Download COMPARING OCCLUSAL ARCH FORM AND BASAL BONE ARCH

COMPARING OCCLUSAL ARCH FORM AND BASAL BONE ARCH
FORM USING CBCT IN BLACK, WHITE AND MEXICAN
AMERICAN MANDIBLES
Angela M. Williams, D.D.S.
An Abstract Presented to the Graduate Faculty of
Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry
2013
Abstract
Introduction: Relapse continues to be a concern for today’s orthodontists. Practitioners agree that stability is a goal of treatment but there are many views on
which method of treatment will produce the most stable result. A change in arch
shape, or form, from the pre-treatment shape has been suggested as a reason
for instability. The literature reports many factors that play into how the shape of
the arch is developed including muscles, periodontal fibers, function, genetics,
race, intercanine width, and keeping teeth within basal bone. Purpose: This
study looks at the arch shape at occlusal plane versus the arch shape at basal
bone to determine if there is any difference between the two levels. Materials
and Methods: Using the CBCT of 150 black, white and Mexican American patients slices were taken at occlusal plane and basal bone levels. A canine ratio
was calculated for each level. Shape was classified into ovoid, tapered and
square based on the mean and standard deviation of the canine ratio. Results:
No significant difference was found between the arch shapes at the two levels.
Ovoid was the shape seen in a majority of patients at both levels. Conclusions:
No significant difference was apparent between the arch shapes at occlusal
plane versus BB levels. No significant difference of arch shape distribution between males and females or among the black, white and Mexican Americans.
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COMPARING OCCLUSAL ARCH FORM AND BASAL BONE ARCH
FORM USING CBCT IN BLACK, WHITE AND MEXICAN
AMERICAN MANDIBLES
Angela M. Williams, D.D.S.
A Thesis Presented to the Graduate Faculty of
Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry
2013
COMMITTEE IN CHARGE OF CANDIDACY:
Associate Professor Ki Beom Kim,
Chairperson and Advisor
Assistant Clinical Professor Nick Azar
Associate Clinical Professor Donald R. Oliver
i
DEDICATION
This work is dedicated to my wonderful husband, Donnie. You have done
nothing but encourage and support through this long road to change my career
path. You know how much I love you.
To my mom, Debbie, who listened to all of my heartaches and stresses
throughout this entire process. Thanks for being there.
Lastly, to the faculty of Saint Louis University, whose guidance and instruction have built a strong foundation for me to grow a fulfilling practice and future.
ii
ACKNOWLEDGEMENTS
This project was not possible without the help and support of the following
individuals:
Dr. Ki Beom Kim. Thank you for your guidance during my thesis preparation
and for enriching my education with your help and guidance in the classroom as
well as the clinic.
Dr. Rolf Behrents. Thank you for your contributions to my thesis and allowing
me to obtain an orthodontic education at Saint Louis University.
Dr. Donald Oliver. Thank you for your attention to detail during my thesis
preparation and revisions. The value of your clinical guidance cannot be measured.
Dr. Nick Azar. Thank you for taking the time to assist in the thesis progression and for contributing to my clinical education.
Dr. Peter Buschang. Thank you for helping me develop this thesis topic and
your meaningful contribution to my clinical education.
Dr. Derik Ure and Dr. Joe Mayes. Thank you for the use of your long-term
records in this study.
Dr. Heidi Israel. Thank you for your assistance with the statistical analysis for
this thesis.
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TABLE OF CONTENTS
List of tables ......................................................................................................... v
List of figures ........................................................................................................ vi
CHAPTER 1: INTRODUCTION ............................................................................ 1
CHAPTER 2: REVIEW OF THE LITERATURE
Basal bone ..................................................................................... 5
Orthodontic stability and relapse.................................................... 7
Basal bone ............................................................................... 7
Orthodontic forces .................................................................... 8
Mandibular incisors .................................................................. 8
Intercanine width ...................................................................... 9
Race and ethnicity .................................................................. 10
Genetics versus environment ................................................. 11
Aging ...................................................................................... 11
Other factors........................................................................... 12
Mandibular arch form ................................................................... 12
Commercial wires ................................................................... 13
Race and ethnicity .................................................................. 13
Frequency of form .................................................................. 15
Intercanine width .................................................................... 15
Mathematical representation of arch form .............................. 17
Cone Beam Computed Tomography ........................................... 17
Statement of thesis ...................................................................... 20
Literature Cited ............................................................................ 22
CHAPTER 3: JOURNAL ARTICLE
Abstract ....................................................................................... 31
Introduction .................................................................................. 32
Materials and methods ................................................................ 35
Sample ................................................................................... 35
Cone Beam Computed Tomography (CBCT) technique ........ 36
Error study .............................................................................. 41
Statistical analysis .................................................................. 42
Results ......................................................................................... 44
Discussion ................................................................................... 45
Conclusion ................................................................................... 48
Literature Cited ............................................................................ 49
Vita Auctoris ....................................................................................................... 52
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LIST OF TABLES
Table 3.1
Calculation of the canine ratio for OP and BB level based on the
digitized landmarks from Dolphin Imaging .................................... 43
Table 3.2
Calculation of the mean and standard deviation for the
canine ratios at the occlusal and BB level. One STD above
and below was calculated in order to classify the shape as
ovoid, square or tapered ............................................................... 44
Table 3.3
Distribution of shape across N=300.
Ovoid is the majority shape ........................................................... 45
v
LIST OF FIGURES
Figure 3.1
Example of plotted points for occlusal plane slice
In Mexican male ............................................................................ 37
Figure 3.2
Example of Mexican male occlusal plane measurements ............. 38
Figure 3.3
Example of B point landmark in Mexican female........................... 39
Figure 3.4
Example of plotted points for basal bone slice
in white female .............................................................................. 40
Figure 3.5
Example of Mexican male BB measurements ............................... 41
Figure 3.6
Example of black female graph ..................................................... 42
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CHAPTER 1: INTRODUCTION
Orthodontic relapse is a major concern in today's practice. One famous quote
by Dr. Hawley states he was willing to give one half of his fee to whomever could
retain his patients.1 It has been shown in animal studies that relapse begins immediately after teeth are left unrestrained.2 Practitioners agree that stability is a
goal of orthodontic treatment but there are many views on which method of
treatment will produce the most stable result. Tweed, Brodie and Nance all
agreed that stability relates to basal bone.3-5 Peck and Peck argued that if the
shape of the anterior teeth was disproportional based on a ratio of mesio-distal
versus bucco-lingual width there would be relapse and suggested the need for
interproximal reduction in order to make the tooth shape more favorable. 6 Strang
argued that intercanine width was key to stability.7 The following paragraphs will
discuss several factors mentioned to attempt to define how an arch form develops and why relapse happens.
There are perioral factors such as pressure from muscles, lips, cheeks or
habits such as musical instruments to describe how the arch form develops.
Many authors have stated the orbicularis oris, mentalis, buccinator, and tongue
dictate arch form and tooth position.8-12 One book discusses how the lower incisor position can lead to remodeling of the bone but that is not the only tissue to
consider since the teeth may be in bone but be periodontally compromised or out
of equilibrium with the oral cavity muscles.12 Burstone and Marcotte continue by
stating the dual muscular components of the orbicularis oris could place pressure
1
on the lower incisors only, upper incisors only or both.12 The buccinator influences the posterior width and the canines can behave like posterior teeth if the
oral slit is mesial to the canine allowing the cheek to apply more pressure than
the lips to the canines.12 There is disagreement on whether or not playing an instrument affects the position of incisors as one study concluded that for an individual patient the effect of an instrument is unpredictable and should not be substituted for orthodontic treatment13 while another study said playing an instrument
can serve as an adjunct to orthodontic tooth movements. 14 Engelman studied
several types of habit-induced pressures and concluded thumb-sucking produced
the highest pressures, swallowing and whistling produced the lowest, and instrument playing lay in between with brass instruments and the flute having some
influence.15
There are anatomical factors to describe the development of the arch such as
divergence of the mandible to cranial base, memory of periodontal fibers or genetic/racial influence. It has been shown that the attachment of periodontal fibers
is not determined by tooth anatomy but by the tooth position and orientation in
the arch16 and that a fibrotomy following orthodontic treatment may decrease the
amount of rotational relapse.17 Little et al. studied children in a rural Mexico village over a 32-year period and showed the cranial complex remodeled to a
shorter head length and a narrower face.18 The study attributed these changes to
a decrease in food coarseness leading to a decrease in masticatory muscle function.18 Horner et al. built upon this research to study how mandibular plane angle
relates to bone development. The study described how mandibular cortical bone
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thickness differs between hyperdivergent (patients that have a large facial divergence and weaker muscle activity) and hypodivergent (patients that have a small
facial divergence and stronger muscle activity) individuals and concluded cortical
bone tends to be thicker in hypodivergent patients leading to a difference in alveolar ridge thickness.19 It has been shown that arch length and mandibular intercanine width both decrease over time as part of the natural aging process. 20
Orthodontic factors that relate to arch form include pre-treatment arch form,
intercanine width, incisor irregularity and keeping teeth within basal bone. Maintaining the pre-treatment arch form has been suggested by some practitioners as
a key to stable orthodontic results.21 Keeping the patient’s arch form while
straightening the teeth might make the end result less likely to relapse.22 There is
a limit to the change in posterior width, and particularly intercanine width, that
can be achieved and remain stable.12 Ball et al. argued there is a different intercanine width between dental and basal arches but that it was unlikely to affect
the arch form as it was only 0.8 mm.23 Incisor irregularity occurs in almost everyone with roughly 50% of untreated adults having little to none and the remaining
50% having moderate to severe.24 Buschang and Shulman concluded that incisor
crowding was multifactorial and included ethnicity, number of first and second
molars, sex and age combined.24 Several studies have shown there is an anatomical difference between whites, blacks and Mexicans. Garcia showed bimaxillary prognathism was seen more in Mexicans than whites,25 Buschang and
Shulman showed Mexicans have more lower incisor irregularity than whites, 24
and Bishara et al. showed Mexicans have larger tooth sizes than whites.26 Stud-
3
ies have shown that blacks have arches with wider mandibular posterior segments than whites or Hispanics and Hispanics have larger anterior ratios than
blacks.27, 28 With anatomical differences such as these one may expect that the
underlying bone is different between the three groups as well which may lead to
differences in the arch form distribution among the three groups.
Several authors believe that stability relates to keeping the original arch form
while maintaining the teeth over the underlying bone.3, 4, 7, 29 Basal bone has
been difficult to define4 so there is no one method of treatment that will ensure
stability. One could argue that arch form does not matter or that basal bone is not
definable.
If the arch shape is the same at the level of basal bone and occlusion then
maybe there is a simple way to determine the basal bone shape based on the
occlusal arch shape. Since basal bone is nebulous according to some,12 can one
even show that arch shape is the same at the two levels? If it is not, as long as
practitioners do not violate the bone and move teeth out of its parameters, stability might not relate to a definition of basal bone. This study will look at the arch
form at the occlusal level and the basal bone level in black, white and Mexican
American patients to see if there is a difference in arch form between the two
levels or between the three groups.
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CHAPTER 2: REVIEW OF THE LITERATURE
Basal Bone
Lundstrom was the first to describe apical base as the portion of the bone
where the teeth rest30 and apical base has become interchangeable with basal
bone over the years. In 2000 the Glossary of Orthodontic Terms defined apical
base as the bone of the jaw that supports the teeth.31 Brash described the development of the arch form as following the underlying bone shape initially and then
being shaped by the eruption of the teeth and forces of the surrounding musculature.8 Proffit discusses alveolar bone being formed and shaped by the teeth within it so orthodontically moved teeth bring bone with them but there are limits as
fenestrations are seen if teeth are expanded beyond the limits of the bone.10 Basal bone is often interchanged with alveolar bone so this may be a reason that
basal bone is ill-defined. For Downs, apical base was defined in relation to point
A and point B on a cephalometric tracing.32 Salzmann combined Downs’ definition with Lundstrom’s to extend the apical base from the most constricted points
of the maxilla and mandible around the body of each parallel to the alveolar processes.33 Howes said the basal arch was the apical portion of the alveolar bone
based on his work sectioning dental casts.34 It has been defined based on gingival reference points,34-37 and tooth crown reference points.38 Bell demonstrated
that basal bone at the level of B point was very similar to basal bone at a level
below the root tips so it is not necessary to consider bone lower than B point in
order to have a continuous CBCT slice back to the 2nd molars.39 That study also
5
denied strongly held believes that basal bone, alveolar bone and teeth have a
strong relationship; the opposite was determined since there was a significant
correlation but it was too weak “to be of any value”.39 A different study showed a
significant correlation between the dental width and basal bone arch width based
on the WALA ridge.40 The WALA ridge was first described by Drs. Will and Larry
Andrews (the acronym derives from Will Andrews and Larry Andrews) as a band
of soft tissue coronal to the mucogingival junction of the mandible being near or
at the center of rotation of the teeth of which reflects the basal bone
underneath.41 Other works agreed that defining basal bone according to the WALA ridge was a relatively simple clinical method of defining basal bone and that
the arch shape between this level and the crowns were not different.23, 42, 43 This
could indicate that keeping teeth in bone is the most important factor and that the
arch shape at the crown level is of sufficiency to base treatment archwires. It has
been suggested that basal bone does not change shape from mesial of mandibular 1st permanent molar to mesial of 1st permanent molar after age 5 years old34
and edgewise appliances do not alter the mandibular arch form 44 nor do they affect the basal bone.45 Howes argued that if you compare the basal bone arch
form of a patient at 5 years of age versus 15 years of age there is no difference
in form or shape even though the form at the “coronal level” has changed to allow
for the eruption of permanent teeth.34 Fujita et al. concluded that the practical
significance of their finding that the dental arch width was associated with the
size of the adjacent skeletal unit but not the shape is that practitioners may use
the posterior basal arch width as a guide for choosing the archwire regardless of
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the shape.46 Kim et al. suggested through their findings that the basal arch might
not be the principal factor in determining dental arch form and that the arch
shape variation is dental only.47 Brodie thought the description of apical base was
ambiguous due to the limits of contemporary methods to find and measure it. 4
Most of the studies mentioned here explored basal arch shape only looking at
cephs or models that can have error due to the accuracy of 2D representation in
the cephs or the method used in defining basal arch perimeter on the model.48
The advent of CBCT could help eliminate the ambiguity and standardize the reporting in the literature about the definition of basal bone to further support the
idea that the arch form at the crown level is no different from the bone level.
Orthodontic Stability and Relapse
Every orthodontist strives to achieve a good treatment result but is constantly
fighting the tendency of the teeth to return to the pre-treatment position. The research available today looks for valid treatment methods to prevent relapse and
to define a reason for relapse such as arch form, wire selection, incisor irregularity or even race. Although the two are related, instead of focusing on relapse potential it may be better to determine what makes treatment most stable.
Basal bone
For Tweed, stability occurred when the mandibular incisors were upright over basal bone and arch form was maintained.3 Brodie also believed that basal bone
7
was the key to stability and moving roots outside of it would result in relapse.4
Nance shared the same view as Tweed that altering arch form was unstable.5
Orthodontic forces
Some authors study the forces applied during orthodontic treatment. One article
found no effect on relapse from force magnitude but continuous forces resulted in
a longer period of relapse and more pronounced relapse than discontinuous
forces.2
Mandibular incisors
A significant portion of the literature focuses on lower incisor relapse because
this area seems to be at high-risk for relapse. An exhaustive review of the literature on mandibular incisor irregularity is beyond the scope of this work but a few
often-cited studies need to be mentioned in order to understand how orthodontists view incisor irregularity. In 1972 Peck and Peck built on the idea that tooth
shape is a factor in mandibular incisor crowding and developed an index based
on mesio-distal versus facio-lingual dimensions. Their article argued that fixed
lingual retainers would only postpone the relapse if the index was too large and
suggested the need for interproximal reduction in order to make the tooth shape
more favorable.6 Little’s 1975 article described a new index to categorize incisor
irregularity based on the linear displacement of the anatomic contact points of the
mandibular incisors mesial of the right canine to mesial of the left canine. He
suggested that the crowding of the mandibular incisors was the 1st evidence of a
8
progressive instability leading to maxillary crowding, bite deepening and loss of
arch length.49 Yu et al. suggested it is widely accepted that the anterior-posterior
thickness of the alveolar bone in the symphysis determines the distance that orthodontics can move the incisors.50 A study by Chaison et al. attempted to show
a way to predict relapse based on the alveolar volume, tooth volume and total
volume. While the study showed the lower incisor irregularity at appliance removal and pre-treatment was a significant predictor for relapse the alveolar bone
volume was not shown to be a predictor.51 Another study showed that there was
no correlation between post-retention changes to incisor irregularity and arch
form but 69% of Class I patients and 64% of Class II patients had a tendency for
their arch form to relapse to the pre-treatment shape after appliance removal.22
The notion that lower incisor irregularity post-retention is relapse may be burdening the orthodontist with more blame than is warranted. The literature reports that
intercanine width decreases and lower incisors crowd the farther out from treatment52-55 but this decrease is also a natural part of the dentition aging56-59, similar
to wrinkles on the face. Maybe orthodontists should not be willing to take the
blame for this shift in teeth after treatment.
Intercanine width
As mentioned before, the literature reports that intercanine width decreases posttreatment52-55 and as a natural aging process.56-58 Strang brought focus to the
mandibular canine to canine width as key to stability suggesting that increasing
this distance was only stable if it was because of moving the canine into a pre-
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molar extraction site.7 Is it just a matter of altering the shape by moving the
crowns or if the change happens at the basal bone level will it be more stable i.e.
upright roots? In an article by McNamara et al. it was shown that most orthodontists who responded to the questionnaire agreed that conserving the pretreatment canine to canine width was important in later stages of treatment but
there was no clear consensus how to do this. Pre-treatment study models, symmetry charts, age-related norms, incisal edges, imagined bracket positions or
buccal surfaces to adapt the archwires were all suggested as ways to preserve
the arch form for stability.21 If stability is related to intercanine width Mutinelli et
al. showed it is possible to keep the intercanine width but change the arch form.
For that study, no matter what the mathematical equation used to describe the
arch form, arch form can be changed by changing the length of the arch through
incisor proclination without changing the intercanine width.60
Race and ethnicity
There is little research into Hispanic oral health issues but, since it is the fastest
growing and largest minority in the United States, orthodontists need more research into the differences, if any, of this population.61 One study by Vela et al.
concluded that European norms should not be used for Mexican-Americans because anterior-posterior position of incisors and proclination are different.62 Relying on “norms” for stability could be flawed due to the biased sample group of
which some of our traditional norms are based. Smith et al. compared whites,
blacks and Hispanics and demonstrated that the Bolton ratios, a ratio of the
10
combined tooth mass of the mesio-distal size of mandibular teeth to maxillary
teeth, should not be used in males of any race, Hispanic or black females because the only group that adhered to the “norms” was the white female group. 27
Genetics versus Environment
Genetics may account for an average of 50% of arch size and 39% of arch shape
(length to width ratios) but both are considered to be subject to environment
more than genetics.9 This could be why a majority of arch forms tend to return to
pre-treatment shape after retention.22 It is not because teeth are programmed to
be in a specific place but may be the environment--such as tongue, cheeks, lips,
bone—that dictates stability. De La Cruz et al. pointed out in their findings that
there was no correlation between post-retention changes in incisor irregularity or
changes to arch width/length and arch form and that maybe the small magnitude
of post-retention changes was associated with the sample being premolar extraction space closure.22 This suggests that even though we may change the arch
form considerably, especially in extraction cases, it can still be stable if the teeth
are in equilibrium with the oral cavity. This idea was supported in another article
that concluded that there was an association between dental arch width and adjacent skeletal unit for size but not shape.46
Aging
We know that growth continues throughout our entire lifetime 63 but it has been
suggested that the arch form does not change from kids to adults 35 therefore the
11
arch form seen in a typical age group for orthodontic treatment should be stable
into adulthood.
Other factors
In their article De La Cruz et al. stated that those patients that had the most
change during treatment were not necessarily the patients that had the most relapse post-retention. They concluded it was erroneous to infer that if the original
arch form was maintained there would be no relapse.22 In 2011 Lee et al. concluded that the arch form was influenced by tooth size, arch width, basal bone
width and inclination of the posterior teeth so if the arch shape was changed at
the occlusal level by tipping the teeth but the basal bone shape was different and
unchanged, this could lead to instability and relapse.64 Some authors argue that
this could relate to the use of pre-formed wires and suggest that commercial
wires are significantly different in shape than the “ideal arch form”.65 Some have
even shown that there is a correlation between tooth size and relapse.66-68 Kanaan failed to show a correlation between basal bone discrepancy and relapse or
between tooth size and relapse.69 Case was at odds with Angle because he believed that extractions were necessary for stability in some patients to harmonize
the teeth with the bone.29
Mandibular Arch Form
It is frequently proposed that arch shape falls into three broad categories:
ovoid, square or tapered.70-72 The classic descriptions used for arch shape have
12
included ellipse,22, 73-76 a parabolic curve,73, 75 straight segments joined to half a
circle,77-79 a catenary curve80, 81 or a hyperbola.75
Commercial wires
For a company to sell wires there has to be a starting point of some kind but caution should be used in applying one shape to all patients. Camporesi et al. compared their ideal arch form and 10 wires. They found a significant shape difference for all the wires compared to the ideal with one particular manufacturer’s
ovoid shape showing the greatest shape difference in the mandibular arch.65
Weaver et al. showed significant changes to the dental arch with preformed wires
compared to the controls but no change with the use of custom wires formed to
the WALA ridge.40 Several templates follow the form of incisal edges and buccal
cusp tips to form a wire since it has been suggested this is elliptical75 but more
recently the facial axis has gained support since that is where the archwire will be
fixed to the crown.41-43, 47
Race and ethnicity
Racial differences in anatomy and physiology have been studied but the literature is lacking in material to suggest whether or not race is a factor for orthodontists in choosing arch form. As mentioned previously, there is little research into
the health needs of Hispanics61 but studies between the developmental differences of whites and Mexicans are available. For skeletal differences Garcia
showed that bimaxillary prognathism was seen more in Mexicans than whites25
13
and Phelan determined that Class II Mexicans had greater protrusion and greater
vertical height measurements than whites.82 For dental differences Buschang
and Shulman showed Mexicans have more lower incisor irregularity than whites24
and Bishara et al. showed Mexicans have larger tooth sizes than whites.26 Blacks
have been shown to have wide palates and large jaws.83 The Mongoloid race
that was a precursor to Mexican-Indians, tended to have arches that were parabolic in form.83 It has been shown repeatedly that whites have predominantly tapered or ovoid arches.71, 84, 85 One study of Brazilian adolescents showed 23 different arch forms present in the mandible alone.86 Previous studies have shown
that blacks on average have arches with wider mandibular posterior segments
than whites or Hispanics and Hispanics have larger anterior ratios than blacks.27,
28
Other studies showed that blacks had larger teeth, larger arches and more
square form than whites.28, 87, 88 Gimlen showed that overall Hispanics had a 70%
distribution of square form followed by tapered and ovoid being equal while
whites had 80% tapered equaling ovoid and the remaining 20% being square. 84
Comparing just Class I patients tapered and ovoid was over 90% in whites while
Hispanics was square, Class II was tapered for whites while Hispanics was
square and Class III was the only subset where square predominated in both
groups.84 Lin’s findings state there was no significant difference found between
the arch parameters of whites, Hispanics and blacks89 but this may be due to
small sample size since the whites were N=16, Hispanics N=8 and blacks N=0.
Ferrario et al. studied Chilean mestizos against Italian whites and found that
overall the white arches were smaller than the mestizo arches.90
14
Frequency of form
The mandibular arch form is often the focus of studies rather than the maxilla due
to it being the one least able to be modified with orthodontics.23, 91 Of several
arch forms Felton et al. showed that no one arch form is seen more often than
another in untreated normal, pre-treatment Class I or pre-treatment Class II dentition but the closest commercial arch form was the Par and Vari-Simplex shapes
at about 50% of all three groups combined.70 That study also concluded that
60% of the treated cases in Class I and Class II patients had a different arch form
post-treatment and 70% had relapse long-term.70 Tajik et al., on the other hand,
concluded that 49.2% of pre-treatment Class I, II and III subjects had a tapered
arch form.11 Nojima et al. showed 42% ovoid in the Japanese sample and 38%
ovoid in the Caucasian sample that is similar but there was a great difference in
the division of the remaining patients as 46% square in the Japanese and only
18% square in the Caucasian.71 Paranhos et al. showed only 20% of the subjects
in the study had tapered form and oval was the most prevalent at 41% but the
authors did point out that this was a subjective choice of people looking at the
arches and comparing to one of the three standard forms.92 Dr. McLaughlin recommends in his textbook that for a Caucasian practice the ratio of wire shapes
should be 45% ovoid, 45% tapered and 10% square.72
Intercanine width
Ball et al. concluded that their sample of Class II subjects did have a different intercanine width between dental and basal arches but that it was unlikely to affect
15
the arch form as it was only 0.8 mm.23 Although it seems logical that moving any
one tooth should be as stable as moving any other tooth orthodontists tend to
value the width of the canines above other arch measurements. 21 This may relate
to the idea that the surrounding musculature and oral environment dictate arch
form most and that the canines are positioned at the corners of the mouth where
pressure can be great due to the circumoral muscles.8-11 This is at odds with
what White concluded that the arrangement of the teeth into an arc was predominantly dictated by the osseous bases of the jaws.93 In a 1999 study Braun et al.
determined that the natural mandibular form of molar to canine ratio was 2.38:1
where the nickel-titanium (NiTi) wires of three different manufacturers had a ratio
of 1.87:1 and that the wires changed the mandibular intercanine width an average of 5.95 mm and intermolar width 0.84 mm.94 Another study by Bhowmik et al.
showed that the mathematical beta function with the least squares method expressed the normal occlusal shape with a correlation coefficient of 0.97 in their
control group and they showed a natural mandibular molar to canine ratio of
2.11:1 while the wires were 1.78:1.95 This study used 0.019x0.025 rectangular
NiTi wires of several different manufactures, a size of wire considered past the
initial leveling and aligning stage of treatment, and had an intercanine width on
average 6.667 mm larger in females and 5.337 mm larger in males than the control group.95 These studies imply the greater change in the area that most orthodontists say should be conserved. Arai and Will argued that measuring a caninecanine width of 22.96-29.0 mm might be all that is needed clinically to classify the
arch as ovoid.96
16
Mathematical representation of arch form
The mathematical Beta function has been shown to be a planar representation of
the natural human arch form.97 However, an alternative function has been suggested to describe tapered, ovoid and square dental arch forms.98 Arai and Will
found a significant positive correlation between subjective rankings of arch form,
canine/molar ratio and 4th order polynomial equation and a significant negative
correlation between subjective rankings of arch form, canine/molar ratio and 2nd
order polynomial equation demonstrating arches with wider intercanine distance
than intermolar distance tend to be ranked square by subjective means. 96 Lee et
al. argued that although higher order polynomials may be more precise in fit, because of the inherent asymmetries in all arches the form may become inaccurate
along the curve so they suggest 3rd order polynomial is sufficient to get the general idea of the curve.64 Alvaran et al. discussed that the bigonial width was the
most important determinant of posterior arch width while the size of the incisors
was the most important for anterior arch width.99 This agrees with Gimlen’s results of a more square arch form in Hispanics84 since their lower anterior teeth
are larger.24, 26, 27
Cone Beam Computed Tomography
Cone Beam Computed Tomography (CBCT) is gaining interest as a diagnostic resource in orthodontics. It evolved from the original computerized tomography (CT) developed by Hounsfield in 1967. The main difference being that the
CBCT allows for a single rotation versus a CT using multiple passes and stacking
17
the slices into one image.100 There is much research on the validity of using
CBCT as well as the accuracy of the measurements derived from it. Tarazona et
al. compared tooth sizes, intercanine width, intermolar width and arch lengths using CBCT against digitized study models and found significant differences for
some individual tooth measurements, mandibular intercanine width and mandibular arch length but the differences were less than 1% therefore clinically irrelevant.101 Timock et al. determined at a correlation coefficient of 0.98 that buccal
bone height can be accurately measured to a mean difference of 0.30 mm.102
Leung et al. said that alveolar bone height can be accurately measured to
0.6 mm when using a voxel size of 0.38 mm at 2 mA and that root fenestrations
could be identified with greater accuracy than dehiscence.103 Damstra et al. determined that an increase in voxel resolution from 0.40 mm to 0.25 mm did not
result in a greater accuracy of linear measurements104 while Sun et al. suggest
that alveolar bone height measurements using a 0.4 mm voxel size might overestimate the loss associated with RPE.105 Periago et al. used human skulls to compare CBCT to direct measurements and although there were statistical differences between the two they were considered clinically equal.106 Hassan et al.
findings agreed with the 3D versus physical measurements and added a comparison with 2D images and determined that the 3D images were closer to the physical measurements than 2D images or 2D slices even when the patient position
was rotated.107 Wang et al. imaged teeth with CBCT scanning before extraction
to compare to Micro-CT scanning after extraction and found that the volumetric
measurement of teeth using a CBCT in vivo is comparable to Micro-CT in vitro
18
indicating that CBCT can be a valuable way to examine root resorption during
orthodontic treatment.108 Another study compared CBCT to digital caliper measurements and found the CBCT to be highly reliable at a correlation greater than
0.90 but the CBCT tended to underestimate slightly the anatomic truth. 109 Zamora et al. compared lateral cephalograms to CBCT and determined no statistically
significant differences for angular or linear measurements.110 Alqerban et al.
showed that CBCT was more sensitive than panoramic x-rays for canine localization and the identification of root resorption on adjacent teeth. 111 Bell compared
CBCT slices to plaster model measurements and found hard tissue measurements were obtained with relative ease.39 He could standardize the orientation
and filter out the soft tissue to allow for an accurate and reproducible method to
make bony measurements.39 Schlicher et al. found that since point B lies along a
curve without clear anatomic boundaries there was error in the y-axis plane but
that the error was no more in the 3D CBCT scans than in the 2D ceph identification.112 There is a need for caution when working with CBCT images as Molen
argued that protocols are needed in the reporting of CBCT research to ensure
correct representation as spatial resolution is the minimum distance needed to
distinguish two objects and it does not equal voxel size because of noise, artifacts and partial volume averaging.113 Despite this caution it is suggested that
CBCT offers an undistorted view of the dentition that shows details of individual
dental morphology, features of roots and spatial orientation of teeth and roots
without any magnification error since CBCT images are recreated using a mathematical algorithm.114
19
Statement of Thesis
This study will be a retrospective look at the natural arch form of black, white
and Mexican American patients before treatment and determine if there is any
difference in overall shape at basal bone level and occlusal level. Since preformed wires tend to be the same shape and not designed to follow the natural
dental arch form94 a difference in arch shape between the two levels may contribute to orthodontic instability. Using CBCT pre-treatment images will be examined looking at the mandibular basal arch shape compared to the occlusal arch
shape. Reorientation of the CBCT to orient the mandible along the functional occlusal plane in order to make image slices that show basal bone in the anterior
as well as the posterior would be the first step. Basal bone will be defined according to Kanaan’s method of a parallel line to functional occlusal plane (FOP)
drawn from B point and a perpendicular line from FOP at mesial contact of mandibular 1st molars.69 The dependent variable measured will be slices taken at basal bone level and slices taken at occlusal level, the mandible only, and placing a
point midway between the cortical plates to give us the arch shape at basal bone
while using the Noroozi method for arch shape at the occlusal level.98 This shape
will be compared to the three prominent arch shapes to classify as ovoid, tapered
or square. The millimetric difference in the arch will not be considered, only the
overall shape. The shape will be classified based on Noorozi’s definition of
square, ovoid and tapered.98 The alternative hypothesis is: there is a difference in
basal bone arch shape vs. functional occlusal arch shape. The null hypothesis is:
20
there is no difference between the functional occlusal and basal arch shapes.
The sample size will be 50 for each group (black, white and Mexican American)
and come from an existing set of patient records located at Saint Louis University
CADE that include pre-treatment CBCT images. The selection criteria will include: permanent lower dentition that includes the second molars, no previous
orthodontic intervention, age 18 or younger, no impacted teeth on the mandible,
and mild crowding without any tooth blocked out of the arch.
21
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30
CHAPTER 3: JOURNAL ARTICLE
Abstract
Introduction: Relapse continues to be a concern for today’s orthodontists. Practitioners agree that stability is a goal of treatment but there are many views on
which method of treatment will produce the most stable result. A change in arch
shape, or form, from the pre-treatment shape has been suggested as a reason
for instability. The literature reports many factors that play into how the shape of
the arch is developed including muscles, periodontal fibers, function, genetics,
race, intercanine width, and keeping teeth within basal bone. Purpose: This
study looks at the arch shape at occlusal plane versus the arch shape at basal
bone to determine if there is any difference between the two levels. Materials
and Methods: Using the CBCT of 150 black, white and Mexican American patients slices were taken at occlusal plane and basal bone levels. A canine ratio
was calculated for each level. Shape was classified into ovoid, tapered and
square based on the mean and standard deviation of the canine ratio. Results:
No significant difference was found between the arch shapes at the two levels.
Ovoid was the shape seen in a majority of patients at both levels. Conclusions:
No significant difference was apparent between the arch shapes at occlusal
plane versus BB levels. No significant difference of arch shape distribution between males and females or among the black, white and Mexican Americans.
31
Introduction
Practitioners agree that stability is a goal of orthodontic treatment but there are
many views on which method of treatment will produce the most stable result.
Tweed, Brodie and Nance all agreed that stability relates to basal bone.1-3 Peck
and Peck argued that if the shape of the anterior teeth was disproportional based
on a ratio of mesio-distal versus bucco-lingual width there would be relapse and
suggested the need for interproximal reduction in order to make the tooth shape
more favorable.4 Strang argued that intercanine width was key to stability.5 The
following paragraphs will discuss several factors mentioned to attempt to define
how an arch form develops and why relapse happens.
There are perioral factors such as pressure from muscles, lips, cheeks or
habits to describe how the arch form develops. Many authors have stated the orbicularis oris, mentalis, buccinator, and tongue dictate arch form and tooth position.6-10 Burstone and Marcotte continue by stating the dual muscular components of the orbicularis oris could place pressure on the lower incisors only, upper incisors only or both.10 The buccinator influences the posterior width and the
canines can behave like posterior teeth if the oral slit is mesial to the canine allowing the cheek to apply more pressure than the lips to the canines.10 Engelman
studied several types of habit-induced pressures and concluded thumb-sucking
produced the highest pressures, swallowing and whistling produced the lowest,
and instrument playing lay in between with brass instruments and the flute having
some influence.11
32
There are anatomical factors to describe the development of the arch such as
divergence of the mandible to cranial base, memory of periodontal fibers or genetic/racial influence. It has been shown that the attachment of periodontal fibers
is not determined by tooth anatomy but by the tooth position and orientation in
the arch12 and that a fibrotomy following orthodontic treatment may decrease the
amount of rotational relapse.13 Little et al. studied children in a rural Mexico village over a 32-year period and showed the cranial complex remodeled to a
shorter head length and a narrower face.14 The study attributed these changes to
a decrease in food coarseness leading to a decrease in masticatory muscle function.14 Horner et al. built upon this research to study how mandibular plane angle
relates to bone development. The study described how mandibular cortical bone
thickness differs between hyperdivergent (patients that have a large facial divergence and weaker muscle activity) and hypodivergent (patients that have a small
facial divergence and stronger muscle activity) individuals and concluded cortical
bone tends to be thicker in hypodivergent patients leading to a difference in alveolar ridge thickness.15 It has been shown that arch length and mandibular intercanine width both decrease over time as part of the natural aging process.16
Orthodontic factors that relate to arch form include pre-treatment arch form,
intercanine width, incisor irregularity and keeping teeth within basal bone. Maintaining the pre-treatment arch form has been suggested by some practitioners as
a key to stable orthodontic results.17 Keeping the patient’s arch form while
straightening the teeth might make the end result less likely to relapse.18 There is
a limit to the change in posterior width, and particularly intercanine width, that
33
can be achieved and remain stable.10 Ball et al. argued that there is a different
intercanine width between dental and basal arches but that it was unlikely to affect the arch form as it was only 0.8 mm.19 Incisor irregularity occurs in almost
everyone with roughly 50% of untreated adults having little to none and the remaining 50% having moderate to severe.20 Buschang and Shulman concluded
that incisor crowding was multifactorial and included ethnicity, number of first and
second molars, sex and age combined.20 Several studies have shown there is an
anatomical difference between whites, blacks and Mexicans. Garcia showed bimaxillary prognathism was seen more in Mexicans than whites,21 Buschang and
Shulman showed Mexicans have more lower incisor irregularity than whites, 20
and Bishara et al. showed Mexicans have larger tooth sizes than whites.22 Studies have shown that blacks have arches with wider mandibular posterior segments than whites or Hispanics and Hispanics have larger anterior ratios than
blacks.23, 24 With anatomical differences such as these one may expect that the
underlying bone is different between the three groups as well which may lead to
differences in the arch form distribution among the three groups.
Several authors believe that stability relates to keeping the original arch form
while maintaining the teeth over the underlying bone.1, 2, 5, 25 Basal bone has
been difficult to define2 so there is no one method of treatment that will ensure
stability. One could argue that arch form does not matter or that basal bone is not
definable.
If the arch shape is the same at the level of basal bone and occlusion then
maybe there is a simple way to determine the basal bone shape based on the
34
occlusal arch shape. Since basal bone is nebulous according to some,10 can one
even show that arch shape is the same at the two levels? If it is not, as long as
practitioners do not violate the bone and move teeth out of its parameters, stability might not relate to a definition of basal bone. This study will look at the arch
form at the occlusal level and the basal bone level in black, white and Mexican
American patients to see if there is a difference in arch form between the two
levels or between the three groups.
Materials and Methods
Sample
The sample demographics consisted of orthodontic patients treated at a
private practice, Dr. Derid Ure and Dr. Joe Mayes (Lubbock, Texas) and at Saint
Louis University Center for Advanced Dental Education (St. Louis, Missouri). Patients presented voluntarily for the purpose of obtaining orthodontic treatment
and the records were taken as part of the initial diagnostic protocol. Patient records were collected based on the criteria that the lower dentition was permanent
and included the second molars with the exception of a retained primary second
molar in the absence of a permanent second premolar. Other criteria included no
previous orthodontic intervention, age 18 or younger, no impacted teeth on the
mandible and mild crowding that did not have any teeth blocked out of the arch.
An a priori power analysis indicated a sample size of fifty samples per group for a
total of 150 samples. It was as close as possible split evenly male and female.
35
Cone Beam Computed Tomography (CBCT) Technique
All CBCT files were imported into Dolphin 11.5 3D Imaging software (Dolphin Imaging Systems LLC, Chatsworth, CA). Using Dolphin the CBCT was reoriented so Y axis was at midline from frontal view and through the incisive foramen and vertebra C1 from the coronal view. X axis was along the functional occlusal plane (FOP) from the right sagittal view and along the buccal cusps of 1st
molars from the frontal view. Z axis was along sella point from the right sagittal
view cut to reveal sella turcica. For occlusal plane arch level the points were
placed at midcontact of central incisors, cusp tip of right and left canines and
cusp tip of distobuccal cusp of right and left 2nd molars starting on the left side of
the mandible and going around the arch (Figure 3.1).
36
Figure 3.1 Example of plotted points for occlusal plane slice in Mexican male.
Lines were created within the CBCT slice for intercanine width, canine
depth, intermolar width and molar depth (Figure 3.2). The Cartesian coordinates
were exported into Microsoft Office Excel 2010 (Microsoft Corp., Seattle, WA).
37
Figure 3.2 Example of Mexican male occlusal plane measurements.
For basal bone (BB) level B point was located on a right sagittal view (Figure 3.3) and moved the X axis until it bisected B point.
38
Figure 3.3 Example of B point landmark in Mexican female.
Points were placed midway between the cortical plates of the mandible at
the midway of central incisors, right and left canines and right and left distal root
of 2nd molars starting on the left side of the mandible and going around the arch
(Figures 3.4).
39
Figure 3.4 Example of plotted points for BB slice in white female.
Lines were created within the CBCT slice for intercanine width, canine
depth, intermolar width and molar depth (Figure 3.5). The Cartesian coordinates
were exported into Microsoft Office Excel 2010 (Microsoft Corp., Seattle, WA).
40
Figure 3.5 Example of Mexican male BB measurements.
Error Study
Ten percent of the total sample was chosen to be re-evaluated by a random number generator at www.random.org.26 Fifteen CBCT records were measured again and the canine ratio was re-calculated. As a general rule, intra-class
correlations greater than or equal to 0.80 are considered adequate.
41
Statistical Analysis
This study tested the null hypothesis that there is no difference in arch
shape between functional occlusal plane level and basal bone level. Excel plotted the X axis and Z axis coordinates of each level and used a best-fit curved line
to create a graphical representation of the arch form (Figure 3.6).
Figure 3.6 Example of black female graph.
42
In accordance with Noroozi’s ratio to describe arch form27 formulas were
designed within Excel to calculate the ratio at the occlusal plane and basal bone
levels (Table 3.1).
Table 3.1 Calculation of the canine ratio of OP and BB level based on the digitized landmarks from Dolphin Imaging.
Digitized Measurement Name
intercanine width OP
canine depth OP
intermolar width OP
molar depth OP
Value
25.2 canine ratio OP
5.4
3.8
48.2
38.9
intercanine width BB
canine depth BB
intermolar width BB
molar depth BB
19.2 canine ratio BB
3.6
3.1
60.1
34.8
The organized data in Excel was analyzed in order to classify the arch
form into ovoid, square and tapered using Noroozi’s description.27 Statistical
analysis using SPSS statistical analysis software (PASW Statistics Version 18.0,
SPSS, Inc.) was performed and means and standard deviations were calculated
for the arch form at both levels (Table 3.2).
43
Table 3.2 Calculation of the mean and standard deviation for the canine ratios at the occlusal and BB level. One STD above and below was calculated in order to classify the shape as
ovoid, square or tapered.
Occlusal plane shape
1
Ovoid =mean +/- 1 STD
2
Square >mean +/- 1 STD
3
Tapered <mean +/- 1 STD
Min/max 1 STD
Mean
3.12
5.25
4.19
BB shape
1
Ovoid =mean +/- 1 STD
2
Square >mean +/- 1 STD
3
Tapered <mean +/- 1 STD
Min/max 1 STD
Mean
2.74
4.46
3.60
STD
1.06
STD
0.86
Since the overall shape was the focus of this study and not the millimeter
difference between the arch shapes, the nonparametric statistical Kruskal-Wallis
and Mann Whitney U analyses were used to interpret the data. Type I error was
set to alpha=0.05.
Results
Cronbach’s alpha intra-class correlations were 0.89 for the occlusal plane
level and 0.87 for the basal bone level indicating adequate reliability of measurements. The Mann Whitney U test showed no significant difference between
the arch shape at the two levels for each group independently, male versus female or the three groups as a whole. The Kruskal-Wallis test found no significant
difference in the distribution of shape across the three groups. This study failed
44
to reject the null hypothesis. The ovoid shape was the majority shape displayed
in all three groups and no difference between genders (Table 3.3). The shapes
were 73.3% ovoid, 12.7% square and 14.0% tapered at the OP level and 72.0%
ovoid, 14.7% square and 13.3% tapered at the BB level.
Table 3.3 Distribution of shape across N=300. Ovoid is the majority shape.
Shape distribution
ovoid
shape square
tapered
Total
Count
% within Variable_grouping
% of Total
Count
% within Variable_grouping
% of Total
Count
% within Variable_grouping
% of Total
Count
% within Variable_grouping
% of Total
Variable_grouping
OP
BB
Shape
Shape
110
108
73.3%
72.0%
36.7%
36.0%
19
22
12.7%
14.7%
6.3%
7.3%
21
20
14.0%
13.3%
7.0%
6.7%
150
150
100.0%
100.0%
50.0%
50.0%
Total
218
72.7%
72.7%
41
13.7%
13.7%
41
13.7%
13.7%
300
100.0%
100.0%
Discussion
This study showed no significance between the arch shapes at the two
levels and might suggest when the millimetric measurement is removed the occlusal plane and basal bone follow each other. This agrees with the findings that
the dental arch form is shaped by the supporting bone, the peri-oral muscles, and
45
functional forces of the teeth.6-8, 10, 28 As Burstone and Marcotte mentioned the
anterior mandible remodels with the position of the incisors10 it is logical that the
shape of the bone is similar to the occlusal shape since the bone will remodel to
support the function of the teeth. The results of this study support the findings
that defining basal bone according to the WALA ridge can be a simple clinical
method to use19, 29-31 since this study did not find a difference between the overall
shape at the occlusal level versus the basal bone level.
Ovoid was the predominant arch seen in this study for blacks, whites and
Mexicans. This supports Lin’s findings32 but disagrees with previous findings that
suggest Mexicans are descended from a parabolic arch form 33 or that Hispanics
have a 70% distribution of square form.34 It also disagrees with the findings that
blacks have more square form than whites.24, 35, 36 Tajik et al. determined tapered
as the predominant arch form at 49.2% but the classification of arch form was a
“best fit” against existing commercial templates.9 Felton et al. showed no predominance of arch form37 which suggests the classification of ovoid, tapered and
square is subjective. What one person sees as a square arch form may be another person’s definition of a large ovoid form. When considering how the arches
were classified the shape distribution is logical. Arches were considered ovoid
within one standard deviation of the mean and in a normally distributed population one would expect about 68% to fall within one standard deviation. Describing
distribution of arch form may therefore be an academic exercise since what one
person describes as ovoid may be another person’s description of tapered. This
further strengthens the idea that arch form is individually unique and requires
46
customized consideration during treatment. The difference between ovoid, tapered and square is really a difference of millimeters. Since size was not a consideration in this study it is not surprising that shape is similar across gender and
across the groups since function dictates a shape that is relatively similar.
Based on the previous research available one might expect there to be
ethnic differences for arch form but the results of this study contradict this idea.
Again, this relates to the fact that this study looked at shape and not the millimetric measurements of the different components. If the canine width and depth remains unchanged and you expand the molar width or decrease the molar depth
(as in a premolar extraction case) it will change a tapered arch form to a more
ovoid arch form. The reverse holds true too that if you expand the canine width or
increase the molar depth without changing the molar width or canine depth the
arch form will become more tapered. A follow-up to this study could examine how
much change in millimeters in the canine or molar region would change the arch
form from one classification to another and if relapse happens in the cases that
the millimetric changes were enough to change the arch form classification.
Using the single arch form for treatment of any arch shape, or in the different groups, should not alone increase the potential for relapse. Using the
ovoid template will be in line with almost 75% of patients according to the results
of this study. Care should be taken to consider the millimetric dimension as using
a wire that is too big could cause other areas of instability i.e. the muscles, periodontal issues, etc.38-40 The ovoid shape was seen in this study as the shape most
often seen but varying definitions of ovoid9, 37, 40 can make this statement clinical-
47
ly irrelevant. In reality, there may never be a generalized arch shape or form that
can be used as a template for in vivo arches. The fact that it is not described
consistently in literature available today may indicate that we need to stop looking and focus on other areas of study to enlighten the search for reducing the risk
of relapse post-orthodontic treatment.
Conclusions
1. No significant difference was apparent between the arch shapes at FOP versus BB levels.
2. No significant difference of arch shape distribution between females and
males or among the black, white and Mexican American groups.
3. Ovoid was the majority of the shape observed in all three groups and at both
levels.
48
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51
VITA AUCTORIS
Angela Williams was born in Poplar Bluff, MO on April 11, 1978. She has an
older brother and a younger sister and she has lived in Missouri and South Carolina. She graduated from Scott City High School in 1996 and attended College of
Charleston earning a Bachelor of Arts in International Business in 2000.
Angela worked in the accounting field until continuing her education at University of Missouri Kansas City Dental School in Kansas City, MO receiving a
Doctor of Dental Surgery degree in May 2011. She began her orthodontic training at Saint Louis University in June 2011.
Angela has been married to her husband, Donnie, since August 1996. She
will complete her Masters of Science in Dentistry degree in December 2013.
Upon graduation, Dr. Williams and her husband plan to remain in Kansas City,
MO where Dr. Williams will take over an existing private practice.
52