FRICTIONAL RESISTANCE EVALUATION OF ......Figure 21. Sequence of canine movement during retraction with sliding mechanics illustrating tip-counter tip cycle. Figure 22. Superimposition

FRICTIONAL RESISTANCE EVALUATION OF ORTHODONTIC BRACKETS AND ARCHWIRES WITH SLIDING MECHANICS USING QUANTIFIED

SIMULATION OF CANINE RETRACTION

A thesis submitted in conformity with the requirements for the Degree of Masters of Science in Orthodontics

Danyl V. Smith Discipline of Orthodontics

Faculty of Dentistry University of Toronto

2001

G Copyright by Darryl V. Smith, 2001

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. . Abstract ............................................................................................ II ... ................................................................................. Acknowledgments iii ....................................................................................... List of Tables iv ....................................................................................... List of Figures vi ... ................................................................................ List of Illustrations mi1

................................................... Introduction and Statement of the Problem 1 ..................................................................... Significance of the Problern 3

........................................................................... Review of the Literature 4 ................................................................. Friction in orthodonties 4 ............................................................... Eff'ect of bracket material 10

................................................ Effet of bracket design and slot size 15 ....................................... Eff'ect of bracket width and interbracket width 18

............................................................ Effect of archwire material 21 E f f i of archwire size and shape ................................................. 26

........................................................... Effect of ligation technique 29 ...................................................... Effect of second order angulation 33

............................................................... Effect of sliding velocity 37 ..................................................... Effet of wet and dry environment 39

........................................................ Summary of review of literature 43 .............................................................................. Purpose of the Study 44

................................................................................ Research Questions 45 ......................................................................................... Hypotheses 47

........................................................................... Operational Definitions 50 ............................................................................................ Materials 51

............................................................................................. Methods 56 ........................................................................................ Assumptions 71

.......................................................................................... Limitations 72 ................................................................................... Analysis of Data 73

............................................................................................... Results 77 ......................................................................................... Discussion 106 ....................................................................................... Conclusions 146

.................................................................................. Future Research 147 ......................................................................................... References 148

............................... Appendix A: Properties of Olthodontic Materials Evaluated 156 ............................................................ Appendix B: List of Manufacturers 157

........................................................................ Appendix C : Illustrations 158 ........................ Appendix D: Frictional Raistance of the Trials For Each Study 162

...................................................... Appendix E: Statistical Anal ysis Output 168

Frictional resistance evaluation of orthodontic brackets and archwires with sliding mechanics using quanM~ed simulation of canine retraction. Smith, DV; Rossouw, PE; Pilliar, R.; Watson, P. University of Toronto, Canada, 2001.

The purpose of this study was to evaluate by quantitative analysis the frictionai resistance of bracketlarchwire combinations using an experimentai canine retraction mode1 capable of tipping and uprighting to approximate orthodontic tooth movements representative of sliding mechanics. The friction testing apparatus for this study was comprised of an Instron testing machine apparatus, a load cell, and a servomotor interface for second order bracket control. This study demonstrated significant effects for bracket type, archwire type, archwire size, and archwire shape, as well as pair-wise interactions for bracket typelarchwire type, bracket typelarchwire size, bracket type/archwire shape, archwire typdarchwire size, archwire typelarchwire shape, and archwire sizelarchwire shape.

ACKNOWLEDGEMENTS

I wish to thank the following individuals for their assistance and contribution in this project:

Dr. P.E. Rossouw, University of Toronto Faculty of Dentistry Discipline of Orthodonties, who ovmaw the details of this project s w i n g as supervisor.

Dr. R. Püliar, University of Toronto Center for Biomaterials, for his valuable suggestions and insight with the project.

Dr. P. Watson, University of Toronto Center for Biomaterials, for his participation and contributions with this project.

Mr. C. Pereira, University of Toronto Center for Biomaterials, for his technical expertise in sening up the equipment and cornputer programrning.

Prof. A. Csima, University of Toronto Department of Statistics, for her provision of the statistical analyses used for this study.

Ms. R. Bauer, University of Toronto Faculty of Dentistry Graphic Services, for providing digital photographs of the fiction testing equipment.

Mr. R. Chernecky, University of Toronto Center for Biomaterids, for providing scanning elecîron microscopy images.

and most importantly my fmily,

Nathan, my son, Rachael, my daughter, and Kelly, my wife, whose love and devotion has meant everything to me.

LIST OF TABLES

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 13.

Table 14.

Table 15.

Table 16.

Variables affecting fiictional resistance in orthodontie sliding mechanics.

Combinations of brackethchwire couples sarnpled for fiictional force.

Mean fiictional force and standard deviation of the trials according to static canine retraction model and archwire type.

Mean frictionai force and standard deviation of the trials according to retraction model.

Mean fiictional force and standard deviation of the trials according to sliding velocity.

Mean fictional force and standard deviation of the trials according to pre- drawing of the archwire.

Mean fiictional force and standard deviation of the trials according to saliva.

Mean nictional force and standard deviation of the trials with Speed bracket according to archwire type.

Mean fnctional force and standard deviation of the trials for each bracket according to archwire combination.

Mean nictional force and standard deviation of the triais according to bracket type.

Mean frictional force and standard deviation of the trials according to archwire type.

Mean fnctional force and standard deviation of the trials according to archwire type for round wires.

Mean fnctional force and standard deviation of the trials according to archwire shape.

Mean fiictional force and standard deviation of the trials according to archwire size.

Rank order of fiction for each factor as determinecl by Duncan's multiple range test.

Significant interactions of pair-wise factors for level of friction as determined bv Least Sauares Mean Tables.

Table 17. Rank order of most efficient bracketlarchwire couples according to bracket type as determined by Least Squared Means table.

Table 18. Material properties of orthodontic archwires evaluated.

Table 19. Material properties of orthodontic brackets evaluated.

Table 20. Frictional force for each trial according to static retraction model and archwire type

Table 21. Frictional force for each trial according to retraction model.

Table 22. Frictional force for each trial according to sliding velocity.

Table 23. Frictional force for each triai according to pre-drawing of the archwire.

Table 24. Frictional force for each triai according to saliva.

Table 25. Frictional force for each triai with Speed bracket according to archwire type.

Table 26. Fnctional force for each trial according to archwire combination for metal brackets.

Table 27. Frictional force for each trial according to archwire combination for ceramic brackets.

Table 28. Frictional force for each trial according to archwire combination for ceramic brackets with metal slots.

Table 29. Fnctional force for each trial according to archwire combination for self- ligating brackets with active ligation.

Table 30. Fnctional force for each trial according to archwire combination for self- ligating brackets with passive ligation.

Table 31. Frictional force for each trial according to archwire combination for self- ligating brackets with variable ligation.

LIST OF FIGURES

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure f O.

Figure 1 1.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Frictional resistance as a function of non-tipped static bracket angulation (O0)-

Frictional resistance as a function of tipped static bracket angulation (IO0).

Frictional resistance as a fwiction of dynarnic and progressive bracket tipping (O0 up to IO0).

Mean fnctional force of the trials according to static canine retraction model and archwire type.

Frictional resistance for a trial illustrating static non-binding canine retraction model (O0 tip).

Frictional resistance for a trial illustrating static binding canine retraction model (6O tip).

Tip/counter-tip cycle for the dynamic canine retraction model illustrating angular displacement as a fùnction of distance.

Frictional resistance of a trial illustrating dynarnic tipping/uprighting canine retraction model (O0 to 6" tip to O0 counter tip).

Mean fnctional force of the trials according to retraction model.

Mean fictional force of the trials according to sliding velocity.

Mean fiictional force of the trials according to pre-drawing of the archwire.

Mean fnctional force of the trials according to saliva.

Mean fictional force of the trials with Speed bracket according to archwire type.

Mean fnctional force for each bracketkchwire combination.

Mean frictional force according to bracket type.

Mean frictional force according to archwire type.

Mean frictional force according to archwire type for round wires.

Mean fictional force according to archwire size.

Mean Çictional force according to archwire shape.

Fipre 20. Components of fiction prior to bracket tipping and afier bracket tipping.

Figure 21. Sequence of canine movement during retraction with sliding mechanics illustrating tip-counter tip cycle.

Figure 22. Superimposition of a trial for each retraction model illustrating fictional resistance as a fûnction of archwire retraction with static or dynarnic bracket tipping.

Figure 23. Frictional resistance as a function of distance for a trial with dynarnic canine retraction model showing concurrent angular displacement as a function of distance.

Figure 24. Frictional resistance from a trial illustrating lowest and highest sliding veloci ty .

Fipre 25. Frictional resistance from trials using a twistedhraided archwire with and without saiiva.

Figure 26. Frictional resistance from trials with twistedhraided archwires.

vii

Illustration 1.

Iilustration 2.

Iilustration 3.

Illustration 4.

Iilustration S.

Illustration 6.

IUustration 7.

Illustration 8.

Iilustration 9.

Friction testing apparatus.

Standardization of bracket bonding to mounting fixture with alignment jig.

Standardized interfacing of bracket mounting fixture to Senomotor within the testing apparatus.

Relationship of Senomotor to Instron Load Cell.

Configuration of LabView for experimental parameter control and data collection.

Orthodontie brackets used in this study.

SEM of Transcend ceramic bracket at 60X and IOOOXmagnification.

SEM of Clarity ceramic bracket with metal dot at 60X and lOOOX magnification.

SEM of Victory metal bracket at 60X and 1000X magnification.

Retraction of canine teeth by sliding mechanics utilizes application of orthodontic

force to guide bracketed teeth along the archwire. This method of canine distalization is

observed to occur through a series of tipping and uprighting movements that

approximates translation of the tooth. Friction occurs at the bracket-archwire interface.

In addition, binding of the bracket on the guiding archwire as the tooth moves will also

occur. The bracket binding that occurs is required in order to create uprighting forces

necessary to ensure tooth translation with sliding mechanics. Therefore, fiictional

resistance is encountered with canine distalization whenever sliding mechanics are

employed. This resistance to sliding is the combination of friction between the bracket

and archwire and binding between the bracket and archwire.

The phenornenon of fiction is multifactorial. The orthodontic literature

demonstrates numerous variables that affect the levels of fiction between the bracket and

archwire. Resistance during tooth movement may be due to physical or biological

parameters. Physical parameters include bracket material and design, bracket width and

slot size, interbracket width, archwire type, archwire size and shape, ligation technique,

second order angulation, and sliding velocity. Biological considerations are saliva,

plaque, and corrosion. In addition, experimental protocol and design ofien affect the

outcome of in-vitro fiictional studies.

However, in-vitro studies of fiictional resistance utilizing static straight-line

traction applied to the bracket-wire interface does not simulate the complexity of tooth

movements of varied wmbinations of tipping and uprighting with canine distalization

utilizing siiding mechanics. Caution should be exercised in interpreting the results of in-

vitro fnctional resistance studies since experimental conditions do not accurately

represent the clinical situation. There fore, anal ysis of the parameters affecting the

fnctional resistance becomes more clinically meaningful when canine distalization via

sliding mechanics is simulated experimentally.

Using an experimental canine retraction mode1 capable of tipping and uprighting,

quantifiable analysis of the fnctional resistance for various brackets and archwires with

varying parameters can be achieved that will be clinically meaningful.

During canine distalization with sliding mechanics, a significant amount of the

applied force may be lost to fiictional resistance during sliding mechanics. Minirnization

of fiictional resistance during canine retraction allows most of the applied force to be

transfmed to the teeth while optimizing orthodontic tooth movement and decreasing

undesirable anchorage loss. Therefore, to achieve clinical success with maximal

efficiency for canine distalization with sliding mechanics, analysis of the fiictional

resistance of brackets and archwires using simulated canine retraction is of paramount

importance for optimization of panuneters.

REVIEW OF THE LITERATURE

Friction in Orthoctontics

Friction, a clinical challenge particularly with sliding mechanics, must be dealt

with efficiently to provide optimal orthodontie results.

Friction is a force that retards or resists the relative motion of two objects in

contact. The direction of fiction is tangential to the common boundary of the two

surfaces in contact (Drescher et al, 1989). As two surfaces in contact slide against each

other, two components of total force arise: the fictional component (F) is parallel but in

opposition to the sliding motion, and the normal force (N) perpendicular to the contacting

surfaces and to the fictional force conïponent (Dickson et ai, 1 994). Fnctional force is

directly proportional to the normal force, such that F= pN, where p=coefficient of fiction

(Kapila et al, 1990). The static tnctional force is the smallest force needed to start the

motion of solid surfaces that were previously at rest with each other, whereas the kinetic

fiictional force is the force that resists the sliding motion of one solid object over another

at a constant speed (Omana et al, 1992). The coefficient of fiction has a value that falls

between zero and one. Its magnitude is dependent mainly on the nature of the matdais

in contact (Gamow, 1976).

The classical laws of fiction state that the following: (1) frictional force is

proportional to the normal force acting perpendicular to the area of contact, (11) fiction is

independent of contact area, and (UI) friction is independent of the sliding velocity

(Jastrzebski, 1976). Of the classical laws of friction, the first and second laws are obeyed

in orthodontics (Kusy and Whitley, 1997). However, the third law is not always obeyed

in orthodontics (Kusy and Whitley, 1989).

Friction in orthodontics is most commoniy encountered as teeth are moved via a

traction force along an archwire, commonly referred to as sliding mechanics (Farrant,

1976). Sliding mechanics use a continuous or segmenta1 wire to guide the orthodontic

bracket in response to a motive force. Consequently, relative motion occurs between the

bracket and the archwire. However, opposition to tooth movement results fiom attendant

fiiction resistance occurring at the bracket-archwire interface.

Upon initiation of orthodontic tooth rnovement, the static fiction between the

bracket-archwire interfaces must be overcome. As the tooth moves in the direction of the

applied force kinetic friction occurs between the bracket and archwire (Bednar et al,

1991). With orthodontic tooth movement, movement of the crown precedes displacernent

of the root because a tipping moment is placed on the crown of the tooth. The moment

that led to the tipping is determined by the combination of the location of the force

application relative to the center of resistance and the amount of resistance to tooth

movement (Yamaguchi et al, 1996). This tipping leads to increased fiction from binding

between the archwire and bracket restricting movement of the entire tooth. Engagement

of the archwire with the bracket creates a counter-moment that will bnng the root of the

tooth in the direction the crown has moved (Drescher et al, 1989). The coupled sequence

of successive crown tipping then root uprighting will continue along the same plane of

space as the direction of the applied motive force. This allows approximation of

translation of the tooth during sliding mechanics.

Orthodontic tooth movement is dependent upon the ability of the clinician to use

controlled mechanical forces to stimulate biologic responses within the periodontium

(DeFranco et al, 1995). Investigators have indicated that applying the proper magnitude

of force dunng orthodontic treatment will result in optimal tissue response and rapid

tooth movement (Schwartz, 1932; Storey and Smith, 1952). In a critical review of some

of the hypotheses relating orthodontic force and tooth movement, Quim and Yoshikawa

(1 985) concluded that the rate of tooth movement increases proportionally with increases

in applied force up to a point, after which additional force produces no appreciable

increase in tooth movement.

With orthodontic mechanotherapy, a biologic tissue response with resultant tooth

movement will occur only when the applied forces adequately overcome the fiction at

the bracket-wire interface (Kapila et al, 1990). This means that the mechanotherapy to

move a tooth via a bracket relative to a wire results in fiiction localized at the bracket-

wire interface that may prevent the attainment of an optimal force in the supporting

tissues. Therefore, orthodontists need to have a quantitative assessrnent of the fnctional

forces encountered to achieve precise force levels to overcome fiction and to obtain an

optimal biologic response for efficient tooth movement (Angolkar et al, 1990; Ogata et

al, 1996).

Problems of loss of applied force due to friction dunng sliding mechanics have

been recognized for some time (Stoner, 1960; Paulson, 1969). The portion of the applied

force lost due to the resistance to sliding can range from 12% to 60% (Kusy and Whitley,

1997). If Wctional forces are hi&, the efficiency of the system is affect4 and the

treatment time may be extended or the outcome compromised because of little or no tooth

movement andior loss of anchorage (Drescher et al, 1989; Kapila et al, 1990; Downing et

al, 1994; Edwards et al, 1995). In addition, the arnount of fictional resistance will

impact on the moment to force ratios of the teeth and consequently their centers of

rotation (Braun, 1999).

Nikolai (1985) stated that to allow optimal tooth movement the static and kinetic

frictional forces should be minimized. However, Kamelchuk (1 998) felt that optimal in-

vivo tooth movement is not necessarily predicated on minimization of fnction at the

bracket-wire interface. More importantly, to prevent undesired tooth movement and to

ensure optimal tooth movement fiction must be understood and controlled. Since

friction is not likely to be eliminated from materials, the best remedy is to control friction

by achieving two clinical objectives: maximizing both the efficiency and the

reproducibility of the orthodontic appliances (Kusy and Whitley, 1997). Efficiency refers

to the fiaction of force delivered with respect to the force applied, while reproducibility

refm to the ability of the clinician to activate the orthodontic appliance so that it behaves

in a predictable manner (Kusy and Whitley, 1997). Therefore, the clinician should be

aware of the characteristics of the orthodontic appliance that contribute to friction during

sliding mechanics and îhe extent of the amount of force expected lost to friction (Frank

and Nikolai, 1980). This will help allow efficient reproducible results to be achieved.

Contemporary studies of ûiction in orhodontics have set forth to characterize the

magnitude and the nature of the resistance to sliding encountered between brackets and

archwires. What is actually being measured by these studies may be a combination of

tnie fiictional resistance and binding at the archwire interface (Dickson et al, 1994).

When the archwire and the bracket have clearance classical fiction exists as the only

component to the resistance to sliding (Articolo and Kusy, 1999). When clearance

disappears and an interference fit occurs between the bracket and the archwires, binding

mises as a second component to the resistance to sfiding superimposed on the classical

fiction (Artimlo and Kusy, 1999).

The nature of fiction in orthodonties is multifactorial, being derived fiom both a

multitude of mechanical or biological factors (Nanda, 1997). Numerous variables have

been assesseci using a variety of mode1 systems with nearly equally varying results. The

following table sumrnarizes these variables (modified fiom Nanda, 1997).

Table 1. Variables affecting fictional resistance in orthodontie sliding mechanics.

A. PHYSICAL B. BIOLOGICAL 1. Arcfiwire 1. Saliva

a. material 2. Plaque b. cross-sectional shape/size 3. Acquired pellicle c. surface texture 4. Corrosion d. stifiess

2. Ligation of Bracket to archwire a. ligature wires b. eiastomerics c. method of ligation

3. Bracket a. material b. manufacturing process c. slot width and depth d. bracket design e. first-order bend f. second-order bend g. third-order bend

4. Orhodontic appliance a. interbracket distance b. level of bracket dots between teeth c. forces applied for retraction

Classically, the gold standard for sliding mechanics had been established as

couples between stainless steel archwires and brackets (Kusy, 2000). But more recent

manufacturing techniques of orthodontic materials has led to lower fnctional resistance

than the same products tested in the past (Articolo and Kusy, 1999). This combined with

new and innovative orthodontic materials being used has led sorne investigators to

challenge this concept.

Certainly, with so many variables affecting the fnctional resistance in orthodontic

sliding mechanics, it is difficult to accurately determine them in a clinical situation

(Nanda, 1995). This is M e r complicated by the fact that there are such a variety of

orthodontic appliances, as well as a vast variability in the biological parameters of

patients. It h a been suggested that clinically these forces due to fiictional resistance may

be overestimated and are less than what is measured in steady state laboratory

experiments (Ho and West, 199 1 ; Braun et al, 1999). However, a critical review of the

pertinent literature will serve to elucidate the general trends of fnctional resistance

encountered in orthodontics and what it means clinically.

Summary

1 .) Friction in orthodonties occurs with sliding mechanics.

2.) The fictional resistance may be a combination of classical fiiction beiween the archwire-bracket interface and binding of the archwire and bracket.

3 .) Friction can compromise orthodontic treatment outcomes.

4.) The nature of friction in orthodontics is multîjàctorial, being derived f iom mechanical and biological factors.

Effect of Bracket Material

The material used for orthodontic brackets c m have a profound effect on its

resistance to sliding. Orthodontists could classically choose fiom stainless steel, ceramic

and plastic brackets. Variables such as the exact composition, as well as the

manufacturing and finishing process of the brackets can Vary even amongst one material

type, while results of the technical performance with regard to fnction can vary

significantly. For reasons of aesthetics andhr biocompatibility issues, more recently

newer matenals have been investigated as alternatives to improve fnction performance.

First of all, stainless steel brackets have been shown by numerous investigators to

have lower frictional forces than ceramic brackets (Popli et al, 1989; Pratten et al, 1990;

Angolkar et al, 1990; Keith, 1990; Bednar et al, 199 1 ; Tanne et al, 199 1 ; DeFranco et al,

1995; Loftus et al, 1999). The suggestion is that metd brackets have smoother surfaces

cornpareci to ceramic brackets (Kusy and Whitley, 1990).

Articolo et al (1999) only found stainless steel brackets to have less fiction than

their ceramic counterparts in the passive configuration, which agrees with the group's

previous work (Kusy and Whitley 1990). However, in the active configuration, when

resistance to sliding is the product of fiction and binding, stainless steel brackets were

less efficient than ceramic brackets.

Ogata et al (1996) found that stainless steel brackets manufactured by sintering

had less fnctional resistance than cast brackets. Vaughn et al (1995) also noted

differences in friction of brackets based on their manufacturing process, finding friction

to be reduced 40 to 45% for sintered brackets over cast brackets. Scanning electron

microscopy (SEM) revealed sintered brackets to have smoother bracket slot surfaces.

The sintering process allowed compression of stainless steel particles into a smooth

c o n t o d shape, as opposed to the casting process that requires milling which creates

sharp angular brackets.

Ceramic brackets have corne into more cornmon use because of their irnproved

esthetics, but many problems are associated with their clinical use (Kusy et al, 1991;

Ghafari, 1992). In particular, ceramic brackets have higher coefficients of fiction (Kusy

and Whitley, 1990; Kusy et al, 199 1) and greater fictional resistances (Pratten et al,

1990; Angolkar et al, 1990; Bednar et al, 199 1 ; Xreland et al, 199 1 ; Keith et a/, 1993;

Tselepis et al, 1 994; Shivapuja and Berger, 1994; Loftus et al, 1 999). Under scanning

electron microscopy, ceramic brackets display a crystalline structure containing many

pores white staidess steel brackets slots are smoother with fewer irregularities (Pratten et

al, 1990; Tanne et al, 199 1 ; Downing et al, 1994). This rougher surface finish of the

ceramic bracket slots has been implicated as the reason for the higher frictional force

(Angolkar et al, 1 990; Pratten et al, 1990; Tanne et al, 199 1 ). Keith et al ( 1 993) using a

full dimension wire with straight-line traction, observed cerarnic brackets to cause

abrasive Wear of the archwire. Kusy and Whitley ( 199 1) suggested that the behaviour of

ceramic brackets might be because of their intrinsic chemical stmcture rather than the

roughness.

A study by Tanne et al (1994) found the fictional resistance was significantly

Iowa for cerarnic brackets that had a mechanically polished slot surface. Rose and

Zernik (1996) also reporteci that rounded slot corners of the brackets generated less

frictional resistance of up to 38 percent less compareâ to control brackets. Ceramic

brackets without rounded slot corners showed a build-up of wire debris along the slot

corners, as seen by SEM (Rose and Zernik, 1996), which was similarly reported by Keith

et al (1 993).

Downing et al (1994) found bracket material had little effect on fictional forces

when comparing stainless steel and ceramic brackets. Similarly, Kusy and Whitley

(1990) found no significant differences between cerarnic and steel brackets. Using a

buccal segment mode1 with three brackets aligned in a row, Ireland et 01 (1991) also

found no differences between brackets. But this study also reported single cerarnic

brackets had less fiiction than stainless steel. The author suggested that friction is

additive for ceramic brackets but not with steel brackets (Ireland et al, 199 1).

Of the ceramic brackets, DeFranco et al (1995) found single crystal alumina

brackets tended to be lower in friction than polycrystalline brackets. Saunders and Kusy

(1 994) showed by scanning electron microscopy that monocrystalline alumina brackets to

be smoother than polycrystalline brackets, but fond no difference in frictional

characteristics. On the other hand, Omana et al (1992) stated that the polycrystalline

injection molded ceramic brackets were smoother and this created less friction than other

ceramic brackets.

To improve the sliding perfomance of ceramic brackets, metal inserts have been

placed in the slots to reduce friction. Loftus et al (1999) found that Clarity ceramic

brackets with a metal slot insert (Unitek Corp., Monrovia, CA) fard as well as

conventional stainless steel brackets in fiction tests.

Researchers have suggested that poycrystalline zirconia brackets, a substitute for

alumina brackets, would have low fiction in clinical use (Springate and Winchester,

199 1). SEM examination revealed zirconia brackets had much smoother surfaces than

alumina, yet failed to dernonstrate lower fictional resistance than the alumina brackets

(Keith et al, 1994). in contrast, Tanne et al (1994) found reduced fiction for a newer

zirconia bracket comparecl to other ceramic brackets. It was speculated that this was the

result of a smoother bracket slot surface as shown by SEM. Moreover, minimal fiction

effects would be noted since the investigators did not ligate or apply a normal force to

direct the wire into the bracket slot.

Plastic brackets have shown higher fictional resistances than stainless steel

brackets (Riley et al, 1 979; Tselepis et al, 1 994). Riley et al ( 1 979) suggested this

resulted fkom deformation of the plastic brackets due to tightening of the steel ligatures

that lead to compression of the slot and binding of the wire. Recently introduced

composite brackets with and without metal dots faired better in fiction studies.

Bazakidou et al (1997) found these newer composite brackets to have lower fictional

resistance than both ceramic and stainless steel brackets.

Titanium brackets were evaluated by Kusy et al (1998) and found to have

coefficients of fiction similar to stainless steel brackets in the passive configuration. The

titaniurn brackets had a much rougher surfâce texture than that of the stainless steel

brackets as revealed by SEM, and would be expected to have greater coefficients of

fiction than stainless steel brackets. But the titanium brackets slide on a passivateci layer

of carbon, oxygen, titanium, and nitrogen, similar to stainless steel brackets sliding on a

passivated layer of chromium and oxygen (Kusy et al, 1998). Therefore, the surface

chemistry may be the reason for the reduced frictional resistance.

Attempts have been made to alter or modify the surface properties of orthodontic

materials because the interaction of the surface chemistry of the bracket slot with the

archwire may affect the fiction (Kusy et al. 1991). Coefficients of fnction for

polycrystalline alumina flats were found to be reduced by ion-implantation with titanium

(Kusy et al, 1992). This was thought to result €rom hardening of the ion implanted

surface layer preventing the plowing tendency of the rough alumina surface. Mendes

(1995) also observed that titanium ion implantation of brackets reduced the tiictional

resistance.

Additionally, with regards to repeated in-vitro friction testing of the sarne

orthodontic bracket a distinct trend for an increase in the mean fiictional force was found

regardless of material type.

1 .) Orthodontie bracket material can have a pro found effect on its resistance to sliding.

2.) Stainless steel brackets tend to have the least fiictional resistance.

3.) Ceramic brackets have greater fiictional resistance owing to increased surfae roughness.

4.) Manufacturing and jinishing of brackets can affect the friction. For example. brackets that are machine injection molded or mechanically polished to give smooth rounded surfaces display less fi-ictional resistance.

5.) Mod~jication of the swface properties of orthodontic &racket materials by ion implantation hus decreased the frictional resistance.

Effect Of Bracket Design And Slot Size

The basic premise behind the design of orthodontie brackets is that a slot allows

ligation of a wire to control movernent of a tooth in some desired direction. However, no

standard design exists, but some designs have been advocated to assist in reduction of

fiction.

Ogata et al (1996) found that bracket designs, which restricted the amount of

force placed on the wire by the ligature, generated lower fiïctional forces. An example is

the Synergy bracket (RMO, Denver, CO) that has six tie-wings for variable ligation.

Ligation of oniy the center wings limits the force of the ligature on the wire. Therefore,

the normal force can be markedly reduced. in another example, Kuroe et al (1994)

claimed that the design of Friction Free brackets (American Orthodonties, Sheboygan,

WI) prevented ligature wires or elastomers fiom exerting their force on the archwire, and

hence there is virtually no vertical load of the archwire on the bracket. These Friction

Free brackets were found to have considerably less fnctional resistance during straight-

line traction than conventional edgewise stainless steel brackets (Kuroe et al, 199 1).

Thomas et al (1998) and Kapur et al (1998) found that self-ligating brackets

produced less fiction than elastomerically-tied conventional edgewise brackets. These

self-ligating brackets tested did not exert pressure on the archwires. Sims et al (1993)

also found self-ligating brackets had less frictional resistance than conventionally tied

brackets. In addition, Sims et al (1993) noted that self-ligating brackets without an active

springclip had about fifieen times less fnctional resistance than self-ligating brackets with

an active springclip. Using a buccal segment model, Taylor and Ison(1994) reported

similar findings with passive self-ligating brackets. The brackets had significantly less

fictional resistance than self-ligating brackets with an active spnng-clip and

conventionally tied brackets. Al1 of these investigations were done with static siraight-

line traction that was not subjected to change in second order angulation.

Sims et a1 (1 994) later reported that increasing angulation had a more profound

effect on self-ligating brackets than conventional brackets, but they still produced less

fnction. Pizzoni er al (1998) reportai similar results. Pizzoni et al (1998) found self-

ligating brackets to have less fnction at al1 angulations than conventional brackets. Also

noted was that self-ligating brackets that closed by capping of the wire slot exhibited

significantly Iowa Wction than those closed by a spnng. Read-Ward et al (1997)

investigated various self-ligating brackets compared to conventional brackets. Results

suggested self-ligating brackets had lower fiictional resistance in the passive

configuration, but fnctional resistance increased for the self-ligating brackets as second

order angulation increased such that they were comparable to conventional brackets.

Shivapuj a and Berger ( 1 994) found sel f-ligating brackets with both active and passive

springclips displayed significantly lower level of fiction than conventional stainless steel

and cerarnic brackets. In contrast, Bednar et al ( 1991) testing self-ligating brackets with

an active spnngclip and Loftus et al (1 999) testing self-ligating brackets with a passive

spnngclip found these brackets types performed no better than conventional stainless

steel brackets ligated by either elastomers or steel ties in fiction tests using an

approximated center of resistance that permitteci free second order tipping.

As for the effect of slot size, most investigators have found slot size to have no

influence on fictional resistance (Kusy and Whitley, 1 989; Tidy, 1 99 1 ). However,

studies by Andreasm and Quevedo (1970) and Rock and Wilson (1989) suggested that

frictional resistance decreased as slot size jurnped fiom 0.018 inch to 0.022 inch due to

reduced binding probably from increased wire stifiess. Based on a mathematical model,

Kusy and Whitley (1 999) suggested that smaller brackets dots compared to larger bracket

dots may cause more binding to occur if the initial alignrnent and leveling are not precise

enough. But there is no conclusive evidence that slot size significantly affects frictional

resistance to sliding at the archwire-bracket interface. More importantly, the size of the

archwire relative to the slot size wiH have a greater impact on fkictional resistance. So as

the wire size increases, the wire occupies more of the slot leading to greater fiction. But

there is a trade off. Maximally filling the slot leads to greater control of the tootb at the

expense of severe binding, whereas minimally filling the dot leads to poor control with

relatively little binding (Kusy, 2000).

1 .) Bracket design that restricts the arnount of force placed on the archwire by the ligature tends to generate lowerfi-ictional forces.

S.) Self-ligating brackets can have less fiiction compared to conventional brackets, particularly with brackets that do not actively engage the archwire,

3 .) Slot size does not tend to have a signijcant effect on fiction, but more importantly the relative size of the archwire within the bracket slot will have a significant influence.

Effect Of Bracket Width and lnterôracket Width

There are conflicting results as to the effect of bracket width on frictional

resistance. Part of the discrepancy is derived from differences in experïmental protocol.

Studies that do not p d t changes in the second order angulation of the bracket relative

to the arch wire typically demonstrate that bracket width and interbracket distance have

an insignifiant effect on fictional resistance compared to variables such as ligation force

and archwire or bracket surface characteristics (Andreasen and Quevedo, 1970; Petersen

et al, 1982). Studies that allow for changes in second order angulation produce binding at

the archwire-bracket interface contributing to the fictional resistance that is summarily

affected by bracket width, interbracket width, and flexural stifiess of the archwire

(Schlegel, 1 996).

Arguments have been made that implicate wider brackets as the cause of greater

fnction at small non-binding angulations. Two main reasons have been set forth to

explain this. Kapila et al (1 990) attributed the increase in fiction with wider brackets to

larger normal forces created by greater stretching of the ligature over the wider brackets.

Frank and Nikolai (1980) felt the reason for more fnction with the wider brackets was

derived fiom a larger contact surface area of the wire with the wider bracket.

Second order binding angulations that restrict the amount of tipping have shown

that narrower brackets produce less fnction than wider brackets (Frank and Nikolai,

1980). This was ascribed to the narrower brackets having less binding than the wider

brackets (Frank and Nikolai, 1980). Similarly, Yamaguchi et al (1996) found that if the

location of force application for retraction was closer to the center of resistance which

controlled the amount of tipping the angulation of the archwire to the bracket would be

less with a nmow bracket compared to a wider bracket, and hence resulted in a lower

retraction force, meaning there was less fiiction.

When second order angulation is not restricted the bracket width has a different

effect on fnction results. Under these conditions, wider brackets have been reported to

produce less fiction than narrow brackets by allowing l e s angulation change of the

archwire, and hence less binding (Drescher et al, 1 989; Tidy, 1989; Omano et al, 1992;

Sims et al, 1994). It was reported that greater tipping occurs with namower brackets

(Drescher et ai, 1989), thus leading to a more acute angle of interface between the bracket

and the archwire (Ornano et ai, 1992). Yamaguchi et al (1996) also found that when a

retracting force was applied at the level of the bracket unrestricted tipping occurred

causing a greater angulation between the bracket and the archwire for narrower brackets

than wider brackets. This led to a significantly higher force of retraction for the narrower

bracket than the wider bracket because of the increased attendant fiiction.

However, the width of the bracket alone cannot simply account for the level of

fiction encountered because a complex relationship exists between the bracket width,

interbracket distance, and wire stiffness, with these variables having a signifiant effect

on fictional forces (Schlegel, 1996). First of all, an inverse relationship exists between

bracket width and interbracket width. So as bracket width decreases, interbracket

distance incrase. The increased interbracket distance increases wire flexibility and

thereby decreases the resultant frictional force fkom second-order binding. With this in

mind, Moore and Waters (1993) dernonstrated that the restoring couple of a bracket

varies with the bracket width and the interbracket distance, leading to the conclusion that

wider brackets have inherently less Wction based on a simple bearn theoy. Most likely

then, if the retraction forces are not too high (undefined), then wider brackets may offer

less fiction owing to less tipping and hence less binding of the bracket with the archwire

(Moore and Waters, 1993). Omano et al (1992) stated that higher retraction forces may

negate the mechanical advantage of the wider brackets and lead to more friction.

However, Schegel (1996) felt that the analysis by Moore and Waters was not valid

because it considereci only one bracket and did not take into consideration tbat the ends of

the beams would be rigidly fixed. Schlegel's (1996) biomechanical analysis

demonstrated an ideal relationship exists between slot length, interbracket distance, and

position of the active bracket so that friction effects would be minimized. The analysis

concluded that daims advocating the use of the widest bracket or the narrowest bracket

were false. This intuitively suggests that an "average" widîh bracket would be more

optimal, although Schlegel(1996) did not state a size.

1 .) Wider brackets have been attributed to produce greaterfiction than narrow brackets because ofgreater force of ligatiun. peuter contact area. and increased binding with the archwire occurs.

2.) Wider brackets have been attributed to produce less _friction than narrow brackets because less tipping results and hence less binding with the archwire will occur.

3.) The amounf of force applied and the level of force application can affect the arnount of bracket tipping and thereby affect the amount affliction.

4.) Increased in ferbracket distance increases wire flexibili~ and decreases the resultant fiictional force fiom second-order binding.

5.) A complex relationship exisfs between bracket width. interbracket distance. and wire stimess, with these variables having a significant effect on fiictional forces. This needs to be investigatedf;rther to morefirli'y understand the relationship.

Studies of in-vitro sliding mechanics have demonstrated that archwire material

greatly affects the fictional resistance. However, static straight-line traction designs at

non-binding angulations relative to a sliding interface demonstrates different orders of

fkictional resistance for archwire material compared to increased second-order

angulations.

First of all, straight-line traction of the archwire relative to the bracket or bracket

relative to the archwire with approximated zero tip and torque does not p m i t tipping of

the bracket relative to the archwire indicating that no binding interaction at the edges of

the bracket-archwire interface will occur. This non-binding sliding has demonstrated that

fictional resistance generally increases respectively with archwire selections of stainless

steel, cobalt-chromium, nickel-titanium, and beta-titanium (Angolkar et al, 1990; Kusy et

al, 199 1). Additional studies by Garner et al (1 986), Drescher et al (1 989), Kapila et a l

(1 990), Prosoki et a l (1 99 l), Downing et al (1 994), Ho and West (1 999 , and Vaughn et

a l (1 995) have also supportecl this. hterestingly, archwire alloys of stainless steel, cobalt-

chromium, nickel-titanium, and beta-titanium have increasing surface roughness

characteristics, which is believed to create higher fiictional resistance (Gamer et al,

1986). However, Prosoki et al (1991) detennined there was no correlation between

surface roughness and fnctiond resistance. Additionally, Kusy and Whitley (1990) felt

that surface roughness did not necessarily correlate with the coefficient of fiction. What

was suggested was that other variables, most significantly surface chemistry and chemical

affinity played the most significant role in overall fiictional resistance (Kusy and Whitley,

1990). For example, Kusy and Whitley (1990) found that beta-titanium wires were

smoother than nickel-titanium wires but had a higher coefficient of fiction. The greater

friction was attributed to a "cold-welding" phenornenon of the beta-titanium wire with the

stainless steel brackets leading to a repeated "stick-slip" movement of the bracket relative

to the archwire (Kusy and Whitley, 1990). Ho and West (1 995) suggested that archwire

stifniess might be more of a controlling factor for fictional resistance than the surface

roughness of the archwire. Articolo and Kusy (1999) concluded that in the passive

configuration, the sliding efficiency of archwires appeared to be greater in

bracketkchwire couples made of a hard archwire in a relatively sofier bracket. For

exarnple, the least fnction occurred with stainless steel archwires, which is stiffer and

harder than the other archwires, and stainless steel brackets, which are the softest of the

brackets.

When archwires are subjected to second order bracket tipping, the level of friction

increased. However, the different archwires experienced varying degrees of increases in

friction. Studies have shown that the rank order of fiction for stainless steel wires and

nickel-titanium wires changes order when fiction is studied at some predetermind

second order angulation (Frank and Nikolai, 1980; Kemp, 1992; Weiss, 1993; Kusy and

Whitley, 1999). This means that at non-binding angulations stainless steel had less

fnction than nickel-titanium wires, but at binding angulations stainless steel had more

friction than nickel-titaniurn wires. It has been suggested that this change in rank ordinals

of the archwires is due to nickel-titanium's lower modulus of elasticity. Rose and Zemik

(1996) also attributed the greater flexibility of nickel-titanium as the main reason for the

lower fkictional resistance as the archwire was drawn through brackets offset via second

order displacement. Similarly, Dickson et a1 (1994) found that more flexible wires, such

as coaxial or fibre-optic g l a s archwires, had significantly lower friction levels than less

flexible wires when subjected to second order angulation. Articolo and Kusy (1 999) has

also reported that in the active configuration, the sliding efficiency of archwires appeared

to be greater in more flexible wires.

Studies that have allowed unrestricted tipping of the bracket relative to the

archwire have not dernonstrated that wires of lower modulus of elasticity have less

fiction. Tidy (1989) used a mode1 that allowed fiee bracket tipping through an

approximated center of resistance by a loaded power arm. Testing showed stainless steel

archwires to have the lowest Wction, nickel-titanium approximately twice as much, and

beta-titanium five times as much. Omana et al (1 992) reported no difference between the

frictional force values of stainless steel and nickel-titanium archwires when brackets are

permitted second order angulation by tipping around a simulated center of resistance.

Loftus et al (1 999) reported that beta-titanium produced the highest frictional resistance,

followed by stainless steel then nickel-titanium. The sentiment that beta-titanium had

significantly more resistance to sliding that stainless was echoed by O'Reilly et al (1999).

While beta-titanium has 42 percent the stiffhess of stainless steel wire, O'Reilly et al

(1 999) felt that other contributions kom the surface roughness, coefficient of friction, and

dissimilar alloys may define the resistance to sliding. O'Reilly et al (1999) also reported

that bracket displacernent to simulate intraoral forces such as mastication reduced the

fiction by only 27 percent for beta-titanium compared to 80 percent for stainless steel

wire of the sarne size.

Coatings have been applied to archwire surface to improve the esthetics andor

performance. But ofien the coating is stripped fiom the wire leading to greater binding

and hence more fiction. Dickson et al (1 994) and Mendes (1995) have both reportecl this

to occur. Zufall et al (1998) investigated the fictional properties of an esthetic fiber-

reinforced polymer composite wire but found that the reinforcement fibers were

abrasively wom tiom the wire surfaces. The release of these glass fibers would be

considered unacceptable within the oral cavity. Subsequent polymeric coating of the wire

still showed coating damage, particularly at higher binding angulations, but it protected

the reinforcernent fibers within the composite materials from darnage (Zufall and Kusy,

2000). However, the kinetic coefficient of friction was found to increase 72 percent,

making it much greater than stainless steel wires. This was unexpected by the author

since this coating was expected to have low fiction capabilities (Zufall and Kusy, 2000),

but the increased fiiction values may have been caused by the coating that was stripped

off creating more binding.

A better approach that has been utilized to alter archwire appearance and/or

material characteristics is surface treatment of the archwire by ion-implantation. Ion-

implantation is a surface modification treatment that can alter the surface properties of a

material without a significant alteration of the dimensional tolerance of the material

(Sioshansi, 1987). Ion-implantation of orthdontic archwires can alter the hardness,

fnction, Wear resistance, and surface color (Burstone and Farzin-Nia, 1995). Studies by

Kusy et al (1992), Burstone and Farzin-Nia (1995), and Mendes (1995) have al1 shown

that nitrogen ion-implantation of beta-titanium archwires significantly reduced the

fnctional resistance. The fictional forces became approximately qua1 to values of

comparably sized stainless steel wires. Additionally, Burstone and Fanin-Nia (1 995)

noted that the variance of the coefficient of fiction also decreased, meaning that the

"stick-slip" phenomenon of beta-titanium was drastically reduced. Walker (1997)

reported that nitrogen implantation into nickel-titanium and beta-titanium produced

significantly more tooth movement than their untreated counterpart, which was infmed

to mean that the ion-implantation process produces less friction during tooth movement

in-vivo .

1 .) Non-binding sliding has demonstrated that frictional resistance generallv increases respectively with archwire seleciions of stainless steel, cobalt-chrornium, nickel- titaniurn, and beta-titanium. This has been main& attributed to being a product of su$ace roughness.

2.) At binding angulations,fi.iction for nickel-titanium has been shown to be less than for stainless steel. This has been attributed to its lower modulus of efasticity.

3.) Coatings have been appled to archwire surfaces to intprove the esthetics and/or performance but have met with poor clinical performance because the coating is ofren strippedfrom the wire leading to greater binding and morejî-iction.

4.) Ion-implantation of orthodontie archwires can alter the hardness, friction. Wear resistance, and surfnce color. Specifcali), i f tas irnproved the Jiiction characteristics of beta-titanium through ion-implantation.

Effect of Archwire Site and Shape

Generally it is assumed that as archwire size increases so does the fictionai

resistance. The sarne is ûue as the geometry of the archwire enlarges from round to

square to rectangular. These sentiments are strongly supportai by numerous studies

(Andreasen and Quevedo, 1970; Riley et al, 1979; Drescher et al, 1 989; Angolkar et al,

1 990; Kapila et al, 1 990; Tanne et al, 1 99 1 ; S ims et al, 1 993; Downing et al, 1 994; Ogata

el al, 1996).

Peterson et al (1 982) and Vaughn et al (1 995) felt, however, that nickel-titanium

did not follow this rule. Both reported that an increase in the size of nickel-titanium wire

does not necessarily cause an increase in the fnctional resistance, possibly owing to the

flexibility of the nickel-titaniurn.

Tidy (1989) also found that there was no difference in friction with respect to wire

size for al1 wire types. Ireland et al (1991) came to the sarne conclusion. Moreover, these

fiction models did not permit second order angulation where binding becomes

significant. Thus, without binding only classical friction would be the main deteminant

of the fnctional resistance. This would support that friction is independent of surface

area, and therefore independent of wire size. When brackets were put out of alignment

via second order offset, Tidy (1989) found that round wires produced less fiction than

rectangula. wires when engaged into the bracket slot which was explained by the p a t e r

flexibility of the round wires.

O'Reilly's et al (1999) fiction mode1 that permitted tipping about an

approximated center of resistance showed that the resistance to sliding significantly

increased as the wire size increases. With this fiiction model, the bracket was repetitively

displaced to represent physiologic tooth movernent in-vivo. If bracket displacement was

increased, the level of fnction decreased for d l wires. In general, smaller size wires had

less reduction in fiction compareci to larger wires because the smaller wire had greater

fieedom within the bracket. This reduction ranged fiom a low of 19 percent for the

srnaller wire up to 85 percent for the larger wire, with the absolute value for the fiiction

encountered still being more for the larger wire (O'Reilly et al, 1999). Since the

resistance to sliding is a binding and releasing phenomenon, in-vivo factors such as tooth

mobility may affect the level of ûiction. However, these factors act only intermittently

and not al1 the time (Braun et al, 1999). Therefore, this reduction in fiction may not be

fully realized when put into the context of an integrated clinical model for sliding

mechanics.

Drescher et of (1989) found that rectangular wires did not have more fiction than

round wires of similar vertical dimension. It was suggested that only the difference in

vertical dimension of archwires would determine the fiictional resistance, since it is in

this plane that the bracket tips relative to the archwire.

Contrary to other researchers, Frank and Nikolai (1980) found that at binding

angulations stainless steel rectangular wires had less friction than round wires. It was

believed that as the bracket tipped and made contact with the wire greater pressure would

be placed on the point contact of the round wire compared to the line contact of the

rectangular wire. This possibly could result in indentation or notching of the stainless

steel archwire, and hence cause more resistance to sliding from this mechanical

impediment.

1 .) As archwire sire and geometry (goingfiom round to square or rectangular) increases so does the fictional resistance.

2 .) Smaller round wires have less fiiction because of their greater jlexibili~ Ho wever, greater friction due to notching of the archwire can occui- ifexcessive force is used.

Effect of Ligation Technique

Ligation of the archwire to the bracket imposes the normal force acting

perpendicularly to the sliding interface. Therefore, the significance of ligation to

fictional resistance depends on the force of ligation, ligation material, and method of

ligation.

Force of ligation can range fiom 50 to 300 grams (Nanda, 1997). Elastomeric

modules will generate approximately 225 grams of force with subsequent decay due to

elastic relaxation, while stainless steel ligation can range fiom O up to 300 gram. Self-

ligating brackets have been reported to produce the least amount of friction but vary

depending on whether the self-ligation mechanism is passive or active.

Consistent with the first law of classical fiction, the fictional resistance increases

with an increase in the normal force provideci by ligation (Frank and Nikolai, 1980). This

increase in normal force is observed to proportionately and linearly increase the fnctional

resistance encountd. However, at binding angulations, ligation force may become

secondary to other factors such as wire material, wire stiflbess, and interbracket distance.

Studies by Stannard et a1 (1986) and Keith et al (1993) that quantified ligation force also

confirmed that as the force of ligation increases the fictional resistance increases.

Bednar et al (1991) found that lightly ligated stainless steel ligatures produced

lower fiction than conventional elastomeric ligatures. Similarly, Taylor and Ison ( 1 996)

found that by pre-stretching elastomeric ligatures or loosely tying stainless steel ligatures

the fictional resistance would be reduced.

Taylor and Ison (1 996) also repoited that the fictional force declined slowly over

a three week period following initial placement of the elastic module. Aller three weeks,

the greater fnction initially encountered for rectangular wires approached the low level of

fnction for round wires. Tselepsis et al (1994) also found that afier stretching the

elastomeric modules for six days the fnctional forces were significantly Iowa compared

to new elastomeric modules. Previous studies on force degradation of elastomerics have

show force reductions of 50 percent (Rock and Wilson, 1986) to 73 percent (Wong,

1976) over a period of a week.

Riley et al (1 979) reported that stainless steel ligatures generated more fnctional

forces than elastomeric modules. Speculation was that hi& force in applying the

stainless steel ligature might have deformed the dot of the plastic brackets causing

archwire binding.

Bazakidou et al (1997), on the other hand, found no significant trend for friction

with either elastomeric or steel ligation. Yet there was up to three times greater

variability in friction with stainless steel ligation that elastomeric ligation, even though it

was attempted to standardize both methods of ligation. Even between different types of

elastomeric modules Dowling et al (1998) found significant differences with regard to

fnction.

Certainly, ligation technique can have a profound effect on the fnctional

resistance. Sims et al (1993) demonstrated that tying elastic ligatures in a figure eight

pattern around identical brackets raised the frictional resistance 70-220 percent depending

on the wire dimensions. Larger wires led to a greater increase in friction compared to

smaller wires.

The bracket itself c m alter the force imposed by the ligature. Kapila et al (1990)

felt that higher ligation forces were encountered with wider brackets resulting from the

greater stretching of elastic ligatures leading to larger nomal forces of fiction. As

previously noted, Ogata et al (1996) and Kuroe et al (1994) found that bracket designs,

such as the Synergy bracket (RMO, Denver, CO) or the Friction Free bracket (American

Orthodontics, Sheboygan, WT), that restrict the amount of force placed on the wire by the

ligature had less fiction. Self-ligating brackets have also been touted as applying less

ligation force and hence producing less fiction than conventionally ligated brackets

(Berger, 1990; Bednar et al, 1993; Sims et al, 1993; Shivapuja and Berger, 1994; and

Kapur et al, 1998). Sims et al (1993) also reported that self-ligating brackets that have a

passive spnng-clip, such as the Activa bracket ("A" Company, San Diego, USA), Iigating

the archwire produce significantly less friction than self-ligating brackets with an active

spring-clip, such as the Speed bracket (Strite Industries, Cambridge, ON).

Defianco et al (1 995) reported decreased fnctional resistance with Teflon coated

stainless steel ligatures compared to elastomeric ligatures. Question remains as to

whether the Teflon coating reduces the fnction compared to uncoated stainless steel

ligatures because no unwated stainless steel ligatures were used as controls in this study.

The difference in fnctional resistance could also be attributed to a lower force of ligation,

which was not quantified in the study.

1.) Frictional resistance increases with an increase in the normal force provided by f igation.

2.) Frictional resistance with stainless steel ligatures can be highly variable.

3.) Frictional force with elastomeric modules experiences a signijicant decline over tirne as stress relaxation occurs.

4.) Technique of applying ligatures can cause a signifcant dtfference in force of ligation and hencejî-iction.

5.) Wider brackets have higher forces of ligation owing to greater stretching of the ligature.

6.) Brackets that restrict ligation force, including self-ligating brackets. have less fi-iction.

7.) Self-ligating brackets thar have a passive springclip have less fiiction than self- ligating brackets with an active springclip thar engages the archwire.

Effect of Second Order Angulation

Second order angulation in orthodontie treatment refers to the orientation of the

tooth rotating in a mesio-distal direction. The angle between the bracket slot and the

archwire in a plane parallel to the bracket slot with the long axis of the bracket slot in a

mesio-distal direction represents the contact angle (Proffit, 1993). When this angle is

great enough to allow the archwire to engage the edges of the bracket slot leading to

binding, the critical contact angle has been met (Articolo and Kusy, 1999).

With increasing second order angulation between the bracket and the archwire,

the fictional resistance to sliding movernent increases (Kemp, 1992; Weiss, 1993; Ogata

et al, 1996; and Kusy and Whitley, 1999). This is attributable to binding rather than

classical fiction (Articolo and Kusy, 1999; Kusy and Whitley, 1999; Zufall and Kusy,

2000). Binding occm when the contact angle (Proffit, 1993) between the archwire and

the bracket exceeds some critical contact angle (Articolo and Kusy, 1999). If the second

order angulation was to increase quite drarnatically beyond the critical contact angle

sliding mechanics could corne to a halt because of mechanical notching of the archwire

fiom contact with the edge of the bracket slot in the latter stages of binding (Kusy and

Whitley, 1997, 1999). The relationship between fiictional resistance and second order

angulation may not be linear and may become more important as the angulation increases

(Kusy and Whitley, 1999).

Based on in-vitro fiction testing, Articolo and Kusy (1999) found that at 3

degrees, the resistance tu sliding dramatically increased. In addition, the active

configuration for binding occurred between 3 to 7 degrees (Articolo and Kusy, 1999).

When tipping occurs the fnctional resistance of nickel-titanium has been reported

to be less than stainless steel, when the factors such as wire stifkess and cross-sectional

size become more important (Frank and Nikolai, 1980; Peterson et al, 1982; Ho and

West, 199 1 ; Kemp, 1992; Weiss, 1993; Dickson et al, 1994; DeFranco et al, 1995;

Articolo and Kusy, 1 999).

Sims et a l (1993) also reported that by increasing both the tip and the torque

nemly linear increases in fictional resistance were produced, although increasing tip had

the more profound effect. Sims et al (1 994) and Articolo and Kusy (1999) both found

that as second order angulation increased, the reproducibility of the resistance to sliding

decreased as evidenced by an increase in the standard deviation of the force

measurements.

So as the second order angulation increases the binding component to the

resistance to sliding increases and is superimposed on the invariant classical fiiction

(Articolo and Kusy, 1999). Under this premise, Articolo and Kusy (1 999) felt that the

relative importance of binding varied rnainly with the archwire alloy as the angle between

the bracket and the archwire increased. Typically, the ernergence of binding dominance

over classical fiction occurred when the second order angle between the bracket and the

archwire was greater than 3 degrees, which had been noted to be greater than the critical

contact angle. Beyond 3 degrees the resistance to sliding quickly became dependent on

binding (Articolo and Kusy, 1 999; Kusy and Whitley, 1 999). Binding had been shown to

occur earlier and be more severe when the bracket slot was more progressively filled by

the archwire size relative to the bracket (Kusy and Whiley, 1999). For orthodontie

archwires, binding was shown io be less important with nickel-titanium compared to

stainless steel (Articolo and Kusy, 1999). For orthodontie brackets, binding was less of a

factor for ceramic brackets than for stainless steel brackets (Articolo and Kusy, 1999).

Zufall and Kusy (2000) felt that the magnitude of the normal force component of

the binding phenomenon is controlled by the stifkess of the wire, the interbracket

distance, the bracket width, and the second order angulation. A mathematicai model was

developed to compare the binding component of fnction based on the magnitude of the

cowitervailing couple between the archwire and the bracket induced as the angulation

increased rather than just on the magnitude of the angulation (Zufall and Kusy, 2000).

With this model binding was found to be lowest for stainless steel when compared to

nickel-titanium, beta-titanium, and coated composite wires.

Clinically, Braun et al (1999) felt that second order angulation did not have a

measurable effect on the fictional resistance in the simulated dpamic of the oral

environment, which is contrary to most other researchers. They felt that superimposed on

the coupled dental tipping and uprighting associated with sliding mechanics are minute

perturbations between the archwire and bracket introduced by various oral functions such

as mastication, speaking, swallowing, tongue and cheek pressure. Braun et al (1 999)

noted that momentarily afier a perturbation was induced on the archwire-bracket couple,

the fictional resistance decreased by 98 to 100 percent. However, the authors did

concede that the complicated dynamics of the intraoral environment might not mean total

reduction of the fnction in sliding mechanics. Moreover, this is because the frequency

and coordination of perturbations would unlikely occur simultaneously as the archwire

moves through several in-line brackets.

It has also been argued that perturbations or loadings on teeth that demonstrate

increased mobility would decrease friction in-vivo (Jost-Brinkmann and Miethkee, 199 1).

An in-vitro study that allowed bracket displacements to simulate in-vivo tooth mobility

and permitted second order angulation by tipping about an approximated center of

resistance demonstrateci that the effects of the binding between the bracket and the

archwire was significantly reduced (O'Reilly et al, 1999). The amount of reduction

ranged fiom 19 percent to 85 percent depending on the archwire material and size.

However, little is known about the magnitude of tootb mobility that is required to release

binding of the bracket and the archwire once it has occurred with second order tipping

(O'Reilly et al, 1999).

1 .) With increosing second order angulation between the bracket and the archwire, the flictonal resistance increases.

2.) At increased second order angulation nickel-titanium archwires have less friction than stainless steel archwires because d i t s Iower moduius of elasticity.

3 .) Studies that incorporate sorne second order tipping may be more clinically relevant.

4.) Eficts of second order tipping may be decreased by in-vivo parameters that cause perturbations of the bracket, arch wire, and/or tooth.

Effect of Sliding Velocity

Typically, to move a tooth 1 mm it requires about one month. This translates to

an approximate average speed of 2.3 x IO-' rnm/min (Kusy and Whitley, 1989). But,

Graber and Swain (1985) have shown clinically that the velocity for reciprocal ctosure of

a diastema between the two central incisors to range fiom O to 2.4 x 104 d m i n .

Frictional tests are based on a first ordet approximation that sliding of the bracket relative

to the archwire is constant. Then experimentally, if the assumption is made that the

process of tooth motion occurs at a constant rate of 2.3 x IO-' mmjmin, the diflerence

between laboratory testing and clinical reality of nearly six orders of magnitude c m o t be

ignored (Kusy and Whitley, 1989). Kusy and Whitley (1989) found that coefficients of

fiction might Vary with extremes in velocity for certain archwire alloys. This is contrary

to the third law of fiction that States that the coefficient of friction is independent of

velocity (Eshbach and Souders, 1975). However, it has been recognized that this law is

not usually followed (Jastrebski, 1 976).

Ireland et al (1 99 1) performed a pilot study varying the cross-head speed of the

hstron Universal testing machine fiom 0.5 up to 50 rnmlminute using stainless steel and

nickel-titanium wires sliding in stainless steel and ceramic brackets. Results showed no

signifiant differences in friction among the various speeds no matter what combination

of brackets or archwires was used. A speed of 5 mm/min was selected for

experimentation because it was felt that higher speeds did not represent the clinical

situation.

Kusy and Whitley (1989) previously reportai that stainless steel and nickel-

titaniurn wires to be largely unaffected by changing sliding velocity. However, the

coefficient of fiction for cobalt-chromium wires decreased with increasing sliding

veiocity, while the coefficient of fiiction for beta-titanium increased with increasing

sliding velocity. With increased sliding velocities, the author suggests that the rate for a

protective oxide to grow was too iow resulting in "cold welding". Shear fracture of the

adhesive bridges would have to occur for sliding to continue, thus affecting the observed

coefficients of sliding. Subsequent fictional testing by Kusy et al ( 1989, 1990, 1998,

1 999) employed a sliding velocity of 10 mrn/minute.

It appears that it would be closer to the in-vivo situation if the sliding velocities

used were as slow as possible to emulate the clinical situation. Practically, sliding

velocities several magnitudes higher experimentally than in-vivo facilitates conservation

of time during experimentation.

Therefore, in-vitro sliding velocities may underestimate the coefficient of fiction

for cobalt-chromium and overestimate the coefficient of fiiction for beta-titanium.

Friction results for stainless steel or nickel-titanium are largely independent of sliding

velocity.

Sumrnary

1 .) D~flerences betweeri in-vivo tooth movement and in-viîro testing Vary nearly six orders of magnitude.

2.) Changes in sliding velocity do not affect thefiictional resistance of stainless steel or nickel-titanium archwires.

3.) With higher sliding velocities the coeficient offiiction for cobalt-chromium increases while the coeflcient of beta-tilanium decreases because of changer in the surfafe chemistry as the oxide layer is removed.

Effect of Wet and Dry Environment

The effect of wet and dry Wction testing environments is an in-vitro mode1

problem that has been a source of debate for researchers. in particular, questions have

arisen as to whether the use of saliva substitutes in-vitro is a valid representation of the

clinical situation. Basically, investigations comparing the wet and dry environment have

met with diffenng results, showing decreases, no change, and increases in fiction.

A reduction in Wctional resistance when artificial saliva was used in testing was

reported by Baker et al (1987) and Tselepis et al (1 994). Baker et uf ( 1 987) found that a

saliva substitute decreased fiictional resistance by 15 to 19 percent compared to dry

conditions, while glycerin had no effect. The author suggested glycerin was probably not

suitable as a lubricant because of its vety high viscosity compared to saliva. Tselepsis et

al (1994) found that in the passive configuration the friction was reduced 8 to 60 percent

in the wet state compared to the dry state. in the active configuration, reductions ranged

Erom 6 to 46 percent, but in some instances the fnction increased by as much as 20

percent. Tselepsis et al (1994) stated the function of a lubricant was to reduce the

strength and number of bridges forrned between the asperities of sliding surfaces. It was

perceived that saliva acted as a lubricant.

Studies by Ireland et ai (1991) reported no significant differences between the dry

and wet state in cornparison to the frictional resistance for combinations of stainless steel

and nickel-titanium wires with stainless steel and cermic brackets. Water was used as

the wetting agent. Andreasen and Quevedo (1970) also found no difference in fnction

levels between trials with and without saliva. Both Andreasen and Quevedo (1970) and

Ireland et al (1991) concluded saliva played an insignificant role in lubncating the surface

of the archwires and the bracket because the archwire touches the bracket at two points

creating pressure that expels the saliva from the area of contact allowing no lubrication

effect.

Shivapuja and Berger (1994) found artificial saliva increased the fnctional

resistance, which was explained by the rapid rate of desiccation of the saliva substitute

leaving cellulose adhering to the archwire. Downing et ai (1 995) reported î?ictional

resistance to increase with artificial saliva ranging from 9.3 to 43.0 percent. Speculation

was that increased adhesion or attraction of polar materials caused more fiction. The

least increase was noted with beta-titanium (TMA, h c o Corp., CA, USA) because the

liquid was thought to fil1 in the irregularities of the wire sufiace and hence make it

relatively smoother. Stannsd ot a1 (1986) found that in the wet state stainless steel,

nickel-titanium, and beta-titanium wires had coefficient of friction that increased, while

the coefficient of friction for cobalt-chromiurn wires were unchanged. Downing et al

(1995) and Stannard et al (1986) speculated that the increase in fiction was expiained by

the presence of polar liquids creating increased atomic attraction among ionic species

leading to adhesion of surface asperities. This is refmed to as the "adhesion theory of

fiction" (Rabinowicz, 1965). Similarly, Pratten et a1 (1990) reported that in an artificial

saliva media the fictional resistance increased because saliva produced shear resistance

to sliding.

Human saliva was used by Kusy et al (1991) in a cornparison of dry and wet

testing conditions and reported that signifiant differences were observed between the dry

and wet state. The overall magnitude and directionai changes depended on the specific

archwire alloy. Stainless steel and nickel-titanium wires displayed adhesive behaviour as

evidenced by increased fiiction in the wet state, while saliva acted as a lubricant for beta-

titanium wires leading to decteased fiiction. The increase in fiction was owing to the

increased surface tension created by the saliva. But for beta-titanium archwires saliva

was felt to reduce the incidence of " d d welding" (Kusy et al, 199 1). Saunders and Kusy

(1 994) also found human saliva to decrease the fiction for titanium wires and for ceramic

brackets.

Pratten et al (1990) suggested discrepancies in results from the effect of wet

versus dry environment might be due to the loading forces between the bracket and

archwires. At low loads saliva may act as a lubricant, but at high loads saliva may

increase Fiction if it is forced out Erom the contacts between the bracket and archwire

producing shear resistance to sliding.

As Tselepsis et al (1994) noted studies comparing the dry and wet testing

environments have many variations, including the materials used, the methodology, and

the lubricant. Lubricants used by different investigators included water, saline, saliva

substitutes, glycerin, and human saliva. Kusy et al (199 1) felt that experiments conducted

in artificial saliva were invalid because artificial saliva is not a satisfactory substitute for

fksh human saliva.

No matter what lubncating media was used or how it was administered, the rank

order of the fnctional resistance of the materials usually did not change or no significant

trend on the effect of saliva exists. For the purposes of comparing the relative fictional

resistance of bracket and archwire materials, it may be adequate to do the testing under

dry conditions. To determine the effects on the coefficients of fiction, human saliva

would provide the most appropriate test conditions, and under these conditions the values

for coefficients of fiction can have various effects depending on the bracketlarchwire

couple.

Presently no studies have investigated the fictional effects of saliva on

braidedtwisted arch wires. These wires may have increased surface area contact with the

saliva owing to capillary action and hence a greater effect during sliding.

Summary

1 .) Dzfferent wetting agents have been employed in orthodontie friction studies.

2.) These wetting agents have been shown to cause the fiictional resistance to increase. remain the same, and decrease.

3 .) Lubricating affects are attributed to the liquid filling irregularities of the wire making it smoother.

4.) Adliesive agects are explained by increased ionic attraction in the presence of polar liquids.

5.) Human saliva is the most appropriate testing environment ifthe study is to be done in the wet state.

Summary of Review of the Literature

Fnctional resistance during sliding mechanics is multifactorial in nature. In-vitro

studies of frictional forces associated with orthodontic materials and their parameters give

varying results but offer some insight into the control of fiction. Generally, fnctional

resistance is decreased with stainless steel brackets, round stainless steel archwires of

smaller diameter, decreased ligation force, and restriction of tipping of the bracket to the

archwire. New materials and manufachiring techniques may produce less fiction.

However, cornparisons between studies are difficult because of the variation of

methodology and materials. To this end, standardization of frictional resistance testing

protocols to emulate the clinical situation would be beneficial.

PURPOSE OF THE STUDY

The purpose of the proposed study is the following:

Validate the fimction of a tating apparatus to achieve concurrent control of linear

and angular bracket displacement while simultaneously acquiring fnctional

resistance data with temporal integration.

Demonstrate that static canine retraction models are not adequate because

experirnental conditions do not accurately represent the clinical situation.

Demonstrate that the fnctional resistance of a dynamic canine retraction mode1

that experimentally approximates orthodontie tooth movements represents an

improvement over static canine retraction models.

Establish testing parameters to measure the frictional resistance using a dynamic

canine retraction model.

Compare the fiictional resistance of various bracketkchwire combinations using

a dynamic canine retraction model.

RESEARCH QUESTIONS

The following research questions have been organized into four sections to address the purpose of the study.

A. Verification of function of frictional testing apparatus

(1) Can a testing apparatus designed for simulated canine retraction achieve

concurrent control of linear and angular bracket displacement while

simultaneously acquiring fiictional resistance data with temporal integration?

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Does the fictional resistance of a static canine retraction model vary as a

function of bracket tip?

(2) Does the fiictional resistance of a dynamic canine retraction model that

experimentally approximates complex orthodontic tooth movements differ from

static canine retraction modeis?

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Does the sliding velocity affect the fiictional resistance using a dynamic canine

retraction rnodel?

(2 ) Does pre-drawing of the wire h o u & the bracket affect the fnctional resistance

using a dynamic canine retraction model?

(3) Does saliva affect the fiictional resistance of braidedltwisted archwires using a

dynamic canine retraction model?

(4) Does use of Speed-D shaped archwires affect the fnctional resistance of Speed

brackets using a dynamic canine retraction model?

O. Frictional resistance evaluation of various orthodontic brackets and archwires with sliding mechanics using quantified simulation of canine retraction

Does orthodontic bracket type affect the Mctional resistance using a dynamic

canine retraction model?

Does orthodontic archwire type affect the frictional resistance using a dynamic

canine retraction model?

Does orthodontic archwire size affect the frictional resistance using a dynamic

canine retraction model?

Does orthodontic archwire shape affect the frictional resistance using a dynamic

canine retraction model?

Do some orthodontic bracketkrchwire combinations have less friction than

others?

HYPOTHESES

The following hypotheses seek to answer the questions put forth in Sections B, C,

and D of the Research Questions by proposing a nul1 hypothesis (Ho) and an alternative

hypothesis (H,), and are accordingly labeled in the following sections. (Note: No

hypothesis is required to answer the question put forth in Section A of the Research

Questions and is therefore no Section A appears under this heading.)

B. Establishment of a rnodel for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) 8.: Frictional resistance measured in a static canine retraction model does not

Vary as a tùnction of bracket tip.

Ha: Fnctional resistance measured in a static canine retraction model varies as

a function of binding or bracket tip.

(2) Ho: Frictional resistance measured in a dynamic canine retraction model that

experimentally approximates orthodontic tooth movements is not significantly

different than static canine retraction models.

Hi: Fnctional resistance measured in a dynarnic canine retraction model that

expenmentally approximates orthodontic tooth movements is significantly

different than static canine retraction models.

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantifiad simulation of canine retraction

(1) H,,: Sliding velocity does not affect the fnctional resistance using a dynamic

canine retraction model .

Ha: Sliding velocity affects the fnctional resistance using a dynamic canine

retraction model.

(2) Ho: Pre-drawing of the archwire through the bracket does not affect the

fictional resistance using a dynamic canine retraction model.

Ha: Pre-drawing of the archwire through the bracket affects the fiictional

resistance using a dynamic canine retraction model.

(3) Ho: Saliva does not affmt the fnctional resistance of braided/twisted archwires

using a dynamic canine retraction model.

H,: Saliva affects the fiictional resistance of braidedtwisted archwires using a

dynamic canine retraction model.

(4) Bo: Speed-D archwires do not affect the fnctional resistance of Speed brackets

using a dynamic canine retraction model.

Ha: Speed-D archwires affect the frictional resistance of Speed brackets using

a dynamic canine retraction model.

D. Frictional resistance evaluation of various orthdontic brackets and archwims with sliding mechanics using quantified simulation of canine retraction

Ho: Bracket type does not affect the Wctional resistance using a dynamic

canine retraction mode1 .

8.: Bracket type affects the fnctional resistance using a dynamic canine

retraction model.

Ho: Archwire type does not affect the fnctional resistance using a dynamic

canine retraction model.

Ha: Archwire type affects the Wctional resistance using a dynamic canine

retraction model.

&: Archwire size does not affect the frictional resistance using a dynamic

canine retraction model.

Ha: Archwire size affects the fictional resistance using a dynamic canine

retraction model.

Ho: Archwire shape does not affect the fnctional resistance using a dynamic

canine retraction model .

Ha: Archwire shape affects the fnctional resistance using a dynamic canine

retraction model.

EI,,: Brackethrchwire combinations do not affect the frictional resistance using

a dynamic canine retraction model.

Hi: Bracket/archwire combinations affect the fictional resistance using a

dynamic canine retïaction model.

Friction: a force that retards or resists the relative motion of two objects in contact, and

its direction is tangential to the cornmon boundary of the two surfaces in contact.

Normal force: the force perpendicular to the contacting surfaces -and to the fnctional

force component.

Binding: the restriction of sliding due to an interference fit between the archwire and the

bracket as one tips relative to the other.

Frictional resistance: the resistance to sliding approximated by the additive effect of

fiiction and binding.

Non-binding friction: the fiction that results fiom the normal force induced by ligation.

Binding friction: the fiction that results fiom the normal force induced by binding,

which is supenmposed on the non-binding friction.

Ligation: method of holding or directing the archwire into the bracket slot.

Second-order tipping: rotation of the bracketed tooth in a vertical plane perpendicular

to a faciolingual axis.

Second-order angulation: the angle between the bracket slot and archwire in a plane

parallel to the bracket slot with the long axis of the bracket dot representing zero degrees.

Contact angle: the second-order angulation between the archwire and the bracket dot.

Critical contact angle: the second-order angulation at which the archwire engages the

edges of the bracket dot leading to binding.

Active configuration: binding of the brackethrchwire interface at high second-order

angulations meeting or exceeding the critical contact angle.

Passive configuration: non-binding of the brackethrchwire interface at iow second-

order angulations below the critical contact angle.

Instrumentation

The instrumentation for this study used the testing apparatus descxibed by

Kamelchuk (1998) (lllustration 1, Appendix C). It is compriseci of the following

modules:

(1 ) Instron Machine: Servo Hydraulic 430 1 instron Machine (Instron inc., Canton,

MA)

(2) Load cell: A load cell of 4,000 gram capacity will be used (A30-38(A);

Transducer Techniques Precision Measurement Systems, Temecula, CA).

(3) Interfacing components for application specific tasks: Aerotech BM250 Servo

Motor (Aerotech Inc., Pittsburgh, PA)

(4) Graphical programming software: LabVIE W Development Software (National

Instruments Version 2.2.1 )

A. Verifkation of function of frictional testing apparatus

Orthodontic brackets:

metal bracket Mini Masters Series (American Orthodonties, S hebo ygan, WI) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

stainless steel Tm-Chrome (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.025"

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of friction using static canine retraction models

Orthodontic brackets:

metal bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

stainless steel Tm-Chrome (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.025"

nickel-titanium Orthonol (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.025"

(2) Comparison of ftiction using static and dynamic canine retraction modeis

Orthodontic brackets:

metd bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

stainless steel Tm-Chrome (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.025"

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of effect of sliding velocity on friction using dynamic canine retraction model

Orthodontic brackets:

metal bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

stainless steel Tm-Chrome (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.025"

(2) Cornparison of effect of pre-dnring of the archwire on friction using dynamic canine retraction model

Orthdontic brackets:

metal bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

stainless steel TmChrome (RMO, Denver, CO) cross-sectional dimension: 0.01 8 x 0.025"

(3) Cornparison of effect of saliva with braideditwisted archwires on friction using dynamic canine retraction mode1

Orthodontic brackets:

metal bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

twisted stainless steel Supra-flex (RMO, Denver, CO) cross-sectional dimension: 0.0 1 75"

braided stainless steel Flex-VI11 ( M O , Denver, CO) cross-sectional dimension: 0.01 8 x 0.025"

twisted nickel-titanium Supercable (Strite Industries, Cambridge, ON) cross-sectional dimension: 0.0 1 8"

(4) Cornparison of effect of Speed archwires with Speed brackets on friction using dynamic canine retraction mode1

Orthodontic brackets:

active sel f-ligating metal bracket Speed (Strite Industries, Cambridge, ON) slot dimension: 0.022 x 0.028"

Orthodontic archwires:

nickel-titaniwn Orthonol ( M O , Denver, CO) cross-sectional dimension: 0.0 1 8 x 0.0 18"

nickel-ti tanium Speed-D shaped (Strite Industries, Cambridge, ON) cross-sectional dimension: 0.0 1 8 x 0.0 1 8"

O. Frictional resistance evaluation of various orthodontie brackets and archwires with sliding mechanics using quantified simulation of canine retraction

Orthodontic brackets:

rnetal bracket Victory (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

cerarnic bracket Transcend 6000 (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

cerarnic bracket with metal slot Clarity (Unitek Corp., Monrovia, CA) slot dimension: 0.022 x 0.028"

active self-ligating metal bracket Speed (Strite industries, Cambridge, ON) slot dimension: 0.022 x 0.028"

passive sel f-ligating metal bracket Darnon SL ('A' Company, San Diego, USA) slot dimension: 0.022 x 0.028"

variable self-ligating metal bracket Tirne (American Orthodontics, Sheboygan, WI) slot dimension: 0.022 x 0.028"

Orhodontic archwires:

stainless steel Tru-Chrome ( M O , Denver, CO) cross-sectional dimension: 0.0 1 8"

0.020" 0.0 18 x 0.025" 0.02 1 x 0.025"

nickel-titaniurn Orthonol (RMO, Denver, CO) cross-sectional dimension: 0.0 1 8"

0.020" 0.01 8 x 0.025" 0.02 1 x 0.025"

twisted stainless steel Supra-flex (RMO, Denver, CO) cross-sectional dimension: 0.0 1 75"

0.0 195"

braided stainless steel Flex-VIiI ( M O , Denver, CO) cross-sectional dimension: 0.01 8 x 0.025"

0.02 1 x 0.025"

twisted nickel-titanium Supercable (Stnte industries, Cambridge, ON) cross-sectional dimension: 0.0 1 8"

0.020"

Note: Material properties of the orthodontie brackets and archwires evaluated are surnmarized in Appendix A.

Testing parameters

(1) The testing apparatus designed and descnbed by Kamelchuk (1 998) was used for al1

trials (Illustration I , Appendix C).

Al1 orthodontic brackets were mounted by the standardized method outlined by

Kamelchuk ( 1 998). This method is described as follows. individual orthodontic

brackets were mounted within custom-fabricated bracket mounting fixtures in a

standardized manner so that the long-axis of the test bracket slot was parallel to the

Instron actuator stroke axis and the test bracket slot center is coincident with the

servo motor drive-shaft. This was achieved by an interface between the individual

bracket mounting fixtures and the mounting fixture alignment jig and then attaching

individual test brackets on a 0.02 15 x 0.028 segment of archwire dunng fixation via

light cunng acrylic (Illustration 2, Appendix C). The bracket mounting fixnireitest

bracket unit was then disassembled fiom the alignrnent jig and transferred for

indexing using an interface with the (shaft-mounted) mounting fixture receptacle

(Illustration 3, Appendix C). Al1 individual test brackets were mounted using this

standardized technique to ensure precise localization of the test bracket relative to

the testing apparatus. Precision of test bracket location was secondarily verified

during the direct interface with the testing apparatus (Illustration 4, Appendix C).

A 0.02 1 5 x 0.028 segment of archwire was suspended nom the archwire grip and

then attached individual test brackets to ensure the long-axis of the test bracket slot

was parallel to the Instron actuator stroke axis.

(3) Individual orthodontie test wires were suspended fiom the load ce11 by an archwire

grip in edgewise orientation relative to the test bracket and such that the test wire

long-axis was parallel to and coincident with the instron actuator stroke mis.

(4) Al1 test wires were suspended fkom the archwire grip at a length of 20 mm to the

test bracket center.

(5 ) The fiee end of the test wires were restrained with another archwire grip weighing

1 13 grams at a length of 20 mm to the test bracket center, unless otherwise noted.

(6) For al1 trials, the 4,000 gram load ce11 accurate to the 0.1 gram level was used with a

full scale load of 1000 grams.

(7) Before each trial the load ce11 was calibrated to compensate for the weight of the

bracket'archwire assernblies.

(8) Al1 test wire segments and test brackets were cleansed with isopropyl alcohol prior

to testing to remove any residue or debris.

(9) For al1 trials, a constant linear traction (Instron actuator displacement) rate was

selected as 0.45 mdminute, yielding 2.25 mm of linear displacement for every 5

minutes of active testing, unless otherwise noted.

( 1 0) Elastorneric ligatures (American Orthodontics, Sheboygan, WI) were placed over

the bracket tie-wings engaging the archwire 24 hours pnor to testing, except for

sel f-ligating brackets that required no ligatures.

(1 1) A new test bracket and a new test wire were paired for each trial and were not re-

used in subsequent triais.

(12) A11 trials first achieved steady state displacement of the bracket relative to the

archwire that dlowed evaluation of kinetic frictional resistance. This occurred

after 0.3 mm (Karnelchuk, 1998). Subsequently, trials then displaced the bracket

relative to the archwire another 2.0 mm.

(1 3) Data sarnpling for al1 trials functioned continuously and was set at 2 samples per

second (1 20 pointdminute), except as noted.

(1 4) Al1 trials were performed under dry conditions, except as noted.

(15) Al1 orthodontic brackets used for testing were for use on the maxillary right canine

tooth.

(16) Bracket angulation and data collection were controlled by LabVIEW Graphical

prograrnrning software (National Instruments Version 2.2.1) (Illustration 5,

Appendix C).

A VeMcation of function of frictional testing apparatus

A series of trials were performed to ver@ the function of the testing apparatus to

achieve concurrent control of 1 inear and angular bracket displacement while

sirnultaneously aquiring fictional resistance data with temporal integration.

Series A. 1.1 : The first series were used for verification of linear motion control with

quantification of fnctional resistance via digital data acquisition. Following the above

listed testing parameters, fnctional resistance was tested as a function of static non-tipped

bracket angulation. The second order angulation was set at zero degrees (O0) and

maintained for the duration of each test. The test wires were unrestrained and were

allowed to passively hang without tension. Stainless steel wire of cross-sectional

dimension 0.01 8 x 0.025" was used with stainless steel brackets. Three bracket/archwire

couples were sarnpled (N=3).

Series A.1.2: The second series was also used for verification of linear motion control

with quantification of fnctional resistance via digital data acquisition. These trials were

exactly the same as the previous protocol except that fnctional resistance was tested as a

function of static tipped bracket angulation. The second order angulation was set at ten

degrees (1 0") and maintained for the duration of each test. The test wires were

unrestrained and were allowed to passively hang without tension. Stainless steel wire of

cross-sectional dimension 0.01 8 x 0.025" was used with stainless steel brackets. Three

bracketkrchwire couples were sampled (N=3).

Series A.1.3: The third series was used for verification of angular motion control and

temporal integration of linear and angular control with quantification of fiîctional

resistance via digital data acquisition. Following the above listed testing parameters,

frictional resistance was tested as a function of dynamic and progressive bracket tipping

concurrent with linear bracket traction. Second order angulation was increased at a rate

of 0.045 degrees/second (2.70 degrees/minute) up to a maximum angular displacernent of

20.03 degrees. Maximal angular displacement occurrd at 1.5 mm of linear displacement

and then held constant for the remaining linear displacement. Deflection of the test wires

fiee-end was unrestrained and was allowed to passively hang without tension. Stainless

steel wire of cross-sectional dimension 0.018 x 0.025" was used with stainless steel

brackets. Three bracketlarchwire couples were sarnpled (N=3).

B. Establishment of a mode1 for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of friction using static canine retraction models

A series of trials were performed to compare the fictional resistance for

orthodontic brackets and archwires as a function of static straight-line traction for binding

and non-binding canine retraction models.

Series B. 1.1 : Following the above listed testing parameters, fictional resistance was

tested as a function of static non-tipped bracket angulation. The second order angulation

was set at zero degrees (O0) and maintained for the duration of each test. Stainless steel

wire of cross-sectional dimension 0.01 8 x 0.025" was used with stainless steel brackets.

Six bracketiarchwire couples were sampled (N=6).

Series B. 1.2: Fotlowing the above listed testing parameters, fictional resistance was

tested as a function of static non-tipped bracket angulation. The second order angulation

was set at zero degrees (O0) and maintained for the duration of each test. Nickel-titanium

wire of cross-sectional dimension 0.018 x 0.025" was used with stainless steel brackets.

Six bracketlarchwire wuples were sampled (N=6).

Series B. 1.3: Following the above listed testing parameters, Wctional resistance was

tested as a function of static tipped bracket angulation. The second order angulation was

set at six degrees (6') and maintained for the duration of each test. Stainless steel wire of

cross-sectional dimension 0.018 x 0.025" was used with stainless steel brackets. Six

bracketlarchwire couples were sampled (N=6).

Series B. 1.4: Following the above listed testing parameters, Wctional resistance was

tested as a fwiction of static tipped bracket angulation. The second order angulation was

set at six degrees (6') and maintained for the duration of each test. Nickel-titanium wire

of cross-sectional dimension 0.01 8 x 0.025" was used with stainless steel brackets. Six

bracketkrchwire couples were sampled (N=6).

(2) Comparison of friction using static and dynamic canine retraction models

A series of trials were performed to compare the fictional resistance of a canine

retraction mode1 that experimentally approximates complex dental movernents with

straight-line canine retraction models.

Series B.2.1: Following the above listed testing parameters, frictional resistance was

tested as a function of static non-tipped bracket angulation. The second order angulation

was set at zero degrees (O0) and rnaintained for the duration of each test. Stainless steel

wire of cross-sectional dimension 0.01 8 x 0.025" was used with stainless steel brackets.

Six bracket/archwire couples were sampled (N=6).

Series B.2.2: Following the above listed testing panuneters, Wctional resistance was

tested as a function of static tipped bracket angulation. The second order angulation was

set at six degrees (6') and maintained for the duration of each test. Stainless steel wire of

cross-sectional dimension 0.018 x 0.025" was used with stainless steel brackets. Six

bracketkchwire couples were sampled (N=6).

Series B.2.3: Following the above listed testing parameters, fictional resistance was

tested as a function of dynamic and progressive bracket tipping and uprighting concurrent

with linear bracket traction. Displacement of the bracket relative to the archwire was

initiated with second order bracket angulation beginning to increasing after 0.3 mm.

Second order bracket angulation was then increased at a rate of 0.045 degrees/sec (2.70

degreedminute) up to a maximal angular displacement of 6.00 degrees and then was

reversed and was decreased at a rate of 0.045 degreeshec (2.70 degreedminute) through

to zero degrees. Stainless steel wire of cross-sectional dimension 0.018 x 0.025" was

used with stainless steel brackets. Six brackethchwire couples were sampled (N=6).

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Comparison of effect of sliding velocity on friction using dynamic canine retraction model

A series of trials were performed to compare the effect of rate of retraction on the

frictional resistance of a canine retraction model that experimentally approximates

complex dental movements.

Series C. 1.1 : Following the above listed testing parameters, fnctional resistance was

tested as a h c t i o n of rate of retraction selected at 0.45 &minute. Displacement of the

bracket relative to the archwire was initiated with second order bracket angulation

beginning to increasing afkr 0.3 mm. Second order bracket angulation was then

increased at a rate of 0.045 degrees/sec (2.70 degreedminute) up to a maximal angular

displacement of 6.00 degrees and then was reversed and was decreased at a rate of 0.045

degreeskec (2.70 degrees/minute) through to zero degrees. Stainless steel wire of cross-

sectional dimension 0.01 8 x 0.025" was used with stainless steel brackets. Six

bracketkchwire couples were sarnpled (N=6).

Senes C.1.2: Following the above listed testing parameters, fnctional resistance was

tested as a function rate of retraction selected at 0.90 mdminute. Displacernent of the

bracket relative to the archwire was initiated with second order bracket angulation

beginning to increasing a h 0.3 mm. Second order bracket angulation was then

increased at a rate of 0.090 degreeslsec (5.40 degreeshinute) up to a maximal angular

displacement of 6.00 degrees and then was reversed and was decreased at a rate of 0.090

degreeslsec (5.40 degreedminute) through to zero degrees. Data sarnpling for al1 trials

fûnctioned continuously and was set at 4 samples per second (240 pointsIrninute).

Stainless steel wire of cross-sectional dimension 0.01 8 x 0.025" was used with stainless

steel brackets. Six bracketlarchwire couples were sampled (N=6).

Series C. 1.3: Following the above Iisted testing parameters, fnctional resistance was

tested as a fünction rate of retraction selected at 2.25 &minute. Displacernent of the

bracket relative to the archwire was initiated with second order bracket angulation

beginning to increasing afier 0.3 mm. Second order bracket angulation was then

increased at a rate of 0.225 degreeslsec (13.50 degreeslminute) up to a maximal angdar

displacement of 6.00 degrees and then was revmed and was decreased at a rate of 0.225

degreeslsec (13.50 degreeshinute) through to zero degrees. Data sampling for a l trials

bc t ioned continuously and was set at 8 samples per second (480 pointslminute).

Stainless steel wire of cross-sectional dimension 0.018 x 0.025" was used with stainless

steel brackets. Six bracketlarchwire couples were sampled (N=6).

Series C. 1.4: Following the above listed testing parameters, fnctional resistance was

tested as a h c t i o n of the rate of retraction selected at 4.5 mm/minute. Displacement of

the bracket relative to the archwire was initiated with second order bracket angulation

beginning to increasing after 0.3 mm. Second order bracket angulation was then

increased at a rate of 0.45 degreedsec (27.0 degrees/minute) up to a maximal angular

displacement of 6.00 degrees and then was reversed and was decreased at a rate of 0.45

degreeslsec (27.0 degreeslminute) through to zero degrees. Data sampling for al1 trials

fünctioned continuously and was set at 16 samples per second (960 pointslminute).

Stainless steel wire of cross-sectional dimension 0.01 8 x 0.025" was used with stainless

steel brackets. Six brackethchwire couples were sampled (N=6).

(2)Comparison of effect of pre-drawing of the archwire on friction using dynamic canine retraction modet

A series of trials were performed to compare the effects of initial pre-drawing of

the archwire on the fnctional resistance of a canine retraction model that experimentally

approxirnates complex dental movements.

Series C.2.1: Following the above listed testing parameters, fnctional resistance was

tested as a fùnction rate of initial pre-drawing of the archwire. No initial pre-drawing of

the archwire was done. Displacernent of the bracket relative to the archwire was initiated

with second order bracket angulation begiming to increasing after 0.3 mm. Second order

bracket angulation was then increased at a rate of 0.045 degradsec (2.70 degreedminute)

up to a maximal angular displacement of 6.00 degrees and then was reversed and was

decreased at a rate of 0.045 degreedsec (2.70 degreesiminute) through to zero degrees.

Stainless steel wire of cross-sectional dimension 0.018 x 0.025" was used with stainless

steel brackets. Six bracketkchwire couples were sampled (N=6).

Series C.2.2: Following the above listed testing parameters, fnctional resistance was

tested as a fùnction initial pre-drawing of the archwire. initial pre-drawing of the

archwire was done by drawing the archwire through the ligated bracket for a distance of

2.0 mm. Displacement of the bracket relative to the archwire was then initiated with

second order bracket angulation beginning to increasing after 0.3 mm. Second order

bracket angulation was then increased at a rate of 0.045 degreedsec (2.70 degrees/minute)

up to a maximal angular displacement of 6.00 degrees and then was reversed and was

decreased at a rate of 0.045 degreedsec (2.70 degrees/minute) through to zero degrees.

Stainless steel wire of cross-sectional dimension 0.01 8 x 0.025" was used with stainless

steel brackets. Six bracketlarchwire couples were sampled (N=6).

(3) Comparison of effect of saliva with braidetütwisted archwires on friction using dynamic canine retraction model

A series of trials were performed to compare the effects of saliva on the Wctional

resistance of braidedtwisted archwires using a canine retraction model that

experimentally approximates complex dental movements with straight-line canine

retraction models.

Series C.3.1: Following the above listed testing parameters, fnctional resistance was

tested as a function of a dry testing environment for twisted stainless steel archwires. No

saliva was placed on the archwirehracket couple. Displacement of the bracket relative to

the archwire was initiated with second order bracket angulation begiming to increasing

afier 0.3 mm. Second order bracket angulation was then increased at a rate of 0.045

degreeslsec (2.70 degreeslminute) up to a maximal angular displacement of 6.00 degrees

and then was reversed and was decreased at a rate of 0.045 degreedsec (2.70

degreedminute) through to zero degrees. Twisted stainless steel wire of cross-sectional

dimension 0.0 175" was used with stainless steel brackets. Six bracketkrchwire couples

were sarnpled (N=6).

Series C.3.2: Following the above listed testing parameters, fnctional resistance was

tested as a function of a wet testing environment. These trials were exactly the same as

the previous protocol except that 1.0 mL of fiesh human saliva provided by the

investigator was applied to the archwirehracket interface. Twisted stainless steel wire of

cross-sectional dimension 0.0175" was used with stainless steel brackets. Six

bracket/archwire couples were sampled (N=6).

Series C.3.3: Following the above listed testing pararneters, fnctional resistance was

tested as a function of a dry testing environrnent for braided stainless steel archwires. No

saliva was placed on the archwirelbracket couple. Displacement of the bracket relative to

the archwire was initiated wiîb second order bracket angulation beginning to increasing

a h 0.3 mm. Second order bracket anplation was then increased at a rate of 0.045

degreeslsec (2.70 degreedminute) up to a maximal angular displacement of 6.00 degrees

and then was reversed and was decreased at a rate of 0.045 degreedsec (2.70

degreeslminute) through to zero degrees. Braided stainless steel wire of cross-sectional

dimension 0.0 18 x 0.025" was used with stainless steel brackets. Six bracketlarchwire

couples were sampled (N=6).

Series C.3.4: Following the above listed testing parameters, fictional resistance was

tested as a fiinction of a wet testing environrnent. These trials were exactly the same as

the previous protocol except that 1.0 mL of fiesh human saliva provided by the

investigator was applied to the archwirelbracket interface. Braided stainless steel wire of

cross-sectional dimension 0.018 x 0.025" was used with stainless steel brackets. Six

brackethrchwire couples were sampled (N=6).

Series C.3.5: Following the above listed testing pararneters, fnctional resistance was

tested as a fiinction of a dry testing environment for twisted stainless steel archwire. No

saliva was placed on the archwire/bracket couple. Displacement of the bracket relative to

the archwire was initiated with second order bracket angulation beginning to increasing

after 0.3 mm. Second order bracket angulation was then increased at a rate of 0.045

degreeslsec (2.70 degreeslminute) up to a maximal angular displacement of 6.00 degrees

and then was revetsed and was decreased at a rate of 0.045 degreeskc (2.70

degreeslminute) through to zero degees. Twisted nickel-titanium wire of cross-sectional

dimension 0.018" was used with stainless steel brackets. Six bracketkrchwire couples

were sarnpled (N=6).

Series C.3.6: Following the above listed testing parameters, fnctional resistance was

tested as a function of a wet testing environment. These triais were exactly the sarne as

the previous protocol except that 1.0 mL of fresh human saliva provided by the

investigator was applied to the archwirehacket interface. Twisted nickel-titanium wire

of cross-sectional dimension 0.0 18" was used with stainless steel brackets. Six

bracketlarchwire couples were sarnpled (N=6).

(4) Cornparison of effect of Speed-D archwires with Speed brackets on friction using dynamic canine retraction model

A series of trials were performed to compare the fnctional resistance of Speed D-

shaped archwires with Speed brackets versus conventionally shaped archwires with Speed

brackets using a canine retraction model that experimentally approximates complex

dental movernents.

Series C.4.1: Following the above listed testing parameters, fictional resistance was

tested with Speed D-shaped archwires. Displacernent of the bracket relative to the

archwire was initiated with second order bracket anguiation beginning to increasing afier

0.3 mm. Second order bracket angulation was then increased at a rate of 0.045

degreedsec (2.70 degreedminute) up to a maximal angular displacement of 6.00 degrees

and then was reversed and was decreased at a rate of 0.045 degreeskec (2.70

degreedminute) through to zero degrees. Speed D-shaped nickel-ti taniurn wire of cross-

sectional dimension 0.01 8 x 0.0 18" was used with Speed brackets. Six bracketkchwire

couples were sarnpled (N=6).

Series C.4.2: Following the above listed testing parameters, frictional resistance was

tested with conventionally shaped rectangular nickel-titanium archwires. These trials

were exactly the same as the previous protocol except that conventionally shaped

rectangular nickel-titanium archwires. Nickel-titanium wire of cross-sectional dimension

0.0 18 x 0.0 18" was used with Speed brackets. Six bracket/archwire couples were sampled

(N=6).

O. Frictional resistance evaluation of various orthodontic brackets and archwires with sliding mechanics using quantified simulation of canine retraction

A series of trials were perfomed to compare the frictional resistance of various

bracketlarchwire combinations using a canine retraction mode1 that experimentally

approximates complex dental movements.

Series D. 1 .O: Following the above listed testing parameters, fnctional resistance was

tested as a b c t i o n of dynarnic and progressive bracket tipping and uprighting concwent

with linear bracket traction. Displacement of the bracket relative to the archwire was

initiated with second order bracket angulation beginning to increasing afier 0.3 mm (1.5

min). Second order bracket angulation was then increased at a rate of 0.045 degreedsec

(2.70 degreedminute) up to a maximal angular displacement of 6.00 degrees and then

was reversed and was decreased at a rate of 0.045 degreeslsec (2.70 degreedminute)

through to zero degrees. Six bracketlarchwire couples were sampled for each

combination of orthodontic bracket type, orthodontic archwire alloy, and orthodontic

archwire dimension (N=6). Table 2 illustrates the 84 different possible combinations of

orthodontic bracket type, orthodontic archwire alloy, and orthodontic archwire dimension.

With 6 samples per combination a total of 504 fiction test were done.

Table 2. Combinations of bracket/archwire couples sampled for frictional force.

Assumptions were made based on the mechanical parameters involved to facilitate

testing and provide meaningfùl analysis of data. These assumptions are listed as follows:

(1) Linear displacement rate was constant - Velocity of the test bracket relative to

the test wire was maintained at a constant rate. Although this does not

represent the clinical situation, this assumption simplified the static and

dynamic canine retraction models. However, the rate of tooth movernent

clinically is of such slow magnitude it c m be refmed to as being constant

(Kusy, 1989).

(2) Angular displacement rate was constant - Angular displacement of the test

bracket relative to the test wire was maintained at a constant rate. Although

this does not represent the clinical situation, this assumption simplified the

dynamic canine retraction model. However, the rate of tooth tipping clinicaily

is of such slow magnitude it can be refmed to as being constant.

(3) Angular displacernent was related directly to the test bracket slot - Angular

displacernent o f the test wire was referenced to the center of the long-axis of

the test bracket to represent orthodontie tipping. Placement of the rotational

axis within the test bracket slot allowed standardization of the bracket

mounting procedure and sufficiently approximates the clinical situation.

The following limitations should be recognized because in-vitro studies do not

represent the in-vivo situation. These limitations include the following:

(1) Nature of exact tooth movement during canine retraction using sliding

mechanics is unknown - Quantified analysis to accurately characterize the

nature of tooth movement during canine distalization has yet to be described.

The canine retraction models are only a representation of the clinical situation.

(2) Biological response of teeth - Simulation of the biological response of teeth

induced by orthodontie forces is not considered in the static and dynamic

canine retraction models.

(3) Testing environment - The in-vitro testing environment does not represent the

in-vivo situation. Factors such as saliva, acquired pellicle, and occlusal forces

are not considerpd in the static and dynamic canine retraction model.

ANALYSIS OF DATA

Estimates of fnctional resistance for each bracketkchwire couple for al1 trials

was detennined fiom an average of the kinetic fiictional resistance encomterd during

displacement of the bracket relative to the archwire. Evahation of kinetic fnctional

resistance was possible by achieving steady state displacement of the bracket relative to

the archwire. This occurred a h 0.3 mm (Kamelchuk, 1998). Subsequently,

displacement of the bracket relative to the archwire was another 2.0 mm. With data

sampling funftioning continuously at 2 sarnples per second, each trial yielded 534

mesures of the fictional force. The mean of these values were calculated to produce one

discrete estimate of the kinetic fnctional resistance of the bracket/archwire couple for

each trial.

A. Verification of function of frictional testing apparatus

Estimates for the level of .friction with the fiction testing apparatus were

established for the trials of static non-tipped angulation (zero degrees) and static tipped

angulation (ten degrees). Estimates for the level of friction with the fiction testing

apparatus were established for the trial of dynamic and progressive bracket tipping (up to

twenty degrees). These estimates were compared to established values from the

literature.

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of friction using static canine retraction models

A two-way analysis of variance (ANOVA) was performed to determine if the

static canine retraction models or archwire types were associated with different frictional

resistances during sliding mechanics. The level of statistical significance was set at

pC0.05 for the two-way ANOVA.

(2) Cornparison of friction using static and dynamic canine retraction rnodel

A one-way analysis of variance (ANOVA) was performed to compare the

fictional resistance of a dynamic canine retraction model that experimentally

approximates complex dental movements with static canine retraction models. The level

of statistical significance was set at p<O.OS for the one-way ANOVA. Duncan's multiple

range test was perfonned to detemine which groups were significantly different. The

level of statistical significance was set at pc0.05 for the Duncan's multiple range test.

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of effect of sliding velocity on friction using dynamic canine retraction model

A one-way analysis of variance (ANOVA) was performed to compare the effect of

speed on the fi-ictional resistance of a dynamic canine retraction model. The level of

statistical significance was set at p<0.05 for the one-way ANOVA. Duncan's multiple

range test was perfomed to determine which groups are significantl y different. The level

of statistical significance was set at p<0.05 for the Duncan's multiple range test.

(2) Comparison of effect of initial pre-drawing of the archwire on friction using dynamic canine retraction mdel

A paired T-test was performed to determine if initial pre-drawing of the archwire

affected the fictionai resistance for a dynamic canine retraction model. The level of

statistical significance was set at p<O.OS for the two-tailed T-test.

(3) Comparison of effect of saliva with braided/twisted archwires on friction using dynamic canine retraction malel

Paired T-tests were performed to determine if speed of retraction affected the

frictional resistance of braidedltwisted archwires for a dynamic canine retraction model.

The level of statistical significance was set at p<O.OS for the two-tailed T-test.

(4) Comparison of effect of Smd-D archwires with Speed brackets on friction using dynamic canine retraction model

Paired T-tests were peiformed to determine if Speed D-shaped archwires affected

the fictional resistance with Speed brackets comparecl to conventionally shaped

rectangular archwires for a dynamic canine retraction model. The level of statistical

significance was set at p<0.05 for the two-tailed T-test.

D. Frictional resistance evaluation of various orthodontic brackets and archwires with sliding rnechanics using quantified simulation of canine retraction

Multiple analysis of variance (ANOVA) with general linear models procedure was

performed to determine if the orthodontic bracket type, orthodontic archwire type,

orthodontic archwire size, and orthodontic archwire shape, including pair-wise

interactions of these factors were associated with different fnctional resistances during

sliding mechanics using a dynamic canine retraction model. The level of statistical

significance was set at p<O.OS for the four-way ANOVA.

Duncan's multiple range tests were performed to determine significant intra-group

differences in the frictional resistances during sliding mechanics using a canine retraction

model associated with the following group of factors: orthodontic bracket type,

orthodontic archwire type, orthodontic archwire size, and orthodontic archwire shape.

The level of statistical significance was set at p<0.05 for the Duncan's multiple range test.

Pair-wise interaction effects were tested by Least Square Means table for

significant differences in the mean values of fictional resistance during sliding

mechanics using a dynamic canine retraction model. The level of statistical significance

was set at pcO.05 for the Least Square Means test.

RESULTS

A. Veritication of function of friction testing apparatus

A series of trials was perfonned to vent) linear motion control with quantification

of fnctional resistance via digital data acquisition for the fiction testing apparatus as a

function of static non-tipped bracket angulation (O0). Afier the static friction was

overcome, a consistent level of kinetic fnction could be seen throughout the trial (Figure

1). The fnctional force was between 80 to 1 10 grams.

I 0.0 0.2 0.4 0.6 0.8 1 .O 1.2 1 -4 1.6 1.8 2.0

Matance (mm)

Figure 1. Frictional resistance as a function of non-tipped static bracket angulation (O0).

The next series of trials to veriG linear motion control with quantification of

frictional resistance via digital data acquisition for the fiction testing apparatus was

perfomed as a function of static tipped bracket angulation (10"). After the static friction

was overcome, a consistent level of kinetic fnction could be seen throughout the trial

(Figure 2). The fiictional force was between 160 to 2 10 grams.

I O 0.2 0.4 0.6 0.8 1 .O 1.2 1.4 1 -6 1.8 2.0

Distance (mm)

Figure 2. Frictional resistance as a function of tipped static bracket angulation (IO0).

The third series of trials was performed to verifi angular motion control and

temporal integration of linear and angular control with quantification of fictional

resistance via digital data acquisition for the fnction testing apparatus as a fùnction of

dpamic bracket angulation (O0 up to 20'). AAer the static fnction was overcome,

initiaily the level of fnction was between 80 to 1 10 grarns but started to steadily increase

as the second order angulation of the bracket increased (Figure 3). The level of kinetic

fnction reached a plateau that coincided with the second order angulation of the bracket

coming to its maximum of 20". The level of fnction at this tirne was 250 to 300 grams.

O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Distance (mm)

O 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Distance (mm)

Figure 3. Fnctional resistance as a function of dynamic and progressive bracket tipping (O0 up to 1 OO).

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1)Comparison of friction using static canine retraction models

Friction for the straight-line canine retraction models is summarized in Table 3

and graphically represented in Figure 4. Stainless steel archwires had 89.2 grams of

fictional resistance with the static non-binding model and 130.5 grams for the static

binding model. This meant the binding model had over 46% more friction than the non-

binding model for stainless steel wires. Nickel-titanium wire displayed 98.1 grams for

fiction with the non-binding model, and about a 10% greater level of Wction for the

binding model at 1 08.3 grams.

Table 3. Mean Wctional force and standard deviation of the trials according to static canine retraction mode1 and archwire type.

- -

RETRACTION WIRE N FORCE ST. DEV. MODEL (grams)

Static, Non-binding, O0 stainless steel 6 89.2 17.4

Static, Binding, 6' stainless steel 6 130.5 9.6

Static, Non-binding, O0 nickel-titanium 6 98.1 10.6

Static, Binding, 6' nickel-titanium 6 108.1 10.0

ANOVA: retraction model: F=25.854, d.f.= 1, p<0.00 1

wire type: F= 1 320, d. f.= 1, p=O. 192 retraction model'wire type: F=9.683, d.E= 1, p=0.005

Multiple analysis of variance (ANOVA) with general linear models procedure

illustrated the effects of the canine retraction model and wire type on the friction

outcorne. First of all, the canine retraction model was found to have a significant effect

on the level of fiiction (p<0.0001). Moreover, wire type had no significant effect on

friction (W. 192). More importantly, the interaction effect of canine retraction model

combined with wire type had a significant detemination for the frictional resistance

(p=0.005). This illustrates that the frictional resistance is significantly dependent on the

canine retraction model, but also on the combination of canine retraction model with

archwire type.

Figure 4. Mean fiictional force of the trials according to static canine retraction model and archwire type. While stainless wires have less friction than nickel-titanium wires with the non-binding retraction rnodel (O degrees), stainless wires have more friction than nickel-titanium wires with the non-binding retraction model (6 degrees). ANOVA ( ~ ~ 0 . 0 5 ) shows that the retraction model causes this significant difference in the level of fiction for the archwires.

(2) Cornparison of friction using static and dynamic canine retraction rnodek

The three canine retraction models exhibited different fiction characteristics as a

function of bracket tip. Examples of a typical trial for each of the different canine

retraction models are graphically shown in Figures 5, 6, and 8. in Figure 5, the static

non-binding canine retraction model (O0) displayed a relatively consistent level of fiction

as seen. Figure 6 showed the static binding retraction model (6') displayed a higher level

of fiction than the static non-binding canine retraction model (O0), but had more erratic

levels of fiction. The pattern of bracket tip for the dynamic canine retraction model is

represented by one tippingfuprighting cycle of 6" (Figure 7). The dynamic canine

retraction model revealed variable levels of fiction dependent on the bracket tip (Figure

8). When the bracket tip was below 4', the pattern of fiction, as well as the amount of

Wction, was similar to the static non-binding retraction model (O0). Above 4', the level

of fiction rose with increasing second order tip. At the maximum tip of 6 O , the level of

fiction was at its greatest and approximated the amount of tnction for static binding

retraction model (64.

Analysis of the mean fictional resistance as a product of canine retraction model

is surnmarized in Table 4 and graphicdly represented in Figure 9. The static non-binding

model had the least çiction with a mean of 89.2 grams, whereas the static binding model

demonstrated the most friction at a mean of 130.5 grams. The binding retraction model

had 30% more friction compared to the non-binding model. An intemiediate level of

fiction was seen with the dynamic tippinghprighting model with a mean frictional force

of 11 1.7 grams. ANOVA showed a statistically significant difference in the mean levels

of fiction for the canine retraction models (p=0.001). Specifically, Duncan's multiple

range test found that the static canine retraction models were significantly different fiom

each other (p<O.OS). However, the dynarnic canine retraction model was not significantly

different fiom the static non-binding retraction model (p>0.05) or fiom the static binding

retraction model (p>0.05).

Figure 5. Frictional resistance for a trial illustrating static non-binding canine retraction model (O0 tip).

u

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

DSTANCE (mm)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

WTANCE (mm)

'igure 6. Fnctional resistance for a trial illustrating static binding canine retraction model (6' ti p).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

~aurcs (mm)

Figure 7. Tiplcounter-tip cycle for the dynamic canine retraction model illustrating angular displacement as a hnction of distance.

iI

I Figure 8. Fnctional resistance of a trial illustrating dynamic tippinglupnghting canine retraction model (O0 to 6' tip to O0 counter tip).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

DISTANCE (mm)

Table4. Mean fnctional force and standard deviation of the trials according to retraction model.

- - - - - - -

RETRACTION N FORCE ST. DEV. DUNCAN'S MODEL (grams) GROUP

Static, Non-binding, 0' 6 89.2 17.4 A

Static, Binding, 6 O 6 130.5 9.6 B

Dynarnic, 0'-6"-O0 6 11 1.7 14.3 A B

ANOVA: F= 12.78, d.K= 17, p=0.001 Duncan's groups: p<0.05

Figure 9. Mean fnctional force of the trials according to retraction model. Duncan's groups ( ~ ~ 0 . 0 5 ) show the significant differences between retraction models.

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of effect of sliding velocity on friction using dynamic canine retraction model

Table 5 surnrnarizes the mean fiictional force for four different sliding velocities

for the dynamic canine retraction model. Figure 10 also highlights the mean fiictional

force for the four d i f i e n t sliding veIocities for the dynamic canine retraction model.

These speeds were over a magnitude of ten-fold. While no statistically significant

difference for sliding velocity was evident (F=1.475; d.f.=3,20; p=0.252), there was a

trend demonstrating that the fictional resistance was slightly less at higher speeds. For

0.45 mm/min the fictional force was at highest with a mean of 1 1 1.7 grams. The lowest

fiictional force was at 4.5 mm/min with a mean of 94.1 grams.

Table 5. Mean fictional force and standard deviation of the trials according to sliding veloci ty.

SLIDING N FORCE ST. DEV. DUNCAN'S VELOCITY (grams) GROUP

ANOVA: F= 1.47, d.f.=23, ~ 0 . 2 5 2 Duncan's Group: p<0.05

0.90 2.25 Sliding Velocity (mrnhnin)

Duncan's groups

Figure 10. Mean fnctional force of the trials according to sliding velocity. Duncan's groups (p>0.05) show that there is no significant difference between mean sliding velocity.

(2) Cornparison of effect of pre-drawing of the archwire on friction using a dynamic canine retraction mode1

The mean fnctional force for the dynamic canine retraction mode1 as a fiinction of

initial pre-drawing of the archwire is summarized in Table 6 and also highlighted in

Figure 1 1. Without pre-drawing the archwire the fi-ictional force was measured at 1 1 1.7

grams. With pre-drawing the archwire the fictional force was 108.8 grams. No

significant effect was seen by initially pre-drawing the archwire through the ligated

bracket (T-test=0.420, d.f.= 1 O, p=0.683).

Table 6. Mean fictional force and standard deviation of the trials according to pre- drawing of the archwire.

PRE-DRAWING N FORCE (grams) ST. DEV.

No

Yes

No Yes

Pre-drawing

Figure 11. Mean fnctional force of the trials according to pre-drawing of the archwire. T-test (p0.05) shows that there is no significant difference whether or not pre-drawing is done.

(3) Cornparison of effect of saliva with braided/twisted amhwires on friction using dynamic canine retraction model

Results for the effect of hurnan saliva on braided!twisted archwires are listed in

Table 7. These results are represented graphically in Figure 12. The 0.01 75" twisted

stainless steel wire had 98.4 grams of friction without saliva compareci to 103.3 gram

with saliva. This difference was not significant (T-test=-0.633, d.E=lO, p=0.541). For

0.018 x 0.025" braided stainless steel the level of fnction was 135.8 grarns in the dry

state and 127.0 grams in the wet state. T-test revealed that saliva had no statistically

significant difference between these two groups (T'-test= 1.052, d.f.= 1 O, p=0.3 18). With

0.01 8" twisted nickel-titanium, the presence of saliva reduced the level of fnction to 84.8

grams down fiom 97.5 grams. However, there also was no difference in fiction when

saliva was introduced for this wire (T-test= 1.642, d. E= 1 O, p=O. 1 32).

Table 7. Mean frictional force and standard deviation of the trials according to saliva.

ARCHWIRE WET N FORCE (grarns) ST. DEV.

0.0 175 twisted SS No 6 98.4 9.0

0.0 175 twisted SS Yes 6 103.3 16.5

0.0 1 8 x 0.025 braided SS No 6 135.8 14.3

0.0 18 x 0.025 braided SS Yes 6 127.0 14.5

0.01 8 twisted NiTi No 6 97.5 15.1

0.0 1 8 twisted NiTi Yes 6 84.8 11.6

T-Test:0.0 175 twisted SS: t= -0.633, d.f.= 1 O, p=OH 1 0.01 8 x 0.025 braided SS: H.052, d.f.40, p=0.3 18 0.01 8 twisted NiTi: t=l.642, d.f.=l O, p=O. 132

Figure 12. Mean frictional force of the trials according to saliva. T-test (p>O.OS) shows that there is no significant difference with saliva for any of these archwires.

(4) Cornparison of effect of Speed-D archwires with Speed brackets on friction using dynamic canine retraction madel

The mean fnctional force and standard deviation of the trials with Speed bracket

according to archwire type are Iisted in Table 8. The means are also highlighted in

Figure 13. The amount of fiction with the conventionally shaped nickel-titaniurn wire is

50.8 grams. Use of Speed-D shaped wire caused minimal change in the level of friction

to 52.0 grarns. This difference between the fiction with these two archwires being used

with the Speed brackets is not statistically significant (T-test= 1.052, d.f.=l O, p=0.3 18).

Table 8. Mean fiictional force and standard deviation of the trials with Speed brackets according to archwire type.

ARCHWIRE TYPE N FORCE (grams) ST. DEV.

Figure 13. Mean fnctional force of the trials with Speed brackets according to archwire type. T-test (pz0.05) shows that there is no significant difference between conventionally shaped and D-shaped nickel-titanium wires.

O. Frictional resistance evaluation of various orthodontic brackets and archwires with sliding mechanics using quantified simulation of canine retraction

With six different brackets and fourteen different archwires, 84 bracketkuchwire

combinations were tested six times, leading to a total of 504 trials using the dynamic

canine retraction model. The calculated fnctional force for each trial is sumrnarized in

Tables 26 to 3 1 according to bracket type (Appendix D). The mean fnctional force (and

standard deviation) for each orthodontic bracket/archwire combination is presented in

Table 9, with Figure 14 graphically showing the mean fictional force.

Table 9. Mean fictional force and standard deviation of the trials for each bracket according to archwire combination.

WIRE TYPE

stainiess steel

stainless steel

stainless steel

stainless steel

WlRE SIZE

0.0 18

0.020

FORCE (and S.D.) DU GRAMS FOR EACH BRACKET TYPE

nickel-

METAL

49.2 (9.2) 60.9

0.0 18~0.025

0.02 1~0.025

nickel- titaniurn twisted stainless steel twisted staidess steel braided stainiess steel braided stainless steel twisted nickel- titanium twisted nickel- ti tanium

0.0 18

CERAMlC

75.9 (9.8) 102.9

(8.9) 111.7

(14.3) 140.7

0.02 1~0.025

0.0 175

0.0195

0.0 18~0.025

0.02 1~0.025

0.0 18

0.020

(20.7) 1 (19.4) 69.2 53.2

CERAMICI METAL SLOT

92.8 (15.9)

95.4 (2.8) 150.1

(14.6) 180.1

132.9 (12.1) ,

98.4 (9.0) 104.1 (8.2) 135.8

(14.3) 164.8

(16.6) 97.5

(15.1) 133.3

(28.5)

(14.3) 68.0

SELF- LlCATlNG

ACTIVE

11.2 (6.6) 54.1

(1 5.7) 111.4

(1 2.6) 141.0

109.8 (21.8) 123.1

(1 7.2) 129.1

(15.1) 129.9

(24.0) 173.3

(15.6) 100.4

(14.3) 124.9

(37.1)

( 16.8) 16.5

SELF- LICATING PASSIVE

2.3 (1.0)

5.1 (8.4) 119.2

(2 1.7) 165.6

109.3 (1 8.2) 144.7

(1 7.8) 128.3

(1 5.1) 146.1

(1 2.3) 171.4

(24.5) 81.1

(14.5) 96.6

( 1 7.4)

SELF- LIGATING VARIABLE

4.9 (2.8)

7.6

( 12.7) 3.3

(1.8) 13.1

(1 1.2) 54.8

(1 8.4) 1.1

99.3 (13.2)

2.6 (1.2) 33.0 (6.0) 73.6

(13.1) 80.6

(1 3.2) 13.2

(10.1) 47.2

(12.1)

(2.9) 27.8 (9.2) 62.8

12.4 (4.8)

3.6 (1.5)

3.5 . (1.2)

3.5 (1.6) 13.5

(3.9) 1.4

(0.5) 3 .O

(0.6)

62.6 (19.9)

0.7 (0.6)

3.0 (1.6)

3.6 (3.5) 35.9

(15.0) 0.3

(0.2) 1.8

(0.7)

I Figure 14. Mean frictional force for each bracketkchwire combination.

The mean fnctional force for the orthodontie bracket/archwire combinations

ranged from a low of 0.3 grams up to a high of 180.1 grarns. The lowest fnction was

encountered with variable self-ligating brackets using 0.018" round twisted nickel-

titanium wire, while the greatest fiction occurred with cerarnic brackets engaging 0.21 x

0.025" rectangular stainless steel archwires.

Multiple ANOVA using general linear models procedure demonstrated significant

effects ( ~ ~ 0 . 0 5 ) for bracket type, archwire type, archwire size, and archwire shape, as

well as pair-wise interactions for bracket typelarchwire type, bracket typekchwire size,

bracket typelarchwire shape, archwire typelarchwire size, archwire typehrchwire shape,

and archwire sizelarchwire shape (See Appendix E for statistical analysis output). These

pair-wise interactions indicated that the fnctional characteristics differed either in

direction or magnitude of effect for one of the factors depending on the specific

combination.

For the orthodontic brackets the mean frictional force is presented in Table 10

and Figure 15. Ceramic brackets with and without a metal dot similarly had the

significantly highest fiction of al1 the bracket types, having 1 14.4 grams and 1 15.9 grarns

respectively. Meta1 brackets at 104.4 grarns of friction followed this. Much lower were

the active ligation brackets at 65.2 grams. Even lower were the variable ligation brackets

with only 19.0 grams of friction and the passive ligation brackets with a mere 10.5 grams

of fiction. These brackets were significantly different from the ceramic brackets and

from each other.

Table 10. Mean frictional force and standard error of the trials according to bracket type.

BRACKET TYPE N FORCE ST. ERROR DUNCAN'S b a r n s ) GROUP (p<0.05)

Ceramic 84 1 15.9 3.8 A

Ceramic/metal 84 1 14.4 4.4 A

Meta1 84 104.4 3.5 B

Active self-ligation 84 65.2 5.1 C

Variable self- 84 19.0 1.5 D ligation

Passive sel f-ligation 84 10.5 2.5 E

I 1 ceramic ceramici metal variable passive

1 metal self-Iigath self-ligation / self-ligation

Figure 15. Mean fiictional force according to bracket type. Duncan's groups (p<0.05) show the significant diffaences between bracket types.

For the orthodontic archwires the fiction is summarized in Table 11 and Figure

16. Stainless steel wires had 76.7 grams of friction and twisted stainless steel wires had

79.4 grams. These wires did not differ statistically, but displayed significantly much

greater friction than nickel-titanium wires of similar size and shape. The nickel-titanium

wires had a mean fnctional force of 58.6 grams.

Table 10. Mean fiictional force and standard error of the trials according to archwire M"Y-

BRACKET TYPE N FORCE ST. ERROR DUNCAN'S (grams ) GROUP (p<O.OS)

Twistedhraided SS 1 44 79.4 4.7

Stainless steel 1 44 76.7 3.5

Nickel-titanium 1 44 58.6 5.4

I twisted/braided SS stainless steel nickel-titanium

Figure 16. Mean fnctional force according to archwire type. Duncan's groups (p<O.05) show the signi ficant di fferences between archwire types.

The values for friction with round wires only are in Table 12 and Figure 17. If

round twisted nickel-titanium wires were included for cornparison with the other types of

archwires, the highest level of fiiction was with twisted stainless steel wires (64.5 grams)

and twisted nickel-titanium (58.4 grams). Stainless steel (46.9 grarns) and nickel-

titaniwn (41.6 grarns) exhibit the lowest level of friction for the round wires.

Table 11. Mean fnctional force and standard error of the trials according to archwire type for round wires.

BRACKET TYPE N FORCE ST. ERROR DUNCAN'S (grams) GROUP (p<0.05)

Twistedhraided SS 84 64.5 4.6 A

Twisted NiTi 84 58.4 3.8 A

Stainless steel 84 46.9 7.0 B

Nickel-titanium 84 41.6 6.2 B

I twistedbraided SS twisted NiTi stainless steel nickel titanium Duncan's groups * 9

(P<O=W A B* Figure 17. Mean fnctional force according to archwire type for round wires. Duncan's groups (p<0.05) show the significant differences between archwire types.

Consideration of the size of the orthodontie archwires illustrateci that the larger

dimension wires had significantly more fiction than the wires of smaller dimension

(Table 13 and Figure 18). The smaller wires with cross-sectional diameters of 0.0 175",

0.018" or 0.018 x 0.025" had a mean level of friction of 61.9 grams. The larger

dimension wires compriseci of cross-sectional dimensions 0.0195", 0.020" or 0.02 1 x

0.025" had a mean level of fnction of 8 1.2 grams.

Table 13. Mean fictional force and standard error of the trials according to archwire size.

ARCHWIRE SIZE N FORCE ST. ERROR DUNCAN'S (grams) GROUP (p<0.05)

Smalf 288 61.9

Large 216 81.2

--- . small

Duncan's Groups A

large a B

Figure 18. Mean frictional force according to archwire size. Duncan's groups (p<0.05) show the significant diffaences between archwire sizes.

A significant increase in frictional resistance was reported to occur when

changing fiom a comparable sized round archwire to a rectangular archwire, for exarnple

0.0 18" to 0.01 8 x 0.025" or 0.020" to 0.020 x 0.025" (Table 14 and Figure 19). Round

wires had 5 1 .O gram of fiction, while the rectangular wires had 92.2 grarns of friction.

The ratio of fiction for round wires to rectangular wires was nearly double.

Table 14. Mean frictional force and standard error of the trials according to archwire size.

-- - - - - - - -

ARCH WIRE SIZE N FORCE ST. ERROR DUNCAN'S ( g r a m GROUP (p<0.05)

Round 388 51.0

Rectangular 216 92.2

1 Duncan's

round a

rectangular a

1 Groups A B

Figure 19. Mean fiictional force according to archwire shape. Duncan's groups @<O.OS) show the significant differences between archwire shapes.

Table 15 serves to summarize the rank order of fiction for each factor that cm

influence the fictional resistance of the various brackets and archwires tested with the

dynamic canine retraction model.

Table 15. Rank order of fiction for each factor as detemined by Duncan's multiple range test.

I l - --

Archmre type twisted SS = SS > NiTi

Bracket type

For round wires:

twisted SS > twisted NiTi > SS > NiTi

Rank order of friction determined by Duncan's multiple range test (from high to low).

C / M = C > M > A > V > P

( Archwire size 1 large > mal1 I

- ceramic brac kets; M - metal brackets; A - active self-ligating brackets; V - variable self-ligating brackets; twisted SS - twisted stainless steei wires; SS - stainless steel wires; NiTi - nickel-titanium wires; twisted NiTi - twisted nickel-titanium wires; srna11 - 0.0 18" or 0.0 18~0.025" wires; large - 0.020" or 0.02 x0.025 wires; round - 0.0 18" or 0.020" wires; rect - 0.0 1 8x0.02S1* or 0.02 1 x 0.025" wires.

Archwire sbap

Exceptions to some of the general trends for fnction encountered with orthodontic

rect > round

brackets and archwires were indicated by statistically significant interaction of pair-wise

Note: Abbreviations used in the table are defhed as follows: C/M - ceramic brackets with metal slots; C

evident from Least squares mean tables. These are summarized in Table 16.

Table 16. Significant interactions of pair-wise factors for level of fiction as detemined by Least Squares Mean Tables.

Bricket type

Arcbwire m e

C/M,C,M: a twisted SS>SS A,V:

twisted SS<SS a twisted SScNiTi P:

twisted SS=NiTi M,V:

SS=NiTi

For round wires:

C/M,A,V,P: twisted NiTi=SS

M: twisted SS= twisted NiTi

P:

Archwire size Archwire shape

A,V,P: no sig. interaction large»srnall effects

rect»round r e c ~ r o u n d

Archwire size small :

CM* V=P C/M,C,M>>A,V,P

large: a C/M,C,M>>A,V,P

small: twisted SS>SS

large: rec~>round

vi - ceramic brackets wit

rec t: C/M<C

a C/M,C=M a C/M,C,M»A,V,P round: c/Mx V=P

O C/M,C,M»A,V,P

round: O twisted S S S S rect: a twisted S S 4 S

rect: a large»sdl

brackets; M - metal brackets; A - active self-ligating brackets; V - variable self-ligating brackets; twisted SS - twisted çtainless steel wires; SS - stainlesç steel wim; NiTi -wires; twisted NiTi - twistd nickel-titanium wires; small - 0.018" or 0.018xO.OZS" wires; large - 0.020 or 0.02 x0.025 wircs; round - 0.018" or 0.020" wires; rect - 0.01 8~0.025" or 0.02 1 x 0.025" wires.

First of dl , bracketkchwire interactions revealed the following observations for

performance of the orthodontie brackets with specific archwires. It had been noted that

overall fictional performance of cerarnic brackets with and without a metal slot are

similar, but signi ficant di fferences existed when these brackets were coupled with various

archwire types. Specifically, ceramic brackets had a significantly higher level of fiction

compared to ceramic brackets with a metal insert when coupled to stainless archwires

(p=0.0011) but a significantly lower level of friction when coupled to nickel-titanium

(p=0.000 1 ) or twisted stainless steel @=0.0272). Typicall y, metal brackets had less

fnctional resistance than ceramic brackets with and without metal slots. However, metal

brackets did not exhibit significantly different levels of fnction compared to metal slotted

ceramic brackets in conjunction with nickel-titanium wires @=0.0845), whereas metal

brackets dmonstrated more fiiction than ceramic brackets when coupled with nickel-

titanium wires (p=0.0001). Metal brackets also typically experienced more fnction than

brackets with an active ligation mechanism, but when coupled with stainless steel

archwires no diffaence with regards to fiiction occumed between these two brackets

e0 .4339) . Similady, fiiction with stainless steel or twisted stainless steel archwires was

not statistically different with brackets that had variable or passive ligation (p=0.0788 and

p=0.23 10, respectively). With round twisted nickel-titanium wires, ceramic and metal

brackets did not have significantly different friction effects (p=0.5750), but both of these

brackets had significantly more fiction than ceramic brackets with a metal slot

@=0.0001). Additionally, variable and passive self-ligating brackets did not have

diffaent levels of fnction when coupled with round twisted nickel-titaniurn wires

@=O. 8 1 93).

Secondly, for individual brackets comparison of the rank order for fictional

resistance of some of the wires varied fiom the general trend. For example, twisted

stainless steel wires had more fiction than stainless steel wires when coupled with

ceramic brackets with (p=0.0001) and without a metal slot @=0.0034) or with metal

brackets (p=0.0001), whereas twisted stainless steel wires had much less fiiction than

conventional stainless steel wires with brackets that had active or variable self-ligation

(p=0.0001). In addition, twisted stainless steel wires had less friction than nickel-

titanium wires with brackets that had active ligation (p=0.0008), while these two wires

had similar levels of fnction with passive ligating brackets @0.8851). Stainless steel

archwires had no statistically significant difference in fiiction fiom nickel-titanium

archwires for metal brackets (p=0.000 1 ) and brackets that had variable ligation

(p=0.0002). Consideration of round twisted nickel-titanium wires revealeâ that these

wires did not have significantly different fnctional effects than round stainless steel wires

for ceramic brackets with metal dots (p=0.2875), and al1 self-ligating brackets (p0.05).

Al1 of the self-ligating brackets also did not have significantly different levels of fnction

for round twisted nickel-titanium wires compared to round nickel-titanium wires

(p0.05). For metal brackets, round twisted nickel-titanium wires had more fnction than

round twisted stainless steel wires @=0.0041), but for passive and variable self-ligating

brackets no diffaence between these two wires were noted (p>0.05).

Next, bracketkchwire size interaction found that with ceramic brackets versus

ceramic brackets with metal slots, smaller dimension wires had less fiiction @=0.0163).

Overall, brackets with variable ligation had more fiction than brackets with passive

ligation, but with smaller archwires no significant difference in fiction was noted

Q~0.2598). Additionally, al1 of the self-ligating brackets demonstrated much less

fiictional resistance than metal brackets and cerarnic brackets with and without metal

slots with smaller dimension archwires. With larger dimension archwires, only self-

ligating brackets with variable or passive ligation had much less friction than the other

brackets.

The interaction effect of bracket and archwire shape showed a strong tendency for

al1 self-ligating brackets to have much less fiction with rectangular than with round

wires. Other specific bracketjshape interactions have been noted. First, rectangular

archwires in metal brackets did not have statistically significantly different fiction than

with ceramic brackets with @=0.5879) or without metal slots @=0.0529), whereas the

general trend had shown ceramic brackets to have more fnction than metal brackets.

Secondly, while variable ligation brackets typically have more fnction than passively

ligated brackets, the fnctional performance was the same with round archwires

(p=0.9 197). Third, opposite effects occurred between cerarnic brackets with and without

a metal slot for the two shapes of wires. Next, round wires had more fiiction with metal

slotted ceramic brackets compared to regular ceramic brackets (p=0.0134), while

rectangular wires had iess fnction with metal slotted ceramic brackets compared to

regular ceramic brackets (p=0.0006). Finally, rectangular archwires exhibited vastly

decreased fictional resistance with variable and passive self-Iigating brackets compared

to the other brackets, and round archwires had much less fiction with al1 of the self-

ligating brackets compared to the other brackets.

A significant interaction effect for smaller dimension archwires occurred

depending on archwire type. Specifically, small stainless steel archwires had significantly

less fnction than twisted stainless steel wires (p=0.0005).

The combination of archwire type and archwire shape had significant interactions

leading to opposite effects between stainless steel and twisted stainless steel archwires

dependent on wire shape. Overall, stainless steel and twisted stainless steel archwires had

similar levels of fiction. However, with rectangular wires, stainless steel wires had more

fiction than the twisted stainless steel wires (p=0.0001), whereas round wires exhibited

less fnction with stainless steel wires than twisted stainless steel wires (p=0.0001).

Additionally, rectangular stainless steel wires and nickel-titanium wires had significantly

much larger values for fnctional force compared to round wires.

The combination of archwire size and shape showed exceptionally greater

frictional resistance for larger dimension rectangular wires compared to smaller

dimension rectangular wires by a factor of nearly two-fold @=0.0001). As well, larger

wires had more friction with rectangular wires than round wires (p=0.0001).

Because of the signi ficant interactions between archwire type and bracket type,

selection of specific archwires to couple with specific brackets will have less fiiction

(Table 1 7). For example, the most efficient couples are either the Darnon S L passive self-

ligating bracket with either nickel-titanium or twisted stainless steel archwires or the

Time variable self-ligating bracket with twisted stainless steel archwires. Next is the

coupled archwirehracket combination of the Speed active self-ligating brackets with

twisted stainless steel wires. The most efficient archwires coupled with conventionally

ligated brackets have much greater fiction than archwires coupled with self-ligating

brackets. But of the conventional ligating brackets, the most efficient couple is the

Transcend ceramic bracket with nickel-titaniurn archwire. Against metal sliding surfaces,

the Clarity metal-slotteà ceramic bracket or the Victory metal bracket nickel-titanium is

most efficient. As well, stainless steel wires coupled with the metal bracket performed as

well as the nickel-titanium wire.

Table 17. Rank order of most efficient bracketkchwire couples according to bracket type as detemiined by Least Squared Means table (p<0.05) ranked fiom low to high.

- -

Rank 1 Bracket type / ~ c h w i r e type / Force (grnms)

1 1 variable self-ligation / hKisted stiinless steel

-- - - - -

1 j passive self-ligation !

2 / active self-ligation 1 twisted stainless steel 1 47.4

pp

nickel-titanium twisted stainless steel

l I 3 1 ceramic nickel-titaniurn , 77.1

4 1 ceramic/metal slot / nickel-titanium ! 90.0 - - - - -

stainless steel nickel-ti tanium

DISCUSSION

A. Verification of function of friction testing apparatus

The first part of the project served to veriG function of the friction testing

apparatus.

Verification of linear motion control with quantification of fiictional resistance

via digital data acquisition was tested as a function of static non-tipped and tipped bracket

angulation. With the static non-tipped trials the normal force of friction is induced by the

ligation of the archwire into the bracket slot. These trials displayed a relativel y consistent

level of kinetic fiction. The level of fiction fell between 80 to 1 10 grams for a metal

bracket coupled with a 0.018 x 0.025 stainless steel archwire. Taylor and Ison (1996)

reported similar levels of fnction that range from 80 to 102 grams.

Increasing the second order angulation of the bracket relative to the archwire

caused tipping of the bracket to create another normal force of friction due to the binding

of the archwire with the walls of the bracket dot. The kinetic fnction increased to

approximately 160 to 2 1 O grams for the sarne bracketkchwire couple. The greater level

of fiction was anticipated because when binding of the bracket and archwire arises as a

second component to the resistance to sliding it is superimposed on the friction imparted

by the force of ligation (Articolo and Kusy, 1999). Agreement with the level of fiction

for the trials by Karnelchuk (1998) is noted. At ten degrees Kamelchuk (1998)

dernonstrated the level of friction to be 180 to 220 gram.

Verification of angular motion control and temporal integration of linear and

angular control with quantification of fnctional resistance via digital data acquisition was

tested as a function of dynamic bracket angulation. This revealed three distinct phases of

Wction that could be characterized as initial non-binding fiiction, progressive binding

fiction, and peak binding fiiction. Initially, as bracket traction and tip started there was

clearance of the archwire from the bracket walls. Since binding is not initially present the

only normal force contributing to fiction would be induced by ligation. The initial level

of kinetic friction nears the range of fiction for the static non-tipped trials fiom 90 to 1 I O

grams. As the archwire started to engage the edges of the bracket walls binding ensued

leading to the level of friction beginning to increase. The friction f5om binding was

added to the initial fnction fiom ligation. As the angulation increased firth= there was a

concomitant nse in the total level of fiction. As the bracket tip came to ten degrees, the

fiiction ranged nom about 140 to 2 10 grams. This level of fiiction is comparable to the

level of friction of the static tipped bracket angulation of ten degrees. When the bracket

angulation reached the maximum bracket tip of twenty degrees the level of fiction

peaked at a plateau in the range of 250 to 300 grams. As the bracket angulation increased

the friction steadily increased at a relatively constant rate. This phenornenon had

previously been reported by Sims et al (1994). Sims stated that increasing bracket tip

produced almost linear increases in fiiction. This fiiction testing apparatus was able to

achieve concurrent control of linear and angular bracket displacernent while

simultaneously acquinng fnctional resistance data with temporal integration. Validation

by comparison of fnction levels with external values report& in the literature for the

static canine retraction models justifies that the fnction testing apparatus is reporting

appropnate levels of friction. Verification by comparison of fiction levels with interna1

values derived fiom the static canine retraction models for the dynamic canine retraction

model justifies that the fiction testing apparatus is reporting appropriate levels of

friction.

The fiction testing apparatus will allow user specified cnteria for friction testing

of orthodontic bracket and archwire couples. More specifically, control of the testing

parameters can attempt to approximate in-vivo orthodontic tooth movement. Therefore,

quantified simulation of canine retraction by a dynamic bracket tippinghprighting model

will make fnctional resistance evaluation of various orthodontic brackets and archwires

more clinicall y relevant.

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Comparison of friction using static canine retraction moâels

The fnctional resistance increased as second order angulation of the bracket

inçreased for both stainless steel and nickel-titanium wires. Several authors have also

reported statistically significant greater fnction at increased second order angulations for

these wires (Frank and Nikolai, 1980; Peterson et al, 1982; Ho and West, 199 1 ; Kemp,

1 992; Weiss, 1 993; Dickson et al, 1994; Sirns et al, 1994; DeFranco et al, 1995; Articolo

and Kusy, 1999).

The higher fnctional resistance associated with increased second order angulation

has been ascribed to binding rather than classical fnction (Articolo and Kusy, 1999; Kusy

and Whitley, 1999; Zufall and Kusy, 2000). The binding component to the resistance to

sliding is superimposed on the invariant non-binding fiction (Articolo and Kusy, 1999).

The relationship between fnctional resistance and second order angulation may be linear

(Sims et al, 1994), but if the angulation increases too much notching of the archwire may

occur (Kusy and Whitley, 1999; Kusy, 2000; Articolo et al, 2000). So if the second order

angulation was to increase dramatically beyond the critical contact angle sliding

mechanics could actually cease because of this notching (Kusy and Whitley, 1999; Kusy,

2000).

Binding occurs when the contact angle (Proffit, 1993) between the archwire and

the bracket exceeds some critical contact angle (Kusy and Whitley, 1999). The critical

contact angle (0,) is a fùnction of the bracket width (width), bracket slot size (slot), and

wire size (size) and can be calculated as follows:

For a nominally sized 0.01 8 x 0.25" archwire engaged in a 0.022" slotted bracket

that is 0.14" wide, the critical contact angle would be less than 2 degrees. Binding would

then be dominant over non-binding fiction when the angle between the bracket and the

archwire was between a range of 3-7 degrees (Articolo and Kusy, 1999; Kusy and

Whitley, 1999). Previous investigators have studied the fnctional resistance due to

binding at 6 degrees of second order tip (Frank and Nikolai, 1980; Sims et al, 1994;

Articolo and Kusy, 1999; Kusy, 2000), which falls into this range.

While the resistance to sliding increases with second order angulation, the relative

efficiencies of particular materials fluctuate because of the inherent physicai properties of

the materials (Articolo and Kusy, 1999). At higher angulations, the wire stifniess and

cross-sectional dimension of the archwire becomes the dominant factor influencing

fnction (Frank and Nikolai, 1980). Many authors have substantiated that

bracket/archwire couples that consist of stainless steel wires have greater fictional

resistance than couples consisting of nickel-titanium for stainless steel brackets as well as

other brackets (Frank and Nikolai, 1980; Peterson et al, 1982; Ho and West, 199 1 ; Kemp,

1992; Dickson et al, 1994; Sims et al, 1994; DeFranco et al, 1995; Articolo and Kusy,

1999). This is thought to occur because binding is less important with nickel-titanium

wire compareci to stainless steel wire because of the increased flexibility (Frank and

Nikolai, 1980; Articolo and Kusy, 1999). This would explain why in this present study

when the bracket was subjected to six degrees of tip relative to the archwire it was shown

that the fiictional resistance for stainless steel wires increased by 41.3g, which was more

than 30%, compared to nickel-titanium wires that increased 10.0 g, or only about 10%.

The increase in fiction due to binding was nearly four times greater for the stainless steel

archwires relative to the nickel-titanium archwires. This led to a transposition of the

relative efficiencies of the wires. Simply put, at non-binding angulations stainless had

significantly less fnction than nickel-titanium, while at binding angulations stainless had

significantly more fnction than nickel-titanium. The principal reason for the change in

relative efficiency is the difference in the flexibility of the archwires (Frank and Nikolai,

1980). Not at al1 unexpectedly, the material stifiess number of stainless steel is nearly

four times that of nickel-titanium, with stainless steel qua1 to 1.00 and nickel-titanium

equivalent to 0.26 (Burstone, 198 1 ).

Multiple anaylsis of variance found significant effects on fictional resistance for

second order angulation but not for archwire type. More importantly, a significant

interaction effect for the combination of second order angulation and archwire material

was noted. This meant that it would be misleading to report the difference in fnctional

resistance for stainless steel and nickel-titanium using static canine retraction models.

In clinical orthodonties, fiction varies as the teeth being moved altematively tip

and upright during movement of the wire through the attachrnents (Ireland et al, 199 1).

Articolo and Kusy (1999) stated that prior to crown tipping, non-binding friction exists as

the only wmponent to the resistance to sliding (Figure 19). The normal force of fiction

is from the force of ligation. The static non-binding canine retraction mode1 represents

this. With root upnghting, binding arises as a second component to the resistance to

sliding superimposed on the non-binding friction (Figure 20). As the archwire and the

bracket edge engage binding creates another notmal force. The static binding canine

retraction model represents this.

Figure 20. Components of fiction prior to bracket tipping (above) and after bmcket tipping (below). Fnctional resistance (FR) impedes the force applied for sliding (F). The normal force (N) is induced by ligation of the archwire to the bracket and also by binding (NB,) when the archwire engages the bracket walls (Articolo and Kusy, 1999).

Clearly, static retraction models are remiss for estimation of fkictional resistance.

To tmly appreciate the total fictional force encountered with sliding mechanics, a model

that integrates the fiction at non-binding angulations with the superimposed binding at

higher angulations will be clinically more meaningfiil. Therefore, the nul1 hypothesis

(Ho(BI)) is rejected because the frictional resistance for static canine retraction models

varies as a function of bracket tip.

(2) Cornpanson of friction using static and dynamic canine retraction models

A dynamic canine retraction model was put forth to simulate orthodontic tooth

rnovement during sliding mechanics. Sliding mechanics initially allows tooth translation

by the coupled sequence of successive crown tipping then root uprighting (Figure 21)

(Nanda, 1997). Crown movement precedes the root apex resulting in tipping of the

bracketed tooth relative to the archwire. This tipping proceeds until the binding at the

bracketkirchwire interface restricts crown movement and creates a couple that uprights

the tooth, with the cycle of tipping and uprighting repeating itself (Drescher et al, 1989).

Figure 2 1. Sequence of canine movement during retraction with sliding mechanics illustrating tip-counter tip cycle (modified fiom Nanda, 1997). N is the normal force of fiiction due to ligation and f i s the fiictional force that which is resisting the direction of tooth movement.

The dynarnic canine retraction model proposed represents a first order

approximation of one tiplcountertip cycle of the in-vivo process (Figure 7). This dynamic

canine retraction model is intended to incorporate the friction induced by the normal

force of ligation prior to bracket tipping and the superimposed binding when bracket

tipping leads to engagement of the archwire with the bracket wall.

ANOVA showed that the levels of fÎiction associated with the canine retraction

models were not al1 the same. It was anticipated that the static canine retraction models

would be significantly different fiom each other because binding of the archwire with the

walls of the bracket is superimposed on the fiction prior to binding (Articolo and Kusy,

1999). However, the dynamic canine retraction model was not significmtfy different

fiom the non-binding static canine retraction model (p>0.05) or the binding static canine

retraction model (p0.05). This would not be unexpected since the dynamic model is

intended to incorporate the fiction fiom ligation with the static non-binding canine

retraction model with the superimposed bracket/archwire binding of the static binding

canine retraction model. If the dynamic canine retraction model were statistically

significantly different fiom one of the static retraction models, the level of friction would

be more profoundly induced by either binding or non-binding and not give a balanced

representation of tipping and upnghting of the bracket.

Closer inspection by way of superimposition of the graphical representations of

the exampfe trials for the canine retraction models (Figure 22) reiterated the point that the

dynamic model approximated the level of friction for the static non-binding mode1 when

the bracket tip was below 4' but with bracket tip greater than 4" the level of fiction

increased to the arnount displayed by the static binding model. For second order bracket

tips between 4 O and 6 O the frictional resistance increased and decreased relatively linearly.

I Figure 22. Superimposition of a trial for each retraction model illustrating fnctional resistance as a fùnction of archwire retraction with static or dynarnic bracket tipping.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

USTANCE (mm)

In-vitro fnction testing by Articolo and Kusy (1999) found that fiom O to 3

degrees the wire was in the passive configuration and not expenencing binding. At 3

degrees the binding component of fnction was first evident with the initiation of the

active configuration. Behveen 3 to 7 degrees binding equaled or exceeded classical

friction. This dynamic mode1 reflects the non-binding resistance to sliding and the

superimposed binding resistance to sliding seen by Articolo and Kusy ( 1999) depending

on the second order bracket tip. From Figure 23, which represents a typical trial with the

dynamic canine retraction model, it is evident that below 4 degrees binding is not

influencing the level of fnction, while at 4 degrees the fnctional resistance increases due

to binding.

This dynamic model that attempts to simulate in-vivo tooth movement will allow

a discrete value for the average kinetic fnctional resistance to be ascertained. The

obtained value integrates the binding and non-binding components of friction seen in-

vivo instead of dissecting the ccmponents into two separate discrete measures that have

limited clinical value.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 l . i 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

Distan- (mm)

O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

Distana (mm)

Figure 21. Frictional resistancc as a function of distance for a trial with dynarnic canine retraction model showing concurrent angular displacement as a function of distance.

However, the validity of atternpting to simulate in-vivo tooth movernent for

fictional resistance evaluation has been questioned by some researchers (Braun et al,

1999; Jost-Brinkmann and Miethkee, 199 1 ; O'Reilly et al, 1999). Braun et a1 (1 999) felt

that in a simulated model of the dynamic oral environment perturbations induced on the

archwire-bracket couple resulted in the fictional resistance to decrease by 98 to 100

percent. These minute perturbations between the archwire and bracket superimposed on

the coupled dental tipping and uprighting associated with sliding mechanics could be

introduced by various oral functions such as mastication, speaking, swallowing, tongue,

and cheek pressure. However, Braun et al (1999) did concede that the complicated

dynamics of the intraoral environrnents may not mean total reduction of the fiiction in

sliding mechanics because the frequency and coordination of perturbations would

unlikely occur simultaneously as the archwire moves through several in-line brackets.

Jost-Bnnkmann and Miethkee (199 1 ) argued that these perturbations or loadings would

be on teeth that demonstrate increased mobility and this would decrease friction in-vivo.

However, little is known about the magnitude of tooth mobility required to release

binding of the bracket and archwire with second order tipping (O'Reilly et al, 1999).

Other fiiction models have attempted to include some form of allowance for

tipping by using counterweights to simulate tooth movement (Drescher et al, 1989; Tidy,

1 989; Bednar et al, 1991 ; Tanne et al, 199 1 ; Omana et al, 1992). However, Sims et al

(1993) argued that models that allow uncontrolled tipping only partially simulate what

happens when a tooth is moved through the bone since only crown tipping is occuming

with no root uprighting.

No model for evaluation of fnctional resistance at present can perfectly reflect the

complexities of the intraoral environment. Moreover, assumptions and limitations for

such testing models do not necessarily handicap the testing or the quality of the results.

Relative cornparisons on the level of friction encountered in-vivo with various

bracketkchwire combinations are possible that is clinically meaningfbl if the friction

model attempts to simulate the complex nature of orthodontic tooth movernent. in

particular, integration of the classical fiction and binding that occur with tipping and

uprighting will include significant effects from the interaction of static second order

angulations and flexibility of the archwire.

Therefore, a dynamic canine retraction model for evaluation of the fiictional

resistance of various brackethrchwire combinations as a h c t i o n of integrated angular

and linear traction movernents concurrent with simultaneous data collection will allow

analysis of the relative resistance to sliding as an approximation of fiction in-vivo. This

means the nul1 hypothesis (Hdezl) is rejected because the fiictional resistance of a

dynamic canine retraction model that expenmentally approximates orthodontic tooth

movements differs fiom static canine retraction models.

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

This part of the project investigated parameters influencing data acquisition with

the dynamic canine retraction. These include the following factors: sliding velocity for

retraction, initial pre-drawing of the archwire relative to the bracket, presence of saliva

with braidedhvisted archwires, and use of Speed-D shaped wires with Speed brackets.

(1) Cornparison of effect of sliding velocity on friction using dynamic canine retraction model

The rate of retraction for experimental canine distalization was tested fiom a low

of 0.45 d m i n u t e up to 4.5 mrn/minute. This represents nearly 2 x 1o5 to 2 x 106 times

higher than the projected average constant rate of typical orthodontic tooth movernent

(Kusy and Whitley, 1 989). However, sliding velocities several magnitudes higher

experimentally than in-vivo facilitates conservation of time during experimentation.

While the classical laws of fiction ascertain that the frictional force is independent of the

sliding velocity (Jastrzebski, 1976), this law is sometimes not obeyed in orthodonties

(Kusy and Whitley, 1989). Therefore, erroneous friction values could possibly ensue

leading to invalid conclusions.

Previous investigations into the effect of sliding velocities by Kusy and Whitley

(1 989) and Ireland et al (1991) found fiction results for couples of stainless steel

brackets and archwires were independent of sliding velocity. As expected, results of this

study also found no statistically significant differences between the various rates of

retraction for the metal brackets and stainless steel archwires tested.

Kusy and Whitley (1 989) also reported nickel-titanium wires, in addition to the

stainless steel wires, were largely unaffected by changing sliding velocity over a range of

5.4 x 1 o4 to 1 O d m i n u t e . The pilot study p e r f o d by Ireland et a1 ( 199 1 ) varied the

cross-head speed of the Instron testing machine from 0.5 up to 50 mdminute. Ireland's

group used stainless steel and nickel-titanium wires witb stainless steel and ceramic

brackets with results showing no signifiant differences between speeds no matter what

combination of brackets or archwires was used.

Subsequent, fiction testing by Kusy' s group ( 1989,1990,1998,1999) employed a

sliding velocity of 10 mrn/minute. Ireland selected a speed of 5 d m i n u t e for

experimentation with the rationale that it was felt that higher speeds did not represent the

clinical situation. However, no M e r argument was made by Ireland to explain why it

would not be akin to the in-vivo environment. Dickson et al (1994) also employed 5

&minute a h an initial pilot study demonstrated that this speed produced the least

variable results for a given archwirehracket couple.

Closer evaluation of the nature of movement and fiction at the brackethrchwire

interface provides evidence why higher sliding velocities do not represent the clinical

situation. While it has been assumed that the process of orthodontie tooth movement

occurs at a constant rate of 2.3 x 1 o4 mdminute (Kusy and Whitley, l989), Graber and

Swain (1985) have reported that clinically the velocity for reciprocal closure of a

diastema between the hvo central incisors range from O to 2.4 x 104 rndminute.

Instantanmus changes occurring in the sliding velocity were also reported by Graber and

Swain (1985). These may result nom the build-up and release of Wction as the bracket

and archwire move relative to each other. This is indicative that a "stick-slip"

phenomenon is occumng (Kusy and Whitley, 1989, 1997).

Graphical comparison of a trial fiom the lowest and the highest retraction rates

qualitatively showed a slightly different nature in sliding between the interfaces (Figure

24). At the lowest retraction rate of 0.45 mdminute, more "noise" attributable to the

stick-slip phenomenon is apparent, represented by the large oscillations in the level of

fiiction. With the highest retraction rate of 4.5 mdminute there tends to be relatively

little noise, evident by the shallowness of the peaks and valleys of the oscillations.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

Diatance (mm)

Figure 24. Frictional resistance fiom a trial illustrating lowest and highest sliding veloci ty.

To emulate clinical orthodontie tooth movernent with laboratory fiiction testing

requires the sliding velocities to be as slow as reasonably possible to illustrate the "stick-

slip" phenomenon as the bracket moves relative to the archwire. Therefore, friction

testing canied out as part of this investigation was done at the retraction rate of 0.45

mm/minute to gain an appreciation of the nature of sliding of the various bracket

hrchwire cornbinations. Since sliding vetocity does not affect the fictional resistance

using a dynarnic canine retraction model, the nuIl hypothesis (HMci ,) is accepted.

(2) Cornparison of effect of pre-drawing of the archwire on friction using dynamic canine retraction model

Pre-drawing the archwire through the bracket serves to stretch the elastorneric

ligature in the direction of relative tooth movement. This would ensure that the initial

static fiction would be overcome prior to commencement of measurement of the kinetic

friction. B a d on a previous sîudy by Karnelchuk (1998) using the same apparatus and

experimental setup, steady state displacernent of the bracket relative to the archwire

occmed afler 0.3 mm. After 0.3 mm, it was assumed that al1 fnction readings were

representative of kinetic friction regardless of initial force being displayed by the testing

instrumentation prior to archwire motion.

Since static fiiction is always higher than kinetic fiiction, the systematic inclusion

of static fnction measurements when only kinetic measurernents are desired would

erroneously elevate the fiiction for the bracketlarchwire couple being tested. However,

testing to determine if initial drawing of the wire relative to the bracket influenced the

calculated fnction output for each trial did not demonstrate any signifiant difference in

measured values.

Initial pre-drawing of the archwire through the bracket would also create some

mechanical Wear of the bracket and archwire. Repeated use of orthodontic brackets has

demonstrated a distinct trend for the mean frictional force to be higher because of

mechanical Wear as revealed by scanning electron microscopy (Kapur et al, 1999). Keith

et al (1993), on the other hand, reported negligible change in frictional resistance

associated with the Wear of stainless steel brackets. Keith et al (1993) felt that only a

considerable amount of second order binding could lead to Wear debns in the bracket

dot, causing increased fiction. With the parameters outlined for friction testing as a

fimction of preconditioning, only minimal Wear effects could possibly be expected

because initial rnovement of the bracket was only 2 mm with no second order angulation.

Therefore, as long as the static Mction is overcome prior to measurernent of the

kinetic fiction initial drawing of the wire relative to bracket does not affect the reported

leveI of fictional resistance. This means the nul1 hypothesis (Hdcz,) is accepted because

pre-drawing of the archwire through the bracket does not affect the fnctional resistance

using a dynamic canine retraction model.

(3) Cornparison of effect of saliva with braidecUtwisted archwires on friction using dynamic canine retraction model

While it may be adequate to do fiiction testing under dry conditions because the

rank order of the fnctional resistance of the materials usually did not change or no

significant trend on the effect of saliva exists, no studies had investigated the fiictional

effects of saliva on braided/twisted archwires. Speculation was that the friction for these

wires might be more influenced by saliva because of increased surface area contact with

the saliva owing to capillary action.

Testing was done with fresh human saliva since friction studies conducted in

artificial saliva were deemed invalid (Kusy, 199 1). Even with human saliva variability

exists between the normal composition and flow amongst individuals (Humphrey and

Williamson, 200 1).

Of the twistedhraided archwires tested with stainless steel brackets no

statistically significant effect on the level of fiiction existed. In fact, cornparison of the

nature of sliding in the wet and dry environment appeared unaltered (Figure 25).

Lubncants have been thought to have an insignificant effect on friction because the

archwire touches the bracket at two points creating pressure that expels the saliva from

the area of contact allowing no lubrication effect (Andreasen and Quevedo, 1970).

Pratten et a1 (1990), on the other hand, argued that the loading forces between the bracket

and archwires would determine the lubricious effeçts of saliva on friction. At low loads

saliva may act as a lubricant, but at high loads saliva may increase friction if it is forced

out fiom the contacts between the bracket and archwire producing shear resistance to

sliding. With the present dynarnic fiction testing model, the force of ligation and the

force of binding would influence the load. So relative to the tipped bracket the total load

would be variable. But what appears to be the deterrnining factor for the Ievel of fiiction

appears to be a mechanical impediment to sliding. These wound wires have gaps that

will engage the edges of the bracket slot. The wire and bracket moved less readily when

these grooves were engaged and so friction increased. When the interlocking is

overcome sliding resumed, with a large drop in fiction. The friction sharply rose again

when the edge of the bracket met the next gap or groove in the wire. It appears that

saliva has no influence on this mechanical interlocking (Figure 25).

I O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

Oistance (mm)

Figure 25. Frictional resistance fiom trials with 0.01 75 twisted stainless steel archwires with and without saliva.

Therehre, the nul1 hypothesis (Hdc3]) is accepteci since saliva does not affect the

fictional resistance of braiddtwisted archwires using a dynamic canine retraction

model. Further testing was not carried out in the presence of saliva.

(4) Cornparison of effect of Speed-D archwires with Speed brackets on friction using dynamic canine retraction mode1

Speed bracket's (Strite industries) edgewise slot will accommodate round, square,

rectangular, or Speed shaped archwires. The Speed " D archwire has a unique half-

round half-square profile for control with sliding mechanics (Strite Industries, 1997).

Studies that have compared the fiction of the Speed bracket versus other brackets have

not used these specially designed Speed wires (Berger, 1990; Bednar et al, 199 1 ; Sims et

al, 1993; Taylor and Ison, 1994; Shivapuja and Berber, 1994; Read-Ward et al, 1997;

Pizzoni et al, 1998).

An estimation of the cross-sectional area of a 0.0 18 xO.0 18" Speed-D shaped wire

compared to a conventionally shaped wire would be 89%. Since wire stiffness changes

as the second power of the ratio of the smaller wire to the larger wire (Profitt, 19931, the

flexibility of the Speed-D wire would be about 80% of the normal wire. This greater

flexibility should improve the efficiency in sliding mechanics (Frank, 1980). However,

no difference in the fiictional resistance was found between comparable sized Speed-D

wires and conventionally shaped wires.

The manu facturing process of a conven tionall y shaped wire square or rectangular

shaped leaves an edge bevel for patient comfort (Meling et al, 1997). This means the

corners of these wires are still rounded. This wouId decrease the anticipated cross-

sectional dimension, and thereby decrease the wires stifiess. Similar to the Speed-D

wire, this would lead to less fiction. Since, Speed-D archwires do not affect the

tnctional resistance of Speed brackets using a dynamic canine retraction mode1 the nul1

hypothesis (HMc4)) is accepted.

D. Frictional resistance evaluation of various orthodontic brackets and archwims with sliding mechanics using quantified simulation of canine retraction

The purpose of the fiction testing apparatus designecl by Kamelchuk ( 1998) was

to allow quantifiable analysis of the fnctional resistance encountered at the

archwirehracket interface using a model to approximate the complexities of orthodontic

tooth movement occumng with in-vivo sliding rnechanics. The system was capable of

setting user specified controls to permit concurrent linear archwire traction with angular

bracket control and wntinuous data collection. This allowed a dynamic canine retraction

model that represented a first order approximation of orthodontic tooth movement in-vivo

to be established for the collection of fnction data between various orthodontic brackets

and archwires.

With six different orthodontic brackets and fourteen different archwires of

varying type, size, and shape, a total of 84 bracketlarchwire couples were tested. Each

bracketkchwire couple was tested six times yielding a discrete value representative of

the fnctional resistance encountered. The total of 504 trials were run under standard

experimental conditions. From this data, analysis of the frictional resistance was made

for the effects of orthodontic bracket type, orthodontic archwire type, archwire size, and

archwire shape, including pairwise interactions.

(1) Effect of Bracket Type

Six distinct types of orthodontic brackets representing different materials and

design features were tested. These brackets included a conventional ligated stainless

steel bracket (Victory, Unitek Corp., Monrovia, CA), a conventional ceramic bracket

(Transcend 6000, Unitek Corp., Monrovia, CA), a ceramic bracket with a metal slot

(Clarity, Unitek Corp., Monrovia, CA), a self-ligating bracket with active ligation (Speed,

Strite industries, Cambridge, ON), a self-ligating bracket with passive ligation (Damon

SL, 'A' Company, San Diego, CA), and a self-ligating bracket with variable ligation

(Time, American Orthodonties, Sheboygan, WI) (Illustration 6, Appendix C).

The Victory bracket is representative of the commonly used conventional ligated

stainless steel brackets. These economic brackets are produced by machine injection

molding procedures. Transcend brackets are made of polycrystalline ceramic to give an

esthetic appearance. Similady, the Clarity bracket are also an esthetic ceramic bracket

but have a milled slot inserted with the presumption of improved frictional characteristics

with sliding. The SPEED self-ligating bracket is a metal bracket with the unique feature

of a resilient spring clip to direct the archwire into the bracket slot. This active spring

clip continuously exerts light forces fiom the elastic strain of the spring to the wire and

this h c t i o n s to permit optimal three-dimensional control while reducing sliding Wction.

The Damon SL is also a metal self-ligating bracket but it passively retains the archwire

by a sliding rnechanism over the dot. Time brackets, also manufactured from metal, self-

ligate the archwire in place with a rigid clip. Smaller archwires sit passively while larger

archwires will have a force exerted on them by the ligation clip.

These brackets offer different clinical features in ternis of appearance and

fùnctionality. With respect to fnctional performance, a very significant difference exists

between bracket types. The most obvious distinction is that the self-ligating brackets

have much less fiction than the conventional brackets ligated with elastomeric ligatures.

The highest levet of fiction measured in the present study was encountered with

the two ceramic brackets. in keeping with several other studies, al1 ceramic brackets

generate more fiiction than stainless steel brackets (Popli et al, 1989; Pratten et al, 1990;

Angolkar et al, 1 990; Keith, 1990; Bednar et al, 1 99 1 ; Tanne et al, 1 99 1 ; DeFranco et al,

1995; Loflus et al, 1999). The Iikely reason is that the cerarnic brackets have rougher

surfaces compared to metal brackets (Pratten et al, 1990; Tanne et al, 1991). Under

scanning electron microscopy, ceramic brackets display a crystalline structure containing

many pores while stainless steel brackets slots are smoother with fewer irregularities

(Pratten et al, 1990; Tanne et al, 199 1; Downing et al, 1994). Results fiom the present

SEM investigation of the brackets clearly revealed that the sliding surface of the cerarnic

bracket slot was very rough compared to the metal slots (Illustrations 7, 8, and 9;

Appendix C). A number of asperities were seen on the surface of the ceramic bracket.

Greater force is required to overcome interlocking of the asperities with the archwire

(Kusy and Whitley, 1999). The asperities of ceramic brackets have been observed to

cause abrasive Wear of the archwire (Keith et al, 1993). Additionally, Rose and Zernik

(1996) observed by SEM the build-up of wire debns along the dot corners of ceramic

brackets indicating abrasive Wear due to the bracketlarchwire binding with second order

displacement of the brackets.

Kusy et a l (1991) felt that the behaviour of ceramic brackets might also be

because of their intrinsic chemical structure.

In contrast, some studies have failed to detect any diffaences in the frictional

forces between ceramic and stainless steel brackets (Kusy and Whitley, 1990; Ireland et

al, 1991; Downing et al, 1994). Those studies used static non-binding models meaning

the archwires would not have engaged the edges of the bracket. Similady, DeFranco et

al (1995) found that in the passive configuration only minor differences in the fictional

forces were detected, but in the active binding configuration, fnction was significantly

higher with ceramic brackets over the stainless steel brackets. With second order

displacement of brackets,

To improve the sliding pedormance of ceramic brackets while maintaining an

esthetic appearance, metal slots have been inserted to reduce fiction. However, the

present study found that these brackets fard no better than the regular ceramic brackets

and had significantly more fiiction than the stainless steel brackets. The differences in

fnction of these brackets might be due to theu manufacturing process, which would yield

a difference in the smoothness of the slot. The Victory bracket is a sintered bracketed,

whereas the metal slot of the Clarity bracket is milled. As demonstrated with orthodontie

brackets, manufacturing by sintering has been found to produce less fiction than casting

(Vaughn et al, 1995; Ogata et al, 1996). SEM revealed sintered brackets to have

srnoother bracket slot surfaces than the cast brackets (Ogata et al, 1996). The sintering

process allowed compression of stainless steel particles into a smooth contoured shape, as

opposed to the casting process that requires milling which can create sharp angular

brackets. SEM investigation of the Clarity and Victory brackets demonstrates that the

milled surface of the Clarity metal slot is rougher than the injection molded Victory

brackets (Illustrations 8 and 9, Appendix C). The edges of the slot of the metal bracket

were also well rounded compared to the sharp edges of the dot with the metal insert in

the ceramic bracket.

in contrast, Loftus et al (1999) found that Clarity ceramic brackets with a metal

slot performed as well as conventional stainless steel brackets in fnction tests. However,

the experimental design by Loftus's group passively ligated the archwire in place with

stainless steel ligatures resulting in fiction levels lower than those recordeci by the

present study for comparable archwires. The lower values would make it more difficult

to detect a statistically signifiant difference in mean fictional force.

Traditionally, stainless steel brackets have been regarded as the "gold standard"

for sliding mechanics (Kusy, 2000). In addition to the latter mentioned study, nwnerous

other studies have found staidess steel brackets to have lower friction than ceramic

brackets (Popli et al, 1989; Pratten et al, 1 990; Angolkar et al, 1990; Keith, 1990; Bednar

et al, 1 99 1 ; Tanne et al, 199 1 ; DeFranco et al, 1995; L o h s et al, 1999). Stainless steel

has been used not only to produce conventional orthodontic brackets, but also self-

ligating brackets. The common design feature of the selEligating brackets is a closing

mechanism to retain the archwire.

The three self-ligating brackets used in the present study c m be broadly classified

based on the fùnction of the closing mechanisrn for ligation. Brackets that continuously

engage the archwire have an active mechanism. An example is the Speed bracket.

Brackets that simply cap the archwire slot and do not exert pressure on the wire are

considered passive. Such is the case with the Damon SL bracket. With some brackets

the level of ligation is variable depending on the size of the archwire or the level of

ligation induced. For example, the Time bracket can be regarded as having variable

ligation.

For al1 self-ligating brackets, the literature supports the general claim that less

fnction is experienced compared to conventionally ligated edgewise brackets (Sims et al,

1993; Shivapuja and Berger, 1994; Taylor and Ison, 1994; Thomas et al, 1998; Kapur et

al, 1998; Pizzoni et al, 1998). Still, significant differences in the level of fnction exist

between different types of self-ligating brackets. This difference is most likely a

reflection of the mechanisrn of ligation. Each of the three mechanisms imparts a different

ligation force on the archwire. This ligation of the archwire to the bracket imposes the

normal force acting perpendicularly to the sliding interface, and it has previously been

established that as the normal force of ligation increases the fictional resistance increases

proportionately (Frank and Nikolai, 1980).

The present study found that in comparing self-ligating brackets Speed brackets

with the active spring clip has more fiction than the other two self-ligating brackets.

Other investigators have also found this self-ligating Speed brackets to have more tilction

than other types of self-ligating brackets (Taylor and Ison, 1994; Pizzoni et al, 1998).

Similar cornparisons by Sims et al (1993) found that the Speed self-tigating bracket with

the active spnngclip had about fifieen times more resistance than the Activa ("A"

Company, San Diego, California, CA) self-ligating bracket with a passive hinged locking

cover.

Pizzoni et al (1998) generally found that the Speed bracket had less friction than

conventional brackets but more than the Damon SL brackets. Moreover, with increased

second order angulation, the Speed brackets exhibited a significantly greater rate of

increase in fiction than the other brackets. Presumably this resulted from the increased

binding resulting fiom second order bracket tip. Similarly, the present study noted that

with stainless steel wires the active ligating Speed brackets and conventional ligated

metal brackets did not have statistically different levels of fiction, which seerningly

resulted Fom the stiffiiess of the stainless steel wire.

Cornparison of the Time and Damon SL bracket in the present study found that

both of these self-ligating brackets had minimal fiction, with the Damon SL bracket

being even significantly lower than the Time bracket. The sanie result has also been

reported by Thomas et a1 (1 998). Interestingly, the Time bracket is designed to provide

near fiction-& movement in the initial stages of orthodontic tooth movement as

claimed by the manufacturer, but as the archwire dimension increases the clip engages

the archwire for torque control (Thomas et al, 1998). Both the present study and

Thomas's study (1998) reported that with smaller initial aligning wires no significant

fnctional difference exists between the Time and Damon SL bracket. Essentially the

Time bracket is only passively ligating the archwire in a manner similar to the Damon SL

bracket .

With the Damon SL bracket nearly negligible fiction existed. Both the present

study and Kapur's (1998) found that this bracket had drarnatically less friction than

conventionally ligated stainless steel brackets. The explanation for such low levels of

fnction is because the locking mechanism slides over the bracket slot and allows the

archwire to sit passively, thereby limiting the normal comportent of the force of ligation.

Binding would be the only nomal component of the force to resist sliding and would

only occur in the active configuration. Sims et al (1999) found that with the similar

passively self-ligating Activa brackets ("A" Company, San Diego, California, USA)

fiiction was still consistently lower than conventional stainless steel brackets during

sliding mechanics under varying degrees of second order tip and even with third order

torque.

Some variation from the general trends for fiction has been noted depending on

the specific coupling of specific bracket sizes or shapes with specific brackets (Table 10).

in particular, variable and passive self-ligating brackets have similar fictional

performance with small, round wires. As previously noted, this can be explained on the

basis that the variable ligating Time bracket would be functioning in a passive marner

sirnilar to the passive ligating Damon SL bracket. Other minor variations show

transposition of the rank order in the level of friction occumng with specific conventional

ligating brackets coupled to specific sized or shaped archwires. For exarnple, with small

archwires ceramic bracket have less fiction than ceramic brackets with metal slots, but

with rectangular archwires ceramic bracket have more fiction than ceramic brackets with

metal slots. Since the binding that occurs with specific bracket/archwire couples can be

affected by the relationship of the relative size of the archwires to the bracket slot

(Articolo and Kusy, 1999), small variations in the dimensions of the wire size or bracket

slot size can influence the binding (Kusy and Whitley, 1999). Kusy and Whitley (1 999)

have shown that the tme dimension of archwires and bracket slots can vary as much as

16% fiom the nominally reported size. Therefore, variations in size of specific archwires

a d o r brackets slots from the nominally reported size can affect the level of fiction

between specific archwire and brackets.

In surnmary, the oxthodontic bracket type can have a very dramatic effect on the

level of fiction. Therefore, the nul1 hypothesis (Hdoi >) is rejected and it is recognized

that bracket type effects the frictional resistance using a dynamic canine retraction model.

(2) Effect of Archw ire Type

Four distinct types of archwires representing di fferent matenals and configurations

were tested. niese wires could be classified based on their function into three categories:

starting wires for initial alignment , working wires for sliding mechanics, and finishing

wires for detailing of tooth position. Small nickel-titanium wires could be considered

starting wires, while large nickel-titaniurn wires could be considered finishing wires. The

twisted nickel-titanium and round twisted stainless wires are seen as starting wires.

Stainless steel wires that are small or round are considered working wires. Large

rectangular wires made of stainless steel or braided stainless steel are typically used as

finishing wires. Even though these wires may have different primary functions, they may

be required to slide relative to the bracket whether it be with initial aligning of a crowded

dental arch with intra-arch elastics providing a distally directed force on the canines,

canine retractioddistalization by inter- or intra-arch mechanics with the working wires,

or final closure of space next to a canine on a finishing wire.

Less fiiction was f o n d with the nickel-titanium wire compared to the stainless

steel wire. When tipping of the bracket occurs relative to the archwire it seerns

advantageous to have a wire that has some flexibility to reduce the level of friction.

Because of the lower modulus of elasticity for nickel-titanium compared to stainless

steel, a lower normal force that was induced by binding occurred resulting in less

resistance to sliding. Other investigators have also noted that the more flexible nickel-

titaniurn wires have less friction at six degrees of second order tip than stainless steel

brackets (Frank and Nikolai, 1 980; Kemp, 1992; Weiss, 1993; Kusy and Whitley, 1999).

O'Reilly et al (1999) felt that other contributions may define the resistance to

sliding for archwires, such as the surface roughness or dissimilar alloys fiom the bracket.

SEM examination has revealed that staùiless steel wires appeared highl y polished, while

nickel-titaniurn wires showed a fibrous structure (S tannard et al, 1 986). However,

surface roughness does not necessarily correlate with fnction for archwires (Kusy and

Whitley, 1990; Prososki et al, 1991). Kusy and Whitley (1 990) suggested that surface

chernisû-y and chemical affinity might play a significant role in overall fnctional

resistance (Kusy and Whi tley, 1 990).

Ho and West (1995) also felt that archwire stifiess was the dominant controlling

factor for fnctional resistance. For example, the stifniess of stainless steel archwires led

to abrasion of the wire with the resultant creation of Wear tracks inscribeci on the surface

of the wire. Evidence of build-up of wire debris was shown dong the slot corners of

brackets by scanning electron microscopy. This phenornenon did not occur with the

more flexible nickel-titaniwn wires (Rose and Zernik, 1 996).

Since wire flexibility seems to explain the reason for the lower fiction of nickel-

titanium compared to stainless steel, it would be anticipated that the highly flexible

twistedhraided stainless steel or twisted nickel-titanium wires would have even less

fiction. Moreover, this was not the case as these wires created significantly more

fnction than their counterparts of similar size and shape. O b s e ~ n g the nature of sliding

for some of the trials of these wires revealed that there are repetitive increases in

fnctional resistance (Figure 26).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3

ûtSTANCE (mm)

Figure 26. Fnctional resistance fiom trials with twistedhraided archwires.

These large increases in friction result from mechanical interlocking of the

archwires with the edges of the bracket dot. Because these brackets are wound together,

gaps exist between the strands. The result is that as the wire moves relative to the bracket

the normal force fiom ligation and binding directs the wire into the bracket slot causing

the gaps or grooves of the wires to corne to rest with the edges of the bracket slot. This is

akin to interlocking of microscopie surface asperities described by Kusy and Whitley

(1997) but on a macroscopic level. Thereby, the wire and bracket moved less readily

when these grooves were engaged and so fnction increased. When the interlocking is

overcome sliding resumed with a large drop in friction. The fiction sharply rose again

when the edge of the bracket met the next gap or groove in the wire.

Al1 combinations of twistedhraided archwires and brackets were seen to show

this pattern o f interlocking fnction.

In summary, the orthodontie archwire type can have a profound effect on the level

of friction. Therefore, the nul1 hypothesis (HMozl) is rejected because archwire type

effects the fnctional resistance using a dynarnic canine retraction model.

(3) Effect of Archw ire Size

Generally it is assumed that as archwire size increases so does the frictional

resistance. These sentiments are strongly supportai by numerous studies (Andreasen and

Quevedo, 1970; Riley et al, 1979; Drescher et al, 1989; Angolkar et al, 1990; Kapila et

al, 1990; Tanne et al, 1991 ; Sims et al, 1993; Downing et al, L 994; Vaughn et al, 1995;

Ogata et al, 1996; O'Reilly et al, 1999). Similarly, the present study found significantly

greater fnction with larger archwires than smaller archwires. The main reason for the

increase in fiction as the wire size increased cm be been attributed to an increase in the

stiffbess of the wire.

The stiflhess of a wire increases by the fourth power of an increase in archwire

diameter. Thus, when comparing a 0.020" versus 0.01 8" or 0.02 1 0.025" v a u s 0.01 8 x

0.025" increases the stifiess nearly 1.7 times the arnount based on Burstone's (1981)

cross-sectional dimension numbers. Wires of greater stifiess will create a greater

normal force with binding of the archwire with the edges of the bracket.

Similarly, O'Reilly's et ai (1999) fiction model that pennitted tipping about an

approximated center of resistance also showed that the resistance to sliding significantly

increased as the wire size increases. However, O'Reilly felt that with increased

displacement of the bracket to represent physiologic tooth movement in-vivo the smaller

size wire had less of a reduction in fiction compared to larger wires because the smaller

wire had greater fieedom within the bracket. This reduction ranged from a low of 19

percent for the smaller wire up to 85 percent for the larger wire, with the absolute value

for the Wction encountered being less for the larger wire (O'Reilly et al, 1999).

Moreover this reduction in f?iction would not be hlIy realized when put into the context

of an integrated clinical mode1 for sliding mechanics because the resistance to sliding is a

binding and releasing phenornenon that may be affected by such Ni-vivo factors as tooth

mobility. These factors act only intermittently and not al1 the time (Braun et al, 1999).

Tidy and Ison (1 989) and Ireland et al (1 99 1) argued that no difference in fiction

with respect to wire size existed. Their fiction models did not permit second order

angulation where binding becomes significant. Thus, without binding only classical

fiction induced by the normal force of ligation would be the main determinant of the

fiictional resistance.

Another contributing factor to the greater friction with larger archwires is from

the force of ligation. The larger archwire would dernand a greater stretch of the

elastomeric ligature which would subsequently impart a larger normal force and hence

more friction (Dowling et al, 1998).

Larger dimension archwires have a much greater increase in fiction than smaller

wires when coupled with self-ligating brackets. Since the self-ligating brackets limit the

force of ligation (Sims et al, 1993), the level of fiction with wires coupled to self-

ligating brackets is mainly determineci by binding. With minimal ligation effects, the

binding of the larger dimension wires predominates over the level of fiction with self-

ligating brackets.

Ln conclusion, the orthodontic archwire size can have a large effect on the level of

Wction. Therefore, the nul1 hypothesis (Ho(D3)) is rejected since archwire size affects the

fictional resistance using a dynamic canine retraction model.

(4) Effect of Archwire Shape

The advantage of rectangular archwires over round wires is that third order

tourquing forces can be delivered to the teeth by the archwire. Rectangular wires are

predominantl y employed during case finishing. Yet, rectangular ma y be engaged sooner

if it is felt that torque control is an issue for proper alignment of the teeth. Alternatively,

residual spaces may still be present that will require sliding for closure. Nevertheless,

changing from a round wire to a comparable shaped rectangular wire will cause the

stiffiess of the wire to increase drarnatically (Profitt, 1997). B a d on the cross-sectional

stiflhess numbers established by Burstone (1 98 1) an 0.01 8 x 0.025 wire compared to an

0.0 1 8 wire or an 0.02 1 x 0.025 wire compared to an 0.020 wire is nearl y 2.5 times stiffer.

In studies that analyze fiiction as a function of second order angulation, the wire stifkess

and cross-sectionai dimension of the archwire become the dominant influencing factors

(Frank and Nikolai, 1980). Therefore, placement of a rectangular wire can drarnatically

increase the fiiction because of the concomitant increase in wire stifiess.

The present study strongly supports the concept that rectangular wires have more

fiiction than round wires. In fact, a very dramatic increase in friction was seen with a

change in the archwire shape. Placement of the rectangular instead of the round wire

resulted in nearly twice the mean level of fiction. Similar results were reportai by Tidy

(1989). When brackets were put out of alignrnent via second order offset, round wires

produced less fiction than rectangular wires when engaged into the bracket slot. The

greater flexibility of the round wires and absence of active torque would explain the latter

observation.

Another contributing factor to the greater fnction with rectangular archwires is

from the force of ligation. It was noted previously that the rectangular archwire would

create a more acute rise and greater stretch of the elastomeric ligature and thus impart a

larger normal force and hence create more friction (Dowling et al, 1998).

Studies that have not pemitted second order tipping of the bracket relative to the

archwire have not found any difference in the fiction of round versus rectangular wires

(Ireland et al, 199 1). Mthough rectangular wires have a larger surface area than round

wires in contact with the slot surface, the second law of classical fnction states that

friction is independent of surface area (Jastrzebski, 1976), and therefore would be

independent of wire shape. Thus, without binding only classical fnction induced by the

force of ligation would be the main deteminant of the fictional resistance.

Contrary to other researchers, Frank and Nikolai (1980) found that at binding

angulations rectangular wires had less fnction than round wires. It was believed that as

the bracket tipped and made contact with the wire greater pressure would be placed on

the point contact of the round wire compared to the line contact of the rectangular wire.

This possibly could result in indentation or notching of the round archwire, and hence

cause more resistance to sliding fkom this mechanical impediment. This indentation

occurred only when the bracket was tipped beyond 6 degrees. Kusy and Whitley (1999)

have characterized this phenornenon as notching. Notching will lead to a dramatic

increase in resistance to sliding by mechanical interlocking.

With rectangular wires, if active third order torque were present the friction would

be even more pronounced (Sims et al, 1993). Another normal force would be introduced

by the archwire engaging the bracket to induce crown or root movement in a labial or

lingual direction. This would help explain why the level of for the self-ligating brackets

is much greater with rectangular wires than with the round wires. The clips of the self-

ligating brackets would not yield or exert greater pressure on the rectangular wires if

torque is present leading to greater friction. Similarly, greater friction with larger

rectangular wires results from the possible introduction of torque since an 0.02 1 x 0.025"

wire has 3.9" of play compared to an 0.018 x 0.025" wire that has 14.8' of play when

engaged into an 0.022'' bracket slot (Creekmore, 1979). This much greater friction with

rectangular wires over round wires is only seen with nickel-titanium and stainless steel

wires because minimal force derived fiom torque would be generated with the braided

stainless steel wires.

Ln surnmary, the orthodontie archwire shape can influence the level of friction.

Therefore, the nul1 hypothesis (Hdwl) is rejected since archwire shape affects the

fnctional resistance using a dynamic canine retraction model.

(5) Bracket/Archwire Interactions

Some deviations fiom the general trends for fiction were observed in the present

study (Table 1 1). Almost invariable these exceptions occurrd with more highly flexible

wires. This reinforces the fact that the normal force induced by binding strongly dictates

the level of fnction. This is particular tme when second order bracket tipping occurs

(Kusy and Whitley, 1990).

One of the most important interactions is that between the bracket and the

archwire. While certain parameters for the reduction or minimization of fiction are

evident from the present study, clinical bracket selection may be influenced by decisions

other than fiction, such as, esthetics mst, ease of use, and treatment planning

(TwelAree, 1994). Therefore, it would be appropriate to select archwires that are most

efficient with the selected bracket to control friction. These bracketkrchwire couples are

highlighted in Table 17.

The most efficient couples are either the Damon SL passive self-ligating bracket

with either nickel-titanium or twisted stainless steel archwires or the Time variable self-

ligating bracket with twisted stainless steel archwires. The very low friction is a product

of two factors. First, low friction with these brackets would be anticipated since these

self-ligating brackets limit the force of ligation (Sims et al, 1993). Additionally, low

friction would be anticipated since these archwires are highly flexible. These same

reasons hold true for the coupled archwirehracket combination of the Speed active self-

ligating brackets with twisted stainless steel wires. However, the resilient springclip of

the Speed bracket engages the wire creating a light continuous normal force fiom ligation

(Read- Ward et al, 1997), thereby lending itself to greater friction compared the other

self-ligating brackets. The friction with al1 archwires coupled to conventionally ligated

stainless steel brackets is much greater than the self-ligating brackets due to the greater

forces of ligation. Of the conventional ligating brackets, the most efficient couple is the

Transcend ceramic bracket with nickel-titanium archwire. This ceramic bracket is a

polycrystalline alumina that is quite hard. Since the hardness of this matenal greatly

exceeds the hardness of nickel-titaniurn the sliding properties would be expected to be

compromised (Kusy and Whitley, 1997). However, nickel-titanium wires slide on a

passivated interstial oxide layer that is harder than the bulk material. Therefore the

surface chemistry of this layer will control the 6ïction (Kusy and Whitley, 1997). Sliding

on metal surfaces showed the most fiction. But to ensure the most efficient couple with

the Clarity metal-slotted ceramic bracket or the Victory metal bracket nickel-titanium

archwires should be used. The flexibility of this wire reduces the tendency for binding

resulting in less fiction (Frank and Nikolai, 1980). Stainless coupied with the metal

bracket performed as well as the nickel-titanium wire even though the stainless steel wire

is dramatically stiffer. The stainless steel wire petfomed as weil as the nickel-titanium

wire in combination with the metal bracket for two possible reasons: one reason is

because of the relative smoothness of the stainless steel wire surface (Pratten et al, 1990);

and the second reason is the compatibility of the surface chemistry of the sliding surfaces

(Kusy and Whitley, 1997).

Clearly, specific archwires are more appropnate for certain brackets to minimize

the level of fiction. Therefore, the nul1 hypothesis (Ham)) is rejected since

bracketlarchwire combinations affect the frictional resistance using a dynamic canine

retraction model.

The first part of this project involved establishment of a model for fnctional

resistance evaluation with sliding mechanics using quantified simulation of canine

retraction. This required demonstrating that a testing apparatus designed for simulated

canine retraction could achieve concurrent control of linear and angular bracket

displacement while simultaneously acquiring fnctional resistance data with temporal

integration. Using this fiction testing apparatus, the fnctional resistance was shown to

Vary depending on whether a non-binding or binding static canine retraction model used

for testing. A dynamic canine retraction mode1 that experimentally approximated

orthodontic tooth movements was establisheà to incorporate the non-binding fiiction and

the superimposed binding friction that occurs with orthodontic tooth movement in sliding

mechanics.

Next, specific parameters that could influence the frictional resistance evaluation

with sliding mechanics using quantified simulation of canine retraction were investigated.

This was to ensure there was no systemic pattern of over-reporting or under-reporting of

the level of fiiction for ail brackethchwire combinations or specific bracketlarchwire

combinations.

Findly, the fnctional resistance was evaluated for various orthodontic brackets

and archwires with sliding mechanics using the dynamic canine retraction model. The

level of friction was profoundly influenced by the orthodontic bracket type, orthodontic

archwire type, orthodontic archwire size, and orthodontic archwire shape. Also, specific

combinations of orthodontic bracketkuchwire combinations were more efficient than

others.

Looking to the fùîure, friction testing of orthodontie brackets, archwires, and

ligatures must explore the interrelationship between some of the following parameters:

non-binding fiction and binding friction, interbracket distance and bracket width, bracket

width and slot size, archwire size and slot size. Friction must also be correlated to wire

and bracket hardness, surface roughness, elasticity, and yield strength (Kusy, 2000).

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APPENDIX A: Properties of Orthodontic Materials Evaluated

(1) Orthodontic Archwires

Table 18. Material properties o f orthodontic archwires evaluated.

General Class Flexural Modulus of Burstone's Material [Composition) Elasticitv (x 1 o6 psi) ' Stifhess Number

stainless steel (7 1% Fe, 18% Cr, 8% Ni)

nickel-titanium (52% Ni, 45% Ti, 3% Co)

twisted stainless steel 0.0 175" 1.7 (71%Fe, 18%Cr, 8%Ni) 0.0 195" 2.0

braided stainless steel 0.0 18~0.025" 2.0 (7 1 % Fe, 18% Cr, 8% Ni,) 0.02xO.025" 1.6

- -

# Goldberg, 1983 * Burstone, 198 1

(2) Orthodontic Brackets

Table 19. Material properties of orthodontic brackets evaluated.

General C lass ~ o u n ~ ' s Modulus of Ultimate Tensile Vicker's Hardness [Com~osition) Elasticity (x 1 O-' Pa) Strength (x 1 0-6 Pa) Scale (kg/mm2)'

stainless steel 200 (7 1 % Fe, 1 8% Cr, 8% Ni)

ceramic (99.8% alumina)

% Kusy, 1990 * Kusy, 1990

APPENDIX 8: List of Manufacturers

The foIIowing is a list of orthodontic rnanufacturers/suppliers whose products were evaluated or used in this orthodontic fiiction study:

American Orthodontics 1 7 14 Cambridge Ave. P.O. Box 1048 Sheboygan, WI USA 53082- 1 O48

3M Unitek 3M Dental Products Division 2724 South Peck Road Monrovia, CA USA 91016

Ormco 'A' Company 1 1436 Sorrento Valley Road San Diego, CA USA 92121-1393

Rocky Mountain Orthodontics PO Box 17085 Denver, CO USA

Speed System Orthodontics Strite Industries Limited 298 Shepard Ave. Cambridge, ON Canada N3C 1 V 1

APPENDIX C: Illustrations

Illustration 1. Friction testing apparatus.

Illustration 2. Standardization of bracket bonding to mounting fixhire with alignrnent jig.

Illustration 3. Standardized interfacing o f bracket mounting fixture to Servomotor within the testing apparatus.

iiiustration 4. Relationship of Servomotor to Instron Load Cell.

Iliustration 5. Configuration of LabView for enperimental parameter control and data collection.

iiiustration 6. Orthodontic brackets used in this study. Top row: metal bracket, ceramic bracket, and ceramic bracket with metal dot. Bottom row: self-ligating wiîh active ligation, self-ligating with passive ligation, and self-ligating with variable ligation.

Illustration 7. SEM of Transcend ceramir : bracl cet at 60X and 1000X magnific

Illustration 8. SEM of Victory metal brac 60X and 1 000X magni fication

Illustration 9. SEM of Clarity ceramic bri magnification.

acket with metal slot at 60X and 100i

Appendix D: Frictional Resistance of the Trials For Each Study

The following tables (Table 1 1 to Table 21) summarize the calculated average

fictional resistance encountered for each trial based on the parameters of each study.

8. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Cornparison of friction using static canine retrâction models

(2) Cornparison of friction using static and dynamic canine retradion rnodels

Table 20. Frictional force for each trial according to static retraction model and archwire We*

RETRACTION MODEL

Static, Non-binding, O"

Static, Binding, 6"

Static, Non-binding, O"

Static, Binding, 6"

Table 21. Frictional force for each trial according to retraction model.

Calcuiated average force (grams) for each trial

RETRACTION MODEL

Static, Non-binding, O"

Static, Binding, 6O

Dynamic, 0"-6"-0"

S.D.

17.4

9.6

10.6

10.0

Calculrted average force (grams) for each trial

3

103.4

132.1

94.5

106.2

S.D.

17.4

9.6

14.3

Mean

89.2

130.5

98.1

2

106.5

112.9

98.8

108.5

4

88.3

132.8

94.6

Wire

SS

SS

NiTi

NiTi

1

92.1

129.2

84.1

1

92.1

129.2

105.0

117.4

2

106.5

112.9

126.3

105.0

5

87.5

141.6

82.3

Mean

89.2

130.5

11 1.7

3

103.4

132.1

112.8

6

57.5

134.5

113.5

91.6

6

57.5

134.5

115.9

4

88.3

132.8

114.5

119.6

5

87.5

141.6

116.8

108.1

C. Establishment of parameters for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Comparison of effect of sliding velocity on friction using dynamic canine retraction model

Table 22. Frictional force for each trial according to sliding velocity.

1 Calculated a iverage force (grams) for each trial I r

(2) Comparison of effect of pre-drawing of the archwire on friction using dynamic canine retraction mde l

SLiDING VELOCITY

0.45 mmhnin

0.90 rnm/min

2.25 mm/min

4.50 d m i n

Table 23. Frictional force for each trial according to pre-drawing of the archwire.

1 Calculated average force (grams) for eacb trial 1

1 2

84.1 126.3

109.0

(3) Comparison of effect of saliva with braidedi'twisted archwires using dynamic canine retraction mode1

3

112.8

118.0

93.2

120.5

81.6

89.5

PRE-DRAWING

No

Yes r

Table 24. Frictional force for each trial according to saliva.

122.8

103.1

1 Calculated average force (grams) for each trial 1

4

114.5

73.0

78.3

80.3

- -

5

116.8

93.6

91.6

79.1

ARCIiWIRE TYPE

0.0 175 twisted SS

0.0175 twisted SS

Mean

111.7

108.8

1

84.1

108.3

0.0 1 8 twisted NiTi

6

115.9

91.9

109.6

92.4

S.D.

14.3

9.5

3

112.8

117.1

2

126.3

104.5

WET

N~

yes

y,,

Mean

1 11.7

99.4

96.2

94.1

4

1 14.5

122.8

1

95.3

128.7

0.018x0,025 braided SS

0.018x0.025 braided SS

0.0 18 twisted NiTi

S.D.

14.3

16.5

17.0

16.7

5 6

116.8 115.9

97.5 102.5

150.9

128.7

105.0

N~

yes

N~ 77.6

2 3

98.6

4

114.5

93.5

98.3

84.2

f 26.4

119.6

119.1

156.7

144.2

79.1

97.3

113.3

122.3

126.4

105.1

88.4

5

98.2

107.8

130.8

139.8

92.8

71.2

6

86.8

92.0

127.9

103.7

83.7 1

75.8 96.9

Mean 98.4

103.3

S.D.

9.0

16.5

135.8

127.0

97.5

84.8

14.3

14.5

15.1

11.6

(4) Cornparison of effect of Sped-D archwires with Speed brackets on friction using dynamic canine retraction model

Table 25. Frictional force for each trial with Speed bracket according to archwire type.

D. Frictional resistance evaluation of various orthodontie brackets and archwires with sliding mechanics using quantified simulation of canine retraction

ARCHWIRE TYPE

0.0 18 X 0.0 18 NiTi

0.0 18 X 0.0 18 NiTi-D

Table 26. Frictional force for each trial according to archwire combination for metal brackets.

Calculated average force (grams) for each trial

1

55.8

66.6

2

50.1

36.7

3

35.7

61.2

Mean

50.8

52.0

S.D.

8.5

10.6

4

59.6

50.2

5

48.1

50.4

6

55.6

47.2

Table 27. Frictional force for each trial according to archwire combination for ceramic brackets.

Table 28. Frictional force for each trial according to archwire combination for ceramic brackets with metal slots.

Wùe size

--

Calculrted average force (gram~) for each trial 1 1 2 3 4 5 6 Mean S.D.

82.5 102.4 113.4 84.0 102.9 71.4 92.8 15.9 i

1 Twisted NiTi / 0.020

Table 29. Fnctional force for each trial according to archwire combination for self- ligating brackets with active ligation.

1 Calculited average force (gram) for each trial 1 Wire type Wire sue 1 2 3 4 5

SS 0.018 8.4 3.7 17.1 13.4 19.9 5.0 11.2 6.6 SS 0.020 63.5 47.1 54.5 43.3 52.3 64.1 54.1 8.4 SS 0.018x0.025 119.6 105.8 154.0 89.4 128.2 118.4 119.2 ( 21.7 SS 0.021x0.025 184.2 151.9 187.9 163.5 147.9 157.9 165.6 1 16.8

Twisted SS -

Twisted SS Braided SS Braided SS Twisted NiTi Twisted NiTi

Table 30. Frictional force for each trial according to archwire combination for self- ligating brackets with passive ligation.

Wire type

SS SS SS SS NiTi NiTi NiTi NiTi Twisted SS Twisted SS

r

Braided SS Braided SS Twisted NiTi , Twisted NiTi

- -

Calculited average force (grams) for each trial

Wire size

0.0 18 0.020 0.0 18~0.025 0.02 1 x0.025 0.0 18 0.020 0.0 18~0.025 0.02 1 x0.025 0.0 175 0.0 195 0.0 18~0.025 0.02 1 x0.025

0.0 18 0.020

S.D.

1 .O 1.8

11.2 12.7 1.8 2.5 3.6 4.8 1.5 1.2 1.6 3.9 0.5 0.6

1

3.8 6.8

23.6 50.4 3.2 3.8 2.6

18.0 3.5 3.4 3.6 9.4 1.0 4.1

5

1.3 5.0

30.7 57.3

6

3.2 3.6 5.0

48.1

4

2.2 2.3 8.7

73.0 1.2 6.2 4.1 7.6 2.5 3.0 2.2

16.8 0.9 2.8

2

1.4 7.1 6.1

63.4 6.4 5.1 1.7 9.8 4.3 5.5 3.2

16.6 2.1 2.9

Mean

2.3 5.1

13.1 54.8

3

1.8 5.8 4.3

36.7 3.2 4.8 1.9

18.0 4.6 -

2.5 4.1

15.3 1.4 3.0

3.3 6.3 4.3

12.4 3.6 3.5 3.5

13.5 1.4

3.0

4.0 1 2.0 1 1.0 4.2

13.1 5.2 2.3 1.6

15.2 1.1 2.6

7.0 11.3 7.7 1.3 4.2 6.1 7.8 1.9 2.4

Table 31. Frictional force for each trial according to archwire combination for self- ligating brackets with variable ligation.

APPENDIX E: Statistical Analysis Output

B. Establishment of a model for frictional resistance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Comparison of static canine retraction models

Source

Class Retraction mode1

-- - -

Corrected model

Intercept

Retraction model

Wire type

Retraction* Wire

Error

Total

Corrected total

squares J 1 square

Levels 2

Sig.

Values O degree; 6 degree

(2) Cornparison of static and dynamic canine tetraction models

One-way AN0 VA

Retraction mode1

Force static 0" tip

dynarnic tip

static 6' tip

Total

--

St. Dev

Sum of squares

Mean square Sig.

Between groups

Within groups

Total

Duncan 's Multiple Range Test

Dynamic, 6 degrees

Static, 6 degrees

Speed

Static, O degrees

N

6

Total

Subset for alpha=0.05

0.01 5

a

89.2

0.036

b

C. Establishment of parameters for frictional resbtance evaluation with sliding mechanics using quantified simulation of canine retraction

(1) Comparison of effect of sliding velocity using dynamic canine rettaction mode1

One-way A N 0 VA

Sliding Velocity

Force 0.45 d m i n

0.90 mm/min

2.25 mmjmin

4.50 d m i n

Total

Duncan 's Multiple Range Test

Between groups

Within groups

Total

0.45 &min

0.90 mm/min

2.25 rnmimin

4.50 mm/min Total

1 Subset for alpha=0.05

S m of squares

1 1 19.235

5059.580

6178.815

d f

3

20

23

Mean square

373.078

252.979

F

1.475

Sig.

0.252

(2) Cornparison of effect of predrawing of the archwire using dynamic canine retraction model

T- Test

d f 1 Sig. (2-tailed)

preconditioning

Force no

Y=

Mean di ff.

Force 1 0.420 1

N

6

6

Mean

11 1.7

108.8

St. Dev

14.3

9.5

(3) Cornparison of effect of saliva on braidedltwisted archwires using dynamic canine retraction model

T-Test - 0.0 175" twisted stainiess steel

Mean 1 St. Dev

Force no saliva

sali va

t I d f 1 Sig. (2-taileci) 1 1 1 l

Force 1 -0.633 1 10 1 0.54 1 -4.8 1

T-Test - 0.01 8 x 0.025" braided stainless steel

df 1 Sig. (2-tailed) 1 Mean diff.

Force no saliva

saliva

1 Force 1 1.052

T'Test - 0.01 8" twisted nickel-titanium

N

6

6

1 Force no saliva

Mean

135.8

127.1

N

saliva

St. Dev

14.3

14.6

Mean

St.Error

5.8

5.9

St. Dev

- - - -

Force

St.Elror

t

1.642

Mean diff.

12.7

- -

d f

10

Sig. (2-tailed)

O. 132

(4) Cornparison of effect of Speed-D archwires with Speed brackets on friction using dynarnic canine retraction model

T- Test

wire

Force D-shape

1 1 t 1 df 1 Sig. (Ztailed) 1 Mean diff. 1

square

7

S t. Error

4.3

N

6

l 6

Force

Mean

52.0

50.8

0.225

St. Dev

10.6

8.5 I 3.5

IO 0.826 1.2

O. Frictional resistance evaluation of various orthodontic brackets and archwires with sliding mechanics using quantified simulation of canine retraction

Mutipie ANOVA

Source

Class Bracket Wire Size Shape -

Mode1

Error

Corrected total

Bracket

Wire

Size

Shape

Bracket* Wire

Bracket * Size

Bracket*Shape

WiresSize

Wire*Shape

Size*Shape

Levels 6 4 2 2

Sum of squares

Values ceramic/metal; ceramic; metal; active; passive; variable NiTi; SS; twisted SS large; small rectangular; round

Mean square

Sig.

Duncan 's Multiple Range Tesî (excludes twisted nickel ti tanium)

1 Bracket ceramic

ceramic/metal

metal

active

variable

passive

Archwire type

twisted SS

SS

NiTi

Subset for alpha=0.05

1 Subset for aipha=0.05

Subset for alpha=0.05

Archwire size a 1 B

Archwireshape

rectangular

round

N

216

216

Subset for alpha=0.05

a

92.2

b

51.0

Leust Squares Meuns Test

cerarnic/metal ceramic/metal ceramic/metal ceramic ceramic ceramic metal metal met al active active active passive passive passive variable variable variable

WIRE

NiTi SS twisted SS NiTi SS twisted SS NiTi SS twisted SS NiTi SS twisted SS NiTi SS twisted SS NiTi SS twisted SS

FORCE LS MEAN

90.02 1 10.14 147.6 1 77.06

127.23 t 38.86 96.85 90.63

125.79 60.77 87.54 47.43 6.57

18.8 1 6.00

20.56 25.77 10.74

LSMEAN number

1 2 3 4 5 6 7 8 9

10 1 1 12 13 14 15 16 17 18

ceramic/met al ceramic/metal ceramic ceramic metal metal active active passive passive variable variable

SIZE

large small large small large small large small large small large small

FORCE LS MEAN

12 1.39 1 10.46 126.08 102.68 114.18 94.66 80.46 50.03 15.93 5.00

29.4 1 8.64

LSMEAN number

1 2 3 4 5 6 7 8 9

10 11 12

BRACKET

ceramidmetal ceramic/metal ceramic cerarnic met al metal active active passive passive variable variable

SHAPE

rectangular round rectangular round rectangular round rectangular round rectangular round rectangular round

FORCE LS MEAN

129.84 102.0 1 137.85 90.92

13 1.59 77.26

102.56 27.93 16-92 4.00

34.37 3.68

LSMEAN nurnber

1 2 3 4 5 6 7 8 9

10 1 1 12

NiTi NiTi SS SS twisted SS twisted SS

NiTi NiTi SS SS twisted SS twisted SS

large large small small

SIZE FORCE LS MEAN

large 67.80 small 49.48 large 89.24 small 64.13 large 86.68 small 72.13

LSMEAN number

1 2 3 4

SHAPE FORCE LS MEAN

rectangular 67.80 round 49.48 rectangular 89.24 round 64.13 rectangular 86.68 round 72.13

LSMEAN number

1 2 3 4 5 6

SHAPE FORCE LSMEAN LS MEAN nurnber

rectangular 106.14 1 round 56.34 2 rectangular 78.23 3 round 45.60 4

Multiple A M VA

Source

Class Bracket Wire Size

Mode1

Error

Corrected total

Bracket

Wire

Size

Bracket* Wire

Bracket*Size

Wire* Size

Levels 6 4 2

Sum of squares

Values ceramidmetal; ceramic; metal; active; passive; variable NiTi; SS; twisted NiTi; twisted SS large; small

Mean square

Sig.

0.000 1

0.000 1

0.000 1

0.000 1

0.000 1

0.000 1

0.004 1

Duncan 's MuIdiple Range Test (includes only round archwires)

Bracket

ceramic

ceramic/metal

metal

active

variable

passive

Subset for alpha=0.05

Archwire type

twisted SS

twisted NiTi

SS

NiTi

1 Subset for alpha=0.05 1

Archwire size 1 Subset for alpha=0.05 1

Least Squares Means Test

ceramic/metal ceramidmetal ceramic/metal cerarn i c/me t al ceramic ceramic ceramic ceramic metal metal metal metal active active active active passive passive passive passive variabie variable variable variable

NiTi SS twisted NiTi twisted SS NiTi SS twisted NiTi twisted SS NiTi SS twisted NiTi twisted SS NiTi SS twisted NiTi twisted SS NiTi SS twisted NiTi twisted SS NiTi SS twisted NiTi twisted SS

FORCE LS MEAN

75.45 94.09 88.89

136.50 57.27 89.38

1 12.65 126.10 75.45 55.06

115.39 101.27 33.34 32.69 30.23 17.77 4.8 1 3.68 2.19 3.52 3.0 1 6.24 1 .O7 1.79

LSMEAN number

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 2 1 22 23 24

BRACKET

ceramiclmet al ceramiclmet al ceramic ceramic meîal metal active active passive passive variable variab t e

SIZE

large small large small large small large small large small large small

FORCE LS MEAN

100.8 1 96.65

104.55 88.15 95.0 1 78.58 46.12 10.90 4.46 2.64 4.30 1.75

LSMEAN nwnber

1 2 3 4 5 6 7 8 9

10 Il 12

WIRE

NiTi NiTi SS SS twisted NiTi twisted NiTi twisted SS twisted SS

SUE

large small large small large small large small

FORCE LS MEAN

47.88 35.24 54.34 39.37 67.82 48.99 66.80 62.18

LSMEAN number

1 2 3 4 5 6 7 8