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AN EVALUATION OF MANDIBULAR ANTERIOR CROWDING AS IT RELATES
TO FACIAL DIVERGENCE IN TREATED AND UNTREATED SUBJECTS
Avrum I. Goldberg, D.D.S.
An Abstract Presented to the Graduate Faculty of
Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry (Research)
2012
ABSTRACT
Purpose:
To better understand the relationship
between vertical facial growth and mandibular anterior
crowding by evaluating untreated subjects cross-sectionally
and treated subjects longitudinally.
Methods:
The sample
consisted of 1) pre-treatment records of 75 untreated Class
I Caucasian patients collected from the archives at Saint
Louis University, and 2) post-treatment and post-retention
records of 76 Caucasian patients, treated on an extraction
basis to a Class I occlusion, collected from one private
practice clinician.
After digitization of models and
cephalograms, two universal measures of crowding (II and
TSALD) were related to four frequently used indices of
divergence (MPA, PMA, PFH:AFH, LFH:AFH).
Results:
There
were weak to moderately weak associations between facial
divergence and crowding, subjects with greater divergence
showed greater amounts of crowding than subjects with
average amounts of divergence.
Females, who were more
hyperdivergent than males, also showed stronger
relationships between divergence and crowding than males.
There were moderate correlations between posterior face
height and crowding in males; eruption of the lower
incisors was moderately associated with crowding in
females.
Conclusions: Vertical growth and incisor
1
eruption, as well as facial divergence, are important
determinants of malalignment.
2
AN EVALUATION OF MANDIBULAR ANTERIOR CROWDING AS IT RELATES
TO FACIAL DIVERGENCE IN TREATED AND UNTREATED SUBJECTS
Avrum I. Goldberg, D.D.S.
A Thesis Presented to the Graduate Faculty of
Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry (Research)
2012
COMMITTEE IN CHARGE OF CANDIDACY:
Professor Peter H. Buschang,
Chairperson and Advisor
Professor Rolf G. Behrents
Associate Clinical Professor Donald R. Oliver
i
DEDICATION
This work is dedicated to my wife Amy. You enrich my
life every day, and without you this pursuit would not have
been meaningful. Thank you for your sacrifices and
unwavering support throughout my graduate education.
To my parents, Debbie and Sheldon, and sister, Lisa,
thank you for your love and support. To my father, thank
you for introducing me to the profession of dentistry and
encouraging me to pursue higher education.
I also wish to dedicate this work to all those fulland part-time faculty, co-residents, and staff members who
have contributed to my professional education and personal
life.
ii
ACKNOWLEDGEMENTS
This project could not have been completed without the help
and support of the following individuals:
Dr. Peter Buschang, your guidance and enthusiasm for
research helped me turn the vision of this project into a
reality. Thank you for your motivation throughout this
project and constantly challenging me to think.
Dr. Rolf Behrents, thank you for your contributions to
my thesis and professional education. I am grateful for
the opportunity to have continued my education at Saint
Louis University.
Dr. Donald Oliver, thank you for your attention to
detail throughout my graduate education and revisions of my
thesis. Your teachings will serve me well throughout my
career.
Dr. Jim Boley and Mrs. Sabrina Boley, for welcoming me
into their practice and allowing the use of their long-term
records. Without Dr. Boley’s efforts to collect long-term
records of his patients, this thesis would not have been
possible. It is both humbling and inspiring to witness
such incredible long-term results.
Mrs. Rita Bauer, who took the time to collaborate and
help me obtain exceptional photographs for my thesis, even
during a trip to the Swiss Alps.
Dolphin Imaging™, particularly Barbara Brinker, Marcus
O’Leary, and the programming department, who donated their
time and services to create a custom model analysis for use
in this study.
My wife, Dr. Amy Mihaljevich, who helped pull cases,
photograph models, and log data. Without her help this
thesis would not have been completed within the rigors of
our program.
iii
TABLE OF CONTENTS
List of Tables............................................vi
List of Figures.........................................viii
CHAPTER 1: INTRODUCTION....................................1
CHAPTER 2: REVIEW OF THE LITERATURE
Overview ..........................................3
Part I – Prevalence and incidence of crowding .....3
The scope of the problem....................3
Crowding in untreated individuals...........6
Crowding in treated individuals............11
Comparisons of crowding in treated
and untreated individuals ..............16
Part II – Etiology of crowding ...................20
Treatment factors..........................20
Soft tissue treatment boundaries .......23
Non-treatment factors......................27
Susceptibilities .......................29
Race ...............................29
Sex ................................30
Age ................................31
Indirect causes ........................33
Tooth size and shape ...............33
Third molars .......................34
Periodontal and gingival fibers ....36
Anterior component of force ........38
Primary tooth loss,
eruption sequence ..............42
Predisposing factors ...................44
Arch form ..........................44
Point-to-point contacts ............46
Facial divergence ......................48
Secular Trends .....................51
Dental eruption and instability ....53
Compensatory rotational changes ....64
Relations in the literature ........67
Cross-sectional studies ........67
Untreated samples...........67
Longitudinal studies ...........68
Untreated samples...........68
Treated samples.............71
Statement of Thesis ..............................73
References .......................................74
iv
CHAPTER 3: JOURNAL ARTICLE
Abstract .........................................93
Introduction .....................................94
Materials and Methods ............................98
Selection criteria ............................98
Cephalometric Analysis .......................100
Model Analysis ...............................101
Reliability of Measurements ..................103
Statistical Analysis .........................104
Results .........................................104
Untreated subjects ...........................104
Treated subjects .............................109
Discussion ......................................119
Untreated subjects ...........................120
Treated subjects .............................121
Summary and Conclusions .........................127
References ......................................128
Appendix A ..............................................135
Appendix B...............................................139
Vita Auctoris............................................141
v
LIST OF TABLES
Table 1.1: Crowding in untreated samples..................10
Table 1.2: Crowding in treated samples....................14
Table 1.3: Summarized data for treated and untreated
samples .......................................16
Table 1.4: Summary of rates for arch perimeter and
Incisor Irregularity change ...................18
Table 3.1: Age distribution in treated groups.............99
Table 3.2: Age distribution in untreated groups..........100
Table 3.3: Crowding in untreated groups..................105
Table 3.4: Comparison of T1 skeletal measures in
untreated groups .............................107
Table 3.5: Comparison of T1 skeletal measures in
untreated groups .............................107
Table 3.6: Correlation between T1 crowding and T1
skeletal measures in untreated groups ........108
Table 3.7: Crowding in treated groups....................109
Table 3.8: Comparison of T1 skeletal measures in
treated groups ...............................111
Table 3.9: Comparison of T1 dental measures in
treated groups ...............................111
Table 3.10: Comparison of skeletal changes in
treated groups ...............................113
Table 3.11: Comparison of dental changes in
treated groups ...............................113
Table 3.12: Correlation between T2 crowding and
T1 skeletal measures .........................116
vi
Table 3.13: Correlation between change in crowding and
T1 skeletal measures .........................117
Table 3.14: Correlation between change in crowding and
change in skeletal measures ..................118
Table A.1: Customized cephalometric analysis.............138
Table A.2: Customized model analysis.....................138
Table B.1: Method error study............................140
vii
LIST OF FIGURES
Figure 1.1: Relation between mandibular irregularity
and age .......................................7
Figure 1.2: Relation between annual irregularity increase
and age .......................................8
Figure 1.3: Changes in crowding with age in untreated
subjects ......................................9
Figure 1.4: Changes in crowding with age in treated
subjects .....................................13
Figure 1.5: Changes in crowding with age in treated and
untreated subjects ...........................17
Figure 2.1: Soft tissue envelope (saggital view)..........24
Figure 2.2: Soft tissue envelope (frontal view)...........24
Figure 2.3: The progression of malalignment...............28
Figure 2.4: Anterior component of force (saggital view)...39
Figure 2.5: Anterior component of force (occlusal view)...40
Figure 2.6: Stability in relation to dental angulation
to the mandibular plane .......................41
Figure 2.7: Maintenance of a functional occlusion.........55
Figure 2.8: Variations in growth rate.....................56
Figure 2.9: Velocity curves for tooth eruption............57
Figure 2.10: Relation between dentoalveolar height
and facial height ...........................59
Figure 2.11: Cross-sectional views of the alveolus in
short, normal, and long-faced individuals ...62
Figure 2.12: Comparison of divergence morphologies........64
Figure 2.13: Relation between facial divergence and
tooth eruption ..............................67
viii
Figure 2.14: Revised progression of malalignment.........126
Figure A.1: Customized cephalometric digitization
regimen .....................................136
Figure A.2: Calculation of arch perimeter................137
Figure A.3: Calculation of intercanine width,
intermolar width, and arch depth ............137
Figure A.4: Calculation of incisor irregularity..........137
ix
CHAPTER 1: INTRODUCTION
Although improved oral health, function, and social
approval are benefits of orthodontic treatment, patients
typically present to maximize facial and dental
appearance.1-4 This is why dissatisfaction with crowding or
irregular anterior teeth is often cited by patients as the
reason for seeking treatment.5-7
This is significant
because the most widespread malocclusion encountered by
orthodontists is crowding.
Still, it remains inconclusive as to why some develop
crowding and others do not.
Research derived from the
University of Washington8,9 suggests that “[t]he only way to
ensure continued satisfactory alignment post-treatment
probably is by use of fixed or removable retainers for
life.”10
This is important because long-term patient
satisfaction with orthodontic treatment is partly
associated with the stability of the final result.11,12
However, the use of permanent retention instills
complacence in orthodontists and ownership is essentially
transferred to the patient for permanency of the result.
Therefore further research is important to understand those
factors affecting stability and relapse, and adjust our
tactics for treatment.13-15
1
Longitudinal studies have consistently shown that
crowding increases over time.10,16-19
These increases are
larger during adolescence and slow into adulthood,10,20,21 and
are found to occur in both treated and untreated
individuals.16,17
Therefore, it has been suggested that
crowding may be the result of facial growth changes and not
necessarily treatment-related relapse.17,20,22
Because the
duration and extent of vertical growth is greater than for
horizontal growth,1,17,23 vertical growth is suspected to play
an important role in dentoalveolar compensations which
could ultimately lead to instability and/or crowding of the
teeth.
It is the purpose of this study to determine whether
differences in vertical growth proportions, as measured by
various indices of facial divergence, relate to crowding in
both treated and untreated subjects.
More than seventy years ago Hellman (1940) stated that
“We are in almost complete ignorance of the specific
factors causing relapses and failures.”
Today, we are
still largely unaware of the causes of relapse.
2
CHAPTER 2:
REVIEW OF THE LITERATURE
OVERVIEW
This section is divided into two parts.
The first
portion discusses crowding and various methods of
measurement.
This is followed by the presentation of data
from various longitudinal studies on the prevalence and
incidence of crowding among treated and untreated
individuals.
These groups are then compared, using
relevant supportive literature.
The second portion
discusses treatment and physiological-related factors that
may be involved in the development of crowding.
These are
introduced in an order that follows the development of
crowding.
The relation of facial divergence to crowding is
presented last, as it is the factor of particular interest
in this thesis.
PART I – PREVALENCE AND INCIDENCE OF CROWDING
THE SCOPE OF THE PROBLEM
A lack of space for teeth within the dental arch can
result in one of two outcomes: either tooth contact-point
displacement, causing irregularity, or flaring of the
anterior teeth, leading to protrusion.24,25
in treated and untreated cases.
3
Both can occur
Because early studies consistently showed incisor
crowding to be appreciably larger in the mandibular than
the maxillary arch,24,25 the literature has tended to focus
on the lower arch.
Boundaries are more stringent in the
mandible, as there is no opportunity for sutural expansion
and lateral dental expansion provides only limited space
gain.26
Incisor proclination can provide the largest
opportunity for arch length increase;26 however, periodontal
defects (i.e., recession and dehiscence) can be
iatrogenically caused if teeth are moved out of their bony
housing.27
Therefore, reduction of tooth structure within
an arch, using either tooth extraction or interproximal
reduction, may be necessary to manage extensive mandibular
crowding.
Mandibular crowding is typically measured in one of
two ways.
Tooth-size-arch-length discrepancy (TSALD) is a
measure of how “crowded” the teeth are, and is the
difference between the space available in the arch (the
alveolar bone) and the amount of space required (the tooth
structure present).28
This can involve the entire arch
(Total TSALD or tTSALD), or the segment of the arch that
includes the six anterior teeth (Anterior TSALD or
aTSALD).29
A TSALD of 4 mm or less can typically be treated
4
without extractions, while 8 mm or more often requires
extractions.30
Alternately, the Irregularity Index (II), devised by
Little,31 is the sum of the contact point displacements of
the anterior teeth, in millimeters.
“crooked” the teeth are.
It measures how
This index is generally used in
epidemiological studies because of its simplicity and
efficiency.
However it does not account for rotations or
changes in inclination.32
An Irregularity Index less than
3.5 mm is considered acceptable, while more than 7 mm is
considered clinically severe.31
Because these indices measure different aspects of
malalignment, they are complementary to one another. A
study by Harris and others33 compared aTSALD and II to
determine whether they were related to one another.
Based
on 70 randomly selected cases, they found a statistically
significant positive correlation (r=+0.53) that accounted
for less than a third of the variation.
Another study by
Bernabé and Flores-Mir32 evaluated tTSALD and II in 200
randomly selected schoolchildren.
Their correlation was
also statistically significant (r=-0.68) but accounted for
less than half of the variation.
These studies suggest a
more accurate relation between TSALD and II is gained by
including more teeth in the space analysis.
5
However, the
lack of a strong correlation indicates that both methods
are necessary for a study evaluating crowding,33,34 as the
use of either method alone could influence the results.17
CROWDING IN UNTREATED INDIVIDUALS
In the 1960s the US Public Health Service conducted a
large-scale survey to evaluate the level of malocclusion in
the United States.
This was conducted during the first
National Health and Nutrition Examination Survey (NHANES
I).35,36
In the late 1980s and early 1990s, statistical
methods were used to collect a sample that would be
representative of the three major racial groups in the US
(whites, blacks, and Mexican-Americans).
The NHANES III
sample studied over 30,000 individuals collected between
1988 to 1994.37
Two papers in the orthodontic literature have
presented tabulated NHANES III data showing differences in
incisor irregularity due to age, sex, race, and various
malocclusions and occlusal relations.30,38
Brunelle et al.38
found that a mean lower incisor irregularity of 1.6 mm for
8-11 year olds, 2.5 mm for 12-17 year olds, and 2.9 mm for
18-50 year olds.
He also reported that 42.4% of 8-50 year
olds had ideal alignment, 27.8% had mild irregularity,
15.1% had moderate irregularity, and 14.7% had severe to
6
extreme irregularity.
However, percentages were not
provided for irregularity based on discrete age groups.
1998, Proffit et al.30 provided more specific data
In
collection in terms of these percentages, based on
ethnicity and age.
The data showed that more than 20% of
8-11 year olds are affected by at least moderate lower
crowding, and this worsens in adolescence (30% by 12-17
years).
In adulthood (age 18+), about 40% have at least
moderate crowding and only about a third have ideal (0-1
mm) irregularity.
The trend for increased crowding with
age is shown in Figure 1.1.
Although these papers
adequately described children in the mixed and early
permanent dentition, they provided only a limited view of
adult irregularity since their data was pooled.
Figure 1.1.
Relation between mandibular irregularity and age.
Adapted from Proffit et al.30
7
In 2003, Buschang and Shulman20 compiled a more
detailed breakdown of the original adult sample, based on a
random sample of 9044 untreated adults collected from the
NHANES III study.
They showed a trend of increased incisor
irregularity at increasing age grades, with significantly
more irregularity in 30-40 year olds than 15-20 year olds.
Increases in irregularity followed a curvilinear
relationship, with annual changes decreasing over time
(Figure 1.2).
Most increases occurred during the teenage
years and early twenties.
Figure 1.2.
Relation between annual irregularity increase and age.
Adapted from Buschang and Shulman.20
Many longitudinal studies have also evaluated changes
in untreated subjects.
summarized in Table 1.1.
Individual and combined data is
Amalgamated data shows increases
in TSALD and II of approximately 0.17 mm/yr and 0.09 mm/yr,
respectively.
When plotted (Figure 1.3), changes in TSALD
8
and II are shown to decrease over time, suggesting that a
relation between age and crowding may be present.
Figure 1.3. Changes in crowding with age in untreated subjects.
9
690
TOTAL
-
Angle
Class
NS
I
NS
I
I/II
I/II
I/II
I
NS
I
NS
NS
NS
-
57%
49%
60%
44%
49%
52%
49%
57%
60%
57%
44%
50%
56%
F
F
F
F
F
F
F
F
F
F
F
F
F
Sex
Sample
features
17.82
13.0
13.1
13.1
13.3
13.9
14.3
16.9
18.0
19.3
21.0
22.8
25.6
36.1
T1
Age
(yrs)
30.36
18.0
20.1
19.3
26.0
16.9
23.2
48.2
21.0
42.9
28.0
33.3
45.7
69.4
T2
Age
(yrs)
12.54
5.0
7.0
6.2
12.7
3.0
8.9
31.3
3.0
23.6
7.0
10.5
20.1
33.3
Δ Age
(yrs)
+1.13
+0.70
+1.57
+0.47
+0.9
+1.59
+2.58
+1.44
Δ II
(mm)
-2.32
-2.78
-2.02
-1.29
-1.1
-2.06
-0.1
-1.73
-0.2
-0.22
-0.80
-0.89
-1.39
+0.09
10
Δ TSALD
(mm)
+0.10
+0.25
+0.16
+0.10
+0.05
+0.11
+0.04
Δ II/yr
(mm/yr)
*NS = not specified; II = Incisor Irregularity; TSALD = tooth-size-arch-length-discrepancy
51
65
25
32
46
44
53
46
25
46
144
30
18
Richardson, 1979
Sinclair & Little, 1983
Eslambolchi et al., 2008
Bishara et al., 1989
Carter & McNamara, 1998
Driscoll-Gilliland et al., 2001
Carter & McNamara, 1998
Richardson & Gormley, 1998
Eslambolchi et al., 2008
Richardson & Gormley, 1998
Bondevik, 1998
Bishara et al., 1994
Eslambolchi et al., 2008
UNTREATED
N
TABLE 1.1. Crowding in untreated samples
-0.17
-0.46
-0.44
-0.16
-0.43
-0.12
-0.07
-0.03
-0.07
-0.03
-0.02
-0.04
-0.03
Δ TSALD/yr
(mm/yr)
CROWDING IN TREATED INDIVIDUALS
A great deal of long-term data has been collected
about crowding in treated subjects, much of which has been
produced at the University of Washington under the guidance
of Little.
In 1981, Little et al.39 investigated long-term changes
in mandibular crowding after orthodontic treatment.
Records for 65 patients treated with first-premolar
extractions were examined at 15 years (post-treatment) and
30 years (10 years post-retention).
In the post-treatment
period, irregularity increased from 1.73 mm to 4.63 mm
(2.9 mm over 15 years); however, there was a great deal of
variation in the sample.
Satisfactory alignment
(II < 3.5 mm) was found in less than 30% of the subjects
post-retention.
A follow-up study10 evaluated irregularity changes
after the 10-year post-retention period, to determine if
additional changes occurred with time.
Thirty-one cases
from the original study were further evaluated at 43 years,
approximately 20 years post-retention.
During the first
follow-up period mandibular irregularity increased 3.59 mm
over 15 years.
This irregularity continued to increase
with time, but to a much smaller extent during the second
11
follow-up period (0.77 mm over 13 years).
Satisfactory
alignment (<3.5mm) declined to 10% at 20 years.
These two studies highlight the process of ongoing
changes in the dentition after treatment.
Changes may be
due to treatment-related relapse or growth-related changes,
which are confounded.
However, because post-treatment
records were collected a considerable period after
treatment was discontinued (i.e., 10-20 years), it is
unlikely that such changes were related to treatment alone.
Because changes in irregularity diminished with time, this
suggests that crowding could be related to facial growth,
which also decreases over time.
This has been discussed in
other treated studies.21
Many other longitudinal studies have evaluated posttreatment dental changes in treated individuals.
Amalgamated data shows increases in TSALD and II of
approximately 0.12 mm/yr and 0.10 mm/yr, respectively
(Table 1.2).
When the data are plotted it appears that
changes in crowding decrease over time (Figure 1.4).
Although some studies show variations from this trend,
treated patients generally appear to follow similar
tendencies as untreated individuals.
Therefore, research
comparisons of crowding between treated and untreated
groups is necessary and valuable.
12
Figure 1.4. Changes in crowding with age in treated subjects.
13
Dugoni et al, 1995
Ferris et al, 2005
Sadowsky et al, 1994
Paquette et al, 1992
Elms et al, 1996
Rossouw et al, 1999
Luppanapornlarp et
al, 1993
Glenn et al, 1987
Moussa et al, 1995
Yavari et al, 2000
TOTAL
EXTRACTION
Haruki & Little, 1998
Paquette et al, 1992
Boese, 1980
Luppanapornlarp et
al, 1993
Rossouw et al, 1999
Harris & Vaden, 1994
Little et al, 1981
Driscoll-Gilliland et
al, 2001
Vaden et al, 1997
McReynolds & Little,
1990
McReynolds & Little,
1990
Little et al, 1988
Boley et al, 2003
Haruki & Little, 1998
Vaden et al, 1997
Little et al, 1988
Harris & Vaden, 1994
TOTAL
NON-EXTRACTION
I/II
NS
I/II
NS
I/II/III
NS
I/II
28
55
55
355
36
33
40
33
39
44
65
I/II/III
I/II
I/II
NS
I
I/II
I/II/III
NS
NS
-
43
36
14
32
31
32
47
36
31
30
622
I/II
NS
I/II
NS
II
-
29
25
20
22
30
42
49
NS
72% F
79% F
81% F
NS
NS
-
75% F
79% F
81% F
63% F
NS
63% F
51% F
62% F
Comb
PP
Comb
PP
Comb
PP
-
Comb
Comb
PP
PP
NS
PP
Comb
Uni
Comb
Uni
PP
PP
PP
PP
-
75% F
61% F
75% F
Uni
PP
PP
PP
Uni
PP
NS
NS
71% F
NS
-
F
F
F
F
F
F
Site
54% F
68%
55%
73%
37%
81%
63%
Sex
Sample features
Angle
Class
I/II
I/II
I/II
NS
II
I/II/III
N
14
15.5
15.5
16.3
21.6
30.4
32.2
17.4
15.3
15.3
15.3
15.2
14.9
15.1
15.2
14.8
14.4
14.4
14.5
14.8
15.7
16.5
14.62
14.8
13.6
13.7
13.9
14.2
14.5
14.5
PostTx Age
(yrs)
TABLE 1.2. Crowding in treated samples
30.4
31.6
32.0
30.5
43.3
36.2
29.3
31.9
29.8
21.6
28.9
20.9
21.7
30.1
30.2
30.6
28.8
20.1
26.6
22.0
28.2
26.14
30.1
27.9
24.3
28.6
28.7
23.1
21.9
PostRt Age
(yrs)
14.9
16.1
15.7
8.9
12.9
4.1
11.9
16.7
14.5
6.3
13.7
6.0
6.6
14.9
15.4
16.2
14.4
5.6
11.8
6.3
11.7
11.52
15.3
14.3
10.6
14.7
14.5
8.6
7.4
Δ Age
(yrs)
+3.59
+0.7
+2.75
+0.81
+0.77
+0.34
+1.60
+2.6
+2.0
+0.58
+1.3
+1.2
+0.55
+2.9
+2.6
+1.53
+2.4
+0.62
+1.2
+0.8
0.0
+1.40
+3.1
+1.61
+1.11
+1.4
+3.0
+0.4
+1.4
Δ II
(mm)
+0.24
+0.04
+0.18
+0.09
+0.06
+0.08
+0.13
+0.16
+0.14
+0.09
+0.10
+0.2
+0.08
+0.19
+0.17
+0.09
+0.17
+0.11
+0.10
+0.13
0.0
+0.12
+0.20
+0.11
+0.10
+0.10
+0.20
+0.05
+0.19
Δ II/yr
(mm/yr)
-2.35
-
-
-
-1.0
-
-3.7
+0.5
-
-1.90
-2.6
-1.81
+0.3
-
Δ TSALD
(mm)
-0.17
-
-
-
-0.09
-
-0.24
+0.03
-
-0.22
-0.17
-0.17
+0.02
-
Δ
TSALD/yr
(mm/yr)
I/II
II
-
604
125
334
189
1252
TOTAL (PP)
TOTAL (Uni)
TOTAL (Comb)
TOTAL (NS)
TOTAL (All)
-
83% F
58% F
-
69% F
63% F
83% F
-
84% E
47% E
-
NS
56% E
84% E
Ext
-
PP
Comb
-
NS
NS
PP
Site
16.7
14.6
19.2
15.5
16.9
21.5
31.1
19.9
17.9
14.7
14.2
PostTx Age
(yrs)
27.4
29.5
34.2
27.9
29.4
37.2
45.1
36.3
47.4
21.5
30.3
PostRt Age
(yrs)
10.7
14.9
15.0
12.4
12.5
15.6
14.0
16.4
29.5
6.7
16.1
Δ Age
(yrs)
+0.86
+2.78
+2.38
+1.45
+1.55
+0.85
+2.86
+1.68
+1.93
+1.28
+1.50
Δ II
(mm)
+0.08
+0.19
+0.16
+0.16
+0.12
+0.06
+0.20
+0.12
+0.07
+0.19
+0.09
Δ II/yr
(mm/yr)
-1.41
-1.38
-1.60
-1.42
-1.60
-1.60
-
Δ TSALD
(mm)
-0.13
-0.09
-0.05
-0.10
-0.05
-0.05
-
Δ TSALD/yr
(mm/yr)
15
*Tx = treatment; Rt = retention; NS = not specified; II = Incisor Irregularity; TSALD = tooth-size-arch-lengthdiscrepancy; PP = Private practice; Uni = University setting; Comb = Combination of Private practice and
University setting
-
I/II
45
78
275
88
13
I/II/III
51
Sex
Sample features
Angle
Class
I/II
EXTRACTION/
NON-EXTRACTION
Park et al, 2010
Rossouw et al,
1993
Carter &
McNamara, 1998
Park et al, 2010
Artun et al, 1996
TOTAL
N
TABLE 1.2 (continued). Crowding in treated samples
COMPARISONS OF CROWDING IN TREATED AND
UNTREATED INDIVIDUALS
As mentioned above, treated and untreated subjects
follow a similar trend in terms of age-related crowding.
Annualized changes in irregularity and TSALD are comparable
in both groups (Table 1.3 and Figure 1.5), implying that
post-treatment crowding is not necessarily related to
treatment itself, but to normal physiological changes such
as growth.17
Table 1.3. Summarized data for treated
and untreated samples
N
Δ Age
(yrs)
Δ II
(mm)
Δ II/yr
(mm/yr)
Δ
TSALD
(mm)
-1.39
-1.07
Δ
TSALD/yr
(mm/yr)
-0.17
-0.13
TOTAL (UnTx)
690
12.5
+1.13
+0.09
TOTAL (All Tx)
1252
12.5
+1.55
+0.12
TOTAL (Non355
11.5
+1.40
+0.12
-1.37
-0.11
exo)
TOTAL (Exo)
622
11.9
+1.60
+0.13
-1.40
-0.10
TOTAL (PP)
604
10.7
+0.86
+0.08
-1.41
-0.13
TOTAL (Uni)
125
14.9
+2.78
+0.19
-1.38
-0.09
TOTAL (Comb)
334
15.0
+2.38
+0.16
TOTAL (NS)
189
12.4
+1.45
+0.16
-1.60
-0.05
*Tx = treatment; Rt = retention; NS = not specified; II = Incisor
Irregularity;
TSALD = tooth-size-arch-length-discrepancy; PP = Private practice;
Uni = University setting; Comb = Combination of Private practice and
University setting; NS = Not specified
16
Figure 1.5. Changes in crowding with age in treated and untreated subjects.
A study by Carter and McNamara16 evaluated changes in
crowding among 82 treated and untreated subjects from the
Michigan Growth Study.
Three groups were compared,
including an untreated sample followed from 14 to 48 years,
an untreated adult sample followed from 32 to 45 years, and
a treated sample followed from 18 to 47 years.
Summarized
changes in arch perimeter and irregularity are shown in
Table 1.4.
Although the untreated adult and treated sample
sizes were small, and no statistical comparisons were made
between groups, similar annualized perimeter loss and
irregularity increases were found, except during puberty.
In contrast, the untreated sample showed much higher rates
of increase during puberty.
Unfortunately, a treated
pubertal group was not available for comparison.
17
Table 1.4. Summary of rates for arch perimeter (AP) and
incisor irregularity (II) change
Untreated (n=53)
Δ AP
(mm)
Δ AP/year
(mm/yr)
Δ II
(mm)
Δ II/year
(mm/yr)
Untreated
Adult (n=10)
Treated
(n=13)
Pubertal
Adult
1.29
2.06
0.51
1.60
0.40
0.07
0.04
0.05
0.47
1.59
0.48
1.93
0.16
0.05
0.04
0.07
*AP = arch perimeter, II = Incisor Irregularity
A study by Driscoll-Gilliland et al.17 also compared
treated and untreated patients to evaluate changes in
growth and crowding during the late adolescent and early
adulthood periods.
Fourty-four untreated subjects from the
Bolton Growth Study and 43 extraction patients treated in
private practice were analyzed during adolescence and early
adulthood.
Superimpositions were used to measure skeletal
and dental changes, while contact irregularity, space
irregularity, and TSALD were measured from models.
Due to
age differences between the samples, annualized changes
were used for comparison.
Over time, both samples showed
significant changes (1-1.5 mm) in contact irregularity,
space irregularity, and TSALD.
These changes were similar
in treated and untreated individuals, except for TSALD
which was significantly greater (0.10 mm) in the untreated
18
group.
Thus, supporting the hypothesis that changes in
crowding are generally similar, regardless of treatment.
In a study by Jonsson and Magnusson,40 the prevalence
of dental crowding and spacing was compared longitudinally
among 58 treated and 250 untreated subjects, from 12 to 38
years.
According to their findings, lower anterior
crowding increased significantly among both treated and
untreated subjects.
No differences were found between
groups at either time point.
However, changes in crowding
prevalence were significant between treated subjects and
untreated subjects.
This disparity related specifically to
the non-extraction group, which increased 8.7% more than
the untreated group.
In adulthood, those treated on a non-
extraction basis were 17.7% more likely to have crowding
(≥2 mm) than those treated with extractions.
This
difference was significant.
These three studies support other longitudinal data
(Table 1.3 and Figure 1.5), showing that differences
between treated and untreated groups are small.
Any
differences appear to be based more on the age period
studied, and the amount of growth that occurred, than
treatment itself.
Although extraction of teeth during
treatment may affect stability (as shown by Jonsson and
Magnusson40), other articles have found no such differences.
19
PART II - ETIOLOGY OF CROWDING
Determining the specific factors that contribute to
crowding is challenging, as correlation coefficients are
typically weak.
Therefore, it seems reasonable to assume
that crowding is the result of many interacting factors.39,41
Commonly reported factors are described below, under the
headings of treatment factors and non-treatment factors.
TREATMENT FACTORS
Studies have examined an assortment of treatment
variables in hopes of finding the cause(s) for relapse and
crowding post-treatment.
However, these factors fail to
explain a significant amount of the variation in posttreatment crowding.
Most studies have not been able to
link treatment with post-treatment changes,42,43 while those
that have were not related to post-retention crowding.23,39,44
Relationships between pre- and post-treatment dental
characteristics with relapse do not appear to show
consistent relations either.39,45
In the 1981 study by Little et al.39 mentioned
previously, dental casts of 65 patients treated with first
premolar extractions were investigated for potential causes
of post-retention mandibular crowding.
20
A wide variation in
crowding was found, and the researchers were unable to
predict future crowding based on dental changes during
treatment.
Angle classification, sex, length of retention,
and age also failed to explain changes in crowding.
Significant, but weak to moderate correlations, were found
between post-retention irregularity and post-treatment arch
length decreases (r=0.52), changes in arch width (r=0.38),
overjet (r=0.26), and overbite (r=0.46).
They concluded
that neither single nor multiple dental factors were able
to accurately predict crowding after treatment.
A follow-up study by Shields et al.23 evaluated
cephalometric variables for 54 patients in relation to
post-retention crowding using a comparable sample of first
premolar extracted cases.
Similar findings in terms of a
lack of predictive ability for post-retention crowding was
found for cephalometric changes during the treatment
period.
No cephalometric changes were able to
significantly predict irregularity or arch length changes.
Mellion41 also had similar findings in his Master’s
thesis.
Several commonly cited causes of relapse
(treatment change in IMPA, axial inclination of the buccal
teeth, irregularity, maxillary and mandibular intercanine
width, maxillary growth, and differential mandibular
growth) were evaluated, and five significant multiple
21
regression equations were found.
Each of these equations
showed low correlation coefficients (r=0.32-0.48),
suggesting that alone or together, treatment factors are
responsible for a relatively small portion of crowding.
Other treatment related factors, such as extraction
versus non-extraction,46-51 or timing of extraction,44,52 do
not show a significant effect on long-term crowding,
although Haruki and Little53 found a significant relation
between serial extractions and improved long-term
alignment.
The experience of the clinician has also been
implicated in affecting relapse.
Although studies from the
University of Washington10,19,50,53 and Saint Louis
University46,47 show poor long-term success rates, the
majority of published literature from cases treated in
private practices shows more acceptable post-treatment
stability.21,54,55
Based on amalgamated data from
longitudinal studies (Table 1.2), subjects treated in a
university setting show larger long-term changes in II
(0.19 mm/year) than subjects treated in private practice
(0.08 mm/year).
Although variation exists from site to
site and clinician to clinician, it is possible that
relapse in university patients is higher because they may
be treated by multiple practitioners.21
22
However, conventional wisdom tells us that maintenance
of arch width, especially in the canine region,39,51,56-59
preservation of arch length,60 and control of incisor
position23,61,62 are important factors in the long-term
stability of treatment.
Although these have become basic
tenets for treatment, the correlations are no stronger than
for other factors.
These tenets are discussed below in
relation to soft tissue treatment boundaries.
SOFT TISSUE TREATMENT BOUNDARIES
The shape of the arches and tooth positions can be
defined relative to an envelope of muscular function.
In
1949, Strang56 suggested that if muscular forces were
violated by arch width increases at the canines or molars,
orthodontic treatment would be unstable.
He applied this
concept of arch width maintenance in clinical practice, and
found that his treated cases remained stable despite a lack
of retention.
The “equilibrium theory,” as described by
Weinstein et al.,63 maintains that tooth position is
dictated by a balance between the musculature of the lips
and cheeks, and that of the tongue (Figure 2.1, 2.2).
For
that reason, displacement of teeth outside of this region
might be expected to result in relapse back to the area of
stability.
23
Figure 2.1. Soft tissue envelope (saggital view).
Adapted from Profitt.64
Figure 2.2. Soft tissue envelope (frontal view). Adapted from Proffit.1
Various studies by Weinstein et al.63 show that tooth
movements occur if this equilibrium is disrupted.
For
instance, in eight patients planned to receive orthodontic
extraction of four bicuspids, two bicuspids were randomly
assigned to receive a 2 mm thick gold onlay on either the
buccal or lingual surface.
These were compared to the
other two bicuspids, which were undisturbed.
After relief
of the proximal and occlusal contacts, these teeth were
allowed to move freely for eight weeks, and observed at
weekly intervals.
A mean movement of 0.48 mm was found for
24
onlayed teeth, while the control teeth remained relatively
stable.
Probably the best source on changes in intercanine
width (ICW) after treatment is a meta-analysis by Burke et
al.65
In this review they examined a total of 1,233
subjects drawn from 26 studies.
at three time points:
and long-term.
Individuals were examined
before treatment, after treatment,
Mean changes in ICW ranged from +0.81 to
+2.02 mm during treatment and -1.00 to -1.60 mm posttreatment (0.5 to 12 years post-retention).
Although there
were inconsistencies in retention protocol and follow-up
duration between studies, increases in intercanine width
during treatment were generally unstable in retention.
They suggest that changes in intercanine width in the range
of 1 mm are maintainable, while changes greater than 1 mm
tend to return to pre-treatment values.
One drawback of
such a study is that there was no long-term control for
comparison.
Thus it is difficult to ascertain whether
post-treatment changes are related to treatment or growth.
Data for untreated individuals from the University of
Michigan Growth Studies66 shows relatively mild decreases
(0.33 mm) in ICW for males and larger decreases (1.73 mm)
for females between 12 and 18 years.
Other long-term
untreated studies show various changes in ICW, ranging from
25
significant decreases of 1.04 mm from 13 to 43 years and
0.82 mm from 36 to 69 years,67 to non-significant increases
of approximately 0.14 mm between 20 and 54 years.68
The
variety of changes in ICW could be due to differences in
sample size and demographics.
The soft tissue equilibrium also applies to the
anteroposterior dimension.
As such, we would expect
proclination or retroclination of the incisors to result in
relapse.
This is relevant because proclination could be an
undesirable consequence of attempts to increase arch
length.
A study by Mills61 looked at deliberate
proclination of the lower incisors during treatment to
determine the long-term position of incisors after
discontinuation of retention.
A sample of 56 cases which
had received a minimum of five degrees of incisor
proclination relative to the mandibular plane (Go-Me), was
compared to an untreated control group of 47 cases.
Cases
were divided into two groups based on proclination of less
than 10 degrees (Group A, mean 7.23 degrees), and 10
degrees or more (Group B, mean 14.4 degrees).
After one
year post-retention, Group A retained 4.8 degrees of
proclination and Group B retained 8.6 degrees of
proclination.
Although this study was limited by its
short-term follow-up, it shows that at least some
26
retroclination occurs post-retention, while a limited
amount of proclination may be stable post-treatment.
NON-TREATMENT FACTORS
As long as basic tenets of treatment are followed,
treatment does not appear to greatly affect the amount of
post-treatment relapse.15,55
This is supported by similar
annual changes in crowding for both treated and untreated
individuals.
Therefore, non-treatment factors such as
physiological changes must be the major players in
crowding.
Many biologic factors can contribute to the movement
of teeth.
As they move, adjacent contact areas may
displace from one another, resulting in a shift of teeth
into malalignment.
Contributing factors can be categorized
as susceptibilities, indirect causes, and predisposing
factors.
These variables are shown in diagrammatic form
(Figure 2.3), and discussed in the text that follows.
27
Figure 2.3.
28
The progression of malalignment.
SUSCEPTIBILITIES
RACE
A review of the National Health and Nutrition Survey
III by Buschang and Shulman20 evaluated incisor irregularity
among whites, blacks, and Mexican-Americans based on a
sample of 9044 subjects.
They found significant
differences in mean irregularity between races, with
Mexican-Americans having the largest irregularity
(3.97 mm), followed by whites (3.77 mm), and then blacks
(2.83 mm).
As will be explained later, tooth size is a
contributing factor to crowding.
Therefore, racial
variations in tooth size could also be an important
contributor to crowding.
A study by Smith et al.69
investigated tooth size variations among 180 pre-treatment
casts divided equally between black, white, and MexicanAmerican subjects.
Although there were no significant
differences between black and Mexican-American subjects
(other than for larger mandibular posterior teeth in
blacks), whites had significantly smaller teeth than both
groups.
These ranged from 3.6-4.8 mm smaller for whites in
the lower arch.
Racial differences and individual variation in arch
form are also evident.70-74
And as will be discussed later,
29
narrower arch widths appear to be a predisposing factor for
crowding.
Several studies have shown that whites have
significantly smaller arch widths and larger arch depths
than Israelis70 and Japanese,71 larger arch widths than
Egyptians,72 and smaller arch widths but similar arch depths
than Koreans.73
However, at the time this review was
written no comparisons for arch sizes between blacks and
Mexican-Americans could be found.
This would be useful in
explaining why these racial groups have similar tooth
sizes, but blacks have less crowding.
SEX
Arch form is also affected by sex.75
On average, men
are generally larger than women,76 and tend to have larger
arches than females.66,68,77,78
teeth than women.69,79,80
Men also generally have larger
For example, Smith et al.69 showed
that mandibular arch lengths were significantly larger for
males than females for anterior and posterior tooth widths.
This amounted to a total tooth size excess in the lower
arch of 3.0 mm for males.
Similarly, Howe et al.80
demonstrated that males had 2.5-3.5 mm larger total tooth
widths, and 0.1-0.6 mm larger individual tooth widths than
females, for the mandibular arch.
differences were not significant.
30
However, these
Conflicting literature makes it difficult to determine
whether one sex has more crowding than the other.
Increased crowding in males16,34 and no sex
differences17,18,48,67,81 have both been described.
In a sample
of 50 white subjects age 18-29, Shah34 found larger crowding
in males than females (II 1.6 mm, TSALD 0.31 mm), although
this did not reach significance (p=0.06).
Similarly,
Bernabé and Flores-Mir82 evaluated a sample of 200 randomly
selected Peruvian schoolchildren between 12 and 16 years,
and found higher TSALD and II in males; they also did not
find significant differences between sexes.
Extensive
population data from the NHANES III study demonstrates that
men have significantly more crowding than women (0.52 mm);
males have 13% greater odds of having crowding.20
Therefore, if sexual differences exist they are likely
small and can only be appreciated by using an extremely
large sample.
AGE
Teeth aligned during orthodontic treatment frequently
show crowding during the post-retention period, but
irregularity is also present among untreated individuals.
Horowitz and Hixon83 alluded to the possibility that
orthodontics could temporarily alter the physiological
31
changes, which resume upon completion of treatment.
This
fosters the idea that crowding may be related to growth.
Buschang and Shulman20 have shown that irregularity
increases in a curvilinear fashion with age in untreated
subjects (Figure 1.2).
These increases are greatest during
the adolescent period and slow after early adulthood.
Other studies show similar trends.
Park et al.84
investigated long-term post-treatment occlusal and arch
changes and consistently found larger decreases in arch
length (0.14 mm) and greater increases in mandibular
irregularity (0.65 mm) and PAR index (1.06) for adolescents
than for adults.
Harris and Vaden54 found lower post-
treatment increases in irregularity among adults (0.21 mm),
although these differences were not significant.
In
addition, Little et al.10 reported that although the
postretention Irregularity Index continued to increase over
time, increases were lower during late adulthood, compared
to early adulthood.
Several other studies discuss the
possibility of a relation between post-treatment crowding
and growth.21,24,57,85,86
32
INDIRECT CAUSES
TOOTH SIZE AND SHAPE
Tooth size is determined by many factors, including
genetics, sex, race, and secular trends,87 and it has been
suggested that larger teeth are more likely to be
crowded.32,87 In a study by Puri et al.,87 forty mandibular
dental casts from untreated subjects were classified as
normal (+3 to -3mm), crowded (<-3mm), or spaced (>+3mm)
based on TSALD.
Measurements for arch perimeter and
mesiodistal tooth sizes were recorded.
Tooth widths were
summed for the total, anterior (2-2) and posterior (3-5)
segments.
Generally, all groups showed significant
differences in size for individual teeth and each arch
segment.
They concluded that spaced arches had smaller
teeth and crowded arches had larger teeth.
A multivariate study by Bernabé and Flores-Mir32 also
evaluated crowding and tooth morphology.
Two-hundred
untreated children age 12-16 were randomly selected.
Subjects were classified as having no, mild, or moderate
crowding based on TSALD.
For each individual, mesiodistal
(MD) and buccolingual (BL) widths were measured, and MD/BL
ratios were calculated for each teeth.
Statistically
significant differences in MD, but not BL, tooth size were
found between the three crowding groups.
33
The lower first
and second premolars and the lower central incisor
contributed most to these variations.
Those with moderate
crowding also had larger MD/BL crown proportions than those
with no crowding.
In contrast, diminutive or missing teeth should create
space to resolve crowding.
For example, Buschang and
Shulman20 found significant reductions in irregularity, and
decreases in the odds ratio, as the number of missing
posterior teeth increased.
Surprisingly, significant
increases in crowding occurred when third molars were
missing.
THIRD MOLARS
There has been much discussion in the literature in
terms of a potential relation between crowding and third
molars.
A survey conducted by Laskin in 1971 found that
65% of orthodontists and oral surgeons believed that third
molars could occasionally cause crowding.88
It was thought
that the force of eruption of third molars may constitute a
mesially directed “push” against the neighboring dentition,
leading to a loss of arch length.
There is some literature
to support this concept.89-91
However, the great majority of research supports the
idea that third molars have no significant effect upon
34
crowding.92-99
One of the most cited studies relating third
molars with crowding is that of Kaplan.99
He investigated
seventy-five orthodontically treated patients divided among
three groups:
those with bilaterally erupted (n=30),
bilaterally impacted (n=20), and bilateral agenesis (n=25)
of third molars.
Model analysis and cephalometric
superimpositions provided information on arch width, arch
length, lower incisor irregularity, lower incisor
rotations, incisor angulation and position, and molar
position.
Crowding increased in all groups, and no
significant differences were found between groups for any
measures, more than 9 years post-retention.
An epidemiological study of 9044 individuals by
Buschang and Shulman20 also showed that erupted third molars
do not appear to affect crowding.
In fact, there was a
greater likelihood of crowding if the third molars were not
present.
In a prospective randomized controlled study,
Harradine and others95 also could not find any significant
statistical or clinical relationship between the presence
of third molars and crowding.
In their study, 164
adolescent patients (14.8 years of age) were randomized to
have either removal or retention of third molars.
5.5 years, 47% of patients presented for follow-up.
After
35
Dental
casts were collected before and after treatment and changes
in irregularity (II), intercanine width (ICW), and arch
length were compared between the two groups.
The removal
group demonstrated 1.0 mm less arch length compared to the
retained group; however, there were no statistical
differences in ICW or II.
They concluded that there was
insufficient support for the removal of third molars in
order to prevent crowding.
PERIODONTAL AND GINGIVAL FIBERS
Reitan100 was the first to relate periodontal fibers
and orthodontic relapse.
By studying relapse in dogs, he
found alterations in the supracrestal periodontal fibers
after tooth rotation.
It was later shown by Edwards,101
using tattoo markings on the attached gingiva, that
reorganization of the tissue did not occur during
orthodontic treatment.
The current thinking is that stretching of the
transseptal fibers creates a tendency for relapse as they
recoil after orthodontic completion.15
These fibers can
take up to 232 days to remodel,100 thus leading credence to
the circumferential supracrestal fiberotomy technique
(CSF).
In fact, a prospective evaluation of CSF showed
that this procedure was effective in reducing rotational
36
relapse in cases with significant initial irregularity.102
However, the procedure is less effective in preventing
relapse in the mandibular anterior region,102 suggesting
that periodontal fiber relapse may play only a small part
in mandibular anterior crowding.
The periodontal fibers are also important for mesial
migration of teeth, also known as approximal drift.103,104
A
split-mouth study by Picton and Moss103 examined this
process in nine adult macaca monkeys.
In the treatment
group, interproximal tissue was traumatized by either
scraping or using a scalpel to cut it to the level of bone
every two weeks.
In the control group, the tissue was
either left untraumatized or the papillae was removed.
A
diamond disc was used to create space between neighboring
teeth, and this was reopened at two week intervals with
further disking if it had closed.
To measure the amount of
migration, the distance between amalgam fillings placed in
the cheek teeth was measured at each follow-up visit using
occlusal radiographs.
In cases with either no trauma or
papillectomies, they found that teeth reapproximated, while
in cases with trauma to the interproximal periodontium, the
teeth showed a marked reduction in reapproximation.
Differences in total drift and rates of drift (micrometers
per week) were statistically significant.
37
No differences
were found between the control or papillectomy, or scraping
versus cutting groups.
This study supports the
contribution of transseptal fibers to mesial drift.
ANTERIOR COMPONENT OF FORCE
In 1923, Stallard speculated that the malalignment of
teeth was related to drift of the buccal segments toward
the front of the mouth.105
He felt that the force of
occlusion was dispersed during chewing by mesial tipping of
the posterior teeth.
As these teeth incline further
forward they create a force, directed through the
interproximal contacts, toward the front of the mouth
(Figure 2.4).94
It was suggested that this anterior
component of force (ACF) could result in mesial drift and
consequent malalignment of the teeth.
Two studies by Southard and coworkers help to
substantiate this proposition.94,106
In the first study,94
the anterior force generated at each interproximal contact
was determined using a dental matrix strip that was placed
interproximally and withdrawn.
A single known axial force
(20 lbs) at the left second molars was used for each
individual, and this was repeated for 15 subjects during
biting and at rest.
They confirmed the existence of an
anteriorly directed force that dissipates exponentially
38
toward the front of the mouth.
This force was higher
during biting than rest, did not progress past any open
contacts, and was reduced after it passed the contact
between the lateral incisor and the canine (Figure 2.5).
The force was also found to cross the midline up to the
contact of the contralateral canine in some cases.
In the second study,106 three groups of five subjects
were selected based on their initial irregularity index.
Group A had <2 mm irregularity, Group B 2-4 mm, and Group C
>4 mm.
Interproximal force recordings were made for each
of these subjects at rest and during biting, as in the
previous study.
Significant correlations were found
between irregularity and both the ACF and resting
interproximal forces.
Thus, the ACF theory helps explain
why decreases in arch length and increases in malalignment
(especially at the lateral incisor/canine region) occur
over time.
Figure 2.4. Anterior component of force (saggital view).
39
Adapted from Southard et al.94
Figure 2.5. Anterior component of force (occlusal view).
Adapted from Southard et al.106
In a recent thesis by Myser et al.,107 interproximal
restorations were also found to increase the amount of
crowding.
This is thought to be due to the creation of a
“tight” contact, which may also result in an anterior
component of force.
This may be related to age, as the
number and extent of filled surfaces generally increases
over time.
Finally, Sanin and Savara108 suggested that the axial
inclinations of the molars and incisors were major
contributors to the development of crowding.
Among 150
children examined at 8 and 14 years of age, those with the
worst prognosis for alignment tended to have more upright
lower incisors and more mesially inclined first molars
(Figure 2.6).
In contrast, children with the most
favorable prognosis had labially inclined incisors and
40
distally inclined first molars.
These angulations may help
resist the ACF.
Figure 2.6. Stability in relation to dental angulation to the mandibular plane.
Adapted from Sanin and Savara.108
However, Picton and Moss109 could not find any relation
between root angulation and the rate or amount of mesial
drift.
In their investigation, tooth movement was assessed
over a period of six to eight weeks by measuring the
distance between two amalgam fillings.
They evaluated 70
pairs of cheek teeth in nine adult macaca monkeys.
Root
angulation was estimated by averaging the angle of the
roots to the occlusal plane for each tooth.
Three
scenarios were compared: migration in normal occlusion,
41
migration in normal occlusion with interproximal tissue
trauma, and migration without occlusal contact
(i.e., opposing teeth extracted).
When the data was
compared, no discernable relationship could be found
between root angulation and the direction or amount of
migration.
PRIMARY TOOTH LOSS, ERUPTION SEQUENCE
Premature loss of a primary tooth can be cause for
concern if space is not maintained.110-112
This is because
teeth drift toward the front of the mouth due to the
anterior component of force94 and transseptal fiber pull.103
As teeth move forward, arch length is lost and there may be
insufficient space for the permanent dentition to erupt.1
Northway and coworkers111 assessed the consequences of
early loss of primary molars in dental casts of 107
children, evaluated annually between 6 and 12 years of age.
Children were classified into two groups: mutilated, based
on either severe caries and/or early tooth loss; or
control, based on restorations and/or lack of (or mild)
caries.
The mutilated group was further divided based on
which primary teeth were affected.
After analysis, a large
difference was found in space loss between the mutilated
and control groups, which was significant at all time
42
points.
Compared to the controls, early loss of a first
primary molar (D) resulted in 3.3 mm more space loss, loss
of a second primary molar (E) resulted in 2.6 mm more loss,
and loss of both the D and E resulted in 3.6 mm greater
loss; severe caries resulted in 2.1 mm greater loss.
No
association was found between the age of tooth loss and the
total amount of space lost, but in all groups the majority
of space was lost during the first year.
In addition,
early loss of the E had a significant effect on the
occlusion, often resulting in mesiocclusion.
Studies such
as this explain why space maintenance has become an
established treatment guideline for any lapse in permanent
tooth eruption of more than 6 months after the deciduous
tooth has been lost.1,112
Eruption sequence may also contribute to crowding if
it promotes a loss of arch length.
Changes in eruption
sequence can occur due to localized alterations in bone
density, tissue thickness, primary tooth resorption rates,
ankylosis, or early loss of primary teeth through caries or
infection.111,113
Lo and Moyers113 found that 17 different
eruption sequences could occur in the mandible: almost half
of the time the premolars erupt before the second molars,
in the sequence 3 4 5 7; but, just under 20% of the time,
the second molars erupt prior to the second bicuspid as
43
3 4 7 5.
If the second primary molar has already been
lost, this can result in mesial movement of the first molar
and a decrease in arch length.1
This limits the amount of
space available for the eruption of the second premolar,
resulting in posterior arch crowding.
Because literature relating eruption sequence to
crowding is sparse, a recent thesis by Lange114 evaluated
this topic.
In her study, the eruption sequence of canines
and premolars was evaluated in 28 patients using panoramic
radiographs and correlated to dental arch measures
(intermolar width, arch depth, and TSALD).
Although a
relatively small sample was used, she found that the lower
arch had a more variable eruption sequence than the upper
arch, and that the sequence 4 3 5 was related to
significantly more crowding (2.5 mm) than the sequence
3 4 5.
PREDISPOSING FACTORS
ARCH FORM
Since the dimensions of the arch affect the amount of
space for the teeth to align, variations in arch form might
be expected to be associated with crowding.107,108
It is well
established that decreases in mandibular arch length,
width, and depth occur over time;54,75,84 however, it is
44
unknown whether crowding causes, or is the result of, these
changes.
Two studies support the notion that narrower arch
widths predispose individuals to crowding.
Howe and
coworkers80 evaluated the contributions of tooth size and
arch size to crowding.
Fifty casts of patients with
significant crowding were compared to 54 casts of patients
without or with only minimal crowding.
Measures of tooth
size and arch width were made, while arch perimeter and
area were estimated.
Their results indicated no
differences between crowded and uncrowded groups for
individual or total tooth size, but significant differences
for all arch dimensions (except arch perimeter in males).
Similarly, Myser107 found that narrower intercanine arch
widths related to post-retention crowding in 66 subjects
evaluated 16 years post-treatment.
Correlation
coefficients were low between intercanine width and TSALD
(r=0.275) but moderate between intercanine width and II
(r=-0.371).
Richardson,115 however, did not find a relation
between crowding and intercanine arch width or skeletal jaw
width among 55 individuals 13 to 18 years of age.
Arch depth is also an important factor in crowding as
shown by Bernabé and others.116
45
In their study, 300
randomly selected casts were divided into no (n=127), mild
to moderate (≤5 mm) (n=122), and significant crowding
(>5 mm)(n=51) groups.
Measures for mesiodistal (MD) and
buccolingual (BL) tooth width, tooth width ratio (MD/BL),
intercanine width, intermolar width, and arch depth were
made.
After modeling with stepwise multiple discriminant
analysis, eight variables were found to differentiate
between the crowding groups.
These included arch length;
intermolar width; central incisor, lateral incisor, canine,
second premolar, and first molar MD sizes; as well as
canine MD/BL ratio.
The total equation accounted for 51%
of the variability in crowding.
After arch depth was
removed, the predictive ability of the equation dropped to
14%.
Removal of intermolar width resulted in a further
decrease to 8%.
Thus, arch depth had the greatest ability
to discriminate between the groups in this sample.
POINT-TO-POINT CONTACTS
Tooth contacts areas, or proximal contacts, are the
areas where a tooth crown contacts a neighbouring tooth.
This corresponds with the area of greatest surface contour,
known as the height of contour.117
They start initially as
point contacts, and as teeth move during function, undergo
surface wear.
As the contact size broadens, they become
46
contact areas.117
Contact areas are larger in the posterior
due to more wear (due to heavier contacts) and also because
the teeth are larger, with more surface area in contact.
Begg118 and Corrucini119 showed that Australian aborigines
have wear at the interproximal surfaces of their teeth,
amounting to approximately 4-6 mm.119
Such wear is thought
to stabilize the teeth and prevent the contacts from
“slipping” past one another.
Contacts may be between two convex surfaces, or
between a concave and convex surface, as in worn aboriginal
teeth.
An investigation into the mechanics of crowding by
Ihlow120 investigated these two contact types using a twodimensional plexiglass model representing 12 teeth of an
arch.
The arch model was compressed with a plexiglass rod
affixed to weights, ranging from 1-5 Newtons, and the arch
height was measured.
averaged.
This was repeated 15 times and
Prior to weight application, both arch forms
were similar, but after the addition of force the point
contacts showed about twice as much displacement as the
overlapping contacts.
Although an in vitro study, this
provides some credibility to the stabilizing nature of
larger contacts.
The concept of broad contacts has also been suggested
by some clinicians who advocate reproximation of lower
47
anterior teeth toward the end of treatment to help prevent
relapse.121
Alexander122 found that in Class I extraction
cases followed from 15.2-32.2 years, individuals with
interproximal reduction (IPR) of the lower incisors had 1.4
mm less irregularity at the end of treatment than those
without IPR.
Wang et al.123 also investigated the use of
anterior tooth reproximation to reduce post-treatment
crowding.
One-hundred-and-twenty-nine patients with
average age 13 years were divided into control (n=81) and
experimental (n=48) groups.
The experimental group
received circumferential fiberotomy (CSF) on the anterior
segments while the control group did not.
Of those
experimental patients, 23 had further treatment involving
contact point reproximation.
for up to two years.
Hawley retainers were worn
Two years after discontinuation of
retention, dental casts were measured for crowding.
They
found that crowding was reduced by 21.6% in the
experimental group, and that contact reproximation reduced
crowding 6.56% more than CSF alone.
FACIAL DIVERGENCE
Vertical growth of the face is the result of many
interacting components.
Dental, skeletal, and soft tissue
structures act in concert to affect development, and are
48
modifiable by environmental inputs.124
Adaptations have
been linked to weak masticatory muscles, reduced orofacial
airways,125-128 and/or variations in craniofacial
anatomy.124,129,130
The vertical morphology of the skull may be described
in terms of “facial divergence,”86,131 defined by the angle
between the cranial base (sella-nasion) and the mandibular
plane.
This may be used to differentiate those who have
small divergence (hypodivergence) from those with normal
(normodivergence) or large divergence (hyperdivergence).
In fact, Reidel132 classified SN-MP quantitatively based
upon one standard deviation from the mean.
However, sexual
differences of the cranial base angle (N-S-Ba) suggest that
the palatomandibular angle (PP-MP) may be a more reliable
indicator of divergence.133,134
Other classification methods such as posterior to
anterior facial height ratio (PFH:AFH),135 upper to lower
face height ratio (UFH:LFH),136 and lower to total anterior
face height (LFH:AFH)137 are also described in the
literature.
These ratios have been shown to relate
significantly to angular measures (i.e., SN-MP and PP-MP),
as well as to one another, ranging from low (r=0.143) to
moderately high (r=0.873) correlations.138
49
The vertical pattern of growth is established at a
young age and is surprisingly stable.133,135,139
For example,
Bishara135 found approximately three-quarters (77%) of
individuals maintained their vertical classification from 5
to 25.5 years.
Jacob and Buschang138 had similar findings,
with 75-86% of individuals maintaining the same
classification from 10 to 15 years; however, 27-53% of
individuals within a category may worsen.
Of those that
did not maintain their classification, it was exceedingly
rare (< 3%) for an individual to change more than one
category.135
Although the mandibular plane angle may
increase in some individuals,140 a tendency toward mild
closure is most common in all groups.133,141
Remodeling of
the mandibular border tends to mask roughly half of any
rotational changes.140
Of particular interest in this paper are those with a
hyperdivergent facial type.
These individuals are
categorized from hypodivergent and normodivergent
individuals by several phenotypic features, including a
downward rotation of the posterior maxilla, backward
inclination of the condylar head, short mandibular ramus,
obtuse gonial angle, antegonial notching of the mandibular
border, forward inclined symphysis, mandibular
retrognathism, acute interincisal or intermolar angles,
50
long lower anterior face height, anterior open bite,
straight mandibular canal curvature, and/or maxillary
transverse deficiency.124,129,130,142
Hyperdivergence may relate to crowding by three
potential relationships.
They include secular trends,
dentoalveolar instability, and compensatory rotational
changes.
These are discussed separately.
SECULAR TRENDS
Malocclusion is a modern phenomenon.
Epidemiological
studies have shown that early traditional populations
generally had worn but acceptable occlusions, while a trend
toward increased crowding and less tooth wear has occurred
in modern civilizations.143,144
This shift mirrored
urbanization, with soft diets consisting of processed
foods, resulting in a decrease of masticatory forces.143,144
These changes have been swift, occurring within only a few
generations.145
Begg118 thought that crowding in “preindustrial”
populations (Australian aborigines) was alleviated by
interproximal tooth wear through vigorous chewing of a hard
diet.
Forty years later, Begg’s sample was re-examined by
Corrucini119 and the wear was found to be much lower, on the
order of only a few millimeters per quadrant, an amount
51
Corrucini145
insufficient to compensate for crowding.
theorized, based on comparisons of “preindustrial” and
“industrial” groups among various ethnicities, that
mastication is important for the development of muscle and
bone mass of the face; a reduction of function could lead
to craniofacial alterations, such as decreases in jaw size,
and insufficient space for the teeth.143
This theory has
been supported by various animal (primates,146-149 rats,150-157
ferrets,158 and minipigs159) and human145,160-164 studies.
Changes in masticatory function have also been closely
linked to skeletal divergence.160,165-176
Studies of
“premodern” and “modern” Finnish skulls by Varrela160 have
shown facial divergence to increase in recent years,
theoretically due to a reduction in masticatory muscle
strength associated with softer diets.
Studies supporting
this link have shown decreased bite force, reduced
mechanical advantage (ratio of muscle length to lever
length),171 reduced muscular efficiency, reduced muscle
activity,172 and reduced muscle thickness and volume177 in
hyperdivergent individuals.
In fact, Garcia-Morales et
al.171 showed that divergence accounted for almost a quarter
(24.3%) of the morphological variance in function.
Specifically, the importance of masseteric muscle function
is supported by the literature.178,179
52
Increases in
mandibular plane angle and other hyperdivergent features
have been produced experimentally by resection of the
masseteric muscles in Wistar rats.180
Finally, the
significance of muscular development and function on
skeletal divergence can be observed in nature.
Individuals
with muscular disorders such as Duchenne and myotonic
muscular dystrophy,181 cerebral palsy,182,183 and spinal
muscular atrophy168
show increased divergence, maxillary
transverse deficiency, long lower anterior face heights,
posterior tooth eruption, anterior open bites, and
increased crowding.
Because secular trends involve increases in both
crowding and facial divergence, it is possible that they
are related through the same environmental influences, such
as musculoskeletal alterations.
Although these trends are
interesting from the viewpoint of studying changes in a
population over time, they are less useful in studying
associations at the level of the individual.
DENTAL ERUPTION AND INSTABILITY
During normal development, eruptive movements maintain
teeth in a functional occlusion.
This occlusion is a
position of homeostasis between the forces of eruption and
those that oppose it, such as biting and soft tissue forces
53
(i.e., lips, cheeks, tongue).184
Growth, especially
pubertal spurts, creates space between the teeth and allows
notable eruption to occur.
For example, Buschang et al.185
found that dentoalveolar heights increased 2.1 to 4.2 mm
(7.6-23.0%) from age 10 to 15 years, depending on the
region.
Peak eruption occurred at around 12 years.186
As
growth slows into adulthood, teeth retain their eruptive
potential and occlusal relations are maintained despite
attritional tooth loss or further growth.184
A study by Slagsvold et al.184 investigated whether
tooth eruption would occur if occlusal forces were removed.
Pre-operative records (impressions, intraoral photographs,
and lateral cephalograms) were collected for three adult
cercopithecus monkeys, followed by cementation of a silver
splint, meant to artificially create tooth separation in
half of the mouth.
After 8.5-11 months, splints were
removed and progress records were collected.
Final records
were collected 2-3 months after splint removal.
In all
three monkeys, dental eruption re-established occlusion of
the teeth (Figure 2.7).
54
Figure 2.7. Photographs showing maintenance of a functional occlusion.
(A) initial, (B) after splint cementation, (C) 10.5 months later, (D) after splint
removal, (E) 3 months later. Adapted from Slagsvold and Karlsen.184
This finding implies that even after growth levels
subside, eruptive potential remains if teeth are taken out
of occlusal contact.
This eruptive potential is also
obvious in humans when an antagonistic tooth is lost, and
supraeruption of the opposing tooth occurs.
Thus, eruption
appears to maintain an efficient and functional chewing
system.
This notion has been described as the
dentoalveolar compensatory mechanism by Solow187 and is
supported by various articles.185,186,188
Nonetheless, Behrents,189 Bishara,190 and others191,192
have shown that facial growth continues far into adulthood,
though at a slower rate, thus implying that facial
dimensions are in no way static.
These growth trends have
been modeled by Björk and Helm193 (Figure 2.8).
55
Figure 2.8. Variations in growth rate.
Adapted from Björk and Helm.193
Growth is particularly pronounced in the vertical
dimension, which is the last dimension to be
completed,10,16-21 increasing approximately two to four times
as much as horizontal growth during the early adulthood
period.24,25
Furthermore, growth continues longer in the
mandible,194 because of the cephalocaudal gradient of
growth.1
Therefore, one could expect that vertical changes
in mandibular growth would have a significant effect on the
dentition and that dental eruption could be related to the
rate of vertical growth of the mandible.
relation was found by Liu and Buschang.186
56
In fact, such a
In a
longitudinal study of 124 untreated females between 10 and
15 years of age, superimpositions of the cranial base and
mandible were used to determine the amount of vertical
mandibular growth and tooth eruption, respectively.
Vertical mandibular growth and mandibular tooth eruption
were found to have similar velocity curves, and mandibular
molar and incisor eruption were found to be closely related
to vertical mandibular displacement (Figure 2.9).
In terms
of dental compensations, 54% of the variation in lower
molar eruption and 13% of the variation in lower incisor
eruption were due to inferior growth displacement of the
mandible.
Figure 2.9. Velocity curves for tooth eruption between 10 and 15 years.
(A) molar and (B) incisor; g = growth, e = eruption, L = lower, U = upper
Adapted from Liu and Buschang.186
57
Having established that vertical growth and dental
compensations are related, the next step is to look at
variations in vertical growth.
Discrepancies between
anterior and posterior vertical growth bring about
different facial proportions, known as facial divergence.
The greater the divergence, the greater the space between
the jaws anteriorly, and the further the incisors must
travel to maintain occlusion.195
Thus dentoalveolar
compensation would be greatest in hyperdivergent
individuals and smallest in hypodivergent individuals.187
This relation is well established in the
literature.134,180,195-198
Janson et al.195 evaluated the relationship between
dentoalveolar height and facial divergence in 344 untreated
Class I and II individuals at 12 years of age.
Using the
upper to lower anterior facial height ratio (UFH:LFH),
subjects were classified as short, normal, or long facial
types.
Dentoalveolar heights were measured at the incisors
and molars from the incisal or occlusal edges to the
palatal and mandibular planes, and analyzed in relation to
facial height.
The alveolus was significantly larger in
those with long lower facial heights and significantly
smaller in those with short lower facial heights (Figure
2.10).
Males also generally had greater dentoalveolar
58
heights than females.
Moderate negative correlations were
found between the facial height ratio and dentoalveolar
heights, with larger coefficients for the upper (r=-0.43
(molar), r=-0.60 (incisor)) than the lower (r=-0.32
(molar), r=-0.49 (incisor)) dentition.
Multiple regression
revealed that the variation in lower face height was
explained by 22% posterior and 41% anterior dentoalveolar
compensation.
These findings indicate that the vertical
position of the incisors is more closely correlated to face
height than the molars, especially for the upper arch.
This data conflicts with other studies that show increased
relation of the lower dentition to variations in facial
height.185,196,197
This could be possible due to sampling,
population characteristics, or the cross-sectional nature
of this study.
Figure 2.10. Relation between dentoalveolar height and facial height.
UPDH = Upper posterior dental height; LPDH = Lower posterior dental
height; UADH = Upper anterior dental height; LADH = Lower anterior
dental height. Adapted from Janson et al.195
59
Enoki and coworkers134 also found significant positive
correlations between lower anterior face height and
dentoalveolar eruption.
In their study, eighty 11-13 year
old Class I skeletal individuals were divided into short,
normal, and long lower face height groups based on the
ratio of lower to anterior facial height (LFH:AFH).
Dentoalveolar heights were measured from the incisors and
molars to the palatal and mandibular planes, and these were
analyzed in relation to lower anterior face height.
Although there was a trend to increasing dentoalveolar
heights with increasing lower anterior face height,
significant differences were found only between the upper
incisor region in long faced individuals, and the molar and
lower incisor regions in short faced individuals.
Correlations between lower face height and incisor heights
were significant for all groups at the 0.001 level, while
molar heights showed a trend toward significance.
Interestingly, although the palatomandibular angle differed
significantly between all groups (p<0.001), the mandibular
plane angle showed no relations.
Sampling, population
characteristics, the cross-sectional nature of the study,
and the lack of a large sample size may have resulted in a
lack of significance between some groups in this study.
60
Beckmann et al.197 compared vertical dentoalveolar
compensations between 460 untreated Caucasian adults with
normal overbite divided into short, normal, and long lower
anterior facial height groups.
segregated by sex.
These groups were also
Dentoalveolar heights were measured
from the midpoint of the base of the symphysis or hard
palate to the incisal edge, using a line bisecting both the
cementoenamel junction and the midpoint of the alveolus;
while dentoalveolar width was measured perpendicular to the
bisecting line, tangential to the incisor apices.
In
general, the researchers found significant differences in
dentoalveolar heights and widths for both jaws; however,
males did not show differences in arch depths.
Incisor
dentoalveolar heights showed strong correlations (r=0.70
and r=0.82, respectively) with lower face height, while
dentoalveolar widths showed moderate to weak correlations
(upper r=-0.25, lower r= -0.48).
The palatomandibular
angle differed significantly between the three groups, also
having a high correlation to lower face height of r=0.78.
This study supports a trend to shorter alveolar heights and
greater widths in short-face individuals and larger heights
and smaller widths in long-face individuals (Figure 2.11).
61
Figure 2.11. Cross-sectional views of the anterior alveolus in short,
normal, and long-face individuals. Adapted from Beckmann et al.197
In a similar study by Kuitert et al.,196 vertical
dentoalveolar compensations were compared between long and
short face groups, separately for men and women.
Records
of 557 untreated Caucasian adults were collected and
subdivided based on overbite (open, edge-edge, normal,
deep) and lower anterior face height (short, normal, long).
Similar to Beckmann’s study, measurements were then made
for dentoalveolar heights and widths, except that widths
were measured perpendicular to the bisecting line through
either A point or B point and the lingual surface of the
alveolus.
In general, greater dentoalveolar heights and
smaller dentoalveolar widths were found in the lower arch
than the upper arch, regardless of facial type.
The
alveolus was also taller and narrower in individuals with
longer face heights than in those with short face heights,
62
which were shorter and thicker.
These differences all
reached statistical significance at the p<.001 level.
In
both groups the lower incisor dentoalveolar heights
explained 32-37% of the variation in overbite, while upper
incisor dentoalveolar heights explained only 3-4% of the
variation.
This suggests that variations in the lower arch
are more related to variations in facial height.
Longitudinal evaluations of dentoalveolar changes in
various facial divergence categories and studies utilizing
measures of divergence other than anterior face height are
lacking.
However, the literature provides evidence of a
relationship between dentoalveolar height and facial
divergence, suggesting that the greater the facial height,
the more the incisors erupt to compensate for changes in
the occlusion.
In addition, the greater the divergence,
the greater the alveolus is in height and the thinner it is
in width, especially in the lower arch.
In summary, long-
face (hyperdivergent) individuals demonstrate a tall and
narrow dentoalveolar process with a steep mandibular plane
angle, while short-face (hypodivergent) individuals, have a
wider and shorter dentoalveolar process with a shallower
mandibular plane angle.
These morphologies are illustrated
below in Figure 2.12.
63
Figure 2.12. Comparison of divergence morphologies.
Adapted from Solow.187
In hyperdivergent individuals, dentoalveolar changes
may be significant, and such variability in incisor
position has been hypothesized to result in instability of
the occlusion,22 potentially leading to crowding or
irregularity.17,122
It is currently unknown whether such a
tall and narrow alveolus provides less protection from
functional and soft-tissue forces that could cause tooth
movements.
COMPENSATORY ROTATIONAL CHANGES
As growth continues, the face can maintain or change
its vertical proportions depending on whether the anterior
64
and posterior face grow equivalently or disproportionately.
If the anterior and posterior face increase similarly,
there is no rotational component.
However, there is
typically a discrepancy favoring the vertical growth of the
condyle and ramus, as compared to vertical growth of the
alveolus, and so the mandible frequently has a rotational
component.199
These rotational tendencies can influence the
direction of eruption of the teeth.
Excessive posterior
growth results in forward mandibular rotation, leading to a
short facial type with greater molar eruption than incisor
eruption.
Insufficient posterior growth, however, results
in backward mandibular rotation, leading to a long facial
type with greater incisor eruption than molar eruption.
As early as 1946, Tweed documented natural variations
in mandibular incisor position associated with facial
morphology.200
He found that displacements from an upright
mandibular incisor position corresponded to differences in
the mandibular plane angle, and recommended that for every
degree the mandibular plane angle (FMA) exceeded the norm
of 25 degrees, the lower incisors should be positioned a
similar amount behind their norm of 90 degrees.201
This
suggests that subjects with a hyperdivergent mandibular
plane would have the lower incisors placed lingually to
65
their typical upright position.
This would reduce the
available arch length and contribute to dental crowding.
Condylar growth direction also has a bearing on the
direction of tooth eruption, as confirmed by Björk.202
This
direction is unpredictable, varying as much as 42
degrees.192
By superimposing serial cephalograms he showed
that condylar growth direction was related to anterior
tooth position (Figure 2.13).
Similar to Tweed’s
observations, Björk and Skieller140 suggested that
compensations in the direction of tooth eruption occur
relative to rotational changes of the mandible.
Individuals with average condylar growth direction showed a
relatively stable position of the anterior teeth, while
vertical and anterior condylar growth was related to
forward eruption, and sagittal condylar growth was related
to backward eruption.
As such, individuals with
hypodivergence should show increased protrusion of the
incisors, while individuals with hyperdivergence should
show a tendency towards retroclination.
This relation is
supported in the literature.77,203,204
Either extreme may relate to crowding.
Those with an
average mandibular plane should show less propensity to
either trend, and should demonstrate less crowding.
66
Figure 2.13. Relation between facial divergence and tooth eruption.
Adapted from Bjork.202
FACIAL DIVERGENCE AND CROWDING IN THE LITERATURE
Although three potential relations between facial
divergence and crowding have been provided, the literature
relating divergence to crowding is sparse.
Studies
relating facial divergence to crowding are described below,
and separated into cross-sectional and longitudinal studies
as well as treated and untreated samples.
CROSS-SECTIONAL STUDIES
Untreated samples:
A study by Nasby et al.204 evaluated differences in
crowding between high and low divergence subjects.
From a
patient population of 150 high angle and 53 low angle
subjects at the University of Minnesota, 20 subjects were
randomly sorted to each group based upon mandibular plane
to sella-nasion angle (±1 SD from Reidel’s mean).
67
Mean
ages were 12.9 and 13.7 years, respectively.
Models were
analyzed for arch perimeter, arch depth, TSALD, and
intermolar width; while cephalograms were used to compare
lower incisor inclination.
Although no statistical
analyses were used, hyperdivergent subjects had an average
of 1.5 mm more crowding than hypodivergent subjects.
They
also showed narrower intermolar widths (2.3mm less) and
more upright incisors (5.9 degrees), both of which could
contribute to crowding.
However, the small sample size and
lack of significance testing detract from the
generalizability of the results.
Insufficient details were
provided as to the demographic composition of the sample.
LONGITUDINAL STUDIES
Untreated samples:
Richardson24 evaluated the effect of facial morphology
on lower arch crowding (TSALD) in 51 subjects evaluated at
13 (T1) and 18 years (T2).
Lateral cephalograms were used
to evaluate 11 linear and angular measures, and changes
were assessed based on superimpositions.
Model analysis
included measures for both anterior and total TSALD.
Total
TSALD was significantly correlated with lower face height
(r=-0.47) and PP-MPA (r=-0.61) in males at T1.
Multiple
regression for the pooled sample revealed a relation
68
between the T1 measurements and change in total TSALD for
ramus height, mandibular body length, lower face height,
and PP-MPA (R=0.60).
Of these, PP-MPA contributed most to
the regression formula.
No significant relations were
found for anterior TSALD and T1 measures.
In terms of
change in measures (T2-T1) and change in TSALD, significant
relations were found only for anterior TSALD; these
included gonial angle, PP-MPA, NSGn, and mandibular
rotation (R=0.58).
However, many variables were studied
and so it is possible that some of the results (5%) could
have been due to chance alone.
Other shortcomings include
a lack of description of the demographic and dental
classification of the sample.
Orthodontic treatment in the
upper arch of some patients may have increased facial
divergence via extrusion, thus confounding the results.
Leighton and Hunter205 compared 88 individuals from the
King’s College and the Burlington Growth Study at 8 (T1)
and 14 years (T2).
Subjects were segregated into spaced,
moderately crowded (≤4 mm), and severely crowded (> 4mm)
groups, and various skeletal measurements were evaluated at
both time points.
Allowances were made for magnification
between the two samples.
Significant differences were
found for facial divergence between each of the crowding
groups, including measures of SN-MP, SN-OP, and SN69
endognathion.
Unfortunately, there was no discussion of
the demographic breakdown of the sample, nor any
description of how crowding was measured.
Sakuda et al.24 evaluated 30 untreated subjects at ages
12 (T1), 14 (T2), and 17 (T3) to determine if crowding was
related to changes in skeletal growth.
Twenty-seven
skeletal measures as well as dental irregularity (in both
the anterior (3-3) and posterior (6-3) regions) were
measured.
In terms of the changes in anterior crowding and
growth changes from T1-T3, facial divergence (PP-MPA and
SN-MP) did not enter the multiple regression formula.
However, multiple regression showed that facial divergence
(PP-MPA) at T1 was significantly, but weakly, related to
the change in anterior crowding for both the upper
(r=+0.18) and lower (r=+0.24) arches.
Using 25 sets of twins studied from age 12-15 to 23-26
years, Lundström203 evaluated the relationship between
various skeletal and dental measures.
Lateral cephalograms
were superimposed and compared with an Adams blinkcomparator.
No covariation was apparent between the
direction of growth of gnathion or increases in lower
crowding, although statistical analyses were not used.
Unfortunately, this study also lacked a description of the
70
demographic composition and it was unclear how crowding was
measured.
Treated samples:
Using 123 patients from the University of Washington,
Fudalej and Årtun206 examined the association between posttreatment crowding and changes in facial divergence in
various facial types.
Subjects were segregated into short,
average, and long facial heights based upon post-treatment
SN-MP angle (≤28 o, 29o-37 o, and ≥37 o, respectively) and
irregularity was measured for each group.
Mean age was
15.8 years post-treatment (T1) and 31.9 years postretention (T2).
No significant differences were found for
irregularity or change in irregularity between the groups.
However, moderate crowding (>5.0 mm) at T2 was found in
13.6% of hypodivergent, 28.6% of normodivergent, and 31.4%
of hyperdivergent individuals.
This was significant at the
0.05 level, supporting the idea of increased crowding with
hyperdivergence.
Although the groups were matched, they
were heterogeneous (including various malocclusions and
treatment types).
In addition, irregularity was the only
measure of crowding and the power to detect a difference of
≥1mm irregularity was just 62%.
71
Another study, by Zaher et al.,207 evaluated whether
post-treatment changes varied between facial types in 66
Class II Division 1 subjects treated on a non-extraction
basis.
Cephalograms and models were collected pre-
treatment (T1), post-treatment (T2), and a minimum of 2
years post-retention (T3).
Subjects were classified as
having either a short (n=20), average (n=26), or long face
(n=20) based on posterior to anterior face height ratio
(PFH:AFH), mandibular plane inclination to Frankfort
horizontal (FMA), and mandibular plane inclination to
sella-nasion (SN-MP).
In case of disagreement between the
measures, two clinicians evaluated Björk’s various facial
structures to determine the appropriate category.
No
significant post-treatment skeletal changes occurred
between groups, except for a significant decrease in the
upper anterior facial height proportion.
In terms of
dental changes, there were no significant differences in
arch widths or arch length over the post-treatment
interval.
Amounts and changes for total and anterior TSALD
were not reported for either treatment or post-treatment
intervals, therefore it is assumed that these measurements
did not differ significantly between the three facial
types.
72
STATEMENT OF THESIS
Many studies have evaluated the causes of crowding,
but it is presently unclear why some patients develop
crowding and others do not.
Comparisons of treated and
untreated individuals show similar changes in terms of the
amount and rate of crowding over time.
growth as a potential causative factor.
This implicates
Vertical growth is
more intense and continues longer than the other facial
dimensions, and thus probably has the greatest effect upon
changes in the dentition.
Relations between vertical
growth and crowding have been previously shown, but few
studies have assessed the association between crowding and
facial divergence.
Of these, heterogeneous study groups, a
failure to segregate sexes, various measures for divergence
and crowding, and conflicting results suggest a need for
further studies.
It is the purpose of this investigation
to determine whether differences in facial divergence
relate to crowding in treated and untreated individuals.
73
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92
CHAPTER 3: JOURNAL ARTICLE
Abstract
Purpose:
To better understand the relationship
between vertical facial growth and mandibular anterior
crowding, this study evaluated untreated subjects crosssectionally and treated subjects longitudinally.
Methods:
The sample consisted of 1) pre-treatment records
of 75 untreated Class I Caucasian patients collected from
the archives at Saint Louis University, and 2) posttreatment and post-retention records of 76 Caucasian
patients, treated on an extraction basis to a Class I
occlusion, collected from one private practice clinician.
After digitization of the models and cephalograms, two
universal measures of crowding (II and TSALD) were related
to four frequently used indices of divergence (MPA, PMA,
PFH:AFH, LFH:AFH).
Results:
There were weak to moderately
weak associations between facial divergence and crowding,
subjects with greater divergence showed greater amounts of
crowding than subjects with average amounts of divergence.
Females, who were more hyperdivergent than males, also
showed stronger relationships between divergence and
crowding than males.
There were moderate correlations
between posterior face height and crowding in males;
eruption of the lower incisors was moderately associated
93
with crowding in females.
Conclusions: Vertical growth and
incisor eruption, as well as facial divergence, are
important determinants of malalignment.
Introduction
Although improved oral health, function, and social
approval are all benefits of orthodontic treatment,
patients typically present to maximize facial and dental
appearance.1-4 This explains why dissatisfaction with
crowding or irregular anterior teeth is often cited as the
reason for seeking treatment.5-7
It is significant because
the most widespread malocclusion encountered by
orthodontists is crowding.
It is presently unclear why some patients develop
crowding and others do not.
It has been suggested that
“[t]he only way to ensure continued satisfactory alignment
post-treatment probably is by use of fixed or removable
retainers for life.”8
This is important because patient
satisfaction with orthodontic treatment is partly
associated with the stability of the final result.9,10
However, the use of permanent retention instills
complacency among orthodontists and it essentially
transfers ownership to the patient for permanency of the
result.
Additional research is needed to further
94
understand those factors affecting stability and relapse,
and adjust our tactics for treatment.11-13
Previous studies have generally found weak
associations between individual dental and/or skeletal
factors and posttreatment relapse.
For example, Little et
al.14 found low to moderate correlations (r=0.26-0.52)
between posttreatment dental changes and irregularity,
while Shields et al.15 found weak correlations (r≤0.60)
between irregularity and cephalometric variables.
Other
factors such as initial irregularity,14,16 incisor flaring
during treatment,17 tooth proportions,18,19 the anterior
component of force,20 horizontal mandibular growth,21,22
vertical dentoalveolar change,17 and intermolar angle21 also
show weak correlations, ranging from 0.09-0.55.
Although
it is likely that many factors are responsible for
crowding, with the exception of a few studies,23,24 multiple
regression equations still explain only about half of the
variation.21,25,19,26
Longitudinal studies have consistently shown that
mandibular crowding increases over time.8,26-28,14
These
increases are greatest during adolescence and slow during
early adulthood.8,29,22
Since crowding occurs similarly in
both treated and untreated individuals,26,27 it has been
suggested that this may be the result of facial growth
95
changes and not necessarily treatment-related relapse.26,29,30
Because the duration and extent of vertical growth is
greater than for horizontal growth,1,26,15 vertical growth is
suspected to play an important role in dentoalveolar
compensations, which could ultimately lead to crowding of
the teeth.
Several studies have examined the associations
between crowding and vertical growth.
For example,
Driscoll-Gilliland et al.26 found that untreated individuals
with more eruption of the lower incisors and greater
vertical ramal growth had greater crowding.
McReynolds and
Little31 showed that greater crowding was associated with
greater posterior face heights and increased upper anterior
facial height.
Others have demonstrated greater
posttreatment mandibular irregularity in individuals with
increased vertical dentoalveolar eruption.17,32
There have been only a few studies that have assessed
the association between crowding and facial divergence.
An
association would be expected since increases in divergence
allow greater space between the jaws, which could result in
greater occlusal instability30 and greater crowding.
Moreover, hyperdivergence results in retroclination of the
incisors, which may cause crowding by reducing the arch
length.33,34
Nasby et al.35 reported greater crowding and
more upright incisors among hyperdivergent subjects, but
96
their sample was small and they did not test the
association statistically.
Leighton and Hunter36 also found
significant differences in crowding related to the
mandibular plane angle.
Positive relationships between
crowding and the palatomandibular plane angle (PMA) have
also been reported.24,23
In the only long-term posttreatment
study evaluating this relationship, Fudalej and Årtun37
found greater prevalence of postretention II
(i.e., >5.0 mm) among hyperdivergent than hypodivergent
patients.
Importantly, there have also been studies that
have evaluated, but did not find an association between
crowding and facial divergence.38,39
It is the purpose of this study to determine whether
differences in vertical facial growth, as measured by
various indices of facial divergence, relate to crowding in
both treated and untreated subjects.
This association
needs to be evaluated longitudinally because it allows us
to study maturational changes without obscuring variability
in growth timing among the sample.1
Furthermore, it is
important to exclude hypodivergent subjects because they
exhibit different dental compensatory patterns than
hyperdivergent individuals;33 while open-bites and severe
deep-bites must be excluded because altered anterior tooth
97
contact relations could distort the pattern of dental
compensations.
Materials and Methods
Selection Criteria
This study evaluated 1) a cross-sectional sample of 75
untreated adults, selected from the archives at the Center
for Advanced Dental Education at Saint Louis University,
and 2) a longitudinal sample of 76 treated subjects with
long-term post-retention records, selected from one private
practice clinician (JCB).
The treated sample was selected based on:
(1) Caucasian subjects 14-18 years of age posttreatment,
(2) Class I molar occlusion at the completion of treatment,
with extraction of four bicuspids during treatment,
(3) lack of orthognathic surgery, syndromes, significant
asymmetries, or hypodivergence, (4) fully erupted occlusion
without missing (other than four bicuspids), impacted,
supernumerary teeth, or excessive cuspal wear, (5) absence
of open-bite or excessively deep-bite, (6) acceptable
quality records post-treatment and post-retention,
including panorex or full mouth series, lateral
cephalograms, and models, (7) post-retention records at
least 5 years post-treatment.
98
The final treated group included 76 subjects (30 males
and 46 females).
Their average post-treatment and post-
retention ages were 15.4 years (interquartile range [IQR]
14.8-16.3 years) and 32.0 years (IQR 26.9-36.7 years),
respectively.
Males were significantly older (0.67 years)
than females at T1 (Table 3.1).
Table 3.1.
Age distribution of males and females in
treated groups
Male (n=31)
Female (n=44)
Diff
Median
IQR
Median
IQR
p
Age at T1
15.92 15.08-16.58 15.25 14.83-15.71 0.018
Age at T2
33.17 27.50-39.67 30.92 26.79-35.46 0.326
Age diff (T2-T1) 16.83 10.75-23.08 15.50 11.50-19.71 0.469
†Bold data is significant at p<0.05
Prior to treatment, 17 of the males and 20 of the
females had Class II malocclusions; at the completion of
treatment all subjects had a Class I molar relationship.
The patients were treated with edgewise mechanics according
to the Tweed philosophy, using extractions to resolve
crowding or incisor protrusion.
Eighty-three percent of
the patients received extraction of four first premolars,
5% had second premolars extracted, and the remainder had
other extraction combinations.
Treatment was followed by
retention with a banded 3-to-3 retainer for 2-3 years.
99
The untreated sample was selected based on the same
criteria as the longitudinal sample, except that they had
to be 15-30 years of age, did not have previous orthodontic
treatment or previous extractions of premolars, and had
Class I molar relationships.
The untreated group included
75 subjects (26 males and 49 females).
The average age for
the untreated subjects was 19.3 years (IQR 17.5-24.2
years).
Females were significantly older than males (3.55
years) (Table 3.2).
Table 3.2.
Age distribution of males and females in
untreated groups
Male (n=26)
Female (n=49)
Diff
Median
IQR
Median
IQR
p
Age at T1
17.25
15.88-19.30
20.80
18.90-25.25 <0.001
†Bold data is significant at p<0.05
Cephalometric analysis
Acceptable post-treatment cephalograms for treated and
untreated groups were screened to exclude hypodivergent
subjects.
Using age and sex specific standards,40 subjects
with MP-SN angles less than 1 standard deviation were
excluded.
Cephalograms were traced on 0.003” acetate paper using
a 0.3 mm mechanical pencil.
Fourteen cephalometric
landmarks were identified, as defined by Riolo et al.40
100
The
tracings were scanned at 300 dpi using a RICOH Aficio MP
5000 printer/scanner, and uploaded into Dolphin Imaging™
(Version 11.0).
All cephalograms were digitized at 7x
magnification to reduce error.
Fifteen measurements were
calculated using a custom analysis, including N-Me
(Anterior Face Height), N-ANS (Upper Face Height), ANS-Me
(Lower Face Height), S-Go (Posterior Face Height), Ar-Go
(Ramus Height), L1-GoMe (IMPA), Overjet, Overbite, L1-Me
(L1 dentoalveolar height), L1-MP (L1 dentoalveolar height),
and L1-APg (L1 protrusion).
This included four measures of
divergence: SN-GoMe (MPA), PP-GoMe (PMA), LFH:AFH (lower
anterior to total anterior face height ratio), and PFH:AFH
(posterior to anterior face height ratio) (See Appendix A,
Figure A.1).
Cephalometric measurements and method error
are shown in Appendix B, Table B.1.
Model Analysis
The models were screened to eliminate individuals with
open-bite (<0 mm) or severe deep-bites (>5 mm).
Photographs were used for the model analysis because they
have been previously shown41 to provide measurements as
reliable as those taken directly from study models.
Photographs were taken using a Canon Rebel EOS SLR T2i
101
camera with 100 mm macro lens and MR-14x ring flash
positioned 580 mm from the occlusal plane.
A
100 mm ruler, placed at the level of the occlusal plane,
was used for calibration.
To reduce error in data
collection, one trained assistant (AM) took all photographs
using standardized procedures.
Photographs were uploaded
as a JPEG format into Dolphin Imaging™ (Version 11.0) for
custom digitization.
Twenty-one dental landmarks, as
described by Moyers et al.42 were digitized at 3x
magnification.
Seven dental measurements, including two
measures of crowding (TSALD and II), were calculated using
a custom analysis (See Appendix A, Figures A.2-A.4),
including:
1) Intercanine width (ICW), measured between cusp tips
of the lower canines.
2) Intermolar width (IMW), measured between central
pits of the lower first molars.
3) Arch depth (AD), the distance measured from the
contact of the mandibular central incisors
perpendicular to a line connecting the mesial
contacts of the first molars.
4) Anterior tooth width (TW), the sum of the
mesiodistal dimension of the lower teeth from canine
to canine.
102
5) Anterior arch perimeter (AP), the sum of four arch
segments, two for each quadrant.
The posterior
segment from the distal contact of the canine to the
contact between the lateral incisor and canine, and
from this to the contact between the lateral and
central incisor.
6) Anterior tooth-size-arch-length-discrepancy (TSALD),
the difference between AP and TW.
7) Little’s irregularity index (II), the sum, in
millimeters, of the contact point displacements of
the six anterior teeth.
Model measurements and method error are shown in Appendix
B, Table B.1.
Reliability of Measurements
To reduce measurement errors, all cephalograms were
traced and digitized by one investigator (AG).
Method
error, which was determined based on 24 replicates and
described with the Dahlberg statistic,43 ranged from 0.510.79 mm and 0.62-0.82 deg (with the exception of IMPA which
was 1.38 deg) for the cephalometric measurements and from
0.09 to 0.46 mm for the model measurements (See Appendix B,
Table B.1).
Systematic errors, evaluated using the
103
Wilcoxon signed ranks test, were not statistically
significant.
Statistical Analysis
Because the skewness and kurtosis statistics showed
that many variables were not normally distributed, nonparametric statistics were utilized.
Medians and
interquartile ranges (IQR) were used to describe the
variables.
The Mann-Whitney’s U test was used to evaluate
differences between males and females.
Changes over time
were evaluated using the Wilcoxon signed ranks test.
Correlations were calculated using Spearman’s rho.
The
calculations were performed using SPSS Statistics software
(version 17.0, SPSS, Chicago, Ill), with the significance
level set at 0.05.
Results
Untreated subjects
The untreated subjects displayed severe irregularity
(8.50 mm) and minor TSALD (-3.40 mm), but there was a wide
range of values (Table 3.3).
No statistically significant
sex differences were found for either measure of crowding.
There was a moderately high correlation (r=-0.782) between
irregularity and TSALD.
104
Table 3.3.
Crowding in untreated groups
T1 (n=75)
Variable
Median
IQR
II
8.50
6.20-10.90
TSALD
-3.40
-5.60-2.30
†Bold data is significant at p<0.001; Data
was pooled since no sex differences were
found for II or TSALD
In terms of the pretreatment skeletal measures, all
linear dimensions were significantly larger in males than
females (Table 3.4).
Sex differences ranged from 2.0 mm
for lower face height to 7.6 mm for posterior face height.
Males also had significantly larger arch forms (Table 3.5).
Intercanine widths were 1.45 mm larger, intermolar widths
were 2.85 mm larger, and arches were 1.50 mm deeper in
males than females.
Both sexes showed greater variation in
intermolar than intercanine width.
No statistically significant sex differences were
found for facial divergence, although females were
generally more hyperdivergent.
All measures of facial
divergence showed highly significant (p<0.001), moderate to
high, inter-correlations (r=0.658-0.921), except for
LFH:AFH and PFH:AFH, which were not associated.
MPA and
PFH:AFH showed the highest correlation (r=-0.921).
Correlations between crowding and measures of
divergence were not statistically significant for the
105
pooled sample (Table 3.6).
When the sexes were evaluated
separately, males showed no significant associations for
the four divergence measures; females showed a significant,
but weak, correlation between PMA and irregularity
(r=0.335, p=0.019).
106
Table 3.5.
107
Comparison of pre-treatment (T1) dental measures in male and female untreated groups
Male (n=26)
Female (n=49)
Diff
Variable
Median
IQR
Median
IQR
p
OB*
4.65
2.23-5.45
4.00
2.55-5.90
0.916
OJ*
2.70
1.98-3.90
3.40
2.25-4.25
0.200
L1-Apg*
2.30
1.20-5.05
2.60
0.75-4.10
0.771
IMPA
95.55
89.28-100.83
93.20
88.00-98.30
0.145
0.010
ICW
25.45
24.35-26.53
24.00
23.00-25.25
0.001
IMW
41.55
39.68-42.50
38.70
37.45-41.15
0.008
Arch depth
-21.60
-22.93--20.53
-20.10
-21.65--18.60
II
8.50
6.03-11.85
8.50
6.45-10.25
0.668
TSALD
-3.00
-5.68--1.28
-3.50
-5.45--2.30
0.504
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Comparison of pre-treatment (T1) skeletal measures in male and female untreated groups
Male (n=26)
Female (n=49)
Diff
Variable
Median
IQR
Median
IQR
p
<0.001
Na-Me (AFH)*
131.65
128.23-138.58
126.30
121.65-130.95
<0.001
Na-ANS (UFH)*
59.10
57.48-62.03
56.60
54.65-58.70
0.021
ANS-Me (LFH)
74.30
70.93-79.13
72.30
68.05-74.50
<0.001
S-Go (PFH)
88.55
82.78-91.03
81.00
78.85-84.35
0.001
Ar-Go (RH)
52.05
48.60-57.15
48.20
46.25-50.40
0.001
L1-MP
45.90
43.78-49.00
43.50
41.15-45.60
0.001
L1-Me
47.20
44.48-49.75
44.30
42.05-46.15
LFH:AFH
0.56
0.55-0.58
0.56
0.55-0.59
0.755
PFH:AFH
0.67
0.64-0.69
0.65
0.62-0.68
0.086
MPA
31.85
28.53-36.73
34.10
30.60-37.05
0.162
PMA
23.50
20.15-27.40
26.10
22.60-29.30
0.063
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Table 3.4.
Variable
AFH
UFH
LFH
PFH
RH
L1-MP
L1-Me
LFH:AFH
PFH:AFH
MPA
PMA
r
0.311
0.179
0.319
0.495
0.517
0.343
0.242
0.174
0.168
0.061
0.027
108
T1 TSALD
p
r
-0.309
0.125
-0.184
0.367
-0.298
0.139
-0.476
0.014
-0.400
0.043
-0.285
0.158
-0.195
0.340
-0.181
0.375
-0.175
0.393
-0.009
0.964
-0.061
0.766
MALE
p
0.122
0.383
0.113
0.010
0.007
0.086
0.234
0.394
0.413
0.767
0.897
T1 II
Table 3.6 (continued)
r
-0.148
-0.251
0.053
-0.270
-0.219
-0.005
-0.005
0.201
-0.188
0.185
0.335
T1 TSALD
p
r
0.337
0.018
0.165
0.256
0.216
0.136
0.247
0.087
0.099
0.500
0.092
0.528
0.136
0.350
0.038
0.793
0.042
0.776
-0.037 0.803
-0.036 0.808
FEMALE
p
0.311
0.082
0.719
0.060
0.131
0.971
0.971
0.166
0.196
0.204
0.019
T1 II
Correlations between T1 crowding and pre-treatment (T1)
skeletal measures in untreated subjects (n=74)
POOLED
T1 II
T1 TSALD
Variable
p
p
r
r
AFH
0.048
0.685
0.109
0.353
UFH
-0.049
0.674
0.058
0.619
LFH
0.164
0.159
0.013
0.909
PFH
-0.001
0.991
0.066
0.572
RH
0.008
0.946
-0.010
0.931
L1-MP
0.146
0.212
-0.022
0.849
L1-Me
0.149
0.351
0.029
0.808
LFH:AFH
0.193
0.097
-0.063
0.588
PFH:AFH
0.084
0.476
-0.012
0.920
MPA
0.155
0.184
-0.062
0.598
PMA
0.192
0.100
-0.070
0.552
†Bold data is significant at p<0.05
Table 3.6.
Treated subjects
After treatment (T1) both sexes showed minor
irregularity (2.00 mm) and mild crowding (-0.20 mm) (Table
3.7).
Over time, II increased 0.90 mm and TSALD increased
0.70 mm.
Some individuals displayed almost no change in
crowding, or even developed spacing.
Post-retention (T2)
irregularity (3.10 mm) and TSALD (-1.00 mm) were minimal.
There were no sex differences in crowding.
Irregularity
and TSALD were not related at T1 (r=+0.097, p=0.435); they
were moderately correlated at T2 (r=-0.612, p<0.001); the
correlation between the T2-T1 changes was low (r=-0.322,
p=0.008).
Table 3.7.
Crowding in treated groups
T1
T2
Change (T2-T1)
(n=67)
(n=75)
(n=67)
Variable Median
IQR
Median
IQR
Median
IQR
II
0.90
2.00
1.50-2.50
3.10
2.40-3.80
0.20-2.10
TSALD
-0.70
-0.20 -0.70-0.20 -1.00 -1.40-0.60
-1.40-0.30
†Bold data is significant at p<0.001; Data was pooled since no
sex differences were found for II or TSALD
In terms of the post-treatment skeletal measures, all
linear measures were significantly larger in males than
females (Table 3.8).
Significant increases in both
anterior and posterior face heights occurred over time in
both sexes (Table 3.9).
Males showed greater increases in
109
posterior face height (2.5 mm) and ramus height (2.1 mm)
than females.
110
111
Comparison of post-treatment (T1) dental measures
in males and females in treated groups
Male (n=26)
Female (n=41)
Diff
Variable
Median
IQR
Median
IQR
p
OB*
1.50
1.20-2.10
1.85
1.10-2.38
0.734
OJ*
2.60
1.90-2.80
2.20
1.80-2.58
0.100
L1-APg
1.50
0.30-2.40
1.45
0.45-2.58
0.609
IMPA
90.60
87.90-95.40
90.50
86.05-95.45
0.423
0.002
ICW
26.95
26.30-27.60
25.90
25.00-26.70
0.018
IMW
36.80
35.78-37.98
35.60
34.40-37.05
Arch depth*
-17.75
-18.88--16.70
-17.10
-17.90--15.85
0.053
II
2.00
1.475-2.525
2.00
1.60-2.60
0.584
TSALD
-0.30
-0.53-0.23
-0.20
-0.70-0.20
0.918
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Table 3.9.
Comparison of post-treatment (T1) skeletal measures
in males and females in treated groups
Male (n=31)
Female (n=44)
Diff
Variable
Median
IQR
Median
IQR
p
AFH
127.90
122.90-132.30
121.75
117.73-124.10 <0.001
<0.001
UFH
57.80
55.50-59.10
53.60
52.25-55.60
0.026
LFH
71.80
69.10-75.60
69.30
66.08-72.88
<0.001
PFH
83.30
78.90-87.80
75.30
73.00-77.45
<0.001
RH*
49.30
45.70-53.80
44.80
43.13-47.30
0.002
L1-MP
42.20
41.10-44.20
40.15
38.68-41.85
0.005
L1-Me
43.00
41.80-45.50
41.10
39.50-43.00
LFH:AFH
0.57
0.55-0.58
0.57
0.56-0.59
0.078
0.001
PFH:AFH
0.66
0.63-0.68
0.63
0.61-0.65
<0.001
MPA
33.80
30.90-36.30
37.20
34.83-40.85
0.001
PMA
24.20
21.50-27.40
28.70
26.20-32.45
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Table 3.8.
Arch forms also showed significant sex differences
(Table 3.10).
Males had significantly larger intercanine
(1.05 mm) and intermolar widths (1.20 mm) than females.
Although the arches were 0.65 mm deeper in males, this
difference was not significant.
Both sexes showed greater
variation in intermolar than intercanine width.
There were
no significant sex differences in the dental changes that
occurred, except for intermolar width, which increased
slightly (0.20 mm) in males and decreased slightly (-0.40
mm) in females.
Generally, there were increases in
overbite, increases in overjet, proclination or
retroclination of the lower incisors, distal movement of
lower incisor relative to the face, decreases in ICW, minor
changes in IMW, decreases in arch depth, and increases in
crowding (Table 3.11).
Females were generally more hyperdivergent than males.
Females had significantly larger mandibular plane
(3.4 degrees) and palatomandibular plane (4.5 degrees)
angles than males.
Males showed reductions in most of the
divergence measures over time, whereas females demonstrated
little or no change. Males showed 2.15 and 1.60 degrees
more closure of the MPA and PMA, respectively.
Lower to
anterior face heights (LFH:AFH) were maintained over time
and showed no significant sex differences.
112
Comparison of dental changes (T2-T1) of males and females in treated groups
Male (n=26)
Female (n=41)
Diff
Variable
Median
IQR
Median
IQR
p
Δ OB
0.75
-0.13-2.15
1.65
0.80-2.20
0.108
Δ OJ
0.15
-0.43-0.95
0.50
0.10-1.08
0.086
Δ L1-APg
-0.50
-1.33-0.90
-0.50
-1.10-0.40
0.893
Δ IMPA
-0.85
-2.70-3.15
0.25
-3.40-3.13
0.692
Δ ICW
-1.45
-1.78--0.75
-1.70
-2.30--0.75
0.325
0.008
Δ IMW
0.20
-0.43-1.03
-0.40
-0.90-0.30
Δ Arch depth
-1.20
-1.83--0.70
-1.90
-2.30--0.95
0.113
Δ II*
0.75
-0.03-1.98
1.10
0.40-2.15
0.367
Δ TSALD*
-0.65
-1.15--0.28
-0.70
-1.65--0.25
0.685
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Table 3.11.
113
Comparison of skeletal changes (T2-T1) in males and females in treated groups
Male (n=30)
Female (n=44)
Diff
Variable
Median
IQR
Median
IQR
p
Δ AFH
3.10
0.90-5.53
4.45
1.65-5.48
0.516
Δ UFH
1.25
-0.13-2.95
1.65
0.70-2.80
0.484
Δ LFH
1.85
0.45-3.03
2.15
0.20-3.28
0.656
<0.001
Δ PFH
5.40
3.50-8.20
2.95
1.68-4.58
<0.001
Δ RH
4.60
3.20-6.30
2.50
1.03-3.10
Δ L1-MP
2.05
0.60-2.75
1.70
1.33-2.50
0.671
Δ L1-Me
2.30
0.35-3.10
1.85
1.25-2.48
0.589
Δ LFH:AFH*
-0.002
-0.008-0.006
-0.001
-0.009-0.004
0.800
<0.001
Δ PFH:AFH*
0.026
0.015-0.040
0.009
-0.003-0.015
<0.001
Δ MPA*
-2.80
-3.93--0.93
-0.65
-1.60-0.55
0.005
Δ PMA*
-2.00
-4.20--0.73
-0.40
-1.85-0.40
†Bold data is significant at p<0.05, *indicates skewed/kurtotic data
Table 3.10.
All measures of posttreatment divergence were
significantly interrelated, with correlations ranging from
0.255 to 0.914.
The lowest correlation was between LFH:AFH
and PFH:AFH (r=-0.255; p=0.027); the strongest association
was between PFH:AFH and MPA (r=-0.914, p=<0.001).
Changes
in divergence also showed moderate to moderately high
correlations (r=0.550-0.937, p<0.001), with the exception
of LFH:AFH with PFH:AFH (p=0.186) and LFH:AFH with MPA
(p=0.112), which were not significantly related.
Based on the entire sample, correlations between posttreatment skeletal dimensions and post-retention crowding
were generally not statistically significant (Table 3.12).
There was a weak correlation (r=0.235, p=0.043) between the
mandibular plane angle and irregularity.
correlations showed
Sex specific
no associations for males, and a
significant association between PMA and II (r=0.320) for
females.
The pooled samples showed statistically significant,
but weak (Table 3.13), correlations between changes in II
and post-treatment ramus height (r=-0.258), posterior to
anterior face height (PFH:AFH) (r=0.261), the mandibular
plane angle (r=0.287), and the palatomandibular angle
(r=0.282).
A weak correlation was also found between the
114
posterior to anterior face height ratio (PFH:AFH) and TSALD
(r=-0.262).
When the sexes were evaluated separately, males again
showed no significant correlations. Females showed moderate
correlations between irregularity changes and AFH, LFH,
LFH:AFH, PFH:AFH, mandibular plane angle, and
palatomandibular angle, ranging from 0.327-0.447.
Correlations between TSALD changes with PFH:AFH and MPA
also attained significance (r=0.414 and 0.361,
respectively).
When changes were related to changes, significant
moderate correlations were found between changes in TSALD
and changes in dentoalveolar heights (Table 3.14).
The
pooled sample showed correlations between changes in TSALD
and changes in L1-MP (r=-0.353), as well as changes in L1Me (r=-0.468). These correlations can again be attributed
to females, who showed that changes in TSALD were related
to changes in L1-MP (r=-0.445) and changes in L1-Me (0.643).
Changes in crowding were unrelated to the skeletal
changes in males.
115
Variable
AFH
UFH
LFH
PFH
RH
L1-MP
L1-Me
LFH:AFH
PFH:AFH
MPA
PMA
r
0.040
0.276
-0.006
-0.057
-0.089
-0.015
-0.043
-0.149
-0.051
0.075
-0.082
116
MALE (n=31)
T3 TSALD
p
p
r
0.830
-0.053
0.777
0.133
0.104
0.579
0.973
-0.156
0.402
0.760
0.158
0.395
0.635
0.181
0.330
0.935
-0.008
0.966
0.818
0.008
0.967
0.424
-0.320
0.079
0.786
0.138
0.459
0.688
-0.129
0.491
0.662
-0.162
0.384
T3 II
Table 3.12 (continued)
FEMALE (n=44)
T3 II
T3 TSALD
p
p
r
r
0.177
0.251
-0.076 0.622
-0.166 0.281
-0.038 0.805
0.231
0.132
-0.061 0.694
-0.091 0.558
0.096
0.534
-0.120 0.437
0.058
0.708
-0.018 0.908
0.012
0.940
0.011
0.944
0.022
0.885
0.285
0.061
-0.059 0.703
-0.185 0.230
0.128
0.407
0.296
0.051
-0.259 0.089
0.320
0.034
-0.056 0.716
Table 3.12. Correlations between post-retention (T2) crowding and
post-treatment skeletal measures (T1) in treated subjects
POOLED (n=75)
T3 II
T3 TSALD
Variable
p
p
r
r
AFH
-0.045
0.704
0.112
0.340
UFH
-0.131
0.262
0.167
0.152
LFH
0.063
0.589
-0.022
0.849
PFH
-0.183
0.116
0.200
0.086
RH
-0.204
0.079
0.143
0.219
L1-MP
-0.104
0.375
0.088
0.453
L1-Me
-0.084
0.475
0.084
0.474
LFH:AFH
0.156
0.182
-0.161
0.168
PFH:AFH
0.164
0.159
-0.125
0.286
0.235
0.043
MPA
-0.198
0.088
PMA
0.221
0.057
-0.103
0.381
†Bold data is significant at p<0.05
Variable
AFH
UFH
LFH
PFH
RH
L1-MP
L1-Me
LFH:AFH
PFH:AFH
MPA
PMA
r
-0.111
0.170
-0.102
-0.267
-0.257
-0.099
-0.113
-0.187
-0.116
0.104
0.002
117
MALE (n=26)
Δ TSALD
p
p
r
0.591
-0.085
0.681
0.405
-0.056
0.786
0.621
-0.156
0.447
0.188
0.026
0.901
0.205
-0.019
0.925
0.631
-0.147
0.473
0.583
-0.126
0.541
0.361
-0.160
0.435
0.571
0.064
0.756
0.615
-0.028
0.893
0.992
0.048
0.815
Δ II
Table 3.13 (continued)
FEMALE
Δ II
p
r
0.342
0.029
0.031
0.845
0.370
0.017
-0.078 0.630
-0.149 0.352
0.063
0.697
0.119
0.460
0.298
0.059
-0.327 0.037
0.398
0.010
0.447
0.003
(n=41)
Δ TSALD
p
r
-0.265
0.094
-0.277
0.079
-0.204
0.200
0.229
0.150
0.250
0.114
-0.124
0.439
-0.121
0.450
-0.059
0.716
0.414
0.007
-0.361
0.021
-0.194
0.224
Table 3.13. Correlations between change in crowding (T2-T1) and
post-treatment skeletal measures (T1) in treated subjects
POOLED (n= 67)
Δ II
Δ TSALD
Variable
p
p
r
r
AFH
0.020
0.871
-0.065
0.603
UFH
-0.040
0.746
-0.052
0.678
LFH
0.121
0.328
-0.140
0.260
PFH
-0.209
0.089
0.202
0.101
-0.258
0.035
RH
0.154
0.212
L1-MP
-0.070
0.575
-0.071
0.568
L1-Me
-0.023
0.854
-0.082
0.507
LFH:AFH
0.136
0.274
-0.086
0.491
0.261
0.033
-0.262
0.032
PFH:AFH
0.287
0.019
MPA
-0.238
0.053
0.282
0.021
PMA
-0.095
0.445
†Bold data is significant at p<0.05
Variable
Δ AFH
Δ UFH
Δ LFH
Δ PFH
Δ RH
Δ L1-MP
Δ L1-Me
Δ LFH:AFH
Δ PFH:AFH
Δ MPA
Δ PMA
r
-0.106
-0.096
-0.179
-0.022
0.062
0.227
0.350
-0.050
0.193
-0.091
-0.209
118
MALE (n=26)
Δ TSALD
p
p
r
0.615
0.122
0.562
0.646
0.091
0.665
0.392
0.300
0.145
0.917
0.110
0.601
0.770
0.017
0.937
0.276 -0.227 0.275
0.086 -0.260 0.210
0.807
0.022
0.917
0.345 -0.249 0.219
0.667
0.224
0.281
0.317
0.208
0.318
Δ II
Table 3.14 (continued)
r
0.246
0.169
0.132
-0.259
-0.232
-0.003
0.092
-0.014
-0.327
0.289
0.086
FEMALE (n=41)
Δ TSALD
p
p
r
-0.343
0.028
0.122
0.291
-0.210
0.188
0.412
-0.230
0.148
0.103
-0.249
0.116
0.144
-0.042
0.796
-0.445
0.004
0.986
-0.643
<0.001
0.567
0.620
0.080
0.620
0.538
-0.099
0.538
0.640
0.075
0.640
0.766
0.048
0.766
Δ II
Table 3.14. Correlations between change in crowding (T2-T1) and
change in skeletal measures (T2-T1) in treated subjects
POOLED (n=67)
Δ II
Δ TSALD
Variable
p
p
r
r
Δ AFH
0.119
0.343
-0.160
0.201
Δ UFH
0.077
0.541
-0.066
0.599
Δ LFH
0.016
0.896
-0.049
0.695
Δ PFH
-0.191
0.124
-0.083
0.508
Δ RH
-0.155
0.214
0.016
0.900
-0.353
0.004
Δ L1-MP
0.098
0.434
-0.468
<0.001
Δ L1-Me
0.184
0.140
Δ LFH:AFH
-0.101
0.420
0.073
0.558
Δ PFH:AFH
0.143
0.252
0.098
0.434
Δ MPA
0.171
0.170
0.129
0.302
Δ PMA
0.014
0.911
0.072
0.586
†Bold data is significant at p<0.05
Discussion
Both incisor irregularity and TSALD must be measured
in studies evaluating crowding.
Correlations between II
and TSALD ranged from moderate to moderately high (r=0.61
and 0.78). Similar correlations have been reported for
pretreatment crowding (r=0.5338; r=-0.6839), and
postretention crowding (r=-0.6040).
These two indices
measure different aspects of crowding, which could affect
the results.26,44,18
Irregularity is “sensitive” to axial
displacements and rotational changes of teeth, whereas
TSALD reflects the difference between space required and
space available.
At best, one measure explains less than
half of the variation in the other.
Most measures of facial divergence showed significant
associations with one another.
However, LFH:AFH repeatedly
showed low to moderately low correlations with the other
variables, except with PMA (r=0.58-0.66).
Our associations
are comparable to those previously reported,45,46 indicating
that, with the exception of anterior facial height
proportions, most of the indices could be substituted for
one another.
The fact that vertical ramus growth is an
important determinant of facial divergence may explain why
the proportions of the anterior face are less related to
the other measures.
119
Untreated Cross-Sectional Sample
The untreated subjects showed relatively large amounts
of incisor irregularity prior to treatment, but only mild
crowding.
Median irregularity was severe (8.5 mm), but
TSALD was relatively small (-3.4 mm).
This suggests only
minor decreases in arch length despite significant changes
in axial and rotational positions of the incisors.
The
amount of II observed in the present study compares
favorably with amounts of II previously reported.14,17,47
Others have reported much lower pretreatment II.22,48-55,16
These differences might be related to sampling variations.
Divergence showed relatively few associations in
untreated individuals.
Although the palatomandibular angle
showed a moderate correlation with irregularity in females,
no other divergence measure was found to relate to crowding
in either sex.
Because of the cross-sectional nature of
this study and younger age of males, variability in growth
status may have obscured the results.
In addition, the
relatively small sample size for males and restricted range
of crowding would tend to provide lower correlation
coefficients.
Importantly, posterior facial height growth is
partially responsible for mandibular crowding.
There were
significant moderate correlations between crowding and
120
increased vertical dimensions of the posterior face in
untreated males; males with the largest posterior heights
exhibited the greatest crowding.
This supports the
findings of McReynolds and Little,31 who found that patients
with greater posterior face height exhibited greater postDriscoll-Gilliland et al.26 also showed
retention crowding.
a positive moderate correlation between the growth of
posterior face height (Ar-Go) and space irregularity in a
sample of 44 untreated individuals studied between 14 to 23
years.
In contrast, Bishara et al.56 found little or no
relationship between posterior face height and TSALD.
It
should be noted however, that because their cephalograms
came from machines with varying magnifications, the linear
results should be approached with caution.
Treated Longitudinal Sample
Increases in mandibular crowding commonly occur after
retention has been discontinued.
Generally, the treated
sample maintained satisfactory stability over the 15.9 year
posttreatment period.
They showed only small, but
significant, post-treatment increases in irregularity
(0.9 mm) and TSALD (-0.7 mm).
After approximately 12 years
without retainers, 93% of the subjects exhibited only minor
TSALD (<4 mm) and 68% has satisfactory II (<3.5 mm).
121
The
crowding that occurred in the present study was similar to
amounts previously reported for patients treated with
extractions in private practices, for which increases in II
range from 0.34-1.3 mm.26,22,48,57
It is difficult to know
whether sample characteristics, retention protocol, band
spaces remaining after treatment, or band space after
removal of fixed retainers, contributed to the lower levels
of crowding observed.
Interestingly, the changes in crowding that occurred
post-treatment, in this and other studies from private
practitioners, were similar to, or on the low end of,
values reported for untreated samples (II ranges from 0.472.58 mm; TSALD ranges from 0.1-2.78 mm).26-28,56,58-62
This
suggests that crowding is probably not related to treatment
itself, but to other factors such as age, sex, ethnicity,
number of teeth present, among others.29
Males and females exhibited similar amounts of posttreatment crowding.
A lack of sex differences in crowding
has been previously reported for other treated26,58,63 and
untreated26,28,60 patients.
Based on a large cross-sectional
sample of 9044 individuals, Buschang and Shulman29 found
significantly larger II (0.48 mm) among males than females.
If a difference exists, it is likely small and can only be
appreciated using an extremely large sample.
122
Generally, females were more divergent than males and
remained more divergent over time.
Females had
significantly larger mandibular plane angles,
palatomandibular angles, and posterior to anterior facial
height ratios than males.
The sex difference could have
been due to the fact that males had greater increases in
posterior face height and ramus height than females.
In
other words, the sex difference pertains mainly to growth
in the posterior aspects of the face; LFH:AFH showed
relatively minor changes in both sexes, indicating that the
anterior portions of the face remain proportional over
time.
The fact that males are less divergent than females
has been previously reported.45,64-66
Individuals with increased facial divergence appear to
be more prone to post-treatment crowding than individuals
with average divergence.
The associations between crowding
and divergence were greater in females than in males,
probably because they exhibited greater mandibular
divergence than males.
Interestingly, the changes in
divergence were not predictive of crowding, likely because
these dimensions showed relatively small changes over time.
Although some studies have not found a relation,38,39 others
have found differences in crowding related to facial
divergence.35,36,24,23
Importantly, the association between
123
crowding and divergence is not strong, indicating that it
is one of many factors that must be considered.
Divergence might be at least partially related to
crowding due to changes in the transverse dimension.
It is
well established that hyperdivergent individuals have
narrower arch forms.35,67,68
Since narrow arches limit the
space available for the teeth, this could result in
crowding.69,70
Postretention, low to moderate correlations
were shown between arch width and crowding (r=0.282-0.443);
arch width was also related to facial divergence (r=0.2580.322).
Other studies have found relations between facial
divergence and transverse dentoskeletal67,71 measures in
untreated subjects.
For example, Forster et al.71 found
decreases in arch width with increasing MP-SN angles, but
only in males, and did not find any relation to crowding.
Other studies have not found relations between arch form
and divergence72 or arch width and crowding.73
Vertical eruption of the lower incisors also appears
to be associated with post-treatment crowding.
Patients
with greater amounts of lower incisor eruption had greater
increases in TSALD (Table 3.14).
This was especially true
for females, although males showed some tendency for
increased irregularity with eruption.
In females, L1-MP
explained 20% and L1-Me explained 41% of the variation in
124
crowding.
Relationships between increased eruption and
crowding have been previously demonstrated.26,17,32
There also was a significant relationship between
TSALD and increases in the anterior face height, which is
reasonable because increases in facial height might be
expected to result in greater incisor eruption.
Men also
showed large increments of anterior face growth, but these
changes were not linked to changes in crowding because
males also underwent even larger increases in posterior
face height.
This suggests that males had greater forward
mandibular rotation, resulting in less lower incisor
eruption and greater proclination of the incisors, both of
which could decrease or limit crowding.
The results of this study have important clinical
implications.
Individuals, particularly females, with
hyperdivergent growth patterns may be predisposed to
crowding.
Therefore, vertical control of growth (i.e.,
high-pull headgear or vertical-pull chin cup) during
treatment could help in preventing future crowding.
Although the associations found between crowding and
divergence were low, they are comparable to correlations
found for other factors relating to crowding, supporting
the belief that there are many small, yet important,
contributors to crowding (Figure 2.14).
125
Patients should be
advised that minor posttreatment alignment changes are a
normal consequence of aging.
Because vertical growth
continues far into adulthood, retention must be a life-long
commitment.
Figure 2.14. Revised progression of malalignment.
126
Summary and Conclusions
Based on a treated sample of 76 Caucasian adolescents
aged 14-18 posttreatment followed for at least 5 years
posttreatment, and an untreated sample of 75 Caucasian
adults aged 15-30 pretreatment, the following conclusions
can be drawn:
1) Posttreatment crowding was generally acceptable and
showed only small increases in patients who had been
out of retention for approximately 12 years.
2) Craniofacial and dental arch measures are larger in
males than females.
3) Females exhibit greater facial divergence than males.
4) Females with greater lower incisor eruption and
reduced posterior facial growth, and males with
greater posterior facial dimensions, show greater
amounts of crowding.
5) Facial divergence is related to crowding, more so in
females, but it is only one of many factors involved
in crowding.
127
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APPENDIX A
Customized Cephalometric and Model Analyses
135
Customized cephalometric digitization regimen
Figure A.1 depicts a customized cephalometric digitization
regimen based upon landmarks from Riolo et al., 1974. The
corresponding cephalometric analysis is found in Table A.1.
Figure A.1.
Customized cephalometric digitization regimen.
Adapted from Riolo et al., 1974
136
Customized model digitization regimen
Figures A.2-4 depict a customized model digitization
regimen based upon landmarks from Moyers et al., 1976.
The corresponding model analysis is found in Table A.2.
Figure A.2. Calculation of Arch perimeter.
Adapted from Kuroda et al., 2010.
Figure A.3.
Figure A.4.
Calculation of intecanine width, intermolar width, and arch depth.
Adapted from Kuroda et al., 2010.
Calculation of Irregularity Index.
137
Adapted from Little, 1975.
Table A.1. Customized cephalometric analysis.
Measures
Angular/Proportional
Linear
SN-GoMe (MPA)
N-Me (AFH)
PP-GoMe (PMA)
N-ANS (UFH)
LFH:AFH
ANS-Me (LFH)
PFH:AFH
S-Go (PFH)
Ar-Go (RH)
L1-GoMe (L1-MP)
L1-Me
L1-APg
IMPA
Overjet
Overbite
Table A.2. Customized model analysis.
Measures
Linear
ICW
IMW
AD
TSALD
II
138
APPENDIX B
Error Study
139
Error Study
Appendix B contains the method error for the cephalometric
and model measurements. Method error was calculated according to
Dahlberg’s statistic, 1980 (√(∑d2/2n)) using 24 replicas.
Table B.1. Method error study (n=24)
Measurement
Interpretation
Units
Method
Error
N-Me
Anterior face height
mm
0.65
N-ANS
Upper face height
(UFH)
“
0.56
ANS-Me
Lower face height
(LFH)
“
0.55
S-Go
Posterior face height
“
0.51
Ar-Go
Ramus height
“
0.60
L1-GoMe
L1 dentoalveolar height
“
0.79
L1-Me
L1 dentoalveolar height
“
0.79
SN-GoMe
Mandibular plane angle
Deg
0.62
PP-GoMe
Palatal plane to mandibular plane angle
“
0.78
(AFH)
(PFH)
(RH)
(L1-MP)
(MPA)
(PMA)
L1-APg
Lower incisor protrusion
“
0.82
IMPA
Lower incisor inclination
“
1.38
Overbite
Vertical distance between U1 and L1 tips
mm
0.76
Overjet
Horizontal distance between U1 and L1
“
0.53
tips
ICW
Intercanine width
0.19
IMW
Intermolar width
“
0.10
Arch Depth
Arch depth
“
0.09
II
Incisor irregularity
“
0.26
TSALD
Tooth-size-arch-length-discrepancy
“
0.46
140
VITA AUCTORIS
Avrum I. Goldberg was born on October 17, 1980 to Mrs.
Debbie and Dr. Sheldon Goldberg in Vancouver, British
Columbia; he is the oldest of two children.
After
graduating from West Vancouver Secondary School he went on
to receive his undergraduate education locally at Capilano
College and the University of British Columbia.
He moved
across the country to pursue his dental education in
Halifax, Nova Scotia, completing a degree of Doctor of
Dental Surgery with distinction in 2006.
Following
graduation he worked for three years in general practice
with his father before returning to school to begin his
graduate orthodontic training at Saint Louis University.
He married Amy Mihaljevich on July 26, 2009 in Tower Grove
Park.
After graduation, Dr. Goldberg plans to return to
Canada to practice orthodontics.
He is currently a
candidate for the degree of Master of Science in Dentistry
(Research).
141