The European Journal of Orthodontics Advance Access published October 30, 2015 European Journal of Orthodontics, 2015, 1–11 doi:10.1093/ejo/cjv063
Original article
In vitro biomechanical analysis of torque capabilities of various 0.018″ lingual bracket– wire systems: total torque play and slot size Nikolaos Daratsianos*, Christoph Bourauel**, Rolf Fimmers***, Andreas Jäger* and Rainer Schwestka-Polly**** *Department of Orthodontics, **Endowed Chair of Oral Technology, ***Department of Medical Biometry, Informatics and Epidemiology, University of Bonn, and ****Department of Orthodontics, Hannover Medical School, Germany Correspondence to: Nikolaos Daratsianos, Poliklinik für Kieferorthopädie, Universitätsklinikum Bonn, Welschnonnenstr. 17, 53111 Bonn, Germany. E-mail: [email protected]
Summary Objectives: To determine the total torque play of various rectangular titanium molybdenum alloy (TMA)/ stainless steel (SS) wires in various 0.018″ upper incisor lingual brackets and slot size measurements. Methods: TMA (0.0175″ × 0.0175″, 0.0170″ × 0.025″, 0.0182″ × 0.0182″, 0.0182″ × 0.025″) and SS wires (0.016″ × 0.022″, 0.016″ × 0.024″, 0.018″ × 0.025″) were twisted in standard (Hiro, Incognito™, Joy®, Kurz 7th generation, STb™: fixation with elastic modules) and self-ligating brackets (Evolution SLT®, In-Ovation® L MTM: closed ligation mechanism) from −20 degrees to +20 degrees with a custom-made machine. The total torque play was calculated by extrapolating the linear portion of the twist/moment curves to the xaxis and adding the absolute negative and positive angle values at the intercepts. The bracket slot height was measured before and after the experiments with a series of pin gauges with round profile. Results: Brackets in ascending order for total torque play with the most slot-filling wire TMA 0.0182″ × 0.025″: Evolution SLT® (0 degree ± 0 degree), Incognito™ (2.2 degrees ±1.1 degrees), Hiro (5.1 degrees ±3.0 degrees), In-Ovation® L MTM (6.3 degrees ±2.2 degrees), STb™ (6.6 degrees ±1.8 degrees), Kurz 7th generation (7.1 degrees ±0.8 degrees), and Joy® (12.0 degrees ±0.8 degrees). Wires in ascending order for total torque play with the most precise slot Incognito™: TMA 0.0182″ × 0.025″ (2.2 degrees ±1.1 degrees), TMA 0.0182″ × 0.0182″ (2.4 degrees ±0.9 degrees), SS 0.018″ × 0.025″ (5.5 degrees ±1.0 degrees), TMA 0.0170″ × 0.025″ (9.4 degrees ±1.8 degrees), TMA 0.0175″ × 0.0175″ (13.0 degrees ±1.5 degrees), SS 0.016″ × 0.024″ (16.1 degrees ±1.4 degrees), SS 0.016″ × 0.022″ (17.8 degrees ±1.0 degrees); differences between some of the experimental groups were not statistically significant. Bracket slot dimensions in ascending order: Evolution SLT® (less than 0.452 mm), Incognito™ (0.460 mm ±0.002 mm), In-Ovation® L MTM (0.469 mm ±0.001 mm), Hiro (0.469 mm ±0.010 mm), STb™ (0.471 mm ±0.002 mm), Kurz 7th generation (0.473 mm ±0.002 mm), and Joy® (greater than 0.498 mm). Limitations: The applied method must be questioned when used with brackets with incomplete slot walls (Evolution SLT®). Slot measurement with pin gauges may not register bracket wing deformation. Conclusions: All brackets showed a differing slot size from the nominal 0.018″ (0.457 mm). Incognito™ presented the most precise and Joy® the widest slot. The main wires for the retraction phase SS 0.016″ × 0.022″/SS 0.016″ × 0.024″ showed poor torque control. Among the finishing TMA wires, TMA 0.0175″ × 0.0175″ exhibited the highest and TMA 0.0182″ × 0.0182″/TMA 0.0182″ × 0.025″ the smallest torque play. Significance: The manufacturers could profit from this investigation towards optimization of the dimensional precision of their products. The orthodontist must be aware of the torque play of the wire– bracket combinations to be able to plan and individualize the appliance by third order customization.
© The Author 2015. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: [email protected]
1
European Journal of Orthodontics, 2015
2
Introduction Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis (1). In orthodontics, torque is described as a moment generated by the torsion of a rectangular wire in the bracket slot (2) and it is employed to alter the buccolingual inclination of the teeth. The dimensions of the working archwires never reach the full dimensions of the bracket slot; therefore, some lack of control exists between the bracket slot and the wire, known as the ‘play’ or deviation angle or engagement angle. This angle is the amount of rotation in degrees that a rectangular or square wire must be twisted in order to engage the slot and generate biomechanical torque. The third-order clearance often extends to 100% of the prescribed buccolingual tooth inclination and makes the appliance equivalent to using round wires (3). Theoretically, third-order moments can be calculated from the nominal dimensions of archwires and brackets given by the manufacturers, however a considerable discrepancy between the theoretical and the measured bracket/archwire play should be taken into consideration (4). This can be attributed to intrinsic variations in archwire cross-sectional diameters, bracket slot dimensions, archwire edge bevelling, and bracket deformations (5). Accurate calculation with the manufacturer’s data is therefore impossible and an experimental approach is recommended instead. Following the development of lingual orthodontics, there was a gradual change from ready-for-use appliances combined with selfbent undersized wires to fully customized systems with slot-filling wires. Besides, most contemporary techniques are based on a set-up as a treatment objective, indirect bonding for high precision, and almost eliminate the need for individual third order wire bends made by the orthodontist. By changing the buccolingual inclination of the bracket slot in relation to the tooth and creating an individual base for each bracket, torque control became more predictable with easy to fabricate non-twisted (straight) arch wires. Having a set-up as a treatment objective almost dictates the need for using slot-filling archwires, in order to achieve the planed tooth position precisely. Furthermore, lingual bracket slots are positioned at a substantial distance from the labial surfaces, making the vertical height of the brackets vary with the torque angle of the labial surfaces and furthermore making torquing adjustments affect not only the inclination of the labial surfaces but also their heights (6), as high as 1.2 mm/10 degrees in the incisor region and 2 mm/10 degrees in the buccal segments (7). For these reasons, torque control in lingual orthodontics is even more important than with buccal appliances, especially for the upper incisors.
Purpose of the study The purpose of this study was to determine the torque play of several commonly used rectangular titanium molybdenum alloy (TMA) and stainless steel (SS) wires in lingual orthodontics for applying or controlling torque in the guiding, retraction, and finishing phase inside the bracket slot of common upper incisor 0.018″ × 0.025″ lingual brackets and to measure their slot size.
base to fit on the flat surface of the metal axis of the testing machine; they underwent the usual quality procedure as patient brackets.
Experimental design Five randomly chosen brackets out of the received 10–20 from each type were used for the measurements. A straight 20 mm long piece of wire was cut and fixed in a slot in a steel axis mounted on the torque sensor on a motor-driven rotation table of a self-developed, custom made testing machine (Figure 1a–c) introduced earlier (8). The brackets were bonded on the surface of another steel axis that was mounted on an opposing motor-driven rotation table by application of a two-component polymethylmetacrylate (Stabilit Express, Henkel AG & Co, Düsseldorf, Germany). The steel axis with the bracket was manually adjusted as needed to an estimated zero torque position in relation to the wire and then immobilized. The wire was secured in the bracket slot with one elastic module (QuiK-StiK™, 3M Unitek Corporation, Monrovia, USA) as a simple overtie, the only ligature type which could be fixed on all brackets in a reproducible way; the self-ligating brackets were tested with closed ligation mechanism. The length of the wire between the end of the bracket slot and the interception into the opposite axis was kept constant through all experiments at 4.6 mm, simulating a typical clinical upper central incisor interbracket distance for a lingual appliance (9). The measuring moment sensor was placed on the wire side on the rotation table, and the wire was fixed exactly in the middle of the rotation table in order to deliver pure moments and prevent linear forces, which would influence the measured moment. The Table 1. The used brackets and wires and their manufacturers. Standard brackets Hiro Incognito™
Joy® Kurz 7th generation STb™
Self-ligating brackets Evolution SLT® In-Ovation® L MTM
All brackets and wires used in this study along with their manufacturers’ information are listed in Table 1. They were sponsored by the companies and received between January and June 2010. The Incognito™ brackets were specially manufactured with a slot used for upper central incisors and a flat instead of a tooth-fitting
Adenta GmbH, Gilching, Germany Dentsply GAC International Bohemia, New York, USA
Wires TMA 0.0175″ × 0.0175″ TMA 0.0170″ × 0.025″ TMA 0.0182″ × 0.0182″ TMA 0.0182″ × 0.025″
Materials and methods
Medics XXI, Spain TOP-Service für Lingualtechnik, 3M Unitek Corporation, Bad Essen, Germany Adenta GmbH, Gilching, Germany Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA
SS 0.016″ × 0.022″ SS 0.016″ × 0.024″ SS 0.018″ × 0.025″
Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA Dental Devices and Supplies Ltd, Leicestershire, UK Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA Dental Devices and Supplies Ltd, Leicestershire, UK Ormco Corporation, Orange, California, USA
3
N. Daratsianos et al.
(a)
Sensor
Motor
A/D
FLEX
computer controlled the motor and registered the torquing moments sent from the sensor for every 0.2 degrees with a resolution of 0.03 Nmm. 200 moment values were registered for the way forward and another 200 for the way back. In a preliminary experiment, the reproducibility of the measuring procedure was tested by comparing three mean curves: an overall mean, a weighted mean (10) x =
1 ⋅ xi σi and a random mean, n 1 ∑ i =1 σ i
∑
n
i =1
plotted after testing different specimens of the same kind, each for five repeated measurements (9). The comparison showed minimal systematic error (e.g. 0.25 degrees at 1.0 Nmm), allowing us to conduct the study without any repeats with identical specimens. However, the experiment was conducted a total of five times for each material combination, each time with different bracket and wire specimens of the same type, to eliminate any systematic error due to manufacture inconsistency of the bracket slot and deformation of the wire. Each bracket specimen was tested with all seven wire types. Each wire specimen was used once.
Data preparation
Figure 1. (a) Scheme of the experimental design. (b) The testing machine had two rotation tables (rectangular black boxes). The right rotation table was disabled but it could be linearly manually adjusted to achieve a full wire engagement in the slot. The bracket was bonded on a steel axis, which was fixed to the right rotation table. The wire was fixed to the left rotation table, which was activated to apply the twist to the wire. The moment sensor (big silver cylinder) was placed between the left rotation table and the fixation point of the wire. (c) Close-up of the testing machine with a stainless steel wire and a STb™ bracket.
motor-driven rotation table on the wire side was rotated against the immobilized bracket into the starting position, −20 degrees from the estimated zero torque position, followed by a continuous rotation to a maximum of +20 degrees and back to −20 degrees. Since the zero torque position was only an estimation and a result of manual adjustment, this procedure ensured that there would be enough linear part of the graph, i.e. that the wire would engage in the slot, so that the torque play calculation would be possible regardless of any third-order misalignment between bracket and wire. A personal
The data were plotted in a graph in Excel 2010 (Microsoft Corporation, Redmond, Washington, USA) (Figure 2a). Since there was a slight difference between the increasing and decreasing slope of the graphs, especially in the middle part while the wire was not fully engaged, an average of the clockwise and counter clockwise twist was calculated (Figure 2b), except for the bracket Evolution SLT®. The difference vanished and the endpoints of the curves coincided once the wire was twisted beyond the torque play angle and engaged in the slot, a behaviour described previously (11) that can be probably explained by unequal friction between the clockwise and counter clockwise twist. Averaging the way forward and backward curves led inherently to a change of the angular values for a given moment—mainly in the middle of each graph—but without influencing the torque play values, which were calculated from the nearly coinciding linear ending parts of the curves. With Evolution SLT®, there was a critical difference in the entire shape of the plots and only the activation curves (from 0 degree to +20 degrees and from 0 degree to −20 degrees) were used for further analysis without any averaging process (Figure 2d). In some cases, the testing came up with plots being off-centre in the horizontal and vertical dimension, due to lack of accuracy in third-order centring of the wire in the bracket slot, especially when using undersized wires. In these cases, the way-forward way-backaveraged plots were centred by moving the data in Excel in a manual procedure, so that the point of change of the direction of convexity in the middle of each graph was approximately at the intercept of the vertical and horizontal axis (Figure 2c). Since the difference of the positive and negative torque play value at the intercepts with the x-axis within one graph was the same regardless of any movement, this procedure did not influence the results; it was only performed to allow better averaging and visualization for the graphical plots.
Calculation of the total torque play After data preparation, the torque play was calculated from every one of the 245 data series (5 specimens of 7 bracket types tested with 7 wire types), each consisting of 200 moment values corresponding to angle values from −20 to +20 degrees in 0.2 degree steps, by extrapolating the linear portion of the twist/moment curve back to the x-axis from both negative and positive twist angle curves.
European Journal of Orthodontics, 2015
4
Figure 2. Data preparation: (a) A typical moment/angle curve without any modifications shows that the clockwise twist of the wire is slightly different than the anticlockwise twist. The difference decreases with increasing twist angle and the ends of the plot nearly coincide. (b) A typical averaged curve, which was calculated by averaging the clockwise and anticlockwise original curves of (a). The graph is a little off centre, both horizontally and vertically, due to imprecise centring of the undersized wire (SS 0.016″ × 0.022″) in the bracket slot. (c) The curve of figure was centred both vertically and horizontally. The reference point was the change of the direction of convexity in the middle of each graph, which was moved to be at the intercept of the vertical and horizontal axis. (d) Typical angle/moment curve of Evolution SLT®. The upper curve shows the way forward and the lower the way backward. On the first part of the way forward and backward, there is a bend at about −14 degrees/+14 degrees, which does not exist in the further part of the curves. This effect is probably due to the elasticity of the active clip and the friction, which create different effects in the activation and deactivation curves. Therefore, only the last part of the way forward and backward (activation part of the curves) was used for the measurements.
The linear parts of the plots were selected with the following procedure: - Most curves became linear beyond 15 degrees (Supplementary Figure 1a); therefore all data between −15.0 degrees and 15.0 degrees were neglected for the calculation. - The graphs of the remaining data were visually checked and were used if they were linear in toto; in a few cases in which this was not the case, only a smaller-linear-part of the curve was considered. - For the curves which had been manually centred, any data being beyond the 20 degrees range were not used; if values beyond 15 degrees were missing, a linear part within the 15 degrees range was chosen after visual confirmation for linearity. The corresponding negative and positive angle at the intercept of the two trendlines of the linear parts with the x-axis were calculated with the function ‘TREND’ in Excel 2010 (Supplementary Figure 1b and 1c), and their absolute values were summarized as the total torque play for every one of the 245 data sets. Within each bracketwire group (consisting of five brackets and wires of the same type) an average and a standard deviation was calculated from the five total torque play values using Excel 2010. If the trendlines for positive moments did not intercept at the positive part of the x-axis and the
trendlines for negative moments at the negative part of the x-axis, the calculated values were neglected and were manually set at 0 degree so as to eliminate invalid torque values. The same was done if the slope of the plots reversed within one twist forward or backward.
Statistical analysis The results were visually summarized in bar graphs using IBM SPSS Statistics 22 (IBM Corporation, New York, New York, USA). The dependence of torque play from bracket and wire type was primarily analysed using a two-factorial analysis of variance. Since this analysis revealed a clear interaction (P 0.498 Kurz 7th 0.473 generation STb™ 0.471 Evolution 0.498 0.476
0.011 0.003
0.002 0.003
0.003
0.004
0.002
0.477
Original article
In vitro biomechanical analysis of torque capabilities of various 0.018″ lingual bracket– wire systems: total torque play and slot size Nikolaos Daratsianos*, Christoph Bourauel**, Rolf Fimmers***, Andreas Jäger* and Rainer Schwestka-Polly**** *Department of Orthodontics, **Endowed Chair of Oral Technology, ***Department of Medical Biometry, Informatics and Epidemiology, University of Bonn, and ****Department of Orthodontics, Hannover Medical School, Germany Correspondence to: Nikolaos Daratsianos, Poliklinik für Kieferorthopädie, Universitätsklinikum Bonn, Welschnonnenstr. 17, 53111 Bonn, Germany. E-mail: [email protected]
Summary Objectives: To determine the total torque play of various rectangular titanium molybdenum alloy (TMA)/ stainless steel (SS) wires in various 0.018″ upper incisor lingual brackets and slot size measurements. Methods: TMA (0.0175″ × 0.0175″, 0.0170″ × 0.025″, 0.0182″ × 0.0182″, 0.0182″ × 0.025″) and SS wires (0.016″ × 0.022″, 0.016″ × 0.024″, 0.018″ × 0.025″) were twisted in standard (Hiro, Incognito™, Joy®, Kurz 7th generation, STb™: fixation with elastic modules) and self-ligating brackets (Evolution SLT®, In-Ovation® L MTM: closed ligation mechanism) from −20 degrees to +20 degrees with a custom-made machine. The total torque play was calculated by extrapolating the linear portion of the twist/moment curves to the xaxis and adding the absolute negative and positive angle values at the intercepts. The bracket slot height was measured before and after the experiments with a series of pin gauges with round profile. Results: Brackets in ascending order for total torque play with the most slot-filling wire TMA 0.0182″ × 0.025″: Evolution SLT® (0 degree ± 0 degree), Incognito™ (2.2 degrees ±1.1 degrees), Hiro (5.1 degrees ±3.0 degrees), In-Ovation® L MTM (6.3 degrees ±2.2 degrees), STb™ (6.6 degrees ±1.8 degrees), Kurz 7th generation (7.1 degrees ±0.8 degrees), and Joy® (12.0 degrees ±0.8 degrees). Wires in ascending order for total torque play with the most precise slot Incognito™: TMA 0.0182″ × 0.025″ (2.2 degrees ±1.1 degrees), TMA 0.0182″ × 0.0182″ (2.4 degrees ±0.9 degrees), SS 0.018″ × 0.025″ (5.5 degrees ±1.0 degrees), TMA 0.0170″ × 0.025″ (9.4 degrees ±1.8 degrees), TMA 0.0175″ × 0.0175″ (13.0 degrees ±1.5 degrees), SS 0.016″ × 0.024″ (16.1 degrees ±1.4 degrees), SS 0.016″ × 0.022″ (17.8 degrees ±1.0 degrees); differences between some of the experimental groups were not statistically significant. Bracket slot dimensions in ascending order: Evolution SLT® (less than 0.452 mm), Incognito™ (0.460 mm ±0.002 mm), In-Ovation® L MTM (0.469 mm ±0.001 mm), Hiro (0.469 mm ±0.010 mm), STb™ (0.471 mm ±0.002 mm), Kurz 7th generation (0.473 mm ±0.002 mm), and Joy® (greater than 0.498 mm). Limitations: The applied method must be questioned when used with brackets with incomplete slot walls (Evolution SLT®). Slot measurement with pin gauges may not register bracket wing deformation. Conclusions: All brackets showed a differing slot size from the nominal 0.018″ (0.457 mm). Incognito™ presented the most precise and Joy® the widest slot. The main wires for the retraction phase SS 0.016″ × 0.022″/SS 0.016″ × 0.024″ showed poor torque control. Among the finishing TMA wires, TMA 0.0175″ × 0.0175″ exhibited the highest and TMA 0.0182″ × 0.0182″/TMA 0.0182″ × 0.025″ the smallest torque play. Significance: The manufacturers could profit from this investigation towards optimization of the dimensional precision of their products. The orthodontist must be aware of the torque play of the wire– bracket combinations to be able to plan and individualize the appliance by third order customization.
© The Author 2015. Published by Oxford University Press on behalf of the European Orthodontic Society. All rights reserved. For permissions, please email: [email protected]
1
European Journal of Orthodontics, 2015
2
Introduction Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis (1). In orthodontics, torque is described as a moment generated by the torsion of a rectangular wire in the bracket slot (2) and it is employed to alter the buccolingual inclination of the teeth. The dimensions of the working archwires never reach the full dimensions of the bracket slot; therefore, some lack of control exists between the bracket slot and the wire, known as the ‘play’ or deviation angle or engagement angle. This angle is the amount of rotation in degrees that a rectangular or square wire must be twisted in order to engage the slot and generate biomechanical torque. The third-order clearance often extends to 100% of the prescribed buccolingual tooth inclination and makes the appliance equivalent to using round wires (3). Theoretically, third-order moments can be calculated from the nominal dimensions of archwires and brackets given by the manufacturers, however a considerable discrepancy between the theoretical and the measured bracket/archwire play should be taken into consideration (4). This can be attributed to intrinsic variations in archwire cross-sectional diameters, bracket slot dimensions, archwire edge bevelling, and bracket deformations (5). Accurate calculation with the manufacturer’s data is therefore impossible and an experimental approach is recommended instead. Following the development of lingual orthodontics, there was a gradual change from ready-for-use appliances combined with selfbent undersized wires to fully customized systems with slot-filling wires. Besides, most contemporary techniques are based on a set-up as a treatment objective, indirect bonding for high precision, and almost eliminate the need for individual third order wire bends made by the orthodontist. By changing the buccolingual inclination of the bracket slot in relation to the tooth and creating an individual base for each bracket, torque control became more predictable with easy to fabricate non-twisted (straight) arch wires. Having a set-up as a treatment objective almost dictates the need for using slot-filling archwires, in order to achieve the planed tooth position precisely. Furthermore, lingual bracket slots are positioned at a substantial distance from the labial surfaces, making the vertical height of the brackets vary with the torque angle of the labial surfaces and furthermore making torquing adjustments affect not only the inclination of the labial surfaces but also their heights (6), as high as 1.2 mm/10 degrees in the incisor region and 2 mm/10 degrees in the buccal segments (7). For these reasons, torque control in lingual orthodontics is even more important than with buccal appliances, especially for the upper incisors.
Purpose of the study The purpose of this study was to determine the torque play of several commonly used rectangular titanium molybdenum alloy (TMA) and stainless steel (SS) wires in lingual orthodontics for applying or controlling torque in the guiding, retraction, and finishing phase inside the bracket slot of common upper incisor 0.018″ × 0.025″ lingual brackets and to measure their slot size.
base to fit on the flat surface of the metal axis of the testing machine; they underwent the usual quality procedure as patient brackets.
Experimental design Five randomly chosen brackets out of the received 10–20 from each type were used for the measurements. A straight 20 mm long piece of wire was cut and fixed in a slot in a steel axis mounted on the torque sensor on a motor-driven rotation table of a self-developed, custom made testing machine (Figure 1a–c) introduced earlier (8). The brackets were bonded on the surface of another steel axis that was mounted on an opposing motor-driven rotation table by application of a two-component polymethylmetacrylate (Stabilit Express, Henkel AG & Co, Düsseldorf, Germany). The steel axis with the bracket was manually adjusted as needed to an estimated zero torque position in relation to the wire and then immobilized. The wire was secured in the bracket slot with one elastic module (QuiK-StiK™, 3M Unitek Corporation, Monrovia, USA) as a simple overtie, the only ligature type which could be fixed on all brackets in a reproducible way; the self-ligating brackets were tested with closed ligation mechanism. The length of the wire between the end of the bracket slot and the interception into the opposite axis was kept constant through all experiments at 4.6 mm, simulating a typical clinical upper central incisor interbracket distance for a lingual appliance (9). The measuring moment sensor was placed on the wire side on the rotation table, and the wire was fixed exactly in the middle of the rotation table in order to deliver pure moments and prevent linear forces, which would influence the measured moment. The Table 1. The used brackets and wires and their manufacturers. Standard brackets Hiro Incognito™
Joy® Kurz 7th generation STb™
Self-ligating brackets Evolution SLT® In-Ovation® L MTM
All brackets and wires used in this study along with their manufacturers’ information are listed in Table 1. They were sponsored by the companies and received between January and June 2010. The Incognito™ brackets were specially manufactured with a slot used for upper central incisors and a flat instead of a tooth-fitting
Adenta GmbH, Gilching, Germany Dentsply GAC International Bohemia, New York, USA
Wires TMA 0.0175″ × 0.0175″ TMA 0.0170″ × 0.025″ TMA 0.0182″ × 0.0182″ TMA 0.0182″ × 0.025″
Materials and methods
Medics XXI, Spain TOP-Service für Lingualtechnik, 3M Unitek Corporation, Bad Essen, Germany Adenta GmbH, Gilching, Germany Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA
SS 0.016″ × 0.022″ SS 0.016″ × 0.024″ SS 0.018″ × 0.025″
Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA Dental Devices and Supplies Ltd, Leicestershire, UK Ormco Corporation, Orange, California, USA Ormco Corporation, Orange, California, USA Dental Devices and Supplies Ltd, Leicestershire, UK Ormco Corporation, Orange, California, USA
3
N. Daratsianos et al.
(a)
Sensor
Motor
A/D
FLEX
computer controlled the motor and registered the torquing moments sent from the sensor for every 0.2 degrees with a resolution of 0.03 Nmm. 200 moment values were registered for the way forward and another 200 for the way back. In a preliminary experiment, the reproducibility of the measuring procedure was tested by comparing three mean curves: an overall mean, a weighted mean (10) x =
1 ⋅ xi σi and a random mean, n 1 ∑ i =1 σ i
∑
n
i =1
plotted after testing different specimens of the same kind, each for five repeated measurements (9). The comparison showed minimal systematic error (e.g. 0.25 degrees at 1.0 Nmm), allowing us to conduct the study without any repeats with identical specimens. However, the experiment was conducted a total of five times for each material combination, each time with different bracket and wire specimens of the same type, to eliminate any systematic error due to manufacture inconsistency of the bracket slot and deformation of the wire. Each bracket specimen was tested with all seven wire types. Each wire specimen was used once.
Data preparation
Figure 1. (a) Scheme of the experimental design. (b) The testing machine had two rotation tables (rectangular black boxes). The right rotation table was disabled but it could be linearly manually adjusted to achieve a full wire engagement in the slot. The bracket was bonded on a steel axis, which was fixed to the right rotation table. The wire was fixed to the left rotation table, which was activated to apply the twist to the wire. The moment sensor (big silver cylinder) was placed between the left rotation table and the fixation point of the wire. (c) Close-up of the testing machine with a stainless steel wire and a STb™ bracket.
motor-driven rotation table on the wire side was rotated against the immobilized bracket into the starting position, −20 degrees from the estimated zero torque position, followed by a continuous rotation to a maximum of +20 degrees and back to −20 degrees. Since the zero torque position was only an estimation and a result of manual adjustment, this procedure ensured that there would be enough linear part of the graph, i.e. that the wire would engage in the slot, so that the torque play calculation would be possible regardless of any third-order misalignment between bracket and wire. A personal
The data were plotted in a graph in Excel 2010 (Microsoft Corporation, Redmond, Washington, USA) (Figure 2a). Since there was a slight difference between the increasing and decreasing slope of the graphs, especially in the middle part while the wire was not fully engaged, an average of the clockwise and counter clockwise twist was calculated (Figure 2b), except for the bracket Evolution SLT®. The difference vanished and the endpoints of the curves coincided once the wire was twisted beyond the torque play angle and engaged in the slot, a behaviour described previously (11) that can be probably explained by unequal friction between the clockwise and counter clockwise twist. Averaging the way forward and backward curves led inherently to a change of the angular values for a given moment—mainly in the middle of each graph—but without influencing the torque play values, which were calculated from the nearly coinciding linear ending parts of the curves. With Evolution SLT®, there was a critical difference in the entire shape of the plots and only the activation curves (from 0 degree to +20 degrees and from 0 degree to −20 degrees) were used for further analysis without any averaging process (Figure 2d). In some cases, the testing came up with plots being off-centre in the horizontal and vertical dimension, due to lack of accuracy in third-order centring of the wire in the bracket slot, especially when using undersized wires. In these cases, the way-forward way-backaveraged plots were centred by moving the data in Excel in a manual procedure, so that the point of change of the direction of convexity in the middle of each graph was approximately at the intercept of the vertical and horizontal axis (Figure 2c). Since the difference of the positive and negative torque play value at the intercepts with the x-axis within one graph was the same regardless of any movement, this procedure did not influence the results; it was only performed to allow better averaging and visualization for the graphical plots.
Calculation of the total torque play After data preparation, the torque play was calculated from every one of the 245 data series (5 specimens of 7 bracket types tested with 7 wire types), each consisting of 200 moment values corresponding to angle values from −20 to +20 degrees in 0.2 degree steps, by extrapolating the linear portion of the twist/moment curve back to the x-axis from both negative and positive twist angle curves.
European Journal of Orthodontics, 2015
4
Figure 2. Data preparation: (a) A typical moment/angle curve without any modifications shows that the clockwise twist of the wire is slightly different than the anticlockwise twist. The difference decreases with increasing twist angle and the ends of the plot nearly coincide. (b) A typical averaged curve, which was calculated by averaging the clockwise and anticlockwise original curves of (a). The graph is a little off centre, both horizontally and vertically, due to imprecise centring of the undersized wire (SS 0.016″ × 0.022″) in the bracket slot. (c) The curve of figure was centred both vertically and horizontally. The reference point was the change of the direction of convexity in the middle of each graph, which was moved to be at the intercept of the vertical and horizontal axis. (d) Typical angle/moment curve of Evolution SLT®. The upper curve shows the way forward and the lower the way backward. On the first part of the way forward and backward, there is a bend at about −14 degrees/+14 degrees, which does not exist in the further part of the curves. This effect is probably due to the elasticity of the active clip and the friction, which create different effects in the activation and deactivation curves. Therefore, only the last part of the way forward and backward (activation part of the curves) was used for the measurements.
The linear parts of the plots were selected with the following procedure: - Most curves became linear beyond 15 degrees (Supplementary Figure 1a); therefore all data between −15.0 degrees and 15.0 degrees were neglected for the calculation. - The graphs of the remaining data were visually checked and were used if they were linear in toto; in a few cases in which this was not the case, only a smaller-linear-part of the curve was considered. - For the curves which had been manually centred, any data being beyond the 20 degrees range were not used; if values beyond 15 degrees were missing, a linear part within the 15 degrees range was chosen after visual confirmation for linearity. The corresponding negative and positive angle at the intercept of the two trendlines of the linear parts with the x-axis were calculated with the function ‘TREND’ in Excel 2010 (Supplementary Figure 1b and 1c), and their absolute values were summarized as the total torque play for every one of the 245 data sets. Within each bracketwire group (consisting of five brackets and wires of the same type) an average and a standard deviation was calculated from the five total torque play values using Excel 2010. If the trendlines for positive moments did not intercept at the positive part of the x-axis and the
trendlines for negative moments at the negative part of the x-axis, the calculated values were neglected and were manually set at 0 degree so as to eliminate invalid torque values. The same was done if the slope of the plots reversed within one twist forward or backward.
Statistical analysis The results were visually summarized in bar graphs using IBM SPSS Statistics 22 (IBM Corporation, New York, New York, USA). The dependence of torque play from bracket and wire type was primarily analysed using a two-factorial analysis of variance. Since this analysis revealed a clear interaction (P 0.498 Kurz 7th 0.473 generation STb™ 0.471 Evolution 0.498 0.476
0.011 0.003
0.002 0.003
0.003
0.004
0.002
0.477
