topic of research in orthodontics. A number of in vitro studies in the literature have investigated various factors in orthodontic treatment that may affect torque expression. Archwire material, bracket material, incisal gingival (I-G) bracket dimension, bracket ligation method, use of pre-torqued archwires, and the effect of rotational misalignments have all been considered in previous research (1 10). All previous work has provided valuable insight to the mechanics of procedures utilizing third-order torque, making it imperative to continue such research as new treatment options arise. One aspect of third-order torque treatment that has yet to be investigated is the effect of altering the buccal lingual (B-L) slot dimension of a passively ligated bracket. Conventionally, passive self-ligating brackets utilize a 0.028 B-L slot dimension. More recently, brackets have been developed with a reduced B-L dimension, namely 0.026 as compared to the typical 0.028. Reducing the B-L dimension may have a number of implications on treatment The Author 2016. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: journals.permissions@oup.com 209

210 European Journal of Orthodontics, 2017, Vol. 39, No. 2 mechanics, one of which being the archwire rotation at which a third-order couple is generated. It is suggested that with the reduced B-L dimension, the archwire could contact the bracket door and base prior to engaging the I-G walls based on geometry of the archwireslot combination. This in turn should result in a couple being generated sooner in third-order archwire rotation from a neutral position. A primary suggested advantage of the reduced B-L dimension is that it could allow clinicians the option of using smaller archwires in correcting third-order misalignments. This in theory would then allow for a larger amount of archwire rotation inside the suggested clinically effective 5 20 Nmm range (11 13) than when using larger, and thus stiffer, archwires. While these potential advantages would be optimal in orthodontic treatment, they have yet to be investigated in the literature. The study presented here investigates the third-order mechanics of 0.026 B-L dimension passive, 0.028 B-L dimension passive, and 0.028 B-L dimension active self-ligating brackets using an in vitro orthodontic torque simulator (OTS). Beta-titanium archwire sizes of 0.017 0.025 and 0.019 0.025 were both tested for each type of bracket. Results from this study were used to understand how B-L slot dimension influences third-order torque mechanics as well as how different archwire sizes effect results. Materials and methods Study design An orthodontic torque simulator, which is fully described in previous research (2 4, 7, 10), was used to examine the mechanics of thirdorder torque on all three types of brackets: the Damon Q (Ormco Corporation, Orange, California, USA) with 0.028 B-L dimension, H4 (Ortho Classic, McMinnville, Oegon, USA) with 0.026 B-L dimension, and 0.028 B-L dimension In-Ovation R (GAC, Bohemia, New York, USA) active-ligation brackets. All brackets tested had a 0.022 I-G dimension. Brackets were mounted on top of individual stainless-steel dowels with LOCTITE E-60HP Hysol Epoxy adhesive (Loctite, Westlake, Ohio, USA) for placement in the OTS, as illustrated in Figure 1. All three types of brackets were ligated using both 0.017 0.025 and 0.019 0.025 rectangular beta-titanium straight wires (G&H Wire Company, Franklin, Indiana, USA). The dowels were mounted onto a six-axis load cell (Nano17, ATI Industrial Automation, Apex, North Carolina, USA) that measures three dimensional forces and moments. Using translational and rotational stages on the OTS, initial loads were minimized to below 0.05 N and 0.035 Nmm for forces and moments, respectively, in all directions. A sample size of 282, 47 brackets per bracket type per archwire, was examined for this study. This sample size was determined from pilot data using 0.017 0.025 beta-titanium archwires and 10 of each bracket type. In order to detect a third-order torque difference of 4 Nmm between brackets with a Type I error rate of 0.05 and power of 0.9, 47 samples of each bracket per archwire was required (14). The test order of brackets was randomized, with the 0.017 0.025 archwire group being tested first followed by the 0.019 0.025 group. Third-order rotations were introduced in 3 increments from a neutral position leading up to a 33 rotation at the end, and then unloaded in the same increments back to the neutral position. Only rotation up to 30 was considered for analysis as the extra step was put in to account for backlash in the motor system. At each of these positions the force and moment readings were logged. The six-axis load cell takes voltage readings and calculates forces and moments at the load cell, and thus a transformation is needed to obtain the torque readings at the bracket base. The offset values and subsequent load transformations for the bracket to dowel interface in all three planes was found using the same procedure defined in previous research (10). The coordinate system at the base of the bracket is defined in Figure 2. Statistical analysis Preliminary analysis of variance (ANOVA) found each factor term archwire angle, archwire type, and bracket type as well as their interaction terms to be statistically significant with P < 0.001. As such, repeated-measures ANOVA was conducted to investigate the response of third-order torque, T x, during archwire loading and unloading. Post hoc pairwise tests of each bracket-archwire combination, using a Bonferroni corrected procedure, for T x at every 3 in the range of 9 30 was completed to determine whether or not the brackets were statistically different, P 0.05. Both loading and unloading data was investigated; however, they were studied separately as the presence of backlash prevents comparison between loading phases. The 9 30 range was selected based on post hoc observation of the data. It was found that during archwire rotation, the earliest that any archwire-bracket combination reached the 5 Nmm clinically relevant threshold was approximately 9. As tooth movement is not expected prior to this threshold, statistical analysis prior to this angle was deemed unnecessary. Additionally, even though archwire rotation up to 33 was utilized, statistical analysis was only considered up to 30. As a result of backlash in the system, measurements between 30 and 33 are not accurate, and as such are not included in the analysis. For these reasons, 9 30 was the selected range for statistical analysis of results. Results The average absolute T x values for each archwire size is plotted in Figure 3. Graphically all three types of brackets follow the same trend for the loading and unloading curves. Additionally, the magnitudes of T x at 30, representing maximum torque expression, and angles at which the 5 Nmm clinical threshold was surpassed during loading for each bracket-archwire combination are reported in Table 1. Figure 1. R (left), Q (middle), and H4 (right) brackets ligated in the OTS for testing.

D. L. Romanyk et al. 211 R, Q, and H4 brackets were found to generate 42.6, 41.3, and 37.9 Nmm of T x, respectively, at 30 during the loading phase of archwire rotation using a 0.019 0.025 archwire. When using a 0.017 0.025 archwire, the T x values at 30 were found to be 27.4, 24.0, and 21.2 Nmm for R, Q, and H4 brackets, respectively. With respect to reaching the 5 Nmm threshold when using a 0.019 0.025 archwire, both the Q and H4 brackets surpassed this level between 9 and 12 of archwire rotation, while the R brackets reached this limit in the 6 9 range. Conversely, when using a 0.017 0.025 archwire the H4 brackets reached the 5 Nmm limit first in the range of 9 12 of rotation, while the R and Q brackets were in the range of 15 18. Figure 2. Right-handed coordinate system defined at the base of the bracket. Comparisons that were found to be statistically different for P 0.05 are tabulated in Tables 2 and 3 for loading and unloading, respectively. Comparisons made between sizes of archwires are not reported either as, in general, it would be expected that a 0.019 0.025 archwire would produce greater torque than a 0.017 0.025 archwire for the same material. As such, since these results are not of great interest in this study and in order to simplify a large dataset, they were not reported. The final sample size of brackets used in this study was 264. Samples were omitted due to data corruption (i.e. data not properly exporting from the software or logging during experiments), software crashes during experiments, or in the case of improper experimental setup before testing (e.g. not fully securing an archwire segment or dowel in the OTS before running a trial). There were no statistically significant differences observed between the Q and R brackets for either size of archwire during loading or unloading phases. During the loading phase, H4 demonstrated greater torque expression than Q between 9 and 15 degrees of rotation with the 0.017 0.025 archwire, but there was no difference for larger rotations. Torque expression for H4 was greater than R at 12 of rotation with the 0.017 0.025 archwire, but less than R for rotation beyond 27. H4 demonstrated less torque expression than R for more than 15 of rotation with the 0.019 0.025 archwire. During the unloading phase, H4 demonstrated less torque expression than R for 30 21 of wire rotation with 0.017 0.025 archwire. H4 demonstrated less torque expression than Q between 21 and 12 of wire rotation with 0.019 0.025 archwire, and less torque expression than R between 30 and 12 wire rotation with 0.019 0.025 archwire. Figure 3. Plots of absolute average T x during archwire rotation for: (top left) 0.019 0.025 archwire loading; (top right) 0.019 0.025 archwire unloading; (bottom left) 0.017 0.025 archwire loading; (bottom right) 0.017 0.025 archwire unloading.

212 European Journal of Orthodontics, 2017, Vol. 39, No. 2 Discussion With respect to the lack of difference between Q and R brackets, previous work (3) found they behaved similarly, especially above approximately 9 of archwire rotation, when using 0.019 0.025 stainless steel archwires. As such, the lack of statistical difference in this study is not unexpected. Table 1. Comparisons of three different bracket types for T x and angle of rotation during the loading phase to reach the 5 Nmm threshold. Bracket type Torque value at 30 ± SD (Nmm) 0.019 0.025 archwires Q 41.3 ± 5.9 9 12 H4 37.9 ± 8.6 9 12 R 42.6 ± 6.5 6 9 0.017 0.025 archwires Q 24.0 ± 5.9 15 18 H4 21.2 ± 7.8 9 12 R 27.4 ± 4.1 15 18 Angle range for 5 Nmm threshold ( ) From a clinical perspective, it is the unloading curve that is of greatest interest. Being that the clinician deforms the archwire and then ligates it in the bracket, it is the peak torque and unloading response that will truly govern treatment. With that being said, the loading curve is also of interest in that it provides information regarding the response of the bracket-archwire pair without any permanent deformation in the system. Having knowledge of this data without any adverse effects can provide valuable information towards future research and bracket development. As a result, both the loading and unloading phases are of interest in the research of third-order torque mechanics and are to be considered here. When studying the H4-Q comparisons, both passive ligating brackets, the change in archwire size resulting in statistically significant differences between loading and unloading phases is immediately interesting. The H4 brackets generated significantly greater torque values than the Q brackets when using a 0.017 0.025 archwire during loading; however, during unloading the brackets were not significantly different. When using a 0.019 0.025 archwire, there was no difference during loading between these brackets, but during the unloading phase the Q brackets generated significantly greater torque than the H4. Table 2. Pairwise comparison of different bracket types for statistically significant (P 0.05) differences, after Bonferroni correction, during the loading phase. Pair for comparison Degree of rotation ( ) Mean difference, T x (Nmm) Std. error Sig. Table 3. Pairwise comparison of different bracket types for statistically significant (P 0.05) differences, after Bonferroni correction, during the unloading phase. Pair for comparison Degree of rotation ( ) Mean difference, T x (Nmm) Std. error Sig. Interval for difference Lower bound H4 Q; 0.017 0.025 9 2.5 0.744 0.011 0.3 4.7 12 3.4 0.937 0.006 0.6 6.1 15 3.7 1.082 0.012 0.5 6.9 H4 R; 0.017 0.025 12 2.8 0.932 0.048 0.1 5.5 27-4.9 1.322 0.003-8.9-1.0 30-6.2 1.365 0.000-10.3-2.2 H4 R; 0.019 0.025 15 4.0 1.132 0.008 7.3 0.6 18 4.7 1.230 0.002 8.4 1.1 21 5.1 1.288 0.001 8.9 1.3 24 5.2 1.344 0.002 9.1 1.2 27 5.0 1.391 0.006 9.1 0.9 30 4.7 1.436 0.016 9.0 0.5 Interval for difference Lower bound H4-Q; 0.19 0.025 21 3.6 1.198 0.044 7.1 0.1 18 3.6 1.095 0.016 6.9 0.4 15 3.4 0.971 0.009 6.2 0.5 12 2.4 0.781 0.036 4.7 0.1 H4-R; 0.017 0.025 30 6.6 1.324 0.000 10.6 2.7 27 6.3 1.288 0.000 10.1 2.5 24 5.8 1.240 0.000 9.5 2.1 21 4.5 1.159 0.002 8.0 1.1 H4-R; 0.019 0.025 30 4.5 1.392 0.021 8.6 0.4 27 4.6 1.355 0.011 8.7 0.6 24 4.8 1.304 0.004 8.7 1.0 21 5.0 1.219 0.001 8.6 1.3 18 4.9 1.114 0.000 8.2 1.6 15 4.5 0.987 0.000 7.4 1.6 12 3.4 0.795 0.000 5.8 1.1 Upper bound Upper bound

D. L. Romanyk et al. 213 The most probable factors leading to these results in the H4-Q comparisons are the reduced B-L dimension of the H4 bracket, and the subsequent deformation of the door on the brackets. As from Table 1, the H4 brackets surpassed the 5 Nmm threshold using 0.017 0.025 archwires between 9 and 12, while the Q brackets were in the range of 15 18. This is most likely a result of the archwire engaging the B-L walls of the H4 bracket sooner than it engages the slot of the Q. This statistical difference only exists at 9, 12, and 15, with no difference afterwards. Beyond 15 of archwire rotation it is suspected that engagement of the I-G walls results in similar torque expression. From the T x generated using 0.017 0.025 archwires during loading, there is a noticeable change in the H4 behaviour. Initially, average T x values of the H4 bracket are larger than the Q; however, in the 18 24 range the H4 brackets shift below the other two. It is suspected that the door of the H4 bracket supports much of the archwire rotation as a result of the reduced B-L dimension. Then, in the 18 24 range it is suspected that the door begins to undergo appreciable plastic deformation resulting in the shift in the T x curve. As a result of the suggested plastic deformation, the slot size of the H4 would increase permanently, and thus causing the lack of any difference between H4 and Q brackets during unloading of the 0.17 0.025 archwire. When using a 0.019 0.025 archwire in the H4-Q comparison, there was no difference during loading, only during unloading. As a result of the larger archwire, it is suggested that the reduced B-L dimension of the H4 had no significant influence on T x as the archwire likely engaged the I-G walls of the bracket at approximately the same time; however, during unloading the Q bracket generated statistically greater T x than the H4 from 21 to 12 of rotation. This difference between loading and unloading phases is likely again due to plastic deformation of the H4 bracket, namely the door. Without this plastic deformation, the brackets should behave the same during loading and unloading. The H4-R comparison resulted in statistically significant differences for both archwire sizes during loading and unloading. With the exception of the 12 comparison during loading with a 0.017 0.025 archwire, the R bracket generated larger T x values than the H4. There are potentially a couple of explanations for this result. Firstly, while the R bracket is designed for active ligation, is it still possible that a 0.017 0.025 archwire remained passive during early archwire rotation. Second, when the archwire engages the door, it is possible that the door on the H4 brackets proved stiffer initially than the active clip of the R brackets. It is also certainly possible that a combination of these factors also lead to the findings at 12. At the upper end of the loading phase, 27 and 30, the R brackets generated significantly greater torque than the H4 when using 0.017 0.025 archwires. For the 0.019 0.025 archwires from 15 to 30, the R brackets produced significantly greater T x than the H4. During unloading, the R brackets generated statistically greater torque than H4 s in the range of 30 21 and 30 12 for 0.017 0.025 and 0.019 0.025 archwires, respectively. It is suggested, as previously mentioned, that this difference is a result of the H4 door weakening and plastic deformation at higher loads. This phenomenon would explain the increasing difference at higher loads during loading, as well as the greater range of archwire rotations at which the brackets differ during unloading. In regards to third-order torque mechanics and using a reduced B-L slot dimension of 0.026, the results indicate in theory that this could lead to earlier bracket-archwire engagement using smaller archwires. From Table 1, during loading the H4 brackets reached the 5 Nmm threshold before the R and Q brackets when using a 0.017 0.025 archwire. Conversely, when using a 0.019 0.025 archwire the actively ligating R bracket reached 5 Nmm before both of the passively ligating brackets. The discrepancy between the archwire sizes is likely a result of the larger archwire engaging the I-G walls of the bracket before or at approximately the same time as it engages the B-L walls. While earlier bracket-archwire engagement with a smaller B-L dimension does result in reaching the 5 Nmm threshold sooner, it also means that more torsional load will be carried by the bracket door and the base of the slot. While the base of the bracket is supported by the tooth and will likely undergo minimal deformation, the door is more susceptible to this. As it is suspected that the H4 bracket door underwent appreciable plastic deformation during larger archwire rotation, as deduced from the discrepancy in loading and unloading results, it was not able to withstand the added load. Though, in theory, if the door were capable of withstanding this added load within its elastic region, then the advantage of using a 0.026 B-L slot dimension could be realized. As unloading is the clinical scenario resulting in tooth movement, it is imperative the bracket integrity remain intact during this phase. Clinically, there are a number of important implications from results of this study. The concept of generating a third-order couple sooner in archwire rotation when using smaller archwires and B-L dimension brackets showed some validity. It is unknown at this time if the unloading curve would also demonstrate greater torque expression with reduced B-L dimension if the maximum archwire rotation were reduced. As there was a change observed in H4 T x values during loading in the 18 24 range, it is possible that if archwire rotation were reduced below this range then the unloading curve would emulate the loading curve more closely. As previously discussed in detail, added loading on the bracket door appears to introduce issues with respect to plastic deformation. When considering orthodontic treatment, should advances be made in brackets to minimize/eliminate this plastic deformation during archwire rotation, this concept could prove useful in allowing for the use of smaller archwires. As a result, lower third-order torque values at higher amounts of archwire rotation could be achieved through use of a 0.017 0.025 archwire as compared to a 0.019 0.025. This could allow for a larger range of tooth movement occurring inside the optimal 5 20 Nmm range. When using a 0.019 0.025 archwire however, there was much less difference, if any, between the type of brackets tested and when they surpassed the 5 Nmm threshold. In clinical practice, if 0.019 0.025 archwires are to be used by the clinician, the potential advantage of using the smaller B-L dimension slot would no longer be relevant with respect to third-order torque mechanics. Another result that requires discussion is the large standard deviation of the H4, or 0.026 slot, brackets shown in Figure 3 and Table 1. The standard deviation of the H4 brackets at the larger degrees of archwire rotation approaches values around 8 9 Nmm for both sizes of archwires; however, R and Q brackets remain in the vicinity of 4 6 Nmm standard deviation at these same larger T x values. It is suspected that the reduced slot dimension, and difficulty obtaining the zero position as a result, was a cause of this. When attempting to locate the neutral, or zero, position of an archwire for experiments with the 0.026 slot dimension, it was found to be particularly difficult in that the archwire frequently engaged the B-L walls for small rotations of the archwire. As such, there were a number of instances where the zero position was thought to be located, but once the experiment began it was found that this position was

214 European Journal of Orthodontics, 2017, Vol. 39, No. 2 slightly off by approximately 1 3. Additionally, since the smaller slot size results in more torsional loading being resisted by the door, the larger standard deviation could result from a variable response of the door. If the door were to begin to slide as opposed to simply deform (e.g. bend), or have some combination of this, it could result in different behaviour between samples. Finally, dimensional variations of the bracket slot and/or larger tolerances could also be a contributing factor to increased sample standard deviations. Clinically, the larger standard deviation could result in a larger variation in results between patients depending on the initial rotation of the archwire and its location in the slot. Furthermore, the zero position in this study was located in a controlled laboratory setting, making it easier to accurately position the archwire than in the clinical environment. Thus, it can be suspected that the difficulty in locating/knowing the zero position of the archwire for third-order rotation would translate, and potentially magnify, when moving to clinical treatment. In fact, given variations in bracket and archwire tolerances/dimensions, it can even be suggested that an occasion could arise where the B-L dimension of the archwire and bracket are actually the same. In this instance, a true zero position may not even be realized, having implications towards patient treatment. While the presented study provides valuable information with respect to third-order torque mechanics in orthodontic treatment, there are a number of limitations that must be mentioned. Firstly, only a single bracket type was tested for each slot size considered in this study. Additionally, only two sizes of rectangular archwires, 0.017 0.025 and 0.019 0.025, were considered. These brackets and wire sizes were chosen due to their availability and commonality, however other options do exist. Future work in this area could include the investigation of other archwire sizes and how they impact third-order torque mechanics. Bracket slot dimensions were not measured prior to testing. As it has been shown that dimensions may vary significantly from the nominal value (15), future work regarding this topic could include measurement before experiments to correlate true slot sizes to third-order torque values. Conventional elastic ligation was also not considered in this study. Finally, the true oral environment, namely periodontal ligament compliance, was also not replicated in this in vitro study; however, previous work has shown that replication of compliance in the periodontium has minimal clinical relevance when investigating third-order torque mechanics (16). A number of future investigations should be conducted to elucidate added topics of interest arising from this study. Firstly, while evidence suggests that plastic deformation of the H4 bracket door is the root of a number of aforementioned discrepancies, the 3D deformation should be thoroughly analyzed. This may be completed using methods previously described in the literature (7), or other similar means. Additionally, a study of H4 bracket slot dimensions and their variation would prove useful in understanding the large standard deviation found here. The use of other archwire materials and sizes, as well as inclusion of elastically ligated brackets, would improve upon the limitations of this study. Finally, only the third-order torque mechanics of reduced B-L dimension brackets was considered here, capturing only one aspect of orthodontic treatment. It would be advantageous to investigate these brackets in other aspects of treatment, namely sliding mechanics, to gain a full understanding of their mechanics. In summary, this study elucidated a number of effects resulting from reducing the B-L slot dimension of orthodontic brackets during thirdorder torque. While there is the potential for a smaller B-L slot dimension to expand third-order treatment possibilities for clinicians, current bracket limitations may prevent this. Future investigation of this topic could include the inclusion of other archwire sizes and/or materials. Acknowledgements The authors would like to acknowledge the financial support of the McIntyre Fund at the University of Alberta in the completion of the research presented here. Conflict of interest The authors declare that there are no conflicts of interest to report. References 1. Gmyrek, H., Bourauel, C., Richter, G. and Harzer W. 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