Characterizing constraining forces in the alignment phase of orthodontic treatment

Original Article Characterizing constraining forces in the alignment phase of orthodontic treatment Christopher G. Gibson a ; Feng-Chang Lin b ; Ceib Phillips c ; Alex Edelman d ; Ching-Chang Ko e ABSTRACT Objectives: To describe the frictional forces (FF) that constrain wire sliding in the initial alignment phase of treatment using a new term, the constraining force (CF), and to hypothesize that CF is dependent on two factors: the hyperelastic behavior of archwires and the specific type of tooth geometric malalignment present. Materials and Methods: A laboratory device that simulates the four distinct malalignment types (inout, rotation, tipping, and vertical step) was used to couple with an Instron testing apparatus. Incremental CF data for the four types of malalignment were recorded. Each type had five trials per increment of severity, from which the CF was averaged using 0.016-inch copper-nickel-titanium (CuNiTi) archwires. Results: Two types of friction curves were obtained: a traditional step function response and a power regression response. For all malalignment types, increasing degrees of irregularity increased power regression responses and CF. A severity turning point, displayed as a sudden increase in CF, occurred for each malalignment. The rotation type of malalignment yielded the lowest CF, while the vertical step type resulted in the highest CF. Conclusions: The data infer a hypothesis that malrotation type having weak CF might act as a limiting factor in the alignment phase to unravel the neighboring teeth. Future investigations to compare clinical and bench data can help explain more fully the constraints impeding alignment resolution and the factors governing the ability to bring malaligned teeth into alignment. (Angle Orthod. 0000;00:000 000.) KEY WORDS: Biomechanics; Orthodontics; Alignment; Constraining force INTRODUCTION The early stages of orthodontic treatment have benefitted greatly from the introduction of shape a Resident, Department of Orthodontics, School of Dentistry, University of North Carolina, Chapel Hill, NC. b Assistant Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC. c Professor, Department of Orthodontics, School of Dentistry, University of North Carolina, Chapel Hill, NC. d Dental Student, School of Dentistry, University of North Carolina, Chapel Hill, NC. e Professor, Department of Orthodontics, and Department of Oral and Craniofacial Health Sciences, School of Dentistry, University of North Carolina, Chapel Hill, NC. Corresponding author: Dr Ching-Chang Ko, DDS, MS, PhD, 275 Brauer Hall, CB#7450, Department of Orthodontics, School of Dentistry, University of North Carolina, Chapel Hill, NC 27599 (e-mail: Ching-Chang_Ko@unc.edu) Accepted: August 2017. Submitted: March 2017. Published Online: September 25, 2017 Ó 0000 by The EH Angle Education and Research Foundation, Inc. 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 DOI: 10.2319/030117-159.1 1

2 GIBSON, LIN, PHILLIPS, EDELMAN, KO Figure 1. The malalignment simulation apparatus. (A) Orientation for tip and vertical step. (B) Orientation for rotation and in-out. 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 Whitley 4 and are influenced by materials 5 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. 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-nickeltitanium (CuNiTi) archwire, a commonly used material for initial tooth alignment. MATERIALS AND METHODS Brackets and Archwires Twin 0.022-inch maxillary premolar brackets without pre-angulation or torque were used for this study. A straight 60-mm segment of 0.016-inch CuNiTi was crimped at one end with a brass cap, allowing mounting on an Instront machine (Model 4411, Instront Corp, Canton, Mass). Testing Apparatus A device was made to simulate the malocclusion scenarios of three brackets outlined above, in which an orthodontic bracket was mounted and manipulated in orientation between Teflon blocks serving as the adjacent brackets. The archwire passed through a channel in the Teflon blocks so the wire only contacted

CONSTRAINING FORCES IN ORTHODONTIC ALIGNMENT 3 Figure 2. Malalignment scenarios on the apparatus. Teflon surfaces, regardless of the orientation. Interbracket distance was set at 7.5 mm. A translation stage allowed the center bracket to be offset either in a buccal-lingual or incisal-gingival dimension in increments of 0.01 mm. A rotational stage allowed the center bracket to be rotated either from a buccal view (simulating tipping) or from an occlusal view (simulating rotation) in increments of 0.28. The device allowed manipulation in all four orientation types (Figure 1). Measuring CF For each test, alignment was verified with a straight segment of 0.021 3 0.025-inch stainless-steel archwire. The test wire was placed through the Teflon blocks attached to the Instront 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 Instront output was balanced to zero. The Instront 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. 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 Angle Orthodontist, Vol 00, No 0, 0000

4 GIBSON, LIN, PHILLIPS, EDELMAN, KO Tip (Figure 4A) CF showed very little change from 08 to 38 of tip. From 48 on, a steady linear rise in CF was observed with increasing tip. Extrapolation of the two linear relations observed provided a theoretical h c at 2.588 (95% CI ¼ 0.768 to 5.938). Rotation (Figure 4B) The CF observed for rotation began by dropping 25 g from 08 to 48. From 68 on, CF rose in a steady linear pattern through the maximum simulated rotation of 508. The piecewise linear regression provided a theoretical h c at 4.838 (95% CI ¼ 1.818 7.958). Figure 3. (A) Data from a single trial. Step function response was observed at low deflections; (B) At high deflections, a power response was observed. 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 28 increments from 08 to 108, followed by tests at 158, 208, 308, and 508. Tip was measured in 18 increments from 08 to 58, followed by tests at 108, 158, 208, and 308. Vertical steps were measured with 1/3-mm increments from 0 mm to 2 mm and with 1-mm increments from 2 mm to 5mm. 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. In-Out (Figure 4C) The CF increased linearly with a positive slope up through 2 mm of buccal displacement. After 2 mm of buccal displacement the CF continued to rise in a linear trend; however, the slope became significantly higher. The theoretical point d c, at which the slope began a sudden increase, was 2.23 mm (95% CI ¼ 1.44 3.02 mm). Vertical Steps (Figure 4D) The drawing force observed when a bracket was vertically displaced steadily rose from 0-mm to 1.67- mm displacement. A significantly greater, constant slope was observed for displacements of 2 mm to 5 mm. The theoretical d c was found at about 1.88 mm (95% CI ¼ 1.66 2.11 mm). Similarities existed among all configurations tested. All simulated scenarios produced an initial (no deflections or rotations present) drawing force of around 150 g. This was the expected result, as all scenarios, regardless of configuration, should represent no malocclusion and, therefore, perfectly aligned brackets. In addition, there only appeared to be one sharp change in slope for each data set. Rotation was associated with lower average CF than that observed in in-out, vertical step, and tipping (P-value ¼.039,.01, and.019, respectively). 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 models 12 ; therefore, it appeared that a plastic-like, nonlinear behavior was occurring at higher magnitudes of deflection. The present data imply a material creep

CONSTRAINING FORCES IN ORTHODONTIC ALIGNMENT 5 Figure 4. Constraining force vs deflection plots. (A) Tip model; (B) rotation model; (C) in-out model; and (D) vertical step model. 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 (h 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 Whitley 8 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 38 to 48. As Angle Orthodontist, Vol 00, No 0, 0000

6 GIBSON, LIN, PHILLIPS, EDELMAN, KO Figure 5. (A) Diagrammatic representation of classical friction orientation in tipping. (B) A small amount of tip is possible before the archwire makes its first contact with the bracket slot. (C) Once the tip becomes significant enough, elastic binding occurs and RS begins to increase significantly. (D) Archwire contacts present in the in-out orientation. (E) Archwire contacts present in the rotation orientation. (F) Archwire contacts present in the vertical step orientation. (G) With a large vertical step, the archwire ultimately experiences four contacts with the bracket slot. 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 h 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 h c encompassed 08; therefore, it is possible that no critical angle exists within the data set. h c was determined by this data; however, this is consistent with the previous literature, 4,8 so it indirectly validates these methods. 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 58, 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 308, 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

CONSTRAINING FORCES IN ORTHODONTIC ALIGNMENT 7 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 Koenig 13 found normal forces and moments on the bracket ranging from 300 g to 500 g and from 900 gmm to 1800 gmm, 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 158, 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 ratelimiting 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 178Cto338C. The storage modulus is 60 GPa and 70 GPa at 258 and 358, respectively (inhouse 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. ACKNOWLEDGMENTS We would like to thank Dr H. Garland Hershey for his input and the Ormco Corporation for donation of archwires and brackets. The study was partially supported by NIH/NIDCR R01DE022816-01. REFERENCES 1. Andreasen G, Brady P. A use hypothesis for 55 nitinol wire for orthodontics. Angle Orthod. 1972;42:172 177. 2. Scott P, DiBiase A, Sherriff M, Cobourne M. Alignment efficiency of Damon3 self-ligating and conventional orthodontic bracket systems: a randomized clinical trial. Am J Orthod Dentofacial Orthop. 2008;134:470e1 470e8. 3. Badawi H, Toogood R, Carey J, Heo G, Major P. Threedimensional orthodontic force measurements. Am J Orthod Dentofacial Orthop. 2009;136:518 528. 4. Kusy R, Whitley J. Friction between different wire-bracket configurations and materials. Semin Orthod. 1997;3:166 177. 5. Kapila S, Angolkar P, Duncanson M, Nanda R. Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four alloys. Am J Orthod Dentofacial Orthop. 1990;98:117 126. 6. Andreasen G, Fernando Q. Evaluation of friction forces in the 0.02230.028 edgewise bracket in vitro. J Biomech. 1970;3:151 160. 7. Frank C, Nikolai R. A comparative study of frictional resistances between orthodontic bracket and arch wire. Am J Orthod Dentofacial Orthop. 1980;78.6:593 609. 8. Kusy RP, Whitley J. Influence of archwire and bracket dimensions on sliding mechanics: derivations and determinations of the critical contact angles for binding. Eur J Orthod. 1999;21:199 208. 9. Matarese G, Nucera R, Militi A, et al. Evaluation of frictional forces during dental alignment: an experiment model with 3 nonleveled brackets. Am J Orthod Dentofacial Orthop. 2008;133:708 715. Angle Orthodontist, Vol 00, No 0, 0000

8 GIBSON, LIN, PHILLIPS, EDELMAN, KO 10. Miles PG, Weyant RJ, Rustveld L. A clinical trial of Damon 2 vs conventional twin brackets during initial alignment. Angle Orthod. 2006;76:480 485. 11. Muggeo V. Estimating regression models with unknown break points. Stat Med. 2003;22:3055 3071. 12. Bellemare S, Dao M, Suresh S. The frictional sliding response of elasto-plastic materials in contact with a conical indenter. Int J Solid Struct. 2007;44:1970 1989. 13. Burstone C, Koenig H. Force systems from an ideal arch. Am J Orthod Dentofacial Orthop. 1974;65:270 289.