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The mesiodistal angulation and faciolingual inclination of each whole tooth in three dimensional space post non-extraction orthodontic treatment

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The mesiodistal angulation and faciolingual inclination of each whole tooth in three dimensional space post non-extraction orthodontic treatment

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THE MESIODISTAL ANGULATION AND FACIOLINGUAL INCLINATION OF EACH
WHOLE TOOTH IN THREE DIMENSIONAL SPACE POST NON-EXTRACTION
ORTHODONTIC TREATMENT
By
Thao Nguyen

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 2013

Copyright 2013 Thao Nguyen

2

Acknowledgements
I would like to give special thanks to Dr. Hongsheng Tong. His knowledge, patience, and
guidance have helped me to complete this research project. I would also like to thank Dr.
Enciso for her time and effort with the statistical analyses.

3

Table of Contents
Acknowledgements 2

List of Tables 4

List of Figures 5

List of Graphs 6

Abstract 7

Chapter 1: Background 9
Non-Extraction Treatment 22
Cone-Beam Computed Tomography (CBCT) 23
Advantages of CBCT 25
Radiation Dose 26

Chapter 2: Research Objective 27

Chapter 3: Materials and Methods 28
Case Selection Criteria 28
Global Three-Dimensional Coordinate Systems 30
Tooth-Specific 3D System for Locating Crown and Root Centers 31
Tooth-Specific 3D System for Mesiodistal Angulation and
Faciolingual Inclination Measurements 34
Measuring Mesiodistal Angulation and Faciolingual Inclination 34
Arch Form 35
Reliability of Measurements 36
Statistics 37

Chapter 4: Results 38
Intra-Examiner Reliability 38
Normality Tests 39
Comparison of the Left and Right Side of the Arches 42
Paired T-test of Pre- and Post-Treatment 45

Chapter 5: Discussion 49
Conclusion 55
References 56

4

List of Tables
Table 1: Andrews Bracket Prescription 11
Table 2: ICC of the Mesiodistal Angulation of Each Tooth 38
Table 3: ICC of the Faciolingual Inclination of Each Tooth 38
Table 4: Normality Test for Pre-Treatment Values 40
Table 5: Normality Test for Post-Treatment Values 41
Table 6: Comparison of the Left and Right Side of the Arches Pre-Treatment 42
Table 7: Comparison of the Left and Right Side of the Arches Post-Treatment 43
Table 8: Results of Paired T-Test Comparing Pre- and Post-Treatment Values 44

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List of Figures
Figure 1: Crown Angulation (Tip) 9
Figure 2: Crown Inclination (Torque) 10
Figure 3: Example of Improper Occlusion 10
Figure 4: FACC and FA 12
Figure 5: Example of Indirect Bonding Technique 15
Figure 6: OrthoCAD 16
Figure 7: Wire-Bending Robot 17
Figure 8: Insignia 19
Figure 9: CBCT vs. medical CT 24
Figure 10: Global Three-Dimensional Coordinate System 30
Figure 11: Digitization of the Center of a Crown 32
Figure 12: Digitization of the Center of a Root 32
Figure 13: All Crown and Root Points Digitized 33
Figure 14: Mesiodistal Angulation and Faciolingual Inclination of Each Tooth 35
Figure 15: Arch Form 36
Figure 16: Mean Angulations of Teeth Before and After Orthodontic Treatment 46

6

List of Graphs
Graph 1: Results of the Study of Tong et al. (2012) 21

7

Abstract
Background: In a recent study by Tong et al. (2012), 76 subjects with near-normal
occlusion, who were never orthodontically treated, were studied using CBCT to measure
the mesiodistal angulation and faciolingual inclination of each whole tooth (crown and
root) in 3-dimensional space. The study provided a standard for positioning each whole
tooth properly in the arches.
Purpose: In this study, a subset of the 76 subjects was studied after they were
orthodontically treated with non-extraction treatment. The purpose of this study is to
determine the changes in mesiodistal angulation and faciolingual inclination after
orthodontic treatment was rendered.
Methods: Of the 76 patients from the previous study, 24 of them also had CBCT records
taken at the completion of the non-extraction orthodontic treatment. Their final CBCT
records were digitized using the custom University of Southern California root vector
analysis software program. Paired t-tests were used to compare pre- and post-treatment
values for mesiodistal angulation and faciolingual inclination.
Results: Results of the paired t-tests showed that there was a statistically significant
difference for the mesiodistal angulation value of lower first molars and faciolingual
inclination values of upper second premolars and lower first molars after orthodontic
treatment was rendered. The range of change was larger and pattern of change was more
variable from tooth to tooth in mesiodistal angulation than in faciolingual inclination
measurement.
Conclusion: The mesiodistal angulation and faciolingual inclination of each tooth was
maintained throughout orthodontic treatment, except upper second premolars and lower
8

first molars. This may be due to difficulty of determining proper band position for lower
first molars and poor visibility for bracket position of upper second premolars. Bracket
position may affect mesiodistal angulation more than faciolingual inclination in the final
outcome of non-extraction treatment. More studies with larger sample sizes are needed.

9

Chapter 1: Background

Despite the many different treatment philosophies and orthodontic appliances that exist
today, orthodontists generally agree that treatment goals for orthodontic patients should
include esthetics, function, and stability. In order to achieve a functional occlusion, teeth
need to be properly oriented in all three planes of space (Ugar and Yukay, 1997). Crown
angulation (tip) and crown inclination (torque) make up two of the six keys of occlusion
described by Andrews (Figure 1 and 2). Andrews (1972, 1976) studied 120
nonorthodontic normal models and measured the faciolingual crown thickness, crown
angulation, and crown inclination of individual teeth. He found that the mesiodistal
angulation and faciolingual inclination of each tooth crown of these normal models fell
within a relatively narrow range to properly affect occlusion and anterior esthetics. For
example, upper and lower anterior teeth need to have sufficient labial crown faciolingual
inclination to allow the posterior teeth to maximally interdigitate. If the anterior teeth are
too upright, it would lead to improper posterior occlusion (Figure 3).

Figure 1. Crown angulation (mesiodistal angulation)—long axis of crown measured from line 90
degrees to occlusal plane.
10

Figure 2. Crown inclination is determined by the resulting angle between a line 90 degrees to the
occlusal plane and a line tangent to the middle of the labial or buccal clinical crown.

Figure 3. Improperly inclined anterior crowns result in all upper contact points being mesial,
leading to improper occlusion

The values from Andrews’s models were averaged and their values incorporated into a
bracket system designed to create the six keys of occlusion (Table 1). By incorporating
these ideal values into his bracket prescription, he produced the first straight-wire
appliance (SWA), which has built-in dimensional and angulation features for each tooth
11

(Andrews, 1976, 1979, 1989). First order bends (in-out) were replaced by customized
bracket base thickness, second order bends (mesiodistal angulation) were incorporated in
the bracket slot, and third order bends (torque) were also built into the bracket base.
Orthodontists now have ideal mesiodistal angulation and faciolingual inclination
angulations built into the bracket prescription to serve the purpose of expressing those
angulations into the patients’ teeth once treatment is completed.

Table 1. Andrews prescription values for mesiodistal angulation and faciolingual inclination.

Even though Andrews’s innovative, pre-adjusted appliance has drastically improved the
quality and efficiency of orthodontic treatment, it does not produce perfect orthodontic
finishes every time. There are many reasons why orthodontic finishing still requires some
compensatory bending of archwires. One major reason is that pre-adjusted brackets
require accurate placement of the bracket on each tooth. For Andrews’s bracket
prescription, it requires that the bracket be placed at the center of the facial surface of the
crown, or the FA point. The FA point is established by first determining the long axis of
the central developmental lobe of the crown of the tooth, i.e. the facial axis of the clinical
crown (FACC). The center point of FACC is the FA point (Figure 4). When a bracket is
12

not placed on the FA point, the tooth cannot accurately express the angulations built into
the bracket. Germane et al.

(2007) found that vertical placement errors of 1 mm can alter
faciolingual inclination values present by up to 10” for the points studied. The
orthodontist will either have to reposition the bracket to the correct center or place bends
in the wire to compensate for the erroneous position of the bracket.

Figure 4. A, The facial axis of clinical crown (FACC). B, The center of the bracket is positioned
over the facial axis point (FA).

Another problem with pre-adjusted appliances is that there is no general consensus on
where brackets should be placed. Angle (1928) recommended that the ideal position to
place the bracket should be at the center of the labial surface of the tooth. Andrews (1976,
1979) proposed that brackets should be placed at the midpoint of the facial axis (FA)
point, as the midpoints of all the clinical crowns are located on the same plane. Ricketts
(1976), and later Kalange (1999), advocated the use of marginal ridges to guide the
vertical positioning of brackets and bands (Armstrong, 2007).

Regardless of which
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method is used for positioning brackets, there seems to be some margin of deviation from
the ideal location and this is before operator error is taken into account. The extent of
error of bracket placement, regardless of which technique is used, demonstrates that
archwire bending adjustments or repositioning of brackets will be necessary to achieve
acceptable treatment results (Armstrong, 2007; Balut, 1992).

In addition to being subject to operator error of determining the correct bracket position,
there are also individual variations in tooth sizes and thicknesses that pre-adjusted
brackets do not account for. Germane et al. (1989) found that facial surface contours are
not consistent among teeth of the same type and the facial surface contours do not vary in
a regular manner from incisal/occlusal to gingival areas. Additionally, this variability
increases progressively between teeth from anterior to posterior in both the upper and
lower arches. In these cases, the orthodontist again will have to place bends in the
archwire to compensate for the individual variations.

Many solutions have come about to remove operator error as a factor during bracket
placement. One solution is to use the indirect bonding technique for positioning brackets
(Joiner, 2010). This technique allows the orthodontist to position the brackets on a plaster
model of the patient’s teeth extraorally. One major advantage of this method is having a
direct view of each tooth from every angle whereas, intraorally, it may be difficult to
visualize the ideal bracket position due to saliva, patient position, mirror angle, etc.
Another advantage of indirect bonding is being able to take more time to position
14

brackets on the plaster model whereas the direct bonding technique is subject to certain
time constraints.

Although the indirect bonding technique uses less clinical chair time, it does require more
laboratory work. One of the techniques involves taking an alginate impression of the
teeth and pouring a stone model. Then brackets are placed precisely as desired on the cast
of the teeth and held in place with a temporary (water-soluble) adhesive (Figure 5). A
transfer tray is formed by adapting a carrier material, usually silicone rubber, over the
working cast and the adapted brackets. The tray is trimmed to remove excess material
from the labial vestibule, but tray material is left extending onto the occlusal and incisal
surfaces of the teeth. The completed tray is removed from the working cast by soaking in
warm water, and the remaining temporary adhesive is washed away from the inner
surface of the brackets with hot water. The adhesive material is applied to the back of
each bracket in the transfer tray. The catalyst portion of a two-paste chemically-cured
resin is placed on the tooth surface, so that mixing occurs when the two components
contact each other when the tray is carried to the mouth. The tray or tray section is carried
to place, and pressed firmly against the teeth. If a light-activated material is the bonding
agent, a translucent transfer tray is needed. After the adhesive has set, the tray material is
gently peeled away from the teeth. Excess bonding material is removed, with a carbide
finishing bur if hardened adhesive is encountered, or with a scaler if unset material is
present. Despite the prospect of improving the accuracy of bracket positioning, this
method of indirect bonding is not used by most orthodontists. This may be due to the fact
that indirect bonding is more technique sensitive and requires more laboratory procedures
15

and time. Furthermore, Koo (1999) reported that although indirect bonding technique
provided better bracket placement with regard to bracket height, no statistically
significant difference was found regarding angulation or mesiodistal position of brackets,
consequently neither direct bonding nor indirect bonding yielded ideal bracket placement.

Figure 5. A, One of the indirect bonding techniques—determine the center of the crown on the
plaster model B, Place the bracket on the plaster model using a temporary adhesive.

With the introduction of computers and imaging software, the indirect bonding technique
has completely evolved and now features computer-assisted treatment planning and
bracket placement which further improves bracket positioning. OrthoCAD (Cadent,
Carlstadt, NJ) generates a 3D model either from a set of alginate impressions and a bite
16

registration or, using the newer technology, from a digital impression process, i.e.
OrthoCAD iTero. Virtual segmentation of the teeth and subsequent virtual setup of teeth
into an ideal occlusion were performed by OrthoCAD lab technicians. Virtual bracket
placement was determined based on the ideal setup using a virtual straight wire as a
guide. With the OrthoCAD software installed locally, the clinician examines the 3D
model setup and makes any desired changes or creates a new setup (Figure 6). Once the
ideal bracket position for each tooth has been determined and approved of virtually,
customized indirect bonding trays are created and then sent to the clinician from the
OrthoCAD lab (Redmond et al., 2004).

Figure 6. A, A 3D model B, A model transmitted to a clinician’s office.
17

Suresmile (OraMetrix, Dallas, Tex) is another system that uses 3-dimensional imaging of
the dentition to select a target treatment plan, including bracket placement, treatment
sequence, and even archwires, unlike OrthoCAD. The indirect bonding trays are
produced by stereolithography and contain individual bracket positions the orthodontist
had virtually determined. Additionally, the archwires are produced with a wire-bending
robot in the sizes and shapes selected by the orthodontist (Figure 7). The company
claims that the precision of the bends with stainless steel wire show less than 1 degree of
error in bends and twists (Mah and Sachdeva, 2011).

Figure 7. A wire-bending robot.

Suresmile also has a slightly different service from the aforementioned approach that
allows orthodontists to treatment plan and bond their brackets first. Once the arches are
relatively leveled and aligned, the orthodontist then scans the patient’s teeth and virtually
treatment plans the rest of the movements that require wire bending. The robotically bent
archwires are then sent to the orthodontist to be used to finish the orthodontic treatment.
18

One of the newest systems is Insignia (Ormco, Orange, Calif.) which claims to be a
completely custom-designed orthodontic treatment for each patient. Starting with a PVS
impression and radiographic information, the patient’s ideal occlusion is constructed
based on the skeletal information and dental landmarks on the tooth objects determined
mathematically, not by lab personnel. After the occlusion has been derived and approved
by the clinician, the software proceeds to reverse engineer the appliance which includes
patient-specific brackets, precision (computer-assisted) bracket placement, and custom
wires (Figure 8).

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Figure 8. A, Insignia individually designed bracket slots B, Custom archwire manufacturing C,
Bracket positioning device.

Despite the improvement for bracket positioning with these newer techniques, one innate
error that they all have in common is that they are using the crowns of the teeth to
determine the long axis of the entire tooth, without including the root or only estimating
the root position. Without knowing where the actual root is, the operator can only, at best,
make an educated guess in determining the long axis of the tooth. In a recent study by
Tong et al. (2012), subjects with near-normal occlusion were studied using CBCT to
measure the mesiodistal angulation and faciolingual inclination of each whole tooth in 3-
dimensional space.

Being able to view the entire tooth, including the root, allowed
20

measurements of tooth inclinations to be more accurate. Comparisons of the mesiodistal
angulation and faciolingual inclination between Andrews’s sample and Tong’s sample (of
Caucasian patients) showed that there are consistent differences in the two samples. This
could be explained by the two different measuring methodologies. It could also indicate
that there may be an improvement in accuracy when measuring mesiodistal angulation
and faciolingual inclination using a three-dimensional model that includes roots of the
teeth versus plaster casts where mesiodistal angulation and faciolingual inclination is
only measured using only the crowns of the teeth.

In Tong’s sample of 76 patients with near-normal occlusion, it was found that the
mesiodistal angulation of central maxillary teeth started at approximately 6°, slightly
increased for the lateral teeth, and ended at about 11° for the maxillary canines. The
mesiodistal angulation of the maxillary premolars was approximately 0° and then
gradually reached -6° for the second molars. The mesiodistal angulation of the
mandibular teeth started at approximately 0° and gradually increased to 17.5° for the
second molars. The maxillary faciolingual inclination was the highest at 33.5° for the
central incisors, gradually decreased to 0° for the maxillary premolars, and again
increased towards the second molars. A similar trend was seen in the mandibular
faciolingual inclination, except the central incisors started at 26.5° (Graph 1).
14

21

Graph 1. Intra-arch fluctuations of mesiodistal angulation and faciolingual inclination (right and
left side average values +/- standard deviations) from the anterior to the posterior teeth in both
arches: A, maxillary teeth mesiodistal angulation. B, mandibular teeth mesiodistal angulation. C,
maxillary teeth faciolingual inclination. D, mandibular teeth faciolingual inclination. *Teeth with
significant differences between the right and the left sides.

In this study, a subset of the 76 near-normal subjects, used in the study of Tong et al.
(2012), was selected and analyzed based on availability of the post-treatment CBCT.
Twenty-four of the near-normal subjects were orthodontically treated with non-extraction
treatment. The purpose of this study is to determine the changes in mesiodistal angulation
and faciolingual inclination when orthodontics is applied to teeth that were in an already
“normal” position. This may allow us to better understand the effect of brackets and
bracket positioning on teeth and whether there is a statistically significant difference
22

when it comes to operator error and bracket prescriptions. Digitization of three-
dimensional imaging, i.e. CBCT, of the pre- and post-treatment records were analyzed
and compared to determine the effect of orthodontic treatment on the mesiodistal
angulation and faciolingual inclination of the treated teeth.

Non-Extraction Treatment
Currently, one of the biggest controversies in the orthodontic specialty is the huge swing
towards non-extraction treatment, in part due to claims from the self-ligation bracket
advocates. In the 1990s, Dwight Damon developed a theory asserting that low friction
and light forces produced more biologically stable results. The Damon system includes
broad archwires and self-ligating brackets that are claimed to lead to biologically friendly
light forces that do not overpower the musculature which allows posterior expansion
similar to the lip bumper effect. However, Vajaria et al. (2011) found that the Damon
system does not maintain the intercanine, interpremolar and intermolar widths as it
claimed to.

Additionally, the mandibular incisors were significantly advanced and
proclined after treatment with the Damon system, contradicting the lip bumper theory of
Damon.

Regardless, extraction rates have decreased from a high of 60-80% during the
1970s to 30% and less currently. O’Connor (1993) found, in a survey, that over half of
more than 800 responding orthodontists had reduced their extraction rate from 37.74% to
29.28% within a period of 5 years during the 1990s.

Other reasons for the preference of
non-extraction treatment include concerns of condylar displacement, narrowed smiles
with dark corners, dished-in profiles with extractions, and suboptimal mandibular growth
(Basciftci et al., 2003).
23

There have been many different bracket prescriptions designed, in part, due to different
treatment needs of non-extraction and extraction treatment. Non-extraction treatment
generally tends to increase the faciolingual inclination of the anterior teeth. Pandis et al.
(2007, 2010) showed that there was an increase in proclination of mandibular incisors in
non-extraction treatment, for both Damon brackets and conventional brackets.

It has been
determined that the soft tissue profile is supported by the incisor position as a positive
correlation between incisor movement and soft tissue changes have been reported
(Talass, 1987).

Therefore, with the increasing popularity of non-extraction treatment among clinicians
and patients, it is imperative to fully understand the effects of non-extraction on the
dentition, especially the faciolingual inclination of the anterior teeth.

Cone-Beam Computed Tomography (CBCT)
Cone beam technology was first introduced in the European market in 1998 and into the
US market in 2001. Until recently, orthodontists were limited to using two-dimensional
radiographs to assess three-dimensional anatomy. Now, with the advent of CBCT, more
diagnostic advantages are available such as: improved image quality, three-dimensional
reconstruction, a 1:1 ratio that allows reliable measurements, the possibility for
craniofacial visualization, and lower radiation doses compared to traditional CT. With the
ability to view the maxillofacial region in 3D, orthodontic diagnosis and treatment
planning may be more thorough.

24

A CBCT machine uses a rotating apparatus to which an x-ray source and detector are
fixed. A divergent pyramidal- or cone-shaped source of ionizing radiation is directed
through the middle of the area of interest onto an area x-ray detector on the opposite side
(Scarfe and Farman, 2008). During a CBCT scan, a scanner rotates around the head to
obtain a series of 2-D images, ranging from 150 to 599 radiographic views (Hatcher,
2010). These multiple 2D projection images are then reconstructed on a computer to for a
3D data set. This differs from a medical CT which uses a fan-shaped x-ray beam in a
helical progression to acquire individual images slices and then stacks the slices to obtain
a 3D representation (Figure 9).

Figure 9. CBCT vs. medical CT.

25

A CBCT image is composed of voxels (a 3D version of the pixel), and each voxel has a
gray-level value based on indirect calculation of the amount of radiation absorbed or
captured by the charge-coupled device and calculated through a filtered-back projection
algorithm (Grauer et al., 2009). CBCT voxels are generally isotropic (i.e. the X, Y, and Z
dimensions are equal), and range from 0.07 to 0.40 mm per side (Hatcher, 2010). Each
voxel is determined transparent or visible by a user-entered critical value for the
threshold filter. The resultant CBCT image is composed of the visible voxels. When
multiple threshold filters are applied, tissues of different densities can be distinguished in
the rendered image, such as soft and hard tissues.

Advantages of CBCT
One of the most important advantages of CBCT is the ability to provide unique images in
3D that intraoral, panoramic, and cephalometric images cannot (Scarfe and Farman,
2008). For example, conventional cephalometrics is limited by a number of factors,
including image magnification, left and right side differences, and head positioning (Mah
et al., 2010). Thus, CBCT has helped in different aspects of orthodontics that 2D images
could not fully provide such as: determining the best TAD location; planning for and
outcomes evaluation of combined orthodontic and surgical treatment; diagnosing and
treatment planning complex cases, such as those involving cleft lip and palate; evaluating
the temporomandibular joint; and locating impacted teeth (Vlijmen et al., 2012).

An important advantage of CBCT is that it scans much faster than the medical CT
because it acquires all the projection images in a single rotation. Its scan time is
26

comparable to a panoramic radiograph. With a rapid scan time, the number of image
artifacts is reduced because subject movement is reduced. Another advantage of CBCT is
the accuracy of the image. It produces images with submillimeter isotropic voxel
resolution ranging from 0.4mm to as low as 0.076 mm (Scarfe and Farman, 2008).
Additionally, in CBCT, the projection is orthogonal, indicating that the x-ray beams are
approximately parallel to one another, and, because the object is very near the sensor,
there is very little magnification effect unlike panoramic or cephalometric radiographs
(Mah, 2004).

Radiation Dose
Although CBCT appears to hold promise for advances in research and clinical
orthodontics, there is some uncertainty and controversy related to its radiation dose,
direct patient benefit and professional guidelines for use (Mah et al., 2010). Orthodontics
involves the use of various radiographic modalities in its diagnostic protocols, ranging
from panoramic radiographs and lateral cephalograms to full mouth radiographic series.
Although studies of radiation dosimetry are not directly comparable, the exposure from
CBCT is within the same range as traditional dental imaging (De Vos et al., 2009). Since
CBCT machines can vary significantly in effective dose, ranging from 29 to 477 mSv,
certain techniques can be applied to help reduce the radiation dose such as: patient
positioning modifications (tilting the chin) and use of additional personal protection
(thyroid collar). Such techniques can reduce the dose by as much as 40% (Ludlow et al.,
2006, 2007).

27

Chapter 2: Research Objective

The purpose of this study is to compare a near-normal group of subjects before and after
orthodontic, non-extraction treatment. We analyzed the effect of orthodontic treatment on
the mesiodistal angulation (tip) and faciolingual inclination (torque) of the treated teeth
using three-dimensional imaging, i.e. CBCT.

28

Chapter 3: Materials and Methods
Case Selection Criteria
Of the 76 near-normal subjects selected in the study by Tong et al. (2012), those who
underwent non-extraction orthodontic treatment and received a final CBCT were
included in this study (n=24). Treatment was rendered between April 2004 to December
2010. The selection criteria for the 76 near-normal subjects used by Tong et al. (2012)
was: 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.

The selection criteria for the photo screening included:
1. Complete dentition of teeth of generally normal shape and size
2. Molar Angle relationship from ≤ a half-step Class II to ≤ a quarter-step Class III
3. Overbite and overjet between 0 and 5 mm
4. Spacing < 6 mm
5. Crowding < 4 mm, and limited to ≤ 3 teeth
6. Rotation < 15°, limited to ≤ 3 teeth
7. Dental crossbite limited to 1 tooth and ≤ 2 mm
8. No apparent facial asymmetry and arch form asymmetry

29

The selection criteria for the radiograph screening included:
1. Panoramic radiograph showing generally parallel roots
2. No missing teeth except the third molars
3. No supernumerary teeth
4. CBCT volumetric image quality from acceptable to good and with teeth in full
occlusion
5. Lateral cephalograms showing ANB between -1° and 6.5°
6. FMA between 14° and 37°
7. Interincisal angle between 110° and 146°
8. No obvious skeletal PA and vertical asymmetry

The CBCT scan for the initial records was taken using a NewTom 3G Volumetric
Scanner. The CBCT scan for the final records was taken using a NewTom 3G or Kodak
Sirona Galileos Comfort. The following conditions were used for the NewTom 3G: tube
voltage (110 kVp), tube current (15 mA), scan time (17 sec), grayscale (12 bit), field of
view (12 in). The patients were placed in a supine position, with the teeth in full
occlusion and the Frankfort horizontal plane perpendicular to the floor. The following
conditions were used for the Kodak Sirona: tube voltage (85 kVp), tube current (7 mA),
scan time (14 sec), grayscale (12 bit), field of view (15 x 15 cm). The patients were
placed in a standing position, with the teeth in full occlusion and the Frankfort horizontal
plane parallel to the floor.

30

Global Three-Dimensional Coordinate Systems
After each patient’s CBCT scan, the digital imaging and communications in medicine
(DICOM) data was imported and the volumetric image was rendered in Dolphin 3-
dimensional program. A global three-dimensional coordinate system is first generated for
the proper orientation of the head and the maxillofacial structure. The three planes were:
sagittal plane, coronal plane, and transverse plane. The sagittal plane divides the left and
right side of the patient using the contact point between the upper central incisors. The
coronal plane is perpendicular to the sagittal plane at the buccal grooves of the right and
left first molars. The transverse plane is the functional occlusal plane, defined as the
plane that intersects the incisal overbite and the molar overbite (at the buccal groove of
the upper first molars) (Figure 10).

Figure 10. Global three-dimensional coordinate system. A, Transverse plane is leveled to bisect
the molar overbite. B, Transverse plane intersects the incisal overbite. C, Coronal plane
intersects at the buccal grooves of the right and left first molars. The sagittal plane is determined
by the contact point between the upper central incisors. D, Proper orientation of the head and
maxillofacial structure once all 3 planes are defined.
31

Tooth-Specific Three-Dimensional System for Locating Crown and
Root Centers

The methodology used for digitization of each subject’s final CBCT was described by
Tong et al. (2012). A three perpendicular plane system specific for each tooth was used
for locating each crown and root center. The 3 coordinates for each crown or root center
were: the anatomic mesiodistal plane, the anatomic faciolingual plane, and the axial plane
(Figure 11 and 12). The mesiodistal angulation and faciolingual inclination of the teeth
were determined by using the true long axis of each tooth, defined as the line that
connects the center of the crown and the center of the root. The true long axis of each
tooth was used because it is easy to define with the imaging software program and is not
affected by the surface contour and structure. In determining the true long axis of each
tooth, the apical third of the root was ignored due to its variable form. Figure 13 shows
the volumetric image after all teeth were digitized, and the lines connecting the crown
and root centers are the long axes of the teeth.

32

Figure 11. Digitization of the center of a crown. The crown is bisected in all three planes.

Figure 12. Digitization of the center of a root. The root is bisected in all three planes.

33

Figure 13. All crown and root points are digitized and a line connecting them is shown
representing the long axis of each tooth.

Tooth-Specific Three-Dimensional System for Mesiodistal Angulation
(Tip) and Faciolingual Inclination (Torque) Measurements

Another tooth-specific three-plane coordinate system was used to study the mesiodistal
angulation and faciolingual 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 mesiodistal plane is also called the arch plane along the curvature of the
dental arch and it changes from tooth to tooth. Each tooth has its own faciolingual plane.

Measuring Mesiodistal Angulation and Faciolingual Inclination
The mesiodistal angulation of the tooth is determined by the angle between the
true long axis on the tooth on the mesiodistal plane to the vertical line formed by
the intersection of the mesiodistal and faciolingual plane (Figure 14). If the root
34

center is distal to the crown center, the measurement is positive. If the root center
is mesial to the crown center, then the measurement is negative.

The faciolingual inclination of the tooth is determined as the angle between the
true long axis of the tooth on the faciolingual plane to the same vertical line
formed by the intersection of the mesiodistal plane and the faciolingual plane
(Figure 14). If the root center is lingual to the crown center, the measurement is
positive. If the root center is facial to the crown center, the measurement is
negative.

The actual mesiodistal angulation and faciolingual inclination measurements were
done automatically by Dolphin using special algorithms. The validity of the
measurements was confirmed as described in Tong et al. (2012) (Figure 14).

35

Figure 14. Measurements of mesiodistal angulation and faciolingual inclination: A, the
mandibular right first premolar’s mesiodistal angulation was measured in the mesiodistal plane,
and it was the angle formed by the projection of its long axis (green line) on the mesiodistal plane
and the line of intersection (red line) between the mesiodistal and the faciolingual planes; B, the
mandibular right first premolar’s faciolingual inclination was measured in the faciolingual plane,
and it was the angle formed by the projection of its long axis (short green line) on the faciolingual
plane and the line of intersection (long green line) between the faciolingual and the mesiodistal
planes; C, transverse plane view showing the perpendicular relationship between the mesiodistal
and faciolingual planes; D, volumetric orthogonal view of the tooth being measured.

Arch Form
Once the maxillary global coordinate system was restored after completion of crown and
root center digitizations, four teeth on the right side of maxillary and mandibular arch
were digitized in the transverse plane view along the facial outline of the dental arch
(Figure 15). The four points were: the mid-incisal tip, the right canine tip, the right
second premolar, and the right second molar. The software program duplicated the right
side half arch to the left side constructing a symmetrical arch form. 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.

36

Figure 15. Determining the arch form of the maxillary arch by placing the points (shown in yellow)
buccal to the mid-incisal, canine, second premolar, and second molar. The left side arch is
duplicated from the right side arch and fits the dental arch well.

Reliability of Measurements
To ensure that the measurements and methodology was reliable and repeatable, all 24
final CBCT were digitized twice. Intra-examiner correlation coefficients (ICC) were
analyzed once all digitizations were obtained to check the reliability of the
measurements. ICC is a general measurement of agreement or consensus, where the
measurements used are assumed to be parametric (continuous and has a normal
distribution). The coefficient represents agreements between two or more repeated
measurements on the same set of subjects.

Statistics
A Kolmogorov-Smirnov normality test was performed first to check for normality in our
pre- and post-treatment data. Then, in order to test the symmetry between each patient’s
left and right side of the arches, a paired t-test was run for the normal data to determine
37

how similar the left and right side values were to each other before and after orthodontic
treatment. The Wilcoxon Signed Rank test was used for the non-parametric data. Because
only one value was statistically different between the left and side of the arches before
and after orthodontic treatment (and the difference was clinically insignificant), the
means of the left and right side were used to compare the pre- and post-treatment values.

Paired t-tests were used to compare the mesiodistal angulation and faciolingual
inclination values of before and after orthodontic treatment, for the data that were
determined by the normality tests to be parametric. If the data was not normal, paired
Wilcoxon Signed Rank test was used.

The Dunn-Bonferroni correction was used to account for the multiple independent tests.
The significance level (p < 0.05) was multiplied by the inverse of the number of
independent tests (12 comparisons for mesiodistal angulation and 12 comparisons for
faciolingual inclination) resulting in a statistical significance of 0.05/12 or p < 0.00412.

All statistics were done utilizing Microsoft Excel and SPSS version 12.0 for Windows.

38

Chapter 4: Results

Intra-Examiner Reliability

MESIODISTAL ANGULATION
UR1 UR2 UR3 UR4 UR5 UR6
0.914 0.861 0.974 0.934 0.943 0.817
UL1 UL2 UL3 UL4 UL5 UL6
0.844 0.916 0.978 0.823 0.883 0.958
LR1 LR2 LR3 LR4 LR5 LR6
0.608 0.867 0.957 0.957 0.931 0.804
LL1 LL2 LL3 LL4 LL5 LL6
0.813 0.888 0.930 0.952 0.858 0.832

Table 2. Intra-examiner correlation coefficient (ICC) for the mesiodistal angulation of each tooth.
R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular); 1,
central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar.

FACIOLINGUAL INCLINATION
UR1 UR2 UR3 UR4 UR5 UR6
0.982 0.957 0.941 0.925 0.925 0.862
UL1 UL2 UL3 UL4 UL5 UL6
0.990 0.964 0.977 0.901 0.922 0.877
LR1 LR2 LR3 LR4 LR5 LR6
0.981 0.987 0.972 0.980 0.956 0.945
LL1 LL2 LL3 LL4 LL5 LL6
0.991 0.983 0.977 0.939 0.949 0.916

Table 3. Intra-examiner correlation coefficient (ICC) for the faciolingual inclination of each tooth.
R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular); 1,
central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar.

The intra-examiner correlation coefficients (ICC) of the 24 patients show that the
measurements and methodology were reliable and reproducible. ICC can be interpreted
as follows: 0-0.2 indicates poor agreement; 0.3-0.4 indicates fair agreement; 0.5-0.6
indicates moderate agreement; 0.7-0.8 indicates strong agreement; and >0.8 indicates
almost perfect agreement. All the values were greater than 0.8 indicating almost perfect
agreement, except for the coefficient of the lower right central incisor (LR1) mesiodistal
39

angulation, 0.608, which indicates moderate agreement (Table 2). The measurement of
faciolingual inclination seems to be more consistent than the measurement of mesiodistal
angulation. The inconsistencies are limited to the upper molars in faciolingual inclination
measurements, whereas it is more spread in mesiodistal angulation measurements.

Normality Tests

The normality tests for the pre-treatment values showed that the non-parametric values
were mesiodistal angulation of upper right second premolar (UR5), lower right second
premolar (LR5), upper left first premolar (UL4), and the two sides mean of the upper
second premolars (U5) (Table 4). As for the pre-treatment faciolingual inclination
values, lower left and lower right central incisors (LL1, LR1), lower left lateral incisor
(LL2), and the two sides mean of the lower central incisors (L1) were non-parametric
(Table 4). Therefore, for those specific values, non-parametric tests were used.

40

Tooth P value Tooth P value Mean (R,L) P value
Mesiodistal Angulation
UR1 0.149 UL1 0.111 U1 0.200
UR2 0.200 UL2 0.200 U2 0.101
UR3 0.200 UL3 0.200 U3 0.200
UR4 0.200 UL4 0.030* U4 0.058
UR5 0.018* UL5 0.200 U5 0.025*
UR6 0.186 UL6 0.123 U6 0.200
LR1 0.200 LL1 0.200 L1 0.200
LR2 0.126 LL2 0.200 L2 0.200
LR3 0.200 LL3 0.200 L3 0.200
LR4 0.200 LL4 0.166 L4 0.200
LR5 0.041* LL5 0.064 L5 0.153
LR6 0.200 LL6 0.200 L6 0.200
Faciolingual Inclination
UR1 0.200 UL1 0.200 U1 0.200
UR2 0.200 UL2 0.196 U2 0.200
UR3 0.200 UL3 0.140 U3 0.200
UR4 0.200 UL4 0.200 U4 0.064
UR5 0.200 UL5 0.200 U5 0.200
UR6 0.149 UL6 0.200 U6 0.200
LR1 0.006* LL1 0.001* L1 0.002*
LR2 0.200 LL2 0.017* L2 0.194
LR3 0.200 LL3 0.200 L3 0.200
LR4 0.114 LL4 0.120 L4 0.152
LR5 0.200 LL5 0.200 L5 0.200
LR6 0.200 LL6 0.200 L6 0.200
Table 4. Normality test for the mesiodistal angulation and faciolingual inclination of teeth
individually and combined (right and left side averaged) before orthodontic treatment. The α is set
at 0.05. R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular);
1, central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar. *
Indicates non-parametric data.

The normality tests for the post-treatment values showed that the mesiodistal angulation
of the upper right central incisor (UR1) and lower left second premolar (LL5) was non-
parametric (Table 5). The faciolingual inclination values that were non-parametric were
the upper right central incisor (UR1), upper right canine (UR3), upper right first premolar
(UR4), upper left lateral incisor (UL2), and the two sides mean of upper canines (U3)
(Table 5).

41

Tooth P value Tooth P value Mean (R,L) P value
Mesiodistal Angulation
UR1 0.022* UL1 0.200 U1 0.200
UR2 0.200 UL2 0.200 U2 0.200
UR3 0.100 UL3 0.200 U3 0.200
UR4 0.200 UL4 0.200 U4 0.200
UR5 0.200 UL5 0.200 U5 0.200
UR6 0.200 UL6 0.109 U6 0.200
LR1 0.200 LL1 0.200 L1 0.200
LR2 0.200 LL2 0.200 L2 0.200
LR3 0.200 LL3 0.200 L3 0.200
LR4 0.200 LL4 0.200 L4 0.200
LR5 0.200 LL5 0.045* L5 0.094
LR6 0.200 LL6 0.200 L6 0.200
Faciolingual Inclination
UR1 0.030* UL1 0.084 U1 0.142
UR2 0.200 UL2 0.033* U2 0.160
UR3 0.001* UL3 0.141 U3 0.017*
UR4 0.037* UL4 0.200 U4 0.111
UR5 0.200 UL5 0.160 U5 0.200
UR6 0.200 UL6 0.052 U6 0.200
LR1 0.200 LL1 0.200 L1 0.200
LR2 0.200 LL2 0.200 L2 0.200
LR3 0.200 LL3 0.200 L3 0.200
LR4 0.200 LL4 0.200 L4 0.134
LR5 0.182 LL5 0.200 L5 0.200
LR6 0.182 LL6 0.091 L6 0.200
Table 5. Normality test for the mesiodistal angulation and faciolingual inclination of teeth
individually and combined (right and left side averaged) after orthodontic treatment. The α is set
at 0.05. R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular);
1, central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar. *
Indicates non-parametric data.

42

Comparison of the Left and Right Side of Arches

Mean, R SD, R Mean, L SD, L Avg (R,
L)
SD, avg
(R, L)
Mean
dif (R-L)
P value
(R and
L)
Mesiodistal angulation (tip)
U1 6.89 4.13 6.05 3.42 6.47 3.45 0.84 0.205
U2 7.54 3.40 7.34 4.62 7.44 3.59 0.20 0.803
U3 12.78 4.73 11.09 3.87 11.93 4.02 1.69 0.016
U4 9.75 5.07 7.92 4.98 8.84 4.70 1.84 0.016 †
U5 4.58 4.63 4.24 4.88 4.41 4.36 0.34 0.597 †
U6 1.88 4.16 1.19 4.28 1.53 4.00 0.69 0.226
L1 -0.37 2.45 0.96 1.82 0.30 1.44 -1.34 0.053
L2 -1.47 4.11 -0.48 2.75 -0.97 3.16 -1.00 0.118
L3 3.61 3.34 3.52 3.58 3.57 3.18 0.09 0.874
L4 3.56 4.38 3.45 3.72 3.51 3.79 0.10 0.862
L5 7.45 3.56 8.02 3.21 7.73 3.11 -0.57 0.376 †
L6 9.62 3.94 9.26 3.50 9.44 3.43 0.36 0.553
Faciolingual inclination (torque)
U1 33.46 7.55 34.38 6.49 33.92 6.92 -0.91 0.098
U2 32.54 5.24 32.98 4.41 32.76 4.57 -0.44 0.506
U3 20.95 5.55 21.55 4.22 21.25 4.64 -0.61 0.378
U4 5.55 5.92 6.09 5.53 5.82 5.27 -0.54 0.564
U5 2.73 6.43 1.53 5.39 2.13 5.27 1.19 0.294
U6 4.43 3.86 4.78 4.68 4.60 3.92 -0.35 0.624
L1 26.16 7.26 25.98 7.20 26.07 7.18 0.18 0.440 †
L2 24.21 6.95 24.32 5.50 24.27 6.07 -0.11 0.898 †
L3 18.61 6.09 17.13 5.52 17.87 5.67 1.48 0.008
L4 7.27 5.81 6.96 5.71 7.12 5.53 0.31 0.644
L5 -0.14 4.56 -1.60 4.55 -0.87 4.34 1.45 0.016
L6 -7.65 5.39 -9.16 5.69 -8.41 5.10 1.51 0.100
Table 6. Twelve pairs of mesiodistal angulation and faciolingual inclination comparisons before
orthodontic treatment, each with the α level adjusted to 0.05/12 = 0.00412 (Bonferroni correction).
R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular); 1,
central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar.
*Statistically significant difference between right and left mean values; †Related-samples
Wilcoxon signed rank tests (non-parametric data) were used.

Paired t-tests were used to compare the left and right side of the patient’s dental arches to
determine if the arches were relatively symmetric. For non-parametric data, Wilcoxon
Signed Rank Test was used.

43

The results showed prior to orthodontic treatment there was a difference (p < 0.05)
between the left and right side for the mesiodistal angulation of the upper canines (U3)
and upper first premolars (U4) (Table 6). For faciolingual inclination, there was a
difference for the lower canines (L3) and lower second premolars (L5). However, once
the Bonferroni correction was made (α level adjusted to 0.05/12 = 0.00412), then there
was no statistically significant difference between the left and right side of the arches
(Table 6). Therefore, the two side averages were used in the following analyses.

Mean, R SD, R Mean, L SD, L Avg (R,
L)
SD, avg
(R, L)
Mean
dif (R-L)
P value
(R and
L)
Mesiodistal angulation (tip)
U1 3.33 3.27 4.71 3.59 4.02 2.74 -1.38 0.095 †
U2 5.95 2.91 7.30 4.44 6.63 3.10 -1.34 0.133
U3 12.23 4.66 12.06 6.10 12.15 4.97 0.17 0.848
U4 7.25 4.62 7.63 3.11 7.44 3.49 -0.38 0.612
U5 1.76 3.97 4.08 3.07 2.92 2.69 -2.32 0.022
U6 -1.32 3.82 1.04 3.83 -0.14 3.35 -2.36 0.005
L1 -0.31 2.62 0.48 2.38 0.09 1.23 -0.79 0.383
L2 0.29 3.28 0.97 2.99 0.63 2.61 -0.69 0.342
L3 7.26 4.61 7.18 3.43 7.22 3.32 0.08 0.931
L4 4.30 3.39 4.35 4.02 4.33 3.30 -0.05 0.944
L5 5.13 3.60 5.95 2.93 5.54 2.84 -0.82 0.253 †
L6 5.41 3.15 4.53 3.68 4.97 2.75 0.88 0.301
Faciolingual inclination (torque)
U1 32.36 5.73 32.51 6.70 32.44 6.09 -0.25 0.710 †
U2 32.11 4.17 30.77 4.51 31.44 4.12 1.34 0.037 †
U3 19.89 3.70 20.04 4.72 19.97 3.94 -0.15 0.732 †
U4 7.28 5.26 6.83 5.18 7.06 4.98 0.46 0.627 †
U5 5.31 4.77 4.64 5.16 4.98 4.57 0.67 0.407
U6 6.56 4.01 6.75 4.16 6.66 3.83 -0.19 0.748
L1 23.97 6.77 24.07 6.53 24.02 6.60 -0.10 0.768
L2 23.58 6.56 23.64 6.30 23.61 6.34 -0.06 0.884
L3 19.01 4.83 17.99 5.57 18.50 5.04 1.02 0.075
L4 9.95 5.60 8.98 5.20 9.47 5.16 0.98 0.148
L5 1.75 3.62 -0.33 3.98 0.71 3.50 2.08 0.002*
L6 -5.51 4.02 -6.88 4.35 -6.20 3.69 1.37 0.104
Table 7. Twelve pairs of mesiodistal angulation and faciolingual inclination comparisons after
orthodontic treatment, each with the α level adjusted to 0.05/12 = 0.00412 (Bonferroni correction).
R, Right; L, left; Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular); 1,
central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar.
*Statistically significant difference between right and left mean values; †Related-samples
Wilcoxon signed rank tests (non-parametric data) were used
44

The results comparing the left and right side of the patients’ arches after orthodontic
treatment showed that there was a difference between the mesiodistal angulations of the
upper second premolars and first molars (U5 and U6, respectively) and faciolingual
inclinations of the upper laterals and lower second premolars (U2 and L5, respectively)
(Table 7). However, once the Bonferroni adjustment was accounted for (p < 0.00412),
then only the faciolingual inclination of lower second premolars (L5) is statistically
different between the left and right sides. However the mean difference was 2.08°, which
is less than the 2.5° mark used for clinical significance. Therefore, the post-treatment
averages of the left and right sides are also used in the following analyses.

Paired T-Test of Pre- and Post-Treatment

Tooth Mean dif
(Pre-Post)
Std. Error P value Tooth Mean dif
(Pre-Post)
Std. Error P value
Mesiodistal Angulation Faciolingual Inclination
U1 2.45 0.803 0.006 U1 1.54 1.112 0.181
U2 0.81 0.917 0.384 U2 1.32 0.933 0.169
U3 -0.22 1.001 0.831 U3 1.28 0.844 0.116 †
U4 1.40 0.625 0.036 U4 -1.23 0.870 0.170
U5 1.49 0.745 0.072 † U5 -2.84 0.719 0.001*
U6 1.67 0.736 0.033 U6 -2.05 0.651 0.005
L1 0.21 0.407 0.610 L1 2.05 1.021 0.059 †
L2 -1.60 0.901 0.089 L2 0.66 0.892 0.466
L3 -3.66 0.940 0.007 L3 -0.63 0.878 0.478
L4 -0.81 0.669 0.236 L4 -2.35 1.008 0.029
L5 2.19 0.768 0.009 L5 -1.58 0.731 0.042
L6 4.47 0.891 0.000* L6 -2.21 0.588 0.001*
Table 8. Comparison between the pre- and post-treatment values for mesiodistal angulation and
labiolingual angulation for each tooth, each with the α level adjusted to 0.05/12 = 0.00412
(Bonferroni correction). Pre, pre-treatment group; Post, post-treatment group. R, Right; L, left;
Avg, average; dif, difference; U, upper (maxillary); L, lower (mandibular); 1, central incisor; 2,
lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar. *Statistically
significant difference between the pre- and post-treatment values †Paired Wilcoxon (non-
parametric data) were used.

45

The results of the paired t-tests comparing the mesiodistal angulation and faciolingual
inclination values before and after orthodontic treatment showed that there was a
statistical difference for the mesiodistal angulation value of upper central incisors (U1),
upper first premolars (U4), upper first molars (U6), lower canines (L3), lower second
premolars (L5) and lower first molars (L6). However, once the Bonferroni correction
was made, only the mesiodistal angulation of the lower first molars (L6) were considered
statistically different. The range of mean change was from -3.66° for lower canines to
4.47° for lower first molars.

For faciolingual inclination measurements, the upper second premolars (U5), upper first
molars (U6), lower first premolars (L4), lower second premolars (L5), and lower first
molars (L6) are statistically different. After Bonferroni correction, however, then only the
faciolingual inclination of the upper second premolars (U5) and lower first molars (L6)
are significant. The range of mean change was from -2.84° for upper second premolars to
2.05° for lower central incisors.

46

Figure 16. Mean angulations of teeth before and after orthodontic treatment. 1, central incisor; 2,
lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar; Blue line, pre-
treatment; Black line, post-treatment.

Comparing the mean values of the mesiodistal angulation and faciolingual inclination
before and after orthodontic treatment of the 24 subjects (Figure 16), showed that the
mesiodistal angulation of the upper teeth tended to decrease after orthodontic treatment
by a few degrees, except for the canines which remained constant at 12° mesiodistal
angulation (Figure 16A). The upper first molars showed the greatest reduction in
-10
-5
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6
Degrees
Tooth Number
Mesiodistal Angulation
of Upper Teeth
-10
-5
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6
Degrees
Tooth Number
Mesiodistal Angulation
of Lower Teeth
-10
-5
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6
Degrees
Tooth Number
Faciolingual Inclination
of Upper Teeth
-10
-5
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6
Degrees
Tooth Number
Faciolingual Inclination
of Lower Teeth
A B
C D
47

mesiodistal angulation at about 4° decrease, although none of the changes were
statistically significant after Bonferroni correction.

The mesiodistal angulation of the lower teeth followed a different, more variable trend.
While there was no change for the lower central incisor, there may be a slight increase for
the lower lateral incisor and more (3°) for the lower canines. Then the trend moved to the
opposite direction, from little change for the lower first premolars to slight reduction for
the lower second premolars and to as much as 6° reduction for the lower first molars
(Figure 16B).

Unlike the mesiodistal angulations of the teeth, the faciolingual inclinations of the teeth
before and after orthodontic treatment were relatively similar and, more importantly,
followed the same trend. For the faciolingual inclination of the upper teeth, the central
incisors started at about 33°, decreased slightly for the lateral incisors at about 31-32°,
decreased further for the canines at about 20°, and then leveled out for the premolars and
molars at approximately 5°(Figure 16C).

The faciolingual inclination of the lower teeth showed a gradual decrease in faciolingual
inclination from central incisors back to the first molars. The central incisors started at
25°, decrease to 22° for the lateral incisors, 17° for the canines, 8° for the first premolars,
0° for the second premolars, and finally ending at -7° for the first molars (Figure 16D).

48

The values for the second molars were left out of the statistical analyses due to
uncertainty of whether they were included in orthodontic treatment, additionally some
pre-treatment values for second molars were non-existent.

49

Chapter 5: Discussion

This study was designed to identify the changes in each tooth mesiodistal angulation and
faciolingual inclination post non-extraction orthodontic treatment. Prior to the advent of
CBCT, mesiodistal angulation and faciolingual inclination measurements were
approximated using plaster models where only the crowns of the teeth (not the roots)
were accessible. With the ability to visualize the teeth in 3-D, the accuracy of
determining the true long axis of the tooth is improved and therefore measurements of
mesiodistal angulation and faciolingual inclination are also positively affected.

Two different CBCT machines were used in this study. That should not have affected the
angular measurements obtained since both machines were calibrated to project 3D
images in 1:1 ratio. Furthermore, the different positions used for the different machines
(supine and standing) should not have made a difference in the study since measurements
were of hard tissue. Patients were instructed to bite in maximum central occlusion in both
situations.

With the exception of the lower second premolar (L5) faciolingual inclination, the left
and right side of the arches were relatively symmetrical before and after orthodontic
treatment as shown by the paired t-tests comparing each tooth to its contralateral tooth.
Assuming there is no difference in the shape and size of the lower second premolars on
both sides, this difference in faciolingual inclination may reflect the difficulty in
accurately position brackets in this area. However, the mean difference between the left
50

and right lower second premolar faciolingual inclination was only 2.08°, which can be
considered clinically insignificant. This indicates that clinicians are generally able to
maintain the symmetry of the arches when it comes to non-extraction treatment. Like in
the previous study by Tong et al. (2012), the left and right sides were combined and the
averages were used to enter into further analyses.

Assuming the initial mesiodistal angulation and faciolingual inclination in the near-
normal patients are ideal, the changes in post-treatment mesiodistal angulation and
faciolingual inclination would indicate deviation from ideal. This happened to the
faciolingual inclination measurement for upper second premolars and both mesiodistal
angulation and faciolingual inclination measurements for the lower first molars, where
statistically significant differences were shown. A number of factors may be accounted
for these changes, namely the size and shape of the teeth, bracket prescription, bracket
position, wire adjustments, etc. In this study, patients with noticeable tooth size and shape
discrepancies were excluded. That leaves the other three factors as the main reasons for
the changes observed.

The different bracket prescriptions used at USC postgraduate clinic included: Edgewise,
MBT, Roth, and Wick. For upper second premolar bracket, the faciolingual inclination is
-7° for MBT and Roth prescription and -8° for Wick prescription. They are very close to
Andrew’s -8.78° for the same tooth. Therefore, bracket prescription may not be the
reason for the difference in faciolingual inclination in these teeth post-treatment as
compared to pre-treatment. The upper second premolars are generally considered difficult
51

to visualize and access intraorally. The larger than normal faciolingual inclination of
these teeth may be a result of brackets placed too far occlusally. Clinically it is quite
common to see a marginal ridge discrepancy between the upper first molars and the upper
second premolars, although the bands or brackets position errors for the upper first
molars are often to be blamed. Our results suggest that the brackets for the upper second
premolars positioned occlusally may be a contributing factor to the marginal ridge
discrepancy as well. For lower first molar mesiodistal angulation, all bracket systems we
used have a prescription of 0°, whereas in Andrews’ original measurement, it was 2°.
Therefore, these brackets may give a small 2° upright to the lower first molars. However,
the 4.5° upright seen in our post-treatment outcome may reflect a common mistake seen
clinically with the lower first molars bands positioned too far gingivally, especially on the
mesial side. There is more variation in the lower posterior teeth faciolingual inclination
between the bracket prescriptions. The faciolingual inclination for the lower first molar is
-20° (-14° from one source) for MBT, -25° for Roth, and -10° for Wick. They are a lot
less than Andrews’ faciolingual inclination for the lower first molars -30.67°. This would
result in lower first molars being less lingually inclined, or more upright post-treatment,
as shown in the treatment outcome of our 24 cases. Therefore, there is a possibility that
the statistically significant differences seen in the lower first molar faciolingual
inclination may be due to bracket prescription.

However, all three major brand bracket systems have higher faciolingual inclinations than
Andrews’ measurements for upper central and lateral incisors, and lower inclinations for
lower canine, lower first and second premolars, and yet those differences were not shown
52

in the treatment outcome of our study. Part of the reason may be there were more non-
Caucasian subjects in our sample and their original incisor faciolingual inclinations were
high to begin with. As for the posterior teeth, faciolingual inclination prescriptions may
not express fully if undersized archwires were used to finish treatment.

Wire bending is often used to compensate for variations in tooth size and shape and for
errors in bracket positioning. Here, in this study, in addition to bracket position errors or
variations in bracket prescriptions, lack of wire bending, rather than wire bending may
likely be the cause for incorrect final tooth positions.

Past studies have shown that there is a significant difference in the initial and final
faciolingual inclination of the anterior teeth when non-extraction treatment is rendered
(Pandis, 2007, 2010). This was not shown to be true in this study. The faciolingual
inclination of the upper and lower anterior were actually very similar before and after
orthodontic treatment. This may be explained by the fact that these patients had near-
normal occlusion initially with arch length discrepancies ranging from minimally positive
to minimally negative, which likely negated the flaring effect that is typically seen in
non-extraction treatment.

The mean difference between pre- and post-treatment values for the mesiodistal
angulation of the lower molars was 4.47° and faciolingual inclination was 2.21°. The
mean difference for the faciolingual inclination of the upper second premolars was 2.84°.
These values may be statistically significant, but clinically these differences are relatively
53

small. However, there may be a trend for a slight reduction in mesiodistal angulation for
most of the teeth. Again, this may have been the effect of the bracket prescription. For
example, most of the bracket systems used have 0° mesiodistal angulation for both
maxillary and mandibular premolars and molars, whereas these teeth tend to have
positive angulations naturally.

Modifications in bracket prescriptions are often made in different bracket systems to
compensate for different mechanics used, although their treatment goals are often quite
similar. In this study, the differences as a result of different mechanics in using different
bracket systems have been ignored. In order to investigate the effect of these factors,
future study may limit to one bracket system and one type of treatment mechanics.

Despite being treated by different orthodontists and different, pre-adjusted bracket
prescriptions, the orthodontic treatment results of the 24 patients were all very similar in
that their initial occlusions were mostly maintained. This is in direct contrast to another
parallel study in which four premolars were extracted. There the results positively
indicated specific changes in mesiodistal and faciolingual inclination of most of the teeth
in accordance with the extraction treatment modality.

In this study, we attempted to use the norms established from the 76 near-normal subjects
used in the previous study as the standards to check against the mesiodistal angulation
and faciolingual inclination outcome of 24 of those 76 cases after non-extraction
treatment. The results clearly indicated that, as a group, the treatment of these 24 cases
54

met the standards. However, variations existed among different individuals. Group
studies are common in research, but clinically, an orthodontist’s evaluation of treatment
outcome is for the individual case. Therefore these norms may need to be both necessary
and sufficient. Further studies are needed to test the efficacy of using these standards for
each individual.

55

Chapter 6: Conclusion
In this study, the 24 out of 76 near-normal patients were treated without extraction by
different orthodontists and with different bracket prescriptions. Despite the potential for
operator error of bracket position and differing treatment techniques, the symmetry of the
mesiodistal angulation and faciolingual inclination of teeth on both the left side and right
side of the arches were generally maintained; the initial mesiodistal angulation and
faciolingual inclination of their teeth were also generally maintained except the
mesiodistal angulation and faciolingual inclination of the lower first molars and
faciolingual inclination of the upper second premolars, which showed small but
statistically significant changes, possibly as the result of bracket prescription, bracket
positioning and lack of wire bending.

56

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Asset Metadata

Creator Nguyen, Thao (author)

Core Title The mesiodistal angulation and faciolingual inclination of each whole tooth in three dimensional space post non-extraction orthodontic treatment

School School of Dentistry

Degree Master of Science

Degree Program Craniofacial Biology

Publication Date 03/15/2013

Defense Date 02/27/2013

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

Tag cbct,non-extraction,OAI-PMH Harvest,orthodontics

Language English

Contributor Electronically uploaded by the author (provenance)

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

Creator Email thaovnguyen@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-225406

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