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A CBCT ANALYSIS OF CLASS I AND II ORTHODONTIC CASES:
A CORRELATIVE STUDY OF AIRWAY MORPHOLOGY AND FACIAL FORM
A Thesis
Presented for
The Graduate Studies Council
The University of Tennessee
Health Science Center
In Partial Fulfillment
Of the Requirements for the Degree
Master of Dental Science
From The University of Tennessee
By
Kyle David Fagala, D.D.S.
May 2013
Copyright © 2013 by Kyle David Fagala.
All rights reserved.
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ACKNOWLEDGEMENTS
I would like to thank Dr. Edward Harris for his expertise, guidance and
inspiration. Under his direction, I gained an enthusiasm for the research process and
valuable experience that I will apply throughout my career. I would also like to thank Dr.
Dan Merwin and Dr. Bill Parris for serving on my thesis committee. Their thoughtful
insight and support were invaluable throughout this process. I would also like to thank
Dr. Ken Dillehay, Dr. Dan Merwin, and Dr. Preston Miller for allowing me access to
their CBCT images. I would also like to thank my parents Bill and Mary Jane and
brother Phil for teaching me hard work and instilling in me a thirst for knowledge.
Lastly, and most of all, I would like to thank my beautiful wife Anna and son Charlie for
all their support during this 3-year process.
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ABSTRACT
Introduction: Morphology of the pharynx affects the volume of airflow and facial
growth patterns, the risk of sleep apnea, and swallowing patterns. Since the pharynx is
housed in the facial structures, there may well be an association between the two.
Evidence to date implies that the type and severity of Class II malocclusion affects the
size and shape of the pharynx. Various researchers have classified Class II malocclusions
into groups based on size and positioning of the maxilla and mandible, and these groups
may exhibit different pharyngeal characteristics. Purpose: This study compares the
pharyngeal sizes of Class II, division 1 orthodontic patients with those of Class I patients.
This study also mimics Class II malocclusion groups to see whether different Class II
types stand out as having distinct pharyngeal dimensions. Methods: This retrospective,
cross-sectional study of 131 routine orthodontic patients (71 Class II, 60 Class I; aged 9
to 13) quantified volume and midsagittal area of the pharynx, defined as (A) the
nasopharynx (dorsal and cranial to the posterior nasal spine), and (B) the oropharynx (the
airway between PNS and the epiglottis), plus (C) the combined dimensions of these two
regions. CBCTs were analyzed using Dolphin3D©. ANCOVA and general linear models
were used to test for sex, age, and skeletal class changes. Additionally, Class II patients
were separated into groups using cluster analysis based on the following criteria: (1) 11
pharyngeal variables, (2) 15 cephalometric variables, and (3) 4 Class II variables.
Results: Airway size and volume increase significantly within each sex with increased
age, but growth is significantly faster in boys. There is no statistically significant
difference in the size of the oropharynx between Class I and Class II patients. By the
time the 71 Class II patients were separated into groups using cluster analysis, the group
sample sizes were too small to find any clinically relevant differences in airway size. The
minimum oropharyngeal constriction occurs inferior to the soft palate in 76% of Class II
patients and in 68% of Class I patients. Conclusions: With due caution for the crosssectional nature of the study, these results show that pharyngeal growth occurs at a linear
pace during the key orthodontic ages. Rather than being tubular, the pharynx is broader
mediolaterally, which cephalometric studies cannot capture. Generally speaking, there is
no difference in size of airway between Class I and Class II patients.
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TABLE OF CONTENTS
CHAPTER 1. INTRODUCTION .....................................................................................1
CHAPTER 2. REVIEW OF THE LITERATURE .........................................................3
The Airway and Pharynx .................................................................................................3
Anatomy of the Pharynx ..............................................................................................3
Soft Tissues of the Nasal Cavity and Pharynx .............................................................3
Three-dimensional Analysis of the Pharynx ................................................................5
Effect of Mandibular Position on the Pharynx ............................................................6
Airway Obstruction..........................................................................................................7
Nasal Obstruction.........................................................................................................7
Effect of an Obstructed Airway on Respiration ...........................................................9
Classification of Airway Obstruction ........................................................................10
Growth and Development ..............................................................................................10
Growth of the Face.....................................................................................................10
Growth of the Pharynx ...............................................................................................11
Relationship Between Muscle and Bone Development .............................................12
Class II Malocclusions ...................................................................................................13
History of the Class II Malocclusion .........................................................................13
Classification of Class II Malocclusions....................................................................13
Imaging ..........................................................................................................................16
Cephalometrics ..........................................................................................................16
Cephalometric Airway Analysis ................................................................................16
Cone-beam Computed Tomography ..........................................................................17
CBCT Airway Analysis .............................................................................................17
Disadvantages of CBCT ............................................................................................19
Technological Aspects of CBCT ...............................................................................19
CHAPTER 3. MATERIALS AND METHODS............................................................21
Sample Description ........................................................................................................21
Pharyngeal Analysis ......................................................................................................21
Volumetric Analysis ......................................................................................................21
Cephalometric Analysis .................................................................................................23
Class II Analysis ............................................................................................................29
Error Calculation............................................................................................................29
Statistical Design ...........................................................................................................32
CHAPTER 4. RESULTS .................................................................................................34
Geographical Cephalometric Differences ......................................................................34
Intraobserver Repeatability ............................................................................................34
ANCOVA ......................................................................................................................41
Summary and Interpretation of ANCOVA Results .......................................................45
Cluster Analysis .............................................................................................................55
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CHAPTER 5. DISCUSSION ..........................................................................................87
CHAPTER 6. SUMMARY AND CONCLUSIONS......................................................96
LIST OF REFERENCES ................................................................................................97
APPENDIX A. RESULTS OF ANCOVA TESTS FOR DIFFERENCES
BETWEEN GEOGRAPHICAL SITES (KANSAS VERSUS TENNESSEE)
WHILE CONTROLLING FOR THE PATIENT’S AGE, SEX, AND CLASS OF
MALOCCLUSION ........................................................................................................107
APPENDIX B. BIVARIATE PLOTS (REGRESSION OF Y ON X) FOR THE
REPEATED MEASUREMENT SESSIONS...............................................................152
VITA................................................................................................................................196
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LIST OF TABLES
Table 3-1.
Cephalometric landmarks .............................................................................26
Table 3-2.
Linear (millimetric) dimensions and angles measured on the lateral
cephalograms................................................................................................28
Table 3-3.
A list of the variables measured from the lateral cephalometric images in
the present study...........................................................................................30
Table 4-1.
Descriptive statistics of intraobserver repeatability, showing the
difference of each variable and a t-test evaluating whether the mean
differed statistically from zero .....................................................................39
Table 4-2.
Results of one-way ANOVAs testing for differences in mean sizes
among the 8 clusters developed using 4 maxillo-mandibular
discrepancies ................................................................................................79
Table 4-3.
Descriptive statistics for SNA among the 8 groupings generated by
cluster analysis .............................................................................................79
Table 4-4.
Descriptive statistics for SNB among the 8 groupings generated by
Table 4-5.
Descriptive statistics for ANB among the 8 groupings generated by
Table 4-6.
Descriptive statistics for Wits among the 8 groupings generated by
Table 5-1.
Results of two-way ANOVA tests for Total Airway Volume factored by
Angle Class and sex .....................................................................................91
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LIST OF FIGURES
Figure 2-1.
Diagrammatic representation of the pharyngeal sections: nasopharynx
(blue), oropharynx (orange), laryngopharynx (green), and trachea
(pink) ............................................................................................................4
Figure 3-1.
Bar charts of age distributions (sexes pooled) by geographical site ..........22
Figure 3-2.
Sketch of lateral view of skull with skeletal and soft tissue landmarks
identified and the airway segments delineated and labeled .......................24
Figure 3-3.
Two-dimensional rendering of the pharyngeal airway ..............................25
Figure 3-4.
Example of a box plot ................................................................................33
Figure 4-1.
Box plots of the age distribution of the sample, partitioned be sex and
geographical site (either Kansas or Tennessee) .........................................35
Figure 4-2.
Histograms of the age distributions (sexes pooled) by geographical site
(Kansas, Tennessee)...................................................................................36
Figure 4-3.
Pie charts of the proportions of Class II patients by geographical
source .........................................................................................................36
Figure 4-4.
A metaphor of a “bull’s eye” characterizes the concepts of precision
and accuracy...............................................................................................37
Figure 4-5.
Bland-Altman plot for the cephalometric angle ANB ...............................42
Figure 4-6.
Bland-Altman plot for the cephalometric distance B to NasionPerpendicular .............................................................................................43
Figure 4-7.
Form of the ANCOVA model used to test for group differences for
(45) cephalometric variables ......................................................................44
Figure 4-8.
Bivariate plot between chronological age (in years, X axis) and
volume of the nasopharynx (in cubic millimeters, Y axis), partitioned
by Angle’s Class ........................................................................................46
Figure 4-9.
Bivariate plot between chronological age (years) and pharyngeal
volume (cubic millimeters), labeled Total Airway Volume ......................47
Figure 4-10.
Bivariate plot between chronological age and the two-dimensional
measure of Total Airway Area (mm2) .......................................................48
Figure 4-11.
Bivariate plot between chronological age and volume of the inferior
oropharynx .................................................................................................49
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Figure 4-12.
Bivariate plot between chronological age (years) and volume of the
total airway (mm3) .....................................................................................51
Figure 4-13.
Box plots showing the difference in distributions between the two
Angle Classes .............................................................................................52
Figure 4-14.
Bivariate graphs showing the difference in distributions between
Angle Class I and Class II samples (sexes pooled) for the
cephalometric angle SNA ..........................................................................53
Figure 4-15.
Twin bivariate plots showing the association between chronological
age (X axis, in years) and size of the angle SNB (degrees; Y axis) ..........54
Figure 4-16.
Box plots showing the difference in distributions by Angle Class ............56
Figure 4-17.
Box plots of the distributions of Wits values (mm) by Angle Class .........57
Figure 4-18.
Box plots of the distributions of IMPA by geographical site and Angle
Class measured at the start of treatment ....................................................58
Figure 4-19.
A depiction of cluster analysis applied to Fisher’s three species of iris
data (150 specimens; 4 variables) ..............................................................60
Figure 4-20.
The “scree plot” associated with the following dendrogram (cluster
analysis) .....................................................................................................60
Figure 4-21.
Dendrogram of the 71 Class II cases analyzed from CBCTs ....................62
Figure 4-22.
Results of cluster analysis using the 11 pharyngeal dimensions ...............63
Figure 4-23.
Results of cluster analysis using the 11 pharyngeal dimensions,
specifically for the airway 1 area (mm2) ....................................................64
Figure 4-24.
specifically for the airway 1+2 volume (mm3) ..........................................65
Figure 4-25.
specifically for the airway 1+2 area (mm2)................................................66
Figure 4-26.
specifically for the airway 2 volume (mm3) ..............................................67
Figure 4-27.
Figure 4-28.
specifically for the airway 1+2+3 volume (mm3) ......................................69
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Figure 4-29.
Figure 4-30.
specifically for the airway 1+2+3 volume (mm3) ......................................71
Figure 4-31.
Figure 4-32.
specifically for the total airway (mm3) ......................................................73
Figure 4-33.
The scree plot for the cluster analysis based on 19 skeletal dimensions ...75
Figure 4-34.
Cluster analysis (dendrogram) of the 71 Class II cases based on 19
skeletal dimensions ....................................................................................76
Figure 4-35.
The scree plot resulting from clustering of four cephalometric
dimensions (SNA, SNB, ANB, and AOBO) .............................................77
Figure 4-36.
The dendrogram produced by four cephalometric variables (SNA,
SNB, ANB, and Wits)................................................................................78
Figure 4-37.
Box plots of the arrangement of the angle SNA among the 8 clusters ......83
Figure 4-38.
Box plots of the arrangement of the angle SNB among the 8 clusters ......84
Figure 4-39.
Box plots of the arrangement of the angle ANB among the 8 clusters......85
Figure 4-40.
Box plots of the arrangement of the Wits measurement among the 8
clusters .......................................................................................................86
Figure 5-1.
Bivariate plots by Angle Class and sex for Total Airway Volume
(mm3) .........................................................................................................91
Figure 5-2.
Bivariate plot between the patient’s age at the start of treatment and
Total Airway Volume for the complete sample (n = 131) .........................92
Figure 5-3.
A stacked chart of the average sizes of the 11 measures of pharyngeal
size analyzed in the present study. .............................................................94
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CHAPTER 1.
INTRODUCTION
Morphology of the pharynx affects the volume of airflow and facial growth
patterns, the risk of sleep apnea, and swallowing patterns. Since the pharynx is housed
within the facial structures, there may well be an association between the two.
Preliminary works by Kim et al. (2010) and Grauer et al. (2009) suggest a link between
craniofacial dimensions and pharyngeal shape. However, sample sizes have been small.
This project will pursue these statistical dependencies (between facial form and
pharyngeal morphology) on a broader scale with a group of 131 American white
adolescents. The purpose was to compare the pharyngeal shapes and sizes of Class II,
division 1 orthodontic patients with those of normal Class I patients. The original
expectation was that Class I subjects would have larger airways than Class II subjects.
Chronic nasal airway obstruction is regarded as one of the prime etiological
factors in malocclusion and disharmonies of the craniofacial skeleton (McNamara 1979).
Disproportionate growth tendencies may result from altered neuromuscular activity and
function of the enveloping craniofacial muscles and soft tissues (Miller and Vargervik
1979, 1980, 1982). Alterations are brought about by the physiologic demand for
adequate ventilation when airflow through the nasal cavity is obstructed. The result is a
recruitment of muscles, whose primary functions are mastication and maintenance of
posture, to aid the primary muscles of respiration in maintaining required gaseous
exchange. The muscles of mastication complement the volume of nasal airflow through a
variety of compensatory lip, tongue, and jaw movements and posture. It is by means of
this altered muscle function that skeletal growth may be affected (McNamara 1979).
The three dimensions of height (craniocaudal), width (mediolateral), and depth
(anteroposterior) determine the size and shape of the pharynx. Studies by Brodie (1941)
and King (1952) found that the total depth of the nasopharynx is established in infancy,
with little change thereafter. Linder-Aronson and Woodside (1979) reported that sagittal
depth of the nasopharynx increases in small increments up to 16 years of age for females
and 20 years of age for males. Johnston and Richardson (1999) found that the bony
periphery of the nasopharynx remains stable during adulthood but soft tissue changes
cause an increase in sagittal depth of the nasopharynx and a reduction in sagittal depth of
the oropharynx posterior to the soft palate. Streight (2011) found that growth of the
pharynx did not decline during childhood, but was linear throughout the child-to-adult
age interval.
Class II malocclusions are some of the most common facial disharmonies
encountered in orthodontics. Edward H. Angle defined the Class II malocclusion as an
occlusal relationship wherein the lower molar is positioned distally relative to the upper
molar (Proffit 2007). However, the Class II malocclusion is more complicated than this
dental definition suggests. A Class II malocclusion can be a dental problem, a skeletal
problem, or some combination of the two (Graber 2005).
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Evidence to date implies that the type and severity of Class II malocclusion
affects the size of the pharynx. For the purposes of this study, we measured various
cephalometric predictors of the Class II malocclusion and then tested for relationships to
linear, area, and volumetric pharyngeal dimensions.
Various researchers (Elsasser and Wylie 1943, Renfroe 1948, Riedel 1952, Henry
1957, Hunter 1967, Hirschfeld 1975, Moyers 1980, McNamara 1981, Whitney 1984, and
Rabosi 1985) have classified Class II malocclusions into groups, but there is
disagreement regarding the relative components of a Class II malocclusion. Most authors
agree that mandibular skeletal retrusion due to size deficiency or posterior positioning is
an important component with an often-occurring maxillary dental protrusion. The studies
also tend to agree that the mandibular incisors are usually in a normal position relative to
the skeletal base and, thus, not an etiologic factor in the malocclusion. The position of
the maxillary skeletal structure relative to the cranial base is the finding most often
disagreed upon. Some of the varying reports of maxillary protrusion, retrusion, or neutral
positioning, can be attributed to differences in the samples or methods of analysis.
However, it is readily apparent there is a wide range of maxillary positioning in this
malocclusion.
The present study mimicked the Class II malocclusion groups of these authors by
using cluster analysis to see whether different Class II types within the continuum stand
out as having distinct pharyngeal dimensions. Pharyngeal measurements were made
using Cone-beam CT imaging. Availability of CBCT systems in dentistry now makes
evaluation of the pharyngeal structures practical.
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CHAPTER 2.
REVIEW OF THE LITERATURE
The Airway and Pharynx
Anatomy of the Pharynx
The pharynx is the muscular tube that is located immediately dorsal to the oral
and nasal cavities, and superior to the esophagus, larynx, and trachea (Netter 2006). The
pharynx is divided into three components: the nasopharynx, laryngopharynx, and
oropharynx (Figure 2-1). The nasopharynx, also known as the epipharynx, is the region
of the pharynx inferior to the nasal cavity that extends from the soft palate to the nasal
passages. The nasopharynx serves as the portal into the oropharynx (Drake et al. 2005)
and permits air to pass from the nasal cavity in and out of the lungs. Bergland (1963)
described the skeletal boundaries of the nasopharynx as follows: The anterior part is
formed laterally by the medial plates of the pterygoid processes and medially by the
dorsal border of the vomer. The posterior part is formed by the pharyngeal surface of the
body of the sphenoid and the basilar part of the occipital bone. The skeletal elements
forming the caudal portion are the posterior border of the horizontal part of the palatine
bones anteriorly and the anterior margin of basilar occipital bone posteriorly.
Bergland (1963) described the bony nasopharynx as having the geometrical shape
of a gable when viewed from the midsagittal plane. A line from posterior nasal spine to
Hormion demarcates the anterior part of the nasopharynx (Hormion is the dorsocaudal
point of contact of the vomer with the sphenoid bone). A line from Hormion to Basion
can delineate the posterior part. The roof is formed by the inferior aspect of the clivus
composed of the midline portions of the sphenoid and occipital bones.
The oropharynx lies dorsal of the oral cavity, superior to the laryngopharynx and
inferior to the nasopharynx, extending from the soft palate to the epiglottis (Netter 2006).
Airway constriction in the oropharyngeal region is often associated with breathing
problems (Ozbek et al. 1998; Singh et al. 2007; Mah et al. 2011).
The laryngopharynx, also known as the hypopharynx, is the region of the pharynx
below the cranial edge of the epiglottis, opening into the larynx and esophagus at the
level of the hyoid bone (Netter 2006).
Soft Tissues of the Nasal Cavity and Pharynx
The mucous membrane that lines the nasal cavity also covers the surface of the
cartilages and bones of the nasal tract and paranasal sinuses. Because this mucosa is
easily irritated and inflamed, even a slight disturbance can cause thickening inflammation
of the membrane. The level of inflammation of the nasal mucous membrane frequently
dictates breathing cycles throughout the day. The nasal turbinates are bony shelves lining
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Figure 2-1. Diagrammatic representation of the pharyngeal sections:
nasopharynx (blue), oropharynx (orange), laryngopharynx (green), and trachea
(pink)
PNS is the abbreviation for posterior nasal spine. C2, C3, and C4 are cervical vertebral
outlines. Diagram provided by Dr. Edward Harris on March 11, 2011.
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the lateral wall of the nasal cavity and are involved in breathing, immunology, and
olfaction. There are three turbinates in each cavity: the superior, middle, and inferior
turbinates (Netter 2006). They are lined with pseudostratified columnar, ciliated
respiratory epithelium. Turbinate size varies greatly among individuals and can be a
primary site for respiratory obstruction (Standring et al. 2005).
The nasal portion of the nasopharynx is similar to the mucosa of the nasal cavity
(Standring et al. 2005). It possesses a highly vascular mucosa that contains an abundance
of lymphoid tissue. The posterior part of the nasopharynx resembles the mucosa of the
oropharynx in that it is comprised of stratified squamous epithelium. The nasopharynx
begins at the level of the superior constrictor muscle and ends at the level of the soft
palate. It communicates with the nasal cavity via the choanae and with the middle ear
cavities via the Eustachian tubes. The bony elements in the walls of the nasopharynx
make it rigid, while the oropharynx is contractile because of the surrounding musculature.
The muscular wall of the oropharynx consists of the middle and inferior constrictor
muscles.
Three-dimensional Analysis of the Pharynx
Kim et al. (2010) studied the three-dimensional airway volume and crosssectional areas of 27 children with a mean age of 11 years. Subjects were sorted into two
groups based on their ANB angle. Statistically significant differences were found
between several cephalometric measurements, including height of the posterior nasal
plane, Pogonion to Nasion-perpendicular distance, ANB angle, mandibular body length,
and facial convexity. Of note, total airway volume was significantly smaller in the Class
II subjects. However, when the total airway was sectioned into 4 subregions, no
significant difference was found between the two groups, though this is likely a type II
statistical problem due to small sample sizes.
Grauer et al. (2009) studied the CBCT records of 62 nongrowing subjects (aged
17-46 years) to evaluate pharyngeal airway volume and shape. Class II subjects had
significantly smaller inferior airways, as measured from PNS to C3, than Class I subjects.
Class II patients also exhibited forward inclination of the airway and a greater frequency
of tongue indentations. Size of the face and sex were positively correlated with airway
volume. No significant relationship was found between vertical skeletal components and
airway volume. In contrast, Alves et al. (2008) found that the majority of airway
measurements were not affected by malocclusion type, with volume and area
measurements that were statistically equivalent between Class II and Class III groups.
Findings did indicate increased airway volume and area for males when compared to
females. However, the results should be considered with caution due to small sample
sizes of 30 adults per skeletal class.
Ogawa et al. (2007) found that patients with obstructive sleep apnea had higher
body mass index, lower total volume of the airway, smaller anteroposterior dimensions of
the minimum cross sectional area. Moreover, the minimal cross sectional area was
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positioned below the occlusal plane in 70% of the cases, and the shape of the airway was
most often concave (exhibiting a dished appearance in the sagittal dimension) or elliptical
(when viewed axially, the airway is wider mediolaterally than anteroposteriorly).
Shigeta et al. (2008) analyzed the CT images of 19 males and 19 females of a
comparable Body Mass Index. The patients’ total and lower oropharynx lengths and
volumes were statistically different in males and females. Males were consistently larger
than females even when controlling for height. In men, the upper oropharynx soft tissue
volume decreased with age while the lower oropharynx soft tissue volume increased.
Age was a significant predictor of oropharynx length.
Streight (2011) analyzed the CBCT images of 263 routine dental patients to
develop normative standards of pharyngeal dimensions by sex and age. Sexual
dimorphism (M > F) develops in childhood because of faster growth in boys, especially
for craniocaudal heights, but the percent dimorphism typically becomes fully developed
in adulthood (> 20 years). Pharyngeal volume, midsagittal area, and craniocaudal height
are significantly larger in men. Sexual dimorphism was greater for craniocaudal than
anteroposterior or mediolateral dimensions. Some variables (upper airway volume, some
cranial pharyngeal areas, Sella-Hyoid distance) continued to increase during adulthood in
men, but not women. No variable became significantly smaller with age, either in
childhood or adulthood.
Effect of Mandibular Position on the Pharynx
Certain conditions have been associated with constriction of the oropharynx,
including a retruded mandibular position and Pierre Robin Sequence. A retruded
mandibular position may be associated with airway constriction by means of the lingual
musculature and its attachment to the hyoid bone (Tsai et al. 2009). A retrusive
mandibular position can cause excessive vertical facial growth, due to a downward,
backward positioning of the mandible (Kiliaridis et al. 1989; Mew 2004). As the
mandible moves downward and backward, there is an increase in lower facial height and
the gonial angle becomes more obtuse (Tsai et al. 2009). When these increases are
combined with the lingual muscular attachment to the hyoid bone, the result is a hyoid
bone that is positioned both more dorsally and inferiorly. An inferior displacement of the
hyoid bone and increased lower facial height are predisposing factors for upper airway
obstruction (Lowe et al. 1986).
Park et al. (2010) studied the pharyngeal airways of 12 subjects who underwent
mandibular setback surgery. Lateral cephalograms and CT images taken before surgery
and 6 months after surgery were used to make linear and volumetric assessments. The
linear analysis showed posterior dorsal movement of the soft palate, tongue, and hyoid
bone following surgery. The oropharyngeal volume decreased following surgery, but the
changes were not significant. The volume of the nasopharynx, however, remained
relatively constant, which suggests that deformation occurs to preserve the airway
capacity in the changed environment following mandibular setback surgery.
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Pierre Robin Sequence (PRS) is a clinical entity consisting of congenital
micrognathia, cleft of the secondary palate, with glossoptosis, and upper airway
obstruction (Figueroa et al. 1991). Figueroa and associates compared the lateral
cephalograms of 17 infants with PRS to groups of 26 normal infants and 26 infants with
isolated cleft palate. While the groups were distinct throughout the two-year period of
study, differences were greater at the earliest age. Initially, the PRS infant had a shorter
tongue and mandibular length, narrower airway, smaller tongue area, and exhibited a
hyoid position that was posterior and inferior when compared to normal infants. PRS
infants did experience “partial mandibular catch-up growth” leading to improved airway
dimensions and concurrent resolution of respiratory distress. The increased growth rate,
however, did not allow PRS infants to recover to values equal to normal.
Airway Obstruction
The relationship between upper airway obstruction, muscular adaptation, and
skeletal modification has been studied in animals by Harvold and Miller (1979). They
were able to demonstrate in monkeys quantifiable, electromyographic change in function
of some respiratory and craniofacial muscles in response to nasal obstruction.
Furthermore, Harvold (1979) documented morphological changes in these same monkeys
with altered EMG muscle patterns. The most notable were 1) an increase in facial height
2) an increase in maxillary height 3) an opening of gonial angle, and 4) increased
incidence of malocclusion. The morphologic changes shown in this animal model were
thought to be redirected growth and remodeling. Changes would only be expected in
bone morphology when muscle function is altered over an extended period of time and is
of sufficient magnitude.
Nasal Obstruction
The effects of compromised nasal respiration on orofacial growth have concerned
investigators for more than a century. Tomes reported in 1872 that children with large
adenoids usually displayed V-shaped dental arches. Ziem, in 1879, placed a piece of
cotton unilaterally into an animal's nostril and studied the consequent asymmetric
development of the face. Angle, in 1907, stated that, "This form of malocclusion (Class
II, division 1) is always accompanied and, at least in its early stages, aggravated, if
indeed not caused by mouth breathing due to some form of nasal obstruction” (Angle
1907).
With the advent of the cephalometric roentgenograph, it became easier to identify
aberrant facial growth patterns. Early studies by Brodie (1941) and King (1952) focused
attention on the changes in both the size and shape of the bony nasopharynx of growing
children. When the craniofacial growth patterns of chronic mouth breathers were found
to exhibit significant differences from established norms, considerable efforts were made
to identify causative agents.
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Harvold (1979, 1981) and Miller and Vargervik (1978, 1979, 1980, 1982, 1984)
induced nasal obstruction in otherwise normal laboratory animals. They found changes
in craniofacial morphology with adaptations of the neuromuscular system in all
experimental animals. In 1979, Miller concluded that experimentally induced nasal
obstruction in monkeys modifies normal sensory feedback, which reflexively induces
changes in neuromuscular function of craniofacial muscles. He further stated that
neuromuscular changes involve the alteration of the discharge of specific facial muscles
in one of two modes: (1) introducing a periodicity in a discharge correlated with
respiratory muscles, i.e., "rhythmicity", and/or (2) sustained tonic discharge. These
clinical and experimental findings strongly suggest that there is a cause-and-effect
relationship between nasal airway impairment and craniofacial morphology.
It is noteworthy that airway obstruction due to adenoid hypertrophy has received
far more attention than any other form of nasopharyngeal restriction (Levy 1967, Quinn
1978, Bluestone 1979, Bushey 1979). Other modes of obstruction such as allergic
rhinitis can lead to altered nasal function resulting in malocclusion. Allergic responses
increase nasal airway resistance, and Hunter (1971) among others, has suggested that the
severity of the malocclusion is proportional to this increase in nasal airway resistance
(Gwyne-Even 1958, Klechak 1972, Harvold 1979). Other causes of nasopharyngeal
airway obstruction may include enlarged tonsils, nasal polyps, a deviated nasal septum, a
small nasal cavity, bony nasal atresia, foreign body obstruction, and combinations of the
above (Ricketts 1954, 1968).
Linder-Aronson (1960, 1979) has offered a more specific description of the
effects due to a compromised nasal airway. In addition to the cranioskeletal aberrations,
such as a Class II skeletal relationship, proclined upper incisors, a narrow V-shaped
upper jaw with a high palatal vault, and increased anterior facial height, he has focused
attention on the enveloping soft tissues. Included here are characteristics such as open
mouth posture, the nose appearing flattened, nostrils that are small and poorly developed,
a short upper lip, a voluminous and everted lower lip and a vacant facial expression
resulting from a hanging posture of the lower jaw.
To further aid in the diagnosis of the cranioskeletal malformations, LinderAronson and Ricketts (1979) described systemic manifestations dependent on altered
nasal airway function. Their findings include restless sleep, poor appetite with
consequent undernourishment, complaints of being tired, hyperkinetic when not resting,
and poor school performance.
During the years of normal development, 60% of adult craniofacial size is reached
by age four, and by age 12 it has reached 90% (Meredith 1953). These percentages
emphasize the need for early interceptive guidance in order to accomplish successful
orthodontic treatment of the growth-linked vertical and anteroposterior discrepancies.
According to Rubin (1979, 1980), even more important than interception is the possibility
of prevention of cranial dysmorphogenesis by identifying and removing adverse
8
influences on normal facial growth. Treatment, focused on prevention or early
interception, would serve to lessen the severity of a developing malocclusion.
Effect of an Obstructed Airway on Respiration
In the following discussion the possible sequelae of craniofacial
dysmorphogenesis is reviewed as occurring by way of four basic events: 1) upper airway
obstruction; 2) deviation from normal physiological respiration as a result of
hypoventilation; 3) recruitment of secondary respiratory muscles because of increased
inspiratory demand resulting in skeletal muscle adaptation; and 4) altered craniofacial
bone growth in response to altered muscle function.
The body protects its tissues by responding rapidly to changes in oxygen and
carbon dioxide concentrations in the blood. Obstruction of the upper airway increases
resistance and decreases the airflow and oxygen volume reaching the lungs.
Simultaneously, airflow is impeded during expiration so that carbon dioxide is not
expelled to the normal extent (shallow respiration). Therefore, obstruction of the nasal
cavity can lead to transient hypoxia and hypercapnia, and these states stimulate neural
receptors, which modulate the respiratory system.
When nasopharyngeal airflow is insufficient, the oral port becomes the
established and predominant route. This alteration not only causes an increased workload
by the primary muscles of respiration, it may also recruit the facial, suprahyoid, and
masticatory muscles as accessory muscles of respiration (Miller 1979, 1980). Both the
rate of onset of the nasal inadequacy and its magnitude are significant factors to be
considered in the adaptive response. This adaptation leading to mouth breathing may
occur as an alteration in the structure or function of a person for survival in an altered
environment (Leoke 1964). This may require that the person continually adapt to better
meet environmental requirements, or it may maintain equilibrium in spite of changing
environmental conditions. Both types of adaptation may be significant in the response of
the muscles of mastication to compromised nasal respiration.
Since respiration can be thought of as an involuntary act under neural control, an
alteration in its function elicits a feedback mechanism from the central nervous system
resulting in altered muscle function to maintain homeostasis (Faulkner 1978). Therefore,
muscles (whether primary respiratory muscles or recruited accessory muscles of the
orofacial complex) provide the link between altered respiratory function and craniofacial
form.
Enlarged tonsils and/or adenoids are the primary source of upper airway
obstruction in young patients (Rowe 1982). The severity and potential detrimental
effects of this obstruction remain in question. In the present study, patients with
adenotonsillar hypertrophy were eliminated in an attempt to focus on airway morphology
associated with malocclusion.
9
Classification of Airway Obstruction
Bluestone (1979) devised a classification scheme, which correlates the degree of
obstruction with known cardiorespiratory complications and potential sequelae. He
characterizes mild obstruction by mouth breathing, stertor (snoring), and speech
distortion.
Either enlarged adenoids and/or tonsils may distort speech; obstructive adenoids
give a hyponasal sound quality, while large tonsils produce a muffled quality to speech.
Moderate obstruction would include some disturbance of sleep and possibly
hypersomnolence. Severe obstruction is not only marked by a more pronounced degree
of these signs and symptoms, but also causes sleep apnea.
Bluestone lists the three most serious complications of upper airway obstruction
as follows: 1) obstructive sleep apnea, 2) alveolar hypoventilation, and 3) cor pulmonale.
Associated potential problems are difficulties in speech and olfaction, maldevelopment of
the nose and perinasal sinuses, maldevelopment of the middle ear, impaired cognition and
language development, diminished school performance and psychosocial development.
These are in addition the sequelae of craniofacial malformations. Of interest, Bluestone
considered that dysmorphogenesis of cranial structures occurs with moderate or even
mild airway obstruction.
Growth and Development
Growth of the Face
The relationship between facial and general body growth has been the subject of
many investigations, and the period of rapid growth known as the pubertal growth spurt
has been of particular interest. Since the first description by Montbeillard in 1759 of the
pubertal growth spurt (Scammon 1927), its influences on the facial structures have been
studied in depth and reported throughout the literature. The numerous methods used to
evaluate body growth during this period include the measurement of height and weight,
determining skeletal age from radiographic assessment of ossification centers, onset of
menarche, and the development of other secondary sexual characteristics.
In a longitudinal study relating the craniofacial skeleton to body height, Bambha
determined that a circumpubertal growth spurt of the face occurs just after the
corresponding spurt in body height (Bambha 1961). While the facial dimensions
followed the general curve of growth in stature, the onset and peak of the growth spurt
displayed large interindividual variability. Females had smaller absolute measurements,
a slower rate of growth, and matured two to three years earlier than males.
10
Growth of the Pharynx
Until the recent advent of CBCT technology, status of the pharynx was limited to
anteroposterior dimensions evaluated from lateral cephalograms. Brodie (1941) and
King (1949) argued that the anteroposterior dimension, as measured from posterior nasal
spine (PNS) to the anterior arch of the first cervical vertebrae (the atlas), does not change
much after the end of the second year of life. Although dimensional growth occurs
during development, Brodie (1941) and King (1952) proposed that the ratios formed in
the anteroposterior dimension remained constant throughout life.
Brodie (1941) looked at sets of 14 serial cephalograms from the Broadbent-Bolton
growth study for 21 children, all boys, from the age of 3 months to 8 years of life. From
a number of cephalometric points, Brodie derived lines and angles that divided the head
into several parts. One part was termed the brain case, another the nasal area, followed
by the upper dental region, and the mandible. By observing the various regions, Brodie
was able to qualitatively assess growth. In reference to growth of the cranium, Brodie
remarked, “The most striking impressions gained from it are the regularity and steadiness
of the process and the fact that the morphologic pattern, once attained, does not change.”
Concurrently, if a child was markedly dolichocephalic at the start of growth, he remained
that way throughout growth. Thus, the proportionality of growth remained constant.
King (1949) studied the serial cephalometric radiographs of 24 boys and 26 girls
that had been taken at three months of age, six months, one year, and then annually to six
years, and biennially from 6 to 16 years. Films were traced and superimposed along the
Sella-Nasion plane with registration at Sella. From the age of three months to 16 years
the anteroposterior growth between the atlas and the posterior nasal spine averaged 3.8
mm in boys and 2.6 mm in girls. Most of this growth occurred in the first year of life.
More inferiorly, in the oropharynx, the distance between the cervical vertebrae and the
hyoid bone was relatively constant until puberty when the hyoid bone moved slightly
forward. This suggests that the anteroposterior dimensions of the pharynx are established
in early infancy. In contrast to the small increases in its anteroposterior dimensions, the
superoinferior growth of the pharynx was much greater. Growth in height of the pharynx
was also continuous, with a slight prepubertal spurt in girls and a slight postpubertal spurt
in boys.
These studies demonstrate that, surprisingly, little growth occurs in the
anteroposterior dimension of the nasopharynx, when viewed laterally. Linder-Aronson
and Woodside (1979) analyzed 140 boys and 120 girls from the Burlington Growth
Center (Toronto, Canada) to cephalometrically evaluate growth in the anteroposterior
depth of the nasopharynx. They concluded that the sagittal depth of the bony
nasopharynx increased in small but steady increments up to 16 years of age in females
and up to 20 years in males. In this sample, the velocity of increases in sagittal depth for
males peaked between the ages of 12 and 14 years. The peak velocity for females was
between the ages of 9 and 12. They found considerable variability in the amount of
increase and in the timing of the peak velocity. They also concluded that the sagittal
increase was unrelated to other cephalometric dimensions of the facial complex.
11
Therefore, both environmental and physiological factors might play a role in size of the
airway.
While the anteroposterior growth of the pharyngeal depth is minor, the greater
increase in size of the pharynx occurs in the vertical dimension. Ricketts (1954)
documented a positive association between cranial base morphology and nasopharyngeal
depth. The more obtuse the angle of the cranial base (Se-Na-Ba), the greater the depth of
the nasopharynx. Growth of the palate occurs in a downward path, and there is little
forward change in the posterior region (Enlow 1965). The growth of the palate as well as
growth of the spheno-occipital synchondrosis occurs in principally a caudal direction.
Tourné (1991) stated that growth of the palate and the spheno-occipital synchondrosis
cause the bony nasopharyngeal height to increase by about 38%. As a consequence, the
superoinferior dimension contributes most to the increase in nasopharyngeal capacity.
Few studies have analyzed changes in the pharynx during adulthood. Johnston
and Richardson (1999) performed a cephalometric study of 16 adults. The adults began
the study with a mean age of 20.2 years and had a cephalometric film repeated 32 years
later. They measured changes in pharyngeal skeletal size, pharyngeal soft tissue
thickness, pharyngeal airway depth, and soft palate dimensions. The results showed
nasopharyngeal skeletal dimensions were unchanged over the 32-year interval, while the
anteroposterior depth of the nasopharyngeal lumen increased as a result of a reduction in
thickness of the posterior nasopharyngeal wall. The oropharynx showed a decrease in
depth of the airway due to the soft palate becoming thicker and longer. The actual size of
the airway and its relative obstruction depend on the growth of the soft tissues of the
pharynx, which the literature shows to be variable.
Relationship Between Muscle and Bone Development
The pharynx is made up of both bone and muscle, and its anatomical shape and
position are partly influenced by the positions of the mandible and tongue. Wolff’s law
suggests that there is an interplay between muscle function and bone development
(Enlow 1968). Functioning muscles exert significant morphogenic effects on skeletal
tissues to which they are attached (Moss 1975). Harvold (1979) demonstrated that, when
bone grafts are implanted under the temporalis muscle, bone formation is stimulated at
that site when associated with a regimen of vigorous muscle activity. However, the same
muscular activity results in bone resorption and remodeling at sites distant to this muscle
force. Decrease in size and alteration in the shape of the coronoid process also has been
shown to be directly related to the amount and position of the functioning temporalis
muscle fibers remaining after experimental partial myectomy (Moss, 1970). An increase
in muscle function, as in human masseteric hypertrophy, produced a corresponding
localized increase in bone size (Bloem 1971). This responsiveness of bone to changes in
muscle function occurs both in the growing animal and in the adult (Moss 1969, 1975).
12
Class II Malocclusions
History of the Class II Malocclusion
Edward H. Angle designated the Class II malocclusion as a molar relationship
where the buccal groove of the mandibular molar is distally positioned when in occlusion
with the mesiobuccal cusp of the upper molar (maximum intercuspation). The Class II
malocclusion can be further divided based on variations in the inclination of the
maxillary anterior teeth. A Class II, division 1 malocclusion, for example, features
maxillary anterior teeth that are proclined with a large overjet. A Class II, division 2
malocclusion, instead, has maxillary anterior teeth that are retroclined with a deep
overbite (Riolo and Avery 2003). While this system provides a means of describing the
anteroposterior relationship of the maxillary and mandibular dentition, it does not
recognize vertical or transverse relationships, which directly affect the anteroposterior
dimension, nor does it differentiate between skeletal and dental causes of the Class II
malocclusion. The system is merely a means of describing dental relationships between
the two arches. As the deficiencies in this system have been well documented (Van Loon
1915, Hellman 1921, Hixon 1958), the need exists for a more complete and
discriminating system for classifying malocclusions of this type.
Classification of Class II Malocclusions
The Class II malocclusion is not a single morphological entity but, instead, results
from combinations of skeletal and dentoalveolar components (Graber 2005). For over 65
years, investigators have examined Class II series to determine the nature and occurrence
of factors contributing to the malocclusion.
Elsasser and Wylie (1943) noted in a sample of Class II individuals that maxillary
protrusion occurred in males while the maxilla was in a relatively neutral position in
females. They found no difference in maxillary molar positioning when compared to a
Class I group. They also found the mandibular length to be within normal limits for
males while it was less than normal in Class II females.
Renfroe (1948) in a study of the facial patterns in Class II malocclusions found
that the average maxilla was in a retrusive position in both sexes with maxillary incisor
protrusion and a molar retrusion relative to a Class I sample. He noted, as did Henry
(1957), that while some Class II individuals have a deficiency in mandibular size, other
individuals had well formed mandibles of normal size that were in a retruded position due
to the posterior position of the glenoid fossa. He concluded that the mandibles of Class II
individuals were retrognathic relative to other craniofacial structures.
Riedel (1952) in an investigation of Class II individuals determined that the
maxillary skeletal base was positioned normally in both sexes but with protrusion of
13
incisors. He also noted that the mandible was in a retrusive position when compared to
averages for Class I individuals.
Henry (1957) studied the lateral cephalograms and dental plaster casts of 103
patients with Class II, division 1 malocclusions. The majority of the malocclusions were
due to posteriorly positioned and slightly underdeveloped mandibles. He suggested that
the cases could be classified into four discernible groups: (1) maxillary alveolar
protrusion; (2) maxillary basal protrusion; (3) a condition Henry describes as
“micromandible” and (4) mandibular retrusion. He also detected an increased
mandibular plane angle compared to his Class I norms, suggesting an increase in lower
facial height.
In assessing a Class II sample, Hunter (1967) found the maxilla to be in a
relatively neutral position but with incisor protrusion. The mandibular incisors were
retruded while the mandibular skeletal position was retrognathic. He also determined
that there was a slight increase in anterior facial height.
Hirschfeld and coworkers (1975) studied a sample of children to develop
categories of facial skeletal types. Of the five groups assessed, three appeared to be
subgroups of Angle's Class II molar relationship.
Moyers et al. (1980) studied 697 lateral cephalograms of North American white
children with Angle Class II malocclusions. They found that, on average, Class II
patients have smaller faces than Class I or Class III patients. The researchers used
methods of numerical taxonomy to construct six subgroups of Class II patients (Types A,
B, C, D, E, and F) distinguished by horizontal variables. Of those six Moyers and
coworkers identified four subgroups (Types B, C, D, and E) that they labeled as
syndromic types with distinctive skeletal and dental features. Those four groups were:
(B) mid-face prognathism; (C) maxillary retrognathism plus dental protraction and
mandibular retrognathism plus dental procumbency; (D) mandibular retrognathism and
maxillary retrognathism plus maxillary dental protraction; and (E) maxillary prognathism
and dental protraction plus dental procumbency. They also detected an increased
mandibular plane angle when compared to Class I norms, suggesting an increase in lower
facial height.
McNamara (1981) reviewed lateral cephalograms of 277 Class II children with an
average age of 9 years. Measures of the craniofacial structures were divided into five
principal components of the Class II malocclusion: (1) maxillary skeletal position; (2)
maxillary dental position; (3) mandibular dental position; (4) mandibular skeletal
position; and (5) vertical development. The average SNA angle was 80.4° and most
cases featured a retruded maxilla relative to established norms. Upper incisors tended to
exhibit protrusion when cephalometric measurements were related to the mandible, but
when measurements were related to the maxilla itself, the incisors appeared normal.
Lower incisors were aligned in a normal relationship to the mandibular plane angle in
more than 60% of the Class II patients. Mandibular skeletal retrusion was the most
common single characteristic of the Class II sample, while almost half of the subjects
14
exhibited excessive vertical development, especially of the lower face. Additionally,
more than 40% had a mandibular plane angle of 28° or greater, further indicating an
increased vertical growth component.
Utilizing a counterpart analysis to analyze an untreated longitudinal Class II
sample population, Whitney (1984) recognized eight groups within this type of
malocclusion. The groups displayed a broad array of skeletal variations and severities of
protrusiveness and retrusiveness of the skeletal base. Overall, there was a distinct
composite mandibular retrusive effect. Whitney also found that the male Class II
malocclusion might exhibit any of several morphological patterns. There was a tendency
for maxillary protrusion with a maxillary bony arch that was consistently longer than the
mandibular corpus. The differential between the two arches increased with age, resulting
in a progressive worsening of the Class II relationship.
In a limited follow-up study using the same sample, Behrents (1985) found that,
while growth continues into adulthood, existing maxillomandibular relationships would
be maintained in a fairly uniform manner with only small variations.
A morphological system of classifying Class II malocclusions has been proposed
by Rakosi (1985), which identifies the area at fault. Rakosi has also offered a more
involved cephalometric system of classification to describe five basic groups of Class II
malocclusions. These include:
1. Class II malocclusion based on a Class II sagittal relationship without a
skeletal component. The ANB angle is usually normal but both SNA and
SNB may be slightly retrusive. The upper incisors are likely to be tipped
labially while the lower incisors may be tipped either lingually or labially.
2. A functionally created Class II malocclusion in which the skeletal base is
normal. The skeletal base is the supporting osseous structure for the alveolar
process. The mandible is forced into a retrusive position upon closure due to
the influence of tooth guidance. A deep anterior overbite and infraocclusion
of the buccal segments are often seen in this condition.
3. Class II malocclusions due to fault in the maxilla. These may be the result of
protrusion of the skeletal base, dento-alveolar, or dental components. In cases
of maxillary protrusion, anterior tipping of the palatal plane downward may
compensate for this discrepancy.
4. Class II malocclusions with the fault in the mandible. The retrognathic
mandible may be small in size or it may be normal in size with a posterior
positioning and an accompanying increase in lower facial height.
5. Class II malocclusions that are some combination of the above four
conditions.
15
Imaging
Cephalometrics
Radiographic cephalometry represents one of the most significant technological
advancements in orthodontic diagnosis and treatment planning. For the past 75 years
(Lamichane et al. 2009), cephalometric imaging has been the gold standard for assessing
relationships among all areas in the craniofacial complex (Berco et al. 2009). However,
two-dimensional cephalometry has disadvantages that are well described in the literature.
Some of the disadvantages are horizontal and vertical displacement of anatomical
structures, imperfect superimposition of right and left sides, image distortion due to
improper patient positioning, inaccurate landmark location or identification, and
inconsistent calibration of source-to-film distances (Lamichane et al. 2009). Despite
these disadvantages, radiographic cephalometry remains the mainstay in orthodontic
diagnosis because it evaluates the spatial evaluation of both skeletal and dental structures
with high resolution (Mah and Hatcher 2005).
Cephalometric Airway Analysis
Two-dimensional lateral cephalometry has traditionally represented the gold
standard in the analysis of airway dimensions (Malkoc et al. 2005). Although useful for
analyzing airway size in the sagittal plane, three-dimensional anatomical measurements
are not imaged (Abramson et al. 2009). Research has revealed many limitations of twodimensional radiographs (Lowe et al. 1986; Finkelstein et al. 2001), particularly
problems with the transverse dimension (Hanggi et al. 2008). Previous studies that used
two-dimensional cephalometric analyses to determine airway dimensions were obliged to
draw major conclusions from the narrowest points in the airway. Simply measuring the
narrowest constriction of a two-dimensional image cannot fully quantify the spatial
relationships between the two structures (Lowe et al. 1986).
Lateral cephalograms are derived from a method called perspective projection.
The result is an image that is magnified, dependent on the distance from the structure to
the film. Because of this, it is difficult to determine whether a double structure (such as
the lower border of the mandible) is the cause of a true skeletal asymmetry or merely a
radiographic artifact. “With CBCT, this projectional magnification is computationally
corrected during primary reconstruction, creating an orthogonal image (Mah et al.
2011).” This allows a CBCT derived lateral cephalogram to be calibrated to a true 1:1
representation of the anatomical structures in question. Furthermore, with CBCTs, it is
possible to correct errors in head position, plus visualization presets allow for enhanced
visualization of both soft and hard tissues (Mah et al. 2011).
16
Cone-beam Computed Tomography
Cone-beam computed tomography (CBCT) records maxillofacial structures in
three dimensions, allowing for a volumetric analysis of the oropharyngeal airway. CBCT
is becoming more commonplace in clinical practice. It provides images comparable to
magnetic resonance imaging (MRI) and computed tomography (CT), but is quicker and
cheaper than either. CBCT differs from medical CT in many ways, including the type of
imaging source detector complex and method of data acquisition. According to Mah and
Hatcher (2004), the x-ray source for CT is a high-output rotating anode generator.
CBCT, on the other hand, uses a low-energy fixed anode, similar to ones used in dental
panoramic machines. CT incorporates a fan-shaped x-ray beam and data are recorded on
solid-state image detectors that are arranged 360° around the patient. Conversely, CBCT
uses a less highly collimated cone-shaped x-ray beam with a specialized image
intensifier. The radiographic image is then captured on a solid-state sensor or an
amorphous silicon plate (Mah and Hatcher 2004). The consequence of reduced
collimation is increased noise and image degradation due to secondary radiation,
resulting in images of lowered gray-scale resolution (Baumrind 2011).
Medical CT and CBCT also differ in mode of image capture. Medical CT images
use a series of axial plane slices to image patients. CBCT is similar to panoramic
radiography and only uses one rotation around the patient, collecting the complete
maxillofacial volume or a small area of interest (Mah and Hatcher 2004). In addition,
CBCT does not require patients to be supine. Patients can be seated in a natural, upright
position, which is important when imaging physiological hard and soft tissue
relationships. CBCT is also the preferred method for airway volume measurement, due
to its relatively low cost, ease of access, availability to dentists, and lower effective
absorbed dose when compared to CT (Ogawa et al. 2007).
CBCT Airway Analysis
Osorio et al. (2008) described CBCT as “X-rays to the head and neck, providing
both two-dimensional and three-dimensional images. The radiograph source is a lowenergy fixed anode tube similar to those used in a dental panoramic machine.” Conebeam images can be used to analyze skeletal cephalometric measurements, soft tissue
structures like the tongue and soft palate, and airway shape and airway caliber. In
addition, three-dimensional reconstructions and volumetric analysis can be performed
(Osorio et al. 2008).
The present study uses Dolphin3D® (Dolphin Imaging and Management
Solutions, Chatsworth, CA) to analyze CBCT images. Shi, Scarfe and Farman (2006)
developed an automatic algorithm that performed segmentation of the airway and
compared it to the more tedious manual segmentation methods. This automatic algorithm
estimated upper airway volume, the minimum distance from the posterior pharyngeal
wall to the caudal region of the soft palate, and the minimum distance from the lower
17
posterior pharyngeal wall to the base of the tongue. The authors were able to
automatically and reproducibly find:
1. Total airway volume (TAV): the volume of the upper airway bounded
superiorly by a horizontal plane at the level of the most posterior extent of the
palate and inferiorly by the maximum extent of the scan.
2. Smallest transaxial-sectional area (TSCA): the smallest cross-sectional area
on the axial images.
3. Largest sagittal view airway area (LCSA): the largest cross-sectional area on
the orthogonal sagittal images.
4. The smallest cross-area and the anteroposterior distance of the retropalatal
space.
5. The smallest cross-area and the anteroposterior distance of the retroglossal
space.
The authors found strong positive correlations between the manually segmented and
automatic measurements. This is important because automating the process allows for an
easy and accurate assessment of the airway every time the patient is scanned.
Aboudara et al. (2009) compared airway space in conventional lateral head films
and the three-dimensional reconstruction from CBCT. They studied 35 consecutive
adolescents (mean age of 14 years) who presented at a dental imaging center for either
orthodontic, temporomandibular, or possible pathology evaluation. Both a lateral
cephalogram and a three-dimensional scan were performed on each subject. One
limitation of this study was that the three-dimensional scans were taken in a supine
position, whereas the lateral head films were taken in an upright position. The supine
position can confound the airway measurements due to the effect of gravity on the soft
tissue of the oropharynx. The following landmarks were used for the lateral
cephalometric analysis and the three-dimensional scans:
1. The axial plane passing through PNS.
2. The plane perpendicular from PNS extending to the superior aspect of the
pterygomaxillary fissure.
3. The soft tissue contour of the posterior pharyngeal wall extending from the
superior aspect of the pterygomaxillary fissure inferiorly to the axial
reconstruction plane.
The following four measurements of the nasopharyngeal airway space were made:
1.
2.
3.
4.
Subjective airway classification (1-5) from the lateral cephalogram.
Airway area of the region of interest from the lateral cephalogram.
Airway volume over the same region of interest from the CBCT scan.
Volume of the soft and hard tissue components of the inferior turbinates that
protruded into the nasopharyngeal potential space.
18
The authors found that there was a significant positive association between
nasopharyngeal airway size on the lateral head film and its true volumetric size from a
CBCT scan. Accurate determination of the airway volume from the lateral head film is
difficult because of great variability in the three-dimensional airway. The authors also
found on the three-dimensional scan that the inferior turbinates often protruded into the
airway space and caused restrictions. This is not visible on a traditional cephalometric
film.
Disadvantages of CBCT
While CBCT offers several advantages to planar cephalometry, there are also a
few disadvantages. Perhaps the most important of these concerns is radiation dose.
Although definitive data are not yet available, it is apparent that the radiation dose of a
CBCT scan (~40 to 135 microsieverts [uSv]), is greater than that typically administered
by a single lateral cephalogram plus a panoramic image (~8 to 18 microsieverts [uSv]).
A further inherent consequence of using cone-beam rather than fan beam geometry is a
reduction in collimation and an increase in noise artifacts, making it much more difficult
to discern differences in soft tissue density in cone-beam images. However, as voxel size
gets smaller (and thus more accurate) with improved technology, this disadvantage will
lessen. Another issue concerns the risk and responsibility for diagnosing pathology
present on CBCT scans (information that orthodontists are not trained to interpret).
Although not legally mandated, referral to a qualified radiologist for full reading of all
CBCT scans is advised (Scholz 2011). In the present study, no new CBCT images were
taken, but rather existing CBCT images were used. Thus, the issues of radiation
exposure and pathology diagnosis were not a direct concern.
Technological Aspects of CBCT
Next Generation iCAT® CBCT machines were used to take all scans for the
present study. The iCAT® “relies on an advanced amorphous silicon flat panel image
sensor, instead of image intensifier technology employed by competitive units, to reduce
the overall size of the unit and deliver a higher image quality and resolution” (Cifelli
2004). Flat panel detectors result in cylindrical-shaped volumes instead of the sphericalshaped volumes produced by image intensifiers. Detectors come in different sizes, but
should be large enough to capture the clinician’s region of interest (ROI) (Molen 2011).
The resolution of the reconstructed scan is influenced by several variables.
Resolution or spatial resolution is the minimum distance between two distinguishable
objects. Resolution is often associated with voxel size, but they are not synonymous.
“The voxel size represents the dimensions of the volume element into which a volume is
being subdivided and is usually measured in millimeters or microns. Each voxel is
assigned a value representing the density of the object contained within its boundaries as
determined by the attenuation of the photons passing through it (Molen 2011).” A
smaller voxel size does not necessarily indicate a higher resolution, due to the effects of
19
scatter radiation, volume averaging, and artifacts. Because of this, it is inappropriate to
compare CBCT systems on voxel size alone.
The gray scale bit depth of a CBCT system is also important to image quality.
CBCT systems range between 12 and 16-bit gray scale. The human eye can only detect
up to 10-bit gray scale, and while most computer monitors are only available in 8- or 10bit gray scale, a higher gray scale does lead to a cleaner or more defined volume (Molen
2011).
20
CHAPTER 3.
MATERIALS AND METHODS
Sample Description
Subjects in the present study were collected from two private orthodontic
practices (Jackson, TN, and Wichita, KS). One cone-beam computed tomography image
per person had been taken for various dental or orthodontic concerns unrelated to this
retrospective project. The pretreatment orthodontic CBCT files were used from the
orthodontic patients. The private practice CBCT scans were made on a Next Generation
iCAT® (Imaging Sciences, Hatfield, PA) with a grayscale resolution of 14 bits and voxel
size of 0.4 mm.
A total of 131 serially selected subjects (65 males; 66 females) were analyzed in
this study. 71 Class II and 60 Class I patients were selected with an age range of 9 to 13
years at the start of treatment. We limited the study to Class II, division 1 malocclusions
by selecting subjects with a positive overjet of at least 3.5 mm. Subjects were
phenotypically normal; no clefts or syndromes were included (Figure 3-1).
Analysis of covariance (ANCOVA) was used to simultaneously test for sex and
age differences (the covariates) so males and females could be analyzed in tandem while
controlling for sexual dimorphism. With cross-sectional data, age trends are somewhat
speculative because there is no information on how the individuals actually grew.
Pharyngeal Analysis
The pharynx was imaged from CBCT images (n = 131) of the head. The skulls
were oriented in Frankfort Horizontal, with care taken to make measurements in the
midsagittal plane. Dolphin 3D® (Dolphin Imaging and Management Solutions,
Chatsworth, CA) was used to collect dimensional data. Version 11.5 was used, which
employs an “airway” module. Images were imported as DICOM (Digital Imaging and
Communications in Medicine) files into Dolphin 3D®, which is an orthodontic imaging
and analysis software program. The DICOM files were used to create a lateral
cephalometric view from within Dolphin. Measurements were made using a custom
analysis wihin the Dolphin program.
Volumetric Analysis
The airway is easily distinguished from the surrounding tissues because of the
large difference in x-ray attenuation between air in the pharynx and the high water
content of the surrounding tissues (Hans 2011). The pharynx was partitioned into three
21
Figure 3-1.
Bar charts of age distributions (sexes pooled) by geographical site
Mean age of Tennessee sample (n=65) was 11.97 years (sd = 1.38); mean age of the
Kansas sample (n=66) was 11.97 years (sd = 1.37).
22
regions (from superior to inferior): nasopharynx, oropharynx, and laryngopharynx
(Drake et al. 2005). Due to the limited view of the laryngopharynx on the majority of the
CBCT images, we did not measure the laryngopharynx.
The nasopharyngeal airway was measured by constructing a triangular area of
interest (Park et al. 2010) (Figure 3-2) using these three planes:
1. Pt Plane: The plane passing through Pt (Pterygomaxillary fissure) and PNS.
2. PNS Plane: A horizontal line parallel to Frankfort Horizontal passing through
Posterior Nasal Spine (PNS).
3. Pharyngeal Tonsil Plane: Soft tissue wall of the posterior nasopharynx.
Three horizontal planes were used to construct a region of interest to surround the
oropharynx and to divide the oropharyngeal airway into superior and inferior
oropharyngeal regions.
1. PNS Plane: The horizontal line parallel to Frankfort Horizontal passing
through Posterior Nasal Spine (PNS).
2. Soft Palate Plane: The horizontal line parallel to Frankfort Horizontal passing
through U point, which is the most inferior point on the soft palate at the
uvular tip (Mazaheri 1994).
3. Epiglottis Plane: The horizontal line parallel with Frankfort Horizontal
passing through Et, the most superior point (tip) of the epiglottis.
Once the airway was defined, the “sensitivity” slider tool in Dolphin, which
allows the software to detect differences in grayscale resolution, was adjusted to best
recognize the airway (sensitivity value of 45). The Dolphin 3D® module calculated the
volume and the minimum cross-sectional area using segmentation and Dolphin’s
computer algorithm. This segmentation method has been shown to be superior to the
manual slicing and manual tracing method (Yushkevich et al. 2006). The level of most
constriction (minimum cross-sectional area) was recorded as well (Figure 3-3).
Cephalometric Analysis
Lateral and anteroposterior cephalograms were constructed from the CBCT scans
with no magnification. Linear skeletal measurements of the size of the pharyngeal
skeletal encasement were obtained. A custom analysis was created in Dolphin version
11.5 and used to make all measurements. The following list (in alphabetical order)
provides descriptions all landmarks used in this study. All minima and maxima assume
the head is oriented in norma lateralis (Table 3-1).
The following linear distances and angles were calculated for each constructed,
non-magnified lateral cephalogram. This list (in alphabetical order) provides definitions
of all measurements used in this study (Table 3-2).
23
Figure 3-2. Sketch of lateral view of skull with skeletal and soft tissue landmarks
identified and the airway segments delineated and labeled
The C3 Plane was removed for this study due to inconsistent field of visisbilty on
selected CBCT images. Thus, the laryngopharyngeal airway was not measured.
Diagram provided by Dr. Edward Harris on March 11, 2011.
24
Figure 3-3.
Two-dimensional rendering of the pharyngeal airway
Dolphin calculated the level of most constriction, airway volume, and airway area.
Diagram provided by Dr. Edward Harris on March 11, 2011.
25
Table 3-1.
Cephalometric landmarks
Landmark
A
Aa
ANS
B
Cd
Et
FH
FOP
Go
Gn
H
Ii
Is
L6
M
Me
Na
Or
Pg
Phw
PNS
Po
Definition
A Point (Subspinale): the most posterior point on the exterior ventral
curve of the maxilla between the anterior nasal spine and Supradentale.
Anterior arch of the atlas: the most anterior point of the atlas vertebrae.
Anterior nasal spine: the spinous process of the maxilla forming the most
anterior projection of the floor of the nasal cavity.
B Point (Supramentale): the most posterior point on the bony curvature of
the mandible between Infradentale and Pogonion.
Condylion: the most superior-posterior point on the curvature of the
capitulum of the condyle.
Tip of epiglottis: the most superior point of the epiglottis.
Frankfort horizontal: a horizontal plane drawn from porion to orbitale,
with patient in natural head position.
Functional Occlusal Plane: a line drawn between the cusp tips of the
permanent first molars and the most mesial premolars (or deciduous
molars in mixed dentition).
Gonion: the most posterior-inferior point on the gonial angle of the
mandible.
Gnathion (anatomic): the most anterior-inferior point of the mandibular
symphysis.
H Point: the most anterior and superior point on the hyoid bone body.
Incision Inferius: the incisal tip of the most anterior mandibular central
incisor.
Incision Superius: the incisal tip of the most anterior maxillary central
incisor.
L6 mesial: the most mesial point on the lower first molar.
M Point: the most posterior point of the mandibular symphysis.
Menton: the most inferior point on the mandibular symphysis.
Nasion: the junction of the frontal nasal suture at the most posterior point
on the curvature at the bridge of the nose.
Orbitale: the most inferior point on the lower margin of the bony orbit.
Pogonion: the most anterior point on the anterior contour of the bony chin
below B point and above Gnathion.
Posterior pharyngeal wall: point on the pharyngeal wall at the level of the
Psp (Posterior soft palate).
Posterior Nasal Spine: the spinous process formed by the most posterior
projection of the juncture of the palatine bones in the midline of the roof of
the oral cavity.
Porion: the midpoint on the superior aspect of the rim of the external
auditory meatus.
26
Table 3-1.
(Continued)
Landmark
Definition
Psp
Pt
Posterior soft palate: the most superior-posterior point of the soft palate.
Pterygomaxillary fissure: the most superior-posterior point on the average
of the right and left outlines of the pterygomaxillary fissure.
Se
Sella turcica: the center of the hypophyseal fossa, determined by visual
inspection.
Se
Sella-Vertical: the imaginary line passing through Sella, perpendicular to
Frankfort Horizontal plane.
U6
U6 mesial: the most mesial point on the upper first molar.
Table developed in consultation with department colleague Dr. James K. Killehay and
reproduced with his permission.
27
Table 3-2.
Linear (millimetric) dimensions and angles measured on the lateral
cephalograms
Dimension
AFH
ANB
AO-BO
Co-A
Co-Gn
FMA
H to FH
Na-Me
Na -A
Na
-B
Na
-Pg
Psp-Phw
Se-Go
Se-Me
Se-Na
Se -A
Se
-B
Se
-M
Se
-Po
SNA
Description
Anterior Facial Height: the linear distance from Nasion to Menton.
the inferior angle formed at the junction of the Nasion-A Point line and the
Nasion-B Point line.
Wits Appraisal: the linear distance between two points along Downs’
occlusal plane obtained from the intersection of a perpendicular line from
point A and from point B to the occlusal plane.
The linear distance from Condylion to A Point.
The linear distance from Condylion to Gnathion.
The anterior inferior-angle formed at the junction of the Frankfort
Horizontal plane and the mandibular plane.
The linear distance from H point to FH, perpendicular to FH.
The linear distance between Nasion and Menton.
The linear distance from point A to Nasion when projected perpendicular to
the Frankfort Horizontal plane.
The linear distance from point B to Nasion when projected perpendicular to
the Frankfort Horizontal plane.
The linear distance from Pogonion to Nasion when projected perpendicular
to the Frankfort Horizontal plane.
Superior Airway Space: the linear distance from Psp to a point directly
posterior to Psp on the posterior pharyngeal wall, parallel to FH.
The linear distance from Sella to Gonion.
The linear distance from Sella to Menton.
The linear distance from Sella to Nasion.
The linear distance from Sella to A point when projected perpendicular to
the Frankfort Horizonal plane.
The linear distance from Sella to B point when projected perpendicular to
The linear distance from Sella to M Point when projected perpendicular to
The linear distance from Sella to Porion when projected perpendicular to
The posterior inferior angle formed at the junction of the Sella-Nasion plane
and the Nasion-A Point plane.
SNB
The posterior inferior angle formed at the junction of the Sella-Nasion plane
and the Nasion-B Point plane.
Y Axis
The angle formed by the intersection of a line from Se-Gn with the FH
plane.
28
Each cephalometric measurement defined above was categorized into skeletal and
dental measurements along with the individual purpose for each measurement in the
cephalometric analysis (Table 3-3).
Class II Analysis
Several methods have been used to distinguish Class I from II malocclusions, but
it seems that the principal cephalometric measurement most pertinent to the present
analysis is the angle ANB. ANB is an imperfect measurement, and its shortcoming
depends primarily on angulation of the Sella-Nasion plane that is variable (Jacobson and
Jacobson 2006). However, its usage is perhaps the most widespread and well understood
by the orthodontic community. We compared the Sella-Nasion line to Frankfort
Horizontal plane and eliminated cases with too large a discrepancy. In order to achieve
proportional sample sizes throughout the range of conditions, the total 131 subjects were
divided into two groups based on ANB classification. Subjects with an ANB between 3°
and -1.5° were classified as Class I. Subjects with an ANB of 3.5° or greater were
labeled as Class II. These allowed us to compare severity of Class II malocclusion with
the pharyngeal values.
In addition, several Class II cephalometric predictors were used to determine
skeletal classification, relative position of the maxilla and mandible, and anteroposterior
length of maxilla and mandible. These Class II predictors were then compared to the
range of pharyngeal outcome variables, and associations between the two were evaluated
statistically.
Lastly, we mimicked the Class II malocclusion groups of Moyers, McNamara,
and Henry by using cluster analysis to see whether different Class II types within the
continuum stand out as having distinct pharyngeal dimensions. It is unlikely that dental
characteristics have any effect on pharyngeal dimensions, so we focused on the maxillary
and mandibular skeletal discrepancies evaluated against pharyngeal shape.
Error Calculation
A total of 28 CBCT scans were randomly selected and their cephalometric
variables, as well as airway dimensions were re-measured two weeks after the initial
measurements by the same investigator. The results of the original and re-measured
groups were compared, and a repeatability index was calculated (Dahlberg 1940), and
error was found to be statistically insignificant. The remaining subjects were then
analyzed according to the established protocol.
29
Table 3-3.
A list of the variables measured from the lateral cephalometric images
in the present study
Dimension
Variable
Cranial Base
Se-Na
Anterior Cranial Base Length (mm)
Midface
Co-A
Horizontal length of the midface (mm)
Facial Height
Na-Me
PFH/AFH
Se-Go
Total Anterior Facial Height (mm)
Ratio of posterior facial height to anterior facial height
Posterior Facial Height (mm)
Maxillary Position
Na Perp-A
SNA
Se -A
A-P positional change in the maxilla (mm)
Positional change in the maxilla relative to anterior cranial base (°)
A-P positional change in the maxilla (mm)
Mandibular Size and Position
Co-Go
Co-Gn
Go-Me
Na Perp-B
Na Perp-Pg
SNB
Se -B
Se -M
Y Axis
Vertical Mandibular Ramus Length (mm)
Mandibular Length (mm)
Mandibular Body Length (mm)
A-P positional change in the mandible (mm)
Protrusive growth of the chin (mm)
Positional change in the mandible relative to anterior cranial base (°)
A-P positional change in the madible (mm)
A-P positional change in the madible (mm)
Rotation of the mandible (°)
Maxillomandibular Relationships
ANB
AO-BO
FMA
Na A-Pg
A-P relationship of the maxilla-mandible (°)
A-P relationship of the maxilla-mandible (mm)
Maxillomandibular divergence (°)
Facial convexity (°)
30
Table 3-3.
(Continued)
Dimension
Variable
Dental Relationships
FMIA
Inclination of lower incisors relative to the Frankfort line. The distal
angle is measured. (°)
IMPA
Inclination of lower incisors relative to the mandibular plane (°)
Overbite
Vertical overlap of the upper and lower central incisors (mm)
Overjet
Horizontal overlap of the upper and lower central incisors (mm)
U1-L1
Angular relationship between the maxillary and mandibular central
incisors (°)
U1-NA
Angulation of the maxillary central incisor to the maxilla (°)
U1-NA mm
Position of the maxillary central incisor to the maxilla (mm)
L1-NB
Angulation of the mandibular central incisor to the mandible (°)
L1-NB mm
Position of the mandibular central incisor to the mandible (mm)
31
Statistical Design
Measurements were exported from Dolphin 3D® into a spreadsheet in Microsoft®
Excel 2010 (Microsoft Corporation, Redmond, WA). The spreadsheet was used to
combine patient information including demographic information (patient’s age, sex,
occlusion classification, and skeletal classification). The measurements were then
transferred to the statistical package JMP® Pro 10.0 (SAS Institute Inc., Cary, NC).
Analysis of covariance (ANCOVA) was used to simultaneously test for differences
between malocclusions while controlling for age and sex differences (the two covariates).
Some size changes tended to be curvilinear with age (faster growth in children than
adolescents), and curvilinear (polynomial) models were used to more accurately model
the curves (Appendix A).
Exploratory data analysis (Tukey 1977) was performed, searching for outliers;
those due to technical errors were corrected. Conventional descriptive statistics (e.g.,
Sokal and Rohlf 1995) were calculated; these (and their abbreviations) were sample size
(n, taken as counts of individuals, not sides), the arithmetic mean ( x ), the standard
deviation (sd), and the standard error of the mean (sem). The conventional alpha level of
0.05 was used throughout, and all of the tests were two-tail. No correction was made for
multiple comparisons. Salient results of the analysis were graphed using Delta Graph®
6.5 for Windows (Red Rock Software, Inc., Salt Lake City, Utah) or the graphics
subroutines within JMP® Pro 10.0.
Box plots were produced to explore the data and to screen for outliers. A box plot
is a graphic technique in the family of descriptive statistics. It is a graphical display of
the sample distribution that resembles a box with two lines or “whiskers” coming out the
ends (Figure 3-4). The box can be drawn horizontally or vertically. The five vertical
lines in each box plot denote 10, 25, 50, 75, and 90th percentiles. The ends of the box
fall at the upper and the lower quartiles of the distribution, QU and QL, so the middle
50% of the cases (the median) falls within the QU-to-QL range of scores. Sample
variability is shown by the height of the box. The line in the middle of the box represents
the median of the distribution. The median is an estimate of the central tendency, and
placement of the median suggests whether the data are skewed. If the median is closer to
the upper quartile, the data are negatively skewed; if the median is closer to the lower
quartile, they are positively skewed. Individual data points above and below the 10th and
90th percentile are denoted by symbols. Data points that fall outside the 10% and 90%
are called outliers (Norman and Streiner 1994).
32
Figure 3-4.
Example of a box plot
The centiles of the sample distribution are labeled to the right. “Jittered” points are offset
to the left and right of the midline simply in order to make the distribution more apparent
(otherwise points might be superimposed and not visible). Diagram provided by Dr.
Edward Harris on March 11, 2011.
33
CHAPTER 4.
RESULTS
Geographical Cephalometric Differences
The CBCTs of the sample of 60 Class I patients and 71 Class II patients were
obtained from two private orthodontic practices, one in Wichita, Kansas, and the other in
Jackson, Tennessee. This provided a total sample of 131 adolescent American white
patients. It was of interest whether these two samples differed geographically in their
pharyngeal and/or cephalometric values. The starting point was a comparison of the
chronological ages at the start of treatment (Figure 4-1), where the distributions were
largely overlapping. As shown in Figure 4-2, the majority of cases were in the range of
10 to 14 years. Slightly different ratios of Class I and II patients were chosen from the
Kansas and Tennessee offices but the difference was not significant (Figure 4-3).
Intraobserver Repeatability
Repeated measurements taken on the same article are never exactly the same.
Dissimilarities are due to a combination of operator differences in selection of landmarks,
differences in how operators define a variable, and also the level of precision or number
of signficiant digits documented (Houston 1983; Houston et al. 1986). Repeatibility can
also differ due to inconsistencies in the measuring instrument. Measuring instruments all
contain a certain number of digits that are only so accurate and can measure only so
precisely. Calipers and computers do not always provide consistent measurements or
work equally well in all planes of space. There are two sources of instrument error,
namely systematic error and random error. Systematic error occurs due to an issue with
the instrument itself. Random error occurs when the measurement is restricted to fixed
increments. For example, evaluations from a computer monitor that has distorted images
or a screen with incorrect resolution will give false readings. Or, in the example of bent
calipers, measurements can be larger or smaller than they should be (Harris and Smith
2009).
Intraobserver reliability, also known as Technical Error of Measurement or TEM,
is a useful measurement since it points out the inherent imprecision in a system. The goal
of systematic methods in a research project is to attain repeated measurements that are
both precise and accurate. Precision (also known as reproducibility and repeatability) is a
calculation of how close together measurements of the same object are. Vierira and
Corrente (2011, p 488) declared: “By definition, repeatability is the closeness of
agreement between successive readings obtained by the same method on the same
material and under the same condition (same operator, same apparatus, same setting and
same time)”.
On the contrary, accuracy is how closely the measured values approximate the
exact value. We have used the classic target comparison (Figure 4-4) to show that
measurements can be accurate but not precise, and vice versa. The objective is to produce
34
Figure 4-1. Box plots of the age distribution of the sample, partitioned be sex and
geographical site (either Kansas or Tennessee)
Visually, there is considerable over-lap of the four distributions. Statistically, by chisquare test (1 degree of freedom) X2 was 1.28 with an associated P-value of 0.2574, so
the distribution of Class by Site did not differ statistically.
35
Figure 4-2. Histograms of the age distributions (sexes pooled) by geographical site
(Kansas, Tennessee)
The majority of ages were from 10 to 14 years at the start of treatment.
Figure 4-3.
source
Pie charts of the proportions of Class II patients by geographical
Somewhat more Class I cases (shown in blue) were chosen from the Kansas office (55%,
39/56), while somewhat more Class II patients (shown in red) were used from the
Tennessee office (55%, 33/65). But, by a chi-square goodness-of-fit test (1 degree of
freedom), there was no statistically significant difference in the ratios of Class II patients
(P = 0.2574).
36
Figure 4-4. A metaphor of a “bull’s eye” characterizes the concepts of precision
and accuracy
(A) The mean of the measurements is close to the center of the bull’s eye, which is the
true value. These measurements have low repeatability, however, because of their scatter
and individual departures from the true value. (B) The measurements are close together
(good precision), but all are approximately equally biased from the true value. For
example, calipers might be out of kilter, so all measurements are exaggerated by, say, 0.1
mm. (C) Here the measurements are all close to the measurement (high accuracy) and
close to one another (high precision). Adapted with permission. Harris EF, Smith RN.
Accounting for measurement error: A critical but often overlooked process. Arch Oral
Biol 2009; 54, Supplement 1:107-17.
37
measurements that are both precise and accurate, with as small a TEM as possible.
Ideally, the TEM is much smaller than the differences between the groups being
compared. A small TEM guarantees that observed differences between groups are not
unfairly influenced by technical measurement errors. Introducing the concept of TEM
makes it impossible to ever determine the true value of a quantity, but with a large
sample size, measurements draw closer and closer to the true size (Winer et al. 1990).
We next analyzed a set of replicate measurements. From the original set of 131
cases, 28 were remeasured two weeks later while blinded to the subject’s original
readings. All variables were remeasured, so there was a sample size of 28 replicated
pairs of numbers per variable.
Systematic Error: It is possible that the operator’s definition of landmark location
has changed during the time between measurements, thus making the second set of
measurements systematically different from the first. Matched (paired) t-tests were used
to test for this (two-tail tests).
Random Error: The Dahlberg statistic (Dahlberg 1940) was calculated for each
variable as:
where X1i and X2i are the two measurements for subject i and n is the number of
replicated (pairs of) subjects (Dahlberg 1940; Knapp 1992). The differences are then
squared to make them all positive. Despite certain claims, this value does not represent
the mean difference of the measurement error. It is rather the standard error of the
measurement difference (Altman and Bland 1983; Bland and Altman 1996, 1999, 2003).
The Dahlberg statistic is a reliable value, but there is certainly value to be found
in the arguments of Vierira and Corrente (2011). They submit that the Dahlberg statistic
only works when readings are (1) identically distributed random variables, (2)
independent, and (3) the average of the differences between readings average to zero.
Bland-Altman plots were first created for the statistically significant variables.
These are provided in Appendix B. Repeated-measures descriptive statistics were then
computed. Particular concentration was placed on differentitating between sessions
(session 1 minus session 2), and testing whether this difference differed significantly
from zero. An average variation of zero would imply a lack of systematic bias between
measurement sessions. A regression slope that was significant indicated that the
difference between repeats was associated with trait size, either by an increase of
differences with trait size (positively) or by a decrease in repeat differences with trait size
(negatively).
Table 4-1 lists the results of the intraobserver data in a different fashion. Using
the differences between the repeats (X1j - X2j), it was tested whether this mean differed
38
Table 4-1.
Descriptive statistics of intraobserver repeatability, showing the
difference of each variable and a t-test evaluating whether the mean differed
statistically from zero
Variable
AFH
Airway 1 Area
(Nasopharyngeal)
Airway 1 Volume
(Nasopharyngeal)
Airway 1+2 Area
Airway 1+2 Volume
Airway 1+2+3 Area
Airway 1+2+3 Volume
Airway 2 Area (Superior)
Airway 2 Volume
(Superior)
Airway 3 Area (Inferior)
Airway 3 Volume
(Inferior)
A-Nasion-Perpendicular
ANB
B-Nasion-Perpendicular
Conylion-A
Conylion-Gnathion
Facial Convexity
FMA
FMIA
Gonion-Menton
IMPA
Interincisal Angle
L1-NB (°)
L1-NB (mm)
Mesial Molar Relation
Minimum Constriction
Overbite
Overjet
PFH
Pogonion NasionPerpendicular
Sella-Vertical-A
Sella-Vertical-B
Mean
Difference
SD of
Difference
t-Test
P Value
0.286
-11.389
1.731
40.486
0.87
-1.49
0.3901
0.1482
17.161
551.191
0.16
0.8704
-2.425
-27.357
-7.582
-482.678
4.289
-44.518
83.603
2374.897
45.858
2125.719
60.098
1980.105
-0.15
-0.06
-0.87
-1.18
0.37
-0.12
0.8792
0.9518
0.3893
0.2487
0.7138
0.9062
-5.157
-360.729
79.210
1286.853
-0.34
-1.48
0.7331
0.1496
-0.321
-0.189
0.271
0.350
0.532
-0.336
0.004
-0.454
0.414
0.446
-0.564
0.275
-0.032
0.100
-0.050
0.054
-0.132
-0.154
-0.404
1.210
0.336
0.487
1.532
1.811
0.698
2.151
2.802
2.428
4.132
5.172
2.571
0.573
0.456
21.965
0.801
0.286
3.250
2.203
-1.41
-2.98
2.95
1.21
1.55
-2.54
0.01
-0.86
0.90
0.57
-0.58
0.57
-0.30
1.16
-0.01
0.35
-2.45
-0.25
-0.97
0.1713
0.0060
0.0065
0.2370
0.1317
0.0170
0.9931
0.3993
0.3746
0.5722
0.5685
0.5760
0.7688
0.2563
0.9905
0.7262
0.0211
0.8045
0.3410
0.932
0.986
3.022
3.448
1.63
1.51
0.1143
0.1420
39
Table 4-1.
(Continued)
Variable
Mean
Difference
SD of
Difference
t-Test
Sella-Vertical-M
Sella-Vertical-Pogonion
SNA
SNB
Superior Airway Space
Total Airway
U1-NA (°)
U1-NA (mm)
U1-Sella-Nasion
Wits Discrepancy
Y-Axis
0.796
-0.271
-0.425
-0.257
0.129
-388.086
0.486
0.011
0.046
-0.096
-0.321
3.599
2.822
0.965
1.081
0.422
2145.194
2.925
0.951
3.310
0.498
2.121
1.15
-0.51
-2.33
-1.26
1.61
-0.96
0.88
0.06
0.07
-1.03
-0.80
40
P Value
0.2607
0.6149
0.0275
0.2189
0.1189
0.3469
0.3873
0.9529
0.9414
0.3144
0.4297
significantly from zero (a two-tail one-sample t-test). Just two of the variables differed
significantly between measurement sessions, ANB and B Point to Nasion-Perpendicular.
This first variable (ANB) is shown in Figure 4-5. The mean difference was -0.189
degrees with a standard deviation of 0.336 (n = 28). The second measurement session of
ANB measurements tended to be larger than those made the first time (Figure 4-5) with a
mean difference of -0.189 degrees.
The second significant variable was B to Nasion-Perpendicular. Here, the mean
difference was significantly positive (0.271 mm), meaning that the first measurements
tended to be larger than the second (Figure 4-6). In both instances, however, we placed
no clinical importance on these very small differences.
ANCOVA
Our next focus of interest was to simultaneously test for differences among
patient’s sex, Angle’s classification (Class I versus Class II), and patient’s age
(specifically, the chronological age at the start of orthodontic treatment).
A series of univariate ANCOVA analyses also were used to test for geographical
differences (Figure 4-7). It was valuable from experience to include four factors in the
model, (1) geographical location (Kansas or Tennessee), (2) patient sex, (3) patient’s
Class of malocclusion (Class I versus II), and (4) patient age at the pretreatment records.
The first three factors are fixed effects, while age is a continuous covariate (Figure 4-7).
The full model (i.e., all interactions) was calculated using the JMP Pro 10.0 software, and
the results are listed in Appendix A.
There were 45 variables studied, and nine of these attained significant differences
between the two geographical sites. Because of the numerous tests in these ANCOVAs,
we discuss just those significant at an alpha of 0.01 or better. The remainder of this
section describes these statistically significant differences.
The reasoning here for the model design was straightforward: Sex was included
in the linear, ANCOVA model to account for the common perception (e.g., Ursi et al.
1993) that boys are larger girls. Particularly after the onset of puberty, sexual
dimorphism is a common finding in the body as a whole (e.g., Wells 2012) as well as the
craniofacial complexes (Riolo et al. 1974). Angle’s classification (Class I versus Class
II) was the dependent variable, so insofar as we were able to correctly classify the
patients’ malocclusion, there may well be a statistical difference between classes
(supposing that cephalometric dimensions are associated with Angle’ classification).
Thirdly, age (chronological age at the start of treatment) was aimed at accounting for the
obvious relationship that chronologically older subadults are larger than younger
subjects—children grow larger with age (Riolo et al. 1974).
41
Figure 4-5.
Bland-Altman plot for the cephalometric angle ANB
The mean difference is a bit above the mean, showing that the first session of
measurements exceeded the second, resulting in a systematic difference.
42
Figure 4-6. Bland-Altman plot for the cephalometric distance B to NasionPerpendicular
For this variable, the mean was a bit below zero, showing that the second measurement
session produced larger values than the first.
43
Figure 4-7. Form of the ANCOVA model used to test for group differences for
(45) cephalometric variables
44
Importantly, these three factors were examined simultaneously (in the same
model) so the correct source of the variation could be identified rather than being
confounded (e.g., Winer et al. 1991; Sokal and Rohlf 1995). For example, a traditional
approach (when calculations were done by hand) would have been to compute a series of
one-way ANOVAs, say testing for class differences, then another series testing for sex
differences, and so on. Unless class and sex are perfectly independent of one another, it
is possible to confound sex differences with class differences and class differences with
sex differences—which would complicate and distort interpretations of the statistical
results. Evaluating the effects simultaneously avoids this pitfall (e.g., Woolf 1968). Sex
and Angle’s class are fixed, model I effects; and age is a continuously-distributed
covariate (Winer et al. 1991. Univariate ANCOVA calculations were performed using
JMP Pro 10.0 (SAS Institute Inc, Cary, NC), and the resulting tables are listed in
Appendix A. The full model was calculated (Winer et al. 1991), so there were three
main effects (Sex, Class, Age), three first-order interactions (Sex-x-Class, Sex-x-Age,
and Class-x-Age), and one second-order interaction (Sex-x-Class-x-Age). In the JMP
design, there is one degree of freedom associated with each of these seven effects.
Summary and Interpretation of ANCOVA Results
Volume of the nasopharynx disclosed both a significant class and age effect
(Figure 4-8). The two classes both showed an increase in airway 1 volume with age, but
at significantly different rates. This measure of the rate of increase in the Class II sample
is significantly steeper (faster) than in the Class I sample. The data also suggested that
the tempos of airway growth differed between classes: In this age interval, size in the
Class I cases grow appreciably but not so in the Class II cases, though the two groups are
similar in size around the end of childhood.
The next noteworthy difference (P < 0.01) was the positive association between
chronological age and the airway volume labeled “Total Airway Volume”. There was no
significant class or sex effect for the variable (Figure 4-9). The best-fit regression line fit
to these data (n = 131 patients) is Volume = 825.5 + 1,382(Age), where, of course,
volume (the dependent variable) was “Total Airway Volume” measured in cubic
millimeters and chronological age was in years (r2 = 11%). This suggested that, within
this age interval, this volume increases almost 1,400 mm3 each year, and the ANCOVA
model suggests that it is of no consequence whether the cases were boys or girls or
whether they had Class I or II malocclusions.
This same theme extends to one of the comprehensive measures of pharyngeal
size used here, namely Airway 1+2+3, or “Total Airway Area” (Figure 4-10). The bestfit regression line to these data is Area = -1962 + 481.4(Age). Several curvilinear
regression models were assessed, but this straight line model had the greatest explained
variation.
In keeping with this theme of growth of airway growth with age, Volume of the
Inferior Oropharynx is also noteworthy (P < 0.01). Here (Figure 4-11), the linear
45
Figure 4-8. Bivariate plot between chronological age (in years, X axis) and volume
of the nasopharynx (in cubic millimeters, Y axis), partitioned by Angle’s Class
The blue crosses are Class I cases; the red squares are Class II cases. The lines are the
least-squares regression lines fit by Angle Class.
46
Figure 4-9. Bivariate plot between chronological age (years) and pharyngeal
volume (cubic millimeters), labeled Total Airway Volume
There was a statistically significant, positive association between these two variables (P =
0.0004).
47
Figure 4-10. Bivariate plot between chronological age and the two-dimensional
measure of Total Airway Area (mm2)
Patient’s class of malocclusion and sex played no significant part in this ANCOVA
model.
48
Figure 4-11. Bivariate plot between chronological age and volume of the inferior
oropharynx
This positive association is highly significant in the ANCOVA model (P = 0.0023). The
line in the graph is the sample’s least-squares regression line.
49
regression accounted for about 8% of the variance (r2 = 0.08122), and the regression
equation was Volume = -1962 + 0.048(Age). Age, of course, is measured in years and
refers to the patient’s age when the pretreatment records were taken.
The suggestion was, then, that all measured segments of the oropharynx increased
with age (they “grew”) and there was no sign in these cross-sectional data of any
plateauing (slowing) of the rate of increase. Growth is expected to stop by the onset of
adulthood (by definition), but the denouement seems to come in the later teenage years,
not in the age interval examined here (which was roughly 8 to 15 years). Moreover, as
noted, growth appeared to be linear in the observed age interval. Curvilinear regression
lines did not significantly improve the explained variance.
Total Airway Volume (mm3) was the final, summary measure of pharyngeal size
examined here. Comparable to its constituent parts, Total Airway Volume exhibited a
significant, positive association with age (Figure 4-12). The best-fit line was Volume = 825.5 + 1,382(Age), which accounts for 10.6% of the variance in the ANCOVA model
(r2) and this association was highly significant statistically (P = 0.0004). The regression
line suggested that three-dimensional volume increased about 1,400 mm3 per year in this
age interval, with no difference among patients of different sexes or malocclusions.
The subsequent analyses of associations in this section involved cephalometric
variables rather than measures of airway size, and the clinically noteworthy associations
(P < 0.01) were less common.
The difference by Angle Class and degree of facial convexity (Na A-Pg) was
significantly smaller in the Class I sample (P < 0.0001). This high level of significance is
not surprising (Figure 4-13), though, because facial retrognathism was one of the
dependent variables used for case selection. What we have, then, is a vindication of the
author’s ability to identify Class I from Class II skeletal relationships.
Similarly, another variable associated with classification of malocclusion is the
angle SNA, which was also significantly different between Classes (Figure 4-14). This
double-paned graph seems to be most informative for showing the results, in that the
Class I and II patients grew differently with age. There was a significant increase in SNA
angle with age in the Class I sample, which reflected normal anterposterior jaw growth
(e.g., Riolo et al. 1974), whereas the average SNA angle did not change with age (in
roughly the 10 to 15 age interval) in the Class II sample.
Similar results were encountered for the SNB angle, which is a measure of
mandibular prominence (Figure 4-15). The slopes of SNB were distinctive by Angle
Class. In the Class I sample, SNB increased with age, but the slope was effectively level
(no change) in the Class II sample.
Given the predictable differences in the angles SNA (increasing with age in Class
I cases) and SNB (increasing with age in Class I cases), the difference between these
maxillary and mandibular angles (angle ANB) is also predictable. Again, though, the
50
Figure 4-12. Bivariate plot between chronological age (years) and volume of the
total airway (mm3)
The increase in size with age is positive and statistically significant. The least-squares,
best-fit line is Volume = -825.5 + 1,382(Age), which accounts for 10.6% of the variance
in the ANCOVA model (r2, P = 0.0004).
Note: Total Airway Volume is the summation of airway parts 1, 2, and 3. So, while the
variable is the same, the interpretation is slighty different.
51
Figure 4-13. Box plots showing the difference in distributions between the two
Angle Classes
The horizontal gray line across the plot is the grand mean. Patient’s age and sex did not
significantly influence the analysis.
52
Figure 4-14. Bivariate graphs showing the difference in distributions between
Angle Class I and Class II samples (sexes pooled) for the cephalometric angle SNA
The mean angle was significantly larger in the Class II series, which reflected their
greater maxillary protrusion. Notably, the angular increase in SNA with age was
significant in the Class I sample, but not in the Class II sample. The blue bands around
the regression lines are the 95% confidence limits.
53
Figure 4-15. Twin bivariate plots showing the association between chronological
age (X axis, in years) and size of the angle SNB (degrees; Y axis)
The blue bands around the regression lines are the 95% confidence limits.
54
difference in ANB reflects selection on the dependent variable. That is, orthodontists
anticipate that ANB will differ between Class I and II cases; indeed, B was used as one of
the key criteria for defining which cases exhibited a Class II skeletal relationship, so
finding a high statistical difference largely just confirms the author’s consistency in
sample selection (Figure 4-16).
The same is true for the Wits appraisal (AO-BO discrepancy) that showed a
highly significant difference (P < 0.0001) between Classes (Figure 4-17).
The next statistically significant variable was IMPA, which measures torque of
the mandibular incisor. Here, too, was one of the few significant differences between
geographical sites. Measurements were at the start of treatment, so these site differences
are thought to reflect geographical differences in the nature of the malocclusions, not
treatment preferences (Figure 4-18).
Cluster Analysis
One of our interests in this study was to see how the present sample of 71 Class II
cases mimics earlier researcher’s efforts at partitioning the sample into groups of subjects
sharing similar craniofacial morphologies. That is, the Class II, division 1 malocclusion
is defined most simply as distoclusion of the permanent first molars viewed
anteroposteriorly (Angle 1907). But, as every orthodontist knows well, a Class II
relationship can be configured from several different conditions, such as a recessive
mandible or a prognathic maxilla or many combinations thereof, including both dental,
skeletal, or skeletodental conditions (Elsasser and Wylie 1943; Renfroe 1948; Riedel
1952; Henry 1957; Hunter 1967; Moyers et al. 1980; McNamara 1981).
The solution to the question of “how many groups” are intermingled in a sample
is not commonly dealt with in orthodontics but the answer certainly has been addressed in
other areas. In other disciplines, such as paleontology and numerical taxonomy, several
approaches to this question are fairly common. The major steps to the question are:
1. Compute some measure on phenetic (phenotypic) “distance,” either a distance
of similarity or of dissimilarity. This converts a visual problem of similarities
among subjects into a quantified arithmetic problem,
2. Use a computer algorithm and a set of assumptions to build a “tree” or
hierarchy, where geometrically similar cases are connected by short lines and,
progressively, less similar cases are connected by longer lines, and
3. Use a test to determine how many clusters are present gauged against some
statistical criterion.
This statistical problem is termed cluster analysis (e.g., Gower 1967; Blackith and
Reyment 1971; Sneath and Sokal 1973), and the procedure just outlined is far more
complex, containing many more statistical and epistemological choices than just outlined.
Fortunately, the JMP statistical package, as with other large packages (e.g., SAS, SPSS,
55
Figure 4-16. Box plots showing the difference in distributions by Angle Class
The mean is around zero for the Class I sample (left panel), but averages about 6 in the
Class II group (right panel). Patient’s age did not affect the ANB angle. There was no
statistical difference within Class between sites.
56
Figure 4-17. Box plots of the distributions of Wits values (mm) by Angle Class
Since the Wits value was a dependent variable for skeletal Class II selection, there should
indeed be little overlap between the Classes.
57
Figure 4-18. Box plots of the distributions of IMPA by geographical site and Angle
Class measured at the start of treatment
IMPA was significantly lower (more upright) in the patients from Kansas compared to
Tennessee. Within each site, IMPA was larger (the incisors were more proclined) in the
Class II patients.
58
ClustanGraphics) contains a package of cluster analysis programs with numerous options,
and that is the platform used for the results described here. For example, it is
fundamental to decide how the clusters are put together. Should the most similar cases be
put together first (agglomerative techniques), so the “tree” successively builds up by
progressively adding more dissimilar subjects, or should the most dissimilar groups be
found first, so the “tree” begins with dissimilar branches and successively adds
phenotypically less-distant subjects.
Cluster analysis probably can be traced back to the eminent statistician and
geneticist, Sir Ronald A. Fisher (1936), though his emphasis was quite different. Fisher
was interested in a different problem: if you have a number of measurements from
samples of specimens from multiple groups, how can you maximally discriminate among
them? Discriminant functions analysis (Fisher 1936) and cluster analysis are actually two
sides of a coin; the groups are known ahead of time in discriminant functions, while
cluster analysis asks how many groups exist. Both are multivariable statistical
techniques. Fisher’s specific example was to use four measurements on 50 specimens
each from three iris species. The object was to use the four measurements
simultaneously (multivariately) to distinguish between the three species. Applying
cluster analysis to these iris data produced the display in Figure 4-19.
The present sample size of 71 Class II cases examined here probably does not
fully encapsulate the breadth and variety of cases accessed by other researchers, for
example the 497 cases studied by Moyers et al. (1980). Also, the results of cluster
analysis are specific to the variables examined. Prior studies have used lateral
cephalometric variables; the present study used CBCT files, with emphasis on pharyngeal
size.
To give an example of agglomerative cluster analysis using Ward’s method
(Ward 1963), our assessment was based on the 11 pharyngeal variables:
1. Airway 1 Volume (Nasopharyngeal)
2. Airway 1 Area (Nasopharyngeal)
3. Airway 1+2 Volume
4. Airway 1+2 Area
5. Airway 2 Volume (Superior)
6. Airway 2 Area (Superior)
7. Airway 1+2+3 Volume
8. Airway 1+2+3 Area
9. Airway 3 Volume (Inferior)
10. Airway 3 Area (Inferior)
11. Total Airway
The “scree plot” of the cluster analysis (e.g., Gorsuch 1983) was used to
determine the number of clusters produced by the analysis (Figure 4-20). So long as the
slope of the scree plot remains relatively flat, the groups are similar. It is at the inflection
point (where the rate of slope rises) that the informational content rises, and the
59
Figure 4-19. A depiction of cluster analysis applied to Fisher’s three species of iris
data (150 specimens; 4 variables)
Cluster analysis was used to array the specimens but they are arrayed here along the
canonical axes. The first two canonical variates (X and Y axes) are labeled “Can1” and
“Can2.”
Figure 4-20. The “scree plot” associated with the following dendrogram (cluster
analysis)
The scree plot begins to rise very slowly from left to right as cases are successively
grouped together; the important point, visually, is where the slope of the plot changes
inflection and begins to rise more rapidly. This analysis, based on 11 pharyngeal
variables suggests that there are four distinctive clusters of Class II cases among the 71
subjects in the study.
60
investigator concludes that subsequent “branches” of the tree (dendrogram) are different
from one another. This particular analysis suggested there were four distinctive
groupings of the 71 Class II cases, based on the 11 pharyngeal dimensions.
The question, of course, is which of the eleven dimensions are important in
distinguishing the clusters of cases and how. In other words, how can these four clusters
be characterized based on these variables? We labeled the clusters, from top to bottom in
the figure, A, B, C, and D.
Our assessment of the cluster derived from the 11 pharyngeal measures was a set
of five clusters (shown to the left of the vertical red line in Figure 4-21). This number (5
clusters) coincides with the deflection point of the scree plot. One-way factorial ANOVA
was then used to assess how the univariate dimensions contributed to the clustering.
Tukey’s HSD (“honestly significant difference”) post hoc test was used to test the
assortment among groups (see, e.g., Mosteller and Tukey1977 for description of the HSD
test). It turns out that all 11 exhibited statistically significant differences among the
clusters.
Just for this first cluster result, the individual variables are detailed in a set of bar
charts, that is, the 11 pharyngeal dimensions. The following graphs (Figures 4-22
through 4-32) detail these differences.
The cluster analysis based on the 11 pharyngeal dimensions suggested four
“kinds” of Class II cases among the 71 subjects analyzed here (Figures 4-22 through
4-32). These were assorted on the basis of pharyngeal size. The most common cluster
consisted of the majority of cases (n = 48) with a midrange of airway sizes. Cluster 2 (n
= 2) had the smallest airways, while cluster 5 had the largest. Clusters 3 and 4 had the
largest dimensions aside from the one, very large individual in cluster 5. The bar charts
show that the orderings of the groups are similar across variables, though, of course, the
units of the dimensions differ.
The next effort was based on an analysis based on 19 skeletal dimensions
(omitting the several tooth-based dimensions often considered in orthodontic diagnosis).
The 19 variables (all assessed at pretreatment) were:
1. Y-Axis
2. Facial convexity
3. SNA angle
4. SNB angle
5. ANB angle
6. Wits appraisal
7. FMA
8. Condylion-A distance
9. Condylion-Gnathion
10. A-Nasion-perpendicular
11. Pogonion-Nasion-perpendicular
61
Figure 4-21. Dendrogram of the 71 Class II cases analyzed from CBCTs
Analysis was based on 11 pharyngeal dimensions (sexes pooled). The shorter the
horizontal branches, the closer the phenotypic similarities connecting the cases. Analysis
suggests five groups (identified by the vertical red line). The case numbers of the
subjects and the icons (left of diagram) simply are the order of case entries and the
cluster, but they do permit analysis of the grouping characteristics. The subjects are
uniformly arrayed vertically, so the vertical closeness of the subjects is immaterial;
indeed a node of a cluster can be rotated without affecting the analysis. The JMP
program color-codes the subjects within the smaller units to aide in visualization.
62
Figure 4-22. Results of cluster analysis using the 11 pharyngeal dimensions
The mean (+ 1 sd) of the size of each cluster is graphed, specifically for the airway 1
volume (mm3). Cluster 1 contained the most cases (n = 48), cluster 2 was n = 2, cluster 3
was 15, cluster 4 was 5, and cluster 5 contained just 1 case (thus, no standard deviation).
63
Figure 4-23. Results of cluster analysis using the 11 pharyngeal dimensions,
specifically for the airway 1 area (mm2)
The mean (+ 1 sd) of the size of each cluster is graphed. Cluster 1 contained the most
cases (n = 48), cluster 2 was n = 2, cluster 3 was 15, cluster 4 was 5, and cluster 5
contained just 1 case (thus, no standard deviation).
64
specifically for the airway 1+2 volume (mm3)
65
specifically for the airway 1+2 area (mm2)
66
specifically for the airway 2 volume (mm3)
67
68
specifically for the airway 1+2+3 volume (mm3)
69
70
specifically for the airway 1+2+3 volume (mm3)
71
72
specifically for the total airway (mm3)
73
12. B-Nasion-perpendicular
13. Anterior Facial Height
14. Posterior Facial Height
15. Gonion-Menton
16. Sella-vertical-to-A point
17. Sella-vertical-to-B point
18. Sella-vertical-to-Pogonion
19. Sella-vertical-to-M point
The scree plot for this cluster analysis suggested that there are just two clusters
(Figure 4-33). The dendrogram itself is illustrated in Figure 4-34.
One other investigation was the use of variables that reflect the degree of maxillamandibular discrepancy. There were four dimensions in this approach, namely SNA,
SNB, ANB, and Wits appraisal (AOBO). The first three of these were measured in
degrees, while the Wits appraisal was recorded in millimeters. A benefit of these angular
variables is that they are not as strongly correlated with size and age as are linear
dimensions (e.g., Proffit 2000). Inspection of the scree plot for this dendrogram
suggested there were eight recognizable clusters (Figures 4-35 and 4-36).
The dendrograms presented here produce different results, of course, depending
on the variables used to construct them and the assumptions chosen. Using the raw sizes
of the cephalometrics is unlikely to be particularly meaningful because these subjects—
examined in late childhood and early adolescence—are actively growing and increasing
their cephalometric dimensions (e.g., Riolo et al. 1974). As such, the subjects’ ages are
reflected in the dimensions, which importantly influenced the results. Though too laborintense for a sidelight of the present study, one solution would have been to standardize
all of the data by age and sex. That is, in place of using the raw data, if the z-scores
based on age- and sex-specific standards had been entered into the clustering algorithm;
the relative sizes of the variables would have been appropriately highlighted. The
simplest and time-honored method of standardization probably is the z-score (or “Tscore”) as described, for instance, in the text by Garn and Shamir (1958). The z-score is
where X is an individual’s measurement and x and s are, respectively, the mean and
standard deviation for that subject’s age and sex. This formula expresses the
measurement as the number of standard deviations away from the group mean, and of
course, this is desirable because it is the relative sizes of the dimensions that determine
the kind of Class II malocclusion and modulate treatment.
The influence of each variable in this cluster analysis was tested using a one-way
factorial ANOVA (alpha = 0.05) (Tables 4-2 through 4-6), and the HSD post-hoc test
(e.g., Abdi et al. 2009) was used to identify the source of statistical significance within
74
Figure 4-33. The scree plot for the cluster analysis based on 19 skeletal dimensions
The inflection point in the scree pattern seems to be toward the far right side, with just
two groups.
75
Figure 4-34. Cluster analysis (dendrogram) of the 71 Class II cases based on 19
skeletal dimensions
The scree plot suggested that there were just two clusters, as defined by the vertical red
line.
76
Figure 4-35. The scree plot resulting from clustering of four cephalometric
dimensions (SNA, SNB, ANB, and AOBO)
The division of the dendrogram using this inflection point produced eight clusters.
77
Figure 4-36. The dendrogram produced by four cephalometric variables (SNA,
SNB, ANB, and Wits)
According to the scree plot (shown here by the red vertical line) there are 8
distinguishable clusters among these 71 cases. That is, there are 8 clusters of Class II
cases emanating from the left of the vertical red line.
78
Table 4-2.
Results of one-way ANOVAs testing for differences in mean sizes
among the 8 clusters developed using 4 maxillo-mandibular discrepancies
Variable
SNA
SNB
ANB
Wits
df
7
7
7
7
Sum of
Squares
665.43
510.19
123.99
339.50
Mean
Square
95.06
72.88
17.71
48.50
F Ratio
76.99
43.01
26.33
22.24
P Value
<0.0001
<0.0001
<0.0001
<0.0001
Adjusted
R-Square
0.88
0.81
0.72
0.68
Table 4-3.
Descriptive statistics for SNA among the 8 groupings generated by
cluster analysis
Cluster
Mean
Standard
Deviation
1
2
3
4
5
6
7
8
77.3
81.3
86.8
84.2
84.3
85.7
87.5
82.2
1.57660
0.70017
0.56821
0.76659
1.01083
1.60375
1.55027
1.58902
SEM
0.45513
0.16063
0.21476
0.24242
0.31965
0.71722
0.89505
0.71063
79
Lower
95%
Confidence
76.323
80.999
86.317
83.642
83.597
83.729
83.616
80.227
Upper
95%
Confidence
78.327
81.674
87.368
84.738
85.043
87.711
91.318
84.173
Table 4-4.
Descriptive statistics for SNB among the 8 groupings generated by
cluster analysis
Cluster
1
2
3
4
5
6
7
8
Mean
Standard
Deviation
SEM
Lower 95%
Confidence
Upper 95%
Confidence
72.7
76.0
81.6
78.4
79.5
77.7
77.8
74.3
1.16421
1.04951
1.10518
1.09565
1.39000
2.01420
1.34288
2.04157
0.33608
0.24077
0.41772
0.34647
0.43956
0.90078
0.77531
0.91302
72.002
75.452
80.592
77.656
78.516
75.179
74.497
71.805
73.481
76.464
82.636
79.224
80.504
80.181
81.169
76.875
Table 4-5.
Descriptive statistics for ANB among the 8 groupings generated by
cluster analysis
Cluster
Mean
Standard
Deviation
1
2
3
4
5
6
7
8
4.59
5.38
5.23
5.77
4.81
8.06
9.63
7.88
0.820707
0.792509
0.760952
0.928619
0.966609
0.450555
0.950438
0.593296
SEM
Lower
95%
Confidence
0.23692
0.18181
0.28761
0.29366
0.30567
0.20149
0.54874
0.26533
4.0702
5.0022
4.5248
5.1057
4.1185
7.5006
7.2723
7.1433
80
Upper
95%
Confidence
5.113
5.766
5.932
6.434
5.501
8.619
11.994
8.617
Table 4-6.
Descriptive statistics for Wits among the 8 groupings generated by
cluster analysis
Cluster
1
2
3
4
5
6
7
8
Mean
2.37
3.75
3.86
4.30
-0.12
2.30
7.07
8.78
Standard
Deviation
1.91849
1.37936
1.03579
1.33583
1.04009
1.10680
1.61658
2.25322
SEM
0.5538
0.3164
0.3915
0.4224
0.3289
0.4950
0.9333
1.0077
81
Lower
95%
Confidence
1.148
3.083
2.899
3.344
-0.864
0.926
3.051
5.982
Upper
95%
Confidence
3.586
4.412
4.815
5.256
0.624
3.674
11.082
11.578
each ANOVA. If—as here—only pairwise comparisons are made, this Tukey-Kramer
HSD method results in a narrower confidence limit (which is preferable and more
powerful) than Scheffé's method.
Calculation of the HSD multiple comparisons were calculated as an option in the
JMP program. The F-ratio for SNA was 77. (df = 7 and 70; P < 0.0001). The HSD
indicated that the source of statistical significance was due to four differences between
the 8 clusters, that is (7-3-6) < (6-5-4) < (8-2) < 1 (Figure 4-37).
The F-ratio for SNB was 43 (P < 0.0001) with 7 and 70 df (Figure 4-38). The
HSD results show that the significance is due to four breaks among five groups, namely
3 > (5-4-7-6) > (2-8) > 1. Some of these cluster numbers are duplicated because, after the
group means were sequenced some of the adjacent groups were not strictly significant,
though farther separations did attain statistical significance. This stated grouping
(3 > (5-4-7-6) > (2-8) > 1), then, is the best available interpretation of the results.
The F-ratio for ANB was 17 (P < 0.0001) with 7 and 70 df (Figure 4-39). The
HSD analysis indicates there are three distinctive groupings of the 8 clusters, namely
(7-6-8) > (4-2-3-5) > 1.
Fourthly, the Wits appraisal produced an F-ratio of 22 (P < 0.0001) with 7 and 70
df (Figure 4-40). The Wits appraisal (AOBO) was smaller (mean < 4 mm) in six of the
eight groups, while the average was above 6 mm in clusters 7 and 8. The HSD analysis
disclosed three breaks among the eight clusters that resulted in four groups, namely
(8-7) > (7-4) > (3-2-1-6) > (6-5).
To attempt to summarize, clusters 3 and 7 were characterized by high SNA angles
(i.e., maxillary excess). SNB was lowest in cluster 8 (i.e., mandibular insufficiency).
The ANB angle was highest in clusters 6, 7, and 8, but for different reasons. ANB was
large in clusters 6 and 7 because of maxillary excess, but large in cluster 8 because of an
underdeveloped mandible. Finer discriminations would seem to await larger sample sizes
and more complete cephalometric measurements aimed at capturing various Class II
characteristics.
Notably, cluster analysis is suggestive (e.g., Blackith and Reyment 1971): It
develops a perspective of possible solutions. It does not provide any sort of definitive
results; instead, the result depends on the assumptions made and the methods chosen. It
also typically depends on a large sample size in order to increase assurances of including
all of the relevant groupings (“types” of Class II malocclusions in the present study).
Consequently, the tentative applications discussed here require more thorough study of a
larger sample.
82
Figure 4-37. Box plots of the arrangement of the angle SNA among the 8 clusters
83
Figure 4-38. Box plots of the arrangement of the angle SNB among the 8 clusters
84
Figure 4-39. Box plots of the arrangement of the angle ANB among the 8 clusters
85
Figure 4-40. Box plots of the arrangement of the Wits measurement among the 8
clusters
AOBO) was smaller (mean < 4 mm) in six of the eight groups, while the average was
above 6 mm in clusters 7 and 8.
86
CHAPTER 5.
DISCUSSION
There is debate over what degree of relationship exists between the pharynx and
the craniofacial structures. Evidence to date implies that the type and severity of Class II
malocclusion affects the size and shape of the pharynx. Several authors contend that
smaller airways are associated with Class II malocclusions. It is also proposed that small
airways can be caused by nasal obstruction, an anatomical circumstance that can lead to
weakened muscle action with a consequently altered facial growth pattern. This scenario
suggests that small airways and small mandibles are developmentally coincident. The
present study questions this claim, and analysis shows that there is likely no correlation
between pharyngeal size and malocclusion type. There is, however, in the conventional
teenage orthodontic patient, linear pharyngeal growth concurrent with age and sex.
Various researchers have classified Class II malocclusions into groups based on
size and positioning of the maxilla and mandible. If there exists a difference in the
airway size and shape between Class II and Class I patients, it is of interest to determine
what specific combination of skeletal presentations causes the greatest airway
differences. For example, if a child at age 11 has a skeletal malocclusion that causes a
concurrent small airway, and if that small airway causes a clinically significant reduction
in respiration, or increases the future likelihood of a condition like sleep apnea, then
correction of the skeletal malocclusion would seem warranted. However, this
hypothetical scenario must first be documented before being given merit.
There have been many research projects conducted on three-dimensional analysis
of the pharynx. Kim et al. (2010) studied the three-dimensional airway volume and
cross-sectional areas of 27 children with a mean age of 11 years. Total airway volume
was significantly smaller in the Class II subjects. However, this is likely a type II
statistical error due to small sample sizes. A sample size of only 27 patients does not
carry enough statistical power to confirm a difference between two groups.
Grauer et al. (2009) studied the CBCT records of 62 nongrowing subjects (aged
17-46 years) to evaluate pharyngeal airway volume and shape. Class II subjects had
significantly smaller inferior airways than Class I subjects. As with the previous study,
62 is likely not a large enough sample size to sufficiently differentiate between two
groups. Furthermore, the authors used the C3 vertebrae as a landmark for dividing the
airway. The position of the C3 vertebrae varies greatly from patient to patient in its
relation to the soft tissue that comprises the pharynx. So, it is likely that the airway was
inconsistently measured from patient to patient. Also, the use of patients that range in
age from 17 to 46 is troubling, given that growth of the pharynx begins to level off after
the age of 20, and even tends to decrease in size in some individuals around the age of 40
(Streight 2011). Furthermore, studying the pharyngeal airway in adults is less reliable
since the quality of the soft tissues of the pharynx is more variable as a result of the aging
process (Johnston and Richardson 1999).
87
In contrast to the studies of Kim and Grauer, Alves et al. (2008) found that the
majority of airway measurements were not affected by malocclusion type, with volume
and area measurements that were statistically equivalent between Class II and Class III
groups. Findings did indicate increased airway volume and area for males when
compared to females. However, as with the studies of Kim and Grauer, small sample
sizes cast doubt on the results.
Streight (2011) analyzed the CBCT images of 263 routine dental patients to
develop normative standards of pharyngeal dimensions by sex and age. They found that
pharyngeal volume, midsagittal area, and craniocaudal height are significantly larger in
men, and that several pharyngeal variables continued to increase during adulthood in
men, but not women. There were a few issues with the methodology of the study,
including an extremely wide age range of 5 to 85 years of age, a sample that includes
both whites and non-whites, and a cross-sectional research design.
A few studies have looked at the relationship between mandibular position and
the pharynx. Park et al. (2010) studied the pharyngeal airways of 12 subjects who
underwent mandibular setback surgery. 2-D and 3-D analysis of images taken before
surgery and 6 months after surgery showed a decrease in oropharyngeal volume, but the
change was not statistically significant. The volume of the nasopharynx, however,
remained relatively constant, which suggests that deformation occurs to preserve the
airway capacity in the changed environment following mandibular setback surgery. It
might also suggest that nasopharyngeal volume is independent of mandibular positioning.
These results should be viewed with caution, due to the extremely small sample size.
Pierre Robin Sequence (PRS) is a clinical entity consisting of micrognathia, cleft
of the secondary palate, with glossoptosis, and upper airway obstruction (Figueroa et al.
1991). Figueroa and associates compared the lateral cephalograms of 17 infants with
PRS to groups of 26 normal infants and 26 infants with isolated cleft palate. While the
groups were distinct throughout the 2-year period of study, differences were greater at the
earliest age. Initially, the PRS infant had a shorter mandibular length and narrower
airway. PRS infants did experience “partial mandibular catch-up growth” leading to
improved airway dimensions and concurrent resolution of respiratory distress. The
increased growth rate, however, did not allow PRS infants to recover to values equal to
normal. It is rational to assume that Class II patients with smaller than normal mandibles,
might exhibit similar characteristics. However, PRS patients exhibited the confounding
factors of cleft of the secondary palate, glossoptosis, and upper airway obstruction,
whereas Class II patients, by definition, may not.
Based on the studies of Harvold, Miller, and Vargervik, it is reasonable to assume
that a small pharyngeal airway could be the product of a past airway obstruction that led
to subsequent altered respiration, skeletal muscle adaptation, and then altered craniofacial
growth (i.e.. Class II malocclusion). However, this supposition has not been documented
and should not be applied to the issue at hand, especially since the presence of airway
obstruction in our sample is unknown.
88
Two growth studies, demonstrate that, surprisingly, little growth occured in the
anteroposterior dimension of the nasopharynx. King (1949) studied the serial
cephalometric radiographs of 24 boys and 26 girls that had been taken at three months of
age, six months, one year, and then annually to six years, and biennially from 6 to 16
years. He found that most of the sagittal growth of the pharynx occurred in the first year
of life. More inferiorly, in the oropharynx, the distance between the cervical vertebrae
and the hyoid bone was relatively constant until puberty when the hyoid bone moved
slightly forward. This suggests that the anteroposterior dimensions of the pharynx are
established in early infancy. Linder-Aronson and Woodside (1979), with a sample size
of 260, also concluded that the sagittal increase of the pharynx was unrelated to other
cephalometric dimensions of the facial complex. This finding coincides with our results,
which suggest that craniofacial positioning has little effect on the pharyngeal dimensions.
The majority of orthodontic research on airway health is restricted by the
technological limitations of cephalometric imaging (Lowe et al. 1986; Finkelstein et al.
2001; Hanggi et al. 2008; Abramson et al. 2009). Using 2-dimensional radiography, no
reliable conclusions can be made about the effects of orthodontic treatment on airway
volume because mediolateral widths are unknown. The advantage of the present study
and other current airway studies that capitalize on CBCT technology is that these
previously unknown widths, areas, and volumes can now be quantified. 3-D imaging is
also preferred because it produces an image that is a true 1:1 representation of the
anatomical structure in question (Mah et al. 2011).
Recent criticisms of the radiation dose of a CBCT scan seem sensible, given that
the average dose varies from ~40 to 135 microsieverts. This is two to 14 times greater
than the dose administered by the typical lateral cephalogram plus panoramic image (~8
to 18 microsieverts). However, newer technology (including the iCAT machines used in
this study) claim radiation doses closer to 35 to 40 microsieverts. Another issue concerns
the risk and responsibility for diagnosing pathology present on CBCT scans. In the
present study, no new CBCT images were taken, but rather existing CBCT images were
studied. Thus, the issues of radiation exposure and pathology diagnosis were not a direct
concern.
The present study analyzed 131 patients with pretreatment CBCT records from
orthodontic practices in Jackson, Tennessee, and Wichita, Kansas. Identical, Next
Generation iCAT® CBCT machines were used to collect all samples and each scan
recorded patients in an upright position, with a 12-inch field of view to include full
craniofacial anatomy. Samples were selected from private practices, with an age range of
9 to 13, in order to reflect current orthodontic practice in the United States.
Of the 131 patients (65 males; 66 females) 71 exhibited a Class II malocclusion
while 60 exhibited a Class I malocclusion. The study was limited to Class II, division 1
malocclusions by confirming labioverted maxillary central incisors, a sign indicated by
an overjet of at least 3.5 mm.
89
It was suggested that the geography of Jackson, TN (being approximately 170
miles further south than Wichita, Kansas, and thus experiencing a warmer climate) might
have some environmental effect on the patients from those areas. Additionally, since
Wichita is located on the Arkansas River, there might exist some environmental effect on
the patients’ respiratory development. However, there was no difference in airway
volume or area between geographical sites. As such, geographical location did not factor
significantly.
Nasopharyngeal volume grows faster with age in Class II patients than in Class I
patients. By this, we mean that the tempo of nasopharyngeal growth was faster in Class
II patients. However, the two groups are similar in size around the end of childhood.
This could represent a form of catch-up growth for the Class II patients. However, it
seems strange that the faster growth tempo presents in the nasopharynx but not in either
section of the oropharynx, nor does the trend appear when considering the Total Airway
Volume. Another possible explanation is the potential variation caused by tonsils and
adenoid tissue in the nasopharynx or from measuring errors caused by the difficulty in
finding the pterygomaxillary fissure, one of three points used to outline the nasopharynx.
There was a positive, statistically significant association between chronological
age and Total Airway Volume (a combination of nasopharyngeal and oropharyngeal
volumes). Figure 5-1 shows this relationship, partitioning the sample by Angle Class
and sex. By visual assessment, these four regression slopes appeared to be
homogemeous, and, by two-way ANOVA (Table 5-1), this was confirmened in that none
of the three F ratios was statistically significant at alpha = 0.05. Because of the
nonsignicance of Class and sex, the sample was reintegrated to recoup degrees of
freedom. Figure 5-2 shows the positive relationship between the age at the start of
treatment and size of Total Airway Volume for the entire sample. Within the age interval
of 9 to 14, the Total Airway Volume increases almost 1,400 mm3 per year. The same can
be said of Total Airway Area, as significant increases in size were seen with age. There
was also a linear increase in oropharyngeal dimensions in the observed age interval. One
aspect of orthodontic treatment that cannot be ignored is that the majority of orthodontic
patients are growing adolescents. In growing patients, structural dimensions expand as
the face grows downward and forward. Normal growth, then, seems like the best
explanation for the increase in pharyngeal size with age.
There was a highly significant difference between Class I and Class II patients in
degree of facial convexity (Na A-Pg). This is not at all surprising, though, since facial
retrognathism is one of the dependent variables used for case selection. This finding
works as vindication that the two samples were appropriately divided into Class I and
Class II groups. The same principle applied to significant Class differences between Wits
appraisal and ANB.
Similarly, both SNA and SNB were significantly different between Classes.
Interestingly, there was a significant increase in SNA angle with age in the Class I
sample, whereas the SNA angle does not change with age in the Class II sample. The
same finding is true with SNB angle between Classes. It is clear from these bivariate
90
Figure 5-1.
(mm3)
Bivariate plots by Angle Class and sex for Total Airway Volume
The least squares regression line was fit to each scatter of points, and the 95% confidence
limits are shown by the blue bands.
Table 5-1.
Results of two-way ANOVA tests for Total Airway Volume factored
by Angle Class and sex
Source
df
SSQ
F Ratio
P Value
Class
1
15096864
0.5201
0.4721
Sex
1
11206226
0.3861
0.5355
Class-by-Sex
1
42581289
1.4671
0.2281
Neither class, sex, nor the interaction term was statistically significant.
91
Figure 5-2. Bivariate plot between the patient’s age at the start of treatment and
Total Airway Volume for the complete sample (n = 131)
The 95% confidence limits are shown by the blue band.
92
plots that the average Class II patient has a less developed maxilla and mandible in
relation to their cranial base when compared with a Class I patient. It would seem also
that the colloquial, orthodontic approach of describing patients as “haves” and “havenots” applies to Class I and Class II patients. In clearer terms, it seems that patients
exhibiting small SNA and SNB values at a young age, do not outgrow these skeletal
conditions.
It was originally anticipated that there would be a size difference in the
pharyngeal airway variables by Angle’s Class. Class II cases were supposed to have
smaller airway dimensions because the mandible was smaller, leaving less space for the
pharynx. This difference had been suggested in the literatrure, and it was speculated that
the present study, with a larger sample size (n = 131) and better statistical control of the
subject’s age and sex, a size difference by Class would be evident. The specifics of the
statistical lack of any difference were detailed in the Results chapter. As a single,
summary graph (Figure 5-3) displays this overall overlap of sizes between Class I and
Class II orthodontic samples. None of the 11 variables differed significantly between
Classes.
Our attempt to separate Class II patients into groups using cluster analysis did not
produce any clinically relevant findings. The primary cause was our relatively small
sample size of 71 Class II patients. Moyers classic study on the subject included a much
larger sample of 497 patients. Future research on Class II groups will require a more
thorough study of a larger sample.
While sleep apnea is a clinically significant topic, it is impractical to apply
conclusions from these findings to sleep apnea since patients were seated during the
CBCT image capture process and not supine. Patients were also awake during image
capture process with no standard tongue position and no way to tell whether patients
swallowed or not. Future airway studies need to image patients in a supine position,
during sleep, and in conjunction with sleep studies. Combining this information with
BMI, nasal airflow measures, and even a pharyngeal flaccidity measure would be helpful
in better understanding sleep apnea.
After measuring 131 airways, there seems to be variability in airway morphology.
Due to the nature of pharyngeal anatomy, the most common airway division methods
require a combination of soft and hard tissue landmarks. Other proposed landmarks such
as vertebrae and the hyoid bone show significant variation from patient to patient and
were eliminated as possibilities. Another limitation is in splitting the oropharynx, since
the dividing line between superior and inferior is determined by position of the soft
palate, which can vary because the patient was swallowing or due to normal
physiological variation in size or shape of the soft palate. Also, positions of most soft
tissue pharyngeal landmarks vary as you move transversely through slices of the pharynx.
We attempted to make all measurements in the midsagittal plane of each patient, by
measuring the slice that was located between the maxillary central incisors.
93
Figure 5-3. A stacked chart of the average sizes of the 11 measures of pharyngeal
size analyzed in the present study
Visually, there is no evident (clinically important) difference in size by Angle’s Class.
94
Another limitation of the present study was that there were possible
methodological differences between the different geographical sites. Both sites used the
same iCAT CBCT machine, with the same settings and exposure time. However, it is
impossible to know, given the retrospective nature of the study, whether the images were
captured in an identical fashion.
Since respiratory health histories were unavailable, it is impossible to know what
effect, if any, a history of tonsillectomy had on the results. All patients with visibly large
tonsils or adenoids were removed from the study. According to Rowe (1982), enlarged
tonsils and adenoids are the primary source of upper airway obstruction in young
patients, so a better knowledge of the patients’ respiratory history would have been
beneficial.
Future research should focus on differences between Class I, Class II, and Class
III patients. A prospective, longitudinal study would best show differences in growth
between Classes. While the current study has the largest sample size to date, a larger
sample (especially of different Class II types) would potentially illustrate airway
differences.
95
CHAPTER 6.
SUMMARY AND CONCLUSIONS
Morphology of the pharynx affects the volume of airflow and facial growth
patterns, the risk of sleep apnea, and swallowing patterns. Since the pharynx is housed
within the facial structures, there may well be an association between the two.
Preliminary works by Kim et al. (2010) and Grauer et al. (2009) suggest a link between
craniofacial dimensions and pharyngeal shape. However, sample sizes have been small.
The three dimensions of height, width, and depth determine the size and shape of
the pharynx. Studies by Brodie (1941) and King (1952) found that the total depth of the
nasopharynx is established in infancy, with little change thereafter. Linder-Aronson and
Woodside (1979) reported that sagittal depth of the nasopharynx increases in small
increments up to 16 years of age for females and 20 years of age for males. Streight and
Harris (2011) found that growth of the pharynx did not decline during childhood, but was
linear throughout the child-to-adult age interval.
Class II malocclusions are some of the most common facial disharmonies
encountered in orthodontics. A Class II malocclusion can be a dental problem, a skeletal
problem, or some combination of the two (Graber 2005). Evidence to date implies that
the type and severity of Class II malocclusion affects the size and shape of the pharynx.
The purpose of the present, retrospective, cross sectional study was to determine
if there is a difference in pharyngeal dimensions between Class I and Class II orthodontic
patients. Oropharyngeal structures were analyzed in 131 healthy adolescents (71 Class II,
60 Class I) before orthodontic treatment. Using CBCT technology, cephalometric
variables and volumetric measurements were analyzed. Major findings are:
1. Pharyngeal growth, as measured by retrospective, cross sectional CBCT
images, occurs at a linear pace during the key orthodontic ages of 9 to 13
years and is significantly faster in boys.
2. Total Airway Volume (a combination of nasopharyngeal, superior
oropharyngeal, and inferior oropharyngeal volumes) is statistically equivalent
between Class I and Class II adolescent whites.
3. Superior and Inferior oropharyngeal volumes are both statistically equivalent
between Class I and Class II patients.
4. There exists no geographical difference between the Jackson, TN, and
Wichita, KS samples except for Class I IMPA being significantly lower in the
Kansas patients.
5. The minimum oropharyngeal constriction occurs inferior to the soft palate in
76% of Class II patients and in 68% of Class I patients.
96
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APPENDIX A. RESULTS OF ANCOVA TESTS FOR DIFFERENCES
BETWEEN GEOGRAPHICAL SITES (KANSAS VERSUS TENNESSEE)
WHILE CONTROLLING FOR THE PATIENT’S AGE, SEX, AND CLASS OF
MALOCCLUSION
107
Table A-1.
Results of ANCOVA test for geographical site difference, while
controlling for patient’s age, sex and class; the dependent variable is Airway 1
Volume (Nasopharyngeal)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
1043311
0.54
0.4623
Class
1
11214369
5.84
0.0171
Sex
1
110276
0.06
0.8109
Chronological Age Initial
1
31626602
16.48
<0.0001
Geographical Site-x-Class
1
35843
0.02
0.8915
Geographical Site-x-Sex
1
2574500
1.34
0.2490
Geographical Site-xChronological Age Initial
1
9855800
5.14
0.0252
Geographical Site-x-Class-x-Sex
1
31278
0.02
0.8986
Geographical Site-x-Class-xChronological Age Initial
1
1845043
0.96
0.3288
Geographical Site-x-Class-xChronological Age Initial-x-Sex
1
1739538
0.91
0.3429
108
Table A-2.
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.002
0.00
0.9994
Class
1
11618.035
2.95
0.0884
Sex
1
832.610
0.21
0.6464
1
26927.100
6.84
0.0101
1
56.550
0.01
0.9048
1
4620.581
1.17
0.2808
1
10150.910
2.58
0.1109
1
954.347
0.24
0.6234
1
11334.805
2.88
0.0923
1
644.180
0.16
0.6865
109
Table A-3.
controlling for patient’s age, sex and class; the dependent variable is Airway 1+2
Volume
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
9364133
0.72
0.3973
Class
1
10559133
0.81
0.3688
Sex
1
1282546
0.10
0.7538
1
198513481
15.30
0.0002
1
882019
0.07
0.7948
1
20487332
1.58
0.2114
1
78140831
6.02
0.0156
1
24836414
1.91
0.1691
1
13017865
1.00
0.3185
1
25836576
1.99
0.1608
110
Table A-4.
controlling for patient’s age, sex and class; the dependent variable is Airway 1+2
Area
Source
df
Geographical Site
1
Class
F Ratio
P Value
9921.08
0.77
0.3815
1
29189.95
2.27
0.1345
Sex
1
754.64
0.06
0.8090
1
11.94
0.0008
1
1744.97
0.14
0.7132
1
29297.72
2.28
0.1338
1
33792.14
2.63
0.1076
1
4051.53
0.32
0.5756
1
13074.69
1.02
0.3153
1
23072.63
1.79
0.1829
111
SSQ
153533.9
Table A-5.
Volume (Superior)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
4156139
0.47
0.4956
Class
1
9861
0.00
0.9735
Sex
1
640666
0.07
0.7889
1
71668549
8.06
0.0053
1
562256
0.06
0.8019
1
8536731
0.96
0.3292
1
32493824
3.65
0.0584
1
23104939
2.60
0.1097
1
5061170
0.57
0.4522
1
14168101
1.59
0.2094
112
Table A-6.
controlling for patient’s age, sex and class; the dependent variable is Airway 2 Area
(Superior)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
9930.539
1.25
0.2667
Class
1
3977.026
0.50
0.4814
Sex
1
1.916
0.00
0.9877
1
51865.157
6.50
0.0120
1
1173.262
0.15
0.7020
1
10648.366
1.34
0.2502
1
6901.4
0.87
0.3541
1
8938.599
1.12
0.2918
1
62.088
0.01
0.9298
1
16006.314
2.01
0.1591
113
Table A-7.
controlling for patient’s age, sex and class; the dependent variable is Airway 1+2+3
Volume
Source
df
Geographical Site
1
Class
F Ratio
P Value
26740339
1.05
0.3065
1
23716420
0.94
0.3355
Sex
1
2646800
0.10
0.7472
1
465903647
18.37
<0.0001
1
3196561
0.13
0.7232
1
24464564
0.96
0.3280
1
148044999
5.84
0.0172
1
32945144
1.30
0.2566
1
15978448
0.63
0.4289
1
42567536
1.68
0.1976
114
SSQ
Table A-8.
controlling for patient’s age, sex and class; the dependent variable is Airway 1+2+3
Area
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
38420.13
1.54
0.2176
Class
1
54135.32
2.16
0.1439
Sex
1
15890.57
0.64
0.4270
1
13.97
0.0003
1
47149.75
1.89
0.1723
1
38732.37
1.55
0.2158
1
68659.84
2.75
0.1002
1
19484.9
0.78
0.3792
1
15200.33
0.61
0.4372
1
43733.57
1.75
0.1886
115
349436.8
Table A-9.
Volume (Inferior)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
4456401
1.03
0.3125
Class
1
2625919
0.61
0.4378
Sex
1
7614257
1.76
0.1874
1
56179823
12.97
0.0005
1
720350
0.17
0.6842
1
176293
0.04
0.8405
1
11073215
2.56
0.1125
1
571795
0.13
0.7170
Geographical Site-xClass-x-Chronological Age Initial
1
151537
0.04
0.8520
1
2077666
0.48
0.4900
116
Table A-10. Results of ANCOVA test for geographical site difference, while
controlling for patient’s age, sex and class; the dependent variable is Airway 3 Area
(Inferior)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
9294.102
1.39
0.2410
Class
1
3821.63
0.57
0.4514
Sex
1
23571.007
3.52
0.0630
1
39719.604
5.93
0.0163
1
30753.602
4.59
0.0341
1
657.39
0.10
0.7545
1
6115.839
0.91
0.3411
1
5766.377
0.86
0.3552
1
80.013
0.01
0.9131
1
3275.154
0.49
0.4856
117
controlling for patient’s age, sex and class; the dependent variable is Total Airway
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
26740339
1.05
0.3065
Class
1
23716420
0.94
0.3355
Sex
1
2646800
0.10
0.7472
1
465903647
18.37
<0.0001
1
3196561
0.13
0.7232
1
24464564
0.96
0.3280
1
148044999
5.84
0.0172
1
32945144
1.30
0.2566
1
15978448
0.63
0.4289
1
42567536
1.68
0.1976
118
controlling for patient’s age, sex and class; the dependent variable is Minimum
Constriction
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
4834.495
0.74
0.3916
Class
1
2189.200
0.33
0.5639
Sex
1
627.303
0.10
0.7573
1
20704.299
3.17
0.0777
1
5900.122
0.90
0.3441
1
1695.615
0.26
0.6115
1
13095.106
2.00
0.1596
1
4234.174
0.65
0.4226
1
298.402
0.05
0.8312
1
5106.071
0.78
0.3787
119
controlling for patient’s age, sex and class; the dependent variable is PFH/AFH %
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.01550063
6.20
0.0142
Class
1
0.00081710
0.33
0.5687
Sex
1
0.00034223
0.14
0.7122
1
0.00438553
1.75
0.1880
1
0.00592204
2.37
0.1266
1
0.00012734
0.05
0.8219
1
0.00449156
1.80
0.1828
1
0.00122842
0.49
0.4848
1
0.00007517
0.03
0.8627
1
0.00505426
2.02
0.1578
120
controlling for patient’s age, sex and class; the dependent variable is Y-Axis
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.000352
0.00
0.9951
Class
1
0.033717
0.00
0.9525
Sex
1
19.074137
2.02
0.1580
1
8.614583
0.91
0.3416
1
35.837276
3.79
0.0538
1
0.971568
0.10
0.7490
1
23.52121
2.49
0.1173
1
71.993714
7.62
0.0067
1
7.231705
0.77
0.3834
1
25.651882
2.71
0.1020
121
controlling for patient’s age, sex and class; the dependent variable is Facial
Convexity
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
3.0705
0.21
0.6466
Class
1
2495.8537
171.69
<0.0001
Sex
1
0.1042
0.01
0.9327
1
24.2037
1.66
0.1994
1
11.5209
0.79
0.3751
1
0.2375
0.02
0.8985
1
1.104
0.08
0.7833
1
0.1018
0.01
0.9335
1
0.4701
0.03
0.8576
1
1.66
0.2005
122
24.088
controlling for patient’s age, sex and class; the dependent variable is SNA
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
17.40294
1.55
0.2159
Class
1
104.32574
9.28
0.0028
Sex
1
0.00062
0.00
0.9941
1
35.66934
3.17
0.0774
1
18.56333
1.65
0.2013
1
0.2334
0.02
0.8857
1
20.63072
1.84
0.1781
1
6.95004
0.62
0.4333
1
11.95348
1.06
0.3046
1
0.28167
0.03
0.8745
123
controlling for patient’s age, sex and class; the dependent variable is SNB
Source
df
SSQ
Geographical Site
1
20.81163
2.20
0.1407
Class
1
145.73328
15.40
0.0001
Sex
1
0.00157
0.00
0.9898
1
52.5042
5.55
0.0201
1
19.80158
2.09
0.1506
1
1.8482
0.20
0.6593
1
23.55167
2.49
0.1173
1
7.52618
0.80
0.3742
1
13.55011
1.43
0.2338
1
4.5927
0.49
0.4873
124
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is ANB
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.2609
0.12
0.7287
Class
1
497.52721
230.50
<0.0001
Sex
1
0.00098
0.00
0.9830
1
1.68894
0.78
0.3782
1
0.0336
0.02
0.9009
1
0.69583
0.32
0.5712
1
0.13348
0.06
0.8040
1
0.00675
0.00
0.9555
1
0.02457
0.01
0.9152
1
2.7247
1.26
0.2635
125
controlling for patient’s age, sex and class; the dependent variable is Wits
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
8.66728
1.43
0.2335
Class
1
727.50065
120.37
<0.0001
Sex
1
3.11177
0.51
0.4744
1
8.76920
1.45
0.2308
1
11.56402
1.91
0.1692
1
0.30888
0.05
0.8215
1
0.14569
0.02
0.8769
1
0.66225
0.11
0.7412
1
9.46431
1.57
0.2132
1
1.16106
0.19
0.6620
126
controlling for patient’s age, sex and class; the dependent variable is FMA
Source
df
SSQ
Geographical Site
1
100.40455
3.83
0.0527
Class
1
18.70501
0.71
0.4001
Sex
1
9.97563
0.38
0.5386
1
50.66647
1.93
0.1671
1
54.92266
2.09
0.1505
1
0.00092
0.00
0.9953
1
28.18389
1.07
0.3020
1
28.319
1.08
0.3008
1
112.99182
4.31
0.0401
1
13.09782
0.50
0.4811
127
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is IMPA
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
454.8385
8.88
0.0035
Class
1
1085.4772
21.19
<0.0001
Sex
1
7.8076
0.15
0.6969
1
9.0952
0.18
0.6742
1
10.9927
0.21
0.6440
1
24.7854
0.48
0.4880
1
8.311
0.16
0.6878
1
5.8934
0.12
0.7350
1
62.9062
1.23
0.2700
1
0.0049
0.00
0.9922
128
controlling for patient’s age, sex and class; the dependent variable is FMIA
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
103.6907
2.30
0.1323
Class
1
763.80475
16.91
<0.0001
Sex
1
0.08545
0.00
0.9654
1
17.30632
0.38
0.5371
1
24.33953
0.54
0.4643
1
35.81901
0.79
0.3749
1
8.266
0.18
0.6696
1
3.64892
0.08
0.7767
1
9.72725
0.22
0.6434
1
15.74274
0.35
0.5560
129
controlling for patient’s age, sex and class; the dependent variable is Interincisal
angle
Source
df
SSQ
Geographical Site
1
672.17291
5.92
0.0164
Class
1
549.61256
4.84
0.0297
Sex
1
106.92944
0.94
0.3337
1
41.35659
0.36
0.5473
1
117.60457
1.04
0.3108
1
61.53509
0.54
0.4630
1
246.40615
2.17
0.1433
1
136.91952
1.21
0.2743
1
274.41772
2.42
0.1226
1
2.43683
0.02
0.8838
130
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is U1-SN
Source
df
SSQ
Geographical Site
1
281.60626
5.70
0.0185
Class
1
98.63634
2.00
0.1602
Sex
1
67.19498
1.36
0.2458
1
154.38768
3.13
0.0796
1
51.31986
1.04
0.3101
1
4.18302
0.08
0.7715
1
269.44896
5.46
0.0212
1
102.13432
2.07
0.1530
1
184.21223
3.73
0.0558
1
21.72639
0.44
0.5085
131
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is L1-NB (°)
Source
df
SSQ
Geographical Site
1
188.99004
4.66
0.0329
Class
1
452.69149
11.16
0.0011
Sex
1
4.82074
0.12
0.7309
1
1.42955
0.04
0.8514
1
0.62082
0.02
0.9018
1
51.39847
1.27
0.2626
1
17.20489
0.42
0.5162
1
19.12483
0.47
0.4937
1
42.46696
1.05
0.3084
1
0.91613
0.02
0.8808
132
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is L1-NB (mm)
Source
df
SSQ
Geographical Site
1
7.242021
1.57
0.2129
Class
1
46.557004
10.08
0.0019
Sex
1
0.108877
0.02
0.8782
1
6.526632
1.41
0.2368
1
0.634524
0.14
0.7115
1
2.254076
0.49
0.4861
1
1.321171
0.29
0.5937
1
1.102936
0.24
0.6259
1
8.366822
1.81
0.1808
1
0.03
0.8532
133
0.158867
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is U1-NA (°)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
156.60116
3.43
0.0664
Class
1
408.33172
8.95
0.0034
Sex
1
67.66073
1.48
0.2257
1
42.14946
0.92
0.3384
1
131.13553
2.87
0.0926
1
2.20659
0.05
0.8263
1
141.71777
3.11
0.0806
1
55.76866
1.22
0.2712
1
102.23842
2.24
0.1371
1
16.71522
0.37
0.5462
134
controlling for patient’s age, sex and class; the dependent variable is U1-NA (mm)
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
6.943109
1.66
0.2002
Class
1
49.087982
11.73
0.0008
Sex
1
7.768519
1.86
0.1756
1
26.196836
6.26
0.0137
1
5.528922
1.32
0.2526
1
2.47794
0.59
0.4431
1
10.775285
2.58
0.1112
1
3.101711
0.74
0.3910
1
4.26
0.0412
1
0.27
0.6070
135
17.81626
1.112974
controlling for patient’s age, sex and class; the dependent variable is Overbite
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.034934
0.01
0.9233
Class
1
70.378269
18.73
<0.0001
Sex
1
0.689915
0.18
0.6691
1
0.012253
0.00
0.9546
1
1.425955
0.38
0.5390
1
0.000166
0.00
0.9947
1
0.379638
0.10
0.7511
1
1.574112
0.42
0.5187
1
11.871508
3.16
0.0780
1
1.134376
0.30
0.5837
136
controlling for patient’s age, sex and class; the dependent variable is Overjet
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.48651
0.18
0.6757
Class
1
209.13751
75.62
<0.0001
Sex
1
0.61641
0.22
0.6377
1
2.78188
1.01
0.3179
1
3.48576
1.26
0.2638
1
2.21336
0.80
0.3728
1
2.83959
1.03
0.3130
1
0.45934
0.17
0.6843
1
1.54789
0.56
0.4559
1
0.84448
0.31
0.5816
137
controlling for patient’s age, sex and class; the dependent variable is Superior
Airway Space
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
77.057896
11.76
0.0008
Class
1
0.659427
0.10
0.7516
Sex
1
29.963885
4.57
0.0345
1
8.870189
1.35
0.2469
1
14.319419
2.19
0.1419
1
0.831728
0.13
0.7222
1
11.661559
1.78
0.1847
1
0.049802
0.01
0.9307
1
1.281198
0.20
0.6591
1
21.724871
3.32
0.0711
138
controlling for patient’s age, sex and class; the dependent variable is Condylion-A
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
482.44406
30.73
<0.0001
Class
1
24.59568
1.57
0.2131
Sex
1
201.17201
12.81
0.0005
1
408.52103
26.02
<0.0001
1
88.05216
5.61
0.0195
1
8.69834
0.55
0.4581
1
1.05997
0.07
0.7954
1
111.06007
7.07
0.0089
1
11.14317
0.71
0.4012
1
2.12465
0.14
0.7136
139
controlling for patient’s age, sex and class; the dependent variable is CondylionGnathion
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
247.2293
7.98
0.0055
Class
1
968.7018
31.26
<0.0001
Sex
1
271.0429
8.75
0.0037
1
1332.4733
42.99
<0.0001
1
25.3193
0.82
0.3679
1
22.4023
0.72
0.3969
1
33.3219
1.08
0.3019
1
163.3256
5.27
0.0234
1
49.2086
1.59
0.2101
1
7.4634
0.24
0.6245
140
controlling for patient’s age, sex and class; the dependent variable is A-NasionPerpendicular
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
3.62009
0.40
0.5271
Class
1
194.43423
21.61
<0.0001
Sex
1
6.11035
0.68
0.4115
1
17.64282
1.96
0.1640
1
17.94349
1.99
0.1605
1
1.39432
0.16
0.6945
1
40.54306
4.51
0.0358
1
46.86571
5.21
0.0242
1
10.06996
1.12
0.2922
1
1.13916
0.13
0.7226
141
controlling for patient’s age, sex and class; the dependent variable is PogonionNasion-Perpendicular
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
11.94612
0.39
0.5322
Class
1
235.13462
7.72
0.0063
Sex
1
37.64117
1.24
0.2684
1
109.36649
3.59
0.0604
1
93.20221
3.06
0.0827
1
5.25976
0.17
0.6784
1
179.23562
5.89
0.0167
1
155.12886
5.10
0.0258
1
21.51021
0.71
0.4022
1
1.11
0.2943
142
33.77933
controlling for patient’s age, sex and class; the dependent variable is B-NasionPerpendicular
Source
df
SSQ
F Ratio
P Value
0.00
0.9985
Geographical Site
1
Class
1
1131.4316
204.02
<0.0001
Sex
1
1.5061
0.27
0.6032
1
0.862
0.16
0.6941
1
1.5677
0.28
0.5959
1
1.9144
0.35
0.5579
1
0.708
0.13
0.7215
1
0.00060994
0.00
0.9916
1
0.021
0.00
0.9510
1
6.1606
1.11
0.2940
143
1.88E-05
controlling for patient’s age, sex and class; the dependent variable is AFH
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
45.2341
1.61
0.2070
Class
1
161.04861
5.73
0.0182
Sex
1
538.91207
19.17
<0.0001
1
731.47495
26.02
<0.0001
1
11.4517
0.41
0.5245
1
5.12096
0.18
0.6703
1
7.25229
0.26
0.6124
1
6.99403
0.25
0.6188
1
54.17536
1.93
0.1676
1
3.2697
0.12
0.7336
144
controlling for patient’s age, sex and class; the dependent variable is Mesial Molar
Relation
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
0.51123
0.36
0.5472
Class
1
108.67676
77.48
<0.0001
Sex
1
2.17107
1.55
0.2159
1
0.03849
0.03
0.8687
1
0.8267
0.59
0.4442
1
1.8224
1.30
0.2566
1
1.77451
1.27
0.2629
1
1.16054
0.83
0.3649
1
3.95039
2.82
0.0959
1
0.01742
0.01
0.9115
145
controlling for patient’s age, sex and class; the dependent variable is PFH
Source
df
SSQ
Geographical Site
1
172.94974
7.81
0.0061
Class
1
123.27556
5.56
0.0200
Sex
1
306.8883
13.85
0.0003
1
724.89909
32.71
<0.0001
1
77.73309
3.51
0.0635
1
2.40444
0.11
0.7424
1
2.84
0.0943
1
1.60826
0.07
0.7881
1
0.00014
0.00
0.9980
1
0.04941
0.00
0.9624
146
63.0314
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is GonionMenton
Source
df
SSQ
Geographical Site
1
128.31015
6.82
0.0101
Class
1
255.26621
13.57
0.0003
Sex
1
29.84732
1.59
0.2102
1
541.71625
28.81
<0.0001
1
27.08395
1.44
0.2325
1
0.10754
0.01
0.9398
1
6.16848
0.33
0.5679
1
35.11424
1.87
0.1743
1
18.23763
0.97
0.3267
1
1.39763
0.07
0.7856
147
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is Sella-VerticalA
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
9.19598
0.69
0.4093
Class
1
244.72081
18.25
<0.0001
Sex
1
85.98894
6.41
0.0126
1
264.61118
19.73
<0.0001
1
29.38346
2.19
0.1415
1
1.1664
0.09
0.7686
1
32.11841
2.39
0.1244
1
144.23164
10.75
0.0014
1
2.34955
0.18
0.6763
1
14.99354
1.12
0.2925
148
controlling for patient’s age, sex and class; the dependent variable is Sella-VerticalB
Source
df
SSQ
Geographical Site
1
21.09166
0.84
0.3602
Class
1
79.36934
3.18
0.0773
Sex
1
42.51379
1.70
0.1947
1
363.55535
14.54
0.0002
1
91.98738
3.68
0.0575
1
11.33788
0.45
0.5020
1
111.42568
4.46
0.0368
1
260.1867
10.41
0.0016
1
0.00638
0.00
0.9873
1
46.77627
1.87
0.1739
149
F Ratio
P Value
controlling for patient’s age, sex and class; the dependent variable is Sella-VerticalPogonion
Source
df
SSQ
F Ratio
P Value
Geographical Site
1
181.04294
18.22
<0.0001
Class
1
5.20629
0.52
0.4706
Sex
1
29.25536
2.94
0.0888
1
0.00
0.9979
1
56.44461
5.68
0.0187
1
4.992
0.50
0.4798
1
46.82989
4.71
0.0319
1
0.02295
0.00
0.9617
1
3.03934
0.31
0.5812
1
2.74
0.1002
150
6.84E-05
27.2656
controlling for patient’s age, sex and class; the dependent variable is Sella-Verticalto M
Source
df
SSQ
Geographical Site
1
20.16816
0.82
0.3669
Class
1
118.73855
4.83
0.0299
Sex
1
1.5339
0.06
0.8032
1
397.1629
16.15
0.0001
1
76.30149
3.10
0.0807
1
8.85587
0.36
0.5495
1
83.13397
3.38
0.0684
1
242.57049
9.87
0.0021
1
0.01892
0.00
0.9779
1
79.54221
3.24
0.0746
151
F Ratio
P Value
APPENDIX B.
BIVARIATE PLOTS (REGRESSION OF Y ON X) FOR THE
REPEATED MEASUREMENT SESSIONS
152
Figure B-1. Bivariate plot of the repeated measurements for the variable AFH
The least squares best fit regression line was Session II = 0.0175052 + 0.9971065 X
Session I, where the standard error for the intercept was 5.911417 (P = 0.9977) and for
the regression coefficient was 0.056321 (P = <0.0001).
153
Figure B-2. Bivariate plot of the repeated measurements for the variable Airway 1
Area (Nasopharyngeal)
The least squares best fit regression line was Session II = 55.999785 + 0.7560649 X
Session I, where the standard error for the intercept was19.9166 (P = 0.0092) and for the
regression coefficient was 0.101841 P = <0.0001).
154
The least squares best fit regression line was Difference = -339.5004 + 0.0750509 x
Mean Size, where the standard error for the intercept was (P = 0.2955) and for the
regression coefficient was 0.063272 (P = 0.2463).
155
Figure B-4.
1+2 Area
Bivariate plot of the repeated measurements for the variable Airway
Mean Size, where the standard error for the intercept was 74.8658 (P = 0.2276) and for
the regression coefficient was 0.147427 (P = 0.2295).
156
Figure B-5. Bivariate plot of the repeated measurements for the variable Airway
1+2 Volume
The least squares best fit regression line was Difference = -2286.46 + 0.1799863 x Mean
Size, where the standard error for the intercept was 1662.852 (P = 0.1809), and for the
157
Figure B-6.
1+2+3 Area
Bivariate plot of the repeated measurements for the variable Airway
Mean Size, where the standard error for the intercept was 40.61369 (P = 0.4414)) and for
158
Figure B-7. Bivariate plot of the repeated measurements for the variable Airway
1+2+3 Volume
Mean Size, where the standard error for the intercept was 1597.142 (P = 0.6108) and for
159
Area (Superior)
The least squares best fit regression line was Difference = 40.921229 - 0.119589 x Mean
Size, where the standard error for the intercept was 51.9017 (P = 0.4379) and for the
160
Volume (Superior)
Mean Size, where the standard error for the intercept was 1228.763 (P= 0.6992) and for
161
Area (Inferior)
162
Volume (Inferior)
163
Figure B-12. Bivariate plot of the repeated measurements for the variable A-Na
Perpendicular
The least squares best fit regression line was Difference = -0.321107 - 0.0901378 x Mean
164
Figure B-13. Bivariate plot of the repeated measurements for the variable ANB
165
Figure B-14. Bivariate plot of the repeated measurements for the variable B-Na
Perpendicular
The least squares best fit regression line was Difference = 0.2985847 + 0.0047287 x
Mean Size, where the standard error for the intercept was 0.16 (P = 0.0742) and for the
regression coefficient was 0.02 mm (P = 0.8366).
166
Figure B-15. Bivariate plot of the repeated measurements for the variable Cd-A
Size, where the standard error for the intercept was 4.26 mm(P = 0.2253) and for the
167
Figure B-16. Bivariate plot of the repeated measurements for the variable Cd-Gn
168
Figure B-17. Bivariate plot of the repeated measurements for the variable Facial
Convexity
Mean Size, where the standard error for the intercept was 0.19 degrees(P = 0.0457) and
for the regression coefficient was 0.02 degrees (P = 0.6640).
169
Figure B-18. Bivariate plot of the repeated measurements for the variable FMA
Size, where the standard error for the intercept was 2.20 degrees (P = 0.5657) and for the
regression coefficient was 0.09 degrees (P = 0.5599).
170
Figure B-19. Bivariate plot of the repeated measurements for the variable FMIA
171
Figure B-20. Bivariate plot of the repeated measurements for the variable GonionMenton
Size, where the standard error for the intercept was 5.89 mm (P = 0.9359) and for the
172
Figure B-21. Bivariate plot of the repeated measurements for the variable IMPA
Size, where the standard error for the intercept was 10.25 degrees (P = 0.5911) and for
the regression coefficient was 0.11 angles (P = 0.6200).
173
Figure B-22. Bivariate plot of the repeated measurements for the variable
Interincisal Angle
Size, where the standard error for the intercept was 14.86 degrees (P = 0.3957) and for
the regression coefficient was 0.11 degrees (P = 0.3745).
174
Figure B-23. Bivariate plot of the repeated measurements for the variable L1-NB
(°)
175
Figure B-24. Bivariate plot of the repeated measurements for the variable L1-NB
(mm)
176
Figure B-25. Bivariate plot of the repeated measurements for the variable Mesial
Molar Relation
Mean Size, where the standard error for the intercept was 0.09 mm (P = 0.3022) and for
177
Minimum Constriction
178
Figure B-27. Bivariate plot of the repeated measurements for the variable Overbite
The least squares best fit regression line was Difference = 0.0325709 + 0.0062688*Mean
179
Figure B-28. Bivariate plot of the repeated measurements for the variable Overjet
The least squares best fit regression line was Difference = -0.186635 + 0.012275*Mean
180
Figure B-29. Bivariate plot of the repeated measurements for the variable PFH
The least squares best fit regression line was Difference = 1.0533452 - 0.0174455*Mean
181
Pogonion-Nasion-Perpendicular
The least squares best fit regression line was Difference = -0.546758 - 0.0287606*Mean
182
Figure B-31. Bivariate plot of the repeated measurements for the variable SellaVertical-A
regression coefficient was 0.14 (P =0.4742).
183
Figure B-32. Bivariate plot of the repeated measurements for the variable SellaVertical-B
184
Figure B-33. Bivariate plot of the repeated measurements for the variable SellaVertical-M
The least squares best fit regression line was Session II = 2.8404744 + 0.920511 x
Session I, where the standard error for the intercept was(P = 0.6628) but for the
regression coefficient was statistically significant (t = 6.58; P < 0.0001).
185
Figure B-34. Bivariate plot of the repeated measurements for the variable SellaVertical-Pogonion
186
Figure B-35. Bivariate plot of the repeated measurements for the variable SNA
187
Figure B-36. Bivariate plot of the repeated measurements for the variable SNB
188
Figure B-37. Bivariate plot of the repeated measurements for the variable Superior
Airway Space
Mean Size, where the standard error for the intercept was 0.28 (P = 0.9858) and for the
189
Figure B-38. Bivariate plot of the repeated measurements for the variable Total
Airway
Mean Size, where the standard error for the intercept was 1,495 (P = 0.3623) and for the
190
Figure B-39. Bivariate plot of the repeated measurements for the variable U1-NA
(°)
191
Figure B-40. Bivariate plot of the repeated measurements for the variable U1-NA
(mm)
192
Figure B-41. Bivariate plot of the repeated measurements for the variable U1-SN
Session I, where the standard error for the intercept was 9.20 (P = 0.3179) and for the
193
Figure B-42. Bivariate plot of the repeated measurements for the variable Wits
Appraisal
Session I, where the standard error for the intercept was 0.09 (P = 0.5183) and for the
194
Figure B-43. Bivariate plot of the repeated measurements for the variable Y-Axis
Session I, where the standard error for the intercept was 8.05 (P =0.1135) and for the
195
VITA
Kyle David Fagala was born in 1984 in Jonesboro, Arkansas. Kyle attended
school in Paragould, Arkansas and graduated from Crowley’s Ridge Academy in 2002.
He attended Harding University in Searcy, Arkansas and then the University of
Tennessee College of Dentistry in Memphis, Teneessee, graduating with a Doctor of
Dental Surgery degree in May 2010. He is currently completing a residency in
orthodontics at the University of Tennessee Health Science Center and plans to graduate
with a Master of Dental Science degree in May 2013. He plans to open a private
orthodontic practice in Germantown, Tennessee in July 2013. Kyle, his wife Anna, and
their son Charlie live in East Memphis.
196

Is this condition - ETD Index Page

Transcription

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