A CBCT ANALYSIS OF CLASS I AND II ORTHODONTIC CASES: A ...

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. 

Table 3-3. 

Table 4-1. 

Table 4-2. 

Table 4-3. 

Table 4-4. 

Table 4-5. 

Table 4-6. 

Table 5-1. 

Linear (millimetric) dimensions and angles measured on the lateral 

cephalograms ................................................................................................28 

A list of the variables measured from the lateral cephalometric images in 

the present study ...........................................................................................30 

Descriptive statistics of intraobserver repeatability, showing the 

difference of each variable and a t-test evaluating whether the mean 

differed statistically from zero .....................................................................39 

Results of one-way ANOVAs testing for differences in mean sizes 

among the 8 clusters developed using 4 maxillo-mandibular 

discrepancies ................................................................................................79 

Descriptive statistics for SNA among the 8 groupings generated by 

cluster analysis .............................................................................................79 

Descriptive statistics for SNB among the 8 groupings generated by 


Descriptive statistics for ANB among the 8 groupings generated by 


Descriptive statistics for Wits among the 8 groupings generated by 


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. 

Figure 4-2. 

Figure 4-3. 

Figure 4-4. 

Box plots of the age distribution of the sample, partitioned be sex and 

geographical site (either Kansas or Tennessee) .........................................35 

Histograms of the age distributions (sexes pooled) by geographical site 

(Kansas, Tennessee) ...................................................................................36 

Pie charts of the proportions of Class II patients by geographical 

source .........................................................................................................36 

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. 

Figure 4-7. 

Figure 4-8. 

Figure 4-9. 

Figure 4-10. 

Figure 4-11. 

Bland-Altman plot for the cephalometric distance B to Nasion- 

Perpendicular .............................................................................................43 

Form of the ANCOVA model used to test for group differences for 

(45) cephalometric variables ......................................................................44 

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 

Bivariate plot between chronological age (years) and pharyngeal 

volume (cubic millimeters), labeled Total Airway Volume ......................47 

Bivariate plot between chronological age and the two-dimensional 

measure of Total Airway Area (mm 2 ) .......................................................48 

Bivariate plot between chronological age and volume of the inferior 

oropharynx .................................................................................................49 

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Figure 4-12. 

Figure 4-13. 

Figure 4-14. 

Figure 4-15. 

Bivariate plot between chronological age (years) and volume of the 

total airway (mm 3 ) .....................................................................................51 

Box plots showing the difference in distributions between the two 

Angle Classes .............................................................................................52 

Bivariate graphs showing the difference in distributions between 

Angle Class I and Class II samples (sexes pooled) for the 

cephalometric angle SNA ..........................................................................53 

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. 

Figure 4-19. 

Figure 4-20. 

Box plots of the distributions of IMPA by geographical site and Angle 

Class measured at the start of treatment ....................................................58 

A depiction of cluster analysis applied to Fisher’s three species of iris 

data (150 specimens; 4 variables) ..............................................................60 

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. 

Figure 4-24. 

Figure 4-25. 

Figure 4-26. 

Figure 4-27. 

Figure 4-28. 

Results of cluster analysis using the 11 pharyngeal dimensions, 

specifically for the airway 1 area (mm 2 ) ....................................................64 


specifically for the airway 1+2 volume (mm 3 ) ..........................................65 


specifically for the airway 1+2 area (mm 2 )................................................66 


specifically for the airway 2 volume (mm 3 ) ..............................................67 




specifically for the airway 1+2+3 volume (mm 3 ) ......................................69 

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Figure 4-29. 

Figure 4-30. 

Figure 4-31. 

Figure 4-32. 




specifically for the airway 1+2+3 volume (mm 3 ) ......................................71 




specifically for the total airway (mm 3 ) ......................................................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. 

Figure 4-36. 

The scree plot resulting from clustering of four cephalometric 

dimensions (SNA, SNB, ANB, and AOBO) .............................................77 

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. 

Figure 5-2. 

Figure 5-3. 

Bivariate plots by Angle Class and sex for Total Airway Volume 

(mm3) .........................................................................................................91 

Bivariate plot between the patient’s age at the start of treatment and 

Total Airway Volume for the complete sample (n = 131) .........................92 

A stacked chart of the average sizes of the 11 measures of pharyngeal 

size analyzed in the present study. .............................................................94 

x

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). 

1

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 

3

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. 

4

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 

5

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. 

6

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. 

7

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, Linder- 

Aronson 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. Subjective airway classification (1-5) from the lateral cephalogram. 

2. Airway area of the region of interest from the lateral cephalogram. 

3. Airway volume over the same region of interest from the CBCT scan. 

4. 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 10- 

bit 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

egions (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. 

Landmark 

A 

Aa 

ANS 

B 

Cd 

Et 

FH 

FOP 

Go 

Gn 

H 

Ii 

Is 

L6 

M 

Me 

Na 

Or 

Pg 

Phw 

PNS 

Po 

Cephalometric landmarks 

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 Posterior soft palate: the most superior-posterior point of the soft palate. 

Pt 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 

Description 

AFH Anterior Facial Height: the linear distance from Nasion to Menton. 

ANB the inferior angle formed at the junction of the Nasion-A Point line and the 

Nasion-B Point line. 

AO-BO 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. 

Co-A The linear distance from Condylion to A Point. 

Co-Gn The linear distance from Condylion to Gnathion. 

FMA The anterior inferior-angle formed at the junction of the Frankfort 

Horizontal plane and the mandibular plane. 

H to FH The linear distance from H point to FH, perpendicular to FH. 

Na-Me The linear distance between Nasion and Menton. 

Na -A The linear distance from point A to Nasion when projected perpendicular to 

the Frankfort Horizontal plane. 

Na -B The linear distance from point B to Nasion when projected perpendicular to 

the Frankfort Horizontal plane. 

Na -Pg The linear distance from Pogonion to Nasion when projected perpendicular 

to the Frankfort Horizontal plane. 

Psp-Phw Superior Airway Space: the linear distance from Psp to a point directly 

posterior to Psp on the posterior pharyngeal wall, parallel to FH. 

Se-Go The linear distance from Sella to Gonion. 

Se-Me The linear distance from Sella to Menton. 

Se-Na The linear distance from Sella to Nasion. 

Se -A The linear distance from Sella to A point when projected perpendicular to 

the Frankfort Horizonal plane. 

Se -B The linear distance from Sella to B point when projected perpendicular to 


Se -M The linear distance from Sella to M Point when projected perpendicular to 


Se -Po The linear distance from Sella to Porion when projected perpendicular to 


SNA 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 

Se-Na 

Co-A 

Na-Me 

PFH/AFH 

Se-Go 

Variable 

Cranial Base 

Anterior Cranial Base Length (mm) 

Midface 

Horizontal length of the midface (mm) 

Facial Height 

Total Anterior Facial Height (mm) 

Ratio of posterior facial height to anterior facial height 

Posterior Facial Height (mm) 

Maxillary Position 

Na Perp-A A-P positional change in the maxilla (mm) 

SNA Positional change in the maxilla relative to anterior cranial base (°) 

Se -A A-P positional change in the maxilla (mm) 

Mandibular Size and Position 

Co-Go Vertical Mandibular Ramus Length (mm) 

Co-Gn Mandibular Length (mm) 

Go-Me Mandibular Body Length (mm) 

Na Perp-B A-P positional change in the mandible (mm) 

Na Perp-Pg Protrusive growth of the chin (mm) 

SNB Positional change in the mandible relative to anterior cranial base (°) 

Se -B A-P positional change in the madible (mm) 

Se -M A-P positional change in the madible (mm) 

Y Axis Rotation of the mandible (°) 

Maxillomandibular Relationships 

ANB A-P relationship of the maxilla-mandible (°) 

AO-BO A-P relationship of the maxilla-mandible (mm) 

FMA Maxillomandibular divergence (°) 

Na A-Pg 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) X 2 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 X 1i and X 2i 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 (X 1j - X 2j ), 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 

Mean 

Difference 

SD of 

Difference t-Test P Value 

AFH 0.286 1.731 0.87 0.3901 

Airway 1 Area 

-11.389 40.486 -1.49 0.1482 

(Nasopharyngeal) 

Airway 1 Volume 

17.161 551.191 0.16 0.8704 

(Nasopharyngeal) 

Airway 1+2 Area -2.425 83.603 -0.15 0.8792 

Airway 1+2 Volume -27.357 2374.897 -0.06 0.9518 

Airway 1+2+3 Area -7.582 45.858 -0.87 0.3893 

Airway 1+2+3 Volume -482.678 2125.719 -1.18 0.2487 

Airway 2 Area (Superior) 4.289 60.098 0.37 0.7138 


-44.518 1980.105 -0.12 0.9062 

(Superior) 

Airway 3 Area (Inferior) -5.157 79.210 -0.34 0.7331 


-360.729 1286.853 -1.48 0.1496 

(Inferior) 

A-Nasion-Perpendicular -0.321 1.210 -1.41 0.1713 

ANB -0.189 0.336 -2.98 0.0060 

B-Nasion-Perpendicular 0.271 0.487 2.95 0.0065 

Conylion-A 0.350 1.532 1.21 0.2370 

Conylion-Gnathion 0.532 1.811 1.55 0.1317 

Facial Convexity -0.336 0.698 -2.54 0.0170 

FMA 0.004 2.151 0.01 0.9931 

FMIA -0.454 2.802 -0.86 0.3993 

Gonion-Menton 0.414 2.428 0.90 0.3746 

IMPA 0.446 4.132 0.57 0.5722 

Interincisal Angle -0.564 5.172 -0.58 0.5685 

L1-NB (°) 0.275 2.571 0.57 0.5760 

L1-NB (mm) -0.032 0.573 -0.30 0.7688 

Mesial Molar Relation 0.100 0.456 1.16 0.2563 

Minimum Constriction -0.050 21.965 -0.01 0.9905 

Overbite 0.054 0.801 0.35 0.7262 

Overjet -0.132 0.286 -2.45 0.0211 

PFH -0.154 3.250 -0.25 0.8045 

Pogonion Nasion- 

-0.404 2.203 -0.97 0.3410 

Perpendicular 

Sella-Vertical-A 0.932 3.022 1.63 0.1143 

Sella-Vertical-B 0.986 3.448 1.51 0.1420 

39

Table 4-1. 

(Continued) 

Variable 

Mean 

Difference 

SD of 

Difference t-Test P Value 

Sella-Vertical-M 0.796 3.599 1.15 0.2607 

Sella-Vertical-Pogonion -0.271 2.822 -0.51 0.6149 

SNA -0.425 0.965 -2.33 0.0275 

SNB -0.257 1.081 -1.26 0.2189 

Superior Airway Space 0.129 0.422 1.61 0.1189 

Total Airway -388.086 2145.194 -0.96 0.3469 

U1-NA (°) 0.486 2.925 0.88 0.3873 

U1-NA (mm) 0.011 0.951 0.06 0.9529 

U1-Sella-Nasion 0.046 3.310 0.07 0.9414 

Wits Discrepancy -0.096 0.498 -1.03 0.3144 

Y-Axis -0.321 2.121 -0.80 0.4297 

40

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 Nasion- 

Perpendicular 

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 (r 2 = 11%). This suggested that, within 

this age interval, this volume increases almost 1,400 mm 3 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 (mm 2 ) 

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

egression accounted for about 8% of the variance (r 2 = 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 (mm 3 ) 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 

(r 2 ) and this association was highly significant statistically (P = 0.0004). The regression 

line suggested that three-dimensional volume increased about 1,400 mm 3 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 (mm 3 ) 

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 (r 2 , 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 (mm 3 ). 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 (mm 2 ) 

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 (mm 3 ) 




65


specifically for the airway 1+2 area (mm 2 ) 




66


specifically for the airway 2 volume (mm 3 ) 




67






68


specifically for the airway 1+2+3 volume (mm 3 ) 




69






70


specifically for the airway 1+2+3 volume (mm 3 ) 




71






72


specifically for the total airway (mm 3 ) 




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 df 

Sum of 

Squares 

Mean 

Square F Ratio P Value 

Adjusted 

R-Square 

SNA 7 665.43 95.06 76.99

Table 4-4. Descriptive statistics for SNB among the 8 groupings generated by 

cluster analysis 

Cluster 

Mean 

Standard 

Deviation 

SEM 

Lower 95% 

Confidence 

Upper 95% 

Confidence 

1 72.7 1.16421 0.33608 72.002 73.481 

2 76.0 1.04951 0.24077 75.452 76.464 

3 81.6 1.10518 0.41772 80.592 82.636 

4 78.4 1.09565 0.34647 77.656 79.224 

5 79.5 1.39000 0.43956 78.516 80.504 

6 77.7 2.01420 0.90078 75.179 80.181 

7 77.8 1.34288 0.77531 74.497 81.169 

8 74.3 2.04157 0.91302 71.805 76.875 

Table 4-5. Descriptive statistics for ANB among the 8 groupings generated by 


Cluster 

Mean 

Standard 

Deviation 

SEM 

Lower 

95% 

Confidence 

Upper 

95% 

Confidence 

1 4.59 0.820707 0.23692 4.0702 5.113 

2 5.38 0.792509 0.18181 5.0022 5.766 

3 5.23 0.760952 0.28761 4.5248 5.932 

4 5.77 0.928619 0.29366 5.1057 6.434 

5 4.81 0.966609 0.30567 4.1185 5.501 

6 8.06 0.450555 0.20149 7.5006 8.619 

7 9.63 0.950438 0.54874 7.2723 11.994 

8 7.88 0.593296 0.26533 7.1433 8.617 

80

Table 4-6. Descriptive statistics for Wits among the 8 groupings generated by 


Cluster 

Mean 

Standard 

Deviation 

SEM 

Lower 

95% 

Confidence 

Upper 

95% 

Confidence 

1 2.37 1.91849 0.5538 1.148 3.586 

2 3.75 1.37936 0.3164 3.083 4.412 

3 3.86 1.03579 0.3915 2.899 4.815 

4 4.30 1.33583 0.4224 3.344 5.256 

5 -0.12 1.04009 0.3289 -0.864 0.624 

6 2.30 1.10680 0.4950 0.926 3.674 

7 7.07 1.61658 0.9333 3.051 11.082 

8 8.78 2.25322 1.0077 5.982 11.578 

81

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 mm 3 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) 


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





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 

Chronological Age Initial 1 26927.100 6.84 0.0101 

Geographical Site-x-Class 1 56.550 0.01 0.9048 

Geographical Site-x-Sex 1 4620.581 1.17 0.2808 

Geographical Site-x- 


Geographical Site-x-Class-x-Sex 1 954.347 0.24 0.6234 

Geographical Site-x-Class-x- 



Chronological Age Initial-x-Sex 1 644.180 0.16 0.6865 

109


controlling for patient’s age, sex and class; the dependent variable is Airway 1+2 

Volume 



Class 1 10559133 0.81 0.3688 

Sex 1 1282546 0.10 0.7538 

Chronological Age Initial 1 198513481 15.30 0.0002 

Geographical Site-x-Class 1 882019 0.07 0.7948 

Geographical Site-x-Sex 1 20487332 1.58 0.2114 



Geographical Site-x-Class-x-Sex 1 24836414 1.91 0.1691 




Chronological Age Initial-x-Sex 1 25836576 1.99 0.1608 

110


controlling for patient’s age, sex and class; the dependent variable is Airway 1+2 

Area 



Class 1 29189.95 2.27 0.1345 

Sex 1 754.64 0.06 0.8090 











111



Volume (Superior) 



Class 1 9861 0.00 0.9735 

Sex 1 640666 0.07 0.7889 











112


controlling for patient’s age, sex and class; the dependent variable is Airway 2 Area 

(Superior) 



Class 1 3977.026 0.50 0.4814 

Sex 1 1.916 0.00 0.9877 











113


controlling for patient’s age, sex and class; the dependent variable is Airway 1+2+3 

Volume 



Class 1 23716420 0.94 0.3355 

Sex 1 2646800 0.10 0.7472 



controlling for patient’s age, sex and class; the dependent variable is Airway 1+2+3 

Area 



Class 1 54135.32 2.16 0.1439 

Sex 1 15890.57 0.64 0.4270 











115



Volume (Inferior) 



Class 1 2625919 0.61 0.4378 

Sex 1 7614257 1.76 0.1874 








Class-x-Chronological Age Initial 1 151537 0.04 0.8520 



116


controlling for patient’s age, sex and class; the dependent variable is Airway 3 Area 

(Inferior) 



Class 1 3821.63 0.57 0.4514 

Sex 1 23571.007 3.52 0.0630 











117


controlling for patient’s age, sex and class; the dependent variable is Total Airway 



Class 1 23716420 0.94 0.3355 

Sex 1 2646800 0.10 0.7472 



controlling for patient’s age, sex and class; the dependent variable is Minimum 

Constriction 



Class 1 2189.200 0.33 0.5639 

Sex 1 627.303 0.10 0.7573 








Class-x-Chronological Age Initial 1 298.402 0.05 0.8312 



119


controlling for patient’s age, sex and class; the dependent variable is PFH/AFH % 



Class 1 0.00081710 0.33 0.5687 

Sex 1 0.00034223 0.14 0.7122 











120


controlling for patient’s age, sex and class; the dependent variable is Y-Axis 



Class 1 0.033717 0.00 0.9525 

Sex 1 19.074137 2.02 0.1580 











121


controlling for patient’s age, sex and class; the dependent variable is Facial 

Convexity 



Class 1 2495.8537 171.69


controlling for patient’s age, sex and class; the dependent variable is SNA 



Class 1 104.32574 9.28 0.0028 

Sex 1 0.00062 0.00 0.9941 











123


controlling for patient’s age, sex and class; the dependent variable is SNB 



Class 1 145.73328 15.40 0.0001 

Sex 1 0.00157 0.00 0.9898 











124


controlling for patient’s age, sex and class; the dependent variable is ANB 



Class 1 497.52721 230.50


controlling for patient’s age, sex and class; the dependent variable is Wits 



Class 1 727.50065 120.37


controlling for patient’s age, sex and class; the dependent variable is FMA 



Class 1 18.70501 0.71 0.4001 

Sex 1 9.97563 0.38 0.5386 











127


controlling for patient’s age, sex and class; the dependent variable is IMPA 



Class 1 1085.4772 21.19


controlling for patient’s age, sex and class; the dependent variable is FMIA 



Class 1 763.80475 16.91


controlling for patient’s age, sex and class; the dependent variable is Interincisal 

angle 



Class 1 549.61256 4.84 0.0297 

Sex 1 106.92944 0.94 0.3337 











130


controlling for patient’s age, sex and class; the dependent variable is U1-SN 



Class 1 98.63634 2.00 0.1602 

Sex 1 67.19498 1.36 0.2458 











131


controlling for patient’s age, sex and class; the dependent variable is L1-NB (°) 



Class 1 452.69149 11.16 0.0011 

Sex 1 4.82074 0.12 0.7309 











132


controlling for patient’s age, sex and class; the dependent variable is L1-NB (mm) 



Class 1 46.557004 10.08 0.0019 

Sex 1 0.108877 0.02 0.8782 











133


controlling for patient’s age, sex and class; the dependent variable is U1-NA (°) 



Class 1 408.33172 8.95 0.0034 

Sex 1 67.66073 1.48 0.2257 











134


controlling for patient’s age, sex and class; the dependent variable is U1-NA (mm) 



Class 1 49.087982 11.73 0.0008 

Sex 1 7.768519 1.86 0.1756 











135


controlling for patient’s age, sex and class; the dependent variable is Overbite 



Class 1 70.378269 18.73


controlling for patient’s age, sex and class; the dependent variable is Overjet 



Class 1 209.13751 75.62


controlling for patient’s age, sex and class; the dependent variable is Superior 

Airway Space 



Class 1 0.659427 0.10 0.7516 

Sex 1 29.963885 4.57 0.0345 











138


controlling for patient’s age, sex and class; the dependent variable is Condylion-A 


Geographical Site 1 482.44406 30.73


controlling for patient’s age, sex and class; the dependent variable is Condylion- 

Gnathion 



Class 1 968.7018 31.26


controlling for patient’s age, sex and class; the dependent variable is A-Nasion- 

Perpendicular 



Class 1 194.43423 21.61


controlling for patient’s age, sex and class; the dependent variable is Pogonion- 

Nasion-Perpendicular 



Class 1 235.13462 7.72 0.0063 

Sex 1 37.64117 1.24 0.2684 











142


controlling for patient’s age, sex and class; the dependent variable is B-Nasion- 

Perpendicular 


Geographical Site 1 1.88E-05 0.00 0.9985 

Class 1 1131.4316 204.02


controlling for patient’s age, sex and class; the dependent variable is AFH 



Class 1 161.04861 5.73 0.0182 

Sex 1 538.91207 19.17


controlling for patient’s age, sex and class; the dependent variable is Mesial Molar 

Relation 



Class 1 108.67676 77.48


controlling for patient’s age, sex and class; the dependent variable is PFH 



Class 1 123.27556 5.56 0.0200 

Sex 1 306.8883 13.85 0.0003 

Chronological Age Initial 1 724.89909 32.71


controlling for patient’s age, sex and class; the dependent variable is Gonion- 

Menton 



Class 1 255.26621 13.57 0.0003 

Sex 1 29.84732 1.59 0.2102 

Chronological Age Initial 1 541.71625 28.81


controlling for patient’s age, sex and class; the dependent variable is Sella-Vertical- 

A 



Class 1 244.72081 18.25



B 



Class 1 79.36934 3.18 0.0773 

Sex 1 42.51379 1.70 0.1947 











149



Pogonion 


Geographical Site 1 181.04294 18.22


controlling for patient’s age, sex and class; the dependent variable is Sella-Verticalto 

M 



Class 1 118.73855 4.83 0.0299 

Sex 1 1.5339 0.06 0.8032 











151

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 =

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 =



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. 

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 



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 Gonion- 

Menton 


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 Sella- 

Vertical-A 



regression coefficient was 0.14 (P =0.4742). 

183


Vertical-B 




184


Vertical-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


Vertical-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

A CBCT ANALYSIS OF CLASS I AND II ORTHODONTIC CASES: A ...

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