Download The Comparison Of Dental Arch Forms Obtained From Teeth

THE COMPARISON OF DENTAL ARCH FORMS OBTAINED FROM TEETH,
ALVEOLAR BONE, AND THE OVERLYING SOFT TISSUE
by
Patrick D. O’Neil, DMD
DR. CHUNG HOW KAU, COMMITTEE CHAIR
DR. AMJAD JAVED
DR. NADA SOUCCAR
DR. CHRISTOS VLACHOS
A THESIS
Submitted to the graduate faculty of The University of Alabama at Birmingham,
in partial fulfillment of the requirements for the degree of
Master of Science
BIRMINGHAM, ALABAMA
2013
i
THE COMPARISON OF DENTAL ARCH FORMS OBTAINED FROM TEETH,
ALVEOLAR BONE, AND THE OVERLYING SOFT TISSUE
Patrick D. O’Neil, DMD
UAB DEPARTMENT OF ORTHODONTICS: DENTISTRY
ABSTRACT
Objective: The objective of this study was to determine if a difference existed between
arch forms created from tooth surfaces, alveolar bone, and overlying soft tissue.
Materials and Methods: The sampling population for this study was 18 individuals
with a Class I malocclusion, mild crowding, and a CBCT image of good diagnostic
quality. The Facial-axis point was chosen to create the arch form from teeth, the
Bowman-Kau point was used to establish the arch form from the alveolar bone, and the
WALA ridge was used to calculate the soft tissue arch form. A predetermined algorithm
was then used to create five separate arch forms per patient. The arch forms were
categorized according to shape and then superimposed on each other within an arch and
the distance between tooth, bone, and tissue was calculated.
Results: For all characteristics of the tooth, bone, and tissue, the calculated distances
were significantly different from 0. The distances between tooth and bone were larger
for the mandible compared to maxilla (mean 3.30 vs. 2.48, respectively). The larger
distances seemed to be located more posteriorly than anteriorly. The distance between
tooth and tissue was largest for the second premolar (2.35±1.59), first molar (2.86±0.63),
and second molar (3.25±0.87). A significant difference in distance between tooth and
bone on both the maxilla and mandible was observed among race but limited to blacks vs.
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whites. There were no significant differences in distance between the tooth and either
bone or tissue in regards to gender and age.
Conclusions: The arch form shapes obtained from the teeth, alveolar bone, and soft
tissue are highly individual. However, there was a significant positive correlation found
between the tooth, alveolar bone, and soft tissue arch forms. The overall distance
between tooth and bone was greatest for the mandible compared to maxilla. The largest
difference between tooth and bone were found at the canine and second molar in the
maxillary arch followed by the first molar, first premolar and then second premolar. In
the mandibular arch the largest difference was found at the first and second molars
followed by the canine, first premolar, and second premolar.
Keywords: alveolar bone, arch form, WALA
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ACKNOWLEDGMENTS
I would first like to thank my wife, Marjorie, for her love and support as we
unfold the next chapter in our lives. Secondly, I would like to thank all the faculty
members of the UAB Department of Orthodontics for their wisdom and expert guidance
during this residence. I would also like to thank and recognize my fellow residents for
their kind and lasting friendships.
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TABLE OF CONTENTS
Page
ABSTRACT........................................................................................................................ ii
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF TABLES............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
CHAPTER
1 INTRODUCTION .........................................................................................................1
Orthodontic Arch Forms ..........................................................................................2
Theories For The Development Of The Arch Form.....................................6
Cone beam imaging technology.......................................................7
2 MATERIALS AND METHODS.................................................................................10
Construction Of The Orthodontic Arch Form .......................................................12
Sequence In Data Evaluation.....................................................................13
Statistical analysis .........................................................................14
3 RESULTS ....................................................................................................................17
Arch Form Analysis...............................................................................................19
4 DISCUSSION ..............................................................................................................26
5 CONCLUSIONS .........................................................................................................31
LIST OF REFERENCES...................................................................................................32
APPENDICES
A. INSTITUTIONAL REVIEW BOARD FOR NON-HUMAN USE
APPROVAL FORM.... ......................................................................................................35
v
LIST OF TABLES
Tables
Page
1
Comparison of the distance between the tooth and bone/tissue by dental arch and
tooth characteristics ...............................................................................................20
2
Comparison of the distance between the tooth and bone/tissue between race by
dental arch and tooth characteristics ......................................................................21
3
Comparison of the distance between the tooth and bone/tissue between genders by
dental arch and tooth characteristics ......................................................................22
4
Comparison of the distance between the tooth and bone/tissue among age groups
by dental arch and tooth characteristics .................................................................22
vi
LIST OF FIGURES
Figure
Page
1
3D image with plotted FA and BK points prior to graphical reconstruction.........15
2
Axial slice with plotted FA points at estimated FACC..........................................16
3
Axial slice with plotted BK points at estimated center of resistance.....................16
4
Maxillary Arch Superimposition of FA and BK Points.........................................23
5
Mandibular Arch Superimposition of FA and BK Points......................................24
6
Mandibular Arch Superimposition of FA and WALA Points ...............................25
vii
1
CHAPTER 1
INTRODUCTION
The human dental arch refers to shape that is configured by the relationship
between the teeth and underlying alveolar bone in the presence of the circumoral
musculature and forces 1. The dental arch can be represented by many shapes and sizes
and is referred to as a dental arch form. The dental arch form that is created by the
relationship between the teeth and alveolar bone can be determined and affected by the
patient’s skeletal pattern, overlying soft tissues, and other environmental influences 2.
Therefore, each dental arch form is unique and their size and shape may have
considerable implications in the diagnosing and treatment planning of patients which may
further affect the esthetics, space available, and ultimately the arch forms future stability
3
. In order for proper esthetics and stability to occur, and for orthodontists to meet their
desired treatment goals, it is critical to establish a harmonious relationship between the
dentition and the underlying basal bone 4. The debate over the correct or most ideal
dental arch form has been ongoing for several years and doesn’t seem to be yielding in
the near future.
The human dental arch form first begins to develop during early embryogenesis. At
around 6 weeks, the dental lamina of the maxillary and mandibular arches begins to
appear flattened in an anterior/posterior direction. At 9.5 weeks the dental lamina begins
to differentiate where it soon emerges as a catenary curve with the underlying tooth
2
germs. This time period from the initial appearance of the dental lamina to its principal
catenary shape, is very critical during human development and can be affected by both
internal and external disruptions 5. Once the arch form has been established in the fetus,
the variability in the eruptive paths of the teeth, development of the supporting alveolar
bone, and change in the position of the teeth due to habits or circumoral musculature may
have differing effects on the arch size and shape. However, with all of the potential
genetic influences discussed, it is has been estimated that arch shape has only a 39%
heritability 6.
Orthodontic Arch Forms
Throughout the history of orthodontics, the search for an ideal arch form has been
explored by a number of orthodontic researchers. The search has varied from using
mathematical equations to calculate the perfect arch form, to taking averages from
several individuals and subsequently manufacturing preformed wires, to customizing
every arch form for each individual patient. A few of the more recognized and common
techniques once used to shape archwires include, the Bonwill-Hawley, Catenary curve,
and Brader arch form techniques.
The Bonwill-Hawley arch form was developed by W. Bonwill in 1885 and was later
modified by C. Hawley. The basis for this arch form design was the observation by
Bonwill that the mandible formed an equilateral triangle with the base being between
each condyle and the apex located where the central incisors meet. It was also noted that
the premolars and molars were in alignment along the sides of the triangle with the
second and third molars migrating medially towards the midline. Hawley then modified
this design when he suggested that the six anterior teeth should lie along an arc of a circle
3
with the radius equaling their combined widths of the six anterior teeth7. This arch form
design has since been refuted as being applicable to all patients, but it has been suggested
that this technique can serve as a general guide in helping to customize each individual
arch form 8.
The Catenary curve was first evaluated as being the natural shape of human dental
arch in 1957 by Scott who first described the natural catenary dental arch shape 9. Then
Burdi in 1966 further supported Scott’s catenary dental arch model 5. The catenary
curve is best explained and represented by a hanging chain held apart at two points where
the two points represent a patient’s inter-molar width7. The catenary curve doesn’t seem
to have much of an obvious relationship with function, however this shape does seem to
most closely resemble the shape of the natural dentition in both pre and post natal
individuals thereby by default, giving us a since of natural stability 8.
The Brader/Trifocal Ellipse Arch was described by A. Brader in 1972 when he
attempted to design a more ideal arch form that allowed for more variability, which in
turn would be applicable to more patients instead of acting as just a guide. He proposed
an arch form that was similar to the catenary shape, but it was more expanded in the
premolar segment and constricted in the 2nd and 3rd molar region. The Brader/trifocal
ellipse arch form was patterned after the idea that the dental arch is a product of the
equilibrium forces exerted by the oral soft tissues and is best approximated by the
constricted portion of the curve of a trifocal ellipse (PR=C). There were five different
arch forms that varied slightly in widths at the second molars. The upper and lower arch
forms were then coordinated with the upper arch being one size larger than the lower 10.
Needless to say, this technique was also met with criticism 8.
4
After much debate and several theories later as to what the ideal arch form should
be, Will and Larry Andrews proposed a term know as the WALA line to help
individualize arch form shaping in orthodontics while providing stability and staying true
to the patient’s original arch form11. The term WALA line refers to a soft tissue marker
at the mucogingival junction along the long axis of each tooth. This point below each
tooth helps to relate the position of the underlying bone to the limits in which the teeth
can be moved. When all points are connected, they create an arch form that can
supposedly be used to create a stable natural arch form while maintaining the teeth within
their natural bony housing 11. This technique is still routinely used today and is supported
by many articles in today’s literature as a useful and predictable way to shape arch forms
4, 12, 13
In further attempts for practitioners to “main stream” their offices and become more
efficient in everyday practice, the production and use of preformed archwires in certain
parabolic or elliptical shapes came to fruition. The introduction of preformed archwires
dates back to the beginning of the Rocky Mountain Data Systems Company. This
company analyzed optimal untreated and stable arch forms from treated cases of Dr. Bob
Ricketts’ personal collection. The cases were then collected by the Foundation of
Orthodontic Research and compared to the ideal arches generated by the RMDS
computer software. After analyzing the data, five arch forms with slight variations were
developed: normal, tapering, ovoid, narrow tapered, and narrow ovoid. Today’s
preformed archwires typically are produced with variations from three similar basic
shapes: narrow, ovoid, and square 7.
5
Despite advancements in technology and research, there is still not a consensus as to
whether an ideal arch form exists. It seems that many dental arch forms fall into a few
differing parabolic shape categories, but no one has successfully related a mathematical
formula or chosen a shape to help in predicting a person’s ideal arch form. Research has
shown that there is just enough variability in each person’s arch form in order to nullify
the existence of a single ideal arch form14.
No two individuals exhibit the exact same arch form and people of similar ethnicities
and comparable malocclusions may fall into a similar parabolic shape category such as a
narrow, ovoid, or broad elliptical form. Studies have shown that individuals of Asian
descent (Korean, Japanese, or similar ethnicities) and those with Class III malocclusions
most frequently posses a broader arch form. Where as those individuals of Caucasian
descent (European, or North American white,) and those with either a Class I or Class II
malocclusion will tend to posses more of a tapered or ovoid shaped arch form 15-17. This
information may help in applying an efficient and stable technique by maintaining the
arch form as close as possible to the initial presentation of the patient.
Stability of final treatment outcomes is one of the most debated aspects of
orthodontic treatment today. It is very important for orthodontists to provide a long-term
result that is both esthetic and stable, while also providing patients with a sense of
satisfaction and worth. Over the years, several historical articles have been written
regarding the stability of orthodontically treated cases. After reading them, suggestions
may be inferred as to methods to help prevent future relapse. Many of the authors have
concluded that if the inter-canine/inter-molar width or initial arch form is changed outside
of its normal limits, there is a strong propensity for the teeth or arch form to return to
6
their initial pre-treatment position or shape. Little and Reidel pointed out that only 10%
of cases displayed acceptable mandibular alignment at 20 years post retention, with the
majority of the relapse taking place in the first 10 years following braces removal 18. It
has also been shown that relapse is not limited to non-extraction cases. Relapse is
prevalent with both extraction and non-extraction treatment mechanics and most relapse
occurs in the canine and molar region if expanded or constricted too generously. The
majority of the relapse cases studied seem to show a decrease in overjet, decrease in
intercanine width, increase in overbite, and also an increase in crowding 19, 20. However,
certain stable expansion can be gained in the premolar region. The current hierarchy of
stability is as follows: 2nd premolars > 1st premolars > molars > canines 21. Also, the
maxillary arch seems to be more resistant to relapse after expansion than the mandibular
arch, just as posterior expansion is more stable than anterior expansion 22, 23. Therefore,
the mandibular arch may be thought of as the rate-limiting step to arch expansion;
meaning that since the mandibular arch is not as resistant to expansion as the maxillary
arch, the mandibular arch form should be used to shape the maxillary arch form. This is
why if the maxillary and mandibular arches are not congruent at the start of treatment, we
tend to use the shape of the mandibular arch as the baseline for the remaining treatment
24
. Just because the amount of expansion or change in arch form is kept to a minimum,
there is no guarantee for stability.
Theories For The Development Of The Arch Form
Over the course of time, no matter how much research, time, or common sense is
applied, there are some issues in orthodontics, like dental arch forms, that cause such a
7
debate that common ground and/or consensus is difficult to reach. To date, there are two
opposing theories as to what dictates the limits to arch shape or form. The first is the
bone-growing theory. Angle first advocated this idea, which stated that the
underlying/supporting alveolar bone grows in response to proper stimulation if the teeth
are aligned correctly in the proper occlusion 25. This theory soon gained much popularity
after the introduction of Wolff’s law, which stated that bone structure changes and/or
adapts in response to external forces 26. In today’s orthodontic culture, the theory is now
referred to as the non-extraction theory. With the stimulation of bone dependant on the
eruption of teeth, mastication, and pressure from the tongue and cheeks 13. The nonextraction theory has again gained much popularity with current marketing trends and the
introduction of certain appliance systems.
The second theory is referred to as the apical base theory. It was first described by
Lundstrom in 1925 where he explained that there is a limit/boundary to the expansion of
the dental arches and that limit is the underlying/supporting bone that houses the teeth 27.
Lundstrom believed that grow of the apical base did not occur in response to the
mechanical movement of teeth 27. The apical base theory states that there is a limit to
dental arch expansion, and if the supporting bony limits are reached, future periodontal
problems and an unstable treatment result may be expected 13.
Cone beam imaging technology. Currently, there is still not a quantitative or
objective limit to which teeth can be moved. And with stability not guaranteed and new
marketing trends on the rise, the non-extraction theory and approach to treatment is
rapidly growing. Nevertheless, some researchers and clinicians are still trying to quantify
8
the limit to which teeth can be moved and with the help of new technologies such as
Cone Beam Computed Tomography, new information may soon be available to help shed
light on an old debate.
Cone Beam Computed Tomography has become a rapidly growing imaging
technique in orthodontics due to its three-dimensional capabilities for more advanced
diagnosis and treatment planning. Cone Beam Computed Tomography images are
acquired by a 360-degree rotation of a tube head that attempts to represent the object in
slice sections. The volume set is composed of voxels, which represent the x-ray density
and can affect the resolution of the scan. In general, the greater the voxel resolution, the
smoother and better the images appear 28. However, with all of the proposed advantages
of CBCT imaging, there are still concerns regarding its use. The first is the amount of
radiation the patient is exposed to with each scan and the second is the accuracy and
reliability of the image produced. The topic of radiation exposure will not be discussed
in this paper due to lack of time and evidence, however it appears that as long as CBCT
imaging is used in select cases and can provide useful information that cannot be
provided by traditional two-dimensional imaging, it is a valid option for patients if it
provides better and more thorough diagnosis.
Since the introduction of Cone Beam Computed Tomography, critics have
questioned that the accuracy and reliability of CBCT imaging. However, recent studies
by Berco and Damstra analyzed dry human skulls with fixed markers. Measurements
were taken with digital calipers and then compared to the digital measurements obtained
from a CBCT image of the same skull. Both studies indicated that all measurements were
accurate in all three planes of space and with varying voxel sizes 29, 30.
9
The purpose of this study is to analyze the relationship of the human dental arch
form created by the teeth and compare it to the arch forms that are created by the
underlying/supporting alveolar bone and its overlying soft tissue. Hopefully, this will
provide a better understanding of the human dental arch form and offer insight into the
limits of tooth movement. Study results will enlighten practicing orthodontists as to the
factors that affect patient arch forms while also providing information to become more
efficient and knowledgeable in selecting arch forms or help reinforce the need to
individualize each patient’s arch form.
10
CHAPTER 2
MATERIALS AND METHODS
This is a retrospective study that included 18 individuals who displayed a Class I
molar and canine relationship with mild dental crowding. None of the 18 patients had
received orthodontic treatment prior to the time of initial evaluation. In order for the
chosen subjects to be included they each had to meet certain selection criteria. This
included a permanent dentition from permanent 2nd molar to permanent 2nd molar in both
the maxillary and mandibular dental arches, a Class I malocclusion in both the molar and
canine position, mild dental crowding, no history of alveolar bone loss or periodontal
disease, and an initial/pre-treatment CBCT image of good diagnostic quality as well as
adequate pretreatment impressions.
All CBCT images were obtained with the Kodak 9500 CBCT imaging system
(Carestream Dental LLC: Atlanta, GA). The Kodak 9500 CBCT has the following
specifications: large field of view: volume 20x18cm, scan time: 10.8 seconds, voxel size:
0.20mm, 90 kV, 10 mA. All images were acquired from the patient database of the UAB
Department of Orthodontics and approved for use by the UAB Institutional Review
Board. In order to relate the arch forms created by the teeth, underlying alveolar bone,
and the overlying soft tissue to one another, one point on each of the three tissues was
plotted in relation to each tooth (2nd molar to 2nd molar). However, due to the inability to
capture intraoral soft tissue on a CBCT image, the soft tissue point that was used in the
11
study was plotted not from a CBCT image, but from an STL file of a digital image of the
subject’s intraoral impression that was then imported into the plotting software. All data
points were plotted using the 3dMD Vultus program (3dMD Vultus: Atlanta, GA). The
Facial Axis point, Bowman-Kau point, and WALA points were plotted on every tooth in
both the maxillary and mandibular arches excluding 3rd molars for a total of 84 points per
patient. Each image was zeroed on the anterior nasal spine (ANS) to create a uniform
point of reference. The Facial-axis point (FA point) was chosen to create the arch form
from the teeth. The WALA ridge was chosen to represent the arch form created by the
soft tissue, and a new point, the Bowman-Kau point (BK point), was used to establish the
arch form created by the alveolar bone.
The BK point is defined as the point located at the most buccal extent of the alveolar
ridge in the axial cross-section taken at the level of the estimated center of resistance of
the tooth with the axes defined by the patient’s natural head position. The FA point is
defined as the point located on the facial axis of the clinical crown (most prominent
portion of a tooth’s central lobe) that separates the gingival and occlusal halves of a tooth.
Figure 1 is a representation of the plotted FA and BK points as they relate to the teeth and
alveolar bone. The WALA point is defined as a soft tissue marker located at the
mucogingival junction along the long axis of each tooth. The WALA points are plotted
at the mucogingival junction because this point also most closely represents the center of
rotation for each tooth. The FA point, BK point, and WALA points were plotted in
correlation to each tooth in both the maxillary and mandibular arches.
12
Construction Of The Orthodontic Arch Form
A predetermined algorithm known as the polynomial algorithm to the 5th expression
was then was used to create two separate arch forms for the maxilla and three arch forms
for the mandible for each patient. Therefore, a total of 5 separate individual arch forms
were created for each patient. The first arch form connected the FA points in the maxilla,
the second arch form connected the BK points in the maxilla, the third arch form
connected the FA points in the mandible, the fourth arch form connected the BK points in
the mandible, and the fifth arch form connected the WALA points in the mandible. The
reason a soft tissue arch form was not created in the maxilla, is because currently the
WALA line is only in reference to the mandibular arch according to Andrews11.
Technically, it may be possible to identify soft tissue markers in the maxillary arch that
resemble those in the mandibular arch that are used to designate the WALA line.
However, this is unnecessary due to the fact that when maxillary and mandibular arch
forms are coordinated with one another, the shape of the mandibular arch should be used
as a baseline because of stability reasons mentioned previously. The arch form created
by the FA points (FA arch) was superimposed on the arch form created by the BK points
(BK arch) and the distance between the FA point and the BK point of each tooth was then
calculated (FA-BK distance). Figures 2 and 3 show a diagram of how the individually
plotted points are transferred into a graphical representation of the arch forms created
from the FA and BK points. The arch forms created by the FA points and the WALA
line were also superimposed on one another and the distance between the FA point and
the WALA line of each tooth was then calculated (FA-WALA distance). The distances
13
measured between the plotted points of each arch form was calculated within the
maxillary and mandibular arches individually. The distances were not measured between
the points plotted in maxillary arch to those plotted in the mandibular arch. Distances
were measured for all teeth but only compared for canines, first premolars, second
premolars, first molars, and second molars due to varying degrees of incisor inclination,
which may cause skewing of the arch form shapes between individuals. Finally, the arch
forms were categorized according to their shape: ovoid, square, tapered.
Sequence In Data Evaluation
In order to correctly and systematically categorize the data for each subject, a data
table was created for each subject that contained 3 coordinates (x, y, z) for each plotted
point. The points plotted in the maxilla represent both the FA/tooth and BK/alveolar
bone points where as those points in the mandible represent the FA/tooth, BK/alveolar
bone, and WALA/tissue points. All points were plotted for each tooth beginning with the
upper right second molar and continuing to the upper left second molar for the maxillary
arch. In the mandibular arch, the points were plotted beginning at the lower right second
molar and continuing to the lower left second molar. In further analysis, the third
dimension (z, vertical) was omitted to better facilitate the comparisons between points
and constructed arch forms. The tables show the millimetric difference between the
FA/tooth point, BK/alveolar bone point, and WALA point for each tooth in the mouth for
each subject in both the maxillary and mandibular arches separately. The arch form
curves created by the FA/tooth points, BK/alveolar bone points, and WALA/tissue points
were also created and then superimposed on one another to evaluate their relationships to
each other. The arch forms representing the tooth, alveolar bone, and overlying soft
14
tissue were produced by connecting the single value plotted points through linear
interpolation.
Statistical analysis. Descriptive statistics including the mean and standard deviation
of the relative distances between the FA/tooth and BK/bone points of the corresponding
teeth were compared to the relative distances between the FA/tooth and WALA/tissue
points of the corresponding teeth and then computed and shown graphically. The
distances between points were calculated and statistically analyzed at the 0.05 level of
significance. These evaluations were done to investigate the relationship between points
representing the dental arch, basal arch, and the overlying soft tissue.
As the points of interest for the tooth, bone, and overlying soft tissue were given
by Cartesian coordinates, the distance from the tooth to either bone or tissue was
calculated using the formula;
,
which is based on the Pythagorean theorem. Due to the fact that the distance is a paired
measure (i.e., the tooth and bone/tissue are within the same person) and the fact that a
person contributed multiple teeth in the analysis, a repeated measures ANOVA was used
to test whether the calculated distance was different from 0. Additionally, a repeated
measures ANOVA was used to determine whether the calculated distance differed
statistically by demographic characteristics (i.e., race, gender, and age). For the latter
comparisons, a post-hoc test was performed for significant associations to determine
which category of the demographic association was significantly different. Probability
values <0.05 were considered significant, and SAS v9.3 was used for all analyses.
15
Figure 1. 3D image with plotted FA and BK points prior to graphical reconstruction.
16
Figure 2: Axial slice with plotted FA points at estimated FACC.
Figure 3: Axial slice with plotted BK points at estimated center of resistance
17
CHAPTER 3
RESULTS
Tables were created to summarize the average relative distances and standard
deviations between the corresponding FA, alveolar bone, and WALA points at each tooth
in the mandible and also the distances between the FA and alveolar bone points at each
tooth in the maxilla. These tables were created by summing the values of the right and
left sides at each corresponding tooth in each dental arch.
For all characteristics of the alveolar bone (BK), tooth (FA), and soft tissue (WALA)
the calculated distances were significantly different from 0 (Table 1); meaning that the
plotted points in each arch form at the level of the tooth, alveolar bone, and soft tissue are
not the same. When examining the overall average distance between tooth and bone
within each arch, the largest distance was found in the mandible compared to maxilla
(mean 3.30mm vs. 2.48mm, respectively). When comparing the linear distances between
the teeth and underlying alveolar bone in the maxilla, the mean distance was found to be
2.48mm ± 1.39 SD. More specifically, the individual tooth distances in the maxilla, were
largest for the central incisor and lateral incisor, followed by canine, second molar, first
molar, first premolar, and second premolar. However, when comparing the linear
distances between the mandibular teeth and adjacent alveolar bone, the mean distance
was found to be 3.30mm ± 2.41 SD. To be more specific, the individual tooth distances
in the mandibular arch are largest among the second molar and the first molar, followed
18
by the central incisor, canine, lateral incisor, second premolar, and then first premolar.
Then, when we compare the linear distances in the mandibular arch between the teeth and
corresponding soft tissue/WALA line, the mean distance was found to be 1.94mm ± 1.23
SD. The individual distances between the teeth and soft tissue in the mandible were
largest for the second molar, first molar, and the second premolar, followed by the
canine, first premolar, lateral incisor, and the central incisor. In general, the distances in
the mandibular arch between the bone and tooth were found to be larger than the
distances between the tissue and tooth, and most of these distances were statistically
significant except for the second premolar. All of the specific distances for each tooth
with regards to the FA/tooth, BK/alveolar bone, and WALA/soft tissue points in both the
maxillary and mandibular arches can be found in Table 1.
After all points were plotted and distances measured, a further breakdown of the
age, race, and sex of the patients were analyzed to see if there was any correlation
between the relative distances or arch form shapes between such parameters. The
demographic breakdown resulted in 10 female and 8 male subjects. There were 14
Caucasian, 3 African American, and 1 Hispanic subjects. The mean age of all subjects
was 18.3 years. It was then discovered that there was a significant difference in the
distance between the alveolar bone and tooth in the maxilla with regards to race (Table
2). A post-hoc test suggests that this difference is limited to African Americans
compared to Caucasians. In the mandible, there was also a moderately significant racial
difference observed for the distance between tooth and bone; similarly, this difference
was also limited to African Americans versus Caucasians. By individual tooth, the
differences in the distances in the mandible were mostly due to differences observed for
19
the central incisor and lateral incisor. Interestingly, the distance was higher among
African Americans compared to Caucasians for the central incisors to the second
premolars, but was lower for the first molar and second molar. In hindsight, even though
a statistically significant difference was found between the different races of the subjects,
the study would have benefited greatly from having the same number of subjects from
each racial background. However, this was not possible due to limited number of
subjects that met all necessary inclusion criteria. There were no significant differences in
distance between the tooth and either alveolar bone or tissue in regards to gender (Table
3) and age (Table 4).
Arch Form Analysis
After subjectively analyzing the arch form shapes and comparing them to
available arch form templates, it was found that each patient was slightly different and
individualized. However, when classified into generalized parabolic shapes, 15 of 18
patients exhibited a more ovoid to slightly tapered shape. Only 3 of 18 patients displayed
a square arch form. All arch form comparisons within a given subject were performed
between both the maxillary and mandibular arches. 14 out of 18 subjects, exhibited arch
forms of the same shape in both the maxillary and mandibular arches. While in the other
4 patients, the arch forms between the maxillary and mandibular arches were different
parabolic shapes. In instances such as these, the shape of the mandibular arch was used
for further quantitative analysis.
20
Table 1. Comparison of the distance between the tooth and bone/tissue by dental
arch and tooth characteristics
Bone (BK)
Tissue (WALA)
Mean
p-value*
Mean
p-value*† p-value*‡
distance
distance
Tooth (FA)
Maxilla
2.48±1.39
<0.0001
1: Central Incisor 4.44±1.43
<0.0001
2: Lateral Incisor
3.27±1.07
<0.0001
3: Canine
2.34±0.98
<0.0001
4: First Premolar
1.72±0.86
<0.0001
5: Second
1.55±0.80
<0.0001
Premolar
6: First Molar
1.98±0.83
<0.0001
7: Second Molar
2.04±1.08
<0.0001
Mandible
1: Central Incisor
2: Lateral Incisor
3: Canine
4: First Premolar
5: Second
Premolar
6: First Molar
7: Second Molar
3.30±2.41
2.78±1.88
2.36±1.37
2.40±1.66
2.17±1.02
2.21±0.85
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
1.94±1.23
0.97±0.64
1.16±0.88
1.57±0.75
1.49±0.85
2.34±1.59
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
<0.0001
0.0003
0.0088
0.0047
0.6494
3.37±1.07
7.78±2.27
<0.0001
<0.0001
2.86±0.63
3.25±0.87
<0.0001
<0.0001
0.0144
<0.0001
* Estimated from repeated measures ANOVA
† Whether mean distance is different from 0
‡ Whether mean distance for bone different compared to tissue
21
Table 2. Comparison of the distance between the tooth and bone/tissue between race
by dental arch and tooth characteristics
Caucasian
African
Hispanic
American
Mean distance
Mean distance Mean distance p-value*
Tooth vs. Bone
Maxilla
Bone
1: Central Incisor
2: Lateral Incisor
3: Canine
4: First Premolar
5: Second
Premolar
6: First Molar
7: Second Molar
Tooth vs. Bone
Mandible
Bone
1: Central Incisor
2: Lateral Incisor
3: Canine
4: First Premolar
5: Second
Premolar
6: First Molar
7: Second Molar
Tooth vs. Tissue
Mandible
Tissue
1: Central Incisor
2: Lateral Incisor
3: Canine
4: First Premolar
5: Second
Premolar
6: First Molar
7: Second Molar
2.39±1.26
4.10±1.30
3.02±0.97
2.25±1.07
1.67±0.75
1.66±0.68
2.96±1.87
6.10±0.96
4.25±1.07
2.70±0.52
2.03±1.43
1.39±1.23
2.33±1.35
4.17±1.31
3.87±0.34
2.52±0.05
1.54±0.31
0.57±0.12
0.0201
0.0673
0.0630
0.6911
0.6518
0.1885
1.90±0.85
2.11±1.00
2.20±0.89
2.02±1.54
2.42±0.02
1.24±0.37
0.6907
0.7164
3.11±2.46
2.06±1.04
1.84±0.94
2.02±1.26
1.89±0.66
2.19±0.81
4.08±1.92
5.94±1.88
4.44±1.12
4.38±2.21
3.43±1.60
2.52±1.07
3.57±2.63
3.46±1.00
3.39±0.77
1.77±0.84
2.41±0.00
1.53±0.59
0.0518
0.0004
0.0009
0.0323
0.0131
0.4604
3.54±1.06
8.23±2.00
2.65±0.87
5.18±2.06
3.10±1.54
9.34±0.16
0.1144
0.0269
2.01±1.13
0.90±0.54
1.16±0.95
1.73±0.76
1.71±0.78
2.22±0.68
1.73±1.68
0.94±0.82
1.03±0.54
0.97±0.33
0.84±0.64
3.20±3.74
1.59±0.94
1.95±1.03
1.52±0.95
1.11±0.46
0.37±0.03
1.50±0.41
0.3393
0.1933
0.8703
0.0697
0.0354
0.2972
2.92±0.65
3.52±0.74
2.48±0.51
2.65±0.44
3.17±0.08
1.51±0.54
0.3813
0.0141
* Estimated from repeated measures ANOVA
22
Table 3. Comparison of the distance between the tooth and bone/tissue between
genders by dental arch and tooth characteristics
Male
Female
Mean distance
Mean distance
p-value*
Dental Arch Form
Maxilla
Bone
2.46±1.36
2.49±1.42
0.8723
Mandible
Bone
3.18±2.08
3.39±2.64
0.5252
Tissue
2.06±1.14
1.84±1.29
0.2454
* Estimated from repeated measures ANOVA
Table 4. Comparison of the distance between the tooth and bone/tissue among age
groups by dental arch and tooth characteristics
12-14
15-19
30-45
Mean distance Mean distance
Mean distance
p-value
Dental Arch Form
Maxilla
Bone
2.33±1.28
2.58±1.49
2.56±1.36
0.3625
Mandible
Bone
3.24±2.36
3.54±2.35
2.77±2.59
0.2208
Tissue
1.90±1.13
2.00±1.37
1.85±1.06
0.8193
* Estimated from repeated measures ANOVA
23
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26
CHAPTER 4
DISCUSSION
Stability is one of the most important outcomes of treatment desired by both the
treating orthodontist and patient. When final treatment results remain stable and
acceptable year after year, the reputation of the orthodontist is enhanced, the orthodontic
practice becomes more desired by the public, and the self worth of the both the patient
and practitioner grows. As such, it is in the best interest of practitioners to understand
those aspects of treatment that may provide the most predictable chance for future tooth
stability. It was mentioned earlier when Little pointed out that no treatment is 100%
stable 18, whether it be extraction or non-extraction treatment, expansion or constriction,
nothing is stable 31. However, there are certain treatment mechanics and rules of thumb
that orthodontists should consider when striving for long term treatment stability. One of
the most important treatment practices to provide stability is to maintain the teeth within
the alveolar bone in which they are supported. This study provides preliminary
information to answer this question by analyzing the arch forms created by points plotted
on the FA points of all teeth in both the maxillary and mandibular dental arches and
compares them to arch forms created by points plotted on the BK points of the underlying
alveolar bone that are correlated to the corresponding teeth. The differences in
millimeters between the tooth and alveolar bone were then calculated to give a better
27
understanding of the limits in which teeth can be moved and also show us the varying
widths of bone at each tooth.
With the recent re-emergence and popularity of the non-extraction theory, the
quest to truly understand and possibly quantify the relationship of teeth to their
underlying bone became inevitable. Our study demonstrated that there are limitations to
which teeth can be moved and also reiterated the fact that there is validity to the Apical
Base Theory described by Lundstrom 27. By quantifying, the distances and relationships
that the teeth and alveolar bone have with one another, this study was able to show that
teeth and most importantly, their alveolar housing are not perfectly aligned in a certain
shape. There are discrepancies at every tooth and they are different for each person. This
helped reiterate the statement by Lee that archwires should be individualized for each
patient 14.
After analyzing the results, it was noted that, in the maxilla, the largest differences
between tooth and bone seemed to be at the central and lateral incisors. Therefore, due to
the large variations in incisor proclination, our efforts were then focused only on the
differences from the canine to the second molar because as teeth are more proclined
facially or rolled lingually, we see a larger relative distance between the arch forms
created by the teeth versus those created by the bone which doesn’t accurately reflect the
true nature of the relationship between the two. Also, in order to make sure that there
were no variable vertical levels in the position of the plotted center of resistance on the
bone of each tooth, we ensured that all patients had no current or prior history of
periodontal disease and bone loss. With that being said, overall, the distance between
tooth and bone was greatest for the mandible compared to maxilla (mean 3.30mm vs.
28
2.48mm, respectively). Looking back at the results, their was a seemingly much larger
difference found between the tooth and bone at the level of the mandibular second molar.
However, this can be explained by the natural shape of the mandible as the mandibular
body begins to transition into the wider part of the mandibular ramus. Or it may have
potentially occurred due to the natural curve of wilson present in the mandibular arch.
Although, if we were to take out the measured distances for the maxillary and mandibular
incisors and second molars from the analysis, the numerical difference between the two
arches might be even closer to one another.
In general, when comparing the distances between the bone and tooth versus the
tooth and soft tissue in the mandibular arch, it was noted that the distances between the
teeth and bone were larger than the tissue and tooth (3.30mm vs. 1.94mm, respectively).
In reality, it is known that the soft tissue overlays the underlying bone. Therefore, the
previous statement regarding the larger distances between tooth and bone in comparison
to those distances between tooth and tissue begins to draw question. It is thought that this
error may have been caused by the slight difference in the plotted vertical position of the
center of resistance compared to the plotted center of rotation. However, after analyzing
the results, it was decided that more than likely, this error was due to the way in which
the soft tissue/WALA points were plotted altogether. Even though these points were
plotted with the same computer software as the tooth and bone points; the soft tissue
points were not plotted using a CBCT image, therefore introducing error due to the
difficulty in properly identifying the soft tissue point that accurately reflected the
underlying bone point.
29
The quantification of distances between all plotted points within a given arch
provides us with information that is important in helping us to better understand the
human dental arch form. However, the distances described are somewhat self-limited in
a clinical setting. Therefore, after quantifying linear distances between the teeth, alveolar
bone, and soft tissue and then analyzing the differences in arch form between the tooth
and bone and the differences between the two at each tooth in both the maxilla and
mandible, we wanted to show how this information could be used clinically, both
efficiently and effectively. In the year 2000, Will and Larry Andrews created a term
called the WALA ridge. This term refers to a soft tissue marker at the level of the
mucogingival junction on the mandibular arch. The reason for developing this marker
was to create a structure that would represent the underlying alveolar bone and help
clinicians shape the mandibular arch. Will and Larry Andrews proposed that by using
this clinically visible structure, arch forms could be created to best represent the shape of
the underlying bone and possibly provide future stability 11. It is interesting to note that
the distances between the soft tissue/WALA line and tooth/FA point that were found in
this study are similar to those average distances noted by Will and Larry Andrews in the
Six Elements of Orofacial Harmony 11. Previous studies by Ronay in 2008, and Gupta in
2010 have shown that the arch forms created by the FA points of teeth and the
corresponding WALA ridge are highly correlated 13 4. This study expanded their results a
step further and compared the arch forms created by the FA/tooth points and WALA
points to those arch forms created by the underlying BK/alveolar bone points to truly see
how accurate the WALA ridge represents the underlying alveolar bone.
30
This investigation demonstrated that there are individual variations to all arch
forms created by the FA/tooth point, BK/alveolar bone, and WALA ridge indicating that,
although most patient arch forms may fall into some sort of generalized shape, all arch
forms created are exceptionally individualized and variable. Even though prior studies
have shown that individuals with similar malocclusions and similar ethnic groups tend to
posses similar arch forms, there are still individual variations within those arch forms 12,
15, 16 17
. This helps to reiterate the fact that orthodontic archwires should be shaped
specifically to each individual during orthodontic treatment. However, with that being
said, there was a positive correlation found between the dental (FA), alveolar bone (BK),
and soft tissue (WALA) arch forms. This suggests that the arch forms created by teeth,
underlying bone, and soft tissue are related and one should be able to look at the
clinically visible WALA ridge and accurately predict the arch form that represents the
underlying alveolar bone. Based on these results one might expect to see a slight
variation in the arch form shape and the distance between the tooth and underlying bone
in patients of different ethnicities. Even though our inclusion criteria consisted of
patients with mild crowding and those that exhibited a class I malocclusion we still saw
much variation in the arch forms and distances between plotted points in all patients.
Most patient arch forms would be classified as ovoid to slightly tapered in shape (15 of
18 patients). There were a few exceptions that were classified as square (3 of 18 patients)
or tapered. These variations can most likely be explained by both environmental and
genetic factors that were possibly influential during growth and development.
31
CHAPTER 5
CONCLUSIONS
1.) The arch form shapes obtained from the tooth (FA point), alveolar bone (BK
point), and soft tissue (WALA ridge) are highly individual. The arch forms
created cannot be grouped or categorized into a single uniform parabolic shape.
Most of the arch forms can be grouped into either a square, ovoid, or tapered arch
form, but as discussed, each patient is different and exhibits characteristics of a
combination of shapes. Therefore, archwires should be individually shaped for
each patient.
2.) There was a positive correlation found between the tooth (FA), alveolar bone
(BK), and soft tissue (WALA) arch forms. This suggests that the arch forms
created by teeth, underlying bone, and soft tissue are related and one should be
able to look at the clinically visible WALA ridge and accurately predict the arch
form that represents the underlying alveolar bone.
3.) Overall, the distance between tooth and bone was greatest for the mandible
compared to maxilla (mean 3.30mm vs. 2.48mm, respectively). The largest
difference between tooth and bone were found at the canine and second molar in
the maxillary arch followed by the first molar, first premolar and then second
premolar. In the mandibular arch, the largest difference was found at the second
and first molars followed by the canine, first premolar, and second premolar.
32
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