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An Ex Vivo Investigation into the Effect of Bracket Displacement on the Resistance to Sliding

Department of Public and Child Dental Health, Dublin Dental School and Hospital, Lincoln Place, Dublin 2, Eire

M. L. Swartz, D.D.S.

16729 La Maida St Encino, CA 91436, U.S.A.

	Abstract

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
This ex vivo study investigated the effect that repeated bracket displacement has on sliding friction and the magnitude of bracket displacement, and hence tooth movement, required to release bracket/archwire binding.

The design consisted of an ex vivo laboratory study. A jig was designed that allowed repeated displacement of a bracket to occur, while the resistance to sliding (friction) was measured using an Instron® universal testing machine. One type of stainless steel bracket was used in conjunction with four archwire types (0.016-inch stainless steel, 0.019 x 0.025-inch stainless steel, 0.021 x 0.025-inch stainless steel, 0.019 x 0.025-inch beta-titanium) and four magnitudes of displacement.

Repeated bracket displacement has a significant effect on the sliding resistance at the bracket/archwire interface (P < 0.001). The reduction in sliding resistance noted with displacement depended on the archwire. Over the range of displacements tested, there was an 85 and 80 per cent reduction associated with 0.021 x 0.025-inch and 0.019 x 0.025-inch stainless steel, respectively. For 0.019 x 0.025-inch beta-titanium and 0.016-inch stainless steel, these reductions were 27 and 19 per cent, respectively.

The importance of true friction, given the likelihood of bracket and/or archwire displacements in vivo, may be lessened.

Key words: Bracket Displacement, Friction, Tooth Mobility

	Introduction

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
Choice of force systems in orthodontics is influenced by an understanding of friction at the bracket/archwire interface. The selection of archwires, brackets, and ligation can all be influenced by some belief in friction. The interaction between bracket slot and archwire plays a most important part in how orthodontists set-up their force systems, anchorage demands, and space closure mechanics.

The literature has numerous studies related to bracket/ archwire friction. Since 1970, there have been more than 70 articles reporting on friction, coefficients of friction, and the related mechanotherapy. All but three of these 70 studies were ex vivo models with test fixtures that limited bracket movement and many of the conclusions from these studies are in contradiction.

Friction is classically described as a force that retards or resists the relative motion of two objects in contact and its direction is tangential to the common boundary of the two surfaces in contact (Bowden and Tabor, 1974). The classical laws of friction state that a frictional force is proportional to the normal force component, independent of the area of contact and independent of the sliding velocity. For metals under normal conditions of use these laws are often reasonably accurate, although for other materials or for extreme conditions the laws break down.

Previous investigations into the frictional characteristics at the bracket/archwire interface have shown that the magnitude of the frictional force varies with certain mechanical or biological variables. Several mechanical variables have been investigated, such as: bracket material, bracket width, bracket/archwire angulation, bracket surface roughness, the number of brackets in series, wire material, wire shape and configuration, surface coatings and surface roughness, bracket/archwire clearance, inter-bracket distance, method and force of ligation, wear, sliding velocity, and vibration (Andreasen and Quevedo, 1970; Frank and Nikolai, 1980; Drescher et al., 1989; Tidy, 1989; Kusy and Whitley, 1990a; Kusy et al., 1990; Keith et al., 1994; Sims et al., 1993; Downing et al., 1994; Tselepsis et al., 1994). The biological variables suggested include saliva (Kusy et al., 1991), plaque (Drescher et al., 1989), acquired pellicle, corrosion, biological resistance (Drescher et al., 1989), mastication, (Frank and Nikolai, 1980; Drescher et al., 1989) bite force, and tooth mobility (Jost-Brinkmann and Miethke, 1991).

Most studies have investigated the mechanical variables using steady state ex vivo models, however, little agreement is forthcoming. Although several authors (Andreasen and Quevedo, 1970; Frank and Nikolai, 1980; Drescher et al., 1989) mention the importance of the biological variables, few have investigated them. However, three investigations in the literature are worth special note. Hixon et al., in 1970, reported on a combined in vivo and ex vivo testing primarily on the subject of stress magnitude. They noted that the test apparatus moved with less force intra-orally than in the laboratory. This difference was attributed to a variety of oral forces, especially from mastication, which produced other motions and permitted the wire to slide through the tube more easily. They then redesigned their previous test fixture, to measure friction by vibrating the apparatus, and the results indicated that kinetic friction was insignificant.

Jost-Brinkman and Meithke (1991) investigated tooth mobility and its effect on the frictional resistance. They measured bracket-archwire friction in vivo, when a tooth was loaded and unloaded, and compared these results to a similar laboratory set-up. They found that the magnitude of friction was similar for both the laboratory set-up and the unloaded tooth. However, when the tooth was loaded, a significant reduction in friction was noted. They concluded that, due to mastication, frictional forces occurring with orthodontic treatment are even smaller in comparison to ex vivo experiments with immovable brackets.

Liew (1993) attempted to replicate masticatory function ex vivo by repeated vertical displacement of an archwire under differing loads (25, 50, 100, 150, 250, and 400 g) using low frequency (91.3 cycles/min) vibration. He found that the resistance to archwire movement through an orthodontic bracket was decreased by continuous repeated vertical displacement of the wire. This reduction was as great as 85 per cent for loads in the range 100–250 g, while loads as small as 25 g reduced friction by more than 50 per cent.

It has been noted by several authors that, clinically, the forces required to overcome friction are less than those measured in steady state laboratory experiments (Anderson, 1956; Ho and West, 1991). Results from ex vivo tests in the literature suggest that titanium alloys have higher friction than stainless steel and should thus be more resistant to sliding, yet clinical observations seem to indicate the opposite. Titanium alloy archwires often spontaneously slide around the arch, while this rarely seems to occur with stainless steel. This discrepancy between clinical and experimental findings seems to suggest that other factors are of importance in governing the resistance to sliding in vivo and the work by Hixon et al. (1970), Jost-Brinkmann and Miethke (1991), and Liew (1993) suggests that masticatory function and tooth mobility may be the reason.

Translatory tooth movement along an archwire is not continuous, but occurs as a series of small tipping and uprighting movements (Drescher et al., 1989). When a force is applied to the crown of a tooth, it tips until an equilibrium is reached between the applied force and the couple produced at the bracket-archwire interface (Frank and Nikolai, 1980; Drescher et al., 1989). This binding between the bracket and archwire stops further crown movement until either wire displacement, tooth mobility or subsequent remodelling releases the binding. It has even been suggested that the resistance to tooth movement, in vivo, is not governed by the classical laws of friction, but is a product of the binding and releasing phenomenon at the bracket-archwire interface. This seems to suggest that bracket-wire sliding in vivo is much more dynamic than at first imagined. The effect that mastication and tooth mobility has on this process is not fully understood and little is known about the magnitude of tooth mobility that is required to release binding once it has occurred.

The objective of this study was to evaluate a laboratory model in which the resistance to a wire sliding in the bracket was measured while the bracket was displaced. Normal tooth mobility allows for bracket displacement. An ex vivo model which allows movement of the bracket may better define the archwire to bracket interactions and help correlate laboratory data to clinical observations. Consequently, an experimental set-up was constructed to investigate the magnitude of bracket movement and, hence, tooth movement, required to release bracket-archwire binding.

	Materials and Methods

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
Test Samples
For the experiment, 320 upper stainless steel premolar brackets (Ormco®), with 0 degrees tip and 0 degrees torque, were assembled. Prior to shipment, the manufacturer modified the brackets by welding two strips of stainless steel over each pair of tie wings in order to eliminate the variables of ligation. The slot size was 0.022 x 0.028-inch and this was checked prior to testing by inserting a length of 0.0215 x 0.028-inch stainless steel wire through the slot. Prior to testing, each bracket was mounted onto a plastic block measuring 6 x 6 x 6 mm using an epoxy-resin adhesive (Araldite®, Ciba-Geigy). This was performed using an alignment fixture, which ensured that the bracket was placed at the centre of each block and the bracket slot was at right angles to the surface of each block.

Four different archwire types were selected for investigation: 0.019 x 0.025-inch stainless steel, 0.019 x 0.025-inch beta-titanium, 0.021 x 0.025-inch stainless steel, and 0.016-inch stainless steel. The archwires used were straight sections, 5 cm in length, with a 90-degree bend at one end. This bend ensured that the archwire did not slip through the fixed brackets during testing. The archwires chosen for investigation represent a variety of dimensions, flexural strengths, and frictional properties.

Measurement Technique
A testing apparatus was constructed to simulate the clinical situation whereby the centre of resistance of a tooth is not in the same plane as that of the bracket. This results in some tipping of the bracket slot relative to the archwire leading to two-point contact between the wire and bracket. This is similar to the method used by Tidy (1989), Drescher et al. (1989), Bednar et al. (1991), and Omana et al. (1992).

The apparatus consisted of two parts (Figure 1): a lower member, swivel mounting, which supported the test bracket and an upper member slide that supported the fixed brackets and the test archwire. The lower member consisted of a mounting mechanism at one end of a freely rotating central axis. Attached to this central axis were two 10-cm long brass arms of equal weight. The mounting mechanism allowed the test bracket to be locked into place during testing and afterwards removed with ease. When the bracket was mounted the slot axis lay at right angles to the two brass arms. Attached to one arm, at a point 10 mm from the central axis, was a 100-g weight.

View larger version (32K): [in this window] [in a new window]   FIG. 1 Schematic representation of two part test apparatus.

The vibrating machine (LDS Oscillator®, Model D207) contacted the displacement arm and thus produced the bracket displacement. An electromagnetic functional generator allowed control of both amplitude and frequency. A frequency of 1.35 Hz (81 cycles/min) was used throughout the experiment and this lies within the reported range for normal chewing (Picton, 1964; De Boever et al., 1978a,b). An Instron® 1011 universal testing machine was used to measure the forces encountered during testing. The crosshead speed used throughout the experiment was 1 mm/min.

Prior to testing the selected wire was wiped with an alcohol wipe and the bracket slot was cleaned with a piece of dental floss soaked in alcohol. The lower member of the test apparatus was attached to the Instron® crosshead, while the upper part was attached to the universal joint and load cell (Figure 1). The test bracket was aligned in the fixture with a straight section of 0.0215 x 0.028-inch stainless steel wire. After assuring a passive alignment of the fixture, the 0.0215 x 0.028-inch wire was removed and the test wire placed through all four brackets in series.

The controls on the Instron® testing machine were adjusted until the readout showed zero. The 100-g weight was gently applied and the entire set-up left to settle for approximately 1 minute prior to testing. Then the displacement arm, attached to the vibrating machine, was carefully lowered until it just contacted the end of the counter-arm (Figure 2). If this procedure altered the force reading on the testing machine, the displacement arm was removed and the entire set-up allowed to settle again. This was repeated until the reading remained unaltered. The oscillator was started and the whole apparatus left to settle, at the chosen amplitude and frequency, for a period of about 10 seconds. Prior to setting up the displacement arm, the amplitude of displacement was checked using a clock gauge and this was repeated after every five test runs to ensure that the amplitude was constant. The test run was then initiated by starting the movement of the crosshead of the Instron® test machine. Each test run lasted 1 minute and the load cell values were recorded by stylus on a strip chart recorder. After each test the offset weight was removed, and the test bracket and archwire were carefully detached and stored. Each bracket and archwire was used only once.

View larger version (46K): [in this window] [in a new window]   FIG. 2 Schematic representation of assembled test apparatus.

Data Analysis
The results of the friction tests were recorded graphically on a strip chart recorder in Newtons. The graph of each represented the change in sliding resistance over a period of one minute. Examples of typical recordings are given inFigure 3. The test runs without displacement showed a relative levelling off after a period of about 15 seconds, while with repeated displacement the curve appeared as a series of peaks and troughs with a periodicity equal to the frequency of displacement. The troughs represent the periods when the displacement was at its maximum, while the peaks represent the periods when the displacement was zero. Eighty-one peaks are evident throughout each test run and these were labelled from T0 through to T80. The force value for each peak, which is representative of the static friction at that point, was recorded and plotted against time. To allow the displacement and non-displacement graphs to be compared, force values along the non-displacement graphs corresponding to the time values T0–T80 in the displacement graphs were taken and these values were then plotted against time.

View larger version (33K): [in this window] [in a new window]   FIG. 3 Sample strip chart recordings (0.019 x 0.025 stainless steel).

Analysis using the Wilks Lambda test, which is a multiple repeated measures analysis of variance (MANOVA) test, was performed on the data to assess the importance that wire type, displacement, and time has on the sliding resistance. This analysis found that over the time period T20–T80, which represents the flat part of the curve, the sliding resistance recorded for each wire type was independent of time. This means that the data recorded for any single time point along the flat part of the curve is representative of all the data from T20-T80. Therefore, for statistical analysis, the data related to only one time point need be analysed. T50 was arbitrarily chosen for analysis as this point lies half-way along the flat part of the curve.

Because the data for T50 were reasonably normally distributed with minimal skewness, a one way analysis of variance (ANOVA) was performed and the Tukey–Kramer Honest Significant Difference (HSD) test was used to adjust for multiple pairwise comparisons.

	Results

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
The effect of displacement was shown to have a significant effect on sliding resistance (P < 0.001) and this was found to be the case whether wire type was considered or not. The relationship between displacement and friction appears to be linear. Linear regression lines shown in Figure 4 show the effect of displacement by wire type.

View larger version (63K): [in this window] [in a new window]   FIG. 4 Linear regression lines for each archwire demonstrating reduction in sliding resistance with bracket displacement.

For the four wires tested, a summary of the means and standard errors is shown inTable 1. For each wire type, the results of the multiple pairwise comparisons are shown inTable 2 with significance at the 5 per cent level. With regard to 0.019 x 0.025- and 0.016-inch stainless steel, a displacement of 0.5 mm was required before a significant reduction in frictional forces was observed (P < 0.05). For the 0.021 x 0.025-inch stainless steel wire a significant reduction was noted at a displacement of 0.25 mm (P < 0.05), while for the 0.019 x 0.025-inch beta-titanium a significant reduction was only noted at a displacement of 1 mm.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
When attempting to translate a tooth along an archwire there is always some degree of tipping in our imperfect system of mechanics. The crown moves before the root apex resulting in tipping of the tooth and the bracket relative to the archwire. This tipping proceeds until the friction or binding at the bracket archwire interface becomes so great that crown movement stops. The couple created by the bracket/archwire interaction works to upright the tooth, and the cycle of tipping and uprighting repeats itself (Drescher et al., 1989). This study sought to simulate the clinical situation in which some tooth tipping occurs during a resultant translation along an archwire by suspending a weight from a counter-arm.

The effect that mastication and tooth mobility have on this process was simulated by repeated displacement of the counter-arm. This repeated displacement produced an angular change between the bracket and archwire that results in a releasing of the binding. If one considers that the average distance between the centre of rotation of a maxillary canine and the centre of its crown is 16 mm (Nikolai, 1975), then an angular change between the bracket and archwire, similar in magnitude to that observed during the present investigation, would occur with a mesio-distal crown movement in the range 0–0.16 mm. This means that a 1-mm displacement at the end of the 10-cm long counter-arm will produce the same angular change at the bracket/archwire interface as a 0.16-mm displacement applied 16 mm from the central axis. One can conclude therefore, that 0.25-, 0.5-, and 1-mm displacements at the end of the counter-arm are equivalent to 0.04-, 0.08-, and 0.16-mm mesio-distal crown movements.

Tooth mobility prior to and during orthodontic treatment has been investigated by several authors (Muhlemann, 1954; Inoue, 1989; Tanne et al., 1995). Muhlemann (1954) found that, over a 4-week period, tooth mobility increased from 0.07 to 0.4 mm per 500 g force, while Inoue (1989) found similar results using a 200-g force. More recently, Tanne et al. (1995) examined a range of applied forces and compared the mobility observed prior to treatment and after 24 days of canine retraction. In the latter study, they found that, before treatment, tooth mobility measured 41.3 and 101.5 µm, on average, when 100- and 500-g forces were applied, respectively. After 24 days of orthodontic movement, these measured 73.1 and 157.6 µm, respectively. Furthermore, if one considers that the forces noted during normal mastication are in the range 3–9 kg (Anderson, 1956), then it is not unreasonable to expect the magnitude of tooth mobility to be at least similar to those mentioned above.

The values recorded for the sliding resistance are similar in magnitude to those reported in other studies for stainless steel brackets (Garner et al., 1986; Tidy, 1989; Omana et al., 1992). However, they are lower than those reported by Drescher et al. (1989). The sliding resistance recorded for the beta-titanium archwire was significantly greater (P < 0.05) than the stainless steel archwires and this concurs with previous studies (Drescher et al., 1989; Tidy, 1989; Angolkar et al., 1990; Kaplia et al., 1990; Kusy and Whitley, 1988, 1989, 1990a,b; Kusy et al., 1990, 1991). It is apparent from the results that the sliding resistance increases significantly as the wire size increases (P < 0.05) and this again agrees with previous studies (Andreasen and Quevedo, 1970; Drescher et al., 1989; Angolkar et al., 1990; Tanne et al., 1991; Sims et al., 1993; Downing et al., 1994; Ogata et al., 1996).

Analysis of the data shows that repeated displacement of the bracket has a significant effect on the resistance to archwire sliding. This relationship appears to be linear in nature, indicating that increased tooth mobility enhances the release of binding. On closer examination it appears that the expected reduction in sliding resistance for a given degree of tooth mobility varies with the wire tested. Over the range of displacements tested (0–0.16-mm crown movement), the reduction in sliding resistance for the 0.016-inch stainless steel wire was 19 per cent, while the reduction for the 0.019 x 0.025-inch beta-titanium wire, over the same range was slightly greater at 27 per cent. For the 0.019 x 0.025 and 0.021 x 0.025-inch stainless wires tested the reduction was 80 and 85 per cent, respectively. The implication is that displacements, with an amplitude equivalent to 0.16 mm of mesio-distal crown movement, can release binding, and significantly reduce sliding resistance. However, the degree to which bracket displacement affects the resistance to sliding also depends on the wire size and alloy.

In comparing the stainless steel wires, there was relatively little reduction in resistance, with displacement, in the 0.016 stainless steel wire, whereas with larger stainless steel wires greater reductions were demonstrated with bracket displacement. One assumption might be that the maximum displacement used in this test (0.16 mm) was less than the difference in freedom between wire and slot and thus insufficient bracket displacement to permit releasing (0.022–0.016 inch = 0.006 inch or 0.15 mm freedom, assuming zero manufacturing tolerances).

Previous studies have suggested that beta-titanium archwires have greater resistance to sliding than a similar size stainless steel wire (Kusy and Whitley, 1988, 1989, 1990a,b; Drescher et al., 1989; Angolkar et al., 1990; Kaplia et al., 1990,Kusy et al., 1990, 1991). This difference was again demonstrated in this investigation however, not to the same magnitude. A comparison of the resistance to sliding between 0.019 x 0.025-inch stainless steel and the same size beta-titanium wire indicates that the wire to bracket interactions are more complex than either a simple friction model, or a binding and releasing model can fully explain. One possible explanation might arise from the significant differences in their relative wire stiffness. The beta-titanium wire, at 42 per cent the stiffness of the stainless steel wire, may be flexing with the bracket displacement and thus might require greater displacement to demonstrate a proportionately larger reduction in the sliding resistance. Future testing with ion impregnated beta-titanium wire, with a coefficient of friction similar to stainless steel, may help define the contributions of surface roughness, friction and dissimilar alloys to the resistance to sliding.

It should be noted that, in this investigation, there was no intentional displacement of the archwire. It is possible that, in the clinical situation, direct or indirect displacement of the archwire could occur, and that this may further reduce the sliding resistance. Since the degree of wire displacement is dependent upon wire resilience, greater movement of the 0.016-inch stainless steel and 0.019 x 0.025-inch beta-titanium wires would be expected during mastication. Hence, this movement may be sufficient to reduce the sliding resistance associated with these wires, to levels similar to those observed with the two rectangular stainless steel wires.

If one considers the clinical situation, where there is intermittent movement between the bracket and archwire, then clinically we may not be looking at true friction, but rather a binding and releasing phenomenon. In the present study, it was found that repeated displacement of a bracket, equivalent to as little as 0.16 mm of mesio-distal crown movement, could reduce the sliding resistance by as much as 85 per cent. Assuming this fact, it is not unreasonable to conclude that the reduced sliding resistance observed in vivo may be a result of this intermittent movement between the bracket and archwire.

	Conclusions

Top Abstract Introduction Materials and Methods Results Discussion Conclusions References

 
If the resistance to sliding is reduced with larger rectangular wires by bracket displacement, then the use of small diameter wires, in the belief of generating less friction, is unjustified. The use of bi-dimensional wires or dual slot sizes, to reduce sliding resistance, may likewise be unfounded. Selecting materials (archwires or bracket type) based upon measurements of coefficients of friction may not be valid.

The present research suggests that the effective sliding resistance between orthodontic brackets and archwires is substantially reduced by repeated displacement equivalent to 0.16 mm of crown movement, which is within the range of normal tooth mobility. Repeated bracket displacement has a highly significant effect on the sliding resistance at the bracket-archwire interface (P < 0.001). Within the no displacement (control group) significant differences were noted between all the wires tested (P < 0.05). The wires were ranked, according to sliding resistance, in the following order: 0.019 x 0.025-inch beta-titanium (highest), 0.021 x 0.025-inch stainless steel, 0.019 x 0.025-inch stainless steel, and 0.016-inch stainless steel (lowest).

The reduction in sliding resistance noted with displacement, depended on the archwire. Over the range of displacements tested, there was an 85 and 80 per cent reduction associated with 0.021 x 0.025 and 0.019 x 0.025-inch stainless steel, respectively. For 0.019 x 0.025-inch beta-titanium and 0.016-inch stainless steel, these reductions were 27 and 19 per cent, respectively.

The influence of friction, given the likelihood of bracket and/or archwire displacements in vivo, is thought to be small and may have significantly less clinical importance than previously stressed.

	Acknowledgments

 
The authors wish to thank Mr Peter O'Reilly and Professor David Taylor (Mechanical Engineering Department, Trinity College Dublin), Mr Alan Kelly, for statistical support, and Ms Anne O'Byrne, for her help in compiling the reference material.

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