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THE EFFECT OF EXTRANEOUS FORCES UPON THE FRICTIONAL
CHARACTERISTICS OF SELF-LIGATING ORTHODONTIC
BRACKETS AND NICKEL-TITANIUM ARCHWIRES
UTILIZING A NOVEL IN VITRO MODEL
David M. Bunkall, B.S., D.D.S.
An Abstract Presented to the Faculty of the Graduate School
of Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry
2006
ABSTRACT
In seeking a greater understanding of friction’s role
in orthodontics, studies have been conducted to identify
which aspects of the archwire, bracket, ligature, and/or
oral environment are associated with frictional forces.
Recent interest in self-ligating appliances that claim low
or reduced frictional properties has added further
incentive within the specialty to characterize friction as
it relates to tooth movement.
Few investigations have
tested in the laboratory brackets and wires arranged in an
actual archform as they exist in clinical reality.
Additionally, few investigations have considered the
effects of extraneous forces or perturbations upon such a
bracket-archwire couple as would exist in the mouth during
chewing or swallowing.
The objectives of the present study
were to 1) identify and evaluate the effects of extraneous
forces or perturbations upon the frictional characteristics
of metal self-ligating brackets in combination with nickeltitanium wires, 2) compare the frictional resistances of
three different self-ligating brackets and three sizes of
nickel-titanium wires, and 3) determine the effect of
facial or palatal displacement of the brackets on
frictional resistance values.
To carry out this study, a
1
new experimental friction testing apparatus was designed
which allowed for the placement of seven brackets
(representing the seven teeth in a given dental
quadrant—central incisor through second molar) into the
desired hemi-archform configuration.
Into this same
apparatus, perturbations were introduced to simulate
extraneous oral forces.
The results of the investigation
indicated that the bracket with the active clip generally
produced greater frictional resistances with the larger two
wires, but there were interactions.
With misaligned
brackets, frictional resistances were directly associated
with the faciolingual dimension of the archwire.
Misalignment of the brackets facially or lingually resulted
in an average of a 10- to 13-fold increase in frictional
resistance.
The introduction of perturbations reduced
frictional resistance in the brackets 35 to 70% compared to
tests performed without perturbations.
Additionally, any
significant difference in frictional resistance across the
three bracket types when the brackets were misaligned did
not exist in the presence of the perturbations.
2
THE EFFECT OF EXTRANEOUS FORCES UPON THE FRICTIONAL
CHARACTERISTICS OF SELF-LIGATING ORTHODONTIC
BRACKETS AND NICKEL-TITANIUM ARCHWIRES
UTILIZING A NOVEL IN VITRO MODEL
David M. Bunkall, B.S., D.D.S.
A Thesis Presented to the Faculty of the Graduate School
of Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry
2006
COMMITTEE IN CHARGE OF CANDIDACY:
Professor Rolf G. Behrents
Chairperson and Advisor
Adjunct Professor Robert J. Nikolai
Assistant Professor Donald R. Oliver
i
With a contained environment, there is the promise of
friction. And that is where the drama comes from.
--Bruce Greenwood
ii
DEDICATION
This thesis is dedicated to my wife, Robyn, and our
two wonderful sons, Cannon and Luke.
May we always
remember the Lord’s goodness and love toward our small
family.
iii
ACKNOWLEDGEMENTS
The author wishes to acknowledge all of the assistance
rendered to him during the creation of this thesis.
He
offers his thanks to Dr. Rolf Behrents, Dr. Robert Nikolai,
Dr. Donald Oliver, Mr. Joe Tricamo and associates at Saint
Louis University’s experimental machine shop, Dr. Heidi
Israel, Mr. Jeff Gardner, Dr. Steven Lemery, and Dr.
Jeffrey Lingenbrink.
The author also wants to acknowledge the support of
GAC International, Ormco Corporation, and 3M/Unitek for
supplying the brackets and wires for this study.
iv
TABLE OF CONTENTS
List of Tables ........................................ vii
List of Figures ........................................ ix
CHAPTER I:
INTRODUCTION ............................. 1
CHAPTER II:
REVIEW OF THE LITERATURE
Background ............................... 3
Friction in Orthodontics ................. 4
Variables Affecting Friction.............. 8
Biologic Variables .................. 8
Saliva ......................... 8
Oral Forces .................... 9
Physical Variables ..................12
Archwires ......................12
Wire Size .................12
Wire Stiffness and Shape ..12
Wire Alloy ................14
Wire Surface Texture ......15
Ligation .......................17
Ligation Force ............17
Ligation Type .............18
Brackets .......................18
Bracket Material ..........19
Slot Size .................20
Bracket Width .............21
Interbracket Distance .....22
Bracket Design ............23
Self-Ligating Brackets ...................25
Summary ..................................29
CHAPTER III:
MATERIALS AND METHODS
A Novel Friction Testing Device ..........32
Test Brackets and Archform Templates .....37
Test Wires ...............................40
Instron™ Testing Machine .................41
Perturbation Machine .....................42
Testing Protocol .........................45
Statistical Analysis .....................48
CHAPTER IV:
RESULTS
Static and Kinetic Frictional Resistance .50
Brackets .................................56
Wires ....................................76
v
CHAPTER V:
DISCUSSION
Variables Affecting Friction .............85
Archwires ...........................85
Brackets ............................86
Bracket Width ..................86
Slot Size ......................88
Bracket Design .................91
Testing Environment .................93
Archform .......................93
Perturbations ..................94
Graphic Data/Stick and Slip ..............96
Limitations ..............................98
CHAPTER VI:
SUMMARY AND CONCLUSION ..................103
References Cited .......................................106
Vita Auctoris ..........................................112
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LIST OF TABLES
Table 1:
Descriptive statistics: Average kinetic
frictional resistance in grams including data
from all three wire sizes......................52
Table 2:
Descriptive statistics: Maximum static
frictional resistance in grams including data
from all three wire sizes......................54
Table 3:
Summary of one-way ANOVAs of average kinetic
and maximum static frictional forces including
contributions from all three wire sizes........57
Table 4:
Results of Tukey HSD post hoc tests to
clarify ranks across the three bracket types
including contributions from all three wire
sizes..........................................59
Table 5:
The amount of average kinetic frictional
resistance reduced by perturbations for each
bracket type...................................62
Table 6:
The amount of maximum static frictional
resistance reduced by perturbations for each
bracket type...................................62
Table 7:
Descriptive statistics: Average kinetic
frictional resistance in grams including data
from both perturbation values..................63
Table 8:
Descriptive statistics: Maximum static
frictional resistance in grams including data
from both perturbation values..................66
Table 9:
Summary of one-way ANOVAs of average kinetic
and maximum static frictional forces including
contributions from both perturbation values....69
Table 10: Results of Tukey HSD post hoc tests to
clarify ranks across the three bracket types
including contributions from both perturbation
values.........................................71
Table 11: The increase in average kinetic frictional
resistance due to misalignment of brackets.....75
vii
Table 12: The increase in maximum static frictional
resistance due to misalignment of brackets.....75
Table 13: Descriptive statistics: Average kinetic
frictional resistance in grams including data
from all three bracket types...................77
Table 14: Descriptive statistics: Maximum static
frictional resistance in grams including data
from all three bracket types...................79
Table 15: Summary of one-way ANOVAs of average kinetic
and maximum static frictional forces including
contributions from all three bracket types.....81
Table 16: Results of Tukey HSD post hoc tests to
clarify ranks across the three wire sizes......83
Table 17: Average bracket widths (in millimeters)........87
viii
LIST OF FIGURES
Figure 1:
Contact angle ............................21
Figure 2:
Damon 2™ .................................29
Figure 3:
In-Ovation™ ..............................29
Figure 4:
SmartClip™ ...............................29
Figure 5:
The friction testing device ..............32
Figure 6:
Diagram of an individual cylinder found
in the experimental device ...............33
Figure 7:
Diagram showing movements of stainless
steel rod and brass ball within the
cylinder..................................35
Figure 8:
Diagram showing rotational movements of
stainless steel rod and brass ball within
the cylinder..............................36
Figure 9:
Aligning brackets with the “zeroing”
archform template ........................39
Figure 10:
Templates for aligning and misaligning
brackets .................................39
Figure 11:
Device mounted in Instron™ machine .......42
Figure 12:
Perturbation machine plunger .............43
Figure 13:
Perturbation machine motor ...............43
Figure 14:
Matrix showing all tested variable
combinations .............................47
Figure 15:
Example of a graph of frictional
resistance values during a test with
aligned brackets..........................51
Figure 16:
Example of a graph of frictional
resistance values during a test with
misaligned brackets.......................51
ix
Figure 17:
Comparisons across three bracket types of
average kinetic frictional resistances....53
Figure 18:
Comparisons across three bracket types of
maximum static frictional resistances.....55
Figure 19:
Additional comparisons across three
bracket types of average kinetic
frictional resistances....................65
Figure 20:
Additional comparisons across three
bracket types of maximum static
frictional resistances....................68
Figure 21:
Comparisons across three wire sizes of
average kinetic frictional resistances....78
Figure 22:
Comparisons across three wire sizes of
maximum static frictional resistances.....80
Figure 23:
Occlusal view of anterior SmartClip™
brackets and a 0.016- x 0.022-inch NiTi™
wire in a misaligned set-up ..............90
Figure 24:
Testing set-up showing bracket arrangement relative to Instron™ pulling arm ....93
Figure 25:
Example of a graph of frictional
resistance values showing the stick-slip
phenomenon................................97
Figure 26:
Close-up of Figure 25 showing the stickslip phenomenon...........................97
Figure 27:
Close-up of a graph showing frictional
resistance during one of the trials of
Damon 2™ brackets with a 0.016-inch NiTi™
wire in the presence of perturbations ...100
x
CHAPTER I – INTRODUCTION
Despite a scarcity of literature on the subject
through the first several decades of the twentieth century,
orthodontists seemed to have accepted the hypothesis that
friction within their treatment mechanics slow down tooth
movement.
In a personal communication to Halderson (1957),
Johnson stated that “When force has been applied to these
light wires, you must not bind or tie them tight in the
brackets.
You must give the wires a chance to move...”
Studies have been carried out to understand friction’s
role in orthodontics.
Recent interest by the specialty in
self-ligating appliances that claim low or reduced
frictional properties has provided further incentive to
more accurately characterize friction as it relates to
tooth movement.
Dozens of studies have sought to identify which
aspects of the archwire, bracket, ligature, and/or oral
environment are associated with frictional forces; however,
few laboratory investigations have tested archwires within
a series of brackets that simulates clinical reality -brackets placed in an archform as they would be found in
the mouth.
Additionally, few laboratory investigations
have considered the effects of extraneous forces or
1
perturbations, as would exist during chewing and
swallowing, upon such an archwire-bracket couple.
To understand friction in orthodontics more fully it
is critical that in vitro studies represent the clinical
situation as closely as possible.
It would be important to
consider the effects of extraneous forces or perturbations
upon frictional resistance levels of self-ligating brackets
arranged in an archform as they would be found in the oral
environment.
Such an investigation would provide
additional insight into the true nature of orthodontic
friction.
2
CHAPTER II – REVIEW OF THE LITERATURE
Background
Friction was characterized as early as the fifteenth
century by Leonardo Da Vinci.
Among his illustrations on
the subject, he proposed two basic laws of friction:
1) maximum frictional resistance is proportional to the
pushing/normal force and 2) frictional resistance is
independent of the contact area of the sliding interface.
Later experimentation by Amontons in 1699 and Coulomb in
1781 formalized the friction laws recognized today as
estimates of dry friction dynamics. (Roussouw, Kamelchuk,
and Kusy, 2003)
Friction can be defined as the force that opposes or
resists the movement of two surfaces sliding over each
other.
Its direction of action is parallel and opposite to
the direction of sliding.
Its maximum magnitude is
hypothesized to be proportional to a normal force; the
constant is termed the coefficient of friction.
The
relationship is shown in mathematical form as F = N * _
where F is the frictional resistance, N is the normal force
and _ is the coefficient of friction. (Roussow, 2003)
The normal force (N) is the force perpendicular to the
direction of sliding as well as the direction of frictional
3
force itself.
It can be viewed as the force pushing the
two surfaces together (Baker et al., 1987).
For example,
the normal force associated with pushing a heavy wooden box
across a concrete floor equals the weight of the box or the
force of gravity pushing the box down against the floor.
The coefficient of friction (_) describes the relative
difficulty of sliding specific surfaces past each other.
Its value is a constant, determined by the combination of
surface characteristics of the two materials involved.
For each pair of contacting surfaces, there are two
coefficients of friction.
The first is the static
coefficient of friction (_s) associated with the resistance
to be overcome to initiate movement.
The second is the
kinetic coefficient of friction (_k) associated with the
resistance continually overcome to keep a moving body
moving at a constant speed.
Based upon the classic laws of
friction, the static coefficient of friction will be larger
than the corresponding kinetic coefficient of friction.
(Nanda and Ghosh, 1997; Rossouw et al., 2003)
Friction in Orthodontics
In 1997, Kusy and Whitley discussed the classical laws
of friction in relation to orthodontic mechanics.
They
pointed out that certain principles remain true under the
4
parameters imposed by orthodontics while others do not.
For example, the first law, states that friction is
proportional to the normal force, the constant being the
coefficient of friction.
This law is followed without
exception in orthodontic movement.
The second law that
notes the independence of friction from apparent contact
area is usually obeyed in orthodontics.
But the third law,
“Coulomb’s Law” regarding the independence of friction
magnitude from sliding velocity, most often never holds
true when it comes to moving teeth with brackets and
archwires.
This departure from classical friction is in
part due to the extremely slow velocity of orthodontic
tooth movement as well as the fact that the velocity is
ever changing.
Rossouw’s group (2003) noted that at extremely low
velocity it is impossible to distinguish static and kinetic
frictional resistance into distinct phases and that the
resultant instability in sliding motion may lead to cycles
characterized by “sticking and slipping” variably involving
a bracket (or tube) and wire.
This inconsistent frictional
force between orthodontic bracket and archwire is thus
thought to play an important role in compromising tooth
movement during various phases of active, orthodontic
treatment.
5
According to Nanda and Ghosh (1997), when closing
spaces between teeth in the mouth, orthodontists usually
employ one of two methods.
First, an orthodontist may use
segmental mechanics utilizing closing loops bent into a
continuous or sectional archwire.
activation of these loops.
technique.
The space(s) close via
This is a “frictionless”
On the other hand, an orthodontist may choose
to close the space(s) using a “sliding mechanics” technique
in which brackets are moved or slid along an archwire, or
the archwire is moved or slid through the brackets.
Such a
technique is strongly influenced by the friction arising at
the interface of the bracket and the archwire (Nanda and
Ghosh, 1997).
Another instance in orthodontics when so-called
“sliding mechanics” are commonly employed occurs at the
beginning of treatment.
Traditionally, orthodontists order
their treatment sequence in such a way that they first
prefer to level and align the crowded, spaced, or otherwise
malposed teeth in each arch.
Initial leveling and
aligning, as it’s known, involves using “light,” highly
flexible wires of relatively small cross-section.
These
wires are capable of engaging misaligned teeth and under
elastic activation move teeth into alignment as the wire
springs-back to its passive form (Waters, 1992).
6
As the
light wire lies in all of the misaligned brackets, it
possesses a set length from the distal end of the bracket
on the most distal tooth on one side of the arch to the
distal end of the bracket on the most distal tooth on the
opposite side of the arch.
As the teeth begin to move
under the force of the elastically deformed wire, they
begin to align themselves.
Alignment of the teeth often
results in a decrease in the total distance between
brackets in the arch.
This decrease is best visualized by
the resulting excess archwire seen beyond the distal ends
of the most distal brackets following alignment.
While the
teeth are moving toward their ideal positions as the
appliance is de-activating, the excess archwire usually
slides past the surfaces of the adjacent brackets.
In this
way, the leveling and aligning phase at the beginning of
orthodontic treatment employs sliding mechanics and,
therefore, is also subject to the influence of friction
(Proffit, 2000).
Orthodontics has sought greater understanding of the
role of friction with various intra-oral bracket/archwire
systems.
Numerous variables have been identified that
explain, in part, the roles that friction plays within the
biomechanics of orthodontic treatment.
7
For simplicity, one
can divide these variables into two categories: biological
and physical. (Nanda and Ghosh, 1997)
Variables Affecting Friction during
Orthodontic Movement
Biological Variables
Saliva
Under normal conditions in the oral cavity, an
orthodontic appliance is consistently being bathed in
saliva.
As a lubricant for our mouths, saliva performs its
role well; however, its role as a lubricant for archwires
and brackets, despite focused research, is still in
question.
Thurow (1975) suggested that saliva acts as an
excellent lubricant, but laboratory studies have shown no
significant or consistent advantage of saliva in reducing
friction (Andreasen and Quevedo, 1970; Ireland, Sherriff,
and McDonald, 1991; Edwards, Davies, and Jones, 1995; Kusy
and Whitley, 2000; Thorstenson and Kusy, 2001; Henao and
Kusy, 2004).
Still, it is possible that saliva may
lubricate certain wire/bracket alloy couples while acting
as an adhesive for couples of other alloys (Kusy, Whitley,
and Prewitt, 1991).
8
Oral Forces
The oral cavity is a changing environment.
Whether
influenced by the tongue, the jaw, or the peri-oral
muscles, the mouth and its structures are subject to the
effects of a variety of forces.
These forces could impact
the position of the teeth in their respective arches
(Proffit, 2000).
Forces produced during biting are transmitted through
the teeth and eventually conveyed to cells and fibers in
the periodontal ligament and adjacent bone.
Often these
forces are distributed and resisted by those tissues.
On
the other hand, if force exists for an adequate duration,
these force-stimulated cells participate in a series of
processes that might ultimately lead to the creation or
destruction of surrounding connective tissue and/or bone.
Such cellular activity, and its consequences, also permits
orthodontic tooth movement within the alveolus. (Proffit,
2000)
Occlusal forces can be characterized by their
magnitude, duration, and frequency.
Proffit (2000) noted
that there is large variation in the magnitude of occlusal
forces produced during function.
Occlusal forces noted
during swallowing varied from only a few kilograms to more
than 30 kilograms, chewing forces measured between 10 to 30
9
kilograms, and maximum bite force ranged from 30 to as high
as 127 kilograms (Gibbs et al., 1981; Proffit, Fields, and
Nixon, 1983).
Graf and Zander (1963) found that individuals show
great variability in the rate of chewing as well as the
frequency and duration of tooth contacts.
The average
length of tooth contact during mastication was measured by
Gibbs and colleagues (1981) to be 194 msec while the
average length of contact during swallowing was more than
three times longer (683 msec).
It is estimated that
approximately 1800 chewing strokes occur during an average
day and that swallowing occurs about 500 times during a 24hour period (Graf, 1969) for a total of 2300 potential
daily tooth contacts.
Some researchers have proposed that these oral forces
and the resultant movement or “jiggling” of the teeth
within the parameters of periodontal ligament tension and
compression significantly reduces the frictional levels
that might exist within an orthodontic appliance during
tooth movement (Andreasen and Quevedo, 1970; Hixon et al.,
1970; Thurow, 1975).
Frank and Nikolai (1980) explained
that occlusion and masticatory action alter the force
levels between the bracket and wire so that any “friction
locks” are broken and then reset over and over again.
10
Such
ideas are not without precedent. In 1959, Fridman and
Levesque described such a phenomenon using an industrial
model consisting of a steel block sliding down an inclined
plane.
They noted that “the coefficient of static friction
can be virtually reduced to zero as a result of increased
[sonic] vibrations.”
Using an orthodontic model, Braun and colleagues
(1999) applied random perturbations to a test wire or
bracket.
Each perturbation produced a corresponding
decline in frictional resistance with the resistance levels
of more than 95% of the tests dropping completely to zero.
When the same idea was tested within the oral cavity,
Iwasaki’s group (2003) found that the vibrations introduced
when the patient chewed gum did reduce static friction, but
did not eliminate friction altogether.
They concluded that
masticatory forces do not consistently and predictably
decrease friction.
It is clear that teeth are subject to a
wide array of light and heavy forces on a daily basis, but
the effect of these forces upon orthodontic mechanics and
tooth movement has yet to be clarified.
11
Physical Variables
Archwires
Parameters associated with the archwire that affect
friction include the size, shape, and stiffness of the wire
and its material composition and surface roughness.
Wire Size
As a wire increases in size, filling the slot of the
bracket, the general trend is for the friction of the
system to increase.
Larger wire sizes decrease the
movement permitted between wire and bracket slot (Andreasen
and Quevedo, 1970) and increase the stiffness of the wire.
Frank and Nikolai (1980) pointed out that for a given
binding angulation, if the stiffness of the wire is
increased, the normal component of contact force between
the wire and bracket will also increase.
Wire Stiffness and Shape
The stiffness of an archwire is not only related to
the dimensions of the wire, but also to its cross-sectional
shape, and its material composition.
It is also influenced
by the length of wire between brackets as determined by
interbracket distance and any addition of loops, bends, or
helices to the length of wire. (Proffit, 2000)
12
Frank and Nikolai (1980) noted that, theoretically, at
a given bracket slot angulation relative to the archwire,
normal force (and by definition, the friction force) will
increase with increasing wire stiffness.
In contrast,
their results showed increased friction levels for 0.020inch round wire compared to the stiffer 0.017- x 0.025- and
0.019- x 0.025-inch rectangular wires.
This finding
indicated the potential influence that a wire’s crosssectional shape can have on frictional resistance.
They
speculated that because the round wire, at higher
angulations, makes only a point contact with the edge of
the bracket-slot while the rectangular wires at the same
angulations make broader line contacts, then the round wire
experiences higher pressures per unit contact area and
indentation (or notching) of the wire occurs.
If correct,
deformation of the wire would lead to increased friction.
Kusy and Whitley (2000) verified the theory put forth
by Frank and Nikolai (1980) that frictional force increases
with increasing wire stiffness.
They found that, as
bracket slot angulation was increased relative to a
straight length of archwire, wire alloys having greater
material stiffness (such as cobalt-chromium or stainless
steel wires) produced greater binding and greater
resistance to sliding.
Similar findings were obtained by
13
Thorstenson and Kusy (2002b) who compared rectangular
stainless steel wires and nickel-titanium-alloy wires
within bracket slots of increasing angulation.
Wire Alloy
The introduction of archwires composed of new
metallics (nickel-titanium and beta-titanium alloys) over
the last few decades has made a dramatic impact upon
orthodontic treatment.
These newer wire-alloys are
associated with super-elasticity and with material
stiffness values smaller than that of orthodontic stainless
steel.
As noted above, decreased stiffness values of these
newer wires result in much smaller frictional resistances
when significant archwire deflection occurs between
brackets.
Although tests (Angolkar et al., 1990; Downing,
McCabe, and Gordon, 1994) have proven that a precise
hierarchy of frictional resistances may never exist among
different wire alloys, a common trend is observed with
titanium alloy archwires often producing increased
frictional levels in laboratory studies (Garner, Allai, and
Moore, 1986; Drescher, Bourauel, and Schumacher, 1989;
Tidy, 1989; Kapila et al., 1990; Kusy and Whitley, 1990a;
14
Kusy and Whitley, 2000).
Drescher’s group (1989)
determined that the wire material was an important factor
in determining resistance to sliding.
Their results showed
TMA™ beta-titanium wires to be associated with the highest
friction levels followed by Nitinol™, cobalt-chromium, and
stainless steel.
On this basis, several investigators have
hypothesized that the reason for the greater frictional
magnitudes from the titanium alloy wires may be due to
sizable surface roughness (Frank and Nikolai, 1980; Garner
et al., 1986).
Wire Surface Texture
Frank and Nikolai (1980), using a microscope at 100x
magnification, found that Nitinol™ wires exhibited greater
surface roughness than cobalt-chromium and stainless steel
wires and rationalized that this finding may explain the
increased frictional resistance associated with this alloy
seen at smaller, non-binding bracket angulations.
Garner
and associates (1986) observed scanning electron
micrographs of various wire surfaces in an attempt to
explain why certain alloys showed larger frictional
resistances than others.
Their findings suggested that the
roughness of the wire surface may account for the variance
in frictional magnitudes seen with different wires.
15
Using laser spectroscopy, Kusy and colleagues (1988)
quantitatively assessed the surface roughnesses of four
orthodontic archwires composed of different alloys.
Their
results showed that nickel-titanium wires have the roughest
surface followed by beta titanium and cobalt-chromium. The
“least rough” wire was stainless steel.
Unfortunately,
Kusy and Whitley (1990b) noted that “a clear relationship
does not always exist between surface roughness and the
coefficients of friction.”
Prososki and associates (1991)
used a surface profilometer to measure surface roughness of
twelve different wires, nine of which were composed of
nickel-titanium alloys.
No correlation could be found
between surface roughness and frictional resistance between
the different wire alloys.
It is now believed that a major factor affecting the
frictional characteristics of a wire is not its surface
roughness but its surface chemistry (Proffit, 2000).
The
greater the titanium content of the wire alloy, the larger
the wire’s reactivity or ability to form metal-metal bonds.
For example, the surface of a beta-titanium wire has shown
enough reactivity to “cold-weld” itself to a stainless
steel bracket, making sliding impossible (Kusy and Whitley,
1990b).
16
Ligation
The amount of force exerted by the ligature and the
type of ligation used are considered important factors
influencing friction of an orthodontic appliance.
Ligation Force
Soft stainless steel replaced brass as the ligature of
choice among orthodontists in the mid twentieth century
(Kusy, 2002).
Like brass wire, stainless steel wire offers
the orthodontist flexibility when ligating the archwire to
the tooth attachments.
Steel ligatures can be tightly tied
or loosely tied, depending upon the reason for their
application.
The larger the ligating or applied force
exerted on the wire-bracket apparatus, the greater the
frictional force (Paulson, Speidel, and Isaacson, 1970,
Frank and Nikolai, 1980; Stannard, Gau, and Hanna, 1986).
This finding has been applied by other investigators to
more recently developed elastomeric ligatures as well.
Kapilla and colleagues (1990) proposed that the reason that
wide brackets were associated with greater frictional
levels was that the wider bracket tended to stretch its
elastomeric ligature more, resulting in a larger normal
force.
17
When comparing several ligation techniques, Edwards
and colleagues (1995) noted that if the elastomerics were
tied down to the bracket in a ‘figure 8’ pattern they
produced a static frictional resistance that was
significantly greater than a conventionally tied
elastomeric or stainless steel ligature.
Ligation Type
The introduction of elastomeric ligatures into
orthodontics has provided the orthodontist with certain
advantages.
For example, elastomerics are simple and quick
to place, and a variety of color options are available and
popular among younger patients.
A definitive answer has
not been found as to the relative frictional levels
associated with this ligation type compared to stainless
steel ligatures.
Certain studies (Frank and Nikolai, 1980;
Edwards et al., 1995, Braun et al., 1999) showed no
difference between the two ligation methods, while others
have demonstrated the superiority of stainless steel
ligatures (Bednar, Gruendeman, and Sandrik, 1991).
Brackets
Studies indicate that bracket characteristics also
appear to affect orthodontic frictional levels.
18
Specific
characteristics include the bracket material, slot size,
bracket width, interbracket distance, and bracket design.
Bracket material
Frictional studies have reported that brackets of
differing compositions show a variance in frictional
characteristics.
Stainless steel brackets tend to generate
less frictional resistance than ceramic brackets (Bednar et
al., 1991; Kusy et al., 1991).
Pratten and associates
(1990) attributed greater friction in the ceramic brackets
to greater surface roughness.
Still, other studies
indicate that ceramic brackets may show similar or even
smaller friction magnitudes than stainless steel brackets
(Kusy and Whitley, 1990a; Ireland et al., 1991; Omana,
Moore, and Bagby, 1992).
Omana’s group (1992) additionally
discovered tremendous variation in the frictional levels
produced by different types of ceramic brackets.
Some of
them showed much larger frictional values than the
stainless steel bracket, while others showed comparable
values.
They attributed the reduced, ‘stainless steel-
like’ frictional values of certain ceramic brackets to the
ability of an injection-molding manufacturing process to
produce very smooth ceramic surfaces.
19
Ireland and colleagues (1991) noted that, while single
ceramic brackets showed lower friction values than their
steel counterparts, when the brackets were placed in
series, ceramic brackets tended to show an additive effect
---friction increased with increased numbers of brackets--while the stainless steel brackets showed no such trait.
Slot Size
With the testing of brackets in the laboratory, slot
size did not play a significant role in determining the
frictional resistance of a given bracket (Tidy, 1989),
although it did influence the critical contact angle (Kusy
and Whitley, 2000).
Contact angle is the angle formed in the frontal view
by the wire and a line parallel to the bracket slot.
Figure 1.
See
The archwire is considered to lie passively
within the slot as long as the contact angle is less than
the critical contact angle which is attained when the wire
begins to press against the slot wall.
Kusy and Whitley
(1999) pointed out that, when this critical contact angle
is reached and surpassed, binding of the archwire and later
notching of the wire begin to overwhelm classic friction,
and resistance to sliding of the wire past the bracket
increases dramatically.
20
Figure 1: Contact angle (modified from Proffit, 2000)
Bracket Width
The width of the bracket is the second factor that
directly influences the critical contact angle of a given
bracket.
As illustrated in Figure 1, narrow brackets
permit greater passive angulations prior to the archwire
binding against the bracket, while the reverse is true for
wide brackets.
The effect of bracket width on friction has been
studied by different investigators under different testing
protocols.
Frank and Nikolai (1980) studied wide-bracket,
maximum-static-friction values of brackets with varied
widths whose slots were set to specific angulations
relative to the archwire.
Their findings showed that
increased bracket width resulted in increased friction.
In contrast, Drescher and associates (1989) found that
just the opposite was true.
Their protocol permitted the
21
bracket to tip under a given retarding force; this design
intended to simulate the effect of intrinsic biologic
factors such as bone density, root configuration, and
occlusion.
In this situation, they found that narrower
brackets were associated with increased friction.
Although
the findings of these two studies appear in conflict, they
actually cannot be compared due to their differing testing
protocols.
In clinical practice it would appear that, when
teeth and bracket slots are initially misaligned, greater
relative friction and archwire binding would exist with
wide brackets compared to narrow ones.
On the other hand,
after the teeth and the bracket slots are aligned and
parallel, wide brackets would show less tipping during
space closure than narrow brackets and, therefore, less
binding of the archwire and lower friction.
Interbracket distance
Closely associated with bracket width is the distance
between brackets.
Greater interbracket distance results
from narrower bracket widths and greater inter-bracket
archwire length and, therefore, less archwire stiffness.
Frank and Nikolai (1980) found that, although interbracket
distance did not contribute substantially to the frictional
resistance, when the distance was reduced and the bracket
22
slot was set at larger angulations, the frictional levels
increased.
Kusy and Whitley (2000) noted that interbracket
distance significantly affected frictional resistance.
Under their testing conditions, as interbracket distance
was reduced from 18 mm to 8 mm, binding of the wire in the
bracket increased about two-and-a-half times.
Bracket design
Many brackets available today are advertised as having
minimal or low friction designs (Mendes and Roussouw,
2003).
This contention seems to be particularly common
among supporters of self-ligating brackets (Berger, 1990;
Damon, 1998; Heiser, 1998).
These claims of small
frictional resistance have in many instances been validated
(Shivapuja and Berger, 1994; Kapur, Sinha, and Nanda, 1998;
Pizzoni, Ravnholt, and Melsen, 1998; Mendes and Rossouw,
2003) and in other instances been challenged (Bednar et
al., 1991; Taylor and Ison, 1996). Shivapuja and Berger
(1994) found that three types of self-ligating brackets all
showed significantly less frictional resistance than
conventional brackets tied with steel or elastomeric
ligatures.
Studies by Kapur’s group (1998) and Pizzoni’s
group (1998) showed that self-ligating brackets offer clear
advantages over conventional brackets.
23
Other studies
comparing ligation methods have shown no significant
difference in frictional resistances between self-ligating
and conventional brackets (Bednar et al., 1991; Taylor and
Ison, 1996; Iwasaki et al., 2003; Mendes and Rossouw,
2003).
This seeming confusion may be explained, in part,
on the basis of the great variety of brackets in
combination with the great variety of ligatures and their
various forms of application.
Bednar’s group (1991) determined that the selfligating SPEED™ bracket (Strite Industries Ltd., Cambridge,
Ontario, Canada) did not always produce the smallest
frictional resistance.
They noted much larger resistance
values with the SPEED™ bracket when a 0.016- x 0.022-inch
stainless steel wire was used.
They reasoned that the
bracket’s spring clip pressed the larger archwire against
the base of the bracket-slot, increasing resistance.
Henao
and Kusy (2004; 2005) confirmed that, while self-ligating
brackets produce less friction with smaller wires, there
was little difference in resistance between them and the
conventional brackets when larger wires were tested.
Likely, the different designs of self-ligating
brackets play a role in the frictional levels generated by
them (Thorstenson and Kusy, 2002a).
Some self-ligating
brackets, such as the SPEED™ bracket noted above, have a
24
spring clip that closes over the bracket slot.
With
smaller wires, the spring clip merely acts as a gate,
passively overlying the wire in the slot, but with larger
wires, the spring clip actively presses the wire against
the base or sides of the slot.
Such an active ligation
should theoretically result in larger normal forces and,
thus, greater frictional forces.
In contrast, other self-
ligating brackets do not possess an active spring clip;
rather, they utilize a simple gate to passively close their
bracket slot.
These brackets act like molar tubes, lacking
ligation that seats the wire against the base or sides of
the bracket slot.
They are often referred to as being
passive self-ligating brackets (Voudouris, 1997).
Self-Ligating Brackets
In 1935, Stolzenberg published an article in the
International Journal of Orthodontics in which he explained
some of the details and advantages of his new invention,
the Russell Attachment.
The Russell Attachment, an early
self-ligating appliance of the modern era, was
characterized by a 0.022- x 0.028-inch horizontal slot, a
nut that was screwed down on the facial aspect of the
attachment to close the slot, and a vertical channel
through which soft-wire ligatures could be tied.
25
When
closing the slot, the facial nut was adjusted with a “key,”
or screwdriver, in such a way as to either passively lie
over the archwire or to actively engage the wire.
According to Stolzenberg (1946), the Russell
Attachment had a distinct advantage over the more common
appliances of the day in that it was simple to operate, it
could be applied to a wide range of tooth movements, the
attachments themselves could be reused, and the appliance
saved time for both the orthodontist and the patient.
Other early self-ligating appliances include the Boyd
bracket and Ford lock which were both introduced in 1933
(Woodside, Berger, and Hanson, 2005).
In 1971, the idea of a self-ligating appliance was reintroduced to orthodontics by Wildman (1972). Wildman’s
Edge-lok™ bracket (Ormco Corp., Glendora, CA) was circular
in shape and had a domed self-ligation cap.
Using a
special instrument, the operator could slide the domed cap
occlusally to access the bracket slot.
After the wire was
in the bracket slot, the cap could be closed simply with
finger pressure.
When the cap was closed, the bracket
became, in essence, a tube with a passive gate (Berger,
2000).
A similar bracket, the Mobil-lock™ (Forestadent
USA, St. Louis, MO) was introduced a couple of years later
(Berger, 2000).
26
Designed by Hanson (1980), the SPEED™ bracket (an
acronym for “Spring-loaded, Precision, Edgewise, Energy,
and Delivery”) features a facial spring or clip which wraps
around the body of the bracket.
When the clip is closed
over a larger archwire, it tends to press the wire against
the base of the bracket slot.
This results in a self-
ligating appliance that is “active” in engaging the
archwire rather than just passively covering the bracketslot.
Hanson (1980) noted that the clip became activated
when a wire wider than 0.017 inches was inserted into the
0.018- x 0.025-inch slot.
Several years later in 1986, Pletcher created the
Activa™ (Ormco/”A” Company, Orange, CA) bracket which had a
rigid curved arm that rotated occluso-gingivally around the
cylindrical body.
This system attained little success in
the marketplace in large part due to the ease at which
patients could open the brackets themselves as well as its
large bracket width and relatively small interbracket
distance (Berger, 2000).
The mid-to-late 1990s saw the development of three new
self-ligating brackets.
The Time™ bracket, created by
Heiser and distributed by American Orthodontics (Sheboygan,
WI), is similar in design to the SPEED™ bracket.
Its stiff
facial clip actively seats any wire larger than 0.018-inch
27
against the base of the slot.
One advantage of having an
active clip is that the clip will ensure full engagement of
the wire and, thus, full torque control (Heiser, 1998).
The other two brackets developed at this time were the
TwinLock™ (Ormco/”A” Company, Orange, CA), by Wildman, and
the Damon SL™ (Ormco/”A” Company, Orange, CA).
These two
brackets featured a sliding “passive” gate, similar to the
Edgelok™ and Mobil-lock™ brackets of the 1970s.
This gate
does not exert a force upon a larger sized archwire to seat
the wire against the base of the bracket as the clips of
the SPEED™ and Time™ brackets do.
Closure of the gate
causes the bracket to become a tube that constrains the
archwire within its lumen.
Damon (1998) proposed that such
“passive self-ligation” results in decreased friction
levels between the wire and bracket.
More recent versions
of the Damon bracket include the Damon 2™ (Figure 2) and
Damon 3™.
In-Ovation™, a self-ligating bracket with a twin
bracket configuration (Harridine, 2003) was introduced to
the market by GAC International (Bohemia, NY) in 2000
(Figure 3).
Like SPEED™ and Time™, In-Ovation™ and the
newer model In-Ovation-R™ have a clip which is passive with
smaller diameter archwires, but active with larger
archwires (Harradine, 2003).
28
Figure 2: Damon 2™
Figure 3: In-Ovation™
Figure 4: SmartClip™
In 2004, 3M/Unitek (Monrovia, CA) introduced the most
recent competitor in the self-ligating market, the
SmartClip™ (Figure 4).
SmartClip™ is a standard twin
bracket with paired nickel-titanium clips lateral to the
tie wings.
Archwires are “snapped” to place and held in
the bracket by the clips which are designed to release the
wire when the force exerted by the wire exceeds a
predetermined magnitude (Weinberger, 2005).
Summary
The literature strongly supports the idea that
friction plays an important role in the interaction of the
bracket and wire during orthodontic tooth movement.
Regardless of the treatment philosophy, appliance, or
technique, frictional force exists in orthodontics.
As noted previously, there are numerous factors/
parameters associated with brackets, wires, ligatures, and
29
the oral environment that potentially influence frictional
resistance.
Acting separately and in concert, these
variables produce a biomechanical system that is still not
fully understood, predictable, nor controllable.
For the practicing orthodontist it would be essential
to know first of all: “Does friction matter?”
We accept
that it exists, but given the conditions of the mouth, does
friction actually affect orthodontic mechanics.
If the
answer to that question is yes, then the next logical
question would be: “How much does it matter?”
If the
answer to the question is that friction significantly
matters, then the orthodontist is left to wonder how he or
she can incorporate and use the knowledge and products that
will best minimize undesired friction.
For such a scenario, it would be important to study
friction by testing a variety of bracket/wire combinations
in differing “real-life” archform configurations under
conditions that best simulate the oral environment.
To
this end the present study has been undertaken.
How do self-ligating brackets differ in their
frictional characteristics?
If self-ligating brackets are
misaligned facially or lingually in the arch with a first
order discrepancy and the wire is forced to press against
the given gate or clip, how is frictional resistance
30
affected?
In addition it might be important to know if
oral forces can be simulated in the laboratory.
Do such
extraneous forces impact frictional resistance levels?
Utilizing a novel in vitro model designed at Saint
Louis University, this study sought to answer these
questions and shed further light upon the significance of
friction during the initial alignment phase of orthodontic
treatment.
31
CHAPTER III – MATERIALS AND METHODS
A Novel Friction Testing Device
A new experimental model, inspired by an earlier model
created by Chimenti’s group (2005), was designed and
manufactured in and by the orthodontic program and
experimental machine shop of Saint Louis University.
This
device (Figure 5) attempts to reproduce an upper quadrant
based upon the dimensions of the teeth and the average male
maxillary archform according to Moyers and colleagues
(1976).
This device is intended to provide the researcher
Figure 5: The friction testing device
32
with a platform upon which he or she can build any
imaginable in vitro friction testing study.
The device consists of a series of seven aluminum
cylinders, representing the seven teeth in an upper
quadrant from upper central incisor to upper second molar.
Within each cylinder (Figure 6) is a brass ball that can be
positioned vertically in the cylinder by the movement of
upper and lower internal screws.
A stainless steel rod
passes through the center of the brass ball with a brass
A
B
C
E
D
F
G
H
Figure 6: Diagram of an individual
device (A = aluminum cylinder, B =
ball, D = knuckle joint set screw,
screw, G = lower internal screw, H
cylinder found in the experimental
upper internal screw, C = brass
E = stainless steel rod F = set
= brass face-plate).
33
face-plate attached to one end of the rod by a knuckle
joint.
Brackets and tubes are bonded to this face-plate
for testing purposes.
The rod is held tightly within the
ball by two set screws.
The cylinders are mounted to an
aluminum block baseplate in a hemi-arch configuration.
The various components of the device permit the
positioning of the mounted bracket in each plane of space
(Figures 7 and 8): vertically (up and down), mesiodistally
(side-to-side), and faciolingually (in and out).
Vertical
position can be adjusted by moving the brass ball within
the cylinder or moving the entire cylinder within its
mounting to the baseplate.
Side-to-side positioning
(mesiodistal) requires either the turning of the ball and
rod or turning of the entire cylinder in the desired
direction as well as compensating for that movement with an
adjustment of the face-plate knuckle joint.
In-and-out
positioning (faciolingual) occurs by moving the rod in-andout of the ball.
Rotations of the bracket about the three axes of
rotation are also permitted within this model.
Rotations
along the vertical axis can be accomplished by rotating the
ball and rod within the cylinder or by rotating the entire
cylinder from side to side.
Rotations along the mesio-
distal axis occur by moving the ball and rod up or down
34
D
A
up
side to
side
in and
out
down
C
B
Figure 7: Diagram showing movements of stainless steel rod
and brass ball within the cylinder. Original drawing in
center. A = right or mesial, B = down, C = out, and D = in.
35
A
B
vertical
axis
C
faciolingual
axis
mesiodistal
axis
E
D
Figure 8: Diagram showing rotational movements of stainless
steel rod and brass ball within the cylinder. Original
drawing in middle on right. A = distal rotation about
vertical axis, B = mesial rotation about vertical axis , C =
twist or rotation about facio-lingual axis, D = up rotation
about mesio-distal axis, and E = down rotation about mesiodistal axis.
36
within the cylinder while rotations along the facio-lingual
axis take place by simply twisting the rod within the brass
ball.
This model is unique because of the following: 1) it
is capable of placing an orthodontic bracket or tube
precisely in any position in all three planes of space;
2) it emulates the six degrees of freedom that can be used
to describe tooth position and tooth movement; 3) it
permits a set of brackets and tubes to be placed in series
in a hemi-archform configuration; 4) it is reusable; and 5)
it operates conveniently with other friction testing
equipment such as a mechanical testing machine.
The same
device was used in a parallel study by Lingenbrink (2006).
Test Brackets and Archform Templates
This new friction testing device was utilized to
assess the frictional resistances of three different selfligating brackets.
The three self-ligating brackets used
were the Damon 2™ (Ormco Corp., Orange, CA), In-Ovation R™
(GAC International, Bohemia, NY), and SmartClip™
(3M/Unitek, Monrovia, CA) (Figures 2, 3, and 4).
The
choice of brackets was based upon the desire to test
brackets that are popular and that represent different
types of self-ligating mechanisms.
37
The Damon 2™ bracket
has a facial gate that passively closes over the bracket
slot, the In-Ovation R™ bracket has a facial clip that will
actively push larger sized wires against the base of the
slot, and the SmartClip™ bracket has clips on either side
of the tie wings which passively contain the archwire
within the slot, but may flex when the wire is pressed
against them.
Each quadrant set-up consisted of five self-ligating
brackets, each with a 0.022-inch slot, spanning the upper
left central incisor to upper left second premolar, a
0.022-inch first-molar tube, and a 0.022-inch second-molar
tube.
Brackets were leveled vertically and aligned into
the desired archform utilizing a special “zeroing” archform
template that attached to the baseplate of the device
(Figure 9).
The template effectively removed all torque
and tip built into the individual brackets, eliminating any
minor differences in bracket prescriptions across the
bracket types.
The archform template was made from a sheet
of steel 0.021-inch in thickness.
Brackets were positioned
so that the edge of the archform template rested against
the base of the slot.
The molar tubes were positioned
accordingly, using a 0.021- x 0.025-inch stainless steel
wire that extended distally from the correctly positioned
second premolar bracket.
38
Figure 9: Aligning brackets with the
“zeroing” archform template
For this study two different archform templates were
used (Figure 10).
The first was an archform based upon the
average male maxillary arch described by Moyers’ group
A
B
Figure 10: Templates for aligning (A) and
misaligning (B) brackets
39
(1976).
The second was a misaligned maxillary left
archform with specific first-order discrepancies meant to
represent a malposed arrangement of teeth common among
individuals that present for orthodontic treatment.
This
archform was based upon a sampling of thirty-five
pretreatment models of the primary investigator’s active
patients.
The models showed an average tendency for the
upper left lateral to be lingual to the central and the
canine to be facial to the lateral and first bicuspid.
From this sampling, the second archform template was
produced that inset the lateral one-mm lingually and offset
the canine one-mm facially from the original “Moyers”
archform.
This set-up created a one-mm first-order
discrepancy between the central and lateral, a two-mm
discrepancy between the lateral and canine, and a one-mm
discrepancy between canine and first bicuspid.
Test Wires
The wires to be tested during the friction study were
of a nickel-titanium alloy (NiTi™, small broad maxillary
archform, Ormco Corp., Orange, CA) in three different
cross-sections: 0.016-inch round, 0.018-inch round, and
0.016 x 0.022-inch rectangular.
Each preformed nickel-
titanium archwire was cut in half at the midline.
40
The
“half-archwire” to be tested was placed into the series of
self-ligating brackets and tubes, and an archwire lock was
attached to its distal end.
A new wire was used for each
trial, and a new set of brackets was used to test each wire
size.
Instron™ Testing Machine
After the wire was placed in the brackets, the entire
apparatus was mounted onto the base of an Instron™
universal testing machine (Model 1011, Instron Corp.,
Canton, MA) with the distal end of the test wire pointing
upward (Figure 11).
The distal end of the wire with its
archwire lock was aligned and connected to a customdesigned hook extending from a flexural load beam attached
to the moveable crosshead of the testing machine.
The wire
was pulled through the brackets distally by the movable
head of the machine at a velocity of one-mm per minute for
a total test period of one-and-one-half minutes.
Resistance levels encountered by the Instron™ testing
machine, as it pulled the test wire through the brackets,
were continuously recorded over the entire testing period.
All testing was performed at room temperature under dry
conditions.
41
Figure 11: Device mounted in Instron™ machine
Perturbation Machine
Based upon the hypothesis that forces and vibrations
conveyed to the teeth during function reduce the magnitude
of frictional resistance during orthodontic tooth movement,
a machine was designed to introduce perturbations into the
present friction testing study.
The machine consisted of a
motor connected to a plunger (Figures 12 and 13).
42
The
Figure 12: Perturbation machine plunger. As viewed from above
the friction testing device. The plunger was positioned to
strike the baseplate from behind.
Figure 13: Perturbation machine motor
perturbator was activated periodically by a current
(initiated by one of the switches) carried to an
electromagnet that, in turn, “launched” the plunger (whose
travel was limited by a stop).
The speed of the rotating
motor could be adjusted in order to control the frequency
43
of the plunger movement.
The plunger was placed adjacent
to the aluminum baseplate containing the seven cylinders
and the brackets.
Each time a switch was activated by the
motor, the plunger struck the baseplate at a force of 200500 grams.
During testing, the plunger hit the baseplate
at a frequency of 1 hit per second or a total of 90 hits
during the entire 90-second test period.
While the frequency of perturbations used in this
study (1x/second) far exceeds the frequency of daily tooth
contacts in man (approximately 100x/hour; Graf, 1969), it
must be remembered that the velocity at which the wire was
being moved through the brackets (1 mm/minute) during the
testing was as much as 43,000 times faster than the
relative velocity of tooth or wire movement intra-orally
that has been estimated to be 0.23 x 10-4 mm per minute or
1 mm per month (Braun et al., 1999).
And so it seems
reasonable to increase the frequency of perturbations
introduced into the system when the wire is moving
relatively quickly through the brackets.
The magnitude of
the plunger force hitting the baseplate is greatly reduced
relative to average intra-oral forces.
200-500 grams is a
very conservative force value compared to swallowing and
chewing forces that can reach as much as 30 kilograms and
44
maximum bite forces that can exceed 100 kilograms (Gibbs et
al., 1981; Proffit et al., 1983).
Testing Protocol
For each wire size, a new set of brackets was used.
The seven brackets were affixed to the brass face-plates
using cyano-acrylate adhesive.
After the brackets were in
place, the cylinders were mounted into the aluminum
baseplate, and the brackets were lined up according to
either the ideal “Moyers” archform alignment template or to
the misaligned archform template with the specified firstorder discrepancies in the lateral and canine areas.
The
brackets and the archwire were wiped with 70% ethanol, and
the wire was placed into the tubes and secured into the
self-ligating brackets.
An archwire lock was attached to the distal end of the
test wire. The baseplate, with the brackets and test wire
in place, was then mounted in the Instron™ testing machine.
Each wire was pulled through the series of brackets at a
velocity of one-mm per minute for a total test time of oneand-one-half minutes.
At the end of the test the baseplate was removed from
its support, the wire was removed from the brackets, and a
new wire was placed in the brackets and tested in the
45
Instron™ machine following the same protocol as above.
This process was repeated for a total of nine tests.
After
the nine tests, the perturbation machine was turned on, and
the same process was again repeated for nine tests under
the same testing conditions, but with the introduction of
vibrations.
After these eighteen tests (nine without perturbations
and nine with perturbations) were complete, the brackets
were repositioned based upon the shape of the second
“zeroing” jig template.
In this new configuration, the
brackets and wires were tested using the same protocol
described above for another set of eighteen tests (nine
without perturbations and nine with perturbations.
For
each bracket type – wire size combination, 36 total tests
were run.
Of the 36 tests run, 9 tests were run under each
of the following four conditions: 1) brackets aligned
without perturbations; 2) brackets aligned with
perturbations; 3) brackets misaligned without
perturbations; and 4) brackets misaligned with
perturbations.
Nine possible unique bracket type – wire
size combinations multiplied by the 36 tests per
combination resulted in a grand total of 324 tests. Figure
14 contains a matrix showing each of the variables and how
they were organized into the tests to be conducted.
46
016 NiTi
018 NiTi
016x022 NiTi
016 NiTi
018 NiTi
016x022 NiTi
Damon 2™
Damon 2™
In-Ovation R™
In-Ovation R™
SmartClip™
SmartClip™
SmartClip™
brackets
aligned
brackets
aligned
018 NiTi
aligned
SmartClip™
brackets
misaligned
016 NiTi
brackets
misaligned
misaligned
with perturbations
3 bracket
types
x
3 wire
sizes
Each of the 36 unique
combinations
without perturbations
x
x
2 alignment
configurations
9 repetition per
combination
x
2 perturbation
options
=
=
36 unique
combinations
324 total trials run
while testing
Figure 14: Matrix showing all tested variable combinations. Each of the
36 cubes represents one unique combination of bracket, wire, alignment
configuration, and perturbation option.
Statistical Analysis
While pulling the test wire through the brackets,
resistance levels encountered by the Instron™ machine were
recorded by a printer connected to the testing machine.
The recorded results of each test were manually evaluated.
As a first step, the point on the graph corresponding to
the value of maximum static resistance was identified.
Starting from that point, values were measured at six
second intervals along the graph for a total of ten values
over sixty seconds.
These ten points were averaged
together to arrive at a kinetic resistance value for each
individual test.
There were three individual tests out of
the total of 324 tests that did not continue for a minimum
of sixty seconds following the point of maximum static
resistance.
These tests were not recognized by the
software (SPSS version 13.0, SPSS Inc., Chicago, IL) used
to analyze the data and were excluded from the analyses
comparing average kinetic frictional resistances.
All of the tests were divided into the following four
groups: 1) aligned brackets and no perturbations present,
2) aligned brackets and perturbations present,
3) misaligned brackets and no perturbations present, and
48
4) misaligned brackets and perturbations present.
Descriptive statistics were determined for the four groups
and each group was analyzed using two separate one-way
analyses of variance with the bracket type and the wire
size serving as the independent variables.
Any differences
found between brackets and/or wires within each of the
groups were further analyzed using the Tukey HSD post hoc
test.
These analyses intended to compare and contrast the
effects of bracket alignment or misalignment and the
absence or presence of perturbations on the frictional
resistance of nickel-titanium archwires and self-ligating
brackets in archforms simulating the early alignment phase
of orthodontic treatment.
Additional one-way analyses of
variance and their corresponding post hoc tests were also
performed to examine in more detail how the frictional
resistance of each bracket type varied in relation to wire
size and whether the brackets were aligned or misaligned.
49
CHAPTER IV – RESULTS
Static and Kinetic Frictional Resistance
Throughout the testing the values for maximum static
and kinetic frictional resistance tended to follow the same
pattern in relation to the various brackets and wires.
Overall, as expected under the laws of classic friction,
when the brackets were aligned, the maximum static
resistance values tended to be greater than the kinetic
resistance values (Tables 1 and 2 and Figures 15 through
18).
On the other hand, when the brackets were misaligned,
just the opposite was true – the kinetic resistance values
tended to be greater than the maximum static resistance
values.
Please note the undersized subgroups in Table 1 for
the Damon 2™ and In-Ovation R™ brackets under the column
“Misaligned brackets, without perturbations, n.”
As noted
previously, smaller subgroup size was due to exclusion by
the SPSS software of three trials that failed to run for a
minimum of sixty seconds following the measured point of
maximum static frictional resistance.
Undersized groups
can also be found in later tables that compare average
kinetic frictional resistances.
50
maximum static
resistance
kinetic resistance range
Figure 15: Example of a graph of frictional resistance values
during a test with aligned brackets. Drawn from original
tracing. Note the relative magnitude of maximum static
resistance versus kinetic resistance.
maximum static
resistance
kinetic resistance
range
Figure 16: Example of a graph of frictional resistance values
during a test with misaligned brackets. Drawn from original
tracing. Note the relative magnitude of kinetic resistance
versus maximum static resistance.
51
Table 1: Descriptive statistics: Average kinetic frictional resistance in grams including
data from all three wire sizes.
Aligned brackets
without
perturbations
Misaligned brackets
with
perturbations
n
mean(g)
SD(g)
n
Damon 2™
27
42.6
29.8
27
In-Ovation R™
27
136.1
115.7
SmartClip™
27
26.6
Total
81
68.4
mean(g)
without
perturbations
with
perturbations
SD(g)
n
mean(g)
SD(g)
n
mean(g)
SD(g)
9.7
11.5
25
352.4
271.5
27
247.3
224.8
27
49.3
55.4
26
623.6
459.4
27
399.2
290.1
13.9
27
6.5
4.3
27
503.6
387.5
27
294.2
256.0
84.0
81
21.8
37.8
78
495.1
393.0
81
313.5
263.0
700.0
Resistance Force (grams)
600.0
500.0
400.0
Damon 2™
In-Ovation R™
SmartClip™
300.0
200.0
100.0
0.0
Aligned without
Perturbations
Aligned with
Perturbations
Misaligned without
Perturbations
Misaligned with
Perturbations
Test Group
Figure 17: Comparisons across three bracket types of average kinetic
frictional resistances. Data include contributions from all three wire
sizes.
Table 2: Descriptive statistics: Maximum static frictional resistance in grams including
data from all three wire sizes.
Aligned brackets
without
perturbations
Misaligned brackets
with
perturbations
without
perturbations
with
perturbations
n
mean(g)
SD(g)
n
mean(g)
SD(g)
n
mean(g)
SD(g)
n
mean(g)
SD(g)
Damon 2™
27
46.5
34.8
27
19.5
13.2
27
382.2
334.5
27
215.4
191.4
In-Ovation R™
27
150.1
121.9
27
54.8
56.0
27
537.8
307.0
27
366.6
242.0
SmartClip™
27
25.9
14.5
27
16.1
5.9
27
543.7
425.6
27
296.4
259.6
Total
81
74.2
91.0
81
30.1
37.4
81
487.9
362.7
81
292.8
238.1
600.0
Resistance Force (grams)
500.0
400.0
300.0
Damon 2™
In-Ovation R™
SmartClip™
200.0
100.0
0.0
Aligned without
Perturbations
Aligned with
Perturbations
Misaligned without
Perturbations
Misaligned with
Perturbations
Test Group
Figure 18: Comparisons across three bracket types of maximum static
frictional resistances. Data include contributions from all three wire
sizes.
For convenience sake, from this point on, whenever
static and kinetic frictional resistance values follow the
same pattern for a given set of parameters, they will not
be discussed separately; rather, they will be discussed
generally as “frictional resistance.”
Brackets
The results of the one-way analyses of variance
identified specific patterns with regard to the levels of
frictional resistance associated with each of the three
self-ligating brackets tested.
During tests when all of
the brackets were aligned, the Damon 2™ bracket and the
SmartClip™ bracket both showed significantly less
frictional resistance compared to the In-Ovation R™ bracket
(Tables 3 and 4 and Figures 17 and 18).
When the brackets
were misaligned, there was overall no significant
difference in maximum static frictional resistance among
the brackets, but, in regard to kinetic resistance, the
Damon 2™ bracket showed significantly less resistance than
the In-Ovation R™ bracket.
Overall, the introduction of perturbations into the
system had no effect upon the rank of average kinetic
frictional differences across the three brackets when they
were aligned, but when misaligned, the introduction of
56
Table 3: Summary of one-way ANOVAs of average kinetic and maximum static frictional
forces including contributions from all three wire sizes.
aligned brackets
and
no perturbations
aligned brackets
and
perturbations
Sum of
Squares
df
mean square
F
Sig.
Rk
between groups
within groups
total
188639.5
376340.7
564980.2
2
78
80
94319.728
4824.881
19.549
.000**
Rs
between groups
within groups
total
239445.4
423022.8
662468.2
2
78
80
119722.704
5423.369
22.075
.000**
Rk
between groups
within groups
total
30735.6
83611.8
114347.4
2
78
80
15367.811
1071.946
14.336
.000**
Rs
between groups
within groups
total
24848.1
87030.7
111878.8
2
78
80
12424.049
1115.778
11.135
.000**
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
Table 3 continued
Sum of
Squares
misaligned brackets
and
no perturbations
misaligned brackets
and
perturbations
df
mean square
F
Sig.
Rk
between groups
within groups
total
940495.7
10950767.0
11891262.7
2
75
77
470247.861
146010.223
3.221
.046**
Rs
between groups
within groups
total
452891.9
10069289.0
10522180.9
2
78
80
226445.938
129093.443
1.754
.180
Rk
between groups
within groups
total
326823.3
5206097.5
5532920.8
2
78
80
163411.630
66744.839
2.448
.093
Rs
between groups
within groups
total
309088.1
4226651.5
4535739.6
2
78
80
154544.049
54187.840
2.852
.064
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
Table 4: Results of Tukey HSD post hoc tests to clarify ranks across the three bracket
types including contributions from all three wire sizes. Means (in grams) in adjacent
columns are statistically unequal.
alpha = .05
n
Rk
aligned brackets
and
no perturbations
Rs
Rk
aligned brackets
and
perturbations
Rs
1
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
42.6
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
46.5
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
9.7
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
19.5
2
3
136.1
26.6
150.1
25.9
49.3
6.5
54.8
16.1
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
Table 4 continued
alpha = .05
n
Rk
misaligned brackets
and
no perturbations
misaligned brackets
and
perturbations
1
Damon 2™
In-Ovation R™
SmartClip™
25
26
27
352.4
Rs
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
382.2
537.8
543.7
Rk
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
247.3
399.2
294.2
Rs
Damon 2™
In-Ovation R™
SmartClip™
27
27
27
215.4
366.6
296.4
503.6
2
3
623.6
503.6
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
perturbations caused the differences in kinetic frictional
resistance among the brackets to disappear.
Perturbations
reduced the magnitude of kinetic frictional resistance of
the brackets by an average of 72.2% and the static
frictional resistance of the brackets by 53.1%.
When the
brackets were misaligned, perturbations reduced the kinetic
frictional resistance by an average of 35.8% and the static
frictional resistance by 40.3% (Tables 5 and 6).
Additional one-way analyses of variance in which frictional
resistances could be compared across brackets were
performed for each wire size individually (Tables 7 through
10 and Figures 19 and 20).
These analyses point out that
in regard to kinetic frictional resistance, when the
brackets were aligned, there was no significant difference
among the brackets when a 0.016-inch NiTi wire was tested,
yet when a 0.018-inch or a 0.016- x 0.022-inch wire was
used, the Damon 2™ and the SmartClip™ brackets both showed
significantly less kinetic frictional resistance than the
In-Ovation R™ bracket.
Maximum static friction resistance
values showed a similar pattern with the larger wires, but
with the 0.016-inch wire, the SmartClip™ bracket exhibited
significantly less resistance than the In-Ovation R™
bracket.
61
Table 5: The amount of average kinetic frictional resistance reduced by perturbations
for each bracket type.
Damon 2™
In-Ovation R™
SmartClip™
grams reduced
32.9
86.8
20.1
Average % reduced:
Aligned
percentage reduced
77.2%
63.8%
75.6%
grams reduced
105.1
224.4
209.4
72.2%
Misaligned
percentage reduced
29.8%
36.0%
41.6%
35.8%
Table 6: The amount of maximum static frictional resistance reduced by perturbations
for each bracket type.
Damon 2™
In-Ovation R™
SmartClip™
grams reduced
27.0
95.3
9.8
Average % reduced:
Aligned
percentage reduced
58.1%
63.5%
37.8%
53.1%
grams reduced
166.8
171.1
247.3
Misaligned
percentage reduced
43.6%
31.8%
45.5%
40.3%
Table 7: Descriptive statistics: Average kinetic frictional resistances in grams
including data from both perturbation values.
016 NiTi
aligned brackets
n
mean(g)
SD(g)
018 NiTi
misaligned brackets
aligned brackets
misaligned brackets
n
mean(g)
SD(g)
n
mean(g)
SD(g)
n
mean(g)
SD(g)
Damon 2™
18
9.4
8.3
18
88.1
48.1
18
17.3
13.0
18
202.5
64.3
In-Ovation R™
18
11.8
9.1
18
148.9
62.0
18
63.2
42.4
17
381.5
71.4
SmartClip™
18
8.4
3.4
18
123.5
53.3
18
17.4
17.7
18
239.4
82.1
Total
54
9.9
7.4
54
120.2
59.3
54
32.7
34.7
53
272.5
105.3
Table 7 continued
016x022 NiTi
aligned brackets
misaligned brackets
n
mean(g)
SD(g)
n
mean(g)
SD(g)
Damon 2™
18
51.8
33.2
16
641.0
136.1
In-Ovation R™
18
203.1
92.3
18
990.4
266.1
SmartClip™
18
23.8
13.9
18
833.7
218.7
Total
54
92.9
97.3
52
828.6
255.5
1200.0
Resistance Force (grams)
1000.0
800.0
600.0
Damon 2™
In-Ovation R™
SmartClip™
400.0
200.0
0.0
Alignment
Misalignment
Alignment
Misalignment
Alignment
Misalignment
with 016 NiTi with 016 NiTi with 018 NiTi with 018 NiTi with 016x022 with 016x022
NiTi
NiTi
Test Group
Figure 19: Additional comparisons across three bracket types of average
kinetic frictional resistances. Data include contributions from both
perturbation values.
Table 8: Descriptive statistics: Maximum static frictional resistances in grams including
data from both perturbation values.
016 NiTi
aligned brackets
n
mean(g)
Damon 2™
18
14.7
In-Ovation R™
18
SmartClip™
Total
SD(g)
018 NiTi
misaligned brackets
aligned brackets
n
mean(g)
SD(g)
n
mean(g)
7.8
18
89.9
54.5
18
23.3
17.1
7.0
18
147.6
67.6
18
18
10.1
2.2
18
136.2
62.3
54
14.0
6.8
54
124.6
65.5
SD(g)
misaligned brackets
n
mean(g)
SD(g)
7.5
18
180.4
62.1
76.2
53.8
18
429.2
117.2
18
25.0
11.8
18
261.8
103.6
54
41.5
40.1
54
290.5
141.5
Table 8 continued
016x022 NiTi
aligned brackets
misaligned brackets
n
mean(g)
SD(g)
n
mean(g)
SD(g)
Damon 2™
18
61.0
36.1
18
626.2
260.6
In-Ovation R™
18
214.1
100.7
18
779.8
161.9
SmartClip™
18
27.8
10.8
18
862.2
308.7
Total
54
101.0
102.1
54
756.0
265.5
1000.0
900.0
Resistance Force (grams)
800.0
700.0
600.0
500.0
Damon 2™
In-Ovation R™
SmartClip™
400.0
300.0
200.0
100.0
0.0
Alignment
with 016
NiTi
Misalignment
with 016
NiTi
Alignment
with 018
NiTi
Misalignment
Alignment
Misalignment
with 018
with 016x022 with 016x022
NiTi
NiTi
NiTi
Test Group
Figure 20: Additional comparisons across three bracket types of maximum
static frictional resistances. Data include contributions from both
perturbation values.
Table 9: Summary of one-way ANOVAs of average kinetic and maximum static frictional
forces including contributions from both perturbation values.
016 NiTi
and
aligned brackets
018 NiTi
and
aligned brackets
016x022 NiTi
and
aligned brackets
Sum of
Squares
df
mean square
F
Sig.
Rk
between groups
within groups
total
108.2
2768.9
2877.1
2
51
53
54.090
54.293
.996
Rs
between groups
within groups
total
455.8
1963.2
2418.0
2
51
53
227.907
34.493
5.921
.005**
Rk
between groups
within groups
total
25196.2
38772.0
63968.2
2
51
53
12598.124
760.235
16.571
.000**
Rs
between groups
within groups
total
32578.8
52462.7
85041.5
2
51
53
16289.389
1028.681
15.835
.000**
Rk
between groups
within groups
total
334876.0
166739.6
501615.6
2
51
53
167437.995
3269.404
51.214
.000**
Rs
between groups
within groups
total
355454.7
196502.3
551957.0
2
51
53
177727.352
3852.986
46.127
.000**
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
.376
Table 9 continued
016 NiTi
and
misaligned brackets
018 NiTi
and
misaligned brackets
016x022 NiTi
and
misaligned brackets
Sum of
Squares
df
mean square
F
Sig.
Rk
between groups
within groups
total
33546.4
153068.0
186614.4
2
51
53
16773.204
3001.334
5.589
.006**
Rs
between groups
within groups
total
33580.7
194044.3
227625.0
2
51
53
16790.352
3804.791
4.413
.017**
Rk
between groups
within groups
total
310011.7
266546.6
576558.3
2
50
52
155005.824
5330.932
29.077
.000**
Rs
between groups
within groups
total
579421.6
481813.9
1061235.5
2
51
53
289710.796
9447.331
30.666
.000**
Rk
between groups
within groups
total
1034723.5
2294792.3
3329515.8
2
49
51
517361.757
46832.496
11.047
.000**
Rs
between groups
within groups
total
516481.8
3220258.1
3736739.9
2
51
53
258240.907
63142.316
4.090
.023**
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
Table 10: Results of Tukey HSD post hoc tests to clarify ranks across the three bracket
types including contributions from both perturbation values. Means (in grams) in
adjacent columns are statistically unequal.
alpha = .05
n
016 NiTi
and
aligned brackets
Rk
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
9.4
11.8
8.4
Rs
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
14.7
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
88.1
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
Rk
016 NiTi
and
misaligned brackets
1
Rs
2
3
14.7
17.1
10.1
123.5
148.9
123.5
89.9
136.2
147.6
136.2
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
Table 10 continued
alpha = .05
n
Rk
018 NiTi
and
aligned brackets
Rs
Rk
018 NiTi
and
misaligned brackets
Rs
1
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
17.3
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
23.3
Damon 2™
In-Ovation R™
SmartClip™
18
17
18
202.5
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
180.4
2
3
63.2
17.4
76.2
25.0
381.5
239.4
429.2
261.8
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
Table 10 continued
alpha = .05
n
Rk
016x022 NiTi
and
aligned brackets
Rs
Rk
016x022 NiTi
and
misaligned brackets
Rs
1
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
51.8
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
61.0
Damon 2™
In-Ovation R™
SmartClip™
16
18
18
641.0
Damon 2™
In-Ovation R™
SmartClip™
18
18
18
626.2
779.8
2
3
203.1
23.8
214.1
27.8
990.4
833.7
779.8
862.2
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
When the brackets were misaligned and a 0.016-inch
wire was tested, the Damon 2™ bracket showed significantly
less frictional resistance than the In-Ovation R™ bracket.
With the 0.016-inch wire, the SmartClip™ showed no
significant difference from the other two brackets.
The
testing of a 0.018-inch wire with the brackets misaligned
showed that the Damon 2™ and the SmartClip™ brackets showed
no significant difference between each other, but both
produced significantly less kinetic resistance than the InOvation R™ bracket.
The maximum static resistance level of
the Damon 2™ bracket was significantly less than that of
the SmartClip™ which, in turn, was significantly less than
that of the In-Ovation R™.
Finally, misaligned brackets
along with a 0.016- x 0.022-inch wire resulted in the Damon
2™ bracket showing significantly less kinetic frictional
resistance than either the SmartClip™ or the In-Ovation R™
bracket and less maximum static frictional resistance than
the SmartClip™ bracket.
The effect of misalignment upon frictional resistance
levels was to increase kinetic resistance by 13 times and
static resistance by over 10 times (Tables 11 and 12).
74
Table 11: The increase in average kinetic frictional resistance due to misalignment
of brackets. Comparing bracket types by wire size.
grams
Damon 2™
78.7
In-Ovation R™
137.1
SmartClip™
115.1
Average % increase
016 NiTi
percentage
937.2%
1261.9%
1470.2%
1223.1%
grams
185.2
318.3
222.0
018 NiTi
percentage
1170.5%
603.6%
1375.9%
1050.0%
016x022 NiTi
grams
percentage
589.2
1237.5%
787.3
487.6%
809.9
3502.9%
1742.7%
Overall average % increase
1338.6%
Table 12: The increase in maximum static frictional resistance due to misalignment
of brackets. Comparing bracket types by wire size.
grams
Damon 2™
75.2
In-Ovation R™
130.5
SmartClip™
126.1
Average % increase
016 NiTi
percentage
611.6%
863.2%
1348.5%
941.1%
grams
157.1
353.0
236.8
018 NiTi
percentage
774.2%
563.3%
1047.2%
794.9%
016x022 NiTi
grams
percentage
565.2
1026.6%
565.7
364.2%
834.4
3101.4%
1497.4%
Overall average % increase
1077.8%
Wires
One-way analyses of variance were conducted to assess
frictional resistance associated with each wire size.
The
analyses revealed that average kinetic and maximum static
resistances followed precisely the same patterns.
When the
brackets were aligned, both the 0.016-inch and the 0.018inch round NiTi wires showed significantly less frictional
resistance than the rectangular 0.016- x 0.022-inch NiTi
wire (Tables 13 through 16 and Figures 21 and 22).
With
misaligned brackets there were significant differences
across all of the three wires.
The 0.016- x 0.022-inch
wires showed greater frictional resistance than the 0.018inch wires that, in turn, showed greater frictional
resistance than the 0.016-inch wires.
The introduction of
perturbations to these testing parameters did not change
the rank of frictional-resistance magnitudes across the
wires, whether the brackets were aligned or not.
76
Table 13: Descriptive statistics: Average kinetic frictional resistance in grams
including data from all three bracket types.
Aligned brackets
without
perturbations
SD(g)
Misaligned brackets
with
perturbations
n
mean(g)
n
mean(g)
016 NiTi
27
16.1
5.0
27
3.7
018 NiTi
27
55.2
36.1
27
016x022 NiTi
27
134.1
113.6
Total
81
68.4
84.0
SD(g)
without
perturbations
with
perturbations
n
mean(g)
SD(g)
n
mean(g)
SD(g)
2.5
27
166.0
44.3
27
74.3
29.2
10.1
10.2
25
330.8
89.5
27
216.3
88.2
27
51.7
53.6
26 1021.5
212.7
27
650.0
131.8
81
21.8
37.8
78
393.0
81
313.5
263.0
495.1
1200.0
Resistance Force (grams)
1000.0
800.0
600.0
016 NiTi
018 NiTi
016x022 NiTi
400.0
200.0
0.0
Aligned without
Perturbations
Aligned with
Perturbations
Misaligned without
Perturbations
Misaligned with
Perturbations
Test Group
Figure 21: Comparisons across three wire sizes of average kinetic
frictional resistances. Data include contributions from all three bracket
types.
Table 14: Descriptive statistics: Maximum static frictional resistance in grams including
data from all three bracket types.
Aligned brackets
without
perturbations
n
mean(g)
016 NiTi
27
17.7
018 NiTi
27
016x022 NiTi
Total
SD(g)
Misaligned brackets
with
perturbations
n
mean(g)
7.6
27
10.3
62.1
48.4
27
27
142.8
121.4
81
74.2
91.0
SD(g)
without
perturbations
with
perturbations
n
mean(g)
SD(g)
n
mean(g)
SD(g)
2.5
27
174.9
47.9
27
74.3
34.7
20.9
7.0
27
357.9
143.4
27
223.1
104.0
27
59.2
53.6
27
931.0
242.3
27
581.1
146.6
81
30.1
37.4
81
487.9
362.7
81
293.8
238.1
1000.0
900.0
Resistance Force (grams)
800.0
700.0
600.0
500.0
016 NiTi
018 NiTi
016x022 NiTi
400.0
300.0
200.0
100.0
0.0
Aligned without
Perturbations
Aligned with
Perturbations
Misaligned without
Perturbations
Misaligned with
Perturbations
Test Group
Figure 22: Comparisons across three wire sizes of maximum static
frictional resistances. Data include contributions from all three bracket
types.
Table 15: Summary of one-way ANOVAs of average kinetic and maximum static frictional
forces including contributions from all three bracket types.
aligned
and
no perturbations
aligned
and
perturbations
Sum of
Squares
df
mean square
F
Sig.
Rk
between groups
within groups
total
195097.0
369883.2
564980.2
2
78
80
97548.508
4742.092
20.571
.000**
Rs
between groups
within groups
total
217128.1
445340.1
662468.2
2
78
80
108564.037
5709.489
19.015
.000**
Rk
between groups
within groups
total
36753.4
77594.0
114347.4
2
78
80
18376.680
994.795
18.473
.000**
Rs
between groups
within groups
total
35741.7
76137.1
111878.8
2
78
80
17870.827
976.117
18.308
.000**
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
Table 15 continued
Sum of
Squares
misaligned
and
no perturbations
misaligned
and
perturbations
df
mean square
F
Sig.
Rk
between groups
within groups
total
10553552.0
1337710.8
11891262.8
2
75
77
5276775.802
17836.144
295.847
.000**
Rs
between groups
within groups
total
8401958.1
2120222.3
10522180.4
2
78
80
4200979.049
27182.337
154.548
.000**
Rk
between groups
within groups
total
4856802.0
676118.7
5532920.7
2
78
80
2428401.021
8668.188
280.151
.000**
Rs
between groups
within groups
total
3664679.4
871060.2
4535739.6
2
78
80
1832339.716
11167.438
164.079
.000**
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
**P<0.05
Table 16: Results of Tukey HSD post hoc tests to clarify ranks across the three wire
sizes. Data include contributions from all three bracket types. Means (in grams) in
adjacent columns are statistically unequal.
alpha = .05
n
Rk
aligned
and
no perturbations
Rs
Rk
aligned
and
perturbations
Rs
1
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
16.1
55.2
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
17.7
62.1
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
3.7
10.1
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
10.3
20.9
2
3
134.1
142.8
51.7
59.2
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
Table 16 continued
alpha = .05
n
Rk
misaligned
and
no perturbations
Rs
Rk
misaligned
and
perturbations
Rs
1
016 NiTi
018 NiTi
016x022 NiTi
27
26
25
166.0
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
174.9
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
74.3
016 NiTi
018 NiTi
016x022 NiTi
27
27
27
74.3
2
3
330.8
1021.5
357.9
931.0
216.3
650.0
223.1
581.1
Rk = kinetic frictional resistance, Rs = maximum static frictional resistance
CHAPTER V – DISCUSSION
The results of this study support the idea that
friction plays an important role in the interaction of
bracket and wire surfaces when the two are sliding past
each other.
Regardless of the type of self-ligating
bracket used and regardless of the dimensions of nickeltitanium wire used, friction was present during testing.
As noted previously, there are numerous factors
associated with archwires, brackets, and the oral or
testing environment that potentially influence frictional
resistance.
Many of these factors or variables can be
evaluated, based upon the results of the present study.
Variables Affecting Friction
Archwires
Following the trend found in previous friction studies
(Andreasen and Quevedo, 1970; Frank and Nikolai, 1980;
Drescher et al., 1989), the results of this study showed a
general tendency for the level of frictional resistance to
increase with increasing wire size.
This was especially
clear when the brackets were misaligned.
Under misaligned
conditions, the 0.016 x 0.022-inch wire showed more than
six times the average kinetic frictional resistance and
85
more than five times the average maximum static frictional
resistance compared to the 0.016-inch wire.
Compared to
the 0.018-inch wire under the same conditions, the 0.016 x
0.022-inch wire had over three times the average kinetic
resistance and two-and-a-half times the average maximum
static resistance.
This bigger, stiffer wire produced a
greater normal component of contact force between itself
and the bracket-slot base and/or the self-ligating
clip/gate, resulting in much larger frictional resistance
magnitudes.
Even when the brackets were aligned, the means
showed a progression of increasing frictional resistance
from 0.016- to 0.018- to 0.016- x 0.022-inch wires,
although there was no statistical difference between the
0.016- and 0.018-inch wires.
Brackets
Bracket Width
Three samples of each of the different brackets
(central incisor through bicuspid – all bracket systems
tested use the same bracket for both 1st and 2nd bicuspids)
and the two molar tubes of the three tested bracket types
were measured using a digital caliper (Chicago Brand
Industrial Incorporated, Fremont, CA) and averaged for
86
Table 17: Average bracket widths (in millimeters).
Central
Lateral
Canine
Bicuspids
Damon 2™
2.66
2.67
2.65
2.66
In-Ovation R™
2.87
2.68
2.89
2.95
SmartClip™
3.63
3.10
3.38
3.35
Mean bracket width
2.66
2.87
3.36
1st molar tube
2nd molar tube
4.07
3.88
3.97
1.94
3.94
2.46
width.
Width was defined as the distance between the
lateral aspect of the tie wings for the Damon 2™ and InOvation R™ brackets and the distance between the lateral
aspect of the self-ligating clips for the SmartClip™
bracket.
Measurements varied across the bracket types
17).
(Table
The Damon 2™ was the narrowest of the brackets (mean
bracket width of 2.66 mm) followed by In-Ovation R™ (2.87
mm) and SmartClip™ (3.36 mm). SmartClip™ showed the
greatest range of bracket widths.
The true extent to which
bracket width influenced the results of the present study
is unclear because of the number of other variables
associated with the brackets such as slot size and selfligation mechanism.
Still, given the inverse relationship
between bracket width and interbracket distance, the direct
relationship between interbracket distance and wire
flexibility, and the inverse relationship between wire
87
flexibility and contact force, one can assume that wider
brackets that are out of alignment experience larger forces
between wire and bracket.
Such forces can, in theory,
result in a relative increase in frictional resistance
experienced by the wire/bracket complex.
If one assumed
that bracket widths did affect the level of frictional
resistance, then one would conclude that in this study, the
SmartClip™ had a larger resistance magnitude and the Damon
2™ and In-Ovation R™ had smaller resistance magnitudes than
they would have shown if each bracket was the same standard
width.
Slot Size
All brackets used in the study had a slot size of
0.022-inch.
The depth of the slot for each bracket is
slightly different.
The SmartClip™ bracket has a depth of
0.028-inch (personal communication with 3M/Unitek, 2005);
the depth of a Damon 2™ and an In-Ovation R™ bracket are
both 0.027 inches (Harradine, 2003).
The presence of an
active clip, though, causes the true “passive” slot depth
of the In-Ovation R™ bracket to be approximately 0.018
inches.
For practical purposes, it can be assumed that the
slot depths of the Damon 2™ and SmartClip™ brackets are
88
approximately equal and both are larger than the “passive”
slot depth of the In-Ovation R™ bracket.
With a 0.016-inch wire, the three brackets showed no
statistical difference in kinetic frictional resistance
when they were aligned (though there was a statistically
significant difference between the maximum static
resistance of the SmartClip™ and In-Ovation R™ brackets).
After the wire size was increased to 0.018-inch or 0.016- x
0.022-inch, although the brackets were still aligned, the
In-Ovation R™ bracket tended to show significantly greater
frictional resistance than the other two brackets.
When considering slot size, slot depth, and bracket
width, one must consider the effect of these upon contact
angle (Figure 1).
In regard to this study, it is not so
much the facial view of contact angle in which we are
interested, but rather, it is the contact angle seen from
the occlusal view that is most interesting (Figure 23).
During part of this study, the self-ligating brackets of
the lateral and canine were respectively displaced one mm
lingually and one mm facially.
In theory, such first-order
discrepancies would minimize the “reduced friction”
properties of self-ligating brackets by pressing the
archwire against the bracket’s gate or clip.
89
Figure 23: Occlusal view of anterior SmartClip™ brackets and
a 0.016- x 0.022-inch NiTi™ wire in misaligned set-up
Hypothetically, under such circumstances, a narrow
bracket with a large slot depth should permit a greater
contact angle (as viewed from the occlusal) prior to
archwire binding.
The possibility of a greater contact
angle prior to binding would, therefore, lead to less
frictional resistance compared to other brackets that
cannot accommodate larger contact angles.
Interestingly,
the bracket that best fits these criteria (narrow width and
large slot depth) is the Damon 2™ bracket.
As expected per
this hypothesis, the Damon 2™ bracket showed the smallest
frictional resistance levels under all scenarios when the
brackets were misaligned.
90
Bracket Design
Confirming the work of previous studies (Thomas,
Sherriff, and Birnie, 1998; Thorstenson and Kusy, 2002a;
Henao and Kusy, 2005), the present study found that selfligating brackets with clips exhibited greater frictional
resistance than self-ligating brackets with slides or
gates.
According to Harradine (2003), any wire with a
diameter greater than 0.018-inch will activate the InOvation R™ clip resulting in increased normal force upon
the wire.
As reported earlier, kinetic frictional
resistance with a 0.016-inch wire when the brackets were
aligned was statistically the same across the three bracket
types, but, after the wire size was increased to 0.018-inch
or 0.016- x 0.022-inch, though all the brackets were still
aligned, the In-Ovation R™ bracket showed significantly
greater frictional resistance than the other two brackets.
Under testing circumstances when the brackets were
aligned, the SmartClip™ bracket consistently showed kinetic
frictional resistance levels that were equal to or less
than the kinetic frictional resistance of the Damon 2™.
Yet when the lateral and canine brackets were misaligned,
the SmartClip™ showed a larger than normal (relative to the
other two brackets) increase in the level of kinetic and
91
static resistance (Tables 11 and 12).
This greater
increase may be related to the bracket’s width (and
relatively reduced interbracket distance), or it may be
associated with the mechanism of the bracket’s selfligating lateral clips.
Weinberger (2005) points out that
the clips are meant to flex and release archwires that
exert forces exceeding a predetermined level.
It’s likely
that under this testing protocol, when the SmartClip™
brackets were misaligned lingually and facially and the
wire was pressed against the clips of the lateral and first
bicuspid brackets, that the clips were forced to flex.
It
is possible that such flexure of the clips exerted an
additional force upon the wire thus explaining the
significant increase in frictional resistance seen during
misalignment of the SmartClip™ bracket.
Additionally, the
larger increase in frictional resistance by the SmartClip™
bracket may be associated with the fact that the lateral
clips are composed of a nickel-titanium alloy.
The
interaction of these nickel-titanium clips with the nickeltitanium wires could help to explain the increased
frictional resistance values associated with the SmartClip™
bracket when the brackets were misaligned.
92
Testing Environment
Archform
This study was different from the majority of past
friction studies in that a seven-tooth dental segment in a
half-arch shape was simulated.
Placing brackets in a
curvilinear arrangement likely caused normal forces to be
continuously changing as the archwire was pulled through
the brackets.
Considering that in the template archform,
the central bracket was turned nearly perpendicular to the
direction of pull (Figure 24), one can assume, that as the
wire was pulled distally, the portion of the wire within
Figure 24: Testing set-up showing bracket arrangement
relative to Instron™ pulling arm
93
the central bracket was being pressed more and more against
the base of the slot.
Taylor and Ison (1996) referenced one of their
preliminary studies that “indicated that any residual curve
in the wire influenced friction.”
Because their bracket
set-up was in a straight line, they made sure to test only
straight lengths of wire.
Clearly, differences between the
archform of the nickel-titanium wires and the archform of
the brackets could result in increased frictional
resistance.
The frictional resistance values from the present
study were consistent with those values noted by Henao and
Kusy (2005), who also tested nickel-titanium wires and
self-ligating brackets in a simulated archform.
They also
concluded that self-ligating brackets with active clips
tended to exhibit greater frictional values than selfligating brackets with slides or gates.
Perturbations
Though not as dramatic as the reductions reported by
Braun and colleagues (1999), the vibrations introduced into
the present system by the perturbation machine caused a
notable decrease in the frictional resistance levels of
each bracket type tested.
The reason for the difference in
94
reduction in the current study is most likely due to the
difference in protocol.
Braun’s group (1999) tested a
single bracket compared to the present seven-bracket
design.
They noted in their conclusions that “Frictional
resistance may...be an important consideration when an arch
wire must simultaneously move through several in-line
brackets...We believe that it is unlikely that
perturbations would result in simultaneous, synchronous
relative motion in all of the related bracket/arch wire
interfaces” (Braun et al., 1999).
Their prediction was shown to be true in this study.
Of the 162 tests conducted in the presence of
perturbations, only 7 of them (4.3%) had kinetic resistance
values of 0 grams.
The vast majority of the tests showed
some level of frictional resistance at all times even in
the presence of perturbations.
In general, when the
brackets were aligned the decrease in kinetic resistance
caused by the perturbations averaged over 70% while the
decrease in maximum static resistance averaged over 50%.
Perturbations caused the misaligned brackets to experience
an average decrease in kinetic resistance of 35% and an
average decrease in maximum static resistance of 40%.
In
light of the increased binding and friction that was likely
occurring from the faciolingual bending activation of the
95
wires and the creation of greater normal forces, the
difference in resistance reduction between aligned brackets
and misaligned brackets is understandable.
Interestingly, this sizable decrease in frictional
resistance occurred using forces that are significantly
smaller (200 – 500 grams) than those found in the oral
environment which range from a few kilograms to over one
hundred kilograms.
Future studies utilizing different
force levels may show similar or even greater reductions in
frictional resistance.
Graphic Data/Stick and Slip
While the test wire was being pulled through the
series of test brackets, an adjacent printer recorded the
resistance encountered by the Instron™ machine in the form
of a graph.
Some of the graphs had a relatively smooth
contour (Figure 16).
This was the result of classic
friction from the bracket and wire sliding past one
another.
Other graphs, such as the one seen in Figure 25,
showed a distinct “peak and valley” pattern.
Most often
these occurred with larger wires when the brackets were
misaligned.
The cause of such peaks is the “stick-slip
phenomenon” discussed by Rossouw and associates in 2003.
96
Figure 25: Example of a graph of frictional resistance values
showing the stick-slip phenomenon. Drawn from original tracing.
Such a phenomenon occurs when the static frictional
resistance builds to a maximum level and then is followed
by a sudden release or slip of the wire (Figure 26).
Peak
Valley
Figure 26: Close-up of Figure 25 showing the stick (dark arrow) slip (white arrow) phenomenon. Peak = maximum static resistance
prior to movement. Valley = end of displacement, beginning of new
static phase.
97
The slip corresponds to rapid displacement of the wire.
This displacement ends after the “valley” is reached and a
new “peak” begins to form, starting the process all over
again. This type of bracket-wire interaction is, therefore,
a series of starts and stops or a repetition of archwire
binding and releasing, binding and releasing.
When the
“slip” occurred during the testing, an audible “click”
could be heard.
According to Rossouw and colleagues (2003), there is
evidence of this kind of stick-slip activity in the
orthodontics.
They explained that this phenomenon “may be
inferred from scanning electron micrographs that reveal
permanent deformation of archwires subjected to
intermittent binding and sliding at bracket surfaces.”
Considering stick-slip and the very slow velocities
associated with tooth movements, it appears that
orthodontics is more influenced by maximum static
frictional resistance than kinetic frictional resistance
(Omana et al., 1992).
Limitations
There are many reasons why one must be cautious in
correlating the results of laboratory in vitro friction
studies with in vivo orthodontic friction because
98
experimental conditions do not always correctly represent
the clinical situation (Rossouw, 2003).
The biggest
limitation to bench-top testing is the inability to
replicate the oral environment and especially to replicate
the extremely slow speeds and irregular nature of tooth
movement.
Slow velocities may produce dynamics that do not
correspond to the classic understanding of friction
(Rossouw et al., 2003).
In vitro studies tend to test at
constant speeds at magnitudes thousands of times greater
than that found in the mouth.
In their study, Drescher’s group (1989) tried to
account for the biologic resistance that a tooth feels in
opposition to its tendency to tip from orthodontic forces.
The incorporation or simulation of investing tissues
associated with a tooth would greatly enhance the
replication of the oral environment.
Unfortunately, the
design of the new friction testing machine did not include
an “artificial” periodontal ligament (PDL).
Because the
connective tissue surrounding the tooth and maintaining the
tooth within its socket absorbs and distributes a
significant portion of the forces encountered by the tooth,
the addition of a simulated PDL to the experimental model
might permit a more realistic testing environment.
99
Maximum static friction measurements, when frictional
resistance levels were relatively low, proved to be a
challenge due to the testing protocol.
According to the
chosen protocol, the primary investigator did not turn on
the perturbation machine until all clearance between the
archwire lock and the hook had been eliminated by the
Instron™ machine and the Instron™ began to experience
resistance.
This choice was based upon the desire to be
able to determine the beginning of each active testing
period.
Often while testing the smaller wires when the
brackets were aligned, the frictional resistance levels
were small - approximately 20 grams or less (Figure 27).
“maximum static resistance”
Figure 27: Close-up of a graph showing frictional resistance during
one of the trials of Damon 2™ brackets with a 0.016-inch NiTi™ wire
in the presence of perturbations. The point of “maximum static
resistance” corresponds to the precise moment the plunger from the
perturbation machine first struck the baseplate and immediately
dropped the frictional resistance to zero.
100
Under such circumstances, if perturbations were introduced,
the resistance level would immediate drop to zero or near
zero precisely at the same time that the plunger struck the
testing baseplate for the first time.
Resistance values
would remain near zero for the entire testing period.
The “maximum” static frictional resistance value
measured under these situations was directly related to the
speed at which the operator would notice the rise in
initial static resistance and then activate the
perturbation machine.
In other words, in theory, the
longer it took to turn on the perturbation machine, the
greater the recorded “maximum” static resistance on the
graph.
If the protocol had been different and the
perturbation machine was activated prior to the start of
the static resistance period of the test, it may have been
shown that for a portion of the tests conducted during this
study the maximum static resistance value was actually
significantly lower (possibly even zero grams) compared to
the measured value.
For this reason, static frictional
resistance levels for the smaller round nickel-titanium
wires in this study should be considered with some
uncertainty.
101
Finally, the present study was limited to selfligating brackets in combination with nickel-titanium wires
arranged in two set archforms: 1) aligned and 2) misaligned
with first-order discrepancies at the lateral and canine.
The flexibility of the new testing machine will permit
multiple future studies incorporating a variety of
different bracket types, wire types, and archform set-ups.
102
CHAPTER VI – SUMMARY AND CONCLUSIONS
The primary purpose of this study was to answer the
question: Do perturbations or vibrations significantly
affect the frictional resistance of self-ligating brackets
and nickel-titanium wires when introduced into an in vitro
model simulating the initial alignment phase of orthodontic
treatment?
The results of this study clearly show that,
when perturbations were introduced into the in vitro model,
both the average kinetic and the maximum static frictional
resistance was reduced by 35 – 70%.
Other questions to be answered include: “How do selfligating brackets differ in their frictional
characteristics?”
Resistance values from this study
provide additional evidence that self-ligating brackets
with slides or gates, otherwise known as “passive selfligating brackets,” contribute less to frictional
resistance than self-ligating brackets with active clips.
The SmartClip™ bracket and its unique self-ligating system
were influenced more than the other two brackets by the
alignment or misalignment of the brackets.
When the
SmartClip™ brackets were aligned, the clips sat passively
over the wire, and the bracket’s frictional resistance
appeared to be at least as small as that of the Damon 2™
103
bracket.
Yet, when the brackets were misaligned and the
wire was pressed against the slot or the clips, the
SmartClip™ bracket showed a considerable increase in
resistance relative to other self-ligating brackets.
This
increase may be explained by the larger width of the
bracket, added friction or binding associated with the
potential flexure of the clips, and/or the nickel-titanium
composition of the clips.
If self-ligating brackets are affixed to teeth that
are misaligned facially or lingually in the arch and the
wire is forced to press against the given gate or clip, how
is frictional resistance affected?
Foremost, frictional
resistance increases dramatically.
Results from this study
showed that, on the average, kinetic frictional resistance
increased thirteen times and maximum static resistance
increased over ten times.
Under some circumstances with
the 0.016- x 0.022-inch wire, those values were as high as
thirty-five times greater than “pre-misaligned” levels.
How does wire size affect frictional resistance?
Simply said, increased faciolingual dimension of the wire,
in the presence of mechanical interaction between the selfligating brackets and the wire, results in increased
frictional resistance.
104
Finally, one may wish to ask the all important
question. “Does friction in orthodontics really matter?”
The answer may be...
With a contained environment, there is the promise of
friction. And that is where the drama comes from.
--Bruce Greenwood
105
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VITA AUCTORIS
David Michael Bunkall was born on March 19, 1974, in
Salt Lake City, Utah, to Larry and Carolyn Bunkall.
He
graduated Magna Cum Laude from Brigham Young University in
Provo, Utah, in 1999 with a Bachelor of Science degree in
Zoology.
From 1999 to 2003, he attended dental school at
the University of Washington in Seattle, Washington and
graduated with honors.
Surgery degree in 2003.
He was awarded a Doctor of Dental
It is anticipated that in January
of 2006, David will graduate from Saint Louis University
with a Master of Science in Dentistry with an emphasis in
Orthodontics.
In May of 1997, David married Robyn Dover.
the parents of two sons, Cannon and Luke.
112
They are