Thalman Thesis

8/3/2019 Thalman Thesis

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UNLOADING BEHAVIOR AND POTENTIAL BINDING OF

SUPERELASTIC ORTHODONTIC LEVELING WIRES:

A GINGIVALLY MALPOSED CUSPID MODEL

Trenton D. Thalman, D.D.S.

An Abstract Presented to the Faculty of the Graduate Schoolof Saint Louis University in Partial Fulfillment

of the Requirements for the Degree ofMaster of Science in Dentistry

2008


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ABSTRACT

Objective: To examine unloading behavior of superelastic

(SE), nickel-titanium-alloy (NiTi) leveling wires within a

gingivally malposed cuspid model. Materials and Methods:

A universal testing machine deflected continuous, 0.014-

inch SE NiTi wires gingivally at the right-cuspid position

of an orthodontic, dental-arch model. Binding points

(smallest deflections at which frictional forces stop

leveling wires from sliding through supporting bracket-

slots) and unloading plots (from beneath binding points)

were obtained with self-ligation (SL) and new (unrelaxed)

elastomeric ligation (EL) at the support sites. Unloading

data were collected with SL from 2.5-, 3.5-, 4.5-, and 5.5-

mm deflections; and from 1.5- and 2.5-mm deflections with

EL. Force-loss was quantified as the ordinate difference

between the peak and the trough of a plot. Descriptive and

inferential statistics, the latter Kruskal-Wallis with

Mann-Whitney U- tests, were run to analyze the force-loss

data. Results: Binding occurred with SL at a deflection of

7.5 mm, and at 3.5 mm with EL. Mean force-loss ranged from

87.0 10.1 grams to 0.0 0.0 grams with SL and EL during

unloading from 5.5 and 1.5 mm, respectively. Significant

differences (p < .01) in force-losses were obtained across

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2

all SL groups, but not between the EL groups. Conclusions:

1. Binding of 0.014-inch SE NiTi leveling wires occurs at

smaller deflection-amplitudes with EL than with SL.

2. Relatively constant aligning forces from 0.014-inch SE

NiTi leveling wires should not be expected in most clinical

situations. 3. Binding of 0.014-inch SE NiTi leveling

wires occurs at a deflection-amplitude threshold rather

than at a deflection-amplitude.


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UNLOADING BEHAVIOR AND POTENTIAL BINDING OF

SUPERELASTIC ORTHODONTIC LEVELING WIRES:

A GINGIVALLY MALPOSED CUSPID MODEL

Trenton D. Thalman, D.D.S.

A Thesis Presented to the Faculty of the Graduate Schoolof Saint Louis University in Partial Fulfillment

of the Requirements for the Degree ofMaster of Science in Dentistry

2008


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COMMITTEE IN CHARGE OF CANDIDACY:

Assistant Professor Ki Beom KimChairperson and Advisor

Professor Emeritus Robert J. Nikolai

Adjunct Associate Professor Kirk D. Satrom

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DEDICATION

This thesis is dedicated to my family: my wonderful

wife Debbie and my four amazing daughters Audrey, Lauryn,

Tricia, and Julia, and to my parents Jeff, Ilene, David,

and Patricia who have provided support and encouragement

throughout my higher education.

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ACKNOWLEDEGMENTS

The author would like to express appreciation to his

committee members: Dr. Ki Beom Kim, Dr. Robert Nikolai, and

Dr. Kirk Satrom. Each has contributed much time and effort

on the authors behalf. A special thanks to Mr. Joe

Tricamo and his associates at the Saint Louis University

machine shop for the many hours spent in manufacturing the

experimental equipment needed to complete this study.

The author would also like to thank GAC International

for donating brackets and tubes, Ormco Corp. for donating

archwires, and TP Orthodontics Inc. for donating ligatures

and a Straight Shooter.

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TABLE OF CONTENTS

LIST OF TABLES........................................... vi

LIST OF FIGURES......................................... vii

CHAPTER 1: INTRODUCTION.................................. 1

CHAPTER 2: REVIEW OF THE LITERATURE...................... 4 INTRODUCTION............................... 4

OCCLUSOGINGIVAL WIRE ACTIVATION ......... 4 DEFLECTION OF THE SE NITI WIRE........ 5 WIRE INDUCED NORMAL FORCES............ 7 DEFLECTED WIRE-LENGTH................. 8

HIGH-CUSPID LEVELING .................... 8 NORMAL FORCES AND TOOTH MOVEMENT..... 11 ARCHWIRE SLIDING DURING LEVELING..... 11

COULOMB FRICTION.......................... 12 SLIDING FRICTION THEORY ................ 12 STATIC VS. DYNAMIC FRICTION ............ 13 FRICTION IN ORTHODONTICS ............... 13

NORMAL FORCES IN ORTHDONTICS......... 14 Potential Normal Forces ........... 14 Ligation Method ................... 16

APPLIANCE STIFFNESS.................. 19 Design Stiffness .................. 19

Wire Stiffness .................... 20 SUMMARY................................... 21 REFERENCES................................ 23

CHAPTER 3: JOURNAL ARTICLE.............................. 26ABSTRACT.................................. 26INTRODUCTION.............................. 27MATERIALS AND METHODS..................... 32

MECHANICAL TESTS ....................... 32STATISTICS ............................. 36

RESULTS................................... 37

DISCUSSION................................ 39BINDING ................................ 39UNLOADING PLOTS ........................ 42LIGATION EFFECTS ....................... 45 FACTORS NOT EXAMINED ...................46CLINICAL RECOMMENDATIONS ............... 48

CONCLUSIONS............................... 48REFERENCES................................ 50

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V

ITA AUCTORIS............................................ 53

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LIST OF TABLES

Table 1. Descriptive Statistics: Force Losses (grams)... 38

Table 2. Mann-Whitney U- Tests of Force Losses (p < 0.01) 39

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LIST OF FIGURES

Figure 1.1: Force-diagram illustrating active andresponsive occlusogingival forces and couples duringcontinuous-wire cuspid-leveling........................... 9

Figure 1.2: An illustration of couples remaining whenbinding occurs........................................... 10

Figure 1.3: Arrows representing potential normal forcesexerted in bracket-slots by ligation or archwires. A, B,C, Facial views of both common edgewise and self-ligatingbrackets. D, A gingival view of a sectioned commonedgewise bracket. E, A gingival view of a sectionedactive self-ligating bracket........................... 16

Figure 2.1: Geometry and formulas to estimate the length(L) of wire between lateral-incisor and first-bicuspidbrackets with that wire sling-tied to the cuspid bracket. 29

Figure 2.2: Diagram illustrating occlusogingival forcesand couples accompanying continuous-wire cuspid leveling. 31

Figure 2.3: The model positioned in its fixture. Thefixture was bolted to the base of the testing machine.... 33

Figure 2.4: A representative unloading plot from the 5.5-mm SL group. The dashed curve includes the estimatedplateau. The dimension-symbol denotes the quantifiedforce-loss............................................... 36

Figure 2.5: Representative unloading plots from each group......................................................... 37

Figure 2.6: An illustration of couples present whenbinding occurs........................................... 41

Figure 2.7: Representative unloading plot from the SL 5.5-

mm group. The solid curve is the recorded plot. Thedashed curve represents an assumed estimate of wire-behavior without friction. The cross-hatched arearepresents the energy-loss occurring as a result offriction present......................................... 44

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Figure 2.8: Comparison of representative unloading plotsfrom the EL and SL 2.5-mm groups. The solid line is the EL2.5-mm plot. The dashed line is the SL 2.5-mm plot. Thecross-hatched area represents the difference in energytransfer from the two groups............................. 45


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CHAPTER 1: INTRODUCTION

Superelastic (SE), nickel-titanium-alloy (NiTi) wires

have become the wires of choice for orthodontic leveling

and aligning mechanics. These wires readily sustain large

deflections without exceeding the elastic limit of the

alloy. The large elastic range of SE NiTi is largely due

to its pseudoelastic characteristic. For example, Burstone

et al. 1 found that an 80 activation of SE NiTi wire

produced a 91% recovery compared to 20% for stainless steel

wire and 65% for martensitic NiTi wire. Some orthodontists

may believe that any large activation with SE NiTi wire

will result in the desired tooth movement; however, four

recent investigations report that friction can stop SE-

NiTi-wire displacements through ligated bracket-slots. 2-5

When a wire does not slide through supporting bracket-

slots, desired tooth movement is unlikely to occur.

Binding is defined herein as a condition in which an

orthodontic leveling wire is prevented from sliding through

ligated bracket-slots. Note that binding in this context

differs from the binding defined by Kusy and Whitley. 6

Binding can alter the desired tooth-moving forces. 7

Factors leading to SE-NiTi-wire binding in leveling

mechanics apparently have not been studied. Binding of


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desired tooth moving force will be completely negated if

the wire binds. Burstone 12 has pointed out that leveling of

a gingivally positioned cuspid with a continuous SE NiTi

wire leads to responsive forces with undesired displacement

tendencies. The aim of this investigation was to determine

the potential for binding and to describe the unloading

behavior of continuous 0.014-inch round SE NiTi wire in the

leveling of a gingivally malposed cupsid.

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CHAPTER 2: REVIEW OF THE LITERATURE

INTRODUCTION

This review of the literature begins with a discussion

of the dynamics of leveling a gingivally positioned cuspid

with a continuous SE NiTi archwire. The frictional forces

that arise in orthodontic leveling are then examined.

Understanding these concepts leads to the rationale for

this study of unloading behavior and potential binding in

bracket-slots supporting SE NiTi leveling wires.

OCCLUSOGINGIVAL WIRE ACTIVATION

When engaging an SE NiTi wire to level a gingivally

malposed cuspid, several mechanics-entities occur

simultaneously. First, the wire is deflected and is

attached to or engaged in the cuspid bracket. Second, in

response to the springback potential of the wire at the

cuspid, normal forces are induced at the adjacent

(supporting) brackets. Third, the effective length of wire

between the adjacent brackets increases as wire is drawn

through those adjacent brackets to reach the crown of the

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gingivally positioned cuspid. Each of these aspects is

examined individually below.

DEFLECTION OF THE SE NITI WIRE

As an SE NiTi wire is deflected, it first deforms in

an elastic manner in the austenitic state. As stress

induced in the wire increases, a phase-transformation

begins (from austenitic toward martensitic metallurgy).

This occurring stress-induced phase-transformation is

accompanied by a lessening in stress-increase needed to

continue the deflection. 13 In practice, the transformation

likely is incomplete at wire-engagement. When the wire is

then allowed to unload, hysteresis occurs and is followed

by a relatively level unloading plot as the (partial)

transformation reverses, and the alloy returns to its

austenite phase. 14 When the wire reaches the austenitic

state, unloading is completed via Hookean elastic

deactivation. The wire, then, may undergo large

deflections and completely return to its initial shape. 13

Throughout activation, the wire will conform to the lowest

energy-state that can be achieved as constrained, resulting

in specific curvatures within the interbracket spaces.

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The flexural stiffness of SE NiTi wire is dependent

upon its size and shape, the temperature-transition range

(TTR), and the amount of wire-deflection. 1,12,14 Flexural-

stiffness measurements for SE NiTi wires are based upon

linear regressions of the unloading curves. 1 These factors

are discussed below.

The cross-sectional size and shape of NiTi wire have

the same influences on its flexural stiffness(es) as they

have on the stiffness(es) of other orthodontic wires. 13

This topic is discussed later.

Stiffnesses of SE NiTi wire are influenced by the TTR;

as the TTR increases, stiffnesses decreases. The TTR can

be altered 1) by adding trace-elements to the alloy or

2) by heat-treating the wire. 14 Copper is added to some

NiTi alloys to lower the TTR, thus lessening wires loading

and unloading stiffnesses. 14

The unloading stiffness of SE NiTi wire is also

dependent upon the extent of activation. As the activating

deflection is increased, the unloading stiffness decreases. 1

Wilkinson et al. 2 found that a wire deflected to 1 mm

generated an initial unloading force of 247 grams. When

the same wires were deflected to 4 mm, they unloaded from

only 74 grams of force. This phenomenon is the rationale

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for Profitts statement, the force delivered by an A-NiTi

wire can be changed by releasing and retying it. 13

Because of the many factors that influence SE-NiTi-wire

stiffnesses, large variations in structural properties

exist between manufacturers 2,15 and within manufacturers.

Only two of these factors are under the direct control of

the orthodontist. First, the wire selected with its size,

shape, and TTR influences the loading and unloading

stiffnesses. Second, the extent of activation/deflection

may be varied, affecting the unloading stiffness.

WIRE INDUCED NORMAL FORCES

When a continuous wire is deflected and attached to a

gingivally malposed, right-cuspid bracket, the wire

contacts the distogingival and mesio-occlusal edges of the

lateral-incisor bracket-slot and the mesiogingival and

disto-occlusal edges of the first-bicuspid bracket-slot.

These contacts create normal forces between the slots and

wire. The magnitudes of these normal forces are partially

dependent upon the loading stiffness as the wire is engaged

and the unloading stiffness as the wire unloads. 8 Wire-

curvatures in relation to the bracket-slots dictate which

normal force will be the greatest. The normal force

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adjacent to the greatest wire-curvature will be the largest

normal force in the system. 16

DEFLECTED WIRE-LENGTH

When an archwire is deflected to reach a gingivally

malpositioned cuspid, the wire is deflected gingivally,

drawing wire through the adjacent brackets toward the

cuspid. The result is a greater length of wire between the

lateral-incisor and first-bicuspid brackets than the

mesiodistal distance between them. To illustrate this

inequality, the geometry can be simplified with two right

triangles, and the Pythagorean Theorem is invoked. If a

wire is deflected 4 mm and sling-tied to a high cuspid with

a 13-mm distance between the lateral-incisor and first-

bicuspid brackets, there is approximately 15.3-mm of wire

between the brackets. If the wire is to level the cuspid,

2.3 mm of wire must slide through the adjacent brackets so

that only 13 mm of wire remains between those brackets.

HIGH-CUSPID LEVELING

With a continuous wire secured to a high cuspid, in

addition to the action against the cuspid, potentially

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counterproductive forces are created, posing potential

problems for the clinician using a straight-wire technique.

Burstone wrote: With a high canine, a [passively] straight

wire tends to tip the buccal segment toward the canine. 9

Creating this undesired displacement potential are

responsive intrusive forces and couples exerted on the

adjacent teeth through their brackets. See Figure 1.1.

Figure 1.1: Force-diagram illustrating active and responsiveocclusogingival forces and couples during continuous-wire cuspid-leveling.

Forces present in the system originate from the elastic

deformation of the wire. As the wire attempts to spring

back toward its original shape, an occlusal force is

created at the cuspid. In response to the occlusal force,

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gingival forces are applied to the anchorage sites. Force-

magnitude at each anchorage site is approximately one-half

of the occlusal force at the cuspid. Additionally, couples

are applied within the first-bicuspid and lateral-incisor

bracket-slots, creating tipping/torquing moments. Couples

are created by the normal forces between bracket-slots and

the archwire. 16 Excessive frictional forces can effectively

cancel the springback potential at the cuspid, and the net

extrusive action disappears, leaving only the couples and

friction until the resistances(s) can be overcome. See

Figure 1.2.

Figure 1.2: An illustration of couples remaining when binding occurs.

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NORMAL FORCES AND TOOTH MOVEMENT

An archwire having been deflected gingivally at the

cuspid, the net normal forces on the adjacent brackets are

individually nearly equally as approximately one-half of

the cuspid force mesially and distally. The normal forces,

local wire-curvatures, and the need for the wire to slide

through the adjacent bracket-slots to progress toward a

correction, create the friction leading to potential

binding of the leveling wire. Potential for binding may

particularly be raised with SE NiTi wires because a large

deflection decreases the unloading stiffness. 1

ARCHWIRE SLIDING DURING LEVELING

As discussed previously, a deflection to level a

gingivally malposed cuspid will produce an excess length

of wire between the lateral-incisor and first-bicuspid

brackets. In order for the desired leveling to occur, this

excess wire must slide through the supporting bracket-

slots. In the presence of wire-slot contact, frictional

forces oppose this sliding motion. The potential for

binding of leveling wires has not been examined, although

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some incidental binding has been reported in the process of

other investigations. 2-5

COULOMB FRICTION

Friction is the force that opposes the tangential

movement of two bodies in contact. The Coulomb model of

friction is characterized by the following equation: F =

N* where F is the frictional force, is the coefficient

of friction, and N is the normal force. 9 Coulomb friction

is explored in Sliding-Friction Theory, Static and Dynamic

Friction, and Friction in Orthodontics to follow.

SLIDING FRICTION THEORY

Sliding friction is defined as friction between two

solid objects in relative translational motion. This type

of friction is associated with orthodontic mechanics. Two

major influences on maximum static and kinetic sliding

friction are the magnitudes of the normal forces and the

relative surface-roughness of the objects in contact. 16

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STATIC VS. DYNAMIC FRICTION

Three categories of Coulomb friction are defined:

static friction, maximum static friction, and dynamic

friction. Static friction is present when relative motion

is attempted, but none occurs. 16 This frictional force

serves to maintain equilibrium when active forces are

insufficient to produce movement. Maximum static friction

is the tangential force present just before motion starts.

This force is ordinarily the greatest resistance before the

object begins to slide. 17 Dynamic friction is usually less

than maximum static friction, and it is the frictional

force present when objects are sliding across one another. 16

Separate coefficients of friction may be determined

experimentally, for a pair of contacting surfaces, for both

maximum static and dynamic friction. 17

FRICTION IN ORTHODONTICS

Coulombs explanation of friction becomes more

complicated in orthodontics. First, the normal forces

present in orthodontics are very situation-dependent and

are rarely constant. Second, the velocity at which

movement occurs is very slow, leading to inconsistency in

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the type of frictional forces present. Third, the surface-

roughnesses of the materials depend upon more than just the

chemical compositions. Each of these aspects is discussed

further within the following subsections.

NORMAL FORCES IN ORTHDONTICS

Two categories of normal force are present in

orthodontic leveling. First, slot-wire contact(s) exist,

due to wire-curvatures at/through the slot. Second, the

ligation securing the wire in the slot can create normal

force. These normal forces for a gingivally displaced and

ligated wire are described below.

Potential Normal Forces

When the wire is activated gingivally, but only

contacts the edge of one wing of the bracket, a normal

force exists at that point only. Depending upon the wire-

curvature through the slot, normal forces may be present at

both ends of the bracket. From a facial perspective, then,

normal forces are possible at opposite slot-edges or in the

middle of the slot as well. Potential normal forces can

also be viewed from the gingival perspective of the

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A CB

ED

Figure 1.3: Arrows representing potential normal forces exerted inbracket-slots by ligation or archwires. A, B, C, Facial views of bothcommon edgewise and self-ligating brackets. D, A gingival view of asectioned common edgewise bracket. E, A gingival view of a sectionedactive self-ligating bracket.

Ligation Method

Conventional ligations are of two material categories:

stainless steel and (polymeric) elastomers. Other

ligations have been introduced in attempts to reduce

friction. These include self-ligating brackets, non-

conventional elastomeric ligatures,4,5

and brackets with six

tie-wings. 18 Self-ligating brackets can be subdivided as

having integral active or passive slot-closures.

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Steel ties are often used to ligate SE NiTi wires. The

normal force created by this ligature may be very small. 19

Bednar et al. 9 found that steel ligatures produced the least

friction when sliding a bracket along a wire when compared

to elastomeric and self-ligations; however, Iwasaski et

al. 20 found significant variances across clinicians in

placing steel ties. This variation ranged between 150 and

1470 grams with steel ties compared to 1600 grams with

elastomers.

Elastomeric ligations initially produce relatively

large normal forces with sizable friction potential, as

confirmed in many investigations; 2,4,5,9,19-21 however, none of

the friction-literature reviewed accounts for sizable

(perhaps 50% or greater) force-losses as the elastomers

relax. 22 Significant variations in initial force magnitudes

for a constant stretch have also been obtained within

samples of alike elastomeric ligatures. 22-24 The normal

force may also vary in magnitude with wire and bracket

sizes. It has been found that an increase in wire- and/or

bracket-dimensions results in more stretch of the

elastomeric ligatures and thus greater normal forces. 25

Self-ligating brackets have been introduced into the

orthodontic marketplace with claims of less friction and

lighter forces. Laboratory testing has confirmed less

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friction with self-ligating brackets; 2,3,19,21,24,26 however,

during straight-wire leveling, larger active forces are

generally produced with these brackets because there is

less friction. 2,3

The slot-closure device varies within the family of

self-ligating brackets; two groups of brackets are termed

active and passive. Within the active brackets the

ligating mechanism presses against the archwire (if it

exceeds a minimum faciolingual dimension, i.e., 0.018

inches), seating it in the bracket. The ligation of a

passive bracket will not press against an archwire. The

stated, seemingly simple difference, active vs. passive

brackets, is flawed, however, because activated archwires

are often (first-order) angulated in the slot, and such

angulations often result in the creation of normal forces.

Differences in normal forces, generated in active vs.

passive self-ligating brackets, have been reported. Hain

et al. 24 found that, with a 0.019- x 0.025-inch stainless

steel archwire, 1.61 Newtons were produced (faciolingually)

in an active bracket, and no normal force existed in a

passive bracket. This difference in normal forces has

been shown to change with wire-size. Shivapuja and Berger 27

found no difference between active and passive self-

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ligating brackets in faciolingual normal forces exerted

against an 0.018-inch stainless-steel wire.

APPLIANCE STIFFNESS

Normal forces can be directly related to the stiffness

of the activated archwire. 8 As the flexural stiffness(es)

of a wire increase, the magnitude(s) of normal forces

produced by the wire increase. Archwire-stiffness depends

upon both the wire itself and the local design of the

appliance. The unit wire-stiffness is dependent upon the

wire-material stiffness and the cross-sectional shape and

size. 28 The unit stiffness of a SE NiTi wire is further

complicated by its deflection-dependence. 1

Design Stiffness

The design-stiffness is dependent upon two variables:

the length(s) of wire and the support(s) of the wire. The

wire-stiffness varies inversely with its length from one

support or between two supports. 13,28 The archwire may be

supported in three ways. First, the wire can be a

cantilever, and the stiffness is dependent upon the length

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of the cantilever. As the length of cantilever increases,

the stiffness decreases. Second (and third), wires can be

supported at both ends either loosely or tightly. When

comparing wires of the same size and shape, with equal

length, stiffness increases as wire-support clearance

decreases. Loosely supported wires are stiffer than

cantilevered wires and tightly supported wires are stiffer

than loosely supported wires. 13

The orthodontist can vary the wire-length between

crown-attachments. A loop can effectively increase wire-

length, and bracket-width alters interbracket distance and

effectively changes wire-length. Frank and Nikolai 8 found

that an increase in bracket-width increased friction during

cuspid-retraction.

Wire Stiffness

Unit wire-stiffness is dependent upon wire material-

stiffness and cross-sectional shape and size. Material-

stiffnesses have been determined for stainless steel, -

titanium ( -Ti) alloys, and stabilized martensitic NiTi

alloys. 29 The material-stiffness of SE NiTi wire is notably

dependent upon the extent of deflection and can vary from

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7% to 41% of the stiffness of orthodontic stainless

steel. 1,13

As wire-size increases, the stiffness of the wire

increases to the fourth power for round wires and generally

as a cubic function of the dimension in the direction of

flexure; for example, if a round wire is doubled in its

dimension in the flexure direction, the stiffness increases

sixteen times (2 4 = 16). For rectangular wires the

dimension in the direction of deflection has the greater

influence on stiffness. 13,28

When an archwire is brought into contact with mesial

and/or distal corners of the slot, due to the local wire-

curvature as activated, wire-stiffness becomes a

predominant factor in friction potential because of the

normal force(s) generated. 8

SUMMARY

It is easily seen that friction in orthodontics is

complex. This complexity is further increased with SE NiTi

archwires. The information that is available currently

concerning friction and SE NiTi wires has been derived

primarily from displacing a bracket along a guiding wire or

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pulling a wire through a bracket-slot or series of

slots. 21,25,26,30-32 More recently, leveling with SE NiTi wires

has been examined from the perspective of friction

affecting forces delivered to the malposed tooth/teeth. 2-5,33

Apparently, though, all of these inquires involved

arbitrarily selected deflections, some of which

incidentally produced binding. 2-4 No attempts to determine

the binding points for SE NiTi leveling wires have been

found in the published literature.

Due to the complex nature of the factors involved,

indirect measures for potential binding of SE NiTi

archwires in leveling are impossible. A model simulating a

gingivally malposed cuspid has been developed to examine

the binding of 0.014-inch-diameter SE NiTi archwires.

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REFERENCES

1. Burstone CJ, Qin B, Morton JY. Chinese NiTi wire--a new orthodonticalloy. Am J Orthod 1985;87:445-452.

2. Wilkinson PD, Dysart PS, Hood JA, Herbison GP. Load-deflectioncharacteristics of superelastic nickel-titanium orthodontic wires. Am JOrthod Dentofacial Orthop 2002;121:483-495.

3. Ward BL. Friction in Alignment Mechanics: The effects of ligation,perturbation, and wire size on orhtodontic aliging forces Center forAdvanced Dental Education. Saint Louis, MO: Saint Louis University;2007.

4. Franchi L, Baccetti T. Forces released during alignment with apreadjusted appliance with different types of elastomeric ligatures. AmJ Orthod Dentofacial Orthop 2006;129:687-690.

5. Camporesi M, Baccetti T, Franchi L. Forces released by estheticpreadjusted appliances with low-friction and conventional elastomericligatures. Am J Orthod Dentofacial Orthop 2007;131:772-775.

6. Kusy RP, Whitley JQ. Influence of archwire and bracket dimensions onsliding mechanics: derivations and determinations of the criticalcontact angles for binding. Eur J Orthod 1999;21:199-208.

7. Rossouw PE. Friction: An Overview. Sem Orthod 2003;9:218-222.

8. Frank CA, Nikolai RJ. A comparative study of frictional resistancesbetween orthodontic bracket and arch wire. Am J Orthod 1980;78:593-609.

9. Bednar JR, Gruendeman GW, Sandrik JL. A comparative study offrictional forces between orthodontic brackets and arch wires. Am JOrthod Dentofacial Orthop 1991;100:513-522.

10. Andreasen GF, Quevedo FR. Evaluation of friction forces in the0.022 x 0.028 edgewise bracket in vitro. J Biomech 1970;3:151-160.

11. Tidy DC. Frictional forces in fixed appliances. Am J OrthodDentofacial Orthop 1989;96:249-254.

12. Burstone CJ. Application of Bioengineering to ClinicalOrthodontics. In: Graber TM, Vanarsdall RL, Vig KWL, editors.Orthodontics: Current Principles and Techniques. St. Louis, MO:

Elsivier, Mosby; 2005. p. 293-330.

13. Proffit WR. Contemporary Orthodontics. 3rd Ed. St. Louis, MO:Mosby; 2000.

14. Matasa CG. Biomaterials in Orthodontics. In: Graber TM, VanarsdallRL, Vig KWL, editors. Orthodontics: Current Principles and Techniques.St. Louis, MO: Elsevier, Mosby; 2005. p. 345-390.

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15. Thayer TA, Bagby MD, Moore RN, DeAngelis RJ. X-ray diffraction ofnitinol orthodontic arch wires. Am J Orthod Dentofacial Orthop1995;107:604-612.

16. Nikolai RJ. Bioengineering Analysis of Orthodontic Mechanics.Philadelphia, PA: Lea & Febiger; 1985.

17. Rossouw PE, Kamelchuk LS, Kusy RP. A Fundamental Review ofVariables Associated with Low Velocity Frictional Dynamics. Sem Orthod2003;9:223-235.

18. Thorstenson GA, Kusy RP. Effects of ligation type and method on theresistance to sliding of novel orthodontic brackets with second-orderangulation in the dry and wet states. Angle Orthod 2003;73:418-430.

19. Hain M, Dhopatkar A, Rock P. The effect of ligation method onfriction in sliding mechanics. Am J Orthod Dentofacial Orthop2003;123:416-422.

20. Iwasaki LR, Beatty MW, Randall CJ, Nickel JC. Clinical ligationforces and intraoral friction during sliding on a stainless steelarchwire. AmJ Orthod Dentofacial Orthop 2003;123:408-415.

21. Henao SP, Kusy RP. Evaluation of the frictional resistance ofconventional and self-ligating bracket designs using standardizedarchwires and dental typodonts. Angle Orthod 2004;74:202-211.

22. Taloumis LJ, Smith TM, Hondrum SO, Lorton L. Force decay anddeformation of orthodontic elastomeric ligatures. Am J OrthodDentofacial Orthop 1997;111:1-11.

23. Khambay B, Millett D, McHugh S. Archwire seating forces produced bydifferent ligation methods and their effect on frictional resistance.

Eur J Orthod 2005;27:302-308.

24. Hain M, Dhopatkar A, Rock P. A comparison of different ligationmethods on friction. Am J Orthod Dentofacial Orthop 2006;130:666-670.

25. Kapila S, Angolkar PV, Duncanson MG, Jr., Nanda RS. Evaluation offriction between edgewise stainless steel brackets and orthodonticwires of four alloys. Am J Orthod Dentofacial Orthop 1990;98:117-126.

26. Henao SP, Kusy RP. Frictional evaluations of dental typodont modelsusing four self-ligating designs and a conventional design. AngleOrthod 2005;75:75-85.

27. Shivapuja PK, Berger J. A comparative study of conventionalligation and self-ligation bracket systems. Am J Orthod DentofacialOrthop 1994;106:472-480.

28. Burstone CJ. Application of Bioengineering to ClinicalOrthodontics. In: Thomas M. Graber RLV, Katherine W.L. Vig, editor.Orthodontics: Current Pricniples and Techniques. St. Louis, MO:Elsivier, Mosby; 2005. p. 293-330.

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25

29. Burstone CJ. Variable-modulus orthodontics. Am J Orthod 1981;80:1-16.

30. Baccetti T, Franchi L. Friction produced by types of elastomericligatures in treatment mechanics with the preadjusted appliance. AngleOrthod 2006;76:211-216.

31. Tecco S, Festa F, Caputi S, Traini T, Di Iorio D, D'Attilio M.Friction of conventional and self-ligating brackets using a 10 bracketmodel. Angle Orthod 2005;75:1041-1045.

32. Kusy RP, Whitley JQ. Effects of surface roughness on thecoefficients of friction in model orthodontic systems. J Biomech1990;23:913-925.

33. Fuck L-M, Drescher D. Force systems in the initial phase oforthodontic treatment -- a comparison of different leveling arch wires.J Orofacial Orthop 2006;67:6-18.


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CHAPTER 3: JOURNAL ARTICLE

ABSTRACT

Objective: To examine unloading behavior of superelastic

(SE), nickel-titanium-alloy (NiTi) leveling wires within a

gingivally malposed cuspid model. Materials and Methods:

A universal testing machine deflected continuous, 0.014-

inch SE NiTi wires gingivally at the right-cuspid position

of an orthodontic, dental-arch model. Binding points

(smallest deflections at which frictional forces stop

leveling wires from sliding through supporting bracket-

slots) and unloading plots (from beneath binding points)

were obtained with self-ligation (SL) and new (unrelaxed)

elastomeric ligation (EL) at the support sites. Unloading

data were collected with SL from 2.5-, 3.5-, 4.5-, and 5.5-

mm deflections; and from 1.5- and 2.5-mm deflections with

EL. Force-loss was quantified as the ordinate difference

between the peak and the trough of a plot. Descriptive and

inferential statistics, the latter Kruskal-Wallis with

Mann-Whitney U- tests, were run to analyze the force-loss

data. Results: Binding occurred with SL at a deflection of

7.5 mm, and at 3.5 mm with EL. Mean force-loss ranged from

87.0 10.1 grams to 0.0 0.0 grams with SL and EL during

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unloading from 5.5 and 1.5 mm, respectively. Significant

differences (p < .01) in force-losses were obtained across

all SL groups, but not between the EL groups. Conclusions:

1. Binding of 0.014-inch SE NiTi leveling wires occurs at

smaller deflection-amplitudes with EL than with SL.

2. Relatively constant aligning forces from 0.014-inch SE

NiTi leveling wires should not be expected in most clinical

situations. 3. Binding of 0.014-inch SE NiTi leveling

wires occurs at a deflection-amplitude threshold rather

than at a deflection-amplitude.

INTRODUCTION

Unloading behavior of superelastic (SE), nickel-

titanium-alloy (NiTi) orthodontic wires has been well

documented from cantilever 1 and three-point 2,3 bending tests.

These tests have shown that SE NiTi wires have large

elastic ranges and can exert relatively constant forces

over sizable portions of those ranges. 1-3 SE NiTi wires

have also displayed deflection-dependent unloading

stiffnesses; larger deflections resulted in smaller

unloading stiffnesses. 1-4 Properties of SE NiTi wires have

led to recommendations from Burstone et al. 1 and Proffit 4

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that they be the wires of choice when large deflections and

relatively constant tooth-moving forces are required.

The unloading behavior of SE NiTi wires has been

tested within rather complex models. 3,5-8 These models all

involved multiple brackets and various ligation methods.

Under some of these conditions Wilkinson et al., 3 Camporesi

et al., 5 Franchi and Baccetti, 6 and Ward 8 found that SE NiTi

wires can cease to slide through supporting bracket-slots.

The archwire failing to slide through supporting bracket-

slots is termed binding herein. Note that this

definition differs from the wire-slot binding described by

Kusy and Whitley. 9 Discovery of binding in leveling

mechanics raises questions concerning the behavior of SE

NiTi wire. Some pertinent questions are as follows: What

activating deflection will cause the SE NiTi wire to bind?

What factors lead to SE NiTi wire-slot binding? How do SE

NiTi wires respond as they begin to bind?

Wire-length between brackets is a source of potential

binding of a continuous leveling wire. 8 As a leveling wire

is deflected to engage a malposed tooth, to obtain the

necessary added length locally, the wire slides through the

adjacent ligated brackets and tubes. For the malposed

tooth/teeth to align, the wire must slide back through the

supporting brackets and tubes. Free wire-length between

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two brackets adjacent to a malposed cuspid can be estimated

by superimposing two right triangles on the curved wire as

illustrated in Figure 2.1. Assuming a 13-mm lateral-

incisor-to-first-bicuspid interbracket distance and a 4-mm

deflection to the cuspid bracket, 15.3 mm is calculated as

the wire-length between the lateral-incisor and first-

bicuspid brackets. An estimated 15.3 mm of wire-length

demonstrates that, for the wire to (deactivate and) become

straight, approximately 2.3 mm of wire must slide through

the slots of the adjacent ligated brackets and tubes.

a

b

L 2c

c 2 =a 2 +b 2

c

Figure 2.1: Geometry and formulas to estimate the length (L) of wirebetween lateral-incisor and first-bicuspid brackets with that wiresling-tied to the cuspid bracket.

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Sliding of a leveling wire may be opposed by frictional

forces. 6 Excessive frictional forces will stop the wire

from sliding, resulting in a bound wire. 3,6,8 Information

currently available concerning friction and SE NiTi wires

has been derived primarily from displacing a bracket along

a guiding wire or pulling a wire through a bracket-slot or

series of slots. 10-15 More recently, leveling with SE NiTi

wires has been examined from the perspective of friction

affecting forces delivered to the malposed tooth/teeth. 3,5-8

Apparently, though, all of these inquiries involved

arbitrarily selected deflections, some of which

incidentally produced binding. 3,6,8 No attempts to determine

the binding points for SE NiTi leveling wires have been

found in the published literature.

Self-ligating brackets have been introduced into the

orthodontic marketplace with claims of less friction and

lighter forces. Laboratory testing has confirmed that

often there is less friction with self-ligating

brackets; 3,8,11,12,16,17 notably, during straight-wire leveling,

larger active forces are generally produced with these

brackets because there is less friction. 3,8

The purpose of this study was to examine the binding

and unloading behavior of a SE NiTi wire within a

gingivally-malposed-cuspid model. Ligation was varied:

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self-ligation or new (unrelaxed) elastomerics. Burstone 18

has pointed out that leveling of a gingivally positioned

cuspid with a continuous wire tends to tip adjacent teeth

towards the cuspid. Forces responsible for these tooth

movements are created by the wire-curvatures at and through

the first-bicuspid and lateral-incisor bracket-slots.

These curvatures induce pairs of normal forces at the

supporting bracket-slots. Wire-curvatures indicate that

the normal forces closest to the cuspid are greater than

the normal forces farther from the cuspid. 19 These

unbalanced pairs of normal forces result in the couples and

the intrusive forces illustrated in Figure 2.2.

Figure 2.2: Diagram illustrating occlusogingival forces and couplesaccompanying continuous-wire cuspid leveling.

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When a leveling wire binds, occlusal springback at the

cuspid bracket temporarily ceases, but the couples remain,

frictional forces disallow wire-sliding, and the curved

shape of the wire is maintained. The responsive couples

are seen to potentially tip/torque the supporting teeth

such that the crowns could move toward the cuspid. Such

responsive displacements would reduce wire-curvatures,

reducing friction, and tend toward unbinding the wire.

MATERIALS AND METHODS

MECHANICAL TESTS

A model was constructed of -inch-thick tool-steel

plate, machined to match the Tru-Arch, maxillary, small

archform (Ormco Corp., Glendora, CA). Attached to the

machined edge were two first-molar tubes with zero first-

order rotation and nine In-Ovation-R brackets (GAC

International, Bohemia, NY) from second bicuspid to second

bicuspid (0.022-inch slots/tubes); material was removed atthe right-cuspid site to permit gingival deflections there.

Brackets and tubes were spaced according to the typical

maxillary tooth size of the adult-male dentition as

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modified by Wilkinson et al. 3 The set of brackets and tubes

was aligned with a 0.022-inch-diameter stainless-steel

archwire, shaped to match the model; the attachments were

direct-bonded with Pad Lock (Reliance Orthodontic

Products, Itasca, IL). See Figure 2.3.

Figure 2.3: The model positioned in its fixture. The fixture wasbolted to the base of the testing machine.

All trials were conducted with a universal testing

machine (Model 1011, Instron Corp., Canton, MA) Tests were

initiated by deflecting small, maxillary, 27C Copper NI-

TI, 0.014-inch, Tru-Arch archblanks gingivally at the

right-cuspid position. Wires were deflected with a 0.010-

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increments of 1 mm until five consecutive wires bound. The

smallest amplitude at which five consecutive wires bound

was defined as the estimated binding point.

Unloading data were collected from ten wires from each

group. (A group is defined by ligation and deflection-

amplitude.) Group tests began at a deflection-amplitude 1

mm below the estimated binding point, and the amplitude was

decreased by 1 mm for each additional group. New groups

were added until a relatively level, unloading plateau was

observed. Groups containing wires that bound were excluded

from the unloading data-set.

Initial unloading plots revealed a trough deviating

from the plateau that is typically obtained in three-point

bending tests of SE NiTi wires. The ordinate difference

between the trough and estimated plateau was defined as

force-loss. See Figure 2.4. Force-loss measurements were

taken from all unloading plots.

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Deflection Distance (mm)

0 1 2 3 4 65

0

50

100

150

200

250

U n

l o a

d i

n g

F o r c e

(

g )

Figure 2.4: A representative unloading plot from the 5.5-mm SL group.The dashed curve includes the estimated plateau. The dimension-symboldenotes the quantified force-loss.

STATISTICS

Force-loss measurements were analyzed with SPSS 14.0

for Windows (SPSS Inc., Chicago, IL). Descriptive

statistics were compiled for each group. A Kruskal-Wallis

test was run to study the effects of deflection-amplitude

and ligation method on a parameter defined as force loss.

Post-hoc Man-Whitney U-tests were conducted. Significant

differences were sought at p < 0.01.

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RESULTS

The estimated binding points were at deflection-

amplitudes of 3.5 mm with EL and 7.5 mm with SL. Unloading

data were collected at deflection-amplitudes of 1.5 and 2.5

mm with EL; and 2.5, 3.5, 4.5, and 5.5 mm with SL. The

6.5-mm SL group was excluded because some wires unloaded

completely and other specimens bound. A large dip from the

SE-characteristic plateau was noted from each of the SL

groups deflected to 4.5 and 5.5 mm; see Figure 2.5.

Legend

SL 5.5

SL 4.5

SL 3.5

SL 2.5

EL 1.5

EL 2.5


0 1 2 3 4 65

0

50

100

150

200

250

U n

l o a

d i

n g

F o r c e

(

g )

Figure 2.5: Representative unloading plots from each group

Descriptive statistics are presented in Table 1.

Force-loss increased from 3.5 grams to 87.0 grams as the

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SL-group deflection-amplitudes approached the estimated

binding point. Mean force-losses from the EL groups were

0.0 grams and 0.5 grams from 1.5- and 2.5-mm deflection-

amplitudes, respectively.

Table 1. Descriptive Statistics: Force Losses (grams)

Group Mean SD Minimum Maximum

SL 5.5-mm 87.0 10.1 75 105

SL 4.5-mm 34.5 6.0 30 50

SL 3.5-mm 15.0 4.7 10 20

SL 2.5-mm 3.5 2.4 0 5

EL 2.5-mm 0.5 1.6 0 5

EL 1.5-mm 0.0 0.0 0 0

The Kruskal-Wallis analysis revealed statistical

differences across the mean force-loss data. Mann-Whitney

U -Tests determined statistically significant differences

within all pairs of SL force-loss groups and with the EL

groups; the force-losses between the EL groups were not

statistically different. See Table 2.

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Table 2. Mann-Whitney U- Tests of Force Losses (p < 0.01)

Groups(mm) SL 5.5 SL 4.5 SL 3.5 SL 2.5 EL 2.5 EL 1.5

SL 5.5 n/a

SL 4.5 Sig n/a

SL 3.5 Sig Sig n/a

SL 2.5 Sig Sig Sig n/a

EL 2.5 Sig Sig Sig Sig n/a

EL 1.5 Sig Sig Sig Sig Non Sig n/a

DISCUSSION

BINDING

SE NiTi wires respond mechanically very differently

from Hookean orthodontic-alloy wires. Within the present

model, the SE NiTi wire may bind. After the wire is

deflected and deactivation begins, wire-slot friction at

the supports has the effect of decreasing the net unloading

force at the cuspid bracket. Changes in frictional and

springback forces occur for two reasons. First, frictional

forces result in particular from wire-and-bracket-slot

contacts at the lateral-incisor and first-bicuspid

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brackets. As deflection-amplitude is increased, wire-

curvatures increase between the cuspid and the supporting

bracket-slots, and greater wire-curvatures result in larger

normal and frictional forces at the supporting bracket-

slots. Second, increases in deflection-amplitude, with SE

NiTi wires, decrease unloading stiffnesses and springback

forces. 1 A deflected state may be reached where the

springback potential of the wire cannot overcome the

frictional forces, and the wire binds in those slots.

Bound wires may free-up and unload because of the

couples exerted that could torque the lateral-incisor and

first-bicuspid toward the malposed cuspid. See Figure 2.6.

The frictional forces are only fractions of the sizes of

the normal forces; thus, the couples dominate in

displacement potential. The torquing could reduce wire-

curvatures, lessen frictional forces, and occlusal

unloading at and movement of the cuspid could resume.

Application of the estimated binding points herein to

clinical practice becomes somewhat challenging. In this

research, binding-point estimates were specified at

deflection-amplitudes where binding occurred consistently.

The SL estimate discounted the binding of several specimens

within the SL 6.5-mm group. In future research, binding

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thresholds , where binding begins to occur, might be more

useful for clinical application.

Figure 2.6: An illustration of couples present when binding occurs.

Understanding that SE NiTi wires may bind is important

clinically. A bound wire will produce either no toothmovement or unwanted tooth movement. 20 It should be noted

that binding occurred here within both SL and EL groups.

Some researchers have (erroneously) claimed that self-

ligating brackets result in a virtually friction-free

appliance where binding cannot occur. 21

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UNLOADING PLOTS

Unloading plots in Figure 2.5 reveal several notable

findings. First, SE NiTi wires activated between two

bracket-slots generally did not produce relatively constant

forces. Plots from the 2.5- and 3.5-mm SL groups exhibited

relatively constant force during 1.5 and 2.5 mm of

unloading, respectively. All other unloading plots

displayed substantially varying forces. Varying unloading

forces resulted from frictional forces impairing leveling-

wire sliding. Attaining constant tooth/teeth moving forces

may not be important for orthodontic displacement, as

optimal tooth/teeth moving forces are unknown. 22 Second,

frictional forces altered unloading plots from the SL

groups, often creating troughs deviating from the

anticipated plateaus. Small troughs occurred in EL 2.5-mm

curves and no troughs occurred within the EL 1.5-mm group.

Third, a step was observed at 200 grams in each unloading

plot. The source of this step is unclear. Fourth, a

spike in unloading force occurs in all SL plots at about

0.5 mm of deflection. This spike, a sudden increase in

force, may reflect the wire undergoing completion of the

reverse transformation back to the austenitic metallurgic

phase.

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FORCE-LOSSES

Force-losses quantified herein, partially evaluating

the SE NiTi wire behavior, demonstrated the increasing

nemesis of friction within the SL groups as deflection-

amplitude was increased. Wire-curvatures between the

cuspid and supporting bracket-slots are responsible for

much of the friction. As wire-curvatures increase, larger

normal forces are induced in the supporting bracket-slots.

The unloading plot from the largest deflection-amplitude is

illustrated in Figure 2.7. This figure compares the

expected behavior of a SE NiTi wire with friction absent to

that with friction impeding wire displacements through the

ligated slots. The energy-loss depicted is a direct result

of frictional forces.

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0 1 2 3 4 65

0

50

100

150

200

250

U n

l o a

d i

n g

F o r c e

(

g )

Figure 2.7: Representative unloading plot from the SL 5.5-mm group.The solid curve is the recorded plot. The dashed curve represents anassumed estimate of wire-behavior without friction. The cross-hatchedarea represents the energy-loss occurring as a result of frictionpresent.

The EL groups also experienced energy-loss as a result

of friction. The pattern of energy-loss was quite

different from that of the SL groups. Figure 2.8 is a

comparison of unloading plots from the EL and SL 2.5-mm

groups. These plots are compared because the deflection-

amplitudes were equal; therefore, the friction-free

deactivation-plot is the same for both groups. Very little

force was lost (3.5 grams) to friction from the SL 2.5-mm

group. The EL plot did not display the trough or much of

the plateau typically exhibited by the SL groups.

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0 1 2 3 4 65

0

50

100

150

200

250

U n

l o a

d i

n g

F o r c e

( g

)

Figure 2.8: Comparison of representative unloading plots from the ELand SL 2.5-mm groups. The solid line is the EL 2.5-mm plot. Thedashed line is the SL 2.5-mm plot. The cross-hatched area representsthe difference in energy transfer from the two groups.

Although, there is greater energy-loss within the EL

2.5-mm group, both groups displayed adequate tooth/teeth

moving forces. Also, the force-loss difference would be

expected to decrease as elastomerics relax. 23

LIGATION EFFECTS

The self-ligating clips of the In-Ovation brackets

were not expected to contribute normal forces with 0.014-

inch wire engaged. Faciolingual space between bracket-slot

base and clip accepts wires (passive from an occlusal

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perspective) less than 0.018 inches in diameter without

contact between the archwire and clip. 24

Beyond the influence of wire-curvatures, frictional

forces also arise from elastomeric ligation stretched

around leveling wires, sliding through support-slots.

Effects of EL in this model resulted in energy-losses that

were greater from the EL 2.5-mm group than from the SL 2.5-

mm group. The greater energy-loss from the EL 2.5-mm group

is displayed as the cross-hatched area in Figure 2.8.

FACTORS NOT EXAMINED

Other factors not studied within this research could

affect binding points and the unloading behavior of SE NiTi

leveling wires. These factors include relaxation of

elastomeric ligatures, simulating extraneous intraoral

forces, and varying interbracket distances, wire diameter,

and wire temperature-transition range (TTR).

Stretched elastomeric ligatures have been shown to

relax, losing one-half or more of their initial force

magnitudes over time. 25 This relaxation results in reduced

normal forces between archwires and bracket-slots and

ligatures. Recently, Petersen 23 found average SE-NiTi-wire

unloading forces of 71 grams with new (unrelaxed)

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elastomerics, 112 grams with relaxed elastomerics, and 128

grams with self-ligation. Binding deflection-amplitudes

and unloading plots from SE NiTi wires may change as

elastomerics relax.

As previously mentioned, leveling-wire curvatures are

responsible for the normal forces between the wire and the

bracket-slots. Changing the local wire-curvature will

alter the associated normal forces and, therefore, the

leveling-wire behavior. Increasing (Decreasing)

interbracket distance(s), particularly from the cuspid,

will decrease (increase) wire-curvatures. Engaging the

archwire in the cuspid-bracket-slot vs. sling-tying the

wire to the bracket will affect curvatures as well.

Perturbations, simulations of extraneous intraoral

forces, are another factor that may alter binding points

and the unloading behavior of SE NiTi wires. Braun et al. 27

found that substantial perturbations momentarily reduced

frictional forces to zero, allegedly sufficient for wire-

slips (as in stick-slip). Ward 8 found that, with small

perturbations, SE NiTi leveling wires can still bind.

Wire-diameter may also play a role in unloading

behavior of SE NiTi wires. Franchi and Baccetti 6 and Ward 8

found that 0.014-inch SE NiTi wire bound, but 0.016-inch SE

NiTi wire did not bind under the same conditions.

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3. Binding of 0.014-inch SE NiTi leveling wires occurs at a

deflection-amplitude threshold rather than at a deflection-

amplitude.

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12. Henao SP, Kusy RP. Frictional evaluations of dental typodont modelsusing four self-ligating designs and a conventional design. AngleOrthod 2005;75:75-85.

13. Tecco S, Festa F, Caputi S, Traini T, Di Iorio D, D'Attilio M.Friction of conventional and self-ligating brackets using a 10 bracketmodel. Angle Orthod 2005;75:1041-1045.

14. Kusy RP, Whitley JQ. Effects of surface roughness on thecoefficients of friction in model orthodontic systems. J Biomech1990;23:913-925.

15. Kapila S, Angolkar PV, Duncanson MG, Jr., Nanda RS. Evaluation offriction between edgewise stainless steel brackets and orthodonticwires of four alloys. Am J Orthod Dentofacial Orthop 1990;98:117-126.

16. Hain M, Dhopatkar A, Rock P. The effect of ligation method onfriction in sliding mechanics. Am J Orthod Dentofacial Orthop2003;123:416-422.

17. Hain M, Dhopatkar A, Rock P. A comparison of different ligationmethods on friction. Am J Orthod Dentofacial Orthop 2006;130:666-670.

18. Burstone CJ. Application of Bioengineering to ClinicalOrthodontics. In: Graber TM, Vanarsdall RL, Vig KWL, editors.Orthodontics: Current Principles and Techniques. St. Louis, MO:Elsivier, Mosby; 2005. p. 293-330.

19. Nikolai RJ. Bioengineering Analysis of Orthodontic Mechanics.Philadelphia, PA: Lea & Febiger; 1985.

20. Rossouw PE. Friction: An Overview. Sem Orthod 2003;9:218-222.

21. Damon DH. Treatment of the Face with Biocompatible Orthodontics.In: Graber TM, Vanarsdall RL, Vig KWL, editors. Orthodontics: CurrentPrinciples and Techniques. St. Louis, MO: Elsevier; 2005. p. 753-831.

22. Ren Y, Maltha JC, Kuijpers-Jagtman AM. Optimum force magnitude fororthodontic tooth movement: A systematic literature review. AngleOrthod 2003;73:86-92.

23. Petersen AM. Force Decay of Elatomeric Ligatures: Influences onunloading force compared to self ligation. Master's thesis. Center forAdvanced Dental Education. St. Louis, MO: Saint Louis University; 2008.

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24. Roth RH, Sapunar A, Frantz RC. The In-Ovation Bracket for FullyAdjusted Appliances. In: Graber TM, Vanarsdall RL, Vig KWL, editors.Orthodontics: Current Principles and Techniques. St. Louis: Elsevier;2005. p. 833-853.

25. Taloumis LJ, Smith TM, Hondrum SO, Lorton L. Force decay anddeformation of orthodontic elastomeric ligatures. Am J OrthodDentofacial Orthop 1997;111:1-11.

26. Frank CA, Nikolai RJ. A comparative study of frictional resistancesbetween orthodontic bracket and arch wire. Am J Orthod 1980;78:593-609.

27. Braun S, Bluestein M, Moore BK, Benson G. Friction in perspective.Am J Orthod Dentofacial Orthop 1999;115:619-627.

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