longitudinal assessment of maxillary and mandibular … heights can be modified, to a certain...

Longitudinal Assessment of Maxillary and Mandibular Molar and

Incisor Dentoalveolar Heights and Growth Rates in Class I Subjects with Varied Craniofacial Growth Patterns as Classified by Directional

and Proportionate Methods

by

Bronsen Schliep D.D.S.

A thesis submitted in conformity with the requirements for the degree of Master of Science (Orthodontics)

Graduate Department of Orthodontics Faculty of Dentistry, University of Toronto

©Copyright by Bronsen Schliep 2014

ii

Longitudinal Assessment of Maxillary and Mandibular Molar and Incisor Dentoalveolar Heights and Growth Rates in Class I Subjects with Varied Craniofacial Growth Patterns

as Classified by Directional and Proportionate Methods

Bronsen Schliep Master of Science Degree, 2014

Discipline of Orthodontics, Faculty of Dentistry, University of Toronto Toronto, Ontario, Canada

Abstract

Objective: To determine if significant differences exist in dentoalveolar heights and dentoalveolar height

growth rates, among skeletal Class I subjects that exhibit differing craniofacial growth patterns.

Methods: One hundred and five subjects with cephalograms available at 9, 12, 14, and 16 years were

categorized into directional (change in Y-axis angle) and proportionate (UFH:LFH) growth pattern

groups. Maxillary and mandibular molar and incisor dentoalveolar heights and dentoalveolar height

growth rates were determined. Comparisons were made by mixed model and ANOVA.

Results: Neither dentoalveolar heights, nor growth rates differed significantly among directional

classification groups in either gender. All dentoalveolar heights differed significantly among all

proportionate classification groups at all ages in both male and female subjects.

Conclusions: No statistically significant differences were found in dentoalveolar heights or dentoalveolar

height growth rates of different directional growth pattern groups. Statistically significant differences

were found in all dentoalveolar heights of different proportionate growth pattern groups.

iii

Acknowledgements I would like to express my gratitude to the following people for their support throughout the course of this investigation: Dr. Sunjay Suri, Thesis Supervisor, Associate Professor, University of Toronto, Faculty of Dentistry, Department of Graduate Orthodontics; for your guidance, patience, and advice from the initial protocol to the last edit of the manuscript. Dr. Bryan Tompson, Committee member, Discipline Head, University of Toronto, Faculty of Dentistry, Department of Graduate Orthodontics; for your encouragement throughout this investigation and during the three years of this Orthodontic residency. Dr. Angelos Metaxas, Committee member, Associate Professor, University of Toronto, Faculty of Dentistry, Department of Graduate Orthodontics; for your encouragement, joyful approach to life, and contagious smile. Dr. Laurel Duquette, statistical advisor, Department of Statistics, University of Toronto; for your statistical expertise. Dr. John Voudouris; for contributing the initial research idea of a longitudinal evaluation of dentoalveolar heights among various craniofacial growth patterns. Most importantly, I dedicate this thesis to my family. To my beautiful wife Priscilla and gorgeous daughters Nataliya and Jaslene; for all the joy, laughter, and love you provide. I am so blessed to have you three in my life and look forward to the memories we are about to create. To my mother Raelene, father Bub, and sister Brandy; for your prayers, love, and unwavering support. God has truly blessed us with an incredible family.

iv

Table of Contents Page

Abstract……………………………………………………………..…………………………………………..……………………………………….ii

Acknowledgements…………………………………………..…………………………………………..……………………………………….iii

List of Tables…………………………………………..…………………………………………..…………………………………………………..v

List of Figures…………………………………………..………………………………………….…………………………………………….……vi

List of Appendices…………………………………………..………………………………………………………………………................vii

List of Abbreviations………………………………………………………………………………………………………………................viii

I. Introduction and Statement of the Problem………………………………………………………………………...1

II. Significance of the Problem…………………………………………..……………………………………………………..2

III. Review of the Literature……………………………………………….…………………………………………..............3

a. Craniofacial Growth Patterns………………………………………………………………………………………….3

b. Determination of Craniofacial Growth Patterns……………………………………………………………..4

c. Assessment of Dentoalveolar Heights and Dentoalveolar Height Growth Rates…………..10

d. Summary………………………………………………………………………………………………………………………15

IV. Purpose of the study…………………………………………..………………………………………………………………16

V. Research Objectives…………………………………………..……………………………………………………………….17

VI. Hypotheses…………………………………………………………………………………………………………………………18

VII. Materials and Methods………………………………………………………………………………………………………19

a. Sample Description………………………………………………………………………………………………………19

b. Cephalometric Analysis………………………………………………………………………………………….…….22

c. Growth Pattern Classification…………………………………………………………………………………..…..26

d. Reliability Analysis………………………………………………………………………………………………………..30

e. Analysis of Results………………………………………………………………………………………………………..31

VIII. Results…………………………………………………………………………………………………………………………….….32

a. Dentoalveolar Heights………………………………………………………………………………………………….32

b. Dentoalveolar Height Growth Rates……………………………………………………………………………..49

c. Evaluation of the effect of gender on dentoalveolar height growth rates…..……………….82

IX. Discussion…………………………………………………………………………………………………………………………..90

X. Study Limitations ……………………………………………………………………………………………………………..100

XI. Future Directions ……………………………………………………………………………………………………………..102

XII. Conclusions………………………………………………………………………………………………………………………103

XIII. References………………………………………………………………………………………………………………………..105

XIV. Appendices…………………………………………………………………………………………………………………….…111

v

List of Tables Page

Table I: Application of Exclusion Criteria – phase I ………….……………….…………………………………….…20

Table II. Application of Exclusion Criteria – phase II……………………………………………………………………21

Table III. Directional Classification: Change in Y-axis angle (9 to 16 y) ………….……………….…………...26

Table IV. Directional growth pattern classification………….……………….……………….……………….……….27

Table V. Directional groups: mean and standard deviation of Y-axis change (9 to 16 years)…...…27

Table VI. Proportionate Classification: UFH:LFH ratio (16 y) ………….……………….……………….………….28

Table VII. Proportionate growth pattern classification………….……………….……………….……………………29

Table VIII. Proportionate groups: mean and standard deviation of UFH:LFH (16 years)……………….29

Table VIII. Reliability Analysis………………………………………………………………………………………………………..30

vi

List of Figures Page

Figure 1. Final Sample Flowchart………….……………….……………….……………….……………….…………………22

Figure 2. Craniofacial and Dental Landmarks………….……………….……………….……………….………………..23

Figure 3. Craniofacial Reference Planes………….……………….……………….……………….……………….……….24

Figure 4. Maxillary and Mandibular Dentoalveolar Height Measurements………….……………….…….25

Figures 5 - 12 Directional Classification: Dentoalveolar heights at the maxillary and mandibular first molar and

central incisor sites in females and males……………………………………………………………………………..33-40

Figure 13 - 20. Proportionate Classification: Dentoalveolar heights at the maxillary and mandibular first molar

and central incisor sites in females and males……………………………………………………………………….41-48

Figures 21 - 44. Directional Classification: Dentoalveolar height growth rates at the maxillary and mandibular first

molar and central incisor sites in females and males in the 9 to 12 year, 12 to 14 year, and 14 to

16 year periods……………………………………………………………………………………………………………………..50-65

Figures 45 - 68. Proportionate Classification: Dentoalveolar height growth rates at the maxillary and mandibular

first molar and central incisor sites in females and males in the 9 to 12 year, 12 to 14 year, and 14

to 16 year periods…………………………………………………………………………………………………………………66-81

Figures 69 - 80. Evaluation of the effect of gender on dentoalveolar height growth rates: Dentoalveolar height

growth rates at the maxillary and mandibular first molar and central incisor sites in females and

males in the 9 to 12 year, 12 to 14 year, and 14 to 16 year periods………………………..…………….82-89

vii

List of Appendices Page

Appendix 1. Directional Classification Data Tables: Dentoalveolar Heights…………………………………………111 Appendix 2. Proportionate Classification Data Tables: Dentoalveolar Heights………………………………….…115 Appendix 3. Directional Classification Data Tables: Dentoalveolar Height Growth Rates………………….…119 Appendix 4. Proportionate Classification Data Tables: Dentoalveolar Height Growth Rates…………….…123 Appendix 5. Dentoalveolar Height Growth Rate Data Tables: Evaluation of the effect of gender ……….127

viii

List of Abbreviations AFH anterior facial height

AFT average facial type

ANS anterior nasal spine

ANS' anterior nasal spine prime

Ar' articulare prime

BGC Burlington Growth Centre

FH Frankfort horizontal

FMA Frankfort horizontal to mandibular plane angle

Gn gnathion

Go gonion

LFH lower facial height

LFT long facial type

MP mandibular plane

Me menton

N nasion

OP occlusal plane

PMG peak mandibular growth

PFH posterior facial height

S sella

SN sella to nasion plane

SFT short facial type

TFH total facial height

UFH upper facial height

1

Introduction and Statement of the Problem

Orthodontists are routinely tasked with the responsibility of managing malocclusions in the transverse,

sagittal, and vertical dimensions. Of these three, the vertical dimension often presents the greatest

difficulty, allowing the least margin of error in a clinical sense. Though vertical dysplasias typically

present in certain fashions, they can take many forms, owing to dental compensation mechanisms at

both the molar and incisor levels. For example, in hyperdivergent patients with open bite tendencies,

dentoalveolar compensation occurring in the anterior region may significantly limit the typical

presentation of a negative overbite. In fact, these patients may even present with an excessive dental

overbite (Beckmann et al., 1998). Thus, dentoalveolar mechanisms have great potential in

compensating vertical skeletal deviations resulting from inherent craniofacial growth patterns.

Regarding craniofacial growth patterns, Bishara and Jakobsen (1985) conducted a longitudinal

evaluation from ages 5 to 25 years of subjects categorized according to three facial types: relatively long,

average, and relatively short faces. Of these, 77% had the same facial type at 5 years and 25 years of

age. There was a strong tendency to maintain the original face type with age. Other studies have

agreed that the morphogenetic craniofacial growth pattern is established early in life and subsequent

growth increments tend to follow that initial pattern (Sassouni and Nanda, 1964; Nanda, 1988; Jacob

and Buschang, 2011).

Though the overall pattern is generally maintained, craniofacial growth has been found to proceed at a

variety of rates in differing directions (Lande, 1952; Subtelny, 1959) with alveolar development

exhibiting regional differences during pubertal growth (Arat and Rubenduz, 2005). Therefore, changes in

facial projection and occlusion may result from the relative motion of the various parts of the

dentofacial complex with growth (Sinclair and Little, 1985), which would disguise easily recognizable

dentoalveolar patterns.

Therefore, the following question arises:

Is there a statistically significant difference in molar and incisor dentoalveolar heights and

dentoalveolar height growth rates in skeletal Class I subjects exhibiting various craniofacial

growth patterns evaluated longitudinally?

2

Significance of the Problem

Dentoalveolar heights can be modified, to a certain extent, by orthodontic treatment (Martina et al.,

2005), and adolescents undergo dramatic changes in maxillary and mandibular dentoalveolar heights

that hold important clinical implications. The vast majority of patients treated orthodontically are

children, and the period between 8 and 14 years of age is the stage at which corrective orthodontic

treatment is most frequently applied (Chen et al., 2007). Therefore, an evaluation of the dentoalveolar

height growth changes normally occurring during this period may provide valuable information.

The amount of growth of the mandible and concurrent eruption of the dentition seems to have post-

treatment stability implications. Alexander (1996) found that Class I extraction cases with the greatest

mandibular vertical growth post-treatment displayed the greatest increases of incisor irregularity during

the retention phase. Increased vertical ramal growth leads to increased dentoalveolar eruption, which

in turn creates the potential for instability. Furthermore, Naumann et al. (2000) evaluated the

multidimensional nature of overbite changes that occur during adolescence. Their multivariate model

suggested that mandibular changes, specifically vertical growth and rotation, are more important than

maxillary changes in determining overbite variations. The large amount of eruption of the lower incisors

that normally occurs – over 7 mm on average – during adolescence provides enormous potential for

modifying the overbite (Naumann et al., 2000).

Thomas Creekmore noted that if it were possible to control the vertical growth of the face, it would be

possible to solve nearly all orthodontic problems (Creekmore, 1967). An understanding of the typical

dentoalveolar height presentations and dentoalveolar height growth rates for patients presenting with

extremes in the vertical dimension may aid the clinician in making proper biomechanical decisions for

both treatment and stability concerns. On the other hand, failure to recognize and manage the vertical

dimension of a challenging case may leave the clinician and patient with few options other than

orthognathic surgery to correct the resulting dentofacial deformity.

Consequently, a thorough understanding of the consequences of an individual’s growth pattern and

potential differences between methods of assessment (e.g. directional versus proportionate) may aid

the clinician in recognizing significant craniofacial and dentoalveolar inter-relationships and

implementing the most ideal orthodontic mechanotherapy to achieve proper overbite, overjet, and

dental relations within such constraints.

3

Review of the Literature

A. Craniofacial Growth Patterns

Orthodontists have long placed considerable attention on the significance of interrelationships between

craniofacial growth and the development of the occlusion (Hellman, 1933; Bjork, 1951). From the

lateral perspective, facial growth direction is determined by the amount of both horizontal and vertical

components. The proportion of facial height to facial depth has not only a direct bearing upon facial

type but also a direct influence upon vertical overbite and dental function (Schudy, 1964). As a result,

one would reasonably expect that dentoalveolar heights are influenced by the vertical facial

development, or lack thereof.

Due to the complexity of the vertical craniofacial dimension, skeletal and dental tendencies have been

extensively studied for correlations with various growth patterns or facial types. In general, individuals

with a predominantly vertical growth pattern are associated with:

short posterior and long anterior facial heights (i.e. long facial type)

a high mandibular plane angle (i.e. hyper-divergent, high-angle)

open bite tendencies

On the other hand, individuals with a horizontal facial growth pattern are associated with:

long posterior and short anterior facial heights (i.e. short facial type)

a low mandibular plane angle (i.e. hypo-divergent, low-angle)

deep bite tendencies

Bishara and Jakobsen (1985) conducted a longitudinal evaluation from 5 to 25 years of age of 35

subjects, who were categorized into three facial types: relatively long, average, and relatively short

faces. Their results showed that 77% of subjects had the same facial type at 5 years and 25 years of age.

Consequently, they concluded that a strong tendency exists to maintain the original face type with age.

Other researchers have also corroborated this finding (Sassouni and Nanda, 1963; Cangialosi, 1984;

Nanda, 1988; Jacob and Buschang, 2011). As a result, multiple quantitative cephalometric measures

have been proposed to identify various craniofacial growth patterns with the intention of aiding the

clinician in prospectively identifying future types of craniofacial growers or simply identifying the

craniofacial region to be addressed in a non-growing individual.

4

B. Determination of Craniofacial Growth Patterns

Methods to determine the vertical or horizontal nature of craniofacial growth patterns are primarily

constrained to soft or hard tissue assessment of either frontal or lateral profile images. Regarding

lateral cephalometric radiographs, the osseous craniofacial measurements generally consist of three

types: angular, linear, or proportionate. Concerning vertical facial parameters, the following measures

are routinely used:

Angular measures

o Mandibular plane angle

SN-MP (sella-nasion plane to mandibular plane)

FH-MP (Frankfort horizontal plane to mandibular plane)

o Y-Axis angle

NSGn (sella-nasion plane to sella-gnathion plane

FH-SGn (Frankfort horizontal plane to sella-gnathion plane)

Linear measures

o N-ANS (nasion to anterior nasal spine)

o N-ANS' (nasion to anterior nasal spine prime)

o N-Me (nasion to menton)

o ANS-Me (anterior nasal spine to menton)

o Ar'-Go (articulare prime to gonion)

o S-Go (sella to gonion)

Proportions (ratios)

o N-ANS:ANS-Me % (nasion to anterior nasal spine : ANS to menton)

Interpretation: Upper facial height : lower facial height (anterior)

o N-ANS‘:N-Me % (nasion to anterior nasal spine prime : nasion to menton)

Interpretation: Upper facial height : total facial height (anterior)

o Ar-Go:S-Go % (articulare to gonion : sella to gonion)

Interpretation: Lower facial height : total facial height (posterior)

o S-Go:N-Me % (sella to gonion : nasion to menton)

Interpretation: Posterior facial height : anterior facial height

5

Angular measurements

In predicting the craniofacial growth pattern of a young patient, the clinician will often consider the

inclination of the mandibular plane (MP). According to Schudy (1964, 1965) and Isaacson et al. (1971),

the degree of inclination of the MP to the anterior cranial base (SN) has an effect on the degree of

mandibular rotation with growth. A greater SN-MP angle causes the mandible to become steeper and

the chin to move backward, which would indicate a vertical growth tendency. A smaller angle indicates

a greater tendency of the mandible to become flatter and the chin to grow forward, indicating more of a

horizontal growth pattern.

When investigating the interaction of anteroposterior and vertical facial dysplasias, Schudy (1964) used

the SN-MP angle to determine the proportions that produced average versus extreme facial types. He

divided his sample of 120 patients into three groups based on their SN-MP angle and coined the phrase

“facial divergence” as a method of indicating vertical variation. The two extremes of facial divergence

were described as “hyperdivergent” for individuals with a large mandibular plane angle and

“hypodivergent” for individuals with a small mandibular plane angle. His description of facial divergence

resounded well in the orthodontic profession and has withstood the test of time.

A variety of SN-MP angle cutoff points for hypodivergent and hyperdivergent classifications have been

used in previous studies. For 120 patients aged 11 to 14 years, Schudy (1964) divided the sample into

average (31-34°), hyperdivergent/retrognathic (>34°), and hypodivergent/prognathic (<31°) groups.

Isaacson (1971) studied 60 young adolescents with extreme variations in vertical facial growth and

stipulated a cutoff point for hyperdivergency of >38° and hypodivergency of <26°. On a sample of 129

subjects, Bishara and Augspurger (1975) used the cutoff of ±1 standard deviation from the sample

mean, which resulted in a definition of high-angle cases as those with values ≥34.8° and low-angle cases

as those with ≤ 22.2°.

Rather than utilizing SN as the plane of reference, the FMA (Frankfort horizontal to mandibular plane

angle) is formed by the intersection of the Frankfort horizontal plane and the mandibular plane. From

clinical research, Tweed (1966) concluded that the normal variations of FMA are 16-35° with an average

angle of 24.57 . According to DiPietro and Moergeli (1976), the rule of thumb is that an FMA of 25° ± 5°

is within normal range. A high-angle patient is considered to have an FMA of 30° or more, whereas a

low angle patient is one with an FMA of 20° or less. With respect to vertical facial types, a high FMA is

6

characterized by an open-bite skeletal pattern while a low FMA is characterized by a closed-bite skeletal

pattern. However, one must be cognizant that variations from this mean are known to exist among

races, age, and sex. In addition, the skeletal patterns should not be confused with open- and closed-bite

dental patterns (DiPietro and Moergeli, 1976), as variations of anterior dental presentation do not imply

a specific type of skeletal pattern. For example, an individual with a vertical skeletal pattern may

present with a deep, open, or normal dental overbite.

Though FMA and SN-MP angle measurements have been and continue to be widely used, the variability

between subjects in the orientation of the Frankfort horizontal plane and sella-nasion plane can be quite

large. Consequently, their validity has come under scrutiny due to the potential for substantial

differences among individuals (Bjerin, 1957; Lundström and Lundström, 1995) that may cause the cutoff

points between mandibular plane divisions to become very sample specific and quite variable.

Furthermore, assessment of the mandibular plane does not come without caution. Using metallic

implants as reference points in the maxilla and mandible, Bjork and Skieller (1972) found a general

feature of facial development was forward rotation of both jaws but greater for the mandible. There

was a strong association between facial rotation and condylar growth. At the lower border of the

mandible, approximately one half of the rotation was masked by compensatory remodeling. At the

posterior border of the ramus, approximately four fifths of the mandibular rotation was masked by

compensatory remodeling. Likewise, the rotation of the maxilla was masked by remodeling of the nasal

floor, which remained almost unchanged in inclination. Interestingly, they found that only 2 of 21

subjects had backward mandibular rotation. Most subjects (19 of 21) showed forward rotation,

including some with a high SN-MP angle. Consequently, the maxillomandibular growth pattern may be

masked by a higher or lesser degree of compensatory osseous remodeling among individuals, and those

variations create the potential for common correlations to falter in outliers of the human population.

Rather than utilizing the mandibular plane, craniofacial growth patterns have also been described in

terms of the Y-axis angle, of which there are two methods used. The original Y-axis angle referred to a

line connecting sella to gnathion and the angle it creates with the Frankfort horizontal plane. The

second uses the reference plane of sella to nasion, assuming the anterior cranial base is relatively more

stable intra-individually than the Frankfort horizontal plane during growth and development. In 1948,

Downs published one of the first cephalometric analyses to quantify variation in facial relationships and

7

described the term “Y-axis” to analyze the growth direction of the face and mandible. In a control group

of 20 individuals equally divided by gender, he found the Y-axis to range from 53 to 66° with a mean

value of 59.4°. Therefore, as the face swings out from under the cranium during its growth and

development from birth to maturity, it grows in a downward and forward direction.

In 1982, Rakosi found the Y-axis angle to decrease as a normally growing individual matures; therefore,

the growth of the face is in a slightly more forward than downward direction (i.e. horizontal growth).

Conversely, the Y-axis angle increases if growth of the face is in a more downward than forward

direction (i.e. vertical growth). Schudy’s (1965) research on facial growth corroborates this account. In

a sample of 50 subjects from 11 to 14 years of age, the relationship of facial height to depth was found

to have a very high correlation with the Y-axis. In other words, as an individual matures, the more the

growth in anterior face height exceeds the individual’s growth in face depth, the more the Y-axis will

increase and vice versa. However, Schudy also noted that the Y-axis is not sensitive enough to relate

information on the vertical growth of the posterior to anterior dental heights, gonion angle, ramus

height, or the relative position of the mandibular molars within the body of the mandible.

Linear measurements

Although several linear dimensions have been studied pertaining to the vertical development of the

face, the exclusive use of linear measurements for craniofacial growth pattern classification is not

justified. In 1948, Downs noted that a comparison of two or more individuals on the basis of linear

measurements is of little value due to differences expected between genders and for growth over time.

Comparing mixed- to permanent-dentition groups, Cangialosi (1984) found that ratios and angles

remained relatively constant over time, indicating that only size (but not facial proportion) changes with

age. Consequently, it is more appropriate to evaluate individuals on the basis of proportions and angles

of linear measurements rather than absolute values.

Proportionate measures (ratios)

In determining the cause of vertical malocclusion relationships, the proportions of the face are far more

important than absolute measurements (Khouw et al., 1970). The same logic applies to the description

of facial or skeletal types and by extension to the determination of craniofacial growth patterns. In

other words, skeletal open bite or vertically growing subjects are characterized by an excessive lower

8

anterior face height relative to the upper anterior face height, while skeletal deep bite or horizontally

growing subjects are characterized by a decreased lower anterior face height (Nanda, 1988).

Nahoum (1971, 1975, and 1977) extensively evaluated UFH:LFH ratios as an indication of open bite

tendency. He reported that in patients with an acceptable, untreated Angle Class I occlusion, the

UFH:LFH ratio averaged 0.81. Open bite patients had an average UFH:LFH ratio of 0.69 while deep bite

patients exhibited UFH:LFH ratios of ≥ 0.90. Similarly, Wylie and Johnson (1952) examined 57 attractive

individuals from a sample of mixed normal subjects between the ages of 11 to 13 years and found the

mean value of the UFH:LFH ratio to be 0.77. In lieu of utilizing the UFH:LFH ratio for facial growth

pattern classification, Nanda (1988, 1990) determined the LFH:TFH (lower face height : total face height)

ratio. Subjects with a relatively larger LFH:TFH ratio were considered to have a skeletal open-bite

tendency, while a smaller LFH:TFH ratio indicated a skeletal deep-bite tendency.

Rather than comparing upper, lower, or total facial heights to one another, the posterior facial height (S-

Go) can be compared to the total anterior facial height (N-Me) in a manner called the “Facial Height

Ratio” or Jarabak quotient (Jarabak and Fizzell, 1972). Jarabak and co-workers (Jarabak and Fizzell,

1972; Siriwat and Jarabak, 1985) defined subjects in the following manner:

Hyperdivergent growth pattern = PFH:AFH ratio < 0.59.

o Face rotates downward and posteriorly with growth.

o Anterior facial height increases more rapidly than posterior height.

o Down’s Y-axis angle tends to open.

Neutral growth pattern = PFH:AFH ratio of 0.59-0.63.

o Growth direction is downward and forward along Down’s Y-axis with about the

same increments anteriorly and posteriorly and no progressive change in most

angular relationships.

Hypodivergent growth pattern = PFH:AFH ratio > 0.63.

o Growth direction is predominantly horizontal.

o Down’s Y-axis tends to close.

Variations in Method Assessment

In general, the Y-axis angle, upper to lower facial height ratio, and the mandibular plane angle tend to

differ significantly between skeletal open- and deep-bite subjects. However, the literature has shown

that various measurements used to classify vertical malocclusions (i.e. overbite, UFH:LFH, PFH:AFH, SN-

9

MP angle, SN-PP angle, PP-MP angle, gonial angle, etc.) do not necessarily always have strong inter-

correlations as one might expect (Jacob and Buschang, 2011). Furthermore, Dung and Smith (1988)

found that different measures of open bite tendency identified different patients.

Due to the complex nature of the vertical craniofacial dimension and variety of landmarks used within

various classification methods, conflicting growth pattern determinations is not uncommon. In 1985,

Bishara and Jakobsen studied the range of variation in craniofacial relationships in a population with

normal occlusion. A sample of 20 males and 15 females was divided into long, average, and short facial

types (LFT, AFT, SFT) based on the adult ratio of posterior to anterior facial height (PFH:AFH) and

mandibular plane angle (FH-MP). Lateral cephalograms were obtained biennially between the ages of

4.5 to 12 years and then annually through age 17 years with an additional record set at 25.5 years.

Descriptive statistics of the Y-axis (NSGn°) absolute values were provided. The absolute Y-axis (NSGn°)

values at ages 5, 10, 15, and 25 years for the males followed the expected pattern (i.e. LFT Y-axis > AFT

Y-axis > SFT Y-axis); however, the female Y-axis values at all four age points did not (e.g. AFT Y-axis > LFT

Y-axis). As predicted by Schudy (1965), SFT subjects evaluated longitudinally should exhibit the greatest

amount of Y-axis closure, followed by AFT subjects, with the LFT subjects potentially having an opening

of the angle. Interestingly, the overall Y-axis angle closure of the Bishara and Jakobsen (1985) sample

between 5 to 25 years of age followed the expected pattern for male groups, but not for female groups.

However, the male groups did not follow the expected pattern for the period between 5 to 10 years of

age.

In 2003, Chung and Mongiovi investigated longitudinal craniofacial growth changes in untreated skeletal

Class I subjects with low, average, and high angle facial types. For a sample of 36 males and 32 females,

cephalograms at ages 9 and 18 years were measured. Subjects were divided based on the presence of

low (≤27°), average (>27°-<37°), or high (≥37°) mandibular plane (SN-MP) angles at age 9 years. The

cross-sectional data at age 9 years of both males and females was provided and showed agreement with

expectations: low-angle facial types had the smallest absolute Y-axis angle (FH-SGn°) while high-angle

facial types had the largest Y-axis angle. However, the longitudinal changes from age 9 to 18 years

exhibited patterns that were not congruent with the expected results. In males, the high-angle group

closed -1.95° while the low-angle group closed -0.22°; conversely, the average-angle group opened

+0.55°. In females, all groups opened but not in the expected pattern: low (+2.02°), high (+1.52°), and

10

average (+0.69°). Consequently, different methods of craniofacial growth pattern assessment may

result in conflicting growth pattern determinations.

C. Assessment of Dentoalveolar Heights and Dentoalveolar Height Growth Rates

The inherent craniofacial growth pattern influences the rotation of the maxillomandibular complex,

which necessitates compensatory adaptation in the eruption paths of the dentition. Although the

relationship is extremely important to orthodontists, very little longitudinal research has been

performed to explicitly compare the absolute value of molar and incisor dentoalveolar heights or their

growth rates in subjects grouped according to various growth patterns. According to Bishara and

Jakobsen (1985), longitudinal analysis of the data provides more consistent and therefore more

meaningful results than cross-sectional comparisons when craniofacial growth trends are evaluated.

This occurs because growth changes are often subtle and of magnitudes not readily observed when the

data is evaluated cross-sectionally (Bishara and Jakobsen, 1985). Furthermore, with cross-sectional

studies, there may be interchange and crossover of the subjects between various types of growth

patterns (Worms et al., 1971), which goes unnoticed.

Reference data for longitudinal vertical growth of adolescents is inconsistent and limited (Jacob and

Buschang, 2011). Such a scarcity is not surprising, since longitudinal studies are, by their nature,

lengthy, costly, and dependent upon the cooperation of the subjects. The following longitudinal and

cross sectional studies were retrieved in the published literature that did have partial relevance

regarding evaluation of dentoalveolar heights between various growth craniofacial growth patterns:

Longitudinal studies

Karlsen (1995) evaluated craniofacial and dentoalveolar dimensions longitudinally in two groups of

males with low (≤ 26°, n=15) and high (≥ 35°, n=15) SN-MP angles for two periods: age 6 to 12 years and

age 12 to 15 years. Maxillary and mandibular molar dentoalveolar heights were not statistically

different between low- and high-angle groups in either growth period. However, both maxillary and

mandibular incisor dentoalveolar heights exhibited larger growth rate values (mm/yr) in the high-angle

subjects but only during the 6 to 12 year period.

Buschang et al. (2008) conducted a mixed longitudinal study on 227 French-Canadians (119 males, 108

females) with cephalograms taken annually between 10 to 15 years of age. The individuals were chosen

11

at random from a pool of untreated normal occlusion and malocclusion subjects. Dentoalveolar heights

increased from 10 to 15 years of age, with the anterior and posterior dentoalveolar heights showing the

smallest and greatest changes, respectively. Male adolescents exhibited larger dentoalveolar heights

than female adolescents with a reduction or lack of sex difference around 12 and 13 years of age. The

greatest difference in dentoalveolar heights between the 10- and 15-year old age groups was for the

maxillary first molar while the maxillary central incisor dentoalveolar height showed the smallest age

effects. The coefficients of variation were greater for the maxillary than the mandibular dentoalveolar

heights, indicating a greater variation of maxillary dentoalveolar height means than the mandibular

dentoalveolar height means.

Arat and Rübendüz (2005) examined the alveolar height dimensions (rather than dentoalveolar) in 62

subjects with normal facial patterns and acceptable occlusions during early and late growth periods, as

determined by Gruelich and Pyle skeletal maturation criteria. During the early stage, the mandibular

anterior alveolar height showed the highest increase in the vertical dimension, while the maxillary

anterior alveolar height exhibited the least increase. Conversely, in the late stage, whereas a substantial

increase occurred in the maxillary posterior alveolar height, no change was observed in maxillary

anterior alveolar height. The authors concluded that alveolar development exhibits regional differences

during pubertal growth, which is crucial for establishing normal occlusal relations during mandibular

growth rotation.

Cross-sectional studies:

Though longitudinal assessment is certainly the gold standard for assessing craniofacial growth and

development correlations, cross-sectional studies do provide valuable information. However, these

“snap shots” in time create difficulty in visualizing the overall influence of growth patterns, and

extrapolation to different age ranges must be made cautiously. Multiple cross-sectional studies

evaluating correlations between dentoalveolar heights and craniofacial dimensions do exist, in which

the subjects are typically categorized according to facial type, mandibular plane angle, or overbite

characteristics (i.e. open vs. deep). As noted previously, their relevance is based on the assumption that

these measures accurately classify the growth pattern present and that pattern remains consistent over

time.

12

Janson et al. (1994) cross-sectionally examined the maxillary and mandibular first molar and central

incisor dentoalveolar height dimensions in 12-year old male and female subjects (188 males, 156

females) who had long, normal, and short lower face height ratios (UFH:LFH). The dentoalveolar heights

were significantly different between faces with long, normal, and short lower face heights, except for

the mandibular molar dentoalveolar height, which showed no difference between short and normal face

height subjects. All dentoalveolar heights were larger for male subjects except for the maxillary molar

dentoalveolar height. The maxillary molars presented a higher correlation to the UFH:LFH ratio than the

lower dentition. Stepwise regression analysis showed that 22% of the variation in the UFH:LFH ratio was

explained by the maxillary and mandibular molar dentoalveolar heights and 41% was explained by the

maxillary and mandibular incisor dentoalveolar heights.

Betzenberger et al. (1999) assessed the dentoskeletal morphology in 191 untreated children with

hyperdivergent mandibular plane angles (> 40°). The subjects were divided into mixed and permanent

dentition groups then further divided into subgroups based on the amount of overbite (OB) as a

measure of dentoalveolar compensation of jaw base hyperdivergency. Regarding the mixed dentition,

deep bite subjects exhibited relative increases of maxillary and mandibular incisor dentoalveolar heights

when compared to open bite subjects. In the molar region, no group differences in dentoalveolar

heights existed. However, in the permanent dentition, deep bite subjects exhibited relative decreases in

maxillary and mandibular molar dentoalveolar heights compared with open bite subjects. In the

anterior region, no group differences in dentoalveolar heights were found.

Ceylan and Eroz (2001) investigated the differences in the maxillary and mandibular morphology related

to overbite. A total of 80 untreated subjects aged 13 to 15 years were divided into 4 groups with normal

overbite, edge-to-edge bite, open bite, or deep bite. Maxillary and mandibular dentoalveolar heights

were greater in the open-bite group than in the other groups. The subjects with open bite showed a

long and narrow symphysis morphology, while the subjects with deep bite had a short and broad

symphysis form.

Martina et al. (2005) tested the hypothesis that molar dentoalveolar heights are positively related to

vertical craniofacial features in a sample of 82 untreated, adult subjects. Females were of age 15 years

or greater while males were of age 18 years or greater. Approximately 70% of the total molar

dentoalveolar height variance was explained by lower facial height (ANS-Me) and the palatal to

13

mandibular plane angle (PP-MP). Increases in the lower face height had a positive correlation with the

molar dentoalveolar heights; conversely, the molar dentoalveolar heights were negatively influenced by

increasing divergency of the jaws (PP-MP angle).

Martina et al. (2009) evaluated a sample of 79 children younger than 9 years of age for the relationship

between posterior dentoalveolar heights and vertical craniofacial patterns. Approximately 54% of the

total variability in molar dentoalveolar heights was explained by the variability in lower facial height

(ANS-Me) and the palatal to mandibular plane angle (PP-MP). Both maxillary and mandibular

dentoalveolar heights were significantly influenced by the length of the lower facial height and

mandibulopalatal plane angle. Increases of ANS-Me and PP-MP had opposite effects on the amount of

molar dentoalveolar heights; thus, an inverse relationship between molar dentoalveolar heights and jaw

divergence was determined to be present when vertical growth is still incomplete.

Kucera et al. (2011) evaluated the skeletal and dentoalveolar components in 69 adult female subjects

with skeletal open bite (SN-MP° > 40°) in the presence or absence of dental compensation. As opposed

to previous findings (Martina et al., 2005 and 2009), increased maxillary and mandibular molar

dentoalveolar height was a common finding in adult skeletal open bite subjects. In addition, incisor

dentoalveolar height was significantly greater in both skeletal open bite groups. Overdevelopment of

lower facial height was compensated by significant elongation of the incisal dentoalveolar heights of

both jaws, with lower incisors playing a more important role.

Nahoum et al. (1972) evaluated the lateral cephalograms of 128 male patients categorized into three

groups: a) good occlusion (n=92); b) Angle Class II anterior open-bite (n=18); and c) Angle Class III

anterior open-bite (n=18). On the average, persons with an open bite had a longer LFH, a shorter

posterior face height, a short maxillary incisor to S-N distance, a smaller mandibular molar to MP

distance, and a smaller UFH:LFH ratio than did normal control subjects.

Kuitert et al. (2006) investigated the vertical dentoalveolar compensation in untreated adults (ages 17 to

56 years) with excessive (long-face, n=112) and deficient (short-face, n=95) lower anterior facial heights.

Subjects were grouped according to both overbite and lower face height (mm) measurements.

Dentoalveolar height compensation occurred in both short-face (SF) and long-face (LF) groups mainly by

adaptations in mandibular incisor alveolar and basal heights. Lower dentoalveolar compensation was

14

found to maintain a normal overbite in long-face subjects to a limited extent. In SF and LF subjects,

overbite was independent of vertical molar dentoalveolar dimensions; consequently, molar

dentoalveolar height was unrelated to overbite.

Haralabakis et al. (1994) evaluated the morphogenetic characteristics that contribute to the

development of open bite in adults. Cephalograms of 22 males and 34 females who exhibited an

anterior open bite of at least 2 mm were compared against a control group. In both male and female

groups with open bites, the total facial height (N-Me) and three dentoalveolar heights (maxillary incisor,

mandibular incisor, and maxillary molar) were significantly greater than control groups.

Tsai (2000) investigated the facial morphologic characteristics in children with long (n=46) and short

(n=42) faces as determined by the ratio of PFH:AFH (S-Go:N-Me) and inclination of the mandibular plane

to Frankfort horizontal (FH-MP angle). Long-face girls had significantly greater maxillary molar and

incisor dentoalveolar heights but not mandibular molar or incisor dentoalveolar heights, as compared to

the short-face group. Similarly, long-face boys had significantly greater maxillary dentoalveolar heights

and mandibular incisor dentoalveolar heights as compared to the short-face group.

Anwar and Fida (2009) evaluated the dental compensation patterns in 186 orthodontic patients (120

females and 66 males; mean age: 15 years, 11 months) as classified by the following SN-MP angle

criteria: a) hyperdivergent (> 36°); b) normal (28-36°); and c) hypodivergent (< 28°). Significant

differences were found for only the mandibular incisor dentoalveolar height between the three vertical

facial types. All dentoalveolar height measurements, except for upper anterior incisor dentoalveolar

height, were significantly correlated with the skeletal parameters and showed compensation. Weak

correlation coefficients for the maxillary incisor dentoalveolar height suggested limited compensation

for vertical skeletal relationships. The mandibular incisor dentoalveolar height was found to be the most

likely parameter to compensate for different skeletal vertical dysplasias, while maxillary incisor

dentoalveolar height showed the least tendency to change according to vertical skeletal relationships.

Han et al. (2013) investigated the relationship between craniofacial growth patterns and mandibular

posterior dentoalveolar complex morphology in a Chinese sample (23 males, 22 females) aged 21 to 41

years with normal occlusion. The subjects were divided into different growth pattern types based on

their Frankfort horizontal to mandibular plane angle (FH-MP) and facial height index (FHI), which

15

resulted in 20 horizontal growth pattern patients (FMA<27°, FHI>65°) and 20 vertical growth pattern

patients (FMA>37°, FHI<62°). The inclination of the molars, the thickness of cortical bone, and the

height of the mandibular alveolus differed significantly between patients with the horizontal growth

pattern and those with the vertical growth pattern. The alveolar height at the first and second molars

and second premolar of subjects with the horizontal growth pattern was greater than that of those with

the vertical growth pattern.

D. Summary

Overall, the orthodontic literature has a void in regards to longitudinal evaluations of dentoalveolar

heights and dentoalveolar height growth rates in relation to various types of facial growth patterns. The

multitude of cross-sectional studies certainly aids the orthodontist in determining correlations between

skeletal markers and dentoalveolar compensation at specific ages, but a longitudinal investigation may

provide more information concerning the overall growth and development process. Although Janson et

al. (1994) did investigate the dentoalveolar height dimensions cross-sectionally at age 12 years, one

cannot extrapolate their results to other ages due to the potential for growth occurring in unequal

amounts and in varying directions (i.e. relative motion of the various parts of the dentofacial complex).

Furthermore, Arat and Rübendüz’s (2005) finding that alveolar development exhibits regional

differences during pubertal growth testifies to the necessity of longitudinal evaluation of the dentition’s

vertical dimension, as a cross-sectional evaluation may miss important compensations in time.

16

Purpose of the Study

The purpose of this longitudinal study is:

To determine if significant differences in maxillary and mandibular molar and incisor

dentoalveolar heights and dentoalveolar height growth rates exist between skeletal Class I

subjects classified into 3 different craniofacial growth patterns by a directional method (Y-Axis

angle change).

To determine if significant differences in the maxillary and mandibular molar and incisor

dentoalveolar heights and dentoalveolar height growth rates exist between skeletal Class I

subjects classified into 3 different craniofacial growth patterns by a proportionate method

(UFH:LFH ratio).

To determine if there are significant gender related differences in dentoalveolar height growth

rates of the maxillary and mandibular molars and incisors in skeletal Class I individuals.

17

Research Objectives

The objectives of this study are to:

Longitudinally evaluate the dentoalveolar heights and dentoalveolar height growth rates of

maxillary and mandibular molars and incisors of skeletal Class I subjects as classified by

directional and proportionate methods.

Determine whether the dentoalveolar height growth rates of skeletal Class I subjects exhibit

sexual dimorphism.

18

Hypotheses

To address the research objectives, the following hypotheses were framed:

Hypothesis #1

Within each gender, there is a significant difference in the dentoalveolar heights and dentoalveolar

height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I subjects

classified into vertical, average, and horizontal growth patterns, as determined by change in Y-axis angle.

Hypothesis #2

Within each gender, there is a significant difference in the dentoalveolar heights and dentoalveolar

height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I subjects

classified into long, average, and short facial type growth patterns, as determined by the UFH:LFH ratio.

Hypothesis #3

There are significant gender related differences in the dentoalveolar height growth rates of the maxillary

and mandibular molars and incisors in skeletal Class I subjects.

19

Materials & Methods

A. Sample Description

Established in 1952, the Burlington Growth Centre (BGC) data is a collection of longitudinal craniofacial

growth records from the town of Burlington, Ontario, Canada. In 1994, the sample was extended to 40

years for a portion of the original sample. The BGC records are currently located in the Burlington

Orthodontic Research Centre at the University of Toronto. The predominant racial group was Caucasian

and mostly Anglo Saxon. The original sample consisted of 1258 children separated into a serial

experimental group and 4 control groups, as follows:

Serial Experimental (SE) – records taken every year from ages 3 to 20 years.

Control at age 6 (C-6) – records were taken at ages 6, 9, 12, 14, 16, and 20 years.

Control at age 8 (C-8) – records were taken at age 8 years, but some other ages were obtained.

Control at age 10 (C-10) – records were taken at age 10 years, with a few other ages.

Control at age 12 (C-12) – records were taken at age 12 years and again at age 20 on

approximately half of the individuals.

For the current investigation, an initial sample of 242 subjects (111 males, 131 females) was collected

from the serial experimental and C6 groups, which were expected to have records available at 9, 12, 14,

and 16 years of age. Radiographs used from the study were lateral cephalometric images taken in the

centric occlusion position. The original film-based lateral cephalograms had an enlargement factor of

9.84% as the anode to center of subject distance was 152.4 cm, and the distance from the center of the

subject to the film was 15.0 cm. Recently, all film-based cephalograms have been digitally converted

(Epson Perfection V700 Photo scanner) and stored as a TIFF (Tagged Image File Format) for long-term

preservation.

Using Adobe Photoshop 6 (San Jose, CA, USA), each image was converted to JPEG (Joint Photographic

Experts Group) format and resampled at a resolution of 300 pixels per inch. The images were imported

into version 11.7 of the Dolphin imaging software (Dolphin Imaging and Management Systems,

Chatsworth, CA, USA) program for cephalometric tracing.

20

Phase I – Exclusion criteria

For each individual, all lateral cephalometric radiographs were examined, and subjects were excluded

according to the following criteria:

Dental agenesis of any permanent tooth (excluding 2nd or 3rd molars)

Failure of eruption of a 1st molar or central incisor

Extraction of any permanent tooth (excluding 2nd or 3rd molars)

Generalized or localized (i.e. 1st molar or central incisor) severe dental wear pattern

Restoration of central incisor incisal edge or 1st molar mesiobuccal cusp tip

Radiographs not of diagnostic quality

Any orthodontic treatment (including lingual holding arches)

Incomplete occlusion (maximum intercuspation) at either age 9 or 16 year cephalogram

In total, 83 subjects (39 males, 44 females) were excluded during phase I. Table I contains the specific

details of each applied criterion.

Table I.

Exclusion Criteria – phase I

# Excluded

Male Female

Dental agenesis of any permanent tooth (excluding 2ndor 3rd molars) 2 1

Failure of eruption of a 1st molar or central incisor 1 0

Extraction of any permanent tooth (excluding 2ndor 3rd molars) 11 16

Generalized or localized (i.e. 1st molar or central incisor) severe dental wear pattern 3 0

Restoration of central incisor incisal edge or 1st molar mesiobuccal cusp tip 3 1

Radiographs not of diagnostic quality 1 0

Any orthodontic treatment (including lingual holding arches) 9 14

Incomplete occlusion (maximum intercuspation) at either age 9 or 16 year cephalogram 9 12

Total Excluded: 39 44

Table I. Application of Exclusion Criteria – phase I

21

Phase II – Exclusion criteria

In an effort to constrain the residual sample (72 males, 87 females) to include skeletal Class I subjects at

age 16 years with minimal changes in dental inclination from ages 9 to 16 years, the following secondary

exclusion criteria were applied:

Age 16 years: Skeletal Class II pattern

o ANB > 4.5°

o McNamara’s unit length difference < 20.0 mm

Age 16 years: Skeletal Class III pattern

o ANB < 0.5°

o McNamara’s unit length difference > 30.0 mm

Age 9 to 16 years: > 10° change of incisor inclination

In total, 54 subjects (23 males, 31 females) were excluded during phase II. Table II contains the specific

details of each applied criterion:

Table II.

Exclusion Criteria – phase II:

# Excluded

Male Female

Skeletal Class II pattern

ANB > 4.5° 3 13

McNamara’s unit length difference < 20.0 mm 6 7

Skeletal Class III pattern

ANB < 0.5° 8 9

McNamara’s unit length difference > 30.0 mm 2 1

> 10° change of incisor inclination 4 1

Total Excluded: 23 31

Table II. Application of Exclusion Criteria – phase II

22

The final study sample included 105 subjects (49 males, 56 females). Of those, three female subjects

were missing their age 14 lateral cephalogram while complete records for the male subjects were

available. Subjects with one missing lateral cephalogram at either age 12 or 14 were decided to be

included in the sample since the missing data would not influence the directional classification, which is

dependent upon the age 9 and 16 cephalograms, or the statistical analyses.

Figure 1. Final Sample Flowchart

B. Cephalometric Analysis

Using the Dolphin Imaging program, a custom cephalometric analysis was created, which utilized the

following craniofacial and dental landmarks (definitions used from Daskalogiannakis, 2000):

A point – the deepest (most posterior) midline point on the curvature between the ANS and

prosthion.

Anterior nasal spine (ANS) – the tip of the bony anterior nasal spine at the inferior margin of the

piriform aperture in the midsagittal plane.

B point – the deepest (most posterior) midline point on the bony curvature of the anterior

mandible, between infradentale and pogonion, in the midsagittal plane.

Condylion (Co) – the most superior posterior point on the head of the mandibular condyle

(bilateral)

242 BGC subjects

111 males 131 females

72 males 87 females

49 males 56 females

Phase I Exclusion Criteria applied

Phase II Exclusion Criteria applied

23

Gnathion (Gn) – the most anterior inferior point on the bony chin in the midsagittal plane

Gonion (Go) – the most posterior inferior point on outline of the angle of the mandible

L1 Root – root apex of the most labially placed mandibular central incisor (unilateral)

L1 Tip – incisal tip of the most labially placed mandibular incisor (unilateral)

L6 Occlusal – mesial buccal cusp tip of the mandibular 1st molars (midsagittal)

Menton (Me) – the most inferior point of the mandibular symphysis, in the midsagittal plane

Nasion (N) – the intersection of the internasal and frontonasal suture, in the midsagittal plane

Pogonion (Pg) – the most anterior point on the contour of the bony chin, in the midsagittal

plane

Posterior nasal spine (PNS) – the most posterior point on the bony hard palate in the midsagittal

plane

Sella (S) – the geometric center of the pituitary fossa (sella turcica) constructed in the

midsagittal plane

U1 Root – root apex of the most labially placed maxillary central incisor (unilateral)

U1 Tip – incisal tip of the most labially placed maxillary central incisor (unilateral)

U6 Occlusal – mesial buccal cusp tip of the maxillary 1st molars (midsagittal)

Figure 2. Craniofacial and Dental Landmarks

The following reference planes were constructed (definitions used from Daskalogiannakis, 2000):

24

Mandibular plane (MP) – a line representing the plane passing through the mandibular borders

(Go-Me) bilaterally.

Palatal plane (PP) – a line joining PNS and ANS.

Y-axis (Growth axis) – a line connecting points sella and gnathion.

Sella-nasion – a line connecting points sella and nasion.

The following linear, angular, and proportionate measurements were recorded:

ANB angle – the difference between angles SNA and SNB, as introduced by R.A. Riedel, aimed at

providing an evaluation of the anteroposterior relationship between the maxillary and

mandibular apical bases.

Lower facial height (LFH) – the linear millimetric distance between the ANS and menton

measured directly.

L1 – MP (⊥ MP, mm) – the linear millimetric distance (perpendicular to MP) from the

mandibular central incisor tip to the mandibular plane.

L6 – MP (⊥ MP, mm) – the linear millimetric distance (perpendicular to MP) from the

mandibular 1st molar mesial buccal cusp tip to the mandibular plane.

Maxillary (midface) length – the linear measurement from condylion to A point.

Mandibular length – the linear measurement from condylion to gnathion.

Figure 3. Craniofacial Reference Planes

25

McNamara’s unit length difference (Co-Gn minus Co-A point) – the maxillomandibular

differential as determined by the mandibular length minus the mid-face (maxillary) length.

Upper facial height (UFH) – the linear millimetric distance between nasion and the ANS.

Upper facial height to Lower facial height ratio (UFH:LFH)

U1 – PP (⊥ PP, mm) – the linear millimetric distance (perpendicular to PP) from the maxillary

central incisor tip to the palatal plane.

U6 – PP (⊥ PP, mm) – the linear millimetric distance (perpendicular to PP) from the maxillary 1st

molar mesial buccal cusp tip to the palatal plane.

Y-axis angle (NSGn) – the anteroinferior angle between the Y-axis (S-Gn) and S-N plane.

Figure 4. Maxillary and Mandibular Dentoalveolar Height Measurements

The dentoalveolar heights (mm) were recorded from the age 9, 12, 14, and 16 year cephalograms. The

maxillary dentoalveolar heights were calculated based on the perpendicular distances of the central

incisor tip and the first molar mesial buccal cusp tip to the palatal plane (ANS-PNS). The mandibular

dentoalveolar heights were calculated based on the perpendicular distance of the central incisor tip and

the first molar mesial buccal cusp tip to the mandibular plane (Go-Me). The dentoalveolar height

growth rates were recorded for three time periods (9 to 12 years, 12 to 14 years, and 14 to 16 years).

Each respective dentoalveolar height growth rate value was calculated by subtracting the dentoalveolar

height recorded at the earlier time point from the later time point (e.g. dentoalveolar height at age 12

years minus dentoalveolar height at age 9 years), then dividing by the number of years between the two

time points (i.e. 2 or 3 years), which resulted in a measurement of millimeters per year (mm/yr).

26

C. Growth Pattern Classification

Classification of the male and female samples was performed according to both the directional (change

in Y-axis angle) and proportionate (UFH:LFH) methods. The gender means and standard deviation of the

means of both the Y-axis angle change between ages 9 to 16 years and the UFH:LFH ratio at age 16 years

were calculated. The average range was considered to be within 1 standard deviation of each gender’s

mean. Subjects exhibiting values greater or lesser than 1 standard deviation were considered to be in

the horizontal or vertical group for the Y-axis classification method and the short or long LFH group for

the proportionate classification method.

Directional Classification: Change in Y-axis angle

The final sample was classified according to the directional growth pattern (Table III) as follows:

• Y-axis measurements at age 9 and 16 years were recorded.

• Change in Y-axis measurement between 9 and 16 years was determined for each individual.

• The mean change in Y-axis:

o For the entire sample was calculated to be -0.73° with a standard deviation of 1.69°.

o For the female sample was calculated to be -0.73° with a standard deviation of 1.62°.

o For the male sample was calculated to be -0.72° with a standard deviation of 1.77°.

Table III. Directional Classification: Change in Y-axis angle (9 to 16 y)

Range Mean Standard Deviation

Entire Sample +3.4° to -5.0° -0.73° 1.69°

Males +3.4° to -5.0° -0.72° 1.77°

Females +3.1° to -4.8° -0.73° 1.62°

Note: (+) → opening of Y-axis angle = Vertical growth pattern

(-) → closure of Y-axis angle = Horizontal growth pattern

• Subjects were classified into vertical, average, or horizontal growth pattern groups as

follows:

o Males

Vertical – subjects whose change in Y-axis was > +1.05° (greater than +1

standard deviation from the male sample mean).

27

Average – subjects whose change in Y-axis was ≤ +1.05° and ≥ -2.49° (within ±1


Horizontal – subjects whose change in Y-axis was < -2.49° (less than -1 standard

deviation from the male sample mean).

o Females

Vertical – subjects whose change in Y-axis was > +0.89 ° (greater than +1

standard deviation from the female sample mean).

Average – subjects whose change in Y-axis was ≤ +0.89° and ≥ -2.35° (within ±1


Horizontal – subjects whose change in Y-axis was < -2.35° (less than -1 standard

deviation from the female sample mean).

As a result, the directional growth pattern classification method grouped the 49 male and 56 female

subjects as follows (Table IV):

Table IV. Directional growth pattern classification

Vertical Average Horizontal

Males 10 31 8

Females 8 38 10

The mean and standard deviations of the Y-axis change for each directional group are listed as follows

(Table V):

Table V. Directional groups: means and standard deviations of Y-axis change (9 to 16 years)

Vertical Average Horizontal

Mean (SD) Mean (SD) Mean (SD)

Males +1.72° (±0.64) -0.82° (±1.02) -3.34° (±0.78)

Females +1.82° (±0.87) -0.64° (±0.82) -3.12° (±0.73)

28

Proportionate Classification: UFH:LFH ratio

The final sample was classified according to the proportionate growth pattern (Table VI) as follows:

• UFH:LFH measurements at age 16 were recorded.

• The mean UFH:LFH value:

o For the entire sample was calculated to be 0.80 with a standard deviation of 0.07.

o For the female sample was calculated to be 0.81 with a standard deviation of 0.07.

o For the male sample was calculated to be 0.80 with a standard deviation of 0.06.

Table VI. Proportionate Classification: UFH:LFH ratio (16 y)

Range Mean Standard Deviation

Entire Sample 0.96 to 0.65 0.80 0.07

Males 0.96 to 0.65 0.80 0.06

Females 0.96 to 0.69 0.81 0.07

• Subjects were classified into short, average, and long facial height growth pattern groups as

follows:

o Males

Short – subjects whose UFH:LFH ratio was > 0.86 (greater than +1 standard

deviation from the male sample mean).

Average – subjects whose UFH:LFH ratio was ≤ 0.86 and ≥ 0.74 (within ±1


Long – subjects whose UFH:LFH ratio was < 0.74 (less than -1 standard deviation

from the male sample mean).

o Females

Short – subjects whose UFH:LFH ratio was > 0.88 (greater than +1 standard

deviation from the female sample mean).

Average – subjects whose UFH:LFH ratio was ≤ 0.88 and ≥ 0.74 (within ±1


Long – subjects whose UFH:LFH ratio was < 0.74 (less than -1 standard deviation

from the female sample mean).

29

As a result, the proportionate growth pattern classification method grouped the 49 male and 56 female

subjects as follows (Table VII):

Table VII. Proportionate growth pattern classification

Long Average Short

Males 11 29 9

Females 10 34 12

The mean and standard deviations of the UFH:LFH ratio for each proportionate group are listed as

follows (Table VIII):

Table VIII. Proportionate groups: means and standard deviations of UFH:LFH (16 years)

Long Average Short

Mean (SD) Mean (SD) Mean (SD)

Males 0.71 (±0.03) 0.80 (±0.02) 0.90 (±0.03)

Females 0.73 (±0.02) 0.79 (±0.03) 0.92 (±0.05)

30

D. Reliability Analysis After a period of four months, intra-rater reliability was determined by having the primary investigator

(B.S.) re-trace and measure the lateral cephalograms of twenty subjects (10 males, 10 females) as

determined by a random number generator using Microsoft Excel (Redmond, WA, USA). Inter-rater

reliability was determined by a secondary investigator (K.K.) tracing and measuring the lateral

cephalograms of the same twenty randomly selected subjects. The following measurements were

assessed: ANB angle, Y-Axis angle, U1 dentoalveolar height, U6 dentoalveolar height, L1 dentoalveolar

height, L6 dentoalveolar height, and McNamara’s unit length difference.

The intraclass correlation coefficients (ICC) analysis was used to determine intra-rater reliability of the 7

measurements and the measurement error (Table IX) was calculated by using Dahlberg’s formula

(Dahlberg, 1940). Results of the ICC showed excellent reliability with minimal measurement error.

Table IX. Reliability Analysis

Intraclass Correlation Coefficient Measurement Error* (mm)

BS1-BS2 BS1-KK BS1-BS2 BS1-KK

ANB .988 .977 .18 .27

Y-Axis .996 .991 .22 .34

U1 .997 .994 .21 .27

U6 .996 .995 .19 .24

L1 .998 .997 .18 .23

L6 .997 .990 .20 .35

ULD .996 .989 .30 .49

C. Analysis of Results

ICC =(σ2

s) / (σ2

s + σ2

i) * = Method error = √(∑d²/2N), where D is the difference between the repeated measurements, and N is the number of paired measurements

31

E. Analysis of Results As described, male and female subjects were placed into Y-axis groups (vertical, average, horizontal)

and UFH:LFH groups (long, average, short) according to their sample means (Y-axis change between

9 to 16 years, or UFH:LFH at 16 years) and standard deviations.

The following descriptive statistics were calculated and recorded:

o Means, standard deviations, and standard error of the means for the dentoalveolar heights

in each of the four sites (U1, U6, L1, and L6) at ages 9, 12, 14, and 16 years.

o Means, standard deviations, and 95% confidence limits for the dentoalveolar height growth

rates (mm/year) of U1, U6, L1, and L6 for three time periods, as follows:

9 to 12 years

12 to 14 years

14 to 16 years

For each classification method, mixed models were constructed for males and females separately to

test for between group differences in dentoalveolar heights at all four ages evaluated together.

Predictors were age and craniofacial growth group. Interactions between “age and group” were

also assessed.

o The dentoalveolar heights were assessed for significant differences for all four dentoalveolar

sites (U1, U6, L1, and L6) within each gender.

For each classification method, mixed models were constructed in order to test for between group

differences in dentoalveolar heights at each of the four ages individually. Predictors were gender

and craniofacial growth group. Interactions between “gender and group” were also assessed.

o The dentoalveolar heights (U1, U6, L1, L6) at each specific age were assessed for significant

differences.

For each classification method, between group one-way ANOVA analyses were used to test for

significant differences of the dentoalveolar height growth rates among the classified groups within

the male and female samples for three time periods (9 to 12 years, 12 to 14 years, and 14 to 16

years) for all four dentoalveolar sites (U1, U6, L1, and L6).

Tukey post-hoc comparisons were used for further evaluation of inter-group differences where the

initial mixed model or ANOVA analysis resulted in a finding of statistically significant differences

(p<0.05). If the mixed model or ANOVA analysis did not reveal statistically significant inter-group

differences, further statistical analyses were not required.

32

Independent t-tests were used to evaluate for gender differences in dentoalveolar height growth

rates for each dentoalveolar site and time period.

The level of significance for comparisons of the dentoalveolar heights and dentoalveolar height

growth rates was set at p<0.05 throughout the analysis.

Results

Overview

A. Dentoalveolar heights

Directional Classification

o U1, U6, L1, L6

Proportionate Classification

o U1, U6, L1, L6

B. Dentoalveolar height growth rates

Directional Classification

o U1, U6, L1, L6

Proportionate Classification

o U1, U6, L1, L6

C. Evaluation of the effect of gender on dentoalveolar height growth rates

Dentalveolar height growth rates

o U1, U6, L1, L6

A. Dentoalveolar heights

Mixed model analyses were used to test for significant differences in dentoalveolar heights (U1, U6, L1,

and L6) between the three different growth patterns within each gender at ages 9, 12, 14, and 16 years,

evaluated both together and separately (i.e. at each of the four time points). The following results

describe the dentoalveolar heights of the different groups within the sample for each site, age and

gender, and can be found in table format in Appendices 1 and 2.

33

Directional classification

a. Maxillary Central Incisor (U1)

i. Females

The maxillary central incisor dentoalveolar heights (U1) for the three female directional growth pattern

groups are as follows. For females at age 9 years, the maxillary central incisor dentoalveolar height was

22.6 ± 1.8 mm for the vertical group, 21.9 ± 2.0 mm for the average group, and 22.7 ± 1.8 mm for the

horizontal group. For females at age 12 years, the maxillary central incisor dentoalveolar height was 24.2

± 2.3 mm for the vertical group, 23.1 ± 2.1 mm for the average group, and 23.8 ± 2.7 mm for the

horizontal group. For females at age 14 years, the maxillary central incisor dentoalveolar height was


horizontal group. For females at age 16 years, the maxillary central incisor dentoalveolar height was


horizontal group (Figure 5). Dentoalveolar height differences at the maxillary central incisor, found

between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant,

both in the overall analysis as well as at any of these time points.

Figure 5. Directional Classification: Dentoalveolar heights at the maxillary central incisor site in females

34

ii. Males

The maxillary central incisor dentoalveolar heights (U1) for the three male directional growth pattern

groups are as follows. For males at age 9 years, the maxillary central incisor dentoalveolar height was


horizontal group. For males at age 12 years, the maxillary central incisor dentoalveolar height was 24.5 ±

1.6 mm for the vertical group, 24.4 ± 2.4 mm for the average group, and 25.1 ± 2.1 mm for the

horizontal group. For males at age 14 years, the maxillary central incisor dentoalveolar height was 25.4


horizontal group. For males at age 16 years, the maxillary central incisor dentoalveolar height was 26.4


horizontal group (Figure 6). Dentoalveolar height differences at the maxillary central incisor, found

between the male directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant,


Figure 6. Directional Classification: Dentoalveolar heights at the maxillary central incisor site in males

35

b. Maxillary first molar (U6)

i. Females

The maxillary first molar dentoalveolar heights (U6) for the three female directional growth pattern

groups are as follows. For females at age 9 years, the maxillary molar dentoalveolar height was 16.1 ±


horizontal group. For females at age 12 years, the maxillary first molar dentoalveolar height was 18.3 ±






horizontal group (Figure 7). Dentoalveolar height differences at the maxillary first molar, found



Figure 7. Directional Classification: Dentoalveolar heights at the maxillary first molar site in females

36

ii. Males

The maxillary first molar dentoalveolar heights (U6) for the three male directional growth pattern

groups are as follows. For males at age 9 years, the maxillary first molar dentoalveolar height was 15.8 ±


horizontal group. For males at age 12 years, the maxillary first molar dentoalveolar height was 17.9 ± 1.4

mm for the vertical group, 18.1 ± 2.1 mm for the average group, and 18.1 ± 1.6 mm for the horizontal

group. For males at age 14 years, the maxillary first molar dentoalveolar height was 20.1 ± 2.2 mm for

the vertical group, 19.8 ± 2.7 mm for the average group, and 19.7 ± 2.1 mm for the horizontal group.

For males at age 16 years, the maxillary first molar dentoalveolar height was 21.3 ± 1.6 mm for the

vertical group, 21.2 ± 2.3 mm for the average group, and 21.1 ± 1.7 mm for the horizontal group (Figure

8). Dentoalveolar height differences at the maxillary first molar, found between the male directional

growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as

well as at any of these time points.

Figure 8. Directional Classification: Dentoalveolar heights at the maxillary first molar site in males

37

c. Mandibular central incisor (L1)

i. Females

The mandibular central incisor dentoalveolar heights (L1) for the three female directional growth

pattern groups are as follows. For females at age 9 years, the mandibular central incisor dentoalveolar

height was 31.1 ± 1.3 mm for the vertical group, 30.6 ± 1.7 mm for the average group, and 31.0 ± 1.9

mm for the horizontal group. For females at age 12 years, the mandibular central incisor dentoalveolar






mm for the horizontal group (Figure 9). Dentoalveolar height differences at the mandibular central

incisor, found between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were

not significant, both in the overall analysis as well as at any of these time points.

Figure 9. Directional Classification: Dentoalveolar heights at the mandibular central incisor site in

females

38

ii. Males

The mandibular central incisor dentoalveolar heights (L1) for the three male directional growth pattern

groups are as follows. For males at age 9 years, the mandibular central incisor dentoalveolar height was


horizontal group. For females at age 12 years, the mandibular central incisor dentoalveolar height was


horizontal group. For males at age 14 years, the mandibular central incisor dentoalveolar height was


horizontal group. For males at age 16 years, the mandibular central incisor dentoalveolar height was


horizontal group (Figure 10). Dentoalveolar height differences at the mandibular central incisor, found



Figure 10. Directional Classification: Dentoalveolar heights at the mandibular central incisor site in males

39

d. Mandibular first molar (L6)

i. Females

The mandibular first molar dentoalveolar heights (L6) for the three female directional growth pattern

groups are as follows. For females at age 9 years, the mandibular first molar dentoalveolar height was


horizontal group. For females at age 12 years, the mandibular first molar dentoalveolar height was 25.0






horizontal group (Figure 11). Dentoalveolar height differences at the mandibular first molar, found



Figure 11. Directional Classification: Dentoalveolar heights at the mandibular first molar site in females

40

ii. Males

The mandibular first molar dentoalveolar heights (L6) for the three male directional growth pattern

groups are as follows. For males at age 9 years, the mandibular first molar dentoalveolar height was


horizontal group. For males at age 12 years, the mandibular first molar dentoalveolar height was 24.4 ±






horizontal group (Figure 12). Dentoalveolar height differences at the mandibular first molar, found



Figure 12. Directional Classification: Dentoalveolar heights at the mandibular first molar site in males

41

Proportionate classification


i. Females

The maxillary central incisor dentoalveolar heights (U1) for the three female proportionate growth

pattern groups are as follows. For females at age 9 years, the maxillary central incisor dentoalveolar

height was 20.1 ± 1.6 mm for the short group, 22.4 ± 1.7 mm for the average group, and 23.6 ± 1.3 mm

for the long group. For females at age 12 years, the maxillary central incisor dentoalveolar height was

21.0 ± 1.6 mm for the short group, 23.7 ± 1.9 mm for the average group, and 25.2 ± 1.8 mm for the long

group. For females at age 14 years, the maxillary central incisor dentoalveolar height was 21.4 ± 1.5 mm

for the short group, 24.3 ± 2.0 mm for the normal group, and 25.8 ± 1.6 mm for the long group. For

females at age 16 years, the maxillary central incisor dentoalveolar height was 21.7 ± 1.4 mm for the

short group, 24.8 ± 2.0 mm for the average group, and 26.5 ± 1.6 mm for the long group (Figure 13).

Dentoalveolar height differences at the maxillary central incisor, found between the female

proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall

analysis and at all four time points.

Figure 13. Proportionate Classification: Dentoalveolar heights at the maxillary central incisor site in

females

42

ii. Males

The maxillary central incisor dentoalveolar heights (U1) for the three male proportionate growth pattern

groups are as follows. For males at age 9 years, the maxillary central incisor dentoalveolar height was


group. For males at age 12 years, the maxillary central incisor dentoalveolar height was 23.0 ± 1.5 mm

for the short group, 24.2 ± 1.6 mm for the average group, and 26.9 ± 1.1 mm for the long group. For

males at age 14 years, the maxillary central incisor dentoalveolar height was 23.6 ± 1.2 mm for the short

group, 25.0 ± 1.6 mm for the normal group, and 28.1 ± 1.2 mm for the long group. For males at age 16

years, the maxillary central incisor dentoalveolar height was 24.4 ± 1.1 mm for the short group, 25.9 ±

1.7 mm for the average group, and 28.9 ± 1.3 mm for the long group (Figure 14). Dentoalveolar height

differences at the maxillary central incisor, found between the male proportionate growth pattern

groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time

points.

Figure 14. Proportionate Classification: Dentoalveolar heights at the maxillary central incisor site in males

43


i. Females

The maxillary first molar dentoalveolar heights (U6) for the three female proportionate growth pattern

groups are as follows. For females at age 9 years, the maxillary molar dentoalveolar height was 14.9 ±

1.3 mm for the short group, 15.9 ± 1.2 mm for the average group, and 16.6 ± 1.4 mm for the long group.

For females at age 12 years, the maxillary first molar dentoalveolar height was 16.6 ± 1.2 mm for the

short group, 17.9 ± 1.4 mm for the average group, and 18.9 ± 1.6 mm for the long group. For females at

age 14 years, the maxillary first molar dentoalveolar height was 17.9 ± 1.3 mm for the short group, 19.4

± 1.6 mm for the average group, and 20.5 ± 1.5 mm for the long group. For females at age 16 years, the

maxillary first molar dentoalveolar height was 18.4 ± 1.2 mm for the short group, 20.0 ± 1.7 mm for the

average group, and 21.6 ± 1.2mm for the long group (Figure 15). Dentoalveolar height differences at the

maxillary first molar, found between the female proportionate growth pattern groups at ages 9, 12, 14,

and 16 years were significant, both in the overall analysis and at all four time points.

Figure 15. Proportionate Classification: Dentoalveolar heights at the maxillary first molar site in females

44

ii. Males

The maxillary first molar dentoalveolar heights (U6) for the three male proportionate growth pattern

groups are as follows. For males at age 9 years, the maxillary molar dentoalveolar height was 14.7 ± 1.1

mm for the short group, 16.3 ± 1.6 mm for the average group, and 16.7 ± 1.3 mm for the long group. For

males at age 12 years, the maxillary first molar dentoalveolar height was 16.2 ± 1.2 mm for the short

group, 18.2 ± 1.8 mm for the average group, and 19.1 ± 1.1 mm for the long group. For males at age 14

years, the maxillary first molar dentoalveolar height was 17.6 ± 1.5 mm for the short group, 19.7 ± 1.9

mm for the average group, and 20.8 ± 1.2 mm for the long group. For males at age 16 years, the

maxillary first molar dentoalveolar height was 19.3 ± 1.5 mm for the short group, 21.3 ± 1.9 mm for the

average group, and 22.4 ± 1.2 mm for the long group (Figure 16). Dentoalveolar height differences at the

maxillary first molar, found between the male proportionate growth pattern groups at ages 9, 12, 14,

and 16 years were significant, both in the overall analysis and at all four time points.

Figure 16. Proportionate Classification: Dentoalveolar heights at the maxillary first molar site in males

45


i. Females

The mandibular central incisor dentoalveolar heights (L1) for the three female proportionate growth

pattern groups are as follows. For females at age 9 years, the mandibular central incisor dentoalveolar


for the long group. For females at age 12 years, the mandibular central incisor dentoalveolar height was


group. For females at age 14 years, the mandibular central incisor dentoalveolar height was 31.8 ± 1.9

mm for the short group, 33.4 ± 1.6 mm for the average group, and 35.2 ± 1.4 mm for the long group.

For females at age 16 years, the mandibular central incisor dentoalveolar height was 32.1 ± 1.8 mm for

the short group, 34.0 ± 1.8 mm for the average group, and 35.7 ± 1.4 mm for the long group (Figure 17).

Dentoalveolar height differences at the mandibular central incisor, found between the female



Figure 17. Proportionate Classification: Dentoalveolar heights at the mandibular central incisor site in

females

46

ii. Males

The mandibular central incisor dentoalveolar heights (L1) for the three male proportionate growth

pattern groups are as follows. For males at age 9 years, the mandibular central incisor dentoalveolar


for the long group. For males at age 12 years, the mandibular central incisor dentoalveolar height was


group. For males at age 14 years, the mandibular central incisor dentoalveolar height was 32.9 ± 1.6

mm for the short group, 34.9 ± 2.4 mm for the average group, and 37.1 ± 2.1 mm for the long group.

For males at age 16 years, the mandibular central incisor dentoalveolar height was 34.4 ± 1.4 mm for the

short group, 36.3 ± 2.2 mm for the average group, and 38.6 ± 2.2 mm for the long group (Figure 18).

Dentoalveolar height differences at the mandibular central incisor, found between the male



Figure 18. Proportionate Classification: Dentoalveolar heights at the mandibular central incisor site in

males

47


i. Females

The mandibular first molar dentoalveolar heights (L6) for the three female proportionate growth pattern

groups are as follows. For females at age 9 years, the mandibular first molar dentoalveolar height was


group. For females at age 12 years, the mandibular first molar dentoalveolar height was 23.6 ± 1.4 mm

for the short group, 24.6 ± 1.5 mm for the average group, and 25.8 ± 1.4 mm for the long group. For

females at age 14 years, the mandibular first molar dentoalveolar height was 24.4 ± 1.5 mm for the

short group, 25.5 ± 1.8 mm for the average group, and 27.4 ± 1.5 mm for the long group. For females at

age 16 years, the mandibular first molar dentoalveolar height was 25.0 ± 1.6 mm for the short group,

26.2 ± 2.0 mm for the average group, and 28.0 ± 1.7 mm for the long group (Figure 19). Dentoalveolar

height differences at the mandibular first molar, found between the female proportionate growth

pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four

time points.

Figure 19. Proportionate Classification: Dentoalveolar heights at the mandibular first molar site in

females

48

ii. Males

The mandibular first molar dentoalveolar heights (L6) for the three male proportionate growth pattern

groups are as follows. For males at age 9 years, the mandibular first molar dentoalveolar height was


group. For males at age 12 years, the mandibular first molar dentoalveolar height was 23.8 ± 1.3 mm for

the short group, 24.2 ± 2.0 mm for the average group, and 26.5 ± 1.3 mm for the long group. For males

at age 14 years, the mandibular first molar dentoalveolar height was 24.8 ± 1.0 mm for the short group,

25.8 ± 2.3 mm for the average group, and 28.1 ± 1.8 mm for the long group. For males at age 16 years,

the mandibular first molar dentoalveolar height was 26.2 ± 1.4 mm for the short group, 27.6 ± 2.2 mm

for the average group, and 29.8 ± 1.9 mm for the long group (Figure 20). Dentoalveolar height

differences at the mandibular first molar, found between the male proportionate growth pattern groups

at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points.

Figure 20. Proportionate Classification: Dentoalveolar heights at the mandibular first molar site in males

49

B. Dentoalveolar height growth rates

Between group one-way ANOVA analyses were used to test for significant differences of the

dentoalveolar height growth rates among the classified groups within each gender for three time

periods (9 to 12 years, 12 to 14 years, and 14 to 16 years) for all four dentoalveolar sites (U1, U6, L1, and

L6). The following results describe the dentoalveolar height growth rates of the different groups within

the sample for each site, time period and gender, and can be found in table format in Appendices 3 and

4.

Directional classification


i. Females

The maxillary central incisor (U1) dentoalveolar height growth rates for the three female directional

growth pattern groups are as follows. For females during the 9 to 12 year period, the maxillary central

incisor dentoalveolar height growth rate was 0.38 ± 0.31 mm/yr for the horizontal group, 0.41 ± 0.24

mm/yr for the average group, and 0.53 ± 0.25 mm/yr for the vertical group. For females during the 12

to 14 year period, the maxillary central incisor dentoalveolar height growth rate was 0.26 ± 0.2 mm/yr

for the horizontal group, 0.3 ± 0.21 mm/yr for the average group, and 0.42 ± 0.25 mm/yr for the vertical

group. For females during the 14 to 16 year period, the maxillary central incisor dentoalveolar height

growth rate was 0.19 ± 0.21 mm/yr for the horizontal group, 0.22 ± 0.19 mm/yr for the average group,

and 0.19 ± 0.16 mm/yr for the vertical group. No statistically significant differences in maxillary central

incisor dentoalveolar height growth rates were found between the female directional growth pattern

groups for any of the three time periods.

50

Figure 21. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor

site in females in the 9 to 12 year period



51



52

ii. Males

The maxillary central incisor (U1) dentoalveolar height growth rates for the three male directional

growth pattern groups are as follows. For males during the 9 to 12 year period, the maxillary central


mm/yr for the average group, and 0.59 ± 0.27 mm/yr for the vertical group. For males during the 12 to

14 year period, the maxillary central incisor dentoalveolar height growth rate was 0.5 ± 0.27 mm/yr for

the horizontal group, 0.42 ± 0.29 mm/yr for the average group, and 0.3 ± 0.31 mm/yr for the vertical

group. For males during the 14 to 16 year period, the maxillary central incisor dentoalveolar height


and 0.53 ± 0.3 mm/yr for the vertical group. No statistically significant differences in maxillary central

incisor dentoalveolar height growth rates were found between the male directional growth pattern



site in males in the 9 to 12 year period

53





54


i. Females

The maxillary first molar (U6) dentoalveolar height growth rates for the three female directional growth

pattern groups are as follows. For females during the 9 to 12 year period, the maxillary first molar

dentoalveolar height growth rate was 0.63 ± 0.3 mm/yr for the horizontal group, 0.66 ± 0.23 mm/yr for

the average group, and 0.72 ± 0.19 mm/yr for the vertical group. For females during the 12 to 14 year

period, the maxillary first molar dentoalveolar height growth rate was 0.65 ± 0.23 mm/yr for the

horizontal group, 0.74 ± 0.26 mm/yr for the average group, and 0.83 ± 0.24 mm/yr for the vertical

group. For females during the 14 to 16 year period, the maxillary first molar dentoalveolar height


and 0.27 ± 0.27 mm/yr for the vertical group. No statistically significant differences in maxillary first

molar dentoalveolar height growth rates were found between the female directional growth pattern


Figure 27. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in

females in the 9 to 12 year period

55





56

ii. Males

The maxillary first molar (U6) dentoalveolar height growth rates for the three male directional growth

pattern groups are as follows. For males during the 9 to 12 year period, the maxillary first molar


the average group, and 0.62 ± 0.3 mm/yr for the vertical group. For males during the 12 to 14 year

period, the maxillary first molar dentoalveolar height growth rate was 0.76 ± 0.36 mm/yr for the

horizontal group, 0.73 ± 0.23 mm/yr for the average group, and 0.91 ± 0.46 mm/yr for the vertical

group. For males during the 14 to 16 year period, the maxillary first molar dentoalveolar height growth

rate was 0.72 ± 0.52 mm/yr for the horizontal group, 0.84 ± 0.35 mm/yr for the average group, and 0.82

± 0.47 mm/yr for the vertical group. No statistically significant differences in maxillary first molar

dentoalveolar height growth rates were found between the male directional growth pattern groups for

any of the three time periods.


males in the 9 to 12 year period

57





58


i. Females

The mandibular central incisor (L1) dentoalveolar height growth rates for the three female directional

growth pattern groups are as follows. For females during the 9 to 12 year period, the mandibular

central incisor dentoalveolar height growth rate was 0.47 ± 0.15 mm/yr for the horizontal group, 0.6 ±

0.25 mm/yr for the average group, and 0.62 ± 0.12 mm/yr for the vertical group. For females during the

12 to 14 year period, the mandibular central incisor dentoalveolar height growth rate was 0.27 ± 0.25

mm/yr for the horizontal group, 0.47 ± 0.29 mm/yr for the average group, and 0.61 ± 0.32 mm/yr for the

vertical group. For females during the 14 to 16 year period, the mandibular central incisor dentoalveolar

height growth rate was 0.24 ± 0.15 mm/yr for the horizontal group, 0.24 ± 0.15 mm/yr for the average

group, and 0.32 ± 0.12 mm/yr for the vertical group. No statistically significant differences in

mandibular central incisor dentoalveolar height growth rates were found between the female

directional growth pattern groups for any of the three time periods.

Figure 33. Directional Classification: Dentoalveolar height growth rate at the mandibular central incisor


59





60

ii. Males

The mandibular central incisor (L1) dentoalveolar height growth rates for the three male directional

growth pattern groups are as follows. For males during the 9 to 12 year period, the mandibular central


mm/yr for the average group, and 0.72 ± 0.29 mm/yr for the vertical group. For males during the 12 to

14 year period, the mandibular central incisor dentoalveolar height growth rate was 0.97 ± 0.37 mm/yr

for the horizontal group, 0.82 ± 0.39 mm/yr for the average group, and 0.79 ± 0.32 mm/yr for the

vertical group. For males during the 14 to 16 year period, the mandibular central incisor dentoalveolar



mandibular central incisor dentoalveolar height growth rates were found between the male directional

growth pattern groups for any of the three time periods.



61





62


i. Females

The mandibular first molar (L6) dentoalveolar height growth rates for the three female directional

growth pattern groups are as follows. For females during the 9 to 12 year period, the mandibular first

molar dentoalveolar height growth rate was 0.33 ± 0.21 mm/yr for the horizontal group, 0.45 ± 0.24

mm/yr for the average group, and 0.53 ± 0.17 mm/yr for the vertical group. For females during the 12

to 14 year period, the mandibular first molar dentoalveolar height growth rate was 0.41 ± 0.32 mm/yr

for the horizontal group, 0.51 ± 0.36 mm/yr for the average group, and 0.52 ± 0.53 mm/yr for the

vertical group. For females during the 14 to 16 year period, the mandibular first molar dentoalveolar



mandibular first molar dentoalveolar height growth rates were found between the female directional

growth pattern groups for any of the three time periods.

Figure 39. Directional Classification: Dentoalveolar height growth rate at the mandibular first molar site

in females in the 9 to 12 year period

63





64

ii. Males

The mandibular first molar (L6) dentoalveolar height growth rates for the three male directional growth

pattern groups are as follows. For males during the 9 to 12 year period, the mandibular first molar


the average group, and 0.36 ± 0.15 mm/yr for the vertical group. For males during the 12 to 14 year

period, the mandibular first molar dentoalveolar height growth rate was 0.78 ± 0.47 mm/yr for the

horizontal group, 0.77 ± 0.51 mm/yr for the average group, and 0.79 ± 0.4 mm/yr for the vertical group.

For males during the 14 to 16 year period, the mandibular first molar dentoalveolar height growth rate

was 0.97 ± 0.4 mm/yr for the horizontal group, 0.83 ± 0.38 mm/yr for the average group, and 0.84 ±

0.54 mm/yr for the vertical group. No statistically significant differences in mandibular first molar

dentoalveolar height growth rates were found between the male directional growth pattern groups for

any of the three time periods.


in males in the 9 to 12 year period

65





66

Proportionate classification


i. Females

The maxillary central incisor (U1) dentoalveolar height growth rates for the three female proportionate

growth pattern groups are as follows. For females during the 9 to 12 year period, the maxillary central

incisor dentoalveolar height growth rate was 0.29 ± 0.26 mm/yr for the short group, 0.44 ± 0.24 mm/yr

for the average group, and 0.53 ± 0.23 mm/yr for the long group. For females during the 12 to 14 year

period, the maxillary central incisor dentoalveolar height growth rate was 0.2 ± 0.13 mm/yr for the short

group, 0.36 ± 0.21 mm/yr for the average group, and 0.32 ± 0.26 mm/yr for the long group. For females

during the 14 to 16 year period, the maxillary central incisor dentoalveolar height growth rate was 0.17

± 0.18 mm/yr for the short group, 0.18 ± 0.17 mm/yr for the average group, and 0.33 ± 0.19 mm/yr for

the long group. No statistically significant differences in maxillary central incisor dentoalveolar height

growth rates were found between the female proportionate growth pattern groups for any of the three

time periods.

Figure 45. Proportionate Classification: Dentoalveolar height growth rate at the maxillary central incisor


67





68

ii. Males

The maxillary central incisor (U1) dentoalveolar height growth rates for the three male proportionate

growth pattern groups are as follows. For males during the 9 to 12 year period, the maxillary central


for the average group, and 0.58 ± 0.36 mm/yr for the long group. For males during the 12 to 14 year

period, the maxillary central incisor dentoalveolar height growth rate was 0.28 ± 0.32 mm/yr for the

short group, 0.38 ± 0.29 mm/yr for the average group, and 0.58 ± 0.21 mm/yr for the long group. For

males during the 14 to 16 year period, the maxillary central incisor dentoalveolar height growth rate was

0.41 ± 0.25 mm/yr for the short group, 0.43 ± 0.28 mm/yr for the average group, and 0.42 ± 0.33 mm/yr

for the long group. No statistically significant differences in maxillary central incisor dentoalveolar

height growth rates were found between the male proportionate growth pattern groups for any of the

three time periods.



69





70


i. Females

The maxillary first molar (U6) dentoalveolar height growth rates for the three female proportionate

growth pattern groups are as follows. For females during the 9 to 12 year period, the maxillary first

molar dentoalveolar height growth rate was 0.59 ± 0.21 mm/yr for the short group, 0.67 ± 0.24 mm/yr


period, the maxillary first molar dentoalveolar height growth rate was 0.63 ± 0.29 mm/yr for the short


during the 14 to 16 year period, the maxillary first molar dentoalveolar height growth rate was 0.25 ±

0.19 mm/yr for the short group, 0.3 ± 0.23 mm/yr for the average group, and 0.53 ± 0.42 mm/yr for the

long group. Statistically significant differences in maxillary first molar dentoalveolar height growth rates

were found between the female proportionate growth pattern groups (short versus long) during the 14

to 16 year period.

Figure 51. Proportionate Classification: Dentoalveolar height growth rate at the maxillary first molar site


71





72

ii. Males

The maxillary first molar (U6) dentoalveolar height growth rates for the three male proportionate

growth pattern groups are as follows. For males during the 9 to 12 year period, the maxillary first molar

dentoalveolar height growth rate was 0.5 ± 0.13 mm/yr for the short group, 0.64 ± 0.31 mm/yr for the

average group, and 0.83 ± 0.38 mm/yr for the long group. For males during the 12 to 14 year period,

the maxillary first molar dentoalveolar height growth rate was 0.7 ± 0.43 mm/yr for the short group,

0.78 ± 0.27 mm/yr for the average group, and 0.82 ± 0.31 mm/yr for the long group. For males during

the 14 to 16 year period, the maxillary first molar dentoalveolar height growth rate was 0.87 ± 0.45

mm/yr for the short group, 0.79 ± 0.39 mm/yr for the average group, and 0.82 ± 0.43 mm/yr for the long

group. No statistically significant differences in maxillary first molar dentoalveolar height growth rates

were found between the male proportionate growth pattern groups for any of the three time periods.



73





74


i. Females

The mandibular central incisor (L1) dentoalveolar height growth rates for the three female

proportionate growth pattern groups are as follows. For females during the 9 to 12 year period, the

mandibular central incisor dentoalveolar height growth rate was 0.62 ± 0.2 mm/yr for the short group,

0.57 ± 0.23 mm/yr for the average group, and 0.59 ± 0.17 mm/yr for the long group. For females during

the 12 to 14 year period, the mandibular central incisor dentoalveolar height growth rate was 0.37 ±


long group. For females during the 14 to 16 year period, the mandibular central incisor dentoalveolar

height growth rate was 0.17 ± 0.14 mm/yr for the short group, 0.28 ± 0.14 mm/yr for the average group,

and 0.25 ± 0.15 mm/yr for the long group. No statistically significant differences in mandibular central

incisor dentoalveolar height growth rates were found between the female proportionate growth pattern


Figure 57. Proportionate Classification: Dentoalveolar height growth rate at the mandibular central

incisor site in females in the 9 to 12 year period

75





76

ii. Males

The mandibular central incisor (L1) dentoalveolar height growth rates for the three male proportionate

growth pattern groups are as follows. For males during the 9 to 12 year period, the mandibular central


for the average group, and 0.74 ± 0.25 mm/yr for the long group. For males during the 12 to 14 year

period, the mandibular central incisor dentoalveolar height growth rate was 0.57 ± 0.22 mm/yr for the

short group, 0.9 ± 0.4 mm/yr for the average group, and 0.88 ± 0.3 mm/yr for the long group. For males

during the 14 to 16 year period, the mandibular central incisor dentoalveolar height growth rate was

0.76 ± 0.31 mm/yr for the short group, 0.72 ± 0.39 mm/yr for the average group, and 0.75 ± 0.56 mm/yr

for the long group. Statistically significant differences in mandibular central incisor dentoalveolar height

growth rates were found between the male proportionate growth pattern groups (short versus long) for

both the 9 to 12 year and 12 to 14 year periods.


incisor site in males in the 9 to 12 year period

77





78


i. Females

The mandibular first molar (L6) dentoalveolar height growth rates for the three female proportionate

growth pattern groups are as follows. For females during the 9 to 12 year period, the mandibular first

molar dentoalveolar height growth rate was 0.41 ± 0.31 mm/yr for the short group, 0.46 ± 0.21 mm/yr


period, the mandibular first molar dentoalveolar height growth rate was 0.39 ± 0.3 mm/yr for the short


during the 14 to 16 year period, the mandibular first molar dentoalveolar height growth rate was 0.31 ±


long group. Statistically significant differences in mandibular first molar dentoalveolar height growth

rates were found between the female proportionate growth pattern groups (short versus long, average

versus long) for the 12 to 14 year period.

Figure 63. Proportionate Classification: Dentoalveolar height growth rate at the mandibular first molar


79





80

ii. Males

The mandibular first molar (L6) dentoalveolar height growth rates for the three male proportionate

growth pattern groups are as follows. For males during the 9 to 12 year period, the mandibular first

molar dentoalveolar height growth rate was 0.39 ± 0.2 mm/yr for the short group, 0.37 ± 0.2 mm/yr for

the average group, and 0.36 ± 0.24 mm/yr for the long group. For males during the 12 to 14 year

period, the mandibular first molar dentoalveolar height growth rate was 0.47 ± 0.5 mm/yr for the short

group, 0.84 ± 0.45 mm/yr for the average group, and 0.82 ± 0.47 mm/yr for the long group. For males

during the 14 to 16 year period, the mandibular first molar dentoalveolar height growth rate was 0.73 ±


long group. No statistically significant differences in mandibular first molar dentoalveolar height growth

rates were found between the male proportionate growth pattern groups for any of the three time

periods.



81





82

C. Evaluation of the effect of gender on dentoalveolar height growth rates

Independent t-tests were used to evaluate for gender differences in dentoalvoeolar height growth rates

for each dentoalveolar site (U1, U6, L1, L6) and for each time period (9 to 12 years, 12 to 14 years, and

14 to 16 years). The following results describe the dentoalveolar height growth rates of the entire

female and male sample for each site and time period, and can be found in table format in Appendix 5.

Dentoalveolar Height Growth Rates

a. Maxillary central incisor (U1)

The maxillary central incisor (U1) dentoalveolar height growth rates for the entire female and male

samples are as follows. For female and male samples during the 9 to 12 year period, the maxillary

central incisor dentoalveolar height growth rate was 0.42 ± 0.25 mm/yr and 0.46 ± 0.28 mm/yr,

respectively. For female and male samples during the 12 to 14 year period, the maxillary central incisor

dentoalveolar height growth rate was 0.31 ± 0.21mm/yr and 0.41 ± 0.29 mm/yr, respectively. For female

and male samples during the 14 to 16 year period, the maxillary central incisor dentoalveolar height

growth rate was 0.21 ± 0.19 mm/yr and 0.42 ± 0.28 mm/yr, respectively. Statistically significant gender

differences were found between maxillary central incisor dentoalveolar height growth rates during the

14 to 16 year time period.

Figure 69. Evaluation of the effect of gender: Dentoalveolar height growth rate at the maxillary central

incisor site for the 9 to 12 year period

83





84


The maxillary first molar (U6) dentoalveolar height growth rates for the entire female and male samples

are as follows. For female and male samples during the 9 to 12 year period, the maxillary first molar

dentoalveolar height growth rate was 0.67 ± 0.24 mm/yr and 0.65 ± 0.32 mm/yr, respectively. For

female and male samples during the 12 to 14 year period, the maxillary first molar dentoalveolar height

growth rate was 0.74 ± 0.25 mm/yr and 0.77 ± 0.31 mm/yr, respectively. For female and male samples

during the 14 to 16 year period, the maxillary first molar dentoalveolar height growth rate was 0.33 ±

0.28 mm/yr and 0.81 ± 0.4 mm/yr, respectively. Statistically significant gender differences were found

between maxillary first molar dentoalveolar height growth rates during the 14 to 16 year time period.

Figure 72. Evaluation of the effect of gender: Dentoalveolar height growth rate at the maxillary first

molar site for the 9 to 12 year period

85





86


The mandibular central incisor (L1) dentoalveolar height growth rates for the entire female and male

samples are as follows. For female and male samples during the 9 to 12 year period, the mandibular

central incisor dentoalveolar height growth rate was 0.58 ± 0.22 mm/yr and 0.6 ± 0.26 mm/yr,

respectively. For female and male samples during the 12 to 14 year period, the mandibular central

incisor dentoalveolar height growth rate was 0.46 ± 0.3 mm/yr and 0.84 ± 0.37 mm/yr, respectively. For

female and male samples during the 14 to 16 year period, the mandibular central incisor dentoalveolar

height growth rate was 0.25 ± 0.15 mm/yr and 0.73 ± 0.41 mm/yr, respectively. Statistically significant

gender differences were found between mandibular central incisor dentoalveolar height growth rates

during the 12 to 14 year 14 to 16 year time periods.

Figure 75. Evaluation of the effect of gender: Dentoalveolar height growth rate at the mandibular

central incisor site for the 9 to 12 year period

87





88


The mandibular first molar (L6) dentoalveolar height growth rates for the entire female and male

samples are as follows. For female and male samples during the 9 to 12 year period, the mandibular first

molar dentoalveolar height growth rate was 0.44 ± 0.23 mm/yr and 0.37 ± 0.21 mm/yr, respectively. For

female and male samples during the 12 to 14 year period, the mandibular first molar dentoalveolar

height growth rate was 0.5 ± 0.38 mm/yr and 0.77 ± 0.48 mm/yr, respectively. For female and male

samples during the 14 to 16 year period, the mandibular first molar dentoalveolar height growth rate

was 0.33 ± 0.25 mm/yr and 0.85 ± 0.41 mm/yr, respectively. Statistically significant gender differences

were found between mandibular first molar dentoalveolar height growth rates during the 12 to 14 year

and 14 to 16 year time periods.

Figure 78. Evaluation of the effect of gender: Dentoalveolar height growth rate at the mandibular first


89





90

Discussion

For orthodontists, management of the vertical dimension is often a top priority due to the associated

complexity and difficulty. Though vertical dysplasias typically present in certain fashions, they can take

many forms, owing to dental compensation mechanisms at both the molar and incisor levels (Beckmann

et al., 1998). Cross-sectional research by Janson et al. (1994) found that dentoalveolar heights at age 12

years are significantly different between subjects with long, average, and short lower face height (LFH)

growth patterns (i.e. proportionate classification method), except for the mandibular first molar

dentoalveolar height which showed no difference between short and average LFH subjects. However,

minimal longitudinal research has been performed to explicitly evaluate the dentoalveolar heights or

dentoalveolar height growth rates of skeletal Class I subjects grouped into craniofacial growth patterns

by any method of classification (i.e. angular, linear, or proportionate).

Modifying dentoalveolar height growth is accepted as a standard treatment protocol for managing

vertical skeletal discrepancies and dentofacial deformities that are not severe enough to warrant

orthognathic surgical correction. In addition, continuation of an initial growth pattern after completion

of orthodontic treatment is a major cause of relapse and requires careful management (Nanda and

Nanda, 1992). Consequently, the ability to accurately recognize relationships between various

craniofacial growth patterns and dentoalveolar height patterns may potentially benefit orthodontic

diagnosis, treatment planning, and biomechanical selection. Therefore, the present study was

undertaken to determine if significant differences in maxillary and mandibular dentoalveolar heights

and dentoalveolar height growth rates exist between skeletal Class I subjects that exhibit differing

craniofacial growth patterns when classified by directional and proportionate methods.

When the subjects were classified by the directional (change in Y-axis) method, the dentoalveolar

heights of maxillary and mandibular first molars and central incisors did not differ significantly (p>0.05)

between vertical, average, and horizontal growth pattern groups, irrespective of gender. No significant

differences were found among any of the studied dentoalveolar sites (U1, U6, L1, and L6), neither in

overall or individual assessments at ages 9, 12, 14, and 16 years. For example, the maxillary first molar

dentoalveolar height for females at age 12 years was 18.3 ± 1.3 mm for the vertical group, 17.7 ± 1.4

mm for the average group, and 17.8 ± 2.2 mm for the horizontal group. For males at age 12 years, the

maxillary first molar dentoalvoelar height was 17.9 ± 1.4 mm for the vertical group, 18.1 ± 2.1 mm for

91

the average group, and 18.1 ± 1.6 mm for the horizontal group. Both instances reflect dentoalveolar

height patterns that seem counter-intuitive when compared to expectations set forth by previous

research, which would be to likely find increased dentoalveolar height dimensions with increased facial

divergency, and vice versa.

Though controversy does exist in the literature, a common finding of hyperdivergent (i.e. high

mandibular plane angle, skeletal open bite) subjects is an increase in the dentoalveolar height of

maxillary and mandibular molars (Kucera et al., 2011; Schendel et al., 1976; Schudy, 1964 and 1965;

Bjork, 1969; Bjork and Skieller, 1972; Sassouni and Nanda, 1964; Isaacson et al., 1971; Nahoum, 1977)

and maxillary and mandibular incisors (Kucera et al., 2011; Cangialosi, 1984; Schendel et al., 1976;

Sassouni and Nanda, 1964; Isaacson et al., 1971). Closely related, Schudy (1965) found that the

relationship of facial height to depth has a very high correlation with the Y-axis angle. In simple terms,

an individual with a relatively greater amount of vertical than horizontal growth will experience an

opening of the Y-axis angle and vice versa for an individual possessing a horizontal growth pattern.

Utilizing a similar sample from the Burlington Growth Centre divided according to the directional

classification method, Lee (2010) found a clinically significant difference in the mean age of peak

mandibular growth (PMG) in females. The female vertical growth pattern group possessed a mean age

at PMG of 11.7 +/- 0.8 years in comparison to the average and horizontal groups, which had a mean age

at PMG of 13.0 +/- 0.7 years and 12.9 +/- .8 years, respectively (Lee, 2010). Since the growth of the

mandible is largely responsible for the change in the relationship between the maxilla and mandible

(Harvold, 1963) and the dentoalveolar units respond via vertical compensation to maintain occlusal

contact succeeding vertical skeletal growth, the three directional growth pattern groups provide

considerably different environments for vertical dentoalveolar development to occur within. As a result,

one might reasonably expect that dentoalveolar heights would be influenced by the vertical facial

development, or lack thereof. However, the lack of significant differences (p>0.05) in dentoalveolar

heights and dentoalveolar height growth rates between directional growth pattern groups evaluated

both in the overall analysis as well as at all four time points (9, 12, 14, and 16 years) is in direct conflict

with such expectations. Consequently, vertical dentoalveolar height development seems to be

independent of the directional growth pattern of the face.

92

Alternatively, when the subjects were classified by the proportionate (UFH:LFH) method, the maxillary

and mandibular first molar and central incisor dentoalveolar heights differed significantly (p<0.05)

between long, average, and short lower face height (LFH) growth pattern groups, in both genders.

Significant differences in dentoalveolar heights at each dentoalveolar site (U1, U6, L1, and L6) were

found both individually at ages 9, 12, 14, and 16 years and in the overall analysis for each site. This

study’s longitudinal results corroborated the cross-sectional findings of Janson et al. (1994) that there is

an inverse relationship between the dentoalveolar heights and the UFH:LFH ratio; that is, as the ratio

increases (i.e. LFH shortens), the dentoalveolar height decreases. Janson et al. (1994) evaluated the

relationship only at age 12 years and noted that extrapolation to different age ranges must be made

cautiously.

Both the male and female samples were consistent in the inverse relationship of UFH:LFH to

dentoalveolar height for each dentoalveolar site at ages 9, 12, 14 and 16 years. For example, the

maxillary central incisor (U1) dentoalveolar height for males at age 12 years was 23.0 ± 1.5 mm for the

short LFH group, 24.2 ± 1.6 mm for the average LFH group, and 26.9 ± 1.1 mm for the long LFH group.

For females at age 12 years, the mandibular first molar (L6) dentoalveolar height was 23.6 ± 1.4 mm for

the short LFH group, 24.6 ± 1.5 mm for the average LFH group, and 25.8 ± 1.4 mm for the long LFH

group. The same trend for both female and male proportionate groups existed over all ages for all

dentoalveolar sites (U1, U6, L1, and L6). In spite of Arat and Rübendüz’s (2005) finding of regional

differences in alveolar development during pubertal growth, the current study’s results confirm the

constancy of the inverse relationship of UFH:LFH to dentoalveolar height for all four dentoalveolar sites

at ages 9, 12, 14, and 16 years.

In accordance with previous research (Janson et al., 1994; Schendel et al., 1976; Fields et al., 1984), all

dentoalveolar heights in long LFH subjects were significantly greater (p<0.05) than in average LFH

subjects. However, in regards to the short LFH subjects, the present study’s findings are in direct

conflict with previous work (Opdebeek and Bell, 1978; Janson et al., 1994). Those two studies found

that in the short LFH group, all dentoalveolar heights were significantly shorter than in the average LFH

group, with the exception of the mandibular first molar. In particular, the difference between the

present study’s findings and those of Janson et al. (1994) was unexpected since the sample source (i.e.

Burlington Growth Centre files) was the same. However, the findings of Janson et al. (1994) were based

93

on an aggregate of the male and female dentoalveolar data, rather than evaluating each gender

separately as was done in the current study.

For both genders, graphical representations (Figures 13 to 20) of dentoalveolar height growth in the

sample classified into groups by the proportionate (UFH:LFH) method clearly display three separate

trends. The long LFH group exhibits the greatest dentoalveolar heights for both genders at all ages and

sites. The short LFH group displays the shortest dentoalveolar heights with the average LFH group falling

somewhere in between. Though the interquartile ranges do overlap to a varying degree depending

upon the spread of the data, statistically significant differences in the dentoalveolar height means were

still noted. Consequently, the dentoalveolar heights of the maxillary and mandibular first molars and

central incisors at ages 9, 12, 14, and 16 years seem to be associated with an individual’s proportionate

growth pattern as determined by their UFH:LFH ratio at age 16 years. Clinically, this study’s longitudinal

findings attest to the possibility of relying on cross-sectional patient evaluations of UFH:LFH ratio to

provide information regarding an individual’s prior vertical dentoalveolar development.

Due to the longitudinal study design, dentoalveolar height growth rates (mm/year) were able to be

calculated and assessed for significant differences from ages 9 to 12 years, 12 to 14 years, and 14 to 16

years. Regarding the directional (change in Y-axis) growth pattern groups, the maxillary and mandibular

first molar and central incisor dentoalveolar height growth rates did not differ significantly (p>0.05) at

any site during all three periods, irrespective of gender. However, during the 12 to 14 year period for

females, the difference in mandibular central incisor (L1) dentoalveolar height growth rates approached

significance (p=0.06). More specifically, the female mandibular central incisor dentoalveoar height

growth rate during the 12 to 14 year period was 0.27 ± 0.25 mm/yr for the horizontal group, 0.47 ± 0.29

mm/yr for the average group, and 0.61 ± 0.32 mm/yr for the vertical group. For females during only the

9 to 12 year period and 12 to 14 year period, all absolute dentoalveolar height growth rate values (U1,

U6, L1, and L6) were smallest for the horizontal growth pattern groups and largest for the vertical

growth pattern groups, though often marginally. Conversely, the male absolute dentoalveolar height

growth rate values generally exhibited no consistent pattern for any time period. For example, during

the 12 to 14 year period, the male mandibular central (L1) incisor dentoalveolar height growth rate was

0.97 ± 0.37 mm/yr for the horizontal group, 0.82 ± 0.39 mm/yr for the average group, and 0.79 ± 0.32

mm/yr for the vertical group. For males during the 12 to 14 year period, the mandibular first molar (L6)


94

the average group, and 0.79 ± 0.4 mm/yr for the vertical group. Consequently, the rate of vertical

dentoalveolar height development seems to be independent of the directional growth pattern of the

face.

Since no other study has compared dentoalveolar height growth rates between craniofacial growth

pattern groups as determined by change in Y-axis angle, no direct comparisons can be made. For

reference, Karlsen (1995) evaluated craniofacial and dentoalveolar dimensions longitudinally in two

groups of males with low (≤ 26°, n=15) and high (≥ 35°, n=15) SN-MP angles for two periods: age 6 to 12

years and age 12 to 15 years. Maxillary and mandibular molar dentoalveolar heights were not

statistically different between low- and high-angle groups in either growth period. However, both

maxillary and mandibular incisor dentoalveolar heights exhibited larger growth rates (mm/yr) in the

high-angle subjects but only during the 6 to 12 year period. Unfortunately, Karlsen’s groups were

determined by their mandibular plane angles at the 12 year mark rather than the change in mandibular

plane angle over time, which would have been more similar to the directional growth pattern

classification method used in the present study and potentially allowed a more meaningful comparison

with the results of the current study.

In general, the Y-axis angle, upper to lower facial height ratio, and the mandibular plane angle tend to

differ significantly between skeletal open- and deep-bite subjects. However, the literature has shown

that various measurements used to classify vertical malocclusions (i.e. UFH:LFH, PFH:AFH, SN-MP angle,

SN-PP angle, PP-MP angle, etc.) do not necessarily always have strong inter-correlations as one might

expect (Jacob and Buschang, 2011). Similarly, Dung and Smith (1988) found that different measures of

open bite tendency identified different patients. Therefore, any dentoalveolar height growth rate

comparison to previous literature must be closely evaluated for similarity of the growth pattern

classification method.

Regarding the proportionate (UFH:LFH) growth pattern groups, select female dentoalveolar height

growth rates differed significantly during the 14 to 16 year period (maxillary first molar, U6; short versus

long LFH group) and 12 to 14 year period (mandibular first molar, L6; short versus long & average versus

long LFH groups). Concerning male proportionate growth pattern groups, mandibular central incisor

(L1) dentoalveolar height growth rates differed significantly during the 9 to 12 year period (short versus

long LFH group) and 12 to 14 year period (short versus average LFH group). Within each gender, several

95

other dentoalveolar height growth rates differences approached significance during a variety of time

periods. Since no other study has compared dentoalveolar height growth rates between proportionate

growth pattern groups as determined by the UFH:LFH ratio, no direct comparisons can be made.

However, the fact that significant differences in certain regional dentoalveolar growth rates do exist

implies that the effectiveness of orthodontic intervention may vary among different types of growers

and at different time periods.

A longitudinal study by Arat et al. (2005) showed that vertical alveolar growth exhibited regional

differentiation in early versus late pubertal growth periods. These changes are crucial for establishing

normal occlusal relations and should be taken into consideration with respect to the treatment and

stability of the treatment of vertical discrepancies (Arat et al., 2005). In late adolescence, continued

growth in the pattern that created the Class II, Class III, deep bite, or open bite problem is often a

primary cause of relapse and requires careful management during the immediate retention phase

(Nanda and Nanda, 1992). Furthermore, long-term studies have shown that very slow growth typically

continues throughout adult life, and the same pattern that led to the initial malocclusion may contribute

to the deterioration of ideal occlusal relationships many years after orthodontic treatment is completed

(Behrents, 1984). As previously mentioned, modifying dentoalveolar height growth via development or

restriction is commonly accepted as a standard treatment for managing vertical skeletal discrepancies.

For example, many orthodontic appliances (e.g. occipital or cervical-pull head gear, Twin Block

appliances designed to allow mandibular posterior eruption, temporary anchorage devices, etc.) are

commonly used to influence the vertical dentoalveolar height dimension in an attempt to correct both

vertical and antero-posterior skeletal and dental relations.

Modification of the maxillary first molar’s vertical and anteroposterior position is often a focus of

contemporary orthodontic therapy, and the implications of increased or decreased maxillary first molar

dentoalveolar height growth rates may influence the decision for a particular course of treatment.

Firouz et al. (1992) found that by directing high-pull headgear force through the center of resistance of

the maxillary molars, it was possible to accomplish simultaneously a substantial distal movement of the

molars (2.6 +/- 0.6 mm) as well as significant intrusion (0.54 +/- 0.54 mm). Utilizing cervical-pull

headgear, the relative increase in molar dentoalveolar height has been reported to be approximately 1

mm, on average (Baumrind et al., 1983; Ulger et al., 2006). Kopecky and Fishman reported that more

favorable cervical headgear treatment results were demonstrated during maturational periods that

96

were associated with a higher degree of incremental growth velocity (Kopecky and Fishman, 1993).

Consequently, the present study’s longitudinal analysis and results may be helpful in providing the

clinician with an improved understanding of the variation and potential modification of dentoalveolar

height growth rate values among proportionate growth pattern subjects over time. As a result, the

clinician may be able to intervene more concisely for a particular type of craniofacial grower in a manner

that is tailored to each individual’s orthodontic needs and expectations of future growth.

An examination of the maxillary first molar dentoalveolar height growth rates of the present study

reveals several distinctions among the various proportionate growth pattern groups. For example, the

annual dentoalveolar height growth rate for female maxillary first molars is seen to drop dramatically

after age 14 years for the short and average LFH groups. Interestingly, the long LFH group continues to

grow at a rate twice that of the short LFH group from 14 to 16 years (0.53 ± 0.42 mm/yr vs. 0.25 ± 0.19

mm/yr, respectively), which implies a longer effective window of opportunity for maxillary first molar

height modification. The extended duration and increased rate of dentoalveolar height growth of the

female maxillary first molar in the long LFH group accentuates the absolute dentoalveolar height

differences between the age of 14 and 16 years. In other words, the proportionate craniofacial growth

pattern differences are contributed by these increased dentoalveolar height growth rates and become

further differentiated in long LFH groups with previously accrued long dentoalveolar heights or short

LFH groups with relatively small dentoalveolar heights from past growth experience. The graphical

representations (Figures 15 and 16) of both genders for the maxillary first molar dentoalveolar heights

display not only three separate trends but also increased divergency over time.

The data from the current study shows that over the 2-year period from 14 to 16 years of age, the

maxillary first molar (U6) dentoalveolar height in long LFH female subjects is expected to increase by

1.06 mm, on average. Utilizing an orthodontic appliance to restrict vertical molar development, the

overbite could be deepened by nearly 2 mm according to the ratio of molar intrusion to incisor closure,

as noted in research by Sherwood et al. (2002). Furthermore, a decrease in the mandibular plane angle

and occlusal plane angle could be expected as well. Clinically speaking, management of the vertical

dimension may be effective at later chronological ages, within certain categories of subjects.

Conversely, long LFH female subjects whose orthodontic treatment is finished prior to the age of 14

years can be expected to experience a significant amount of post-treatment dentoalveolar height

growth, which may increase the potential for post-treatment relapse. Sustained skeletal growth has the

97

potential to alter the position of teeth as well as occlusal relationships, and late mandibular growth

appears to be the major contributor to post-treatment crowding that occurs later in adulthood (Proffit

et al., 2007). Since the male maxillary first molar dentoalveolar height growth rates are nearly equal for

all proportionate groups during all time periods, this indicates a broader window of opportunity to

direct male maxillary molar dimensions but also an increased potential for post-treatment relapse of all

types of proportionate growth groups for a greater period of time.

Although the maxillary first molar has been the primary dentoalveolar site utilized by high- or low-pull

headgear appliances to apply biomechanical forces, with recently developed techniques, vertical

dentoalveolar modification can also be achieved readily at the other three dentoalveolar sites. For

example, Buschang et al. (2011) utilized temporary anchorage devices (e.g. mini-screws or mini-

implants) for absolute or relative mandibular and maxillary molar intrusion in adolescents to achieve

orthopedic correction of growing hyperdivergent, retrognathic patients. In general, temporary

anchorage devices can be used to modify the vertical dentoalveolar development of nearly all dental

sites, including maxillary and mandibular incisors. The levels of absolute intrusion achieved by mini-

screws in adults have been reported to be 1.8 to 3.4 mm and 0.1 to 1.3 mm for maxillary and

mandibular first molars, respectively (Erverdi et al., 2004; Kuroda et al., 2007; Xun et al., 2007; Akay et

al., 2009, Baek et al., 2010; Park et al., 2010). Heravi et al. (2011) achieved a significant amount of

intrusion (2.1 ± 0.9 mm) of supraerupted maxillary molars but experienced a mean value of relapse of

0.4 ± 0.2 mm. The mean value for residual intrusion was 1.7 ± 0.6 mm (Heravi et al., 2011). Using bone-

anchored plates and monocortical screws, Sugawara et al. (2002) intruded mandibular first and second

molars an average of 1.7 mm and 2.8 mm, respectively. However, the average relapse rates were 27.2%

at the first molars and 30.3% at the second molars.

The female mandibular first molar dentoalveolar growth rates were nearly equal for all proportionate

groups during all time periods, except for the long LFH group during the 12 to 14 year period, which was

nearly twice as high as the others. For females during the 12 to 14 year period, the mandibular first

molar dentoalveolar growth rate was 0.39 ± 0.3 mm/yr for the short LFH group, 0.43 ± 0.35 mm/yr for

the average LFH group, and 0.82 ± 0.4 mm/yr for the long LFH group. For all three male proportionate

growth pattern groups, the mandibular first molar (L6) dentoalveolar growth rates exhibited not only an

increased but also sustained rate during the 12 to 14 year and 14 to 16 year periods. The increased rate

of mandibular molar dentoalveolar height development during the middle growth period for long LFH

98

females and all male proportionate groups may offer clinicians an adjunct site for relative or absolute

intrusion, if maxillary molar dentoalveolar control alone is deemed to be insufficient. However, valid

concern exists regarding post-treatment occlusal stability due to continued dentoalveolar growth and an

expected intrusion relapse rate of approximately 20 to 30% (Sugawara et al., 2002; Baek et al., 2010;

Heravi et al., 2011).

The maxillary and mandibular central incisor (U1, L1) dentoalveolar height growth rates among the

three male and female proportionate growth pattern groups are unremarkable due to their relative

uniformity across all time points. As such, the steady vertical dentoalveolar development maintains the

general proportionate growth patterns differences with only a slight amount of differences among the

three groups over time. For example, the graphical representation of the male mandibular central

incisor dentoalveolar heights (Figure 18) shows a small increase in the interquartile and mean

dentoalveolar height differences of the three proportionate groups from age 9 to 16 years.

Significant gender differences were found between mandibular central incisor (L1) dentoalveolar growth

rates during the 12 to 14 year and 14 to 16 year time periods. For the female and male samples during

the 12 to 14 year period, the mandibular central incisor dentoalveolar growth rate was 0.46 ± 0.3 mm/yr

and 0.84 ± 0.37 mm/yr, respectively. For the female and male samples during the 14 to 16 year period,

the mandibular central incisor dentoalveolar growth rate was 0.25 ± 0.15 mm/yr and 0.73 ± 0.41 mm/yr,

respectively. The significant differences are likely due to the gender variation in overall size and

pubertal growth spurt intensity and duration. Though a high degree of individual variation exists, the

pubertal growth spurt occurs, on average, nearly 2 years earlier in females than in males (Bambha,

1961; Pileski et al., 1973; Marshall and Tanner, 1986). In addition, the female growth spurt is

considerably shorter in duration than the male growth spurt at approximately 3.5 years versus 5 years,

respectively (Marshall and Tanner, 1986). Similarly, significant gender differences were found between

maxillary central incisor (U1) dentoalveolar growth rates during the 14 to 16 year time period only. For

the female and male samples during the 14 to 16 year period, the maxillary central incisor dentoalveolar

growth rate was 0.21 ± 0.19 mm/yr and 0.42 ± 0.28 mm/yr, respectively. The disparate dentoalveolar

growth rate of maxillary and mandibular central incisors between genders, especially during the latter

growth period, accentuated the modest dentoalveolar height differences at the age 14 year time point.

99

An evaluation of the molar dentoalveolar height growth rate values between genders reflects a similar

trend. Significant gender differences were found between mandibular first molar (L6) dentoalveolar

height growth rates during the 12 to 14 year and 14 to 16 year time periods. For female and male

samples during the 12 to 14 year period, the mandibular first molar (L6) dentoalveolar height growth

rate was 0.5 ± 0.38 mm/yr and 0.77 ± 0.48 mm/yr, respectively. For female and male samples during

the 14 to 16 year period, the mandibular first molar dentoalveolar height growth rate was 0.33 ± 0.25

mm/yr and 0.85 ± 0.41 mm/yr, respectively. The gender difference in mandibular first molar

dentoalveolar height growth rates was 0.27 mm/yr for the 12 to 14 year period but increased to 0.52

mm/yr for the 14 to 16 year period, which again accentuated the absolute gender differences by the age

16 year time point. Furthermore, the absolute mandibular first molar dentoalveolar height growth rates

declined for all female proportionate groups from the 12 to 14 year and 14 to 16 year time periods,

while the male mandibular first molar dentoalveolar height growth rates increased in absolute value for

all proportionate groups.

Significant gender differences were found between the maxillary first molar (U6) dentoalveolar height

growth rates during the 14 to 16 year time period only. For female and male samples, the maxillary first

molar (U6) dentoalveolar height growth rate was 0.33 ± 0.28 mm/yr and 0.81 ± 0.4 mm/yr, respectively.

The absolute maxillary first molar dentoalveolar height growth rates substantially declined for all female

proportionate groups from the 12 to 14 year and 14 to 16 year time periods, while the male maxillary

first molar dentoalveolar height growth rates were generally stable across all proportionate groups from

the middle to latter period. The combination of the delayed and protracted male growth spurt and

general decline in female growth velocity accentuated the gender differences at the molar level by the

age of 16 years. As a result, the gender differences became progressively greater from the 9 to 12 year

to the 14 to 16 year time period, which may influence the clinical treatment timing decision in order to

either take advantage of a specific growth period or wait until the majority of growth has ceased.

Modifying dentoalveolar growth is accepted as a standard treatment protocol for managing vertical

skeletal discrepancies and dentofacial deformities that are not severe enough to warrant orthognathic

surgical correction. The present study’s results reveal that different amounts and rates of vertical

dentoalveolar development lead to the different phenotypic presentations that are exhibited by various

proportionate growth pattern classification methods. Consequently, the significant differences among

dentoalveolar heights and dentoalveolar height growth rates that were identified, both within and

100

between proportionate growth pattern groups, highlight the need for recognizing an individual’s growth

pattern for accurate treatment planning, biomechanical selection, and a realistic expectation of post-

treatment stability.

Study Limitations As with all retrospective cephalometric studies, certain limitations are inherent in the methodology due

to the fact that craniofacial measurements must be obtained by means of a radiographic projection. In

order to standardize the method of evaluating dentoalveolar heights, the perpendicular distance from

either the incisal edge or mesiobuccal cusp tip to a reference plane was measured in similar fashion to

previous studies (Buschang et al., 2008; Kuitert et al., 2006; Kucera et al., 2011; Enoki et al., 2004).

However, variations in the dental inclinations or presentation of landmarks that define the palatal plane

(ANS-PNS) or mandibular plane (Go-Me) could affect the accuracy of these landmarks.

During growth, Bjork (1963) showed that the lower border of mandible is resorptive posteriorly from

antegonial notch to gonion, which would effectively cause measurement of the mandibular molar to be

underestimated at age 16 years as compared to age 9 years. Furthermore, the lower border of the

mandible experiences apposition of bone anteriorly from the antegonial notch to gnathion, which would

cause longitudinal measurements of the lower incisor to be progressively overestimated until cessation

of growth. Similarly, Enlow and Bang (1965) reported that the palate and floor of the nasal cavity move

in a downward direction through bone deposition at the palatal surface of the maxillary bone together

with resorption from the contralateral superior surfaces. Therefore, the entire superior surface of the

maxillary bone (i.e. ANS-PNS) is resorptive, which would cause longitudinal measurements of the

maxillary dentition to be progressively underestimated until cessation of growth.

The sella to nasion (SN) reference plane for determination of the change in the Y-axis angle has its own

limitations as well. There is a general agreement that points nasion and sella are not completely stable

(Steuer, 1972; Melsen, 1974; Baumrind et al., 1976; Houston and Lee, 1985; Lewis et al., 1985), which

may result in displacement of these points both in the horizontal and vertical direction due to growth

(Arat et al., 2003). Movement that changes the original inclination of the plane between the ages of 9 to

16 years of age could potentially influence the determination of the amount of change in Y-axis angle

and thus influence the constitution of each group. With radiographs of pristine quality, one can make

101

an argument to use the “Structural Method” as described by Bjork and Skieller (1983), which has a high

level of validity but moderate-to-high reproducibility. On other hand, the SN plane (registered at sella)

method has a lower degree of validity but a higher degree of reproducibility (Athanasiou 1995), and

works quite well for radiographs of slightly lesser quality.

Since physiologic growth may continue into the early twenties, it would have been preferable to follow

both male and female subjects to at least age 20 years. An initial attempt to collect age 18 year

cephalograms revealed an insufficient sample size at that age. Consequently, the decision was made to

restrict the final age to 16 years to allow sufficient statistical power and valid data analysis.

Finally, the results of this study apply only to those individuals of Caucasian descent due to the ethnic

origin of the study sample described previously. Therefore, the conclusions may or may not be

applicable to other ethnic groups.

102

Future Directions In order to improve the understanding of the development of the vertical dimension in the human face

during childhood and adolescence, an increase in the number of longitudinal research studies

performed for craniofacial evaluation of dentoalveolar height and dentoalveolar height growth rate

should be a top priority. Fortunately, increased accessibility to longitudinal normative cephalometric

resources is becoming possible with the AAOF Growth Legacy Collection’s efforts, which will allow

studies to be undertaken with sufficiently large number of subjects to conduct powerful analyses.

Since the majority of orthodontic patients are skeletal Class I individuals from 12 to 14 years of age, the

current investigation focused on evaluating an untreated, skeletal Class I sample during that time period

in order to better understand dentoalveolar height development in normal facial growth in growing

children in this age group. Future evaluations of similar research objectives could be extended to

untreated, skeletal Class II or III subjects utilizing the methods used in this study.

Future studies would be best served by utilizing annual time points, which may provide more precision

in regards to the timing of clinical intervention. Furthermore, it would be more ideal to evaluate

dentoalveolar dimensions up to age 20 years, which may provide a better understanding of the

anticipated decrease in dentoalveolar height growth rates and modification effectiveness among groups,

as an individual nears their adult dentoalveolar height growth rate values.

103

Conclusions The following conclusions were drawn from the present study:

Directional (change in Y-axis angle) classification method:

o No statistically significant differences in maxillary and mandibular first molar and central

incisor dentoalveolar heights were found among the vertical, average, and horizontal

growth pattern groups within either gender.

o No statistically significant differences in maxillary and mandibular first molar and central

incisor dentoalveolar height growth rates were found among the vertical, average, and

horizontal growth pattern groups within either gender for all three time periods (9 to 12

years, 12 to 14 years, and 14 to 16 years).

o The hypothesis: “Within each gender, there is a significant difference in the

dentoalveolar heights and dentoalveolar height growth rates of the maxillary and

mandibular molars and incisors in skeletal Class I subjects classified into vertical,

average, and horizontal growth patterns, as determined by change in Y-axis angle” was

rejected. Consequently, it was concluded from the longitudinal assessment that the

vertical dentoalveolar dimensions develop without significant association with the

directional growth pattern of the face in skeletal class I subjects.

Proportionate (UFH:LFH) classification method:

o Statistically significant differences in maxillary and mandibular first molar and central

incisor dentoalveolar heights were found among the long, average, and short LFH

groups within both genders.

o Female sample

Statistically significant differences were found in the dentoalveolar height

growth rates during the 14 to 16 year period of the maxillary first molar (short

versus long LFH group) and 12 to 14 year period of the mandibular first molar

(short versus long, average versus long LFH groups).

o Male sample

Statistically significant differences were found in the dentoalveolar height

growth rates of the mandibular central incisor during the 9 to 12 year (short

104

versus long LFH group) and 12 to 14 year periods (short versus average LFH

group).

o The hypothesis: “Within each gender, there is a significant difference in the

dentoalveolar heights and dentoalveolar height growth rates of the maxillary and

mandibular molars and incisors in skeletal Class I subjects classified into long, average,

and short facial type growth patterns, as determined by the UFH:LFH ratio” was

accepted. Consequently, it was concluded from the longitudinal assessment that there

is an association between the development of the vertical dentoalveolar dimension and

the proportionate growth pattern of the face in skeletal class I subjects.

Evaluation of the effect of gender on dentoalveolar height growth rates

o Statistically significant gender differences in dentoalveolar height growth rates were

seen at the maxillary central incisor (14 to 16 year period), mandibular central incisor

(12 to 14 year and 14 to 16 year periods), maxillary first molar (14 to 16 year period),

and mandibular first molar (12 to 14 year and 14 to 16 year periods).

o The hypothesis: “There are significant gender related differences in the dentoalveolar

height growth rates of the maxillary and mandibular molars and incisors in skeletal Class

I subjects” was accepted. Consequently, it was concluded that vertical dentoalveolar

height growth rates during childhood and adolescence exhibit sexual dimorphism in

skeletal class I subjects.

ale sampleatistically significant differences (p<0.05) wer

105

References Akay MC, Aras A, Günbay T, Akyalçin S, Koyuncue BO. Enhanced effect of combined treatment with corticotomy and skeletal anchorage in open bite correction. J Oral Maxillofac Surg. 2009;67:563-9. Alexander, JM. A comparative study of orthodontic stability in Class I extraction cases [MS Thesis]. Dallas: Baylor College of Dentistry; 1996. Anwar N, Fida M. Compensation for vertical dysplasia and its clinical application. Eur J Orthod. 2009;31:516-22. Arat ZM, Rübendüz M. Changes in dentoalveolar and facial heights during early and late growth periods: a longitudinal study. Angle Orthod. 2005;75:69-74. Arat ZM, Rübendüz M, Akgül AA. The displacement of craniofacial reference landmarks during puberty: a comparison of three superimposition methods. Angle Orthod. 2003;73:374-80. Athanasiou AE. Orthodontic Cephalometry. Mosby-Wolfe Co., 1995. Baek MS, Choi YJ, Yu HS, Lee KJ, Kwak J, Park YC. Long-term stability of anterior open-bite treatment by intrusion of maxillary posterior teeth. Am J Orthod Dentofacial Orthop. 2010;138:396-8. Bambha JK. Longitudinal cephalometric roentgenographic study of face and cranium in relation to body height. J Am Dent Assoc. 1961;63:776-99. Baumrind S, Korn EL, Isaacson RJ, West EE, Molthen R. Quantitative analysis of the orthodontic and orthopedic effects of maxillary traction. Am J Orthod. 1983;84:384-98. Beckmann SH, Kuitert RB, Prahl-Andersen B, Segner D, The RP, Tuinzing DB. Alveolar and skeletal dimensions associated with lower face height. Am J Orthod Dentofacial Orthop. 1998;113:498-506. Behrents RG. A treatise on the continuum of growth in the aging craniofacial skeleton. Ann Arbor, Mich: University of Michigan Center for Human Growth and Development; 1984. Betzenberger D, Ruf S, Pancherz H. The compensatory mechanism in high-angle malocclusions: a comparison of subjects in the mixed and permanent dentition. Angle Orthod. 1999;69:27-32. Bishara SE, Augspurger EF Jr. The role of mandibular plane inclination in orthodontic diagnosis. Angle Orthod. 1975;45:273-81. Bishara SE, Jakobsen JR. Longitudinal changes in three normal facial types. Am J Orthod. 1985;88:466-502. Bjerin R. A comparison between the Frankfort Horizontal and the sella turcica-nasion as reference planes in cephalometric analysis. Acta Odontol Scand 1957;15:1-13.

106

Bjork A. The significance of growth changes in facial pattern and their relationship to changes in occlusion. Dent Rec (London). 1951;71:197-208. Bjork A. Variations in the growth pattern of the human mandible: longitudinal radiographic study by the implant method. J Dent Res. 1963;42:400-11. Bjork A. Prediction of mandibular growth rotation. Am J Orthod. 1969;55:585-99. Bjork A, Skieller V. Normal and abnormal growth of the mandible. A synthesis of longitudinal cephalometric implant studies over a period of 25 years. Eur J Orthod. 1983;5:1-46. Bjork A, Skieller V. Facial development and tooth eruption. An implant study at the age of puberty. Am J Orthod. 1972;62:339-83. Buschang PH, Carrillo R, Liu SS, Demirjian A. Maxillary and mandibular dentoalveolar heights of French-Canadians 10 to 15 years of age. Angle Orthod. 2008;78:70-6. Cangialosi TJ. Skeletal morphologic features of anterior open bite. Am J Orthod. 1984;85:28-36. Ceylan I, Eroz UB. The effects of overbite on the maxillary and mandibular morphology. Angle Orthod. 2001;71:110-5. Chen F, Wu L, Terada K, Saito I. Longitudinal intermaxillary relationships in Class III malocclusions with low and high mandibular plane angles. Angle Orthod. 2007;77:397-403. Chung CH, Mongiovi VD. Craniofacial growth in untreated skeletal Class I subjects with low, average, and high MP-SN angles: a longitudinal study. Am J Orthod Dentofacial Orthop. 2003;124:670-8. Creekmore TD. Inhibition or stimulation of the vertical growth of the facial complex, its significance to treatment. Angle Orthod. 1967;37:285-97. Dahlberg G. Statistical methods for medical and biological students. New York: Interscience Publications, 1940. Daskalogiannakis J. Glossary of orthodontic terms. Quintessence Publishing, 2000. DiPietro GJ, Moergeli JR. Significance of the Frankfort-mandibular plane angle to prosthodontics. J Prosthet Dent. 1976;36:624-35. Downs WB. Variations in facial relationships; their significance in treatment and prognosis. Am J Orthod. 1948;34:812-40. Dung DJ, Smith RJ. Cephalometric and clinical diagnoses of open bite tendency. Am J Orthod Dentofacial Orthop. 1988;94:484-90. Enlow DH, Bang S. Growth and remodeling of the human maxilla. Am J Orthod. 1965;51:446-64.

107

Enoki C, Telles Cde S, Matsumoto MA. Dental-skeletal dimensions in growing individuals with variations in the lower facial height. Braz Dent J. 2004;15:68-74. Erverdi N, Keles A, Nanda R. The use of skeletal anchorage in open bite treatment: A cephalometric evaluation. Angle Orthod. 2004;74:381-90. Fields HW, Proffit WR, Nixon WL, Phillips C, Stanek E. Facial pattern differences in long-faced children and adults. Am J Orthod. 1984;85:217-23. Firouz M, Zernik J, Nanda R. Dental and orthopedic effects of high-pull headgear in treatment of Class II, division 1 malocclusion. Am J Orthod Dentofacial Orthop. 1992;102:197-205. Han M, Wang RY, Liu H, Zhu XJ, Wei FL, Lv T, Wang NN, Hu LH, Li GJ, Liu DX, Wang CL. Association between mandibular posterior alveolar morphology and growth pattern in a Chinese population with normal occlusion. J Zhejiang Univ Sci B. 2013;14:25-32. Haralabakis NB, Yiagtzis SC, Toutountzakis NM. Cephalometric characteristics of open bite in adults: a three-dimensional cephalometric evaluation. Int J Adult Orthodon Orthognath Surg. 1994;9:223-31. Harvold E. Some biologic aspects of orthodontic treatment in the transitional dentition. Am J Orthod. 1963;49:1-14. Hellman M. Growth of the face and occlusion of the teeth in relation to orthodontic treatment. Int J Orthod. 1993;19:1116-1145. Heravi F, Bayani S, Madani AS, Radvar M, Anbiaee N. Intrusion of supra-erupted molars using miniscrews: clinical success and root resorption. Am J Orthod Dentofacial Orthop. 2011;139:S170-5. Houston WJ, Lee RT. Accuracy of different methods of radiographic superimposition on cranial base structures. Eur J Orthod. 1985;7:127-35. Isaacson JR, Isaacson RJ, Speidel TM, Worms FW. Extreme variation in vertical facial growth and associated variation in skeletal and dental relations. Angle Orthod. 1971;41:219-29. Jacob HB, Buschang PH. Vertical craniofacial growth changes in French-Canadians between 10 and 15 years of age. Am J Orthod Dentofacial Orthop. 2011;139:797-805. Janson GRP, Metaxas A, Woodside DG. Variation in maxillary and mandibular molar and incisor vertical dimension in 12-year-old subjects with excess, normal, and short lower anterior face height. Am J Orthod Dentofacial Orthop. 1994;106:409-18. Jarabak JR, Fizzell JA. Technique and treatment with light wire Edgewise appliances. 2nd ed. St. Louis: CV Mosby Co. 1972. Karlsen AT. Craniofacial growth differences between low and high MP-SN angle males: a longitudinal study. Angle Orthod. 1995;65:341-50.

108

Khouw FE, Proffit WR, White RP. Cephalometric evaluation of patients with dentofacial disharmonies requiring surgical correction. Oral Surg Oral Med Oral Pathol. 1970;29:789-98. Kopecky GR, Fishman LS. Timing of cervical headgear treatment based on skeletal maturation. Am J Orthod Dentofacial Orthop. 1993;104:162-9. Kucera J, Marek I, Tycova H, Baccetti T. Molar height and dentoalveolar compensation in adult subjects with skeletal open bite. Angle Orthod. 2011;81:564-9. Kuitert R, Beckmann S, Van Loenen M, Tuinzing B, Zentner A. Dentoalveolar compensation in subjects with vertical skeletal dysplasia. Am J Orthod Dentofacial Orthop. 2006;129:649-57. Kuroda S, Sakai Y, Tamamura N, Deguchi T, Takano-Yamamoto T. Treatment of severe anterior open bite with skeletal anchorage in adults: comparison with orthognathic surgery outcomes. Am J Orthod Dentofacial Orthop. 2007;132:599-605. Lande MJ. Growth behavior of the human body facial profile as revealed by serial cephalometric roentgenology. Angle Orthod 1952;22:78-90.

Lewis AB, Roche AF, Wagner B. Pubertal spurts in cranial base and mandible. Comparisons within individuals. Angle Orthod. 1985;55:17-30. Lee, BSG. Timing of Peak Mandibular Growth in Different Facial Growth Patterns and Resultant Mandibular Projection [MS Thesis]. Toronto: Faculty of Dentistry; 2010. Lundström A, Lundström F. The Frankfort horizontal as a basis for cephalometric analysis. Am J Orthod Dentofacial Orthop. 1995;107:537-40. Marshall WA, Tanner JM. Puberty. In: Falkner F, Tanner JM, Eds. Human Growth, vol 2, ed 2. New York: Plenum Publishing; 1986. Martina R, Cioffi I, Tagliaferri R, Michelotti A, Paduano S, Farella M. Relationship between molar dentoalveolar and craniofacial heights in children. Prog Orthod. 2009;10:64-9. Martina R, Farella M, Tagliaferri R, Michelotti A, Quaremba G, van Eljden TMGJ. The relationship between molar dentoalveolar and craniofacial heights. Angle Orthod. 2005;75:974-9. Melsen B. The cranial base. Acta Odontol Scand. 1974;12:9-125. Nahoum HI. Vertical proportions and the palatal plane in anterior open bite. Am J Orthod. 1971;59:273-82. Nahoum HI, Horowitz SL, Benedicto EA. Varieties of anterior open-bite. Am J Orthod. 1972;61:486-92. Nahoum HI. Vertical proportions: a guide for prognosis and treatment in anterior open bite. Am J Orthod. 1977;72:128-46.

109

Nahoum HI. Anterior open bite: a cephalometric analysis and suggested treatment procedures. Am J Orthod. 1975;67:523-21. Nanda SK. Growth patterns in subjects with long and short faces. Am J Orthod Dentofacial Orthop. 1990;98:247-58. Nanda SK. Patterns of vertical growth in the face. Am J Orthod Dentofacial Orthop. 1988;93:103-16. Nanda RS, Nanda SK. Considerations of dentofacial growth in long-term retention and stability: is active retention needed? Am J Orthod Dentofacial Orthop. 1992;101:297-302. Naumann SA, Behrents RG, Buschang PH. Vertical components of overbite change: A mathematical model. Am J Orthod Dentofacial Orthop. 2000;117:486-95. Opdebeek H, Bell WH. The short face syndrome. Am J Orthod. 1978;73:499-511. Park HS, Kim JY, Kwon TG. Occlusal plane change after intrusion of maxillary posterior teeth by microimplants to avoid maxillary surgery with skeletal Class III orthognathic surgery. Am J Orthod Dentofacial Orthop. 2010;138:631-40. Pileski RC, Woodside DG, James GA. Relationship of the ulnar sesamoid bone and maximum mandibular growth velocity. Angle Orthod. 1973;43:162-70. Proffit WR, Fields HW, Sarver DM. Contemporary Orthodontics. 4th Ed. St. Louis. Elsevier Mosby: 2007. Rakosi T. An atlas and manual of cephalometric radiography. London. Wolfe Medical Publications: 1982. Sassouni V, Nanda S. Analysis of dentofacial vertical proportions. Am J Orthod 1964;50:801-823. Schendel SA, Eisenfeld J, Bell WH, Epker BN, Mishelevich D. The long face syndrome--vertical maxillary excess. Am J Orthod. 1976;70:398-408. Schudy FF. Vertical Growth Versus Anteroposterior Growth As Related To Function And Treatment. Angle Orthod. 1964;34:75-93. Schudy FF. The rotation of the mandible resulting from growth: its implications in orthodontic treatment. Angle Orthod. 1965;35:36-50. Sherwood KH, Burch JG, Thompson WJ. Closing anterior open bites by intruding molars with titanium miniplate anchorage. Am J Orthod Dentofacial Orthop. 2002;122:593-600. Sinclair PM, Little RM. Dentofacial maturation of untreated normals. Am J Orthod. 1985;88:146-56. Siriwat PP, Jarabak JR. Malocclusion and facial morphology. Is there a relationship? Angle Orthod. 1985;55:127-38. Steuer I. The cranial base for superimposition of lateral cephalometric radiographs. Am J Orthod. 1972;61:493-500.

110

Subtelny JD. A longitudinal study of soft tissue facial structures and their profile characteristics, defined in relation to underlying skeletal structures. Am J Orthod. 1959;45:581–607.

Sugawara J, Baik UB, Umemori M, Takahashi I, Nagasaka H, Kawamura H, Mitani H. Treatment and posttreatment dentoalveolar changes following intrusion of mandibular molars with application of a skeletal anchorage system (SAS) for open bite correction. Int J Adult Orthodon Orthognath Surg. 2002;17:243-53. Tsai HH. Cephalometric studies of children with long and short faces. J Clin Pediatr Dent. 2000;25:23-8. Tweed, CH. Clinical Orthodontics, Vol. 1. St. Louis, CV Mosby Co: 1966. Ulger G, Arun T, Sayinsu K, Isik F. The role of cervical headgear and lower utility arch in the control of the vertical dimension. Am J Orthod Dentofacial Orthop. 2006;130:492-501. Worms FW, Meskin LH, Isaacson RJ. Open-bite. Am J Orthod. 1971;59:589-95. Wylie WL, Johnson EL. Rapid evaluation of facial dysplasia in the vertical plane. Angle Orthodontist 1952;22: 165–181. Xun C, Zeng X, Wang X. Microscrew anchorage in skeletal anterior open-bite treatment. Angle Orthod. 2007;77:47-56.

111

Appendix

Appendix 1. Directional Classification Data Tables: Dentoalveolar Heights

Table 1. Directional Classification: Female subjects – Maxillary central incisor (U1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with vertical (N=8), average (N=38), and horizontal (N=10) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.

Age Site Growth Pattern Mean (mm) Std. Deviation Std. Error P value

9 U1 Vertical 22.6 1.8 0.6 0.42

Average 21.9 2.0 0.3

Horizontal 22.7 1.8 0.6

12 U1 Vertical 24.2 2.3 0.8 0.42 Average 23.1 2.1 0.4






Table 2. Directional Classification: Female subjects – Maxillary first molar (U6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with vertical (N=8), average (N=38), and horizontal (N=10) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










112

Table 3. Directional Classification: Female subjects – Mandibular central incisor (L1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with vertical (N=8), average (N=38), and horizontal (N=10) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.


9 L1 Vertical 31.1 1.3 0.4 0.68 Average 30.6 1.7 0.3








Table 4. Directional Classification: Female subjects – Mandibular first molar (L6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with vertical (N=8), average (N=38), and horizontal (N=10) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










113

Table 5. Directional Classification: Male subjects – Maxillary central incisor (U1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with vertical (N=10), average (N=32), and horizontal (N=8) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










Table 6. Directional Classification: Male subjects – Maxillary first molar (U6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with vertical (N=10), average (N=32), and horizontal (N=8) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










114

Table 7. Directional Classification: Male subjects – Mandibular central incisor (L1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with vertical (N=10), average (N=32), and horizontal (N=8) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










Table 8. Directional Classification: Male subjects – Mandibular first molar (L6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with vertical (N=10), average (N=32), and horizontal (N=8) directional growth patterns. P values from mixed model analyses comparing dentoalveolar height means of directional growth pattern groups.










115

Appendix 2. Proportionate Classification Data Tables: Dentoalveolar Heights

Table 9. Proportionate Classification: Female subjects – Maxillary central incisor (U1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with short (N=12), average (N=34) and long (N=10) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.

Age Site Growth Pattern Mean (mm) Std. Deviation Std. Error P value P value (post hoc)

9 U1 Short 20.1 1.6 0.5 0.00

0.0002 (S v. A)

Average 22.4 1.7 0.3 <0.0001 (S v. L)

Long 23.6 1.3 0.4 0.13 (A v. L)

12 U1 Short 21.0 1.6 0.5 0.00

0.0001 (S v. A)

Average 23.7 1.9 0.3 <0.0001 (S v. L)

Long 25.2 1.8 0.6 0.09 (A v. L)

14 U1 Short 21.4 1.5 0.4 0.00

<0.0001 (S v. A)

Average 24.3 2.0 0.4 <0.0001 (S v. L)

Long 25.8 1.6 0.5 0.1 (A v. L)

16 U1 Short 21.7 1.4 0.4 0.00

<0.0001 (S v. A)

Average 24.8 2.0 0.4 <0.0001 (S v. L)

Long 26.5 1.6 0.5 0.04 (A v. L)

Table 10. Proportionate Classification: Female subjects – Maxillary first molar (U6)

Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with short (N=12), average (N=34) and long (N=10) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 U6 Short 14.9 1.3 0.4 0.01

0.06 (S v. A)

Average 15.9 1.2 0.2 0.006 (S v. L)

Long 16.6 1.4 0.4 0.22 (A v. L)

12 U6 Short 16.6 1.2 0.4 0.00

0.003 (S v. A)

Average 17.9 1.4 0.2 0.002 (S v. L)

Long 18.9 1.6 0.5 0.13 (A v. L)

14 U6 Short 17.9 1.3 0.4 0.00

0.02 (S v. A)

Average 19.4 1.6 0.3 0.0007 (S v. L)

Long 20.5 1.5 0.5 0.11 (A v. L)

16 U6 Short 18.4 1.2 0.3 0.00

0.007 (S v. A)

Average 20.0 1.7 0.3 <0.0001 (S v. L)

Long 21.6 1.2 0.4 0.02 (A v. L)

116

Table 11. Proportionate Classification: Female subjects – Mandibular central incisor (L1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with short (N=12), average (N=34) and long (N=10) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 L1 Short 29.2 1.4 0.4 0.00

0.003 (S v. A)

Average 30.8 1.4 0.2 <0.0001 (S v. L)

Long 32.1 1.5 0.5 0.05 (A v. L)

12 L1 Short 31.1 1.8 0.5 0.00

0.03 (S v. A)

Average 32.5 1.6 0.3 0.0006 (S v. L)

Long 33.9 1.6 0.5 0.07 (A v. L)

14 L1 Short 31.8 1.9 0.6 0.00

0.02 (S v. A)

Average 33.4 1.6 0.3 <0.0001 (S v. L)

Long 35.2 1.4 0.4 0.01 (A v. L)

16 L1 Short 32.1 1.8 0.5 0.00

0.007 (S v. A)

Average 34.0 1.8 0.3 <0.0001 (S v. L)

Long 35.7 1.4 0.4 0.02 (A v. L)

Table 12. Proportionate Classification: Female subjects – Mandibular first molar (L6)

Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for female subjects with short (N=12), average (N=34) and long (N=10) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 L6 Short 22.4 0.8 0.2 0.00

0.16 (S v. A)

Average 23.2 1.4 0.2 0.001 (S v. L)

Long 24.6 1.6 0.5 0.02 (A v. L)

12 L6 Short 23.6 1.4 0.4 0.01

0.13 (S v. A)

Average 24.6 1.5 0.3 0.0005 (S v. L)

Long 25.8 1.4 0.5 0.1 (A v. L)

14 L6 Short 24.4 1.5 0.4 0.00

0.16 (S v. A)

Average 25.5 1.8 0.3 0.0004 (S v. L)

Long 27.4 1.5 0.5 0.008 (A v. L)

16 L6 Short 25.0 1.6 0.5 0.00

0.17 (S v. A)

Average 26.2 2.0 0.3 0.002 (S v. L)

Long 28.0 1.7 0.5 0.03 (A v. L)

117

Table 13. Proportionate Classification: Male subjects – Maxillary central incisor (U1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with short (N=9), average (N=29) and long (N=11) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 U1 Short 22.1 1.3 0.4 0.00

0.33 (S v. A)

Average 22.9 1.5 0.3 <0.0001 (S v. L)

Long 25.2 1.1 0.3 <0.0001 (A v. L)

12 U1 Short 23.0 1.5 0.5 0.00

0.1 (S v. A)

Average 24.2 1.6 0.3 <0.0001 (S v. L)

Long 26.9 1.1 0.3 <0.0001 (A v. L)

14 U1 Short 23.6 1.2 0.4 0.00

0.04 (S v. A)

Average 25.0 1.6 0.3 <0.0001 (S v. L)

Long 28.1 1.2 0.4 <0.0001 (A v. L)

16 U1 Short 24.4 1.1 0.4 0.00

0.05 (S v. A)

Average 25.9 1.7 0.3 <0.0001 (S v. L)

Long 28.9 1.3 0.4 <0.0001 (A v. L)

Table 14. Proportionate Classification: Male subjects – Maxillary first molar (U6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with short (N=9), average (N=29) and long (N=11) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 U6 Short 14.7 1.1 0.4 0.01

0.015 (S v. A)

Average 16.3 1.6 0.3 0.01 (S v. L)

Long 16.7 1.3 0.4 0.73 (A v. L)

12 U6 Short 16.2 1.2 0.4 0.00

0.005 (S v. A)

Average 18.2 1.8 0.3 0.0004 (S v. L)

Long 19.1 1.1 0.3 0.21 (A v. L)

14 U6 Short 17.6 1.5 0.5 0.00

0.005 (S v. A)

Average 19.7 1.9 0.4 0.0004 (S v. L)

Long 20.8 1.2 0.4 0.21 (A v. L)

16 U6 Short 19.3 1.5 0.5 0.00

0.009 (S v. A)

Average 21.3 1.9 0.4 0.0005 (S v. L)

Long 22.4 1.2 0.4 0.17 (A v. L)

118

Table 15. Proportionate Classification: Male subjects – Mandibular central incisor (L1) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with short (N=9), average (N=29) and long (N=11) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 L1 Short 30.4 1.5 0.5 0.00

0.37 (S v. A)

Average 31.3 1.7 0.3 0.003 (S v. L)

Long 33.1 2.0 0.6 0.011 (A v. L)

12 L1 Short 31.8 1.4 0.5 0.00

0.18 (S v. A)

Average 33.1 2.0 0.4 0.0004 (S v. L)

Long 35.4 1.9 0.6 0.0047 (A v. L)

14 L1 Short 32.9 1.6 0.5 0.00

0.54 (S v. A)

Average 34.9 2.4 0.4 0.0003 (S v. L)

Long 37.1 2.1 0.6 0.02 (A v. L)

16 L1 Short 34.4 1.4 0.5 0.00

0.05 (S v. A)

Average 36.3 2.2 0.4 0.0002 (S v. L)

Long 38.6 2.2 0.7 0.01 (A v. L)

Table 16. Proportionate Classification: Male subjects – Mandibular first molar (L6) Dentoalveolar height means, standard deviations, and standard error of the means at ages 9, 12, 14 and 16 years for male subjects with short (N=9), average (N=29) and long (N=11) proportionate growth patterns. P values from mixed model analyses comparing dentoalveolar height means of proportionate growth pattern groups and subsequent post hoc comparisons.


9 L6 Short 22.7 1.3 0.4 0.00

0.79 (S v. A)

Average 23.0 1.6 0.3 0.0006 (S v. L)

Long 25.4 1.4 0.4 0.0002 (A v. L)

12 L6 Short 23.8 1.3 0.4 0.01

0.87 (S v. A)

Average 24.2 2.0 0.4 0.004 (S v. L)

Long 26.5 1.3 0.4 0.001 (A v. L)

14 L6 Short 24.8 1.0 0.3 0.00

0.35 (S v. A)

Average 25.8 2.3 0.4 0.002 (S v. L)

Long 28.1 1.8 0.5 0.007 (A v. L)

16 L6 Short 26.2 1.4 0.5 0.00

0.16 (S v. A)

Average 27.6 2.2 0.4 0.0005 (S v. L)

Long 29.8 1.9 0.6 0.008 (A v. L)

119

Appendix 3. Directional Classification Data Tables: Dentoalveolar Height Growth Rates

Table 17. Directional Classification: Female subjects – Maxillary central incisor (U1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=10), average (n=38) and vertical (n=8) groups.

Period Group Mean (mm/yr)

Std Dev 95% Confidence Limits Significance (P value) Lower Upper

9-12 Years

Horizontal 0.38 0.31 0.15 0.6

0.43 Average 0.41 0.24 0.34 0.49

Vertical 0.53 0.25 0.32 0.73

12-14 Years

Horizontal 0.26 0.2 0.11 0.42

0.28 Average 0.3 0.21 0.23 0.37

Vertical 0.42 0.25 0.21 0.63

14-16 Years

Horizontal 0.19 0.21 0.03 0.35

0.88 Average 0.22 0.19 0.15 0.28

Vertical 0.19 0.16 0.06 0.32

Table 18. Directional Classification: Female subjects – Maxillary first molar (U6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=10), average (n=38) and vertical (n=8) groups.



9-12 Years

Horizontal 0.63 0.3 0.41 0.84

0.68 Average 0.66 0.23 0.59 0.74

Vertical 0.72 0.19 0.57 0.88

12-14 Years

Horizontal 0.65 0.23 0.48 0.82

0.37 Average 0.74 0.26 0.65 0.83

Vertical 0.83 0.24 0.63 1.02

14-16 Years

Horizontal 0.33 0.37 0.05 0.62

0.85 Average 0.34 0.27 0.25 0.43

Vertical 0.27 0.27 0.05 0.5

120

Table 19. Directional Classification: Female subjects – Mandibular central incisor (L1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=10), average (n=38) and vertical (n=8) groups.



9-12 Years

Horizontal 0.47 0.15 0.36 0.58

0.21 Average 0.6 0.25 0.52 0.69

Vertical 0.62 0.12 0.52 0.72

12-14 Years

Horizontal 0.27 0.25 0.08 0.47

0.06 Average 0.47 0.29 0.38 0.57

Vertical 0.61 0.32 0.35 0.88

14-16 Years

Horizontal 0.24 0.15 0.13 0.36

0.38 Average 0.24 0.15 0.19 0.29

Vertical 0.32 0.12 0.22 0.42

Table 20. Directional Classification: Female subjects – Mandibular first molar (L6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=10), average (n=38) and vertical (n=8) groups.



9-12 Years

Horizontal 0.33 0.21 0.18 0.47

0.15 Average 0.45 0.24 0.37 0.53

Vertical 0.53 0.17 0.39 0.68

12-14 Years

Horizontal 0.41 0.32 0.17 0.65

0.77 Average 0.51 0.36 0.39 0.63

Vertical 0.52 0.53 0.07 0.96

14-16 Years

Horizontal 0.34 0.2 0.19 0.49

0.89 Average 0.32 0.25 0.23 0.4

Vertical 0.36 0.33 0.08 0.64

121

Table 21. Directional Classification: Male subjects – Maxillary central incisor (U1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=8), average (n=31) and vertical (n=10) facial groups.



9-12 Years

Horizontal 0.43 0.31 0.17 0.69

0.27 Average 0.43 0.28 0.33 0.53

Vertical 0.59 0.27 0.4 0.79

12-14 Years

Horizontal 0.5 0.27 0.27 0.73

0.35 Average 0.42 0.29 0.31 0.52

Vertical 0.3 0.31 0.08 0.52

14-16 Years

Horizontal 0.36 0.31 0.11 0.62

0.35 Average 0.4 0.27 0.3 0.5

Vertical 0.53 0.3 0.32 0.75

Table 22. Directional Classification: Male subjects – Maxillary first molar (U6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=8), average (n=31) and vertical (n=10) facial groups.



9-12 Years

Horizontal 0.69 0.3 0.44 0.94

0.9 Average 0.65 0.33 0.53 0.78

Vertical 0.62 0.3 0.4 0.84

12-14 Years

Horizontal 0.76 0.36 0.46 1.06

0.29 Average 0.73 0.23 0.65 0.82

Vertical 0.91 0.46 0.58 1.24

14-16 Years

Horizontal 0.72 0.52 0.29 1.15

0.76 Average 0.84 0.35 0.71 0.97

Vertical 0.82 0.47 0.48 1.15

122

Table 23. Directional Classification: Male subjects – Mandibular central incisor (L1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=8), average (n=31) and vertical (n=10) facial groups.



9-12 Years

Horizontal 0.55 0.3 0.31 0.8

0.26 Average 0.58 0.24 0.49 0.67

Vertical 0.72 0.29 0.52 0.93

12-14 Years

Horizontal 0.97 0.37 0.66 1.28

0.54 Average 0.82 0.39 0.67 0.96

Vertical 0.79 0.32 0.56 1.02

14-16 Years

Horizontal 0.7 0.58 0.22 1.18

0.9 Average 0.72 0.36 0.59 0.86

Vertical 0.79 0.46 0.45 1.12

Table 24. Directional Classification: Male subjects – Mandibular first molar (L6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between horizontal (n=8), average (n=31) and vertical (n=10) facial groups.



9-12 Years

Horizontal 0.27 0.29 0.03 0.51

0.29 Average 0.4 0.19 0.33 0.47

Vertical 0.36 0.15 0.25 0.47

12-14 Years

Horizontal 0.78 0.47 0.38 1.17

0.99 Average 0.77 0.51 0.58 0.95

Vertical 0.79 0.4 0.5 1.07

14-16 Years

Horizontal 0.97 0.4 0.63 1.3

0.69 Average 0.83 0.38 0.69 0.97

Vertical 0.84 0.54 0.45 1.23

123

Appendix 4. Proportionate Classification Data Tables: Dentoalveolar Height Growth Rates

Table 25. Proportionate Classification: Female subjects – Maxillary central incisor (U1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=12), average (n=34) and long (n=10) facial groups and subsequent post hoc comparisons.


Std Dev 95% Confidence Limits Significance (P value)

Post Hoc significance

(P value) Lower Upper

9-12 Years

Short 0.29 0.26 0.12 0.45

0.06

0.16 (S v. A) 0.06 (S v. L) 0.53 (A v. L)

Average 0.44 0.24 0.35 0.52

Long 0.53 0.23 0.37 0.7

12-14 Years

Short 0.2 0.13 0.12 0.28

0.09

0.08 (S v. A) 0.38 (S v. L) 0.88 (A v. L)

Average 0.36 0.21 0.28 0.43

Long 0.32 0.26 0.14 0.5

14-16 Years

Short 0.17 0.18 0.06 0.29

0.05

0.98 (S v. A) 0.09 (S v. L) 0.06 (A v. L)

Average 0.18 0.17 0.12 0.24

Long 0.33 0.19 0.2 0.47

Table 26. Proportionate Classification: Female subjects – Maxillary first molar (U6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=12), average (n=34) and long (n=10) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.59 0.21 0.46 0.72

0.31

0.60 (S v. A) 0.28 (S v. L) 0.63 (A v. L)

Average 0.67 0.24 0.58 0.75

Long 0.75 0.26 0.56 0.93

12-14 Years

Short 0.63 0.29 0.45 0.82

0.22

0.35 (S v. A) 0.22 (S v. L) 0.77 (A v. L)

Average 0.75 0.25 0.66 0.84

Long 0.82 0.2 0.67 0.96

14-16 Years

Short 0.25 0.19 0.12 0.37

0.03

0.85 (S v. A) 0.04 (S v. L) 0.06 (A v. L)

Average 0.3 0.23 0.21 0.38

Long 0.53 0.42 0.23 0.83

124

Table 27. Proportionate Classification: Female subjects – Mandibular central incisor (L1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=12), average (n=34) and long (n=10) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.62 0.26 0.45 0.78

0.8

0.79 (S v. A) 0.97 (S v. L) 0.94 (A v. L)

Average 0.57 0.23 0.49 0.65

Long 0.59 0.17 0.47 0.71

12-14 Years

Short 0.37 0.27 0.19 0.54

0.05

0.78 (S v. A) 0.06 (S v. L) 0.09 (A v. L)

Average 0.43 0.29 0.32 0.54

Long 0.66 0.29 0.45 0.87

14-16 Years

Short 0.17 0.14 0.08 0.26

0.06

0.06 (S v. A) 0.32 (S v. L) 0.84 (A v. L)

Average 0.28 0.14 0.23 0.33

Long 0.25 0.15 0.15 0.36

Table 28. Proportionate Classification: Female subjects – Mandibular first molar (L6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=12), average (n=34) and long (n=10) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.41 0.31 0.21 0.61

0.64

0.78 (S v. A) 0.99 (S v. L) 0.70 (A v. L)

Average 0.46 0.21 0.39 0.54

Long 0.4 0.23 0.23 0.56

12-14 Years

Short 0.39 0.3 0.2 0.58

0.01

0.92 (S v. A) 0.02 (S v. L) 0.01 (A v. L)

Average 0.43 0.35 0.3 0.56

Long 0.82 0.4 0.53 1.11

14-16 Years

Short 0.31 0.17 0.2 0.41

0.7

0.88 (S v. A) 0.96 (S v. L) 0.74 (A v. L)

Average 0.35 0.28 0.25 0.45

Long 0.28 0.25 0.1 0.46

125

Table 29. Proportionate Classification: Male subjects – Maxillary central incisor (U1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=9), average (n=29) and long (n=11) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.32 0.19 0.18 0.47

0.12

0.39 (S v. A) 0.10 (S v. L) 0.42 (A v. L)

Average 0.46 0.26 0.36 0.56

Long 0.58 0.36 0.34 0.83

12-14 Years

Short 0.28 0.32 0.03 0.53

0.06

0.61 (S v. A) 0.06 (S v. L) 0.13 (A v. L)

Average 0.38 0.29 0.27 0.49

Long 0.58 0.21 0.44 0.72

14-16 Years

Short 0.41 0.25 0.22 0.61

0.1

0.99 (S v. A) 0.99 (S v. L) 0.99 (A v. L)

Average 0.43 0.28 0.32 0.53

Long 0.42 0.33 0.2 0.64

Table 30. Proportionate Classification: Male subjects – Maxillary first molar (U6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=9), average (n=29) and long (n=11) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.5 0.13 0.4 0.6

0.06

0.46 (S v. A) 0.06 (S v. L) 0.19 (A v. L)

Average 0.64 0.31 0.52 0.75

Long 0.83 0.38 0.57 1.08

12-14 Years

Short 0.7 0.43 0.37 1.03

0.7

0.80 (S v. A) 0.68 (S v. L) 0.93 (A v. L)

Average 0.78 0.27 0.67 0.88

Long 0.82 0.31 0.61 1.03

14-16 Years

Short 0.87 0.45 0.53 1.22

0.88

0.86 (S v. A) 0.96 (S v. L) 0.97 (A v. L)

Average 0.79 0.39 0.64 0.94

Long 0.82 0.43 0.54 1.11

126

Table 31. Proportionate Classification: Male subjects – Mandibular central incisor (L1) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=9), average (n=29) and long (n=11) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.46 0.26 0.26 0.66

0.05

0.29 (S v. A) 0.04 (S v. L) 0.28 (A v. L)

Average 0.6 0.25 0.51 0.69

Long 0.74 0.25 0.57 0.9

12-14 Years

Short 0.57 0.22 0.39 0.74

0.05

0.04 (S v. A) 0.14 (S v. L) 0.98 (A v. L)

Average 0.9 0.4 0.75 1.06

Long 0.88 0.3 0.68 1.08

14-16 Years

Short 0.76 0.31 0.52 1

0.96

0.96 (S v. A) 0.99 (S v. L) 0.98 (A v. L)

Average 0.72 0.39 0.57 0.87

Long 0.75 0.56 0.37 1.12

Table 32. Proportionate Classification: Male subjects – Mandibular first molar (L6) Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of ANOVA tests comparing mean dentoalveolar height growth rates between short (n=9), average (n=29) and long (n=11) facial groups and subsequent post hoc comparisons.





9-12 Years

Short 0.39 0.2 0.23 0.54

0.1

0.98 (S v. A) 0.95 (S v. L) 0.98 (A v. L)

Average 0.37 0.2 0.29 0.45

Long 0.36 0.24 0.2 0.52

12-14 Years

Short 0.47 0.5 0.09 0.86

0.11

0.1 (S v. A) 0.22 (S v. L) 0.99 (A v. L)

Average 0.84 0.45 0.67 1.02

Long 0.82 0.47 0.5 1.14

14-16 Years

Short 0.73 0.36 0.45 1.01

0.6

0.58 (S v. A) 0.77 (S v. L) 0.98 (A v. L)

Average 0.89 0.35 0.76 1.02

Long 0.86 0.6 0.46 1.26

127

Appendix 5. Dentoalveolar Height Growth Rate Data Tables: Evaluation of the effect of gender on dentoalveolar height growth rate values

Table 33. Evaluation of the effect of gender – Maxillary central incisor (U1) dentoalveolar height growth rates

Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of t-tests comparing mean dentoalveolar height growth rates between male (n=49) and female subjects (n=56).

Period

Gender Mean (mm/yr)


Lower Upper

9-12 Years Female 0.42 0.25 0.36 0.49 0.4

Male 0.46 0.28 0.38 0.55

12-14 Years Female 0.31 0.21 0.26 0.37 0.08

Male 0.41 0.29 0.32 0.49

14-16 Years Female 0.21 0.19 0.16 0.26 <0.0001

Male 0.42 0.28 0.34 0.5

Table 34. Evaluation of the effect of gender – Maxillary first molar (U6) dentoalveolar height growth rates Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of t-tests comparing mean growth rates between male (n=49) and female subjects (n=56).

Period

Gender Mean (mm/yr)


Lower Upper

9-12 Years Female 0.67 0.24 0.6 0.73 0.81

Male 0.65 0.32 0.56 0.74

12-14 Years Female 0.74 0.25 0.67 0.81 0.52

Male 0.77 0.31 0.68 0.86

14-16 Years Female 0.33 0.28 0.25 0.41 <0.0001

Male 0.81 0.4 0.7 0.93

128

Table 35. Evaluation of the effect of gender – Mandibular central incisor (L1) dentoalveolar height growth rates Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of t-tests comparing mean dentoalveolar height growth rates between male (n=49) and female subjects (n=56).

Period

Gender Mean (mm/yr) Std Dev 95% Confidence Limits Significance (P value)

Lower Upper

9-12 Years Female 0.58 0.22 0.52 0.64 0.64

Male 0.6 0.26 0.53 0.68

12-14 Years Female 0.46 0.3 0.38 0.54 <0.0001

Male 0.84 0.37 0.73 0.94

14-16 Years Female 0.25 0.15 0.21 0.29 <0.0001

Male 0.73 0.41 0.61 0.85

Table 36. Evaluation of the effect of gender – Mandibular first molar (L6) dentoalveolar height growth rates Dentoalveolar height growth rate means, standard deviations, and 95% confidence limits for time periods 9 to 12 years, 12 to 14 years, and 14 to 16 years. Results of t-tests comparing mean growth rates between male (n=49) and female subjects (n=56).

Period

Gender Mean (mm/yr) Std Dev 95% Confidence Limits Significance (P value)

Lower Upper

9-12 Years Female 0.44 0.23 0.38 0.5 0.1

Male 0.37 0.21 0.31 0.43

12-14 Years Female 0.5 0.38 0.39 0.6 0.002

Male 0.77 0.48 0.63 0.91

14-16 Years Female 0.33 0.25 0.26 0.4 <0.0001

Male 0.85 0.41 0.73 0.97

longitudinal assessment of maxillary and mandibular … heights can be modified, to a certain...

Documents