University of Southern California Dissertations and Theses

Proper mesio-distal angulation and bucco-lingual inclination of the whole tooth in three-dimensional space -- a standard for orthodontic patients

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Proper mesio-distal angulation and bucco-lingual inclination of the whole tooth in three-dimensional space -- a standard for orthodontic patients

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Content PROPER MESIO-DISTAL ANGULATION AND BUCCO-LINGUAL INCLINATION
OF THE WHOLE TOOTH IN THREE-DIMENSIONAL SPACE – A STANDARD FOR
ORTHODONTIC PATIENTS

by

Donald Kwon

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(CRANIOFACIAL BIOLOGY)

May 2011

Copyright 2011 Donald Kwon
ii
Acknowledgements

I would like to give special thanks to Dr. Hongsheng Tong who has helped me greatly
through this whole process. He has given me invaluable guidance and advice and has
devoted countless hours to help me complete this research project. In addition, I would
like to thank Dr. Shi who helped with the initial digitizations and suffered through the
trials and errors of starting this project. Dr. Sakai helped greatly with the final
digitizations and data collection, without her help we would still be digitizing cases and
collecting data. Dolphin created the program that allowed us to collect the data from the
digitized points, without their help there would be no research. Lastly, I would like to
thank Dr. Enciso for helping me with the final statistics.

iii
Table of Contents

Acknowledgements ii

List of Tables v

List of Figures vii

List of Graphs ix

Abstract x

Chapter 1: Background 1
CBCT History 17
How Cone Beam CT Works 18
Image Resolution 22
Radiation Dosage 23
CBCT Accuracy 23
Limitations 25

Chapter 2: Purpose 27

Chapter 3: Material and Methods 28
Case Selection Criteria 28
Photo Screening 28
X-ray Screening 29
Coordinate Systems 30
3D System for Locating Crown & Root Centers 31
3D System to Determine Mesio-Distal Angulation and 34
Bucco-Lingual Inclination
Mesio-Distal Angulation 35
Bucco-Lingual Inclination 36
Arch Form 37
Reliability of Measurements 40
Statistics 40

Chapter 4: Results 42
Inter/Intra-Examiner Reliability 42
Left and Right Side Comparison 46
Paired T-Test 49
Ideal Tip and Torque 51
Interdental Tip and Torque 51
Gender Studies 55
Ethnic Comparisons 59
iv

Chapter 5: Discussion 65

Conclusion 73

References 75

v
List of Tables

Table 1: Inter/Intra Examiner Correlation Coefficient (ICC) 42
of the upper right tip

Table 2: ICC of the Upper Left Tip 42

Table 3: ICC of the Lower Left Tip 42

Table 4: ICC of the Lower Right Tip 43

Table 5: Mean, Range, and SD for the Tip ICC 43

Table 6: ICC of the Upper Right Torque 43

Table 7: ICC of the Upper Left Torque 44

Table 8: ICC of the Lower Left Torque 44

Table 9: ICC of the Lower Right Torque 44

Table 10: Mean, Range, and SD for the Torque ICC 45

Table 11: Left and Right Tip 46

Table 12: Left and Right Torque 46

Table 13: Paired T-Test for Upper and Lower Tip 49

Table 14: Paired T-Test for Upper and Lower Torque 50

Table 15: Ideal Tip and Torque 51

Table 16: Interdental Tip of the Left and Right Side 51

Table 17: Interdental Torque of the Left and Right Side 52

Table 18: Male Tip and Torque 55

Table 19: Female Tip and Torque 55

Table 20: One-way ANOVA for M/F Tip and Torque 56

Table 21: Sample for Ethnic Comparison 59
vi

Table 22: Average Upper Tip for all Ethnicities 59

Table 23: Average Lower Tip for all Ethnicities 60

Table 24: Average Upper Torque for all Ethnicities 60

Table 25: Average Lower Torque for all Ethnicities 61

Table 26: One-way ANOVA for the Tip and Torque 61
for all Ethnicities

vii
List of Figures

Figure 1: Standard Edgewise Brackets 2

Figure 2: First, Second, and Third Order Bends 2

Figure 3: Models of Lawrence Andrew’s 120 Cases 3

Figure 4: Pre-adjusted Brackets 4

Figure 5: FACC and FA Points 5

Figure 6: Example of FACC for Each Type of Tooth 6

Figure 7: FACC and FA Points for (+) and (–) Crown Inclinations 6

Figure 8: FACC and FA Points in Bucco-Lingual Dimension 7

Figure 9: Indirect Bonding 9

Figure 10: Virtual Model Set-up 10

Figure 11: OrthoCad Bracket Placement 11

Figure 12: Geodigm TARG System 13

Figure 13: SureSmile Set-up 14

Figure 14: Mechanism of Traditional Panoramic X-ray 15

Figure 15: Non-orthogonal Panoramic X-ray 16

Figure 16: CT vs. CBCT: Fan vs. Cone 19

Figure 17: CT vs. CBCT: Base Projections 20

Figure 18: Isotropic vs. Anisotropic Voxels 22

Figure 19: Functional Occlusal Plane 31

Figure 20: Digitization of the Center of the Crown 32

Figure 21: Digitization of the Center of the Root 33

viii
Figure 22: Long Axis of all Teeth 34

Figure 23: Determination of Mesio-Distal Angulation 36

Figure 24: Determination of Bucco-Lingual Angulation 37

Figure 25: Determination of Upper Arch Form 38

Figure 26: Determination of Lower Arch Form 39

Figure 27: Measurement of Interdental Tip 52

Figure 28: Measurement of Interdental Torque 53

ix
List of Graphs

Graph 1: Upper Left and Right Tip 47

Graph 2: Lower Left and Right Tip 47

Graph 3: Upper Left and Right Torque 48

Graph 4: Lower Left and Right Torque 48

Graph 5: Left and Right Interdental Tip 52

Graph 6: Left and Right Interdental Torque 54

Graph 7: Male and Female Upper Tip 56

Graph 8: Male and Female Lower Tip 57

Graph 9: Male and Female Upper Torque 57

Graph 10: Male and Female Lower Torque 58

Graph 11: Upper Tip of all Ethnicities 62

Graph 12: Lower Tip of all Ethnicities 62

Graph 13: Upper Torque of all Ethnicities 63

Graph 14: Lower Torque of all Ethnicities 63

x
Abstract

The purpose of this study was to determine the ideal standard for the mesio-distal
angulation (tip) and bucco-lingual inclination (torque) for each tooth (crown and root) in
three-dimensional space utilizing CBCT. After determining a set of inclusion and
exclusion criteria, 76 “near normal” cases were chosen and measured. To determine the
reliability of our methodology we had 10 cases digitized by Dr. Tong and Dr. Kwon at
two different time points and 10 cases digitized by Dr. Tong and Dr. Sakai at one time
point and Dr. Kwon at another time point. The inter/intra-examiner correlation
coefficients were 0.919 for the average of all the mean values for tip and 0.957 for the
average of all the mean values for torque. We tested for symmetry of each case by
comparing the left side to the right side using a paired T-Test. From our data the upper
canine tip, the upper central torque and the lower 2
nd
premolar torque are the only values
that fall below the p value (0.00357). After determining that there is near perfect
symmetry we took an average of the left and right side to come up with one value for the
ideal tip and torque for every tooth. In addition, we also were able to compare the
differences in the tip and torque between male (n=22) and females (n=54) and between
various ethnicities. While all genders and ethnicities follow the same trend there were a
few teeth that had statistically significant differences in the tip or torque. Lastly, we also
calculated the interdental tip (180
o
– (upper tip + lower tip)) and torque (180
o
– (upper
torque + lower torque)). All the interdental tip angles fell within a 10 degree range of
xi
each other while the interdental torque angles increased from the central incisors all the
way to the 2
nd
molars, reaching close to 180 degrees.
1
Chapter 1: Background

Orthodontics is the branch of dentistry that specializes in the diagnosis, prevention, and
treatment of dental and facial irregularities. Most commonly it involves the straightening
of teeth by way of moving crooked teeth into proper alignment. Orthodontic treatment
objectives can be stated as obtaining ideal functional occlusion, esthetics, and stability.
One of the criteria for obtaining a functional occlusion is to have ideal axial inclinations
of all teeth in all three planes of space at the end of active treatment.
1

Dr. Edward Angles (1855-1930), who is considered by most as the father of modern
orthodontics is credited for developing the first-generation fixed orthodontic appliances
about 100 years ago. The so-called standard edge-wise appliance uses “universal”
brackets for almost all the teeth (Figure 1). However, teeth that are in an ideal position
do not just follow a general alignment; each tooth differs more or less from the adjacent
tooth in position and inclination in all three planes of space. Therefore standard edge-
wise appliances with “universal” rectangular brackets slots would call for 3-dimensional
bending of rectangular wires (1
st
, 2
nd
and 3
rd
order bends) for each tooth to achieve proper
tooth position (Figure 2).

2

Figure 1 Standard Twin Edgewise Bracket

Figure 2 A – First order bends, B – Second order bends, C – Third order bends

Since Dr. Edward Angle first introduced standard edgewise fixed orthodontic appliances
more than a century ago, there have been innumerable modifications and improvements.
The most significant contribution in the last century was by Dr. Lawrence Andrews. Dr.
Andrews studied 120 people with optimal tooth alignment and occlusion and found that
the positions of the same type of teeth among different individuals fall within a narrow
3
range (Figure 3).
2
He also found six common features or “six keys” that were shared by
those optimal natural occlusion cases.
2
Based on these, he developed and designed the
Straight-Wire Appliance (SWA), which have built-in dimensional and angulation features
for each tooth.
3-5
Thus the tedious work of wire bending at each patient’s appointment
has been reduced dramatically due to these pre-adjusted appliances (Figure 4).

Figure 3 Models of the 120 cases, from Dr. Lawrence Andrews office, used for the initial
study.

4

Figure 4 Pre-adjusted brackets showing the torque built into the brackets.

His pre-adjusted appliances have built in the positional and inclinational features (1
st

order bracket base thickness, 2
nd
order bracket slot tip, 3
rd
order bracket base torque) for
each type of tooth. Therefore, orthodontist can finish cases with basically straight
rectangular wires without placing bends in the arch wires.
3-5

Since then, the vast majority of orthodontists have adopted various types of fully-
programmed appliances which not only allow us to treat patients with less effort and
more efficiency, but have also brought about a dramatic improvement in the quality of
our orthodontic finishes.
6-7

5
According to Dr. Andrews, to take full advantage of the fully-programmed appliances, it
is critical to locate 1) the long axis of the central developmental lobe of each crown,
defined as the facial axis of clinical crowns (FACC) and 2) the center point of the FACC
(center of the clinical crown), or the FA point (Figure 5-8). However, almost all
orthodontists accept the fact that it is sometimes impossible or impractical to locate the
FACC and the FA point clinically.
8-9

Figure 5 The FACC drawn through the central developmental lobe of the clinical crown.
The FA point is determined as the center of the FACC. Examples of positive and negative
crown angulation are shown relative to a line drawn perpendicular to the occlusal plane.

6

Figure 6 The FACC drawn for upper and lower incisors, canines, bicuspids, and molars.

Figure 7 FACC and FA points are shown with both a positive and negative crown
inclination, which is determined by how much torque exists in the incisors. (The FACC is
tangent to the crown at the FA point)

7

Figure 8 FACC and FA points are shown in the bucco-lingual dimension showing
variation in the crown inclination due to the different position and different shape of each
tooth.

Furthermore, the straight wire technique requires that each bracket is bonded at the center
of the crown with the bracket long axis coincident with the FACC. Imprecise bracket
positioning would negate the advantage of the straight wire appliances and call for
compensational wire bending.
10-11
In addition, the inability to see the posterior teeth
directly, patient salivation, moisture from the patient’s breath, limited time given, stress
for the patient, staff and the orthodontist have all contributed to making accurate bonding
very difficult.
12-13
As Balut et al. demonstrated, even well-trained orthodontists were
incapable of placing brackets with sufficient precision to justify the use of a particular
SWA. Displacement greater than 0.4 mm had a major influence on the torque implicit in
a bracket, resulting in changes varying from 2° to 10° dependent on the tooth and the
individual.
10

The difficulty in determining the location of FACC may be due to 1) the excessive wear
of the surface structure, making it hard to identify the central developmental lobe used to
8
define FACC; 2) the buccal surface of some of the teeth taking the round shape rather
than spear or shovel shape, making it hard to visualize the long axis especially if the tooth
is angulated; and 3) the crowns partially being covered by the gums.
14
Furthermore, the
clinical crown can be short relative to the root, and a slight error in FACC angulation will
send the root far off its proper position.

Germane et al. also pointed out in their study, the consistency of the FACC and
especially the FA points are in question due to 1) inherent variation in the contour of the
labial surfaces and 2) sensitivity to errors in the vertical position of bracket placement on
the curvature of the labial surfaces.
15
This makes accurate bracket placement very
difficult and minimizes the advantages that Dr. Andrews hoped for when designing the
straight wire appliance.

Indirect bonding was introduced to help solve the problems of inaccurate bracket
placement: due to anatomy, patient discomfort, visibility, identification of the long axis
(FACC), etc. By virtue of bonding the brackets on stone models first, where reference
lines on model teeth are drawn, the accuracy of bracket positioning, especially on the
posterior teeth, increased dramatically (Figure 9).
12-13
A wide variety of techniques have
been suggested to provide accurate transfer of brackets from the model to the patient’s
teeth.

9

Figure 9 Indirect bonding – the intersection of the line represents the center of the crown.

The recent advent of imaging software has brought the practice of orthodontics to a
whole new level. The latest imaging technologies allow a patient’s study model to be
scanned and 3D digital models to be generated. Orthodontists can use this imaging
software to take measurements, make diagnoses, plan treatment, simulate treatment
progress and foresee projected treatment outcomes through a process called virtual model
setup. The setup can be viewed and checked from all different angles, even from the
back while the teeth are in occlusion, or by cross-sections, both absolutely impossible
clinically, yet very important for cases to be finished with the uttermost detail and
accuracy. Once the orthodontist and the patient are satisfied with the virtual model setup,
the orthodontist can work backward on the computer to find the bracket positions for all
teeth in 3D that will bring about the projected treatment outcome utilizing a full size
straight rectangular wire with a predetermined arch shape (Figure 10). All these can be
accomplished before any brackets are ever put in the patient’s mouth.
Original
Brackets on set-up
10

Figure 10 (Left to Right) Original, set-up, original with brackets, set-up with brackets.
(Courtesy of OrthoCad)

In order to carry out the virtual treatment in a real patient, the accurate transfer of the
brackets from the computer images to the patient’s mouth is very important. Direct
bonding is out of the question due to the degree of accuracy required. At the present,
there are three approaches, all through indirect bonding, to bridge between the virtual
images and the patients’ teeth in real life.

OrthoCad is the current front-runner in offering indirect bonding services. They position
brackets on a stone model, according to a computerized virtual set-up, with a special
wand designed after a military style pattern recognition algorithm (Figure 11). The pen-
sized wand has three main components: 1). a curved tip for steering the bracket on the
Brackets on set-up
11
tooth surface of the stone model, 2). a miniature video camera projecting real-time
images from the steering area, including a view of the bracket, and 3). a curing light to
cement the bracket once the correct spot has been located. The lab technician pushes the
tip of the wand into the bracket slot and steers the bracket so that real-time images of the
bracket are exactly overlaid over the ones in the virtual set-up. Once the target is
acquired, the wand will beep and light cure the adhesive. Using their system, all
commercial brackets are customized by the shape and thickness of the light cured
adhesive formed to fit each specific tooth’s contour. This is determined by software and
corresponds to the space between the tooth and any commercial bracket base. This
technology used by OrthoCad, although very advanced, is not short of weaknesses: 1) the
superimposition of the virtual set-up and the real-life bracket position is a two-
dimensional overlay and not 3D overlay. Torque control is significantly lacking; 2) the
indirect bonding is done by lab technician and human error cannot be avoided. The
information about the sensitivity of the wand to error is not available from OrthoCad.

12

Figure 11 Placement of brackets using a pen-sized wand.

Geodigm is a company that offers e-models, bracket e-placement, and indirect bonding
services. For indirect bonding, they use a system similar to the Torque Angulation
Reference Guide (TARG) system, derived from indirect bonding of lingual braces. The
TARG system offers 3D control. Although the readings from the parallelometer in most
sophisticated TARG systems are digital, the positioning of the brackets are still done with
hands by lab technicians (Figure 12). It is not only tedious and time-consuming, but also
prone to human errors.

13

Figure 12 Torque Angulation Reference Guide (TARG) system

SureSmile has another approach. They allow orthodontists to do direct bonding on
patients first and scan the patient’s teeth a few months later. Using their software, a
virtual set-up of the ideal treatment outcome is projected. Instead of perfecting the
bracket positions, they use robot to make precise bends in the arch wires to achieve the
treatment goal (Figure 13). Although the use of a robot is the first in orthodontics and
that gives them the high-tech edge, their approach is like putting the cart before the horse.
If the brackets are bonded correctly in the first place, there will be no need for bending
wires.
14

Figure 13 Ideal set-up of the teeth with preadjusted wires

However, all these new techniques use the measurements of the crown tip and torque,
while the root position is largely ignored. As mentioned before, since the FACC and FA
points are sometimes hard to locate and may not necessarily represent the long axis of the
whole tooth, it only makes sense to include the roots when setting up all the teeth. For
most orthodontists, the only x-ray records available are panoramic x-rays and lateral
cephalograms. The problem is, these traditional x-rays are simply projection images of
three-dimensional structures on two dimensional planes and do not truly reflect the three-
dimensional relationship between different structures (Figure 14-15). Although study
models are three-dimensional, they do not show the roots.

15

Figure 14 Shows the mechanism of image formation for the PANO machine. It explains
how images of the target structure (ABCD, in that order) form when both the X-ray
source and the sensor move in opposite directions while the target stays in between.

16

Figure 15 Example of how an X-ray beam from a traditional panoramic machine is not
always orthogonal to the target tooth. Non-orthogonal X-rays always cause distortion in
the images.

Just as three-dimensional imaging in the medical field has revolutionized medical
diagnosis and the delivery of treatment since the introduction of computed tomography
(CT) in 1971 by Dr. Hounsfield in England, the Cone-Beam CT has opened up a new
horizon for three-dimensional diagnosis and treatment planning in dentistry, particularly
in orthodontics where shape, form, structure, and position are of critical importance.
Utilizing this new technology, we can now visualize each whole tooth in all three planes
of space.

17
Cone Beam CT History
Since Broadbent introduced cephalometric radiology to orthodontics in 1931, imaging
has been a crucial adjunct to orthodontic diagnosis and treatment planning. Orthodontists
rely on these cephalometric radiographs to derive angular and linear measurements from
anatomical landmarks. Current radiographs, such as panoramic radiographs and lateral
cephalograms, are limited to a two-dimensional (2D) projection. These 2D diagnostic
radiographic images are inherently subject to magnification, distortion, superimposition,
and misrepresentation of structures.

Since, the development of the first CT in 1967 by an engineer named, Sir. Godfrey
Hounsfield, CT technology has rapidly evolved. The first generation of CT scanners
used a single detector element to capture a beam of X-rays. Both the detector and source
rotated one degree at a time, a design known as the "translate-rotate" or "pencil-beam"
scanner. In 1975, a second generation of CT known as "hybrid" CT was introduced.
These machines used more than one detector and a small fan-beam X-ray, as opposed to a
pencil-beam. In 1976, a third generation CT scanner was introduced. These scanners
used a large, arc-shaped detector that acquires an entire projection without the need for
translation. This rotate-only design utilizes the power of the X-ray tube much more
efficiently than the previous generations. A fourth generation scanner shortly followed,
replacing the arc-shaped detector with an entire circle of detectors. In this design the X-
ray tube rotates around the patient, while the detector stays stationary.

18
The introduction of cone beam computed tomography (CBCT) specifically dedicated to
imaging the maxillofacial region heralds a true paradigm shift from a 2D approach to a
3D approach to data acquisition and image reconstruction.
16
CBCT was initially
developed for angiography
17
, but other applications have included mammography.
18

CBCT was originally developed as an alternative to conventional CT to provide a more
rapid acquisition of an image by using a larger field of view (FOV), and a comparatively
less expensive x-ray detector. Through the use of a cone shaped x-ray beam, the CBCT
produces shorter radiation exposure, faster x-ray acquisition time, reduced image
distortion due to patient movements, and increased x-ray efficiency. The use of a larger
FOV increases the amount of x-ray scatter. Since the CBCT uses a larger FOV, the
image quality related to noise and contrast resolution is limited.

How Cone Beam Computed Tomography (CBCT) works
Typically, CBCT machines scan patients in one of three positions: sitting, standing, or
supine. Unlike having the patient upright, a patient supine during a scan can alter the 3D
soft tissue profile, thus it is important to look at additional photographs to accurately
evaluate the soft tissue.

CBCT imaging is accomplished by using a rotating gantry to which an x-ray source and
detector are fixed. A divergent cone-shaped source of ionizing radiation is directed
throughout the middle area of interest onto an x-ray detector on the opposite side. To
acquire an image, a single rotation of the x-ray source and detector rotates around a fixed
19
fulcrum within the center of interest (Figure 16). During the rotation, multiple sequential
planar projection images of the FOV are acquired in a complete or sometimes partial arc.
This procedure varies from a traditional medical CT, which uses a fan-shaped x-ray beam
in a helical progression to acquire individual image slices of the FOV. A computer stacks
the acquired slices to obtain a 3D representation. Each slice requires a separate scan and
separate 2D reconstruction. Because CBCT exposure incorporates the entire FOV, only
one rotational sequence of the gantry is necessary to acquire enough data for image
reconstruction (Figure 17).
16

Figure 16 Traditional CT vs. CBCT; Traditional CT uses a “Fan” of x-rays and need
multiple helical passes around the subject; CBCT uses a “cone of x-rays and only needs a
single pass around the subject.

20

Figure 17 Conventional CT vs. CBCT; reconstructions of the base projections differ,
CBCT scans are subject to much more radiation scatter.
16

The resolution of CBCT imaging is gauged by the volume elements or voxels produced
from the 3D volumetric data. The voxel dimension depends on the pixel size on the
detector. The detector typically detects pixels that range from 0.09 mm to 0.4 mm.
Therefore, the detector determines the final resolution and clarity of the 3D volumetric
image. Because CBCT raw data is obtained in one rotation of the x-ray source, CBCT
voxels are isotropic, which means that all three dimension are of equal length.
Traditional CT scanners rotate multiple times around the object to produce an image. To
create CT voxels, the computer must combine all the obtained slices, and construct a z
dimension depending on slice thickness. These resulting compositional voxels are
21
anistropic, which is of unequal dimensions. The voxel shape is columnar and has an
equal x and y dimension, but an unequal z dimension (Figure 18). Once the patient has
been scanned with a CBCT scanner, data must be processed to create a 3 dimensional
volume. This process of reconstruction combines a number of individual base
projections, each frame resembling a lateral cephalogram that contains more than one
million pixels (Figure 17). Each pixel is assigned 12 or 16 bits of data. A computer
processes the multiple base projections to reconstruct the desired 3D volume. 3D image
processing time varies based on voxel size, FOV, number of projections, and computer
processing speed.

22

Figure 18 Isotropic Voxels vs. Anisotropic
16

Image Resolution: Pixel and Voxel Size
A pixel represents the smallest sampled 2D element in an image. The image has
dimensions along two axes in millimeters, dictating in-plane spatial resolution. A voxel
is the volume element, defined in 3D space. Its dimensions are given by the pixel,
together with the thickness of the slice (the measurement along the third axis).
Resolution which determines the ability to distinguish structures as separate and distinct
from each other is inherently related to the acquired voxel volume. The FOV, acquisition
matrix, and the slice thickness determine voxel volume. The pixel size (FOV/matrix)
determines the in-plane resolution. Reducing the FOV, increasing the matrix number, or
reducing the slice thickness results in an image with reduced voxel volume. A smaller
23
voxels produces images with a higher resolution, but a lower signal-to-noise ratio (SNR),
which may cause the image to look grainy.

CBCT Radiation Dosage
Previous studies indicate that the effective radiation dose varies, ranging from 29 to 477
mSv, depending on the type and model of CBCT and FOV selected.
19-20
Comparing
these doses with multiples of a single panoramic dose or background equivalent radiation
dose, CBCT provides an equivalent patient radiation dose of 5 to 74 times that of a single
film based panoramic x-ray, or 3 to 48 days of background radiation. The use of a
thyroid collar and chin position can substantially reduce the dose by up to 40%. In
comparison to a traditional CT, CBCT radiation exposure of the maxillofacial region is
76.25% to 98.5% less.
19-21

CBCT Accuracy
Traditional orthodontic analysis typically requires a 2D lateral cephalogram and
panoramic x-ray of the skull, which can be highly inaccurate due to magnification,
anatomic superimposition, beam projection angle, and patient position.
22
These
distortions were unavoidable, until the advent of CBCT imaging. Unlike 2D radiographs,
cephalometric radiographs constructed from CBCT scans can use the right or left half of
the skull, thereby overcoming the superimposition of the ramus, body, molar and
condyles. Also, in 2005, Hutchinson showed that linear and angular dimensions are more
24
accurate using a CBCT derived panoramic radiograph, compared to traditional
radiographs.
23
Furthermore, in a CBCT imaging, because the x-ray beams emitted are
almost parallel to one another and the raw data is obtained in one rotation, the voxels are
isotropic eliminating the magnification and distortion of the image. After the CBCT scan
is complete, the computer software processes the data, and the resulting image has a 1-to-
1 measurement ratio to the original object. To ensure that error is kept to a minimum and
that other operational systems are functioning correctly, a water phantom is used to
calibrate the 3D scanner.
24
In 2005, Hilgers studied the accuracy of CBCT in the TMJ.
He found that CBCT accurately and precisely depicts the TMJ complex in a 3D model.
The measurements were reproducible and significantly more accurate than those made
with conventional cephalograms in all 3 dimensional planes.
25
In 2004, Lascala studied
the accuracy of linear measurements obtained by cone beam computed tomography. The
group studied 13 measurements in 8 dried skulls and recorded measurements with an
electronic caliper. The skulls were then scanned and analyzed with a NewTom QR-DVT
9000. The radiographic

distance measurements of the same dry skull were then
compared. They concluded that the CBCT image underestimates the real distances
between skull

sites. Differences were only significant for the skull base, and

therefore, it
is reliable for linear evaluation measurements

of other structures more closely associated
with maxillofacial

imaging.
26
CBCT scans are highly accurate and provide a three-
dimensional image of the skull, which is paramount to effective orthodontic treatment
planning.
25

Limitations of CBCT
CBCT image artifacts arise because of the inherent polychromatic nature of the x-ray
beam. The x-ray source produces a heterogeneous mix of low and high energy photons,
which passes through an object. The low energy photons are absorbed more than the
higher energy photons, resulting in a richer high energy photon penetrating beam or beam
hardening. Beam hardening manifests as a cupping artifact, or streaks and dark bands.
Cupping artifacts occur when x-rays passing through the center of an object become
harder than x-rays passing through the edges of an object. Since the x-ray beam becomes
harder in the center, the image is processed incorrectly and produces the artifact.

Patient motion can cause blurriness of the reconstructed 3D image. This type of error can
be minimized by placing a head restraint on the patient before the scan is taken.

Undersampling can also occur if too few basis projections are used in the reconstruction.
A reduced number of projections can lead to blurriness and a noisier 3D image.
Resolution of fine detail will be affected.

Scanner related artifacts can manifest as a circular or ring shaped artifacts. These
artifacts are caused by poor scanner detection or improper scanner calibration. These
problems will consistently result in circular artifacts.

26
CBCT image noise is mostly caused by scattered radiation. Since CBCT uses a cone
shaped x-ray beam, scattered radiation is unavoidable. This scattered radiation becomes
omnidirectional and is recorded by the CBCT detector. This nonlinear attenuation is
contributes to the overall image noise.

A cone beam effect can be a source of artifacts. Since the x-ray beam diverges and the
beam rotates around the patient, the amount of information for peripheral structures is
reduced. The outer rows of the detector record less than the inner rows, resulting in
image distortion, streaking, and greater peripheral noise.

27
Chapter 2: Research Objective

The purpose of this study is to establish the optimal standard for the mesio-distal
angulation and bucco-lingual inclination for each whole tooth including the root in three-
dimensional space.

28
Chapter 3: Material and Methods

Case Selection Criteria
The selection criteria were comparable with those used by Andrews: no history of past
orthodontic treatment; subjects in good health and exhibiting normal growth; well-related
vertical, transverse, and anteroposterior relationships; pleasing profiles; arches well
aligned with normal-appearing teeth; low decayed, missing, filled tooth index numerical
value; no large restorations or fixed replacements; and no supernumerary teeth.
Furthermore, all subjects had close to Angle Class I molar relationships, and overjet and
overbite close to within normal limits.

Photo Screening
1. Complete dentition (a few cases with the second molars not fully erupted;
as long as the anatomy of the crowns are preserved, we have accepted
some cases with large fillings or crowns)
2. Molar relationship from < 1/2 step Class II to 1/4 step Class III
3. Overbite and Overjet between 0-5 mm
4. Spacing < 6 mm
5. Crowding < 4 mm (limit to 3 teeth max)
6. Rotation < 15
0
(limit to 3 teeth max)
7. No dental X-bite (limit to no more than 1 tooth)
8. No apparent arch form asymmetry.
29

X-Ray Screening
1. Panoramic X-rays show generally parallel roots
2. ANB between -1
o
to 6.5
o

3. FMA between 14
o
to 37
o

4. U1/L1 angulation between 110
o
to 146
o

5. No obvious skeletal PA and vertical asymmetry

From April 2004 to October 2009 approximately 2000 cases with CBCT were started.
From this group, we selected 125 near normal patients after initial photo screening. After
applying the above inclusion/exclusion criteria (x-ray screening), 76 patients qualified for
the “Near Normal” group.

Each CBCT scan was taken using a NewTom 3G under the following conditions: the tube
voltage – 110 kVp, tube current – 15 mA, scan time – 17 seconds, grayscale – 12 bit,
field of view – 200 mm (12 inch). Before the scan was acquired, each patient was placed
in a supine position and oriented perpendicular to the rotation axis of the CBCT x-ray
source. The patient was to remain as still as possible during the entire scan time to
minimize distortion and noise in the final image. Based on our specific requirements and
instructions, Dolphin developed a customized 3D analysis program that allowed us to
digitize each tooth in all three planes of space and obtain the tip and torque measurements
from these digitizations.
30

Global Three-Dimensional Coordinate Systems
A global three-dimensional coordinate system is first generated for the proper orientation
of the head and the maxillofacial structure. We use a sagittal plane, a coronal plane, and a
transverse plane, each perpendicular to the other two. The sagittal plane is the plane that
evenly divides left and right, the coronal plane is the one that is perpendicular to the
sagittal plane at the buccal grooves of the right and left first molars, and the transverse
plane is the functional occlusal plane, defined as the plane that intersects the incisal
overbite and the molar overbite (defined at the buccal groove of the upper first molars)
(Figure 19). It is also worth noting that the occlusal plane we use is different from
Andrews’ occlusal plane, which touches the incisal edges and the second molars cusp
tips. Since upper and lower incisal edges and molar cusp tips are at different levels, each
arch has a different occlusal plane in Andrews’ studies, and the two are often not
perfectly parallel.

31

Figure 19 Image of all 3 planes established at the functional occlusal plane (Intersection
of the overbite of the central incisors and first molars at the buccal groove of the upper
molars).

Tooth-Specific Three-Dimensional System for Locating Crown and Root Centers
A different three-perpendicular-plane system specific for each tooth was used for locating
each crown and root center: the anatomical mesio-distal plane, the anatomical bucco-
lingual plane, and the transverse plane at the crown and root center level (Figure 20-21).
We choose to use the true long axis of each tooth, defined as the line that connects the
center of the crown and the center of the root (Figure 22). The tooth long axis is not
affected by the surface contour and structure (central developmental lobe), therefore, it is
easier to define with the imaging software program and less variable. We have also
removed another variable by intentionally ignoring the apical third of the root, which has
shown tremendous variation from the true long axis of many teeth.
32

Figure 20 A point being placed at the center of the crown utilizing all three planes of
space to accurately determine the proper location.

33

Figure 21 A point being placed at the center of the root utilizing all three planes to
accurately determine the proper location.

34

Figure 22 All crown and root points are digitized and a line connecting them is shown
representing the true long axis of each tooth.

Tooth-Specific 3D System for Mesio-Distal Angulation (Tip) and Bucco-Lingual
Inclination (Torque) Measurements
Another tooth-specific three-plane coordinate system is used to study the mesio-distal
angulation and bucco-lingual inclination of each whole tooth in three-dimensional space.
The transverse plane is the same functional occlusal plane as in the global coordinate
system. The mesio-distal plane is also called the arch plane along the curvature of the
dental arch and it changes from tooth to tooth. Each tooth also has its own bucco-lingual
plane.

35
Mesio-Distal Angulation Measurement (Tip)
As illustrated in the figure below, the mesio-distal angulation of the tooth should
be measured from the projection of the true tooth long axis on the mesio-distal
plane to the vertical line formed by the intersection of the mesio-distal and the
bucco-lingual plane (Figure 23). If the root center is distal to the crown center,
the measurement is positive, otherwise it is negative. Ideally this measurement
should agree with Andrews’ crown angulation measurement since the FACC and
the long axis of the whole tooth should have the same angulation.

36

Figure 23 Determining the mesio-distal angulation (tip) of the lower right first
molar from the mesio-distal view.

Bucco-Lingual Inclination Measurement (Torque)
The bucco-lingual inclination of the tooth should be measured from the projection
of true tooth long axis on the bucco-lingual plane to the same vertical line formed
by the intersection of the mesio-distal plane and the bucco-lingual plane (Figure
24). If the root center is lingual to the crown center, the measurement is positive,
otherwise it is negative. This measurement may not agree with the crown bucco-
lingual inclination due to the contour of the labial surface of the tooth measured.

37

Figure 24 Determining the bucco-lingual angulation (torque) of the upper left
first molar from the bucco-lingual view.

Arch Form
Four teeth on the right side of both the upper and lower arches are digitized along
the arch outline: the mid incisal tip, the right canine tip, the right second premolar,
and the right second molar. The software program will duplicate the right side
half arch to the left side constructing a symmetrical arch form (Figure 25-26). If
this constructed arch form does not fit the patient’s real arch form, the midpoint
can be adjusted to the left or right to get a better adaptation of the arch form to the
teeth.

38

Figure 25 Determining the arch form of the maxillary arch by placing the points
(shown in yellow) buccal to the midincisal, canine, second bicuspid and second
molar. The left side arch is duplicated from the right side arch and it fits the dental
arch perfectly.

39

Figure 26 Determining the arch form of the mandibular arch by placing the points
(shown in yellow) buccal to the midincisal, canine, second bicuspid and second
molar. The left side arch is duplicated from the right side arch and it fits the dental
arch perfectly.

Once the arch form is constructed, the customized program will add two lines to
each tooth. The shorter green line represents the bucco-lingual plane that is
perpendicular to the arch plane and the shorter blue line represents the mesio-
distal plane that is parallel to a plane that is tangent to the arch plane at the point
where the bucco-lingual plane intersects the arch plane. The dark blue dot
represents the crown center of each tooth. These three planes (the bucco-lingual
plane, the mesio-distal plane, and the occlusal plane) form the tooth-specific
three-dimensional coordinate system from where the mesio-distal angulation and
bucco-lingual inclination are measured.
40

At this point, the software program can measure and print out the tip and torque
measurements for all the teeth automatically.

Reliability of Measurements
In order to ensure that the measurements and methodology that we described above was
repeatable, we had two examiners digitize 10 cases initially and re-digitize those same 10
cases at a later time. In addition, we had two examiners digitize 10 separate cases and two
different examiners re-digitize those same 10 cases at a later time. After obtaining all the
measurements from these cases, inter- and intra-examiner correlation coefficients (ICC)
tests were performed to check the reliability of the measurements.

Statistics
Formal Kolmogorov-Smirnov normality test was performed to check for normality in all
our data.

In order to determine the symmetry of each patient we digitized each individual tooth and
compared the left side to the right side. In order to test the symmetry we ran a paired T-
test to determine how similar the left and right side values were to each other. For the
non-normal data (the U6 tip, L1 torque, and L2 torque) we used the Wilcoxon Signed
Rank test to compare for differences between the pairs.

41
To compare for the male and female tip and torque, because they are independent
samples, we used an independent T-Test to compare the means. In addition, we checked
for equality of variance with the Levene’s Test. If the data did not pass the Levene’s test
we used the P-value for non-equal variance groups. For the values that were not normal
(the U6 and L3 tip, and the U3, U4, L2 and L5 torque) we used the Mann-Whitney test to
test for differences between the two genders.

A one-way ANOVA with Bonferroni post hoc correction for multiple comparisons was
used to test for significant differences between the 5 ethnic groups and to determine
which ethnicities were significantly different from each other. For the non-normal data
(the U7 and L7 tip, the L2, L6 and L7 torque), the Kruskal-Wallis test was used to
compare the differences between all five groups. For the post hoc analysis, a Mann-
Whitney test to test for differences between pairs of ethnicities was used to determine
which ethnicities were significantly different from each other.

We also utilized the Dunn-Bonferroni correction to address the problem of multiple
comparisons. In order to account for the multiple independent tests we took the
significance level (p < 0.05) and multiplied that by the inverse of the number of
independent tests we tested for (14 comparisons for tip and 14 comparisons for torque),
0.05/14, giving us a statistical significance of p < 0.00357.

All statistics were done utilizing Microsoft Excel, SPSS, and PASW Statistics 18.
42
Chapter 4: Results

Inter/Intra-Examiner Reliability
Tip UR 7 UR 6 UR 5 UR 4 UR 3 UR 2 UR 1
ICC T/T 0.943 0.936 0.974 0.964 0.944 0.855 0.851
ICC D/D 0.981 0.947 0.571 0.956 0.961 0.926 0.857
ICC D/T 0.950 0.844 0.969 0.989 0.951 0.871 0.873
ICC N/D 0.991 0.902 0.964 0.905 0.790 0.974 0.937
Average 0.966 0.907 0.870 0.954 0.912 0.907 0.880

Table 1 Inter/intra-examiner correlation coefficient (ICC) of the upper right tip (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

Tip UL 1 UL 2 UL 3 UL 4 UL 5 UL 6 UL 7
ICC T/T 0.865 0.932 0.983 0.982 0.949 0.838 0.972
ICC D/D 0.878 0.905 0.911 0.905 0.878 0.956 0.977
ICC D/T 0.939 0.962 0.926 0.955 0.933 0.849 0.956
ICC N/D 0.901 0.913 0.912 0.953 0.973 0.941 0.983
Average 0.896 0.928 0.933 0.949 0.933 0.896 0.972

Table 2 Inter/intra-examiner correlation coefficient (ICC) of the upper left tip (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

Tip LL 7 LL 6 LL 5 LL 4 LL 3 LL 2 LL 1
ICC T/T 0.940 0.905 0.983 0.939 0.996 0.959 0.937
ICC D/D 0.976 0.959 0.939 0.971 0.836 0.822 0.900
ICC D/T 0.926 0.789 0.968 0.981 0.864 0.891 0.946
ICC N/D 0.977 0.772 0.917 0.938 0.962 0.808 0.835
Average 0.955 0.856 0.952 0.957 0.915 0.870 0.905

Table 3 Inter/intra-examiner correlation coefficient (ICC) of the lower left tip (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

43

Tip LR 1 LR 2 LR 3 LR 4 LR 5 LR 6 LR 7
ICC T/T 0.828 0.949 0.964 0.916 0.986 0.969 0.969
ICC D/D 0.846 0.922 0.926 0.988 0.977 0.880 0.976
ICC D/T 0.841 0.826 0.920 0.925 0.839 0.943 0.981
ICC N/D 0.969 0.946 0.970 0.948 0.956 0.610 0.954
Average 0.871 0.911 0.945 0.944 0.940 0.851 0.970

Table 4 Inter/intra-examiner correlation coefficient (ICC) of the lower right tip (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

Tip Mean Median Max Min SD
ICC T/T 0.937 0.947 0.966 0.828 0.048
ICC D/D 0.912 0.926 0.988 0.571 0.082
ICC D/T 0.915 0.930 0.989 0.789 0.055
ICC N/D 0.914 0.944 0.991 0.610 0.083
Average 0.919 0.921 0.972 0.851 0.036

Table 5 Mean, median, range and standard deviation of the ICC tip and the averages.

Torque UR 7 UR 6 UR 5 UR 4 UR 3 UR 2 UR 1
ICC T/T 0.926 0.870 0.925 0.963 0.980 0.970 0.977
ICC D/D 0.954 0.955 0.976 0.952 0.993 0.967 0.969
ICC D/T 0.953 0.929 0.989 0.943 0.973 0.982 0.983
ICC N/D 0.961 0.941 0.964 0.982 0.984 0.966 0.992
Average 0.949 0.924 0.964 0.960 0.983 0.971 0.980

Table 6 Inter/intra-examiner correlation coefficient (ICC) of the upper right torque (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

44
Torque UL 1 UL 2 UL 3 UL 4 UL 5 UL 6 UL 7
ICC T/T 0.986 0.977 0.972 0.980 0.925 0.800 0.881
ICC D/D 0.984 0.969 0.923 0.904 0.945 0.898 0.967
ICC D/T 0.978 0.981 0.976 0.961 0.969 0.889 0.885
ICC N/D 0.993 0.982 0.984 0.969 0.954 0.888 0.979
Average 0.985 0.977 0.964 0.954 0.948 0.869 0.928

Table 7 Inter/intra-examiner correlation coefficient (ICC) of the upper left torque (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

Torque LL 7 LL 6 LL 5 LL 4 LL 3 LL 2 LL 1
ICC T/T 0.957 0.974 0.974 0.925 0.980 0.987 0.981
ICC D/D 0.958 0.844 0.950 0.899 0.975 0.980 0.986
ICC D/T 0.961 0.968 0.961 0.942 0.968 0.965 0.979
ICC N/D 0.921 0.883 0.927 0.916 0.960 0.987 0.985
Average 0.949 0.917 0.953 0.921 0.971 0.980 0.983

Table 8 Inter/intra-examiner correlation coefficient (ICC) of the lower left torque (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

Torque LR 1 LR 2 LR 3 LR 4 LR 5 LR 6 LR 7
ICC T/T 0.993 0.983 0.994 0.951 0.960 0.974 0.980
ICC D/D 0.987 0.980 0.976 0.973 0.915 0.947 0.927
ICC D/T 0.969 0.980 0.953 0.982 0.950 0.976 0.966
ICC N/D 0.975 0.978 0.961 0.973 0.937 0.962 0.917
Average 0.981 0.980 0.971 0.970 0.941 0.965 0.948

Table 9 Inter/intra-examiner correlation coefficient (ICC) of the lower right torque (Drs.
Hongsheng Tong (T), Donald Kwon (D), Nicole Sakai (N)).

45
Torque Mean Median Max Min SD
ICC T/T 0.955 0.974 0.994 0.800 0.044
ICC D/D 0.952 0.963 0.993 0.844 0.035
ICC D/T 0.961 0.968 0.989 0.885 0.026
ICC N/D 0.958 0.965 0.993 0.883 0.031
Average 0.957 0.964 0.985 0.869 0.027

Table 10 Mean, median, range and standard deviation of the ICC torque and the
averages.

The inter- and intra-examiner correlation coefficients (ICC) show the reproducibility of
the methodology. All of the values were taken from 10 cases that were digitized twice at
different time points. The intra-examiner correlation was done by Dr. Tong (T/T) and Dr.
Kwon (D/D) at two separate times. The inter-examiner correlation was done between Dr.
Kwon and Dr. Tong (D/T) and Dr. Sakai and Dr. Kwon (N/D) at two separate times. The
ICC values were compared for both the tip (Tables 1-4) and the torque (Tables 6-9) of
all the teeth. While the mean values for the intra and inter-examiner correlation
coefficients show a high degree of consistency (0.919 for the average of all the mean
values for tip, 0.957 for the average of all the mean values for torque) (Tables 5 & 10),
individually the results showed some variation. For the tip, the canines, 1
st
premolars, and
the second molars consistently had the highest ICC averages. The centrals, laterals, and
the first molars consistently had the lowest ICC averages. For the torque, the centrals and
laterals had the highest ICC averages, while the 1
st
molars had the lowest ICC average.

46
Left and Right Comparison
Tip Upper Left Upper Right Lower Left Lower Right
Central 5.79 6.04 0.58 0.18
Lateral 6.92 7.02 -0.53 -0.09
Canine 10.79 11.99 4.24 4.70
1
st
Premolar 7.20 8.19 4.89 5.00
2
nd
Premolar 5.01 4.41 8.26 7.97
1
st
Molar 1.59 1.79 9.45 9.82
2
nd
Molar -6.09 -6.86 17.77 17.20

Table 11 The mean values for the upper and lower tip of the left and right side.

Torque Upper Left Upper Right Lower Left Lower Right
Central 33.96 33.04 26.34 26.54
Lateral 32.70 32.02 25.35 25.36
Canine 21.18 20.33 18.82 19.71
1
st
Premolar 6.13 5.69 7.56 8.01
2
nd
Premolar 2.21 2.41 -1.59 -0.24
1
st
Molar 4.96 4.51 -9.02 -7.99
2
nd
Molar 10.90 10.88 -12.80 -12.09

Table 12 The mean values for the upper and lower torque of the left and right side.

47

Graph 1 Comparison of upper tip. The star indicates significant differences.

Graph 2 Comparison of lower tip.

-10
-5
0
5
10
15
1 2 3 4 5 6 7
Upper Tip
LEFT RIGHT
-5
0
5
10
15
20
1 2 3 4 5 6 7
Lower Tip
LEFT RIGHT
48

Graph 3 Comparison of upper torque. The star indicates significant differences.

Graph 4 Comparison of lower torque. The star indicates significant differences.

In order to examine the symmetry of the “near normal” cases, the measurements of both
the left and right tip and torque were plotted using line graphs (Tables 11-12). These
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7
Upper Torque
LEFT RIGHT
-15
-10
-5
0
5
10
15
20
25
30
1 2 3 4 5 6 7
Lower Torque
LEFT RIGHT
49
graphs show the trend of the tip and torque change from tooth to tooth. The upper teeth
tip increased for the first three teeth and then decreased after that (Graph 1). The upper
teeth torque decreased until the last three teeth and then gradually began to increase
again, following a smooth curve (Graph 3). The lower teeth tip increased "in steps" from
the lateral incisor to the second molar (Graph 2). Lastly, the lower teeth torque gradually
decreased from the central incisor to the second molar (Graph 4). What we can see from
the graphs is that the left side is almost identical to the right side with only a few
exceptions.

Paired T-Test

Table 13 Paired T-Test comparing all the upper right tips to the upper left tips and the
lower right tips to the lower left tips of the 76 “near normal” cases. * indicates non-
normal data (Wilcoxon Signed Rank test).

Paired T-Test Upper Tip Lower Tip
Central 0.5296 0.3761
Lateral 0.8165 0.2918
Canine 0.0009 0.2113
1
st
Premolar 0.0247 0.7798
2
nd
Premolar 0.1549 0.4262
1
st
Molar * 0.6790 0.2333
2
nd
Molar 0.0389 0.1567
50
Paired T-Test Upper Torque Lower Torque
Central 0.0018 * 0.2720
Lateral 0.0516 * 0.8750
Canine 0.0405 0.0150
1
st
Premolar 0.4063 0.2267
2
nd
Premolar 0.7071 0.0016
1
st
Molar 0.3533 0.0322
2
nd
Molar 0.8704 0.2084

Table 14 Paired T-Test comparing all the upper right torques to the upper left torques
and the lower right torques to the lower left torques of the 76 “near normal” cases. *
indicates non-normal data (Wilcoxon Signed Rank test).

A paired T-Test was done for each tooth (central, lateral, etc.) comparing the right and
the left side. If the data was not normal (*) a Wilcoxon Signed Rank test was done to
compare the right and left side. A total of 14 pairs of t-tests for the tip and 14 pairs of t-
tests for the torque were done for the upper and lower teeth (Tables 13-14). Because
there are multiple comparisons, the p value or significance should be adjusted based on
the Bonferroni formula (dividing the p value by the total number of pairs of teeth), which
in this case is 0.05/14 = 0.00357. If the p value for any pair comparison is < 0.00357,
they are significantly different. From our data the upper canine tip (p = 0.0009), the upper
central torque (p = 0.0018) and the lower 2
nd
premolar torque (p = 0.0016) are the only
values that fall below this p value, indicated by the stars in the graphs (Graphs 1-4).

51
Ideal Tip and Torque
Final Upper Tip Lower Tip Upper Torque Lower Torque
Central 5.92 0.38 33.50 26.44
Lateral 6.97 -0.31 32.36 25.36
Canine 11.39 4.47 20.76 19.27
1
st
Premolar 7.70 4.95 5.91 7.79
2
nd
Premolar 4.71 8.12 2.31 -0.92
1
st
Molar 1.69 9.64 4.74 -8.51
2
nd
Molar -6.48 17.49 10.89 -12.45

Table 15 Averaged tip and torque of the left and right sides.

After comparing the tip and torque of the right and left side it was determined that most
of the differences were statistically insignificant. Clinically, most of the differences are
within 1 degree, with a few < 1.5
o
. Moreover, symmetry is expected when comparing the
two sides; therefore, we averaged the two values to determine the optimal tip and torque
for all teeth (Table 15).

Interdental Tip and Torque

Central Lateral Canine 1
st
Pre 2
nd
Pre 1
st
Molar 2
nd
Molar
Left 173.63 173.60 164.97 167.91 166.73 168.97 168.32
Right 173.78 173.92 163.30 166.80 167.62 168.39 169.67

Table 16 The interdental tip of the left and right side.

52

Figure 27 Measuring the interdental tip utilizing the long axis of each tooth. 180
o
–
(upper tip + lower tip) = interdental tip, which is the angle that is shown with the thick
yellow arc.

Graph 5 Interdental tip angle of the left and right side.
100
120
140
160
180
200
1 2 3 4 5 6 7
Interdental Tip
LEFT RIGHT
53

Central Lateral Canine 1
st
Pre 2
nd
Pre 1
st
Molar 2
nd
Molar
Left 119.70 121.95 140.00 166.31 179.38 184.06 181.90
Right 120.43 122.62 139.96 166.31 177.83 183.48 181.21

Table 17 The interdental torque of the left and right side.

Figure 28 Measuring the interdental torque utilizing the long axis of each tooth. 180
o
–
(upper torque + lower torque) = interdental torque, which is the angle that is shown with
the thick yellow arc.

54

Graph 6 Interdental torque angle of the left and right side.

The interdental tip angles were calculated by adding the upper and lower tip of each
central, lateral, etc. and subtracting that sum from 180 degrees (180 - (Upper + Lower
Tip)) (Table 16). All of the interdental tip angles fell within a 10 degree range from one
another (Graph 5). The interdental torque angles were calculated by adding the torques
of the respective teeth and subtracting that sum from 180 degrees (180 - (Upper + Lower
Torque)) (Table 17). The interdental torque angles increased from the central incisors all
the way to the 2
nd
molars, reaching close to 180 degrees for the second premolar, 1
st

molar, and 2
nd
molar (Graph 6).

100
120
140
160
180
200
1 2 3 4 5 6 7
Interdental Torque
LEFT RIGHT
55
Gender Studies
Male (N=22) Upper Tip Lower Tip Upper Torque Lower Torque
Central 5.91 0.49 35.04 27.28
Lateral 7.39 -0.16 33.79 26.70
Canine 12.64 5.59 21.30 20.23
1
st
Premolar 8.47 5.50 7.60 10.19
2
nd
Premolar 5.37 7.55 3.54 1.28
1
st
Molar 1.86 8.21 4.47 -5.79
2
nd
Molar -7.00 14.17 11.58 -10.39

Table 18 Male tip and torque.

Female (N=54) Upper Tip Lower Tip Upper Torque Lower Torque
Central 5.91 0.34 32.87 26.09
Lateral 6.80 -0.97 31.77 24.81
Canine 10.89 4.02 20.53 18.87
1
st
Premolar 7.38 4.72 5.22 6.80
2
nd
Premolar 4.44 8.34 1.81 -1.81
1
st
Molar 1.61 10.21 4.84 -9.61
2
nd
Molar -6.01 18.95 10.48 -13.25

Table 19 Female tip and torque.

56
Independent T-Test Upper Tip Lower Tip Upper Torque Lower Torque
Central 0.997 0.714 0.232 0.450
Lateral 0.509 0.323 0.132 * 0.194
Canine 0.030 * 0.051 * 0.429 0.299
1
st
Premolar 0.304 0.455 * 0.045 0.002
2
nd
Premolar 0.341 0.352 0.111 * 0.001
1
st
Molar * 0.492 0.009 0.696 0.000
2
nd
Molar 0.599 0.000 0.409 0.049

Table 20 Independent T-Test comparing male and female tip and torque. * indicates non-
normal data (Mann-Whitney test). After Bonferonni correction – 0.05/14 = 0.00357 only
the L7 tip and the L4, L5, and L6 torque values are significant.

Graph 7 Comparison of male and female upper tip.

-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Upper Tip
MALE FEMALE
57

Graph 8 Comparison of male and female lower tip.

Graph 9 Comparison of male and female upper torque.

-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Lower Tip
MALE FEMALE
*
-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Upper Torque
MALE FEMALE
58

Graph 10 Comparison of male and female lower torque.

Of the 76 cases that were considered “near normal”, 54 were female (71%) and 22 were
male (29%). For the gender study, the left and right side data are combined. The data
showed only minor variations when comparing the male and female tip and torque values
(Tables 18-19). Since the male and female sample are independent samples we ran a
independent T-Test (the Mann-Whitney test was for non-normal data) to determine if
there were any statistically significant differences between the mean values for the male
and female tip and torque (Table 20). Just as was seen when comparing the left and right
tip and torque of the upper and lower dentition, the pattern of the tip and torque of the
male and female cases followed the same trends. The upper teeth tip increased initially
and then decreased after that (Graph 7). The upper teeth torque decreased initially and
then gradually began to increase again (Graph 9). The lower teeth tip increased
incrementally from the lateral incisor to the second molar with the females having a
-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Lower Torque
MALE FEMALE
* *
*
*
59
larger tip in the 2
nd
molars (difference of 2.4
o
) (Graph 8). Finally, the lower teeth torque
showed a gradual decrease from the central incisor to the second molar, like the upper
torque, the male values were all higher than the female values, significantly so from the
1
st
premolar to the 1
st
molar (difference of 3.4
o
, 3.1
o
and 3.8
o
, respectively) (Graph 10).

Ethnic Comparison
Ethnicity Number
Asian 8
Black 15
Hispanic 33
Middle Eastern 7
White 13

Table 21 Number of patients in each group.

Upper Tip Asian Black Hispanic Middle Eastern White
Central 7.77 8.05 5.24 4.65 4.70
Lateral 9.39 8.59 6.19 4.32 7.03
Canine 11.97 12.01 11.43 10.63 10.66
1
st
Premolar 9.61 8.44 7.38 8.34 6.12
2
nd
Premolar 5.00 5.76 4.95 2.29 4.03
1
st
Molar 3.01 2.42 1.59 0.70 0.80
2
nd
Molar -3.78 -6.49 -6.29 -8.00 -7.01

Table 22 Average upper tip of each ethnicity.

60
Lower Tip Asian Black Hispanic Middle Eastern White
Central 0.61 0.59 0.03 0.15 1.00
Lateral -0.49 -0.84 -1.33 -0.83 0.80
Canine 4.61 4.59 3.82 5.52 5.33
1
st
Premolar 7.37 4.87 4.39 5.41 4.71
2
nd
Premolar 11.14 7.72 8.07 7.96 6.88
1
st
Molar 9.13 9.02 10.24 9.06 9.40
2
nd
Molar 14.63 16.54 18.84 18.74 16.12

Table 23 Average lower tip of each ethnicity.

Upper Torque Asian Black Hispanic Middle Eastern White
Central 37.60 38.32 32.65 30.96 28.93
Lateral 32.98 34.70 32.95 31.58 28.20
Canine 20.74 21.96 21.92 19.27 17.21
1
st
Premolar 6.86 7.83 5.73 4.85 4.13
2
nd
Premolar 2.83 3.47 2.24 1.20 1.42
1
st
Molar 5.82 5.77 4.33 3.11 4.77
2
nd
Molar 13.07 11.53 9.82 7.78 13.15

Table 24 Average upper torque of each ethnicity.

61
Lower Torque Asian Black Hispanic Middle Eastern White
Central 23.84 28.21 25.60 28.08 27.24
Lateral 24.67 28.36 24.49 26.35 23.99
Canine 20.00 22.23 18.28 19.31 17.88
1
st
Premolar 6.02 9.50 7.43 8.53 7.38
2
nd
Premolar -0.98 0.23 -1.43 -1.05 -0.81
1
st
Molar -8.12 -6.25 -9.68 -7.27 -9.04
2
nd
Molar -14.01 -9.79 -14.30 -10.03 -10.44

Table 25 Average lower torque of each ethnicity.

ANOVA Upper Tip Lower Tip Upper Torque Lower Torque
Central 0.003 0.425 0.002 0.415
Lateral 0.009 0.398 0.016 * 0.286
Canine 0.765 0.694 0.023 0.118
1
st
Premolar 0.361 0.485 0.281 0.425
2
nd
Premolar 0.339 0.066 0.697 0.704
1
st
Molar 0.678 0.673 0.485 * 0.170
2
nd
Molar * 0.722 * 0.136 0.116 * 0.009

Table 26 One-way ANOVA comparing the tip and torque for all ethnicities. * indicates
non-normal data (Kruskal-Wallis H test). After the Bonferroni correction only the U1 tip
and torque are significant.

62

Graph 11 Comparison of upper tip of each ethnicity.

Graph 12 Comparison of lower tip of each ethnicity.

-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Upper Tip
Asian Black Hispanic Mid Estern White
-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Lower Tip
Asian Black Hispanic Mid Estern White
63

Graph 13 Comparison of upper torque of each ethnicity.

Graph 14 Comparison of lower torque of each ethnicity.

The ethnic diversity of our patient pool was broken down into 8 Asian, 15 African
American, 33 Hispanic, 7 Middle Eastern, and 13 Caucasian patients (Table 21). We also
-10
0
10
20
30
40
50
1 2 3 4 5 6 7
Upper Torque
Asian Black Hispanic Mid Estern White
-20
-10
0
10
20
30
40
1 2 3 4 5 6 7
Lower Torque
Asian Black Hispanic Mid Estern White
64
combined the left and right side data before comparing the different ethnicities. The
values for the upper tip for each ethnicity followed the same pattern of increase through
the anterior teeth, peaking at the canine, and decreasing thereafter (Table 22). The values
of the lower tip decreased from the central to the lateral and progressively increased
through the remaining dentition (Table 23). The values for the upper torque decreased
from the anterior teeth to the bicuspids and increased again through the molars (Table
24). The torque of the lower teeth showed a general decrease in value from the central
incisor to the 2
nd
molar (Table 25). A one-way ANOVA with Bonferroni post hoc for
multiple comparisons was run to determine if any of the differences in the mean values
were statistically significant (Table 26). If the data was not normal to begin with a
Kruskal-Wallis H non-parametric test was used to compare the different ethnicities. We
found that the African Americans and Caucasians had significant differences in the upper
central tip and in the upper central torque. While African Americans and Hispanics had
significant differences in just the upper central tip (Graphs 11-14).

65
Chapter 5: Discussion

The purpose of this study is to establish the optimal standard for the mesio-distal
angulation and bucco-lingual inclination for each whole tooth including the root in three-
dimensional space by studying 3D CBCT x-ray images of the dento- and maxillofacial
structures of people who have near normal occlusions. We hope that orthodontists will be
able to use this as a guide to achieve the optimal position for each whole tooth.

As we know, using straight-wire techniques, orthodontic finishes at the end of
orthodontic treatment depend heavily on the correct placement of brackets. This relies on
the proper identification of the FACC and the FA points. Traditionally the only way for
orthodontists to identify the facial axis of clinical crowns was to utilize study models,
panoramic x-rays, or clinically. However, traditional x-rays show distortions when
projected on a two-dimensional surface and stone models, although three-dimensional, do
not show the roots of teeth. Clinically, almost all orthodontists accept the fact that it is
sometimes impossible or impractical to locate the facial axis of clinical crowns (FACC)
and the FA point. As we established before, excessive wear of the surface structure
makes it hard to identify the central developmental lobe; the buccal surface of some teeth
having a round shape rather than spear or shovel shape, making it hard to visualize the
long axis especially if the tooth is angulated; and the crowns partially being covered by
the gums all contribute to the difficulty in identifying the FACC. The advantage of
utilizing 3D technology over traditional 2D panoramic and cephalometric x-rays is that it
66
allows us to visualize each tooth in the proper orientation without any distortions. It also
enables us to see the entire tooth (crown and root) in three different planes.

However, even with the ability to visualize the whole tooth in three different planes of
space, the methodology is not without errors. Since we manually digitize the center of the
crown and the root, human error is always a factor. By digitizing each point from the
mesio-distal, bucco-lingual, and transverse planes for each tooth and making sure that
each point was in the center of the crown or root in all three planes, we minimized the
amount of error we had in identifying the points (Figure 12). Compared to 2D x-rays,
where the center of the crown and root can only be identified in one plane, 3D imaging
has allowed us to more accurately visualize each tooth. In addition, we defined the
functional occlusal plane to be a plane that intersected the incisor overbite and the molar
overbite at the buccal groove of the first molars. Rather than relying on the cusp tips
which can be worn out through attrition or restorations, there was less chance that the
buccal groove was altered. By relying on a clearly defined set of guidelines and utilizing
the advantages that 3D technology provides we hope to minimize the amount of human
error.

Even with the advanced technology of NewTom three-dimensional imaging, the quality
of the images depends on the cooperation of the patient. The NewTom has one of the
longest scan times (17 seconds) and any movement of the patient, however slight it may
be, during the scan acquisition stage can cause an orientation shift in the base projections.
67
During reconstruction, the software will combine the series of base projections, including
the distorted base projections, leading to an inaccurate and blurry 3D volumetric image.
In order to obtain a higher quality 3D volumetric image, micro-motions of the head must
be kept to a minimum.

Due to fear of radiation exposure, getting NewTom 3D x-rays from people who did not
need orthodontics was nearly impossible. We had to use the existing patient pool that we
had at the USC Orthodontic clinic to meet the requirements that we had determined
would qualify for “near normal”. As far as 3D imaging involving radiation, this may be
the best we can do for now until totally non-invasive new 3D imaging technology
becomes available in the future. We hope from this “near normal” sample, we may derive
tip and torque features that would apply to the majority of orthodontic patients.

In order to ensure that our methodology could be repeated at different times by the same
examiner or at different times by different examiners, we had 10 cases digitized by Dr.
Tong at two different time points, 10 cases digitized by Dr. Kwon at two different time
points, 10 cases that were digitized by Dr. Tong and Dr. Kwon at two separate time
points, and 10 cases that were digitized by Dr. Sakai and Dr. Kwon at two separate time
points. Although there exist some discrepancy in the results between individual teeth,
overall the results showed a high degree of correlation between all examiners at differing
times points. We obtained an average of 0.919 for all the mean values for tip (Table 5)
and an average of 0.957 for all the mean values for torque (Table 10). The tip of all the
68
second molars was good, as was for all the first premolars. However, the incisors were
not as consistent and the first molars were inconsistent (most likely due to the curvature
of the roots, making the digitization more prone to user error and interpretation). With the
torque, the centrals and laterals were good and the canines were consistently good, but
the first molars were consistently bad. The difficulty of accurately digitizing all the points
of each tooth was more evident with the tip than the torque because the curvature of the
roots typically curves in a way that affects the mesio-distal measurements more than the
bucco-lingual measurements.
27-30
So while not perfect, the high value of the average of
the means shows that the methodology for determining the points of each tooth has a high
degree of reliability and reproducibility between the same examiner at different time
points or between different examiners at different time points. We were able to show that
our methodology of determining the functional occlusal plane, digitizing the center of the
crown and root, and determining the arch forms was repeatable by multiple examiners
and by the same examiners on the same patients at different times.

By comparing left and right measurements, we have confirmed that the subjects in our
sample have almost complete symmetry as far as tip and torque of each tooth concerned
(Tables 13-14). The upper canine tip, the upper central torque and the lower 2
nd
premolar
torque were the only teeth to be statistically different. However, the differences between
the L and R means for these were 1.2, 0.9, and 1.3 degrees, respectively. Although
significant statistically, these differences are not significant clinically. Overall this result
implies that the method we used in measuring the tip and torque is quite reliable since we
69
measured the two sides independently.
31
That also allowed us to combine the left and
right side data as a way to increase sample size. From a practical point of view,
combining the two sides also makes a lot of sense as symmetry is always expected and
orthodontists almost always use the same design brackets for both sides.

In addition, we were able to determine the optimal tip and torque based on our “near
normal” cases. Similar to Andrew’s study, but looking at the entire tooth not just the
crowns, we measured the ideal tip and torque of all 76 cases in both the mesio-distal and
bucco-lingual dimensions (Table 15). What we found was that the upper tip increased
until the canines and slowly decreased after that. The upper torque started out high with
the centrals and decreased through the bicuspids and then gradually began to increase
again. The lower tip increased incrementally from the lateral incisor to the second molar.
Finally, the lower torque gradually decreased from the central incisor (buccal crown
torque) to the second molar (lingual crown torque). All these patterns are similar to the
findings that Andrew’s had with the exception that we incorporated the root of the tooth
and the true long axis of each tooth drawn through the center of the crown and root in all
three dimensions.

The interdental tip and torque angles were calculated by adding the upper and lower tip
of each opposing tooth and subtracting that sum from 180 degrees (Tables 16-17). All of
the interdental tip angles fell within a 10 degree range from one another (Graph 5). For
these “near normal” cases, none of the interdental tips fell below 160 degrees. The
70
interdental torque angles increased from the central incisors all the way to the 2
nd
molars,
reaching about 180 degrees for the second premolar, 1
st
molar, and 2
nd
molar (Graph 6).
This makes sense from a functional occlusion standpoint, the posterior teeth bear the
most occlusal force and therefore, to pass that force along through the crown and root,
they should be the most upright.

Due to the diversity of our sample size, we were able to compare the differences in the tip
and torque values of male and female patients. Of the 76 cases, 54 were female and 22
were male. Overall the pattern of the tip and torque showed no significant differences
from each other (Graphs 7-10). However, the tip showed that in some teeth, most
significantly the lower second molars, females had greater values. As a whole, the male
torque values were slightly higher than the females in both the upper and lower dentition,
but significantly so in the lower 1
st
and 2
nd
premolars and the lower 1
st
molar (Tables 18-
19). While the values were relatively similar, suggesting that tip and torque may not be
gender specific, studies have shown that sexual dimorphism does exist, especially when it
comes to the size of the teeth.
32-34
With the male teeth generally being larger, it makes
identification of the points for digitization more accurate and thus minimizes the amount
of error, however, because of the larger sample size of female cases, we were able to get
a larger data set and thus were able to average out any large variation or error.

Although our sample size was not large enough to provide us with adequate numbers for
each ethnicity, we were able to obtain a diverse enough sample size to do preliminary
71
comparisons between different ethnicities. The breakdown of the 76 cases came down to:
8 Asian, 15 African American, 33 Hispanic, 7 Middle Eastern, and 13 Caucasian patients.
As we saw before with the gender breakdown, the pattern of the tip and torque for all
ethnicities was similar (Graphs 11-14). However, we found that different ethnic groups
may differ significantly in the upper central tip by as much as 3.4 degrees and may differ
significantly in the upper centrals torque by as much as 9.4 degrees. Both of these are
statistically and clinically significant. Differences in facial profiles among different
ethnic groups have been studied extensively and have been well documented. It appears
that there is a close relationship between different ethnic facial profiles and the upper
central incisor tip and torque, but not so much the tip and torque of any other tooth.
Previous studies have compared the different morphologies of different ethnicities
without finding any significant difference to identify one ethnicity vs. another.
34-35
The
specific differences noted such as the size of the laterals or the marginal ridges did not
have a significant effect on our digitization due to the use of 3D imaging to visualize the
entire tooth rather than just the crown.
36-38
While the differences between each ethnicity
may be insignificant for most teeth (except for the central incisor tip and torque), the
overall pattern indicates that when treating patients of different ethnicities, a
consideration must be made into the amount of tip and torque that we put into our final
treatment. Expecting to treat each patient the same with a straight-wire appliance may be
inadequate because every ethnicity has slightly different normal values for tip and torque.

72
As we continue to expand our knowledge of orthodontic treatment and the technology at
hand advances, we are developing newer and better ways to treat patients. CBCT has
allowed us to visualize teeth in a way that traditional orthodontic records have not
previously allowed. We can see the entire tooth, its position in three-dimensions, rather
than relying on 2D x-rays and images. As we utilize technology more in our treatment
and cater treatment to the individual patients, we can provide greater and more efficient
results. Expanded studies on the different gender characteristics is needed, if there truly is
a difference between males and females, treatment can be further specialized to
accommodate such. In addition, the ethnic comparisons did show differences in tip and
torque between different ethnicities, however, because the sample size was minimal,
further research is definitely needed. This too can be utilized to customize treatment to
optimize results.

Furthermore, by establishing a “norm” for the tip and torque of all teeth, we can set goals
for treatment before braces are even started. Utilizing virtual set-ups, we can place teeth
in their “ideal” positions (tip and torque) and then we can place a straight wire with
brackets attached and adjust the base to match this “ideal” tooth position. The
prescription of the brackets will not matter because we can modify the bases to
compensate for different prescriptions. This would enable us to have a “true” straight
wire technique.

73
Conclusion

1. We have developed a method to measure the tip and torque of a patient’s each whole
tooth, including the root. The validity of the three-dimensional method was confirmed
with high intra/inter-examiner correlation coefficients: 0.919 for the average of all the
mean values for tip, 0.957 for the average of all the mean values for torque.
2. Comparing the left and right side to each other, fairly good symmetry is present in our
76 "near normal" sample, with the exception of the upper canine tip and the upper
central and lower 2
nd
premolar torque.
3. We averaged the left and right side values from the 76 “near normal” patients to
establish the “Norm” for each whole tooth tip and torque.
4. The upper teeth tip increased for the first three teeth (from U1~U3) and then
decreased after that. The upper teeth torque decreased until the last three teeth
(U5~U7) and then gradually began to increase again. The lower teeth tip increased "in
steps" from the lateral incisor to the second molar. The lower teeth torque gradually
decreased from the central incisor to the second molar.
5. We had 54 female (71%) cases and 22 male (29%) cases. The data showed almost no
significant variations when comparing the male and female tip and torque values.
However, almost all male torque values were greater than female torque values.
6. Our sample size broke down into 8 Asian, 15 African American, 33 Hispanic, 7
Middle Eastern, and 13 Caucasian patients. The values for tip and torque followed the
same pattern as the overall ideal tip and torque. The only significant data was that the
74
African Americans and Caucasians had significant differences in the upper central tip
and torque and African Americans and Hispanics had significant variation in the
upper central tip. The data suggested a close relationship between different ethnic
facial profiles and the upper central tip and torque, but not so much for the tip and
torque of any other tooth.
7. Comparison of the interdental tip and torque showed that all the interdental tip angles
fell within a 10 degree range from one another. The interdental torque angles
increased from the central incisors all the way to the 2
nd
molars, reaching close to 180
degrees for the second premolar, 1
st
molar, and 2
nd
molar.
8. From our research we were able to not only find the ideal tip and torque for each
tooth utilizing 3D imaging, we were also able to compare the trends between male
and female and between different ethnicities. We were also able to see the pattern
between the interdental tip and torque of these “near normal” cases. While all of these
studies could use further research, we have established a methodology that can be
utilized for all similar future research.

75
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Abstract (if available)

Abstract The purpose of this study was to determine the ideal standard for the mesio-distal angulation (tip) and bucco-lingual inclination (torque) for each tooth (crown and root) in three-dimensional space utilizing CBCT. After determining a set of inclusion and exclusion criteria, 76 “near normal” cases were chosen and measured. To determine the reliability of our methodology we had 10 cases digitized by Dr. Tong and Dr. Kwon at two different time points and 10 cases digitized by Dr. Tong and Dr. Sakai at one time point and Dr. Kwon at another time point. The inter/intra-examiner correlation coefficients were 0.919 for the average of all the mean values for tip and 0.957 for the average of all the mean values for torque. We tested for symmetry of each case by comparing the left side to the right side using a paired T-Test. From our data the upper canine tip, the upper central torque and the lower 2nd premolar torque are the only values that fall below the p value (0.00357). After determining that there is near perfect symmetry we took an average of the left and right side to come up with one value for the ideal tip and torque for every tooth. In addition, we also were able to compare the differences in the tip and torque between male (n=22) and females (n=54) and between various ethnicities. While all genders and ethnicities follow the same trend there were a few teeth that had statistically significant differences in the tip or torque. Lastly, we also calculated the interdental tip (180o – (upper tip + lower tip)) and torque (180o – (upper torque + lower torque)). All the interdental tip angles fell within a 10 degree range of each other while the interdental torque angles increased from the central incisors all the way to the 2nd molars, reaching close to 180 degrees.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Kwon, Donald Taejoon (author)

Core Title Proper mesio-distal angulation and bucco-lingual inclination of the whole tooth in three-dimensional space -- a standard for orthodontic patients

School School of Dentistry

Degree Master of Science

Degree Program Craniofacial Biology

Degree Conferral Date 2011-05

Publication Date 03/28/2011

Defense Date 03/10/2011

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,orthodontics,tip,torque

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Paine, Michael L. (committee chair), Enciso, Reyes (committee member), Moon, Holly (committee member), Sameshima, Glenn T. (committee member)

Creator Email donaldkw@usc.edu,kwon.donald@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3699

Unique identifier UC163695

Identifier etd-Kwon-4424 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-441142 (legacy record id),usctheses-m3699 (legacy record id)

Legacy Identifier etd-Kwon-4424.pdf

Dmrecord 441142

Document Type Thesis

Rights Kwon, Donald

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu