UNLOADING BEHAVIOR AND POTENTIAL BINDING OF SUPERELASTIC ORTHODONTIC LEVELING WIRES: A GINGIVALLY MALPOSED CUSPID MODELTrenton D. Thalman, D.D.S. An Abstract Presented to the Faculty of the Graduate School of Saint Louis University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Dentistry 2008 ABSTRACT Objective: To examine unloading behavior of superelastic (SE), nickel-titanium-alloy (NiTi) leveling wires within a gingivally malposed cuspid model. Materials and Methods: A universal testing machine deflected continuous, 0.014inch SE NiTi wires gingivally at the right-cuspid position of an orthodontic, dental-arch model. Binding points (smallest deflections at which frictional forces stop leveling wires from sliding through supporting bracketslots) and unloading plots (from beneath binding points) were obtained with self-ligation (SL) and new (unrelaxed) elastomeric ligation (EL) at the support sites. Unloading data were collected with SL from 2.5-, 3.5-, 4.5-, and 5.5mm deflections; and from 1.5- and 2.5-mm deflections with EL. Force-loss was quantified as the ordinate difference Descriptive and between the peak and the trough of a plot. inferential statistics, the latter Kruskal-Wallis with Mann-Whitney U-tests, were run to analyze the force-loss data. Results: Binding occurred with SL at a deflection of Mean force-loss ranged from 7.5 mm, and at 3.5 mm with EL. 87.0 ± 10.1 grams to 0.0 ± 0.0 grams with SL and EL during unloading from 5.5 and 1.5 mm, respectively. Significant differences (p < .01) in force-losses were obtained across 1 all SL groups, but not between the EL groups. Conclusions: 1. Binding of 0.014-inch SE NiTi leveling wires occurs at smaller deflection-amplitudes with EL than with SL. 2. Relatively constant aligning forces from 0.014-inch SE NiTi leveling wires should not be expected in most clinical situations. 3. Binding of 0.014-inch SE NiTi leveling wires occurs at a deflection-amplitude threshold rather than at a deflection-amplitude. 2 UNLOADING BEHAVIOR AND POTENTIAL BINDING OF SUPERELASTIC ORTHODONTIC LEVELING WIRES: A GINGIVALLY MALPOSED CUSPID MODEL Trenton D. Thalman, D.D.S. A Thesis Presented to the Faculty of the Graduate School of Saint Louis University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Dentistry 2008 COMMITTEE IN CHARGE OF CANDIDACY: Assistant Professor Ki Beom Kim Chairperson and Advisor Professor Emeritus Robert J. Nikolai Adjunct Associate Professor Kirk D. Satrom i DEDICATION This thesis is dedicated to my family: my wonderful wife Debbie and my four amazing daughters Audrey, Lauryn, Tricia, and Julia, and to my parents Jeff, Ilene, David, and Patricia who have provided support and encouragement throughout my higher education. ii ACKNOWLEDEGMENTS The author would like to express appreciation to his committee members: Dr. Ki Beom Kim, Dr. Robert Nikolai, and Dr. Kirk Satrom. Each has contributed much time and effort A special thanks to Mr. Joe on the author’s behalf. Tricamo and his associates at the Saint Louis University machine shop for the many hours spent in manufacturing the experimental equipment needed to complete this study. The author would also like to thank GAC International for donating brackets and tubes, Ormco Corp. for donating archwires, and TP Orthodontics Inc. for donating ligatures and a Straight Shooter. iii TABLE OF CONTENTS LIST OF TABLES........................................... vi LIST OF FIGURES......................................... vii CHAPTER 1: CHAPTER 2: INTRODUCTION.................................. 1 REVIEW OF THE LITERATURE...................... 4 INTRODUCTION............................... 4 OCCLUSOGINGIVAL WIRE ACTIVATION ......... 4 DEFLECTION OF THE SE NITI WIRE........ 5 WIRE INDUCED NORMAL FORCES............ 7 DEFLECTED WIRE-LENGTH................. 8 HIGH-CUSPID LEVELING .................... 8 NORMAL FORCES AND TOOTH MOVEMENT..... 11 ARCHWIRE SLIDING DURING LEVELING..... 11 COULOMB FRICTION.......................... 12 SLIDING FRICTION THEORY ................ 12 STATIC VS. DYNAMIC FRICTION ............ 13 FRICTION IN ORTHODONTICS ............... 13 NORMAL FORCES IN ORTHDONTICS......... 14 Potential Normal Forces ........... 14 Ligation Method ................... 16 APPLIANCE STIFFNESS.................. 19 Design Stiffness .................. 19 Wire Stiffness .................... 20 SUMMARY................................... 21 REFERENCES................................ 23 JOURNAL ARTICLE.............................. 26 ABSTRACT.................................. 26 INTRODUCTION.............................. 27 MATERIALS AND METHODS..................... 32 MECHANICAL TESTS ....................... 32 STATISTICS ............................. 36 RESULTS................................... 37 DISCUSSION................................ 39 BINDING ................................ 39 UNLOADING PLOTS ........................ 42 LIGATION EFFECTS ....................... 45 FACTORS NOT EXAMINED ...................46 CLINICAL RECOMMENDATIONS ............... 48 CONCLUSIONS............................... 48 REFERENCES................................ 50 iv CHAPTER 3: VITA AUCTORIS............................................ 53 v LIST OF TABLES Table 1. Table 2. Descriptive Statistics: Force Losses (grams)... 38 Mann-Whitney U-Tests of Force Losses (p < 0.01) 39 vi LIST OF FIGURES Figure 1.1: Force-diagram illustrating active and responsive occlusogingival forces and couples during continuous-wire cuspid-leveling........................... 9 Figure 1.2: An illustration of couples remaining when binding occurs........................................... 10 Figure 1.3: Arrows representing potential normal forces exerted in bracket-slots by ligation or archwires. A, B, C, Facial views of both common edgewise and self-ligating brackets. D, A gingival view of a sectioned common edgewise bracket. E, A gingival view of a sectioned “active” self-ligating bracket........................... 16 Figure 2.1: Geometry and formulas to estimate the length (L) of wire between lateral-incisor and first-bicuspid brackets with that wire sling-tied to the cuspid bracket. 29 Figure 2.2: Diagram illustrating occlusogingival forces and couples accompanying continuous-wire cuspid leveling. 31 Figure 2.3: The model positioned in its fixture. The fixture was bolted to the base of the testing machine.... 33 Figure 2.4: A representative unloading plot from the 5.5mm SL group. The dashed curve includes the estimated plateau. The dimension-symbol denotes the quantified force-loss............................................... 36 Figure 2.5: Representative unloading plots from each group ......................................................... 37 Figure 2.6: An illustration of couples present when binding occurs........................................... 41 Figure 2.7: Representative unloading plot from the SL 5.5mm group. The solid curve is the recorded plot. The dashed curve represents an assumed estimate of wirebehavior without friction. The cross-hatched area represents the energy-loss occurring as a result of friction present......................................... 44 vii Figure 2.8: Comparison of representative unloading plots from the EL and SL 2.5-mm groups. The solid line is the EL 2.5-mm plot. The dashed line is the SL 2.5-mm plot. The cross-hatched area represents the difference in energy transfer from the two groups............................. 45 viii CHAPTER 1: INTRODUCTION Superelastic (SE), nickel-titanium-alloy (NiTi) wires have become the wires of choice for orthodontic leveling and aligning mechanics. These wires readily sustain large deflections without exceeding the elastic limit of the alloy. The large elastic range of SE NiTi is largely due For example, Burstone to its pseudoelastic characteristic. et al.1 found that an 80˚ activation of SE NiTi wire produced a 91% recovery compared to 20% for stainless steel wire and 65% for martensitic NiTi wire. Some orthodontists may believe that any large activation with SE NiTi wire will result in the desired tooth movement; however, four recent investigations report that friction can stop SENiTi-wire displacements through ligated bracket-slots.2-5 When a wire does not slide through supporting bracketslots, desired tooth movement is unlikely to occur. Binding is defined herein as a condition in which an orthodontic leveling wire is prevented from sliding through ligated bracket-slots. Note that “binding” in this context differs from the binding defined by Kusy and Whitley.6 Binding can alter the desired tooth-moving forces.7 Factors leading to SE-NiTi-wire binding in leveling mechanics apparently have not been studied. Binding of wires in bracket-slots during sliding mechanics has been studied extensively;8-11 however, contributing factors may Larger not play the same roles during leveling mechanics. wires are more likely to bind during sliding mechanics; smaller wires may more readily bind during leveling mechanics. Ward3 and Franchi and Baccetti4 found that 0.014-inch SE NiTi wire bound, and 0.016-inch SE NiTi wire did not bind, under the same leveling conditions. These findings were incidental and not intended results of the investigations. Not surprisingly, binding in leveling mechanics is somewhat unlike binding in sliding mechanics. During sliding mechanics, when binding causes resistance to sliding, active retraction forces can be increased in size to overcome the friction; however, in leveling mechanics the only forces present to overcome friction are those generated by the springback potential of the deflected wire. If the archwire does not produce sufficient force to overcome the friction present, binding will occur. Understanding the factors that lead to SE NiTi wire-binding in leveling mechanics are important in establishing clinical guidelines for the efficient use of this wire. Binding of SE NiTi wire in clinical practice could lead to no tooth movement or undesired tooth movement. 2 The desired tooth moving force will be completely negated if the wire binds. Burstone12 has pointed out that leveling of a gingivally positioned cuspid with a continuous SE NiTi wire leads to responsive forces with undesired displacement tendencies. The aim of this investigation was to determine the potential for binding and to describe the unloading behavior of continuous 0.014-inch round SE NiTi wire in the leveling of a gingivally malposed cupsid. 3 CHAPTER 2: REVIEW OF THE LITERATURE INTRODUCTION This review of the literature begins with a discussion of the dynamics of leveling a gingivally positioned cuspid with a continuous SE NiTi archwire. The frictional forces that arise in orthodontic leveling are then examined. Understanding these concepts leads to the rationale for this study of unloading behavior and potential binding in bracket-slots supporting SE NiTi leveling wires. OCCLUSOGINGIVAL WIRE ACTIVATION When engaging an SE NiTi wire to level a gingivally malposed cuspid, several mechanics-entities occur simultaneously. First, the wire is deflected and is Second, in attached to or engaged in the cuspid bracket. response to the springback potential of the wire at the cuspid, normal forces are induced at the adjacent (supporting) brackets. Third, the effective length of wire between the adjacent brackets increases as wire is drawn through those adjacent brackets to reach the crown of the 4 gingivally positioned cuspid. examined individually below. Each of these aspects is DEFLECTION OF THE SE NITI WIRE As an SE NiTi wire is deflected, it first deforms in an elastic manner in the austenitic state. As stress induced in the wire increases, a phase-transformation begins (from austenitic toward martensitic metallurgy). This occurring stress-induced phase-transformation is accompanied by a lessening in stress-increase needed to continue the deflection.13 In practice, the transformation When the wire is likely is incomplete at wire-engagement. then allowed to unload, hysteresis occurs and is followed by a relatively level unloading plot as the (partial) transformation reverses, and the alloy returns to its austenite phase.14 When the wire reaches the austenitic state, unloading is completed via Hookean elastic deactivation. The wire, then, may undergo large deflections and completely return to its initial shape.13 Throughout activation, the wire will conform to the lowest energy-state that can be achieved as constrained, resulting in specific curvatures within the interbracket spaces. 5 The flexural stiffness of SE NiTi wire is dependent upon its size and shape, the temperature-transition range (TTR), and the amount of wire-deflection.1,12,14 Flexural- stiffness measurements for SE NiTi wires are based upon linear regressions of the unloading curves.1 are discussed below. The cross-sectional size and shape of NiTi wire have the same influences on its flexural stiffness(es) as they have on the stiffness(es) of other orthodontic wires.13 This topic is discussed later. Stiffnesses of SE NiTi wire are influenced by the TTR; as the TTR increases, stiffnesses decreases. The TTR can These factors be altered 1) by adding trace-elements to the alloy or 2) by heat-treating the wire.14 Copper is added to some NiTi alloys to lower the TTR, thus lessening wires’ loading and unloading stiffnesses.14 The unloading stiffness of SE NiTi wire is also dependent upon the extent of activation. As the activating deflection is increased, the unloading stiffness decreases.1 Wilkinson et al.2 found that a wire deflected to 1 mm generated an initial unloading force of 247 grams. When the same wires were deflected to 4 mm, they unloaded from only 74 grams of force. This phenomenon is the rationale 6 for Profitt’s statement, “the force delivered by an A-NiTi wire can be changed by releasing and retying it.”13 Because of the many factors that influence SE-NiTi-wire stiffnesses, large variations in structural properties exist between manufacturers2,15 and within manufacturers. Only two of these factors are under the direct control of the orthodontist. First, the wire selected with its size, shape, and TTR influences the loading and unloading stiffnesses. Second, the extent of activation/deflection may be varied, affecting the unloading stiffness. WIRE INDUCED NORMAL FORCES When a continuous wire is deflected and attached to a gingivally malposed, right-cuspid bracket, the wire contacts the distogingival and mesio-occlusal edges of the lateral-incisor bracket-slot and the mesiogingival and disto-occlusal edges of the first-bicuspid bracket-slot. These contacts create normal forces between the slots and wire. The magnitudes of these normal forces are partially dependent upon the loading stiffness as the wire is engaged and the unloading stiffness as the wire unloads.8 Wire- curvatures in relation to the bracket-slots dictate which normal force will be the greatest. 7 The normal force adjacent to the greatest wire-curvature will be the largest normal force in the system.16 DEFLECTED WIRE-LENGTH When an archwire is deflected to reach a gingivally malpositioned cuspid, the wire is deflected gingivally, drawing wire through the adjacent brackets toward the cuspid. The result is a greater length of wire between the lateral-incisor and first-bicuspid brackets than the mesiodistal distance between them. To illustrate this inequality, the geometry can be simplified with two right triangles, and the Pythagorean Theorem is invoked. If a wire is deflected 4 mm and sling-tied to a high cuspid with a 13-mm distance between the lateral-incisor and firstbicuspid brackets, there is approximately 15.3-mm of wire between the brackets. If the wire is to level the cuspid, 2.3 mm of wire must slide through the adjacent brackets so that only 13 mm of wire remains between those brackets. HIGH-CUSPID LEVELING With a continuous wire secured to a high cuspid, in addition to the action against the cuspid, potentially 8 counterproductive forces are created, posing potential problems for the clinician using a straight-wire technique. Burstone wrote: “With a high canine, a [passively] straight wire tends to tip the buccal segment toward the canine.”9 Creating this undesired displacement potential are responsive intrusive forces and couples exerted on the adjacent teeth through their brackets. See Figure 1.1. Figure 1.1: Force-diagram illustrating active and responsive occlusogingival forces and couples during continuous-wire cuspidleveling. Forces present in the system originate from the elastic deformation of the wire. As the wire attempts to spring back toward its original shape, an occlusal force is created at the cuspid. In response to the occlusal force, 9 gingival forces are applied to the anchorage sites. Force- magnitude at each anchorage site is approximately one-half of the occlusal force at the cuspid. Additionally, couples are applied within the first-bicuspid and lateral-incisor bracket-slots, creating tipping/torquing moments. Couples are created by the normal forces between bracket-slots and the archwire.16 Excessive frictional forces can effectively cancel the springback potential at the cuspid, and the net extrusive action disappears, leaving only the couples and friction until the resistances(s) can be overcome. Figure 1.2. See Figure 1.2: An illustration of couples remaining when binding occurs. 10 NORMAL FORCES AND TOOTH MOVEMENT An archwire having been deflected gingivally at the cuspid, the net normal forces on the adjacent brackets are individually nearly equally as approximately one-half of the cuspid force mesially and distally. The normal forces, local wire-curvatures, and the need for the wire to slide through the adjacent bracket-slots to progress toward a correction, create the friction leading to potential binding of the leveling wire. Potential for binding may particularly be raised with SE NiTi wires because a large deflection decreases the unloading stiffness.1 ARCHWIRE SLIDING DURING LEVELING As discussed previously, a deflection to level a gingivally malposed cuspid will produce an “excess” length of wire between the lateral-incisor and first-bicuspid brackets. In order for the desired leveling to occur, this “excess” wire must slide through the supporting bracketslots. In the presence of wire-slot contact, frictional The potential for forces oppose this sliding motion. binding of leveling wires has not been examined, although 11 some incidental binding has been reported in the process of other investigations.2-5 COULOMB FRICTION Friction is the force that opposes the tangential movement of two bodies in contact. The Coulomb model of friction is characterized by the following equation: F = N*µ where F is the frictional force, µ is the coefficient of friction, and N is the normal force.9 Coulomb friction is explored in Sliding-Friction Theory, Static and Dynamic Friction, and Friction in Orthodontics to follow. SLIDING FRICTION THEORY Sliding friction is defined as friction between two solid objects in relative translational motion. This type Two of friction is associated with orthodontic mechanics. major influences on maximum static and kinetic sliding friction are the magnitudes of the normal forces and the relative surface-roughness of the objects in contact.16 12 STATIC VS. DYNAMIC FRICTION Three categories of Coulomb friction are defined: static friction, maximum static friction, and dynamic friction. Static friction is present when relative motion This frictional force is attempted, but none occurs.16 serves to maintain equilibrium when active forces are insufficient to produce movement. Maximum static friction is the tangential force present just before motion starts. This force is ordinarily the greatest resistance before the object begins to slide.17 Dynamic friction is usually less than maximum static friction, and it is the frictional force present when objects are sliding across one another.16 Separate coefficients of friction may be determined experimentally, for a pair of contacting surfaces, for both maximum static and dynamic friction.17 FRICTION IN ORTHODONTICS Coulomb’s explanation of friction becomes more complicated in orthodontics. First, the normal forces present in orthodontics are very situation-dependent and are rarely constant. Second, the velocity at which movement occurs is very slow, leading to inconsistency in 13 the type of frictional forces present. Third, the surface- roughnesses of the materials depend upon more than just the chemical compositions. Each of these aspects is discussed further within the following subsections. NORMAL FORCES IN ORTHDONTICS Two categories of normal force are present in orthodontic leveling. First, slot-wire contact(s) exist, Second, the due to wire-curvatures at/through the slot. ligation securing the wire in the slot can create normal force. These normal forces for a gingivally displaced and ligated wire are described below. Potential Normal Forces When the wire is activated gingivally, but only contacts the edge of one wing of the bracket, a normal force exists at that point only. Depending upon the wire- curvature through the slot, normal forces may be present at both ends of the bracket. From a facial perspective, then, normal forces are possible at opposite slot-edges or in the middle of the slot as well. Potential normal forces can also be viewed from the gingival perspective of the 14 bracket.8 When the wire is ligated, contact may be present along the entire bracket-width to produce a normal force between the bracket and archwire. Normal forces from ligation may differ between self-ligated and conventional edgewise brackets. A potential contact exists at the lingual surface of the slot of both self-ligated and common edgewise brackets. Potential contacts may be made between the ligature and the wire at both the mesial and distal aspects of a common edgewise bracket. The self-ligated bracket, at its clip, may receive a facially directed normal force from the wire. illustrated in Figure 1.3. The various normal forces are 15 A B C D E Figure 1.3: Arrows representing potential normal forces exerted in bracket-slots by ligation or archwires. A, B, C, Facial views of both common edgewise and self-ligating brackets. D, A gingival view of a sectioned common edgewise bracket. E, A gingival view of a sectioned “active” self-ligating bracket. Ligation Method Conventional ligations are of two material categories: stainless steel and (polymeric) elastomers. Other ligations have been introduced in attempts to reduce friction. These include self-ligating brackets, non- conventional elastomeric ligatures,4,5 and brackets with six tie-wings.18 Self-ligating brackets can be subdivided as having integral “active” or “passive” slot-closures. 16 Steel ties are often used to ligate SE NiTi wires. The normal force created by this ligature may be very small.19 Bednar et al.9 found that steel ligatures produced the least friction when sliding a bracket along a wire when compared to elastomeric and self-ligations; however, Iwasaski et al.20 found significant variances across clinicians in placing steel ties. This variation ranged between 150 and 1470 grams with steel ties compared to 1600 grams with elastomers. Elastomeric ligations initially produce relatively large normal forces with sizable friction potential, as confirmed in many investigations;2,4,5,9,19-21 however, none of the friction-literature reviewed accounts for sizable (perhaps 50% or greater) force-losses as the elastomers relax.22 Significant variations in initial force magnitudes for a constant stretch have also been obtained within samples of alike elastomeric ligatures.22-24 The normal force may also vary in magnitude with wire and bracket sizes. It has been found that an increase in wire- and/or bracket-dimensions results in more stretch of the elastomeric ligatures and thus greater normal forces.25 Self-ligating brackets have been introduced into the orthodontic marketplace with claims of less friction and lighter forces. Laboratory testing has confirmed less 17 friction with self-ligating brackets;2,3,19,21,24,26 however, during straight-wire leveling, larger active forces are generally produced with these brackets because there is less friction.2,3 The slot-closure device varies within the family of self-ligating brackets; two groups of brackets are termed “active” and “passive.” Within the “active” brackets the ligating mechanism presses against the archwire (if it exceeds a minimum faciolingual dimension, i.e., 0.018 inches), seating it in the bracket. The ligation of a The “passive” bracket will not press against an archwire. stated, seemingly simple difference, “active” vs. “passive” brackets, is flawed, however, because activated archwires are often (first-order) angulated in the slot, and such angulations often result in the creation of normal forces. Differences in normal forces, generated in “active” vs. “passive” self-ligating brackets, have been reported. Hain et al.24 found that, with a 0.019- x 0.025-inch stainless steel archwire, 1.61 Newtons were produced (faciolingually) in an “active” bracket, and no normal force existed in a “passive” bracket. This difference in normal forces has Shivapuja and Berger27 been shown to change with wire-size. found no difference between “active” and “passive” self- 18 ligating brackets in faciolingual normal forces exerted against an 0.018-inch stainless-steel wire. APPLIANCE STIFFNESS Normal forces can be directly related to the stiffness of the activated archwire.8 As the flexural stiffness(es) of a wire increase, the magnitude(s) of normal forces produced by the wire increase. Archwire-stiffness depends upon both the wire itself and the local design of the appliance. The “unit” wire-stiffness is dependent upon the wire-material stiffness and the cross-sectional shape and size.28 The unit stiffness of a SE NiTi wire is further complicated by its deflection-dependence.1 Design Stiffness The design-stiffness is dependent upon two variables: the length(s) of wire and the support(s) of the wire. The wire-stiffness varies inversely with its length from one support or between two supports.13,28 supported in three ways. The archwire may be First, the wire can be a cantilever, and the stiffness is dependent upon the length 19 of the cantilever. As the length of cantilever increases, Second (and third), wires can be When the stiffness decreases. supported at both ends either loosely or tightly. comparing wires of the same size and shape, with equal length, stiffness increases as wire-support clearance decreases. Loosely supported wires are stiffer than cantilevered wires and tightly supported wires are stiffer than loosely supported wires.13 The orthodontist can vary the wire-length between crown-attachments. A loop can effectively increase wire- length, and bracket-width alters interbracket distance and effectively changes wire-length. Frank and Nikolai8 found that an increase in bracket-width increased friction during cuspid-retraction. Wire Stiffness Unit wire-stiffness is dependent upon wire materialstiffness and cross-sectional shape and size. Material- stiffnesses have been determined for stainless steel, βtitanium (β-Ti) alloys, and stabilized martensitic NiTi alloys.29 The material-stiffness of SE NiTi wire is notably dependent upon the extent of deflection and can vary from 20 7% to 41% of the stiffness of orthodontic stainless steel.1,13 As wire-size increases, the stiffness of the wire increases to the fourth power for round wires and generally as a cubic function of the dimension in the direction of flexure; for example, if a round wire is doubled in its dimension in the flexure direction, the stiffness increases sixteen times (24 = 16). For rectangular wires the dimension in the direction of deflection has the greater influence on stiffness.13,28 When an archwire is brought into contact with mesial and/or distal corners of the slot, due to the local wirecurvature as activated, wire-stiffness becomes a predominant factor in friction potential because of the normal force(s) generated.8 SUMMARY It is easily seen that friction in orthodontics is complex. This complexity is further increased with SE NiTi The information that is available currently archwires. concerning friction and SE NiTi wires has been derived primarily from displacing a bracket along a guiding wire or 21 pulling a wire through a bracket-slot or series of slots.21,25,26,30-32 More recently, leveling with SE NiTi wires has been examined from the perspective of friction affecting forces delivered to the malposed tooth/teeth.2-5,33 Apparently, though, all of these inquires involved arbitrarily selected deflections, some of which incidentally produced binding.2-4 No attempts to determine the binding points for SE NiTi leveling wires have been found in the published literature. Due to the complex nature of the factors involved, indirect measures for potential binding of SE NiTi archwires in leveling are impossible. A model simulating a gingivally malposed cuspid has been developed to examine the binding of 0.014-inch-diameter SE NiTi archwires. 22 REFERENCES 1. Burstone CJ, Qin B, Morton JY. Chinese NiTi wire--a new orthodontic alloy. Am J Orthod 1985;87:445-452. 2. Wilkinson PD, Dysart PS, Hood JA, Herbison GP. Load-deflection characteristics of superelastic nickel-titanium orthodontic wires. Am J Orthod Dentofacial Orthop 2002;121:483-495. 3. Ward BL. Friction in Alignment Mechanics: The effects of ligation, perturbation, and wire size on orhtodontic aliging forces Center for Advanced Dental Education. Saint Louis, MO: Saint Louis University; 2007. 4. Franchi L, Baccetti T. Forces released during alignment with a preadjusted appliance with different types of elastomeric ligatures. Am J Orthod Dentofacial Orthop 2006;129:687-690. 5. Camporesi M, Baccetti T, Franchi L. Forces released by esthetic preadjusted appliances with low-friction and conventional elastomeric ligatures. Am J Orthod Dentofacial Orthop 2007;131:772-775. 6. Kusy RP, Whitley JQ. 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The effect of ligation method on friction in sliding mechanics. Am J Orthod Dentofacial Orthop 2003;123:416-422. 20. Iwasaki LR, Beatty MW, Randall CJ, Nickel JC. Clinical ligation forces and intraoral friction during sliding on a stainless steel archwire. AmJ Orthod Dentofacial Orthop 2003;123:408-415. 21. Henao SP, Kusy RP. Evaluation of the frictional resistance of conventional and self-ligating bracket designs using standardized archwires and dental typodonts. Angle Orthod 2004;74:202-211. 22. Taloumis LJ, Smith TM, Hondrum SO, Lorton L. Force decay and deformation of orthodontic elastomeric ligatures. Am J Orthod Dentofacial Orthop 1997;111:1-11. 23. Khambay B, Millett D, McHugh S. Archwire seating forces produced by different ligation methods and their effect on frictional resistance. Eur J Orthod 2005;27:302-308. 24. Hain M, Dhopatkar A, Rock P. A comparison of different ligation methods on friction. Am J Orthod Dentofacial Orthop 2006;130:666-670. 25. Kapila S, Angolkar PV, Duncanson MG, Jr., Nanda RS. Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four alloys. Am J Orthod Dentofacial Orthop 1990;98:117-126. 26. Henao SP, Kusy RP. Frictional evaluations of dental typodont models using four self-ligating designs and a conventional design. Angle Orthod 2005;75:75-85. 27. Shivapuja PK, Berger J. A comparative study of conventional ligation and self-ligation bracket systems. Am J Orthod Dentofacial Orthop 1994;106:472-480. 28. Burstone CJ. Application of Bioengineering to Clinical Orthodontics. In: Thomas M. Graber RLV, Katherine W.L. Vig, editor. Orthodontics: Current Pricniples and Techniques. St. Louis, MO: Elsivier, Mosby; 2005. p. 293-330. 24 29. Burstone CJ. Variable-modulus orthodontics. Am J Orthod 1981;80:116. 30. Baccetti T, Franchi L. Friction produced by types of elastomeric ligatures in treatment mechanics with the preadjusted appliance. Angle Orthod 2006;76:211-216. 31. Tecco S, Festa F, Caputi S, Traini T, Di Iorio D, D'Attilio M. Friction of conventional and self-ligating brackets using a 10 bracket model. Angle Orthod 2005;75:1041-1045. 32. Kusy RP, Whitley JQ. Effects of surface roughness on the coefficients of friction in model orthodontic systems. J Biomech 1990;23:913-925. 33. Fuck L-M, Drescher D. Force systems in the initial phase of orthodontic treatment -- a comparison of different leveling arch wires. J Orofacial Orthop 2006;67:6-18. 25 CHAPTER 3: JOURNAL ARTICLE ABSTRACT Objective: To examine unloading behavior of superelastic (SE), nickel-titanium-alloy (NiTi) leveling wires within a gingivally malposed cuspid model. Materials and Methods: A universal testing machine deflected continuous, 0.014inch SE NiTi wires gingivally at the right-cuspid position of an orthodontic, dental-arch model. Binding points (smallest deflections at which frictional forces stop leveling wires from sliding through supporting bracketslots) and unloading plots (from beneath binding points) were obtained with self-ligation (SL) and new (unrelaxed) elastomeric ligation (EL) at the support sites. Unloading data were collected with SL from 2.5-, 3.5-, 4.5-, and 5.5mm deflections; and from 1.5- and 2.5-mm deflections with EL. Force-loss was quantified as the ordinate difference Descriptive and between the peak and the trough of a plot. inferential statistics, the latter Kruskal-Wallis with Mann-Whitney U-tests, were run to analyze the force-loss data. Results: Binding occurred with SL at a deflection of Mean force-loss ranged from 7.5 mm, and at 3.5 mm with EL. 87.0 ± 10.1 grams to 0.0 ± 0.0 grams with SL and EL during 26 unloading from 5.5 and 1.5 mm, respectively. Significant differences (p < .01) in force-losses were obtained across all SL groups, but not between the EL groups. Conclusions: 1. Binding of 0.014-inch SE NiTi leveling wires occurs at smaller deflection-amplitudes with EL than with SL. 2. Relatively constant aligning forces from 0.014-inch SE NiTi leveling wires should not be expected in most clinical situations. 3. Binding of 0.014-inch SE NiTi leveling wires occurs at a deflection-amplitude threshold rather than at a deflection-amplitude. INTRODUCTION Unloading behavior of superelastic (SE), nickeltitanium-alloy (NiTi) orthodontic wires has been well documented from cantilever1 and three-point2,3 bending tests. These tests have shown that SE NiTi wires have large elastic ranges and can exert relatively constant forces over sizable portions of those ranges.1-3 SE NiTi wires have also displayed deflection-dependent unloading stiffnesses; larger deflections resulted in smaller unloading stiffnesses.1-4 Properties of SE NiTi wires have led to recommendations from Burstone et al.1 and Proffit4 27 that they be the wires of choice when large deflections and relatively constant tooth-moving forces are required. The unloading behavior of SE NiTi wires has been tested within rather complex models.3,5-8 These models all involved multiple brackets and various ligation methods. Under some of these conditions Wilkinson et al.,3 Camporesi et al.,5 Franchi and Baccetti,6 and Ward8 found that SE NiTi wires can cease to slide through supporting bracket-slots. The archwire failing to slide through supporting bracketslots is termed “binding” herein. Note that this definition differs from the wire-slot binding described by Kusy and Whitley.9 Discovery of binding in leveling mechanics raises questions concerning the behavior of SE NiTi wire. Some pertinent questions are as follows: What activating deflection will cause the SE NiTi wire to bind? What factors lead to SE NiTi wire-slot binding? NiTi wires respond as they begin to bind? Wire-length between brackets is a source of potential binding of a continuous leveling wire.8 As a leveling wire How do SE is deflected to engage a malposed tooth, to obtain the necessary added length locally, the wire slides through the adjacent ligated brackets and tubes. For the malposed tooth/teeth to align, the wire must slide back through the supporting brackets and tubes. 28 “Free” wire-length between two brackets adjacent to a malposed cuspid can be estimated by superimposing two right triangles on the curved wire as illustrated in Figure 2.1. Assuming a 13-mm lateral- incisor-to-first-bicuspid interbracket distance and a 4-mm deflection to the cuspid bracket, 15.3 mm is calculated as the wire-length between the lateral-incisor and firstbicuspid brackets. An estimated 15.3 mm of wire-length demonstrates that, for the wire to (deactivate and) become straight, approximately 2.3 mm of wire must slide through the slots of the adjacent ligated brackets and tubes. b a c L≈2c c2=a2+b2 Figure 2.1: Geometry and formulas to estimate the length (L) of wire between lateral-incisor and first-bicuspid brackets with that wire sling-tied to the cuspid bracket. 29 Sliding of a leveling wire may be opposed by frictional forces.6 Excessive frictional forces will stop the wire Information from sliding, resulting in a bound wire.3,6,8 currently available concerning friction and SE NiTi wires has been derived primarily from displacing a bracket along a guiding wire or pulling a wire through a bracket-slot or series of slots.10-15 More recently, leveling with SE NiTi wires has been examined from the perspective of friction affecting forces delivered to the malposed tooth/teeth.3,5-8 Apparently, though, all of these inquiries involved arbitrarily selected deflections, some of which incidentally produced binding.3,6,8 No attempts to determine the binding points for SE NiTi leveling wires have been found in the published literature. Self-ligating brackets have been introduced into the orthodontic marketplace with claims of less friction and lighter forces. Laboratory testing has confirmed that often there is less friction with self-ligating brackets;3,8,11,12,16,17 notably, during straight-wire leveling, larger active forces are generally produced with these brackets because there is less friction.3,8 The purpose of this study was to examine the binding and unloading behavior of a SE NiTi wire within a gingivally-malposed-cuspid model. 30 Ligation was varied: self-ligation or new (unrelaxed) elastomerics. Burstone18 has pointed out that leveling of a gingivally positioned cuspid with a continuous wire tends to tip adjacent teeth towards the cuspid. Forces responsible for these tooth movements are created by the wire-curvatures at and through the first-bicuspid and lateral-incisor bracket-slots. These curvatures induce pairs of normal forces at the supporting bracket-slots. Wire-curvatures indicate that the normal forces closest to the cuspid are greater than the normal forces farther from the cuspid.19 These unbalanced pairs of normal forces result in the couples and the intrusive forces illustrated in Figure 2.2. Figure 2.2: Diagram illustrating occlusogingival forces and couples accompanying continuous-wire cuspid leveling. 31 When a leveling wire binds, occlusal springback at the cuspid bracket temporarily ceases, but the couples remain, frictional forces disallow wire-sliding, and the curved shape of the wire is maintained. The responsive couples are seen to potentially tip/torque the supporting teeth such that the crowns could move toward the cuspid. Such responsive displacements would reduce wire-curvatures, reducing friction, and tend toward unbinding the wire. MATERIALS AND METHODS MECHANICAL TESTS A model was constructed of ¼-inch-thick tool-steel plate, machined to match the Tru-Arch, maxillary, small archform (Ormco Corp., Glendora, CA). Attached to the machined edge were two first-molar tubes with zero firstorder rotation and nine In-Ovation-R brackets (GAC International, Bohemia, NY) from second bicuspid to second bicuspid (0.022-inch slots/tubes); material was removed at the right-cuspid site to permit gingival deflections there. Brackets and tubes were spaced according to the typical maxillary tooth size of the adult-male dentition as 32 modified by Wilkinson et al.3 The set of brackets and tubes was aligned with a 0.022-inch-diameter stainless-steel archwire, shaped to match the model; the attachments were direct-bonded with Pad Lock® (Reliance Orthodontic Products, Itasca, IL). See Figure 2.3. Figure 2.3: The model positioned in its fixture. bolted to the base of the testing machine. The fixture was All trials were conducted with a universal testing machine (Model 1011, Instron Corp., Canton, MA) Tests were initiated by deflecting small, maxillary, 27°C Copper NITI®, 0.014-inch, Tru-Arch archblanks gingivally at the right-cuspid position. Wires were deflected with a 0.01033 inch-wide-by-0.31-inch-long blade at a crosshead speed of 8 mm per minute and deactivated at a crosshead speed of 2 mm per minute. A chart-recorder (Model 2310-069, Instron Corp.) plotted force vs. deflection during unloading. Tests were carried out in a dry field within a Plexiglas® case where the temperature was maintained at 36 ± 5° Celcius. Archwires were ligated in the brackets with either In-Ovation-R clips or new (unrelaxed) elastomerics (#361080, TP Orthodontics, Inc., La Porte, IN); the elastomerics were placed with a Straight Shooter® (TP Orthodontics, Inc.). Tests were run first on all self-ligation (SL) specimens; then the clips were removed from the brackets to enable solely new elastic ligation (EL) placements. Initial binding-point estimates, separately with SL and EL strap-ups, were obtained by repeatedly cycling a single wire with deflection-amplitudes increasing by 0.5 mm. When a force of zero grams was observed throughout attempted deactivation, the test was terminated, and the last deflection-amplitude became the initial binding-point estimate. Five wires were deflected to each initial bindingpoint estimate. If all five wires did not bind during deactivation, the deflection-amplitude was increased in 34 increments of 1 mm until five consecutive wires bound. The smallest amplitude at which five consecutive wires bound was defined as the estimated binding point. Unloading data were collected from ten wires from each group. (A “group” is defined by ligation and deflectionamplitude.) Group tests began at a deflection-amplitude 1 mm below the estimated binding point, and the amplitude was decreased by 1 mm for each additional group. New groups were added until a relatively level, unloading plateau was observed. Groups containing wires that bound were excluded from the unloading data-set. Initial unloading plots revealed a trough deviating from the plateau that is typically obtained in three-point bending tests of SE NiTi wires. The ordinate difference between the trough and estimated plateau was defined as force-loss. See Figure 2.4. Force-loss measurements were taken from all unloading plots. 35 250 Unloading Force (g) 200 150 100 50 0 0 1 2 3 4 5 6 Deflection Distance (mm) Figure 2.4: A representative unloading plot from the 5.5-mm SL group. The dashed curve includes the estimated plateau. The dimension-symbol denotes the quantified force-loss. STATISTICS Force-loss measurements were analyzed with SPSS 14.0 for Windows (SPSS Inc., Chicago, IL). Descriptive A Kruskal-Wallis statistics were compiled for each group. test was run to study the effects of deflection-amplitude and ligation method on a parameter defined as “force loss.” Post-hoc Man-Whitney U-tests were conducted. differences were sought at p < 0.01. Significant 36 RESULTS The estimated binding points were at deflectionamplitudes of 3.5 mm with EL and 7.5 mm with SL. Unloading data were collected at deflection-amplitudes of 1.5 and 2.5 mm with EL; and 2.5, 3.5, 4.5, and 5.5 mm with SL. The 6.5-mm SL group was excluded because some wires unloaded completely and other specimens bound. A large dip from the SE-characteristic plateau was noted from each of the SL groups deflected to 4.5 and 5.5 mm; see Figure 2.5. 250 Unloading Force (g) 200 Legend 150 SL 5.5 SL 4.5 100 SL 3.5 SL 2.5 50 EL 2.5 EL 1.5 0 0 1 2 3 4 5 6 Deflection Distance (mm) Figure 2.5: Representative unloading plots from each group Descriptive statistics are presented in Table 1. Force-loss increased from 3.5 grams to 87.0 grams as the 37 SL-group deflection-amplitudes approached the estimated binding point. Mean force-losses from the EL groups were 0.0 grams and 0.5 grams from 1.5- and 2.5-mm deflectionamplitudes, respectively. Table 1. Group SL 5.5-mm SL 4.5-mm SL 3.5-mm SL 2.5-mm EL 2.5-mm EL 1.5-mm Descriptive Statistics: Force Losses (grams) Mean 87.0 34.5 15.0 3.5 0.5 0.0 SD ±10.1 ±6.0 ±4.7 ±2.4 ±1.6 ±0.0 Minimum 75 30 10 0 0 0 Maximum 105 50 20 5 5 0 The Kruskal-Wallis analysis revealed statistical differences across the mean force-loss data. Mann-Whitney U-Tests determined statistically significant differences within all pairs of SL force-loss groups and with the EL groups; the force-losses between the EL groups were not statistically different. See Table 2. 38 Table 2. Groups (mm) SL 5.5 SL 4.5 SL 3.5 SL 2.5 EL 2.5 EL 1.5 Mann-Whitney U-Tests of Force Losses (p < 0.01) SL 5.5 n/a Sig Sig Sig Sig Sig n/a Sig Sig Sig Sig n/a Sig Sig Sig n/a Sig Sig n/a Non Sig n/a SL 4.5 SL 3.5 SL 2.5 EL 2.5 EL 1.5 DISCUSSION BINDING SE NiTi wires respond mechanically very differently from Hookean orthodontic-alloy wires. model, the SE NiTi wire may bind. Within the present After the wire is deflected and deactivation begins, wire-slot friction at the supports has the effect of decreasing the net unloading force at the cuspid bracket. Changes in frictional and First, frictional springback forces occur for two reasons. forces result in particular from wire-and-bracket-slot contacts at the lateral-incisor and first-bicuspid 39 brackets. As deflection-amplitude is increased, wire- curvatures increase between the cuspid and the supporting bracket-slots, and greater wire-curvatures result in larger normal and frictional forces at the supporting bracketslots. Second, increases in deflection-amplitude, with SE NiTi wires, decrease unloading stiffnesses and springback forces.1 A deflected state may be reached where the springback potential of the wire cannot overcome the frictional forces, and the wire binds in those slots. Bound wires may “free-up” and unload because of the couples exerted that could torque the lateral-incisor and first-bicuspid toward the malposed cuspid. See Figure 2.6. The frictional forces are only fractions of the sizes of the normal forces; thus, the couples dominate in displacement potential. The torquing could reduce wire- curvatures, lessen frictional forces, and occlusal unloading at and movement of the cuspid could resume. Application of the estimated binding points herein to clinical practice becomes somewhat challenging. In this research, binding-point estimates were specified at deflection-amplitudes where binding occurred consistently. The SL estimate discounted the binding of several specimens within the SL 6.5-mm group. In future research, binding 40 thresholds, where binding begins to occur, might be more useful for clinical application. Figure 2.6: An illustration of couples present when binding occurs. Understanding that SE NiTi wires may bind is important clinically. A bound wire will produce either no tooth It should be noted movement or unwanted tooth movement.20 that binding occurred here within both SL and EL groups. Some researchers have (erroneously) claimed that selfligating brackets result in a “virtually friction-free” appliance where binding cannot occur.21 41 UNLOADING PLOTS Unloading plots in Figure 2.5 reveal several notable findings. First, SE NiTi wires activated between two bracket-slots generally did not produce relatively constant forces. Plots from the 2.5- and 3.5-mm SL groups exhibited relatively constant force during 1.5 and 2.5 mm of unloading, respectively. All other unloading plots Varying unloading displayed substantially varying forces. forces resulted from frictional forces impairing levelingwire sliding. Attaining constant tooth/teeth moving forces may not be important for orthodontic displacement, as optimal tooth/teeth moving forces are unknown.22 Second, frictional forces altered unloading plots from the SL groups, often creating troughs deviating from the anticipated plateaus. Small troughs occurred in EL 2.5-mm curves and no troughs occurred within the EL 1.5-mm group. Third, a “step” was observed at 200 grams in each unloading plot. The source of this “step” is unclear. Fourth, a “spike” in unloading force occurs in all SL plots at about 0.5 mm of deflection. This spike, a sudden increase in force, may reflect the wire undergoing completion of the reverse transformation back to the austenitic metallurgic phase. 42 FORCE-LOSSES Force-losses quantified herein, partially evaluating the SE NiTi wire behavior, demonstrated the increasing nemesis of friction within the SL groups as deflectionamplitude was increased. Wire-curvatures between the cuspid and supporting bracket-slots are responsible for much of the friction. As wire-curvatures increase, larger normal forces are induced in the supporting bracket-slots. The unloading plot from the largest deflection-amplitude is illustrated in Figure 2.7. This figure compares the expected behavior of a SE NiTi wire with friction absent to that with friction impeding wire displacements through the ligated slots. The energy-loss depicted is a direct result of frictional forces. 43 250 Unloading Force (g) 200 150 100 50 0 0 1 2 3 4 5 6 Deflection Distance (mm) Figure 2.7: Representative unloading plot from the SL 5.5-mm group. The solid curve is the recorded plot. The dashed curve represents an assumed estimate of wire-behavior without friction. The cross-hatched area represents the energy-loss occurring as a result of friction present. The EL groups also experienced energy-loss as a result of friction. The pattern of energy-loss was quite Figure 2.8 is a different from that of the SL groups. comparison of unloading plots from the EL and SL 2.5-mm groups. These plots are compared because the deflection- amplitudes were equal; therefore, the “friction-free” deactivation-plot is the same for both groups. Very little force was lost (3.5 grams) to friction from the SL 2.5-mm group. The EL plot did not display the trough or much of the plateau typically exhibited by the SL groups. 44 250 Unloading Force (g) 200 150 100 50 0 0 1 2 3 4 5 6 Deflection Distance (mm) Figure 2.8: Comparison of representative unloading plots from the EL and SL 2.5-mm groups. The solid line is the EL 2.5-mm plot. The dashed line is the SL 2.5-mm plot. The cross-hatched area represents the difference in energy transfer from the two groups. Although, there is greater energy-loss within the EL 2.5-mm group, both groups displayed adequate tooth/teeth moving forces. Also, the force-loss difference would be expected to decrease as elastomerics relax.23 LIGATION EFFECTS The self-ligating clips of the In-Ovation brackets were not expected to contribute normal forces with 0.014inch wire engaged. Faciolingual space between bracket-slot base and clip accepts wires (passive from an occlusal 45 perspective) less than 0.018 inches in diameter without contact between the archwire and clip.24 Beyond the influence of wire-curvatures, frictional forces also arise from elastomeric ligation stretched around leveling wires, sliding through support-slots. Effects of EL in this model resulted in energy-losses that were greater from the EL 2.5-mm group than from the SL 2.5mm group. The greater energy-loss from the EL 2.5-mm group is displayed as the cross-hatched area in Figure 2.8. FACTORS NOT EXAMINED Other factors not studied within this research could affect binding points and the unloading behavior of SE NiTi leveling wires. These factors include relaxation of elastomeric ligatures, simulating extraneous intraoral forces, and varying interbracket distances, wire diameter, and wire temperature-transition range (TTR). Stretched elastomeric ligatures have been shown to relax, losing one-half or more of their initial force magnitudes over time.25 This relaxation results in reduced normal forces between archwires and bracket-slots and ligatures. Recently, Petersen23 found average SE-NiTi-wire unloading forces of 71 grams with new (unrelaxed) 46 elastomerics, 112 grams with relaxed elastomerics, and 128 grams with self-ligation. Binding deflection-amplitudes and unloading plots from SE NiTi wires may change as elastomerics relax. As previously mentioned, leveling-wire curvatures are responsible for the normal forces between the wire and the bracket-slots. Changing the local wire-curvature will alter the associated normal forces and, therefore, the leveling-wire behavior. Increasing (Decreasing) interbracket distance(s), particularly from the cuspid, will decrease (increase) wire-curvatures. Engaging the archwire in the cuspid-bracket-slot vs. sling-tying the wire to the bracket will affect curvatures as well. Perturbations, simulations of extraneous intraoral forces, are another factor that may alter binding points and the unloading behavior of SE NiTi wires. Braun et al.27 found that substantial perturbations momentarily reduced frictional forces to zero, allegedly sufficient for wireslips (as in “stick-slip”). Ward8 found that, with small perturbations, SE NiTi leveling wires can still bind. Wire-diameter may also play a role in unloading behavior of SE NiTi wires. Franchi and Baccetti6 and Ward8 found that 0.014-inch SE NiTi wire bound, but 0.016-inch SE NiTi wire did not bind under the same conditions. 47 The TTR is another factor that may influence binding points. Wilkinson et al.3 found that 0.016-inch 35˚C Copper NI-TI® (Ormco Corp.) bound, but other 0.016-inch SE NiTi wires, with lower TTRs, did not bind. CLINICAL RECOMMENDATIONS A recommendation of 0.014-inch 27˚C Copper NI-TI® wire (Ormco Corp.) to level a gingivally malposed cuspid can be made from the present data. Conservative suggestions would be to sling-tie activations with 3-mm maximum deflections with conventional edgewise brackets and elastomeric ligatures and sling-tied activations to 5-mm deflections with self-ligating brackets. CONCLUSIONS 1. Binding of 0.014-inch SE NiTi leveling wires occurs at smaller deflection-amplitudes with EL than with SL. 2. Relatively constant aligning forces from 0.014-inch SE NiTi leveling wires should not be expected in most clinical situations. 48 3. Binding of 0.014-inch SE NiTi leveling wires occurs at a deflection-amplitude threshold rather than at a deflectionamplitude. 49 REFERENCES 1. Burstone CJ, Qin B, Morton JY. Chinese NiTi wire--a new orthodontic alloy. Am J Orthod 1985;87:445-452. 2. Thayer TA, Bagby MD, Moore RN, DeAngelis RJ. X-ray diffraction of nitinol orthodontic arch wires. Am J Orthod Dentofacial Orthop 1995;107:604-612. 3. Wilkinson PD, Dysart PS, Hood JA, Herbison GP. Load-deflection characteristics of superelastic nickel-titanium orthodontic wires. Am J Orthod Dentofacial Orthop 2002;121:483-495. 4. Proffit WR. Contemporary Orthdontics. 3rd Ed. St. Louis, Mo: Mosby; 2000. 5. Camporesi M, Baccetti T, Franchi L. Forces released by esthetic preadjusted appliances with low-friction and conventional elastomeric ligatures. Am J Orthod Dentofacial Orthop 2007;131:772-775. 6. Franchi L, Baccetti T. Forces released during alignment with a preadjusted appliance with different types of elastomeric ligatures. Am J Orthod Dentofacial Orthop 2006;129:687-690. 7. Fuck L-M, Drescher D. Force systems in the initial phase of orthodontic treatment -- a comparison of different leveling arch wires. J Orofacial Orthop 2006;67:6-18. 8. Ward BL. Friction in Alignment Mechanics: The effects of ligation, perturbation, and wire size on orhtodontic aliging forces. Master's thesis. Center for Advanced Dental Education. Saint Louis, MO: Saint Louis University; 2007. 9. Kusy RP, Whitley JQ. 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. 10. Baccetti T, Franchi L. Friction produced by types of elastomeric ligatures in treatment mechanics with the preadjusted appliance. Angle Orthod 2006;76:211-216. 11. Henao SP, Kusy RP. Evaluation of the frictional resistance of conventional and self-ligating bracket designs using standardized archwires and dental typodonts. Angle Orthod 2004;74:202-211. 50 12. Henao SP, Kusy RP. Frictional evaluations of dental typodont models using four self-ligating designs and a conventional design. Angle Orthod 2005;75:75-85. 13. Tecco S, Festa F, Caputi S, Traini T, Di Iorio D, D'Attilio M. Friction of conventional and self-ligating brackets using a 10 bracket model. Angle Orthod 2005;75:1041-1045. 14. Kusy RP, Whitley JQ. Effects of surface roughness on the coefficients of friction in model orthodontic systems. J Biomech 1990;23:913-925. 15. Kapila S, Angolkar PV, Duncanson MG, Jr., Nanda RS. Evaluation of friction between edgewise stainless steel brackets and orthodontic wires of four alloys. Am J Orthod Dentofacial Orthop 1990;98:117-126. 16. Hain M, Dhopatkar A, Rock P. The effect of ligation method on friction in sliding mechanics. Am J Orthod Dentofacial Orthop 2003;123:416-422. 17. Hain M, Dhopatkar A, Rock P. A comparison of different ligation methods on friction. Am J Orthod Dentofacial Orthop 2006;130:666-670. 18. Burstone CJ. Application of Bioengineering to Clinical Orthodontics. In: Graber TM, Vanarsdall RL, Vig KWL, editors. Orthodontics: Current Principles and Techniques. St. Louis, MO: Elsivier, Mosby; 2005. p. 293-330. 19. Nikolai RJ. Bioengineering Analysis of Orthodontic Mechanics. Philadelphia, PA: Lea & Febiger; 1985. 20. Rossouw PE. Friction: An Overview. Sem Orthod 2003;9:218-222. 21. Damon DH. Treatment of the Face with Biocompatible Orthodontics. In: Graber TM, Vanarsdall RL, Vig KWL, editors. Orthodontics: Current Principles and Techniques. St. Louis, MO: Elsevier; 2005. p. 753-831. 22. Ren Y, Maltha JC, Kuijpers-Jagtman AM. Optimum force magnitude for orthodontic tooth movement: A systematic literature review. Angle Orthod 2003;73:86-92. 23. Petersen AM. Force Decay of Elatomeric Ligatures: Influences on unloading force compared to self ligation. Master's thesis. Center for Advanced Dental Education. St. Louis, MO: Saint Louis University; 2008. 51 24. Roth RH, Sapunar A, Frantz RC. The In-Ovation Bracket for Fully Adjusted Appliances. In: Graber TM, Vanarsdall RL, Vig KWL, editors. Orthodontics: Current Principles and Techniques. St. Louis: Elsevier; 2005. p. 833-853. 25. Taloumis LJ, Smith TM, Hondrum SO, Lorton L. Force decay and deformation of orthodontic elastomeric ligatures. Am J Orthod Dentofacial Orthop 1997;111:1-11. 26. Frank CA, Nikolai RJ. A comparative study of frictional resistances between orthodontic bracket and arch wire. Am J Orthod 1980;78:593-609. 27. Braun S, Bluestein M, Moore BK, Benson G. Friction in perspective. Am J Orthod Dentofacial Orthop 1999;115:619-627. 52 VITA AUCTORIS Trenton Dayle Thalman was born on February 15, 1976, in Salt Lake City, Utah. five boys and two girls. He is the second child of seven: Upon graduation from high school Trent attended Snow College in Ephraim, Utah, for one quarter. He then served a two-year voluntary mission for Trent returned to his his church in British Columbia. studies at Snow College and graduated with an Associate’s degree. He further studied at Southern Utah University in Cedar City, Utah, and at Utah Valley State College in Orem, Utah. In March of 1998, Trent married his sweet wife Debbie. They are the parents of four daughters: Audrey, Lauryn, Tricia, and Julia. From July 2001 to May 2005 he attended the Indiana University School of Dentistry. From IU he received the degree of Doctor of Dental Surgery. In 2005 he began graduate studies in orthodontics at Saint Louis University in St. Louis, Missouri, where he is currently a Candidate for the degree of Master of Science in Dentistry. After graduation he and his family will return home to Richfield, Utah, to begin private practice and enjoy time with friends and family. 53