INTRODUCTION

The early stages of orthodontic treatment have benefitted greatly from the introduction of shape memory alloy (SMA) wires almost 50 years ago.¹ Inexplicably, unraveling crowding in the initial alignment phase with SMAs can be quite unpredictable. Clinical questions such as “Why might one tooth derotate slower than another” and “Does one need to open space for a partially blocked out tooth or will the deflected wire push the adjacent teeth out to make room in the arch?” are legitimate questions with elusive answers. Few data exist in the literature to address the biomechanical conditions that govern initial arch unraveling.

An area that has received considerable attention in the literature is the description of how the wire slides within the bracket's slot. Frictional force has been recognized as a component of the forces governing the efficiency of tooth sliding.² In the past decade, the term “friction” has become devalued in orthodontics, to the point at which its role in orthodontic therapy is a controversial topic. It has been well demonstrated that multiple forces (tangential and perpendicular to the long axis of the wire) mingle in the movement between a bracket and archwire and that frictional force rapidly turns up when even small degrees of malalignment are present.³ For this reason, in this article the culmination of all these forces will be referred to as the “constraining force” (CF), a compelling force that sticks the wire in the bracket. The CF would act as an opening coil as the wire attempts to return to its original shape. The present study aims to characterize the tangential component of CF in alignment.

The most perseverant tangential components of CF and their relation to orthodontic space closure have been described as “resistance to sliding” (RS) by Kusy and Whitley⁴ and are influenced by materials⁵ and dimensions of brackets and archwires.⁶ Constricted to sliding movement, the tipping malalignment of a bracket is known to contribute to an increased RS.^7,8 As the definition aforementioned, CF participates in broader types of stage 1 tooth movements (eg, tipping, in-out, rotation, and vertical step); however, its characteristics and clinical implications have not yet been explored. The use of passive self-ligating brackets emphasizes the idea that minimizing friction in CF between a bracket and wire allows the teeth to slide easily along the archwire and improves the efficiency of alignment.⁹ However, studies^2,10 have shown no significant differences in efficiency of alignment between traditional and self-ligating appliances. In the present study, it was hypothesized that CF between a wire and bracket potentially could help produce the expansion necessary to allow tooth alignment.

Clinically, impeded tooth movement along an archwire can be attributed to four major geometric malalignment types: in-out, tipping, rotation, and vertical step (Figure 1), each serving as a limiting factor to alignment of the dentition. Previous studies^4–8 evaluating friction have been limited primarily to sliding treatment goals, focused on how tipping affected tooth sliding while correcting anterior-posterior discrepancies. Alignment is most commonly associated with crowding and arch expansion. Being able to understand the limiting factors imposed in the initial stages of orthodontic treatment can help to produce more predictable and efficient tooth movement.

View Figure

• Download as Powerpoint
• Download Figure

The working hypothesis was that CF in Stage 1 of straight-wire appliance treatment is dependent upon the type of geometric malalignment and the behavior of hyperelastic archwire materials. The purpose of this study was to characterize CF for all four types of malalignment (in-out, tipping, rotation, and vertical step) in the laboratory setup using a copper-nickel-titanium (CuNiTi) archwire, a commonly used material for initial tooth alignment.

MATERIALS AND METHODS

Measuring CF

For each test, alignment was verified with a straight segment of 0.021 × 0.025-inch stainless-steel archwire. The test wire was placed through the Teflon blocks attached to the Instron^® and ligated into the bracket slot using an elastic ligature tie. The desired offset or rotation was then applied to the mounted bracket. Once positioned, the Instron^® output was balanced to zero. The Instron^® was then activated to pull the archwire at a constant velocity of 10 mm/min, and the force was recorded digitally.

CF was calculated as the linear average of the force measured from 1 mm to 10 mm of displacement. The first millimeter of data was not utilized in the average as a result of a nonlinear rising slope observed in trials with larger deflections.

Four separate individual tooth malposition types were simulated, as follows (Figure 2):

• (1) 

  In-outs were tested by displacing the bracket in the buccal-lingual dimension.

• (2) 

  Rotations were tested by simulating rotation around the long axis of the tooth.

• (3) 

  Tip was tested by rotating the bracket within the plane of the bracket face.

• (4) 

  Vertical steps were tested by displacing the bracket in the incisal-gingival dimension.

View Figure

• Download as Powerpoint
• Download Figure

In all four orientations, several positional increments were evaluated. Based on Kusy and Whitley's report,⁸ the first six positions were set at relatively small changes to provide a higher resolution of the area in which a critical change in CF was expected. The final four positions were at larger steps to provide a wide range of testing and to help identify if any other critical changes in the CF trend existed. In the first six positions, the same bracket was utilized; however, for the final four positions a new bracket was placed each time because of the increased chance of microscopic damage to the bracket. The archwire was changed for every trial.

In-outs were tested with 1/3-mm increments from 0 mm to 2 mm and with 1-mm increments from 2 mm to 5 mm. Rotations were tested with 2° increments from 0° to 10°, followed by tests at 15°, 20°, 30°, and 50°. Tip was measured in 1° increments from 0° to 5°, followed by tests at 10°, 15°, 20°, and 30°. Vertical steps were measured with 1/3-mm increments from 0 mm to 2 mm and with 1-mm increments from 2 mm to 5 mm.

For each type of malposition, five trials were run at each prescribed displacement. A segmented regression was fit to assess whether the average values differed among the displacements after the transition point and whether the position was linearly associated with the average value. Level of significance was set at 0.05. The five CF values at each displacement were then averaged and plotted against all other displacement values for a particular malposition scenario. From this data, the transition point with a 95% confidence interval (CI) was estimated by a piecewise linear regression analysis using R package “segmented.”¹¹ The averaged CFs for different malposition types were compared using the Student's t-test.

RESULTS

The two time-dependent frictional responses were observed. Figure 3 shows a step function, as would be expected by a traditional Newtonian friction response. A decaying slope was observed during the larger increments of deflection/rotation in all geometric malalignments.

View Figure

• Download as Powerpoint
• Download Figure

Tip (Figure 4A)

CF showed very little change from 0° to 3° of tip. From 4° on, a steady linear rise in CF was observed with increasing tip. Extrapolation of the two linear relations observed provided a theoretical θ_c at 2.58° (95% CI = −0.76° to 5.93°).

View Figure

• Download as Powerpoint
• Download Figure

DISCUSSION

When observing CF, the magnitude of a CuNiTi archwire's deflection was related to the time-dependent force response. With larger wire deflections, the response moved from a traditional step function to a power regression response. Power regressions are most commonly observed in plastic deformation models¹²; therefore, it appeared that a plastic-like, nonlinear behavior was occurring at higher magnitudes of deflection. The present data imply a material creep at points of contact or, equivalently, time-dependent reductions of near surface hardness as the cause of time-dependent changes in CF. This has not been reported in previous tests using stainless-steel and TMA wires in Stage 2 tooth movement.⁴ The change from a linear to a power response was observed to coincide with the critical values (θ_c, d_c) obtained in the malocclusion scenarios. This further implies that the change may be attributed to some form of surface ploughing in the archwire at high magnitudes of deflection.

In calculating CF, excluding the first millimeter of data provided a method to standardize measurement from a power-rule response. Two distinct regions of how CF responds to malposition severity were observed in each malocclusion scenario. We would declare the first region “classical friction,” as it would seem that no physical deformations were experienced by the archwire. At the point at which a much more significant draw force was experienced, a form of physical deformation was likely producing “binding” for both elastic binding adapted from the study of Kusy and Whitley⁸ and plastic binding, as discussed above.

The present data support the hypothesis that malalignment type and severity affect the magnitude of CF. Tip appeared slightly different from that associated with the other three scenarios, as CF appeared to be unchanged within the first 3° to 4°. As a result of the archwire being a smaller dimension than the bracket slot (0.016-inch archwire in a 0.022-inch bracket slot), there was a space in which a few degrees of bracket tip would result in no actual contact with the slot walls and, therefore, no deformation of the wire (Figure 5A). Before the slot walls are contacted, the only friction would come from the base of the slot and the elastic tie. The normal force is unchanged, and, therefore, the friction also remains unchanged throughout the classical friction region. Once the archwire contacts the slot walls (Figure 5B), a linear increase in CF is expected as tip increases. At θ_c, a large-enough deflection was produced in the archwire by these contacts and elastic binding was observed (Figure 5C). It should be noted, for tipping, the confidence interval for θ_c encompassed 0°; therefore, it is possible that no critical angle exists within the data set. θ_c was determined by this data; however, this is consistent with the previous literature,^4,8 so it indirectly validates these methods.

View Figure

• Download as Powerpoint
• Download Figure

The scenarios of in-out and rotation both had immediate wire deformation with bracket displacement. Unlike tip, this means that the normal force is changing with each increment, and the CF response is expected to immediately show a non-zero slope. In the case of in-out, any displacement of the bracket resulted in the archwire flexing over the base of the slot and producing a point of contact on either side of the slot base (Figure 5D). At a displacement of about 2.2 mm, a shift to elastic deformation occurred, producing the significantly increased CF response of the elastic binding region. As rotation increased, the wire actually made less overall contact with the slot base, which could account for the initial drop in resistance to sliding. In a small rotation angle, one point of contact was formed at the side of the slot positioning buccally; however, the archwire lifted (escaped) away from the side positioning lingually (Figure 5E). This escaping phenomenon is likely influenced by the method of ligation, which is beyond the subject of the present study. After reaching about 5°, the distinct change from classical friction to elastic binding occurred, and a greater sloped linear CF response continued from there. However, even at a high rotation of 30°, the CF value was only half that of tip.

While vertical step immediately appeared to show a positively sloped CF response, one would theoretically expect to observe no change in the normal force from 0 mm to 0.15 mm, as some “slop” should exist in the inciso-gingival dimension of the slot (similar to the tip scenario). As a result of the resolution used being larger than 0.15 mm, such a region could not be observed in these data. The archwire was immediately in contact with the gingival slot wall (Figure 5F), and once a significant enough deflection occurred, contacts on all four slot walls were observed (Figure 5G). A clear shift to the elastic binding region occurred at 1.85 mm of displacement. A steady linear CF response was present for the remainder of the displacement values. The highest increment (5 mm) yielded a CF value that was 2.5 times greater than that of in-out.

In 1974, Burstone and Koenig¹³ found normal forces and moments on the bracket ranging from 300 g to 500 g and from 900 g·mm to 1800 g·mm, respectively, using a 0.016-inch high-temper wire. Based upon the law of friction, these normal forces and moments can result in friction (horizontal) force approximating 150 g to 290 g, which is in the same order of CF. Nevertheless, the CF is approximately two times higher when the vertical step and tipping angle reach 3 mm and 15°, respectively. The discrepancy might be attributed to the high-friction CuNiTi wire used in this study (rather than the stainless-steel wire sometimes used).

In the clinic, in-outs and rotations tend to be the rate-limiting factors in alignment, while the correction of tips and vertical steps tend to be more rapid and predictable. These results lend to the theory that increased CF can actually produce more efficient alignment. Clinically, this could be observed as a lower incisor stepped lingual to its adjacent incisors and an archwire flexed lingually to fully engage the displaced incisor. This large deflection would cause significant CF at each incisor bracket, and the excess amount of archwire between the three brackets, assuming it is unable to slide through the brackets, would act as an opening coil as the wire attempts to reform its original shape. As alignment is achieved, the CF will drop until the wire can more easily slide, releasing the open coil effect.

While a laboratory study cannot completely reproduce the incredibly complex environment experienced in vivo (ie, saliva, periodontal ligament presence, intermittent occlusal forces), it is clear that complex CF exists in the malaligned dentition, and significant patterns form related to its severity. This study only focused on traditional brackets and ligation. Future studies should investigate how the wire ligation, passive self-ligation, and bracket design affect the magnitude of CF and its turning point in both the clinical and bench settings. Furthermore, the active martensitic CuNiTi used has the temperature transitional range from 17°C to 33°C. The storage modulus is 60 GPa and 70 GPa at 25° and 35°, respectively (in-house data). At oral temperatures, the modulus and CF may increase 16%. Because the current experiment was conducted at room temperature, a small increase in CF is expected at oral temperatures; this remains to be tested in a future study.

CONCLUSIONS

• A significant CF, ranging from 134 g to 1174 g per malaligned bracket, exists in Stage 1 (initial alignment) when using a conventional twin bracket with an elastomer tie.

• A critical point of deflection exists for all malocclusion scenarios in which the constraint of an archwire to slide through a bracket increases.

• The malposition type of “rotation” is associated with lower CF than that observed in “in-out,” “tipping,” and “vertical step.”