the comparison of dental arch forms … · bonwill that the mandible formed an equilateral triangle...

i

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

ii

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.

iii

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

iv

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

vi

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

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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

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 non-

extraction 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

distance p-value* Mean

distance p-value*† p-value*‡

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 Premolar

1.55±0.80 <0.0001 - - -

6: First Molar 1.98±0.83 <0.0001 - - - 7: Second Molar 2.04±1.08 <0.0001 - - -

Mandible 3.30±2.41 <0.0001 1.94±1.23 <0.0001 <0.0001

1: Central Incisor 2.78±1.88 <0.0001 0.97±0.64 <0.0001 <0.0001 2: Lateral Incisor 2.36±1.37 <0.0001 1.16±0.88 <0.0001 0.0003 3: Canine 2.40±1.66 <0.0001 1.57±0.75 <0.0001 0.0088 4: First Premolar 2.17±1.02 <0.0001 1.49±0.85 <0.0001 0.0047 5: Second Premolar

2.21±0.85 <0.0001 2.34±1.59 <0.0001 0.6494

6: First Molar 3.37±1.07 <0.0001 2.86±0.63 <0.0001 0.0144 7: Second Molar 7.78±2.27 <0.0001 3.25±0.87 <0.0001 <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 American

Hispanic

Mean distance Mean distance Mean distance p-value*

Tooth vs. Bone Maxilla

Bone 2.39±1.26 2.96±1.87 2.33±1.35 0.0201 1: Central Incisor 4.10±1.30 6.10±0.96 4.17±1.31 0.0673 2: Lateral Incisor 3.02±0.97 4.25±1.07 3.87±0.34 0.0630 3: Canine 2.25±1.07 2.70±0.52 2.52±0.05 0.6911 4: First Premolar 1.67±0.75 2.03±1.43 1.54±0.31 0.6518 5: Second Premolar

1.66±0.68 1.39±1.23 0.57±0.12 0.1885

6: First Molar 1.90±0.85 2.20±0.89 2.42±0.02 0.6907 7: Second Molar 2.11±1.00 2.02±1.54 1.24±0.37 0.7164

Tooth vs. Bone

Mandible

Bone 3.11±2.46 4.08±1.92 3.57±2.63 0.0518 1: Central Incisor 2.06±1.04 5.94±1.88 3.46±1.00 0.0004 2: Lateral Incisor 1.84±0.94 4.44±1.12 3.39±0.77 0.0009 3: Canine 2.02±1.26 4.38±2.21 1.77±0.84 0.0323 4: First Premolar 1.89±0.66 3.43±1.60 2.41±0.00 0.0131 5: Second Premolar

2.19±0.81 2.52±1.07 1.53±0.59 0.4604


Tooth vs. Tissue

Mandible

Tissue 2.01±1.13 1.73±1.68 1.59±0.94 0.3393 1: Central Incisor 0.90±0.54 0.94±0.82 1.95±1.03 0.1933 2: Lateral Incisor 1.16±0.95 1.03±0.54 1.52±0.95 0.8703 3: Canine 1.73±0.76 0.97±0.33 1.11±0.46 0.0697 4: First Premolar 1.71±0.78 0.84±0.64 0.37±0.03 0.0354 5: Second Premolar

2.22±0.68 3.20±3.74 1.50±0.41 0.2972


* 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


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


23

Figure 4: Maxillary Arch Superimposition of FA and BK Points

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24

Figure 5. Mandibular Arch Superimposition of FA and BK Points

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Figure 6. Mandibular Arch Superimposition of FA and WALA Points

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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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the comparison of dental arch forms … · bonwill that the mandible formed an equilateral triangle...

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