Timing of Peak Mandibular Growth in Different Facial Growth Patterns and Resultant Mandibular Projection

by

Bennet Shung-Geu Lee D.M.D.

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

Graduate Department of Dentistry University of Toronto

© Copyright by Bennet Shung-geu Lee 2010

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Timing of Peak Mandibular Growth in Different Facial Growth Patterns and Resultant Mandibular Projection

Bennet Shung-geu Lee

Master of Science Degree

Discipline of Orthodontics, Faculty of Dentistry

University of Toronto

2010

Abstract

Objective: To determine if significant differences exist in timings and rates of Peak

Mandibular Growth (PMG) and mandibular projections of subjects with vertical, average and

horizontal facial growth patterns.

Methods: Sixty-three Caucasian orthognathic subjects with cephalograms (9 to 18 years)

available from the Burlington Growth Centre were categorized into average, vertical and

horizontal growth pattern groups based on their change in Y axis from age 10 to 16 years.

PMG timing and rates were determined and mandibular projections measured. Comparisons

were made by ANOVA.

Results: Inter-group differences of PMG timing or rate were not statistically significant.

Although not statistically significant, PMG of vertically growing females was 14 month

earlier than all other subgroups. Horizontal mandibular projection differences approached

significance in older children.

Conclusions: No statistically significant differences were found in the timing or rate of PMG

in different facial growth patterns. Differences in horizontal mandibular projections

approached significance with growth.

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Acknowledgements

I would like to thank the following people for their support throughout the course of this

investigation:

Dr. Sunjay Suri, Thesis Supervisor, Assistant Professor and Director of the Center for

Clinical Research, University of Toronto, Faculty of Dentistry, Department of Graduate

Orthodontics; for your valuable advice, support and encouragement,

Dr. Bryan Tompson, Committee member, Discipline Head, University of Toronto, Faculty of

Dentistry, Department of Graduate Orthodontics; for your motivation and guidance

throughout my orthodontic education and this investigation,

Mr. Derek Stephens, Committee member, Biostatistician/Manager, BDA, SickKids Hospital,

Toronto, Ontario; for your assistance and statistical expertise during the preparation of my

thesis,

Dr. Demitrios Halazonetis, Associate Professor, University of Athens, Developer of dHAL®

software, Athens, Greece; for generously donating the use of his cephalometric program,

Viewbox® 3.1

Most importantly, I dedicate this thesis to my family.

To my pregnant wife, Esther, for your unconditional love, for your encouragement and

patience, and for supporting me each and every day. I am overjoyed that we are expecting a

new addition to our growing family. I could not have asked for a greater gift after

completing this investigation.

To our daughter Emma, for all the joy and laughter you have given me every day. You have

touched my heart like no other and I am so blessed to have you in my life.

To my sister Petra, for always being there for me in good times and bad, and for having the

most contagious laugh I have ever heard.

To my brother Shung-il, for always being someone I could turn to for advice.

And finally to my parents, for all the sacrifices you have made in order to provide us with the

best possible environment in which to live and be raised, and for instilling in me the qualities

needed to be successful in any endeavors I pursue. This thesis represents the culmination of

all the love, sacrifice and hard work you have given me and I dedicate this thesis especially

to you.

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Table of Contents

Abstract……………………………………………………..………………….…………..…

Acknowledgements…………………………………………………………………………....

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

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

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

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

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

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

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

A. Mandibular growth…………………………………………………………………

B. Facial Growth Patterns……………………………………………………………

IV. Purpose of the Study………………………………………………………………......

V. Research Questions……………………………………………………………………

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

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

A. Sample Description…………………………………………………….…………

B. Reliability………..…………………………………………………………………

C. Analysis of Results…………………………………………………………………

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

A. Age at Peak Mandibular Growth………….………………………………………

B. Peak Mandibular Growth Rate………….…..………..……………………………

C. Mandibular Projection……………………………………………………………

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

X. Future Directions…………………………………………………………………..

XI. Study Limitations……………………………………………………………………

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

XIII. Bibliography…………………………………………………………………………

XIV. Appendix……………………………………………………………………………..

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List of Tables Table I: Summary of Peak Mandibular Growth Studies………………………………

Table II: Facial Growth Pattern Classification According to Change in Y-axis

from 10 to 16 years………………………………………………………….…

Table III: Intra-rater Reliability for Mandibular Length Measurements………………….

Table IV: Vertical Mandibular Projection (N-Gn’) in Relation to Nasion by

Growth Pattern and Gender…………………………………………………

Table V: Vertical Mandibular Projection (S-S’) in Relation to Sella by Growth

Pattern and Gender……………………………………………………………

Table VI: Horizontal Mandibular Projection (Gn-Gn’) in Relation to Nasion by

Growth Pattern………………………………..………..………………..……

Table VII: Horizontal Mandibular Projection (Gn-Gn’) in Relation to Nasion by

Growth Pattern and Gender……………………………………………………

Table VIII: Horizontal Mandibular Projection (S’-Gn) in Relation to Sella by

Growth Pattern………………………..…….…………………..…………….

Table IX: Horizontal Mandibular Projection (S’-Gn) in Relation to Sella by

Growth Pattern and Gender……………………………………………………

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List of Figures Figure 1: Vertical and Horizontal Facial Growth Patterns (Female Burlington

Templates)…………………………………………………………………….

Figure 2: Y-axis………………………………………………………………………..

Figure 3: Final Sample Flowchart……………………………………..………………….

Figure 4: Cephalometric Tracing ………………………………………..……………….

Figure 5: Mandibular Growth Rate Graph for Subject #27………………….…..……….

Figure 6: Cumulative Mandibular Length vs. Age Graph……...………………………..

Figure 7: Age Distribution at Peak Mandibular Growth (PMG) by Gender ………….

Figure 8: Age Distribution at Peak Mandibular Growth by Growth Pattern……………

Figure 9: Age at PMG - Distribution by Growth Pattern and Gender …………………

Figure 10: Age at PMG – Collapsed Average & Horizontal Groups……….……………

Figure 11: Interaction (A + H) – Age at PMG by Growth Pattern and Gender………..

Figure 12: Distribution of Peak Mandibular Growth (PMG) Rate by Gender ……………

Figure 13: Distribution of PMG Rate by Growth Pattern ……………………….………

Figure 14: Mandibular Growth Rate at PMG and PMG +/- 1 year………….……………

Figure 15: Distribution of PMG Rate by Growth Pattern and Gender ….……………….

Figure 16: PMG Rate – Collapsed Average and Horizontal Group….…………………….

Figure 17 N-Gn’ – Vertical Mandibular Projection in Relation to Nasion……………….

Figure 18: Vertical Projection (N-Gn’) - Distribution by Age, Growth Pattern

and Gender………………………………………………………..…………..

Figure 19: Vertical Projection (N-Gn’) – Boxplots for Age 10 and 16 years

by Growth Pattern and Gender...………………………………….……………

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Figure 20: S-S’ – Vertical Mandibular Projection in Relation to Sella……………………

Figure 21: Vertical Projection (S-S’) - Distribution by Age, Growth Pattern

and Gender………………………………………………………………..…

Figure 22: Vertical Projection (N-Gn’) – Boxplots for Age 10 and 16 years

by Growth Pattern and Gender..………………………………….……………

Figure 23: Gn-Gn’ – Horizontal Mandibular Projection in Relation to Nasion………….

Figure 24: Horizontal Projection (Gn-Gn’) - Distribution by Age, Growth Pattern

And Gender……………………………………………………………..……

Figure 25: Horizontal Mandibular Projection (Gn-Gn’) – Boxplots for Age 10 and

16 years by Growth Pattern and Gender…………………………………….

Figure 26: S’-Gn – Horizontal Mandibular Projection in Relation to Sella……………….

Figure 27: Horizontal Projection (S’-Gn) - Distribution by Age, Growth Pattern

and Gender …………………………………………………………………

Figure 28: Horizontal Mandibular Projection (S’-Gn) – Boxplots for Age 10 and

16 years by Growth Pattern and Gender………………………………………

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List of Appendices

Appendix 1: Age at Peak Mandibular Growth……………………………………………….

Appendix 2: Rate at Peak Mandibular Growth………………………………………………

Appendix 3: Rate at PMG +/- 1 year…………………………………………………………

Appendix 4: Cumulative Mandibular Length and Projections.………….…..………………

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List of Abbreviations

A – Average

AFT – Average facial type

ANB – Angle formed by intersection of lines NA and NB

BGC – Burlington Growth Center

Co – Condylion

CO – Centric occlusion

CR – Centric relation

FH – Frankfort horizontal

Gn – Gnathion

Gn-Gn’ – Horizontal mandibular projection in relation to nasion

H – Horizontal

LFT – Long facial type

N – Nasion

NA – Line connecting nasion and point A

NB – Line connecting nasion and point B

N-Gn’ – Vertical mandibular projection in relation to nasion

MP – Mandibular plane

PMG – Peak mandibular growth

PPM – Pre-pubertal mandibular growth minimum

S – Sella

S’-Gn – Horizontal mandibular projection in relation to sella

SFT – Short facial type

SNA – Angle formed by intersection of lines SN and NA

SNB – Angle formed by intersection of lines SN and NB

SN – Line connecting sella and nasion

S-S’ – Vertical mandibular projection in relation to sella

V – Vertical

Y-axis – Angle formed by the intersection of the line sella-gnathion with the Frankfort

horizontal

1

Introduction and Statement of the Problem

The timing of orthodontic treatment to coincide with the pubertal growth period is an

important part of correcting any skeletal disharmony that may exist in an individual’s

dentofacial complex. Using the period of accelerated growth to carry out early interceptive

treatment allows the orthodontist to improve an individual’s maxillomandibular relationship.

Early intervention, if successful, may help to circumvent more invasive treatment such as

orthognathic surgery to correct the discrepancy after skeletal maturation.

Peak mandibular growth has been described for samples of the male and female population,

however no studies have been reported that clarify whether any significant difference in

incremental mandibular growth exists in subjects having vertical, average, and horizontal

facial growth patterns. Horizontal and vertical facial growth patterns may exhibit differences

in the projection of the mandible and their peak mandibular growth which can help determine

the timing and type of treatment for individuals with these growth patterns.

Some characteristics of hyperdivergent facial types include a high mandibular plane angle,

short posterior and long anterior facial heights whereas hypodivergent facial types have low

mandibular plane angles, long posterior and short anterior facial heights. These

characteristics are in large part influenced by the morphology and position of the mandible.

Therefore identifying any differences in peak mandibular growth between these facial

patterns could aid in planning treatment more effectively and maximize outcomes of early

treatment.

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Significance of the Problem

Determining a relationship between the peak mandibular growth in vertical and horizontal

facial patterns provides the orthodontist with a valid method to coordinate the timing of

orthodontic treatment differentially according to their growth pattern. A difference in the

timing of maximum growth rate of the mandible between horizontal and vertical growing

subjects, if found, would suggest that treatment should be initiated according to this

difference in peak growth to derive maximal benefits of growth.

Recent studies by Ball and Jamal (Ball, 2008; Jamal, 2008) examined peak mandibular

growth and the cervical vertebral maturation in males and females respectively, from among

the subjects in the Burlington facial growth center archives. The present study proposed to

characterize skeletal Class I subjects based on measured ANB values and select samples of

untreated individuals from this group. Based on the facial patterns of these subjects, they

were grouped into average, vertical and horizontal growth patterns. The incremental

mandibular growth and resultant projection of the mandible in vertical and horizontal

growing individuals were studied and compared. By pooling subjects from the same

population as that used in the studies by Ball and Jamal, the results from this study can be

used to corroborate some of the findings of their investigations. We would further understand

the influence of facial growth patterns on mandibular growth increments since these studies

did not evaluate differences in incremental mandibular growth in the various growth patterns.

The results from this investigation are also applicable to those of previous studies on facial

growth conducted from samples from the Burlington Growth Center.

3

Review of the Literature

Growth and development has been studied extensively in orthodontics due to the significant

influence it has on comprehensive orthodontic treatment. During normal growth and

development, the overall change in bodily proportions follows a general pattern of growth.

Early in fetal development, the head is approximately half the total body length. However by

the time of birth, the proportion of the head is reduced to approximately one third of the total

body length and becomes further reduced as the limbs and trunk grow increasingly faster

than the head and face. This normal pattern of growth is termed the cephalocaudal gradient

of growth, which means that there is an axis of growth from the head to the feet (Proffit et

al., 2007).

Growth of different parts of the body such as the head and face also are strongly influenced

by a cephalocaudal gradient of growth in that the mandible grows more than the cranium.

The mandible also grows later than the cranium. This pattern of growth is evident in the

anteroposterior relationship between the maxilla and the mandible. At birth, the mandible is

generally retrognathic to the maxilla. This condition is usually corrected over time by rapid

mandibular growth and forward displacement of the mandible, eventually establishing a

skeletal class I maxillomandibular relationship during normal development (Sperber, 2006).

Underdevelopment of the mandible leads to a retrognathic skeletal class II relationship and

overdevelopment results in a skeletal class III or prognathic profile. Vertical patterns of

growth also exist in facial growth, as will be discussed later.

Dentofacial orthopedics, in particular, attempts to control or modify facial growth in order to

correct developing skeletal dysplasias. These dysplasias arise due to differences in the

magnitude and direction of growth of different facial components such as the maxilla and

mandible. These growth discrepancies can lead to deviations in the normal

maxillomandibular relationship and therefore contribute to malocclusions which develop

during growth. In order to efficiently use an individual’s growth potential to help correct

these skeletal dysplasias, the orthodontist must be able to reasonably estimate how much

growth remains, in what direction growth is occurring and the timing of the greatest amount

of growth.

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A key principle in dentofacial orthopedics is in the timing of its application. It is widely

accepted that for treatment to be effective, it should be timed to include the pubertal growth

spurt (Baccetti et al., 2000; Faltin Jr et al., 2003; Hagg and Pancherz, 1988; Kopecky and

Fishman, 1993; Malmgren and Omblus, 1985; Malmgren et al., 1987; Omblus et al., 1997)

Baccetti et al.(Baccetti et al., 2009) evaluated the role of treatment timing in non extraction

comprehensive class II therapy. Sixty subjects were separated into three samples based on

the timing of their treatment with respect to the pubertal growth spurt. Lateral cephalograms

were taken before therapy and on an average of 6 months after therapy. They found that the

greatest amount of favorable skeletal correction (ie. enhanced mandibular growth) occurred

in patients treated during the pubertal growth spurt.

Malmgren et al.(Malmgren et al., 1987) studied the effects of functional appliance therapy on

24 girls and 32 boys with severe skeletal class II malocclusions. The patients varied in age

from 8.5 to 15 years. Treatment with a functional appliance was initiated before and during

peak pubertal growth. Although the number of patients treated during the postpeak period

was too small for statistical analysis, they found the skeletal effect to be greater during the

peak period than in those treated during the prepeak period. Similarly, Kopecky and

Fishman (Kopecky and Fishman, 1993) attempted to identify optimal timing of cervical

headgear treatment, and they reported more favorable results during periods that were

associated with greater incremental growth velocity.

In order to develop a treatment plan and determine when an appliance should be inserted and

activated, the orthodontist must have some knowledge of normal growth patterns. Studies

have shown that growth after birth does not occur at a constant rate but varies with periods of

acceleration and deceleration. As a result, growth curves for somatic growth generally

follow a smooth sigmoid shape. On examining such a curve, Tanner’s longitudinal study of

statural height (Tanner, 1964) found a continuous deceleration of growth during infancy and

early childhood which leveled out somewhat during the later childhood years. In many

children, this deceleration was followed by a slight acceleration of growth rate which he

referred to as the juvenile spurt. This mid growth acceleration was followed by a marked

deceleration, and then a sudden acceleration of growth, which was recognized as the pubertal

5

growth spurt or adolescent growth acceleration. After the pubertal spurt, growth then

decelerated to near zero levels as the individual reached maturity.

Bayer and Bayley’s (Bayer and Bayley, 1959; Bayley, 1956) incremental growth curve was

based on a sample of 300 children followed from birth to 21 years of age. It followed a

similar pattern to Tanner’s growth curve with periods of acceleration and deceleration of

growth. A juvenile growth spurt was also noted in later childhood. During the adolescent

growth spurt, peak velocity reached the same level as when a child was growing at 2 years of

age. Bayer and Bayley found the average age of maximum velocity in height to be 14.5 years

for males and 11.5 years for females while Tanner et al found it to be 14.1 years and 12.1

years for males and females, respectively.

Growth and velocity curves have also been demonstrated for facial growth. Generally, facial

growth exhibits similar sigmoid distance curves as for general somatic growth. The

exceptions are the bones of the cranial base which tend to follow a neural type growth curve

(Bambha, 1961; Nanda, 1955). In his study, Johnston (Johnston et al., 1965) stated that in

most children a similar pattern of facial growth exists, both in terms of the shape of the

curve, as well as its timing.

Nanda (Nanda, 1955) analyzed the growth patterns of the human face from serial lateral

cephalometric roentgenograms of fifteen people (10M and 5F) covering an age range of 4 to

20 years. Seven linear facial measurements were recorded. He noted that these growth

curves have the basic characteristics of a statural growth curve, except that one of the marked

differences was the occurrence of secondary maximums that were seen often before and

sometimes after the circumpubertal growth cycle. All the curves started off with a

decelerating trend, which was sometimes interrupted between the ages of 5 and 10 years by

small secondary maximums. During adolescence, all the increment curves show a

circumpubertal maximum which was followed by a process of gradual decrease in the rate of

growth until the increments approached zero.

The time of the prepuberal maximums varied from as early as 7 years to as late as 11 years

and the growth of the face tended to have its circumpubertal maximum slightly later than that

6

for general body height. As expected, females attained peak growth earlier than the males

and showed relatively less facial growth during adolescence.

Nanda also noted the curves for sella-gnathion and nasion-gnathion were most like other

skeletal growth curves, whereas the curve for sella-nasion appeared to be a composite of the

patterns of both neural and skeletal growth. Growth of sella-nasion slowed off more

markedly after the age of 6 years and had barely a perceptible circumpubertal spurt. This

perhaps would be expected since sella-nasion is a common dimension between the cranium

and the face.

Studies investigating the difference in timing with respect to maximum stature velocity and

maximum facial growth velocity appear to be varied. Hunter (Hunter, 1966) studied the

longitudinal records of 34 females and 25 males from approximately 7 years through

adolescence and found that the age of maximum facial growth velocity was coincident with

that of stature in the majority of subjects in his study. In sixty six percent of the subjects, a

majority of the greatest increments of the seven facial measurements recorded occurred

coincident with the maximum increments of height.

This was confirmed by Pike (Pike, 1968) and Bergersen (Bergersen, 1972). Pike used

statistical computation of data to analyze the theories of linear regression and correlation in

the growth rates of certain facial parameters and body stature in 14 male and 11 female

subjects from age 7 to 12 years. He found there was a positive correlation between statural

growth rate and the growth rate of facial skeletal dimensions. The correlation coefficient

ranged from 0.419 to 0.647 for the various facial dimensions he studied. However, a

relatively high degree of variation between individuals existed in the sample and he did not

find any gender differences for any of the dimensional changes considered.

Bergersen (Bergersen, 1972) recorded seven linear measurements of the face including

anterior cranial base length, upper face height and depth, lower face height and depth, and

total face height in twenty three males from birth to maturity. Data on standing height was

taken on a semi-annual basis. He also found a significant correlation between the male

adolescent spurt of the face and standing height. He noted there was no difference in the

intensity of growth during the peak spurt between the facial dimensions and standing height.

7

Others such as Baughn et al. (Baughan et al., 1979), Nanda (Nanda, 1955) and Bambha

(Bambha, 1961) have stated that the peak of facial growth, although closely associated

usually occurs at a slightly later time. Baughan et al. (Baughan et al., 1979) analyzed the

longitudinal records of 50 French Canadian girls and found the facial pattern of growth

showed a distinct pubertal peak but that it was quantitatively less than that for stature. In

terms of timing, the two peaks were closely aligned although the evidence favoured a slightly

later development for the face.

Bambha (Bambha, 1961) found that in 80 percent of the subjects in his sample, the

maximum facial growth velocity (S-Gn and S-Go) followed maximum height velocity by 9

months. He also found that females reached their adolescent growth spurt 2 years earlier than

males and had a lower peak velocity. As noted previously, a similar relationship was

reported by Nanda (Nanda, 1955), however both investigators reported considerable

individual variation.

8

A. Mandibular Growth

Mandibular growth, as mentioned earlier, follows a general pattern similar to that of general

body growth (Bayley, 1956; Tanner, 1964). Tanner (Tanner, 1964) found that an

individual’s mandibular growth tend to channelize on a stature distance curve prior to

adolescence ie. children tend to remain in approximately the same percentile with respect to

population standards. Hunter (Hunter, 1966) studied the correlation of facial growth with

body height and found that among all the dimensions studied, mandibular length exhibited

the most consistent relationship with growth in height.

These findings were confirmed by Woodside (Woodside, 1968). He measured mandibular

length increments from the longitudinal records of 141 male and 120 female subjects of the

Burlington Growth study from ages 3 to 20 years. He found that the mandible underwent

similar phases of growth as compared to stature, including an adolescent growth spurt. In

males, the mandibular growth spurt occurred between the ages of 14 and 15 years while in

females the spurt occurred between 11 and 12 year of age.

In his study of mandibular growth, Harris’ (Harris, 1962) sample of 22 males and 18 females

both demonstrated periods of acceleration and deceleration in growth patterns. He identified

four periods of change in growth velocity: 1) a rapid acceleration of growth during the early

years of life, 2) a gradual acceleration of growth in early childhood ending in a plateau, 3) a

preadolescent period of deceleration of growth, and 4) the beginning of an adolescent spurt.

In addition to the adolescent growth spurt, Woodside (Woodside, 1968) and Savara (Savara

and Tracy, 1967) both noted a juvenile growth acceleration of the mandible occurring about

the ages of seven to nine years. Nanda (Nanda, 1955) also reported juvenile growth

accelerations however they occurred as late as 11 years in his sample. This juvenile growth

acceleration was found to bear a relationship to the adolescent growth spurt.

A summary of studies investigating the age and rate of peak mandibular growth is shown in

Table I.

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Table I – Summary of Peak Mandibular Growth Studies

From these included studies, it was seen that in males, the age at peak mandibular growth

ranged from 12.6 years to 14.5 years. Most of the studies reported PMG to occur between

13.6 years to 14.5 years with the exception of the investigation by Harris (Harris, 1962). He

analyzed mandibular length increments between the ages of 4 and 12 years in both females

and males and noted that males exhibited a strong acceleration of growth at 12 years of age.

However, he did not record any mandibular increments beyond this age. Therefore, Harris

recorded only the onset of the juvenile acceleration of growth for males.

Differences between males and females were found by several investigators with respect to

the age of peak mandibular growth velocity (Bambha, 1961; Harris, 1962; Lewis et al., 1985;

Pileski et al., 1973; Savara and Tracy, 1967; Tracy and Savara, 1966; Woodside, 1968). The

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timing of the peak pubertal growth of the mandible showed variation among these studies

however, females were consistently found to have an earlier adolescent growth spurt

compared to males. Peak mandibular growth in females varied from 10 years to 12.4 yearsa

among the studies. A twelve month phase difference was found by Harris (Harris, 1962),

with females reaching their peak mandibular growth velocity earlier than males. Bambha

(Bambha, 1961) noted a longer gender difference with the female adolescent growth spurt

occurring at 12.4 years and the male spurt occurring almost 2 years later. Within each

gender, Bambha also reported a four year range in the difference in timing of the age at

maximum mandibular growth velocity.

Pileski and Woodside (Pileski et al., 1973) measured mandibular growth from the

longitudinal records of 108 females and 91 males. Their findings supported those of Bambha

in that they found a gender difference of 2 years in the timing of the mandibular pubertal

growth spurt. Lewis and Roche (Lewis et al., 1982) and Tracy and Savara (Savara and

Tracy, 1967; Tracy and Savara, 1966) also reported a gender difference in the age of peak

mandibular growth. However, they found a difference of 1.5 years and noted that males

showed greater variation with respect to the timing of the peak velocity compared to females.

In terms of peak mandibular growth rate, gender differences were also found by Tracy and

Savara (Savara and Tracy, 1967; Tracy and Savara, 1966), Harris (Harris, 1962) and Lewis

and Roche (Lewis et al., 1985). All of these investigators found that annual mandibular

growth increments were generally greater for males. Males demonstrated a peak in

mandibular growth velocity between 3.26 mm/yr to 6.69mm/yr, whereas females reached a

peak mandibular growth velocity ranging from 2.43 mm/yr to 4.5 mm/yr.

The type of sample used in the various investigations could be a cause for the differences

encountered in the timing and rate of growth at the pubertal growth spurt in the various

studies. Many of the studies used mixed longitudinal samples which included longitudinal

and cross sectional records, therefore can lead to variation in the findings. Most studies also

used heterogeneous samples in terms of skeletal classification. Many studies have

demonstrated that the facial growth of subjects with skeletal class II and III is different from

those individuals with normal skeletal relationships. Ngan (Ngan et al., 1997) found that

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skeletal Class II individuals showed a combination of horizontal and vertical abnormalities of

the mandible and noted that increments of facial growth are not uniform, both in direction or

rate. It is also known that individuals with skeletal Class III tend to have mandibles which

grow larger and for longer periods of time compared to skeletal Class I or II subjects

(Baccetti et al., 2007; Reyes et al., 2006; Riesmeijer et al., 2004; Williams and Andersen,

1986).

The selection of landmarks used for mandibular measurements can also lead to variation.

The measurement selected was not always the same among the various studies. The method

of measuring mandibular length largely determines the accuracy of studies examining

mandibular growth. A frequent reference point used in these studies is the mandibular

condyle which is very difficult to determine accurately in a closed mouth lateral

cephalogram. Due to this difficulty, some studies used articulare in place of condylion (Ball,

2008; Hunter et al., 2007; Jamal, 2008).

To measure changes in mandibular length and changes in vertical and horizontal mandibular

condyle growth, Pancherz and Hagg (Hagg and Pancherz, 1988; Pancherz and Hägg, 1985)

and Weislander (Wieslander, 1993) recommended that these changes be analyzed by means

of open mouth lateral cephalograms. A study by Haas et al. (Haas et al., 2001) was designed

to compare these two techniques in measuring mandibular length. A strong correlation was

found to exist between the measurement of articulare to pogonion (Ar-Pg) by using closed

mouth lateral cephalograms in CO and CR positions. They also found a strong correlation

between condylion to pogonion (Co–Pg) by open mouth lateral cephalograms, which is not

dependent on whether the patient was in CO or CR.

A potential and unexplored cause of variation in the timing and rate of mandibular pubertal

growth spurts in these studies could be due to any differences in PMG of individuals with

vertical and horizontal facial growth patterns within the samples they studied.

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B. Facial Growth Patterns

It is well known that facial growth is composed of horizontal and vertical growth

(Creekmore, 1967; Schudy, 1964; Scott, 1958). Schudy (Schudy, 1964) investigated the

interaction of vertical and horizontal facial dysplasias and emphasized the importance of the

vertical facial dimension in orthodontic treatment. He described horizontal and vertical

growth as opposing forces, each vying for control of the anterior portion of the mandible.

The final vector of facial growth was therefore a result of the combination effects of these

two components of growth. He later introduced the term ‘facial divergence’ to describe facial

type based on indicators such as the occlusal mandibular (OM) and SN-MP angle. He used

the terms ’hyperdivergent’ and ‘hypodivergent’ to describe the extremes of facial divergence.

Other terms which have been used to describe different vertical facial types include high and

low angle, which also refer to the degree of facial divergence, and long or short facial types,

based on linear measurements of facial height.

Individuals with predominantly vertical growth patterns are associated with short posterior

and long anterior facial heights, a high mandibular plane angle, and open bite tendencies

whereas individuals with a horizontal facial pattern may exhibit long posterior and short

anterior facial heights, a low mandibular plane angle, and deep bite tendencies. Popovich

and Thompson (Popovich and Thompson, 1977) used records of 120 males and 90 females

from the Burlington growth center to produce cephalometric templates for six different ages

for females and seven different ages for males between 4 and 20 years of age. Based on the

longitudinal growth direction of the anterior part of the mandible, these templates were

separated into vertical, horizontal and average growth patterns to be used as a practical

approach to orthodontic case analysis and craniofacial growth (Figure 1).

13

Figure 1. Vertical and Horizontal Facial Growth Patterns (Female Burlington Templates).

©1977 The Governing Council, University of Toronto, Burlington Growth Center. The use of these figures are

by permission of the copyright holder

Creekmore (Creekmore, 1967) studied the longitudinal records of 62 untreated children (32

males and 30 females) with high and low angle facial types. His sample included subjects

with class I and class II malocclusions. He found that rotation of the mandible was the result

of a difference in vertical growth of the condyle and vertical growth in the molar area.

Therefore, when rotation of the mandible occurred, vertical growth of the condyle was

greater than the vertical growth in the molar area and the resultant forward growth of the chin

was less than the horizontal growth of the condyle. In contrast, when vertical growth of the

condyle was greater than vertical growth of the molar area, the forward growth of the chin

was greater than the horizontal growth of the condyle. This was also confirmed by Isaacson

(Isaacson et al., 1971) in his study. He stated further that the larger the inclination of the

mandible to the cranial base, steeper the mandibular plane and the more the chin moved

backward. Also, the smaller the inclination of the mandible to the cranial base, the flatter the

mandibular plane and the more the chin moved forward.

14

Creekmore also studied the effect of orthodontic treatment on facial growth and concluded

that the cant of the mandible is increased by treatment therefore affects both the horizontal

and vertical position of the mandible. He stated that this increase is permanent unless there

is post-treatment growth of the condyles in excess of the vertical growth in the molar area.

Metallic implant studies concerning mandibular growth patterns by Bjork and Skieller

(Bjork, 1963; Bjork and Skieller, 1983) demonstrated forward and backward rotation of the

mandible. They also demonstrated the true extent of mandibular rotation during growth is

masked by periosteal resorption and apposition along the mandibular border. They noted the

anterior portion of the chin underwent no visible remodeling whereas the most pronounced

remodeling occurred beneath the angular portion of the mandible. Therefore, they concluded

that the lower border of the mandible was unsuitable as a reference line for accurate

orientation of the mandible.

Vertical and horizontal growth patterns have also been described in terms of the Y-axis. The

Y-axis refers to a line connecting sella to gnathion and to the angle it creates with the

Frankfort horizontal. Downs (Downs, 1948) published the first complete analysis to quantify

variation in facial relationships and introduced this term to analyze the direction of growth of

the face and the mandible. In a control group of 20 individuals equally divided by gender, he

found the Y-axis to range from 53 to 66 degrees with a mean value of 59.4 degrees. As the

face swings out from under the cranium in its growth and development from birth to

maturity, it grows in a downward and forward direction. In normal development, Rakosi

(Rakosi, 1982) found this angle to decrease as an individual matures, therefore the growth of

the face is in a more forward than downward direction (horizontal growth). Conversely, the

Y-axis increases if growth of the face is in a more downward than forward direction (vertical

growth). This was confirmed by Schudy (Schudy, 1965) in his study of facial growth. In a

sample of 50 subjects from age 11 to 14 years he found that the relationship of facial height

to depth has a very high correlation with the Y-axis. In other words, as an individual

matures, the more the growth in face height exceeds the individual’s growth in face depth,

the more the Y-axis will increase and vice versa.

15

Several investigators have studied differences in facial parameters from samples of

individuals with various degrees of vertical facial dysplasia (Baccetti et al., 2008; Bishara

and Jakobsen, 1985; Chung and Mongiovi, 2003; Chung and Wong, 2002; Nanda, 1988).

Bishara and Jakobsen described the range of variation in the cranio-facial-dental

relationships in a population with normal occlusion. They divided a sample of 20 males and

15 females into normal, short and long facial types based on their ratio of posterior to

anterior facial height and mandibular plane angle. Records were taken from 4.5 to 12 years

of age biennially and annually through age 17 years with an additional record set at 25.5

years. In comparing absolute data, they found that long facial type (LFT) males and females

had a greater Y-axis than those with average (AFT) and short facial types (SFT) and that the

average facial type males and females had a greater Y-axis than those with a short facial

type. When comparing incremental changes, they found the SFT group had the greatest

closure in Y-axis and the LFT group had the least closure with some opening of Y-axis in

some subjects.

In terms of mandibular length, Bishara and Jakobsen found significant differences in males

with LFT having greater absolute mandibular length (Ar-Pog) compared to males with AFT

and SFT whereas in females, those with SFT had greater incremental change in Md length

(Ar-Pog) than females with AFT and LFT during the 10 to 15 year period.

More recently, Chung and Mongiovi (Chung and Mongiovi, 2003) investigated the

longitudinal craniofacial growth changes in untreated skeletal Class I subjects with low,

average, and high angle facial types. Cephalograms at ages 9 and 18 years were measured

for each subject in a sample of 36 males and 32 females. Their results showed a significant

difference in the change of Y-axis from age 9 to 18 years between average and high angle

males. High angle males had a mean closure of Y-axis of 1.95 degrees whereas average

males had a mean change of 0.55 degrees. Low angle males had a mean closure of 0.22

degrees however this finding was not significantly different from the other two groups. They

also found that females had a smaller change in mandibular body length compared to males

and that average males had a smaller longitudinal increase in mandibular body length

compared to low angle males.

16

Nanda (Nanda, 1988; Nanda and Rowe, 1989) investigated the developmental patterns and

pubertal growth spurts in the faces of individuals exhibiting divergent vertical dysplasias. He

used longitudinal data from 16 male and 16 female subjects, covering the ages of 3 through

18 years. His sample was divided into skeletal open bite and deep bite groups based on the

ratio of lower face height to total face height as measured from a single lateral cephalogram

at age 15 yrs for males and 13.5 years for females. He however, did not separate his subjects

according to sagittal skeletal pattern (Class I, II, or III). Longitudinal changes in face height

measurements and ramal height were analyzed. His results showed that female open-bite

subjects had the earliest timing of the adolescent growth spurt in the five facial dimensions

studied, followed in succession by the deep-bite female subjects, the open-bite male subjects,

and finally the deep-bite male subjects. The mean age of adolescent growth spurt for the

open-bite female subjects ranged from 11.3 for total anterior face height to 12.7 years for

total posterior face height.

Often when describing craniofacial growth, individuals with extreme variations of facial

form are either excluded from the study or the entire sample is assumed to have the same

growth potential. However, studies such as those described above, have found that

individuals with significant variation in facial form exhibit facial growth that is different

from average subjects (Baccetti et al., 2008; Bishara and Jakobsen, 1985; Chung and

Mongiovi, 2003; Nanda, 1988). It is possible that there are differences in the timing and rate

of peak mandibular growth for patients with vertical or horizontal facial growth patterns.

Such differences would have implications for initiating orthodontic therapy and maximizing

treatment effectiveness in that knowledge of the timings and magnitudes of PMG in vertical,

average, and horizontal facial growth patterns would necessitate an adjustment in the timing

of orthodontic and dentofacial orthopedic treatment according to a child’s facial growth

pattern.

17

Purpose of the Study

The purpose of this study was to determine if there are differences in peak mandibular

growth in skeletal class I individuals with different facial growth patterns and to determine if

there are differences in the resulting projection of the mandible in the horizontal and vertical

axes in different facial growth patterns.

18

Research Questions

1. Does the timing of peak mandibular growth in individuals with skeletal class I vertical

growth pattern differ from that in skeletal class I horizontal and average growth patterns?

2. Is there a gender related difference in the timing of peak mandibular growth in

individuals with skeletal class I horizontal, average and vertical growth patterns?

3. Does the peak mandibular growth velocity differ in individuals with skeletal class I

horizontal, average and vertical growth patterns?

4. Does the projection of the mandible relative to the cranial base differ among male and

female subjects with horizontal, average and vertical growth patterns?

19

Hypotheses

To address these research questions the following null hypotheses and alternate hypotheses

were framed:

Null Hypothesis: There is no difference in the timing of peak mandibular growth in

individuals with skeletal class I vertical, average and horizontal growth patterns.

Alternate Hypothesis: There exists a significant difference between the timing of peak

mandibular growth of individuals with skeletal class I vertical, average and horizontal

growth patterns.

Null Hypothesis 2: The timing of peak mandibular growth does not differ between skeletal

class I male and female subjects with vertical, average and horizontal growth patterns.

Alternative Hypothesis 2: There is a significant difference between the timing of peak

mandibular growth in skeletal class I male and female subjects with vertical, average and

horizontal growth patterns.

Null Hypothesis 3: The peak mandibular growth rate does not differ between vertical,

average and horizontal growing subjects.

Alternative Hypothesis 3: There exists a difference in the peak mandibular growth rate

between vertical, average and horizontal growing subjects.

Null Hypothesis 4: The projection of the mandible relative to the cranial base does not differ

between male and female subjects with vertical, average and horizontal growth patterns.

Alternative Hypothesis 4: There exists a difference in the projection of the mandible

relative to the cranial base between male and female subjects with vertical, average and

horizontal growth patterns.

20

Materials and Methods

A. Sample Description

The Burlington Growth Centre (BGC) data is a collection of longitudinal growth records

from the town of Burlington, Ontario, Canada established in 1951 by the Faculty of Dentistry

at the University of Toronto. The sample represented 85 to 90 percent of the children in

Burlington and the collection of data was completed in 1971. The BGC records are located

in the Burlington Orthodontic Research Centre at the University of Toronto. Practically all

study subjects were of Northern European ancestry and representative of the Canadian

Caucasian population. Excluding siblings and parents, it initially had 1248 participating

subjects separated into a serial experimental group and 4 control groups. The serial

experimental group initially consisted of 303 subjects, however due to attrition the size of the

sample diminished with increasing age. Records were taken annually, as close to the

subject’s birthday as was possible from age 3 to 18 years and older. Annual lateral

cephalometric radiographs included those taken in centric occlusion, centric relation and

open mouth positions.

An initial sample of 180 subjects (90 males and 110 females) had lateral cephalometric

records available from age 9 to 18 years. Only those subjects from the initial sample who

were untreated or had minimal orthodontic treatment were included. Sixty two subjects did

not have a treatment classification therefore the records of these individuals were examined

and the type of treatment, if any, was recorded for the study as a preliminary step for sample

selection.

These individuals were then categorized according to the Burlington classification as

follows:

UT - Untreated, habit consult

UT1 - Space maintainer, equilibration, extraction of any C, removal of

supernumerary tooth, facebow or monobloc for only 3-4 months or no cooperation,

upper and/or lower lingual archwires (space maintenance)

21

UT2 - Upper and/or lower lingual archwires for expansion, upper and/or lower bands

for correction of rotation only, extraction of 4’s, 5’s, or 6’s and no bands

T - Facebow, Monobloc, Full bands over an extended period of time (1-2 years)

Patients with a UT or UT1 classification were included in the sample. Eighty eight subjects

were excluded due to classification of UT2 or T. From the remaining 92 subjects, 7 were

excluded due to consecutive records being more than 24 months apart since it was decided

that this long an interval in consecutive growth records would render the data unusable to

make valid calculations of peak mandibular growth rate or its timing. The residual 85

subjects were classified into skeletal class I, II or III based on ANB measurements on lateral

cephalograms in centric occlusion at age 16 years according to the following criteria:

Class I: 1 ANB 4.5

Class II: ANB > 4.5

Class III: ANB < 1

For subjects whose records were not taken at age 16 years or where lateral cephalograms at

age 16 years were not of diagnostic quality, records for the next available age were used.

Twenty two subjects with skeletal Class II and III were excluded from the final sample.

The final study sample included 63 subjects (35 M and 28 F). This sample was further

classified into horizontal, vertical and average growth patterns based on longitudinal Y-axis

(N-S-Gn) measurements. Downs (Downs, 1948) described the y-axis as an expression of the

direction of growth of the face. It is a cephalometric indicator of the vertical and horizontal

coordinates of mandibular growth expressed in degrees of the inferior facial angle formed by

the intersection of the sella-gnathion plane with the Frankfort horizontal reference line

(Figure 2). The mean y-axis of his sample was 59.4 degrees with a range of 53 to 66 degrees.

Therefore, when y-axis is large (opened), the growth of the mandible is said to be expressed

in a more downward than forward direction compared to a normally growing subject.

22

Conversely, when y-axis is small (closed), the growth the mandible is said to be expressed in

a more forward than downward direction.

Figure 2. Y-axis

The final sample was classified (Table II) as described below:

Y-axis measurements at age 10 years and 16 years were recorded

Change in Y-axis measurements between ages 10 years and 16 years was recorded

for each subject.

The mean change in Y-axis for the entire sample was calculated to be -1.82 degrees.

Rounded to the nearest degree the mean reduction in Y-axis was 2 degrees.

Subjects were classified into Average, Vertical or Horizontal growth pattern groups

according to their change in Y-axis from 10 to 16 years as follows:

Average – Subjects whose Y-axis closed between 2 and 0 degrees (Y- axis

remained largely unchanged)

Vertical – Subjects whose change in Y-axis was greater than 0 degrees (Y-

axis opened)

23

Horizontal – Subjects whose change in Y-axis closed greater than 2 degrees

Average

(-2° ≤ Y-axis ≤ 0°) Vertical

(Y-axis > 0°) Horizontal

(Y-axis < -2°) Total

Male 9 8 18 35

Female 9 6 13 28

Total 18 14 31 63

Table II. Facial Growth Pattern Classification According to Change in Y-axis from 10 to 16 years

The final sample (n=63) had the following characteristics (Figure 3).

Inclusion criteria:

1. Serial lateral cephalograms from ages 9 through 18 years with no two consecutive

radiographs having been taken more than 24 months apart.

2. Skeletal Class I maxillomandibular relationship: ANB angle between 1 to 4.5

(inclusive) at age 16 years.

3. No or minimal orthodontic treatment.

Exclusion criteria:

1. A history of full orthodontic fixed appliance or functional appliance therapy

2. An ANB angle less than 1 or greater than 4.5 at age 16.

3. Consecutive lateral cephalograms greater than 24 months apart.

24

Figure 3. Final Sample Flowchart

Annual centric occlusion and open mouth lateral cephalograms for each subject from ages 9

through 18 years were scanned (Epson Perfection V700 Photo: 200 dpi, 16 bit,

uncompressed TIFF) and digitized (Viewbox 3.1). Due to superimposition of cranial

structures in the area of the temporomandibular joint, the head of the mandibular condyle

may be difficult to visualize in the centric occlusion lateral cephalogram. For this reason, the

open mouth lateral cephalogram was used to digitize mandibular length. The following

points were digitized:

Sella (S) - the midpoint of the cavity of sella turcica.

Nasion (N) - the most anterior point of the nasofrontal suture where the nasal bones intersect

with the frontal bone.

Gnathion (Gn) - the point on the lower margin of the mandible in the midsagittal plane,

where the anterior curvature becomes confluent with the base. The midpoint between the

most anterior and inferior point on the bony chin.

Condylion (Co) - the most superior and posterior point on the head of the condyle

25

Figure 4. Cephalometric Tracing

The following reference line and constructed points were also recorded. See Figure 4.

Surrogate FH (Frankfort Horizontal) – A line constructed 7 degrees below SN. The

reference line to which all measurements for Gn were recorded.

S’ – represented the intersection of S perpendicular (to surrogate FH) and a

perpendicular (to S perp) constructed through Gn.

Gn’ – represented the intersection of N perpendicular (to surrogate FH) and the line

S’-Gn.

26

The following measurements were recorded:

Mandibular length (Co to Gn)

Horizontal mandibular projection relative to S (S’ to Gn)

Vertical mandibular projection relative to S (S to S’)

Horizontal mandibular projection relative to N (Gn to Gn’)

Vertical mandibular projection relative to N (N to Gn’)

Mandibular growth rate (mm/yr) was determined by subtracting the preceding year’s

mandibular length measurement from the current year divided by the time interval.

Peak mandibular growth was determined as the maximum yearly incremental growth

following the pre-pubertal mandibular growth minimum (PPM). PPM was defined as

the age of minimal annual mandibular growth between ages 9 and 15 years as

determined from the incremental mandibular growth graphs.

27

B. Reliability

Peak mandibular growth

Identification of the age at peak mandibular growth was done by two examiners (B.L. and

S.S.) independently and at different times for the entire sample of 63 subjects. As described

previously, peak mandibular growth was determined by inspection of each subject’s annual

incremental mandibular growth graphs. The determinations of the age of PMG by both

examiners were 100 percent in agreement, which show that there was excellent inter-rater

reliability of this determination.

Mandibular Length and Projection Measurements

Intra-rater reliability for mandibular length measurements was determined by the investigator

(B.L.) re-tracing, digitizing and measuring the open mouth and centric occlusion lateral

cephalograms of thirty subjects randomly selected by the supervisor (S.S.). The investigator

(B.L.) was blinded to the identity of the subjects and the second tracings were done 6 months

after the first tracings. Intraclass-correlation coefficient analysis was used to determine

intraexaminer reliability of the 5 measurements (Table III) and the method error was

calculated by using Dahlberg’s formula (Dahlberg, 1940). Results of the ICC showed

excellent reliability with minimal method error.

28

* = Method error = √Ʃ D2/ 2 N where D is the difference in the repeated measurements and N is the number of

double measurements # = Intraclass correlation coefficient

Table III. Intra-rater Reliability for Mandibular Length Measurements

29

C. Analysis of Results

Subjects were placed into groups according to their growth pattern (Average, Horizontal,

Vertical) and each group was further subdivided according to gender. Data from the

following groups of subjects were analyzed:

1. Average

i. Males

ii. Females

2. Horizontal

i. Males

ii. Females

3. Vertical

i. Males

ii. Female

Mandibular growth rates were calculated, horizontal and vertical mandibular projection

relative to S and N were recorded for each subject from ages 9 through 18 years.

Yearly mandibular incremental growth and mandibular projection measurements were

recorded graphically at the age at which records were taken for each subject.

Age and rate of peak mandibular growth were determined for each individual from the

mandibular growth graphs (Figure 5). Mean age and rate of peak mandibular growth

were calculated for each group and subgroup.

Statistically, a two way analysis of variance (ANOVA) was used to test for significant

differences in the timing of peak mandibular growth and its magnitude between groups

and gender using the statistical softwares SAS (version 9.1, SAS Institute Inc., Cary, NC)

and Minitab (version 14.20, Minitab Inc., State College, PA).

Repeated measures of ANOVA were used to test for significant differences in the

mandibular growth velocity between groups, as well as differences in the horizontal and

vertical projection of the mandible.

To create a more clinically meaningful comparison, subjects whose Y-axis opened were

compared to those subjects whose Y-axis closed between the ages of 10 and 16 years.

The average and horizontal growth pattern groups were combined and this larger group

was compared to the vertical group.

30

An ANOVA was used test if mandibular growth rates significantly differed between the

different growth pattern groups one year prior to the peak in mandibular growth and one

year after its peak (PMG +/- 1 year). This analysis was also used to test if peak

mandibular growth rate significantly differed from the mandibular growth at PMG +/- 1

year.

The level of significance for comparisons of the age and rate of peak mandibular growth

was p<0.05.

In consideration of multiple testing for the comparisons of the cumulative mandibular

length and mandibular projection data, the level of significance was adjusted to be

p<0.01.

Figure 5. Mandibular Growth Rate Graph for Subject #27

31

Results

A. Age at Peak Mandibular Growth

All statistical calculations pertaining to the age at peak mandibular growth can be found in

Appendix 1.

Gender

The cumulative mandibular growth graph as shown in Figure 6 indicates a highly significant

gender difference in mandibular length over time (p< 0.0001). Using repeated measures of

ANOVA, the difference in mandibular length was statistically significant (p<0.001) at time

point 7 to 10 (ages 15 to 18 years) where the overall difference between males and females

was 4.13 +/- 1.21 mm.

32

Figure 6. Cumulative Mandibular Length vs. Age Graph

Overall, the males reached their peak mandibular growth at a mean age of 14.28 +/- 1.21

years. Females reached peak mandibular growth at a mean age of 12.66 +/- 0.91 years as

shown in Figure 7. The difference in the mean age at peak mandibular growth between the

males and females was statistically significant (p < 0.001).

33

Figure 7. Age Distribution at Peak Mandibular Growth (PMG) by Gender

34

Growth Pattern

The mean age of peak mandibular growth for each growth pattern group was not

statististically significant between the three groups. The vertical group had a mean age at

PMG of 13.23 years +/- 1.80 years, the average group had a mean age of 13.61 years +/- 1.11

years and the horizontal group had a mean age of 13.68 years +/- 1.27 years as shown in

Figure 8.

Figure 8. Age Distribution at Peak Mandibular Growth by Growth Pattern

35

Growth Pattern and Gender

Separating the growth pattern groups by gender, the subgroups had the following mean ages

at peak mandibular growth. For males, the mean age at PMG was 14.39 +/- 1.39 years for

the vertical group, 14.18 +/- 1.15 years for the average group, and 14.28 +/- 1.22 years for

the horizontal group. For females, the vertical groups had a mean age at PMG of 11.68 +/-

0.81 years, for the average group it was 13.03 +/- 0.72 years and for the horizontal group it

was 12.86 +/- 0.80 years (Figure 9). There was no statistically significant difference between

any of these subgroups.

Figure 9. Age at PMG - Distribution by Growth Pattern and Gender

36

Comparison of Combined Average + Horizontal and Vertical Groups

Subjects whose Y-axis opened were compared to those subjects whose Y-axis closed from

age 10 to 16 years by combining the Average and Horizontal groups (change in y-axis < 0)

and comparing this new group to the vertical group (change in y-axis > 0). For males, the

vertical group had a mean age at PMG of 14.39 +/- 1.38 years and the combined average and

horizontal group had a mean of 14.25 +/- 1.18 years. For females, the mean age at PMG for

the vertical group was 11.68 +/- 0.81 years and for the combined average and horizontal

group it was 12.93 +/- 0.76 years (Figure 10). However, no statistically significant

difference was found between any of these subgroups.

Figure 10. Age at PMG – Collapsed Average & Horizontal Groups

37

Interaction of Combined Growth Pattern with Gender

Although there was no significant difference in the main effects between the new growth

pattern groups, a significant interaction was found between gender and the new growth

pattern groups (p< 0.05) as shown in Figure 11.

Figure 11. Interaction (Combined A & H) – Age at PMG by Growth Pattern and Gender

38

B. Peak Mandibular Growth Rate

The rate at which mandibular growth occurred during the adolescent growth spurt was also

analyzed using a two way ANOVA. The following results describe the peak mandibular

growth rate of the different groups within the sample. All statistical calculations with respect

to the rate at peak mandibular growth can be found in Appendix 2.

Gender

Overall, males had a significantly higher mandibular growth rate during the adolescent

growth spurt compared to the females (p<0.0005). Peak mandibular growth rate was 5.31 +/-

1.4 mm/yr for males and 4.2 +/- 0.9 mm/yr for females (Figure 12).

Figure 12. Distribution of Peak Mandibular Growth (PMG) Rate by Gender

39

Facial Growth Pattern

The peak mandibular growth rate was calculated to be 4.6 +/- 1.4 mm/yr for the vertical

facial growth pattern group, 5.0 +/- 1.5 mm/yr for the average group, and 4.8 +/- 1.8 mm/yr

for the horizontal group (Figure 13). No significant difference in PMG rate was found

between the groups.

Figure 13. Distribution of PMG Rate by Growth Pattern

40

PMG +/- 1 year

Statistical calculations for the rate of peak mandibular growth +/- 1 year can be found in

Appendix 3. An ANOVA was used test if mandibular growth significantly differed between

the different growth pattern groups prior to the peak in mandibular growth and after its peak.

Mandibular growth rates one year prior to the adolescent growth spurt and one year after the

peak spurt are shown graphically in Figure 14.

1 – Average; 2 – Vertical; 3 – Horizontal

Figure 14. Mandibular Growth Rate at PMG and PMG +/- 1 year

41

The mean mandibular growth rate one year prior to peak mandibular growth (PMG – 1 year)

was calculated to be 2.2 +/- 1.4 mm/yr for the vertical group, 2.8 +/- 1.7 mm/yr for the

average group and 2.7 +/- 1.1 mm/yr for the horizontal group.

One year after peak mandibular growth (PMG + 1 year), the growth rate was 2.3 +/- 1.0

mm/yr for the vertical group, 2.2 +/- 1.4 mm/yr for the average group and 2.5 +/- 1.1 mm/yr

for the horizontal group.

For each facial growth pattern group, the mandibular growth rate for PMG – 1 year as well as

PMG + 1 year were significantly lower than the mandibular growth rate at PMG (p<0.0001).

However, no statistically significant differences were found in growth rate among the three

different growth pattern groups at PMG – 1 year or at PMG + 1 year.

42

Growth Pattern and Gender

The peak mandibular growth rates for the three growth patterns separated by gender are as

follows. For males, the peak mandibular growth rate was 4.6 +/- 1.6 mm/yr for the vertical

group, 5.7 +/- 1.6 mm/yr for the average group, and 5.4 +/- 1.3 mm/yr for the horizontal

group. For females, the rates were 4.5 +/- 1.2 mm/yr for the vertical group, 4.2 +/- 1.0

mm/yr for the average group, and 4.0 +/- 0.8 mm/yr for the horizontal group (Figure 15). No

significant differences were found between the growth pattern groups among the male and

the female samples.

Figure 15. Distribution of PMG Rate by Growth Pattern and Gender

43

Comparison of Combined Average + Horizontal and Vertical Groups

When the average and horizontal groups were combined, the mandibular growth rate during

peak adolescent spurt was 5.5 +/- 1.4 mm/yr for the males and 4.0 +/- 0.9 mm/yr for the

females (Figure 16). These mandibular growth rates were again not significantly different

from the growth rates of the male vertical (4.6 +/- 1.6 mm/yr) and female vertical (4.5 +/- 1.2

mm/yr) groups. There was also no significant interaction between growth pattern and

gender.

Figure 16. PMG Rate – Collapsed Average and Horizontal Groups

44

C. Mandibular Projection

Two way within subject repeated measures ANOVA was used to test differences in

mandibular projection between the three different growth patterns within each gender.

Horizontal and vertical mandibular projection in relation to Sella (S) and Nasion (N) from 9

to 18 years of age are presented below. All statistical calculations based on mandibular

projections can be found in Appendix 4.

Vertical mandibular projection in relation to Nasion (Fig. 17)

The statistical results for vertical mandibular projection relative to nasion indicate that there

were no significant differences between the growth pattern groups within the male and

female samples from age 9 to 18 years (Figure 18). From age 9 to 13 years no significant

gender effect was found however, from ages 14 to 18 years, the mandibular projection

significantly differed between the male and female samples (p<0.0001). The mean gender

difference at age 14 was 3.1 +/- 1.5 mm and increased to 7.3 +/- 1.5 mm by age 18 years.

Figure 17. N-Gn’ – Vertical Mandibular Projection in Relation to Nasion

45

Measurements of vertical projection in relation to nasion are shown in Table IV below.

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table IV. Vertical Mandibular Projection (N-Gn’) in Relation to Nasion by Growth Pattern and Gender

46

Figure 18. Vertical Projection (N-Gn’) - Distribution by Age, Growth Pattern and

Gender

47

Focusing on the change between ages 10 and 16 years, the mandibular projection (N-Gn’)

increased by 15.3 +/- 2.2 mm during that time interval for the male vertical group, 14.4 +/-

2.2 mm for the male average group, and 15.0 +/- 2.2 mm for the male horizontal group

(Figure 19). For female subjects, the vertical mandibular projection relative to nasion

increased by 10.6 +/- 2.2 mm for the vertical group, 11.0 +/- 2.2 mm for the average group

and 9.4 +/- 2.2 mm for the horizontal group during the interval between 10 and 16 years.

Figure 19. Vertical Projection (N-Gn’) – Boxplots for Age 10 and 16 years by Growth

Pattern and Gender

48

Vertical mandibular projection in relation to Sella (Fig. 20)

The difference in vertical mandibular projection relative to sella was also not statistically

significant from 9 to 18 years between the facial growth pattern groups among the male and

female samples (Figure 21). From 9 to 14 years no significant gender effect was found,

however from age 15 to 18 years the gender difference in projection was significant

(p<0.0001). At 15 years, the difference in mandibular projection between male and female

subjects was 4.7 +/- 1.6 mm and by 18 years it increased to 6.5 +/- 1.6 mm. Measurements

of vertical projection in relation to sella are shown in Table V below.

Figure 20. S-S’ – Vertical Mandibular Projection in Relation to Sella

49

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table V. Vertical Mandibular Projection (S-S’) in Relation to Sella by Growth Pattern and Gender

50

Figure 21. Vertical Projection (S-S’) - Distribution by Age, Growth Pattern and

Gender

51

The change in vertical projection relative to sella from age 10 to 16 years was 14.5 +/- 2.2

mm, 13.7 +/- 2.2 mm and 14.1 +/- 2.2 mm for males with a vertical, average, and horizontal

growth pattern, respectively. For the female subjects, it was 10.2 +/- 2.2 mm, 10.5 +/- 2.2

mm and 9.0 +/- 2.2 mm, for the vertical, average and horizontal groups, respectively (Figure

22).

Figure 22. Vertical Projection (N-Gn’) – Boxplots for Age 10 and 16 years by Growth Pattern and Gender

52

Horizontal mandibular projection in relation to Nasion (Fig. 23)

Boxplots for the distribution of horizontal mandibular projection by growth pattern and

gender from 9 to 18 years is shown in Figure 24. There was no statistically significant

difference in horizontal mandibular projection relative to nasion at any age between the

growth pattern groups. However, a trend towards statistical significance is evident between

the three growth pattern groups from age 9 to 18 years. When separated by gender, the

difference between the three facial growth pattern groups also showed no significance. A

significant gender difference was also not demonstrated. Measurements of horizontal

projection in relation to nasion for the different growth pattern groups are shown in Table VI

below. Table VII summarizes the horizontal projection data of each growth pattern group

separated by gender.

Figure 23. Gn-Gn’ – Horizontal Mandibular Projection in Relation to Nasion

53

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table VI. Horizontal Mandibular Projection (Gn-Gn’) in Relation to Nasion by Growth Pattern

54

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table VII. Horizontal Mandibular Projection (Gn-Gn’) in Relation to Nasion by Growth Pattern and Gender

55

Figure 24. Horizontal Projection (Gn-Gn’) - Distribution by Age, Growth Pattern and

Gender

56

The change in horizontal projection over time was relatively less pronounced in comparison

to the vertical changes. From age 10 to 16 years, the male sample had a change in horizontal

projection relative to nasion of 0.4 +/- 2.2 mm for the vertical group, 3.4 +/- 2.2 mm for the

average group and 5.9 +/- 2.2 mm for the horizontal group. The change in mandibular

projection for the female sample was 3.3 +/- 2.2 mm for the vertical, 2.8 +/- 2.2 mm for the

average and 5.2 +/- 2.2 mm for the horizontal groups (Figure 25).

Figure 25. Horizontal Mandibular Projection (Gn-Gn’) – Boxplots for Age 10 and 16

years by Growth Pattern and Gender

57

Horizontal mandibular projection in relation to Sella (Fig.26)

Boxplots for the distribution of horizontal mandibular projection by growth pattern and

gender from 9 to 18 years is shown in Figure 27. There was no statistically significant

difference in horizontal mandibular projection relative to sella at any age between the growth

pattern groups. A trend towards statistical significance is also evident between the three

growth pattern groups from age 9 to 18 years. When separated by gender, the difference

between the three facial growth pattern groups also showed no significance. Overall, no

significant gender difference was found except at age 17 and 18 years where the gender

difference in projection at age 17 years was 4.9 +/- 1.8 mm (p<0.0001). Measurements of

horizontal projection in relation to sella are shown in Table VIII below. Table IX shows

horizontal mandibular projections of the growth pattern groups separated by gender.

Figure 26. S’-Gn – Horizontal Mandibular Projection in Relation to Sella

58

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table VIII. Horizontal Mandibular Projection (S’-Gn) in Relation to Sella by Growth Pattern

59

Note: Number of subjects at age 17 and 18 years were smaller than at earlier ages

Table IX. Horizontal Mandibular Projection (S’-Gn) in Relation to Sella by Growth Pattern and Gender

60

Figure 27. Horizontal Projection (S’-Gn) - Distribution by Age, Growth Pattern and

Gender

61

The mandible projected forward from 10 to 16 years by 5.2 +/- 2.2 mm in the male vertical

group, 9.5 +/- 2.2 mm in the male average group and 12.4 +/- 2.2 mm in the male horizontal

group. For the female groups the horizontal projection was 6.4 +/- 2.2 mm for the vertical

group, 6.5 +/- 2.2 mm for the average and 8.7 +/- 2.2 mm for the horizontal (Figure 28).

Figure 28. Horizontal Mandibular Projection (S’-Gn) – Boxplots for Age 10 and 16

years by Growth Pattern and Gender

62

Discussion

The success of orthodontics and dentofacial orthodopedic treatment depends largely on facial

growth. Harvold (Harvold, 1963) examined growth of the maxillomandibular complex of

children from the Burlington Growth Center and found that growth of the mandible is largely

responsible for the change in the relationship between the maxilla and mandible. As there are

pubertal growth spurts during statural and facial growth, adolescent growth spurts have also

been shown to occur during mandibular growth (Bergersen, 1972; Daigle, 1974; Gomes and

Lima, 2006; Luks, 1969; Mitani and Sato, 1992). Growth occurs at an increased rate during

the mandibular pubertal growth spurt until it reaches a maximum, the peak mandibular

growth. Orthodontic or functional jaw orthopedic treatment can take advantage of this peak

mandibular growth to help correct any skeletal dysplasia that develops between the maxilla

and mandible. Therefore, in order to increase the likelihood of a successful outcome,

orthodontic and orthopedic treatment should be timed to include this period of maximum

mandibular growth. There is reasonable evidence to indicate that the patterns of facial

growth in individuals with extreme facial form are different than those with ‘normal’ facial

form (Chung and Mongiovi, 2003; Ferrario et al., 1999; Jamroz et al., 2006; Nanda, 1988;

Nanda and Rowe, 1989; Sassouni and Nanda, 1964). Therefore, the present study was

undertaken to determine if there are differences in the timing and rate of peak mandibular

growth and the resultant projection of the mandible in individuals with different facial

growth patterns.

Corroborating the findings of previous studies, a significant gender related difference

(p<0.001) in the timing of peak mandibular growth was detected, with females reaching their

peak mandibular growth earlier than males. Peak mandibular growth occurred at a mean age

of 12.66 +/- 0.91 years in females whereas males reached their peak mandibular growth at a

mean age of 14.28 +/- 1.21 years. In the present study, growth increments were recorded at

the record date after which the growth increment took place. Therefore, the age at peak

mandibular growth was recorded as the age the records were taken, as opposed to the

midpoint between yearly age intervals. This should be kept in cognizance when comparing

the age at PMG that was found in this study with that reported by Savara and Tracy

63

(Savara and Tracy, 1967), Pileski (Pileski et al., 1973), Nanda (Nanda, 1988), and Hunter

(Hunter et al., 2007), who used the midpoint between two successive records. This may

explain the 6 months difference that was seen in the age at PMG between their results and

the results from this investigation. Pileski found that males reached their peak mandibular

growth at 13.94 +/- 1.26 years and females at 11.97 +/- 1.02 years (p<0.05). Similarly,

Savara and Tracy found that males reached PMG at 13.6 +/- 1.83 years while Hunter found

that males reached their peak mandibular growth at 13.9 +/- 1.2 years. These results are

approximately 0.5 year earlier than the mean ages from the current study. On the other hand,

the age at PMG found in this study is similar to the findings of Ball (Ball, 2008) and Bambha

(Bambha, 1961) who used the age at the time the records were taken. Ball studied peak

mandibular growth in a longitudinal sample from the Burlington Growth Center and found

that males reached PMG at 14.4 years while Bambha found that males reached PMG at 14.26

years of age and females reached PMG at 12.41 years (p<0.05).

The timing of peak mandibular growth was not significantly different between the different

facial growth pattern groups. The vertical group had a mean age at PMG of 13.23 years +/-

1.80 years, the mean age at PMG for the average group was 13.61 years +/- 1.11 years and

for the horizontal group it was 13.68 years +/- 1.27 years. Each of these groups consisted of

both male and female subjects.

When separated by gender, comparison of the timing of PMG between the growth pattern

groups did not reveal any statistically significant differences. For males, the mean age at

PMG was 14.39 +/- 1.39 years for the vertical group, 14.18 +/- 1.15 years for the average

group, and 14.28 +/- 1.22 years for the horizontal group. This is consistent with a report by

Nanda (Nanda, 1988), who also did not find significant differences in four of five facial

dimensions he studied between males with skeletal open bite and deep bite facial types. The

open bite subjects were characterized by an excessive lower anterior vertical face height

whereas the deep bite subjects had a deficient lower anterior vertical facial height. He found

that the timing of peak pubertal growth varied for each facial dimension he studied. Peak

growth varied from 13.6 +/- 1.8 years to 14.2 +/- 1.9 years for open bite males and from 15.1

+/- 1.7 years to 15.6 +/- 1.0 years for deep bite males.

64

The female vertical group in the present study had a mean age at PMG of 11.68 +/- 0.81

years, the mean age for the female average group was 13.03 +/- 0.72 years and for the female

horizontal group it was 12.86 +/- .80 years. Nanda found that the adolescent growth spurt in

female open bite subjects occurred from 11.3 +/- 1.1 years to 12.7 +/- 2.6 years and in female

deep bite subjects the growth spurt varied from 12.4 +/- 1.4 years to 13.8 +/- 1.1 years.

Within the female sample, Nanda also did not find a significant difference in the timing of

peak pubertal growth between the facial types in all facial dimensions he studied. It should

be noted that comparison of the results from the present study to those from Nanda’s study is

limited in that he examined face height and ramal height as opposed to mandibular length

and his sample was divided on the basis of lower face height as a percentage of total face

height on a single cephalogram in contrast to the present study where the sample was

separated according to their change in Y-axis between cephalograms taken at ages 10 and 16

years.

Growth implies a change over time, therefore vertical and horizontal growth patterns are

more appropriately based on the changes observed between two cephalograms taken at

different time points. Although characteristics such as an open or deep bite are often

observed in subjects with vertical or horizontal growth patterns, they do not necessarily

develop in individuals with these types of growth patterns. Nanda also did not distinguish his

subjects into skeletal class I, II, or III. As noted previously, it is well known that facial

growth is different in individuals with different sagittal growth patterns (Baccetti et al., 2007;

Chung and Wong, 2002; Johnston et al., 1965; Karlsen and Krogstad, 1999; Ngan et al.,

1997; Riesmeijer et al., 2004; Stahl et al., 2008; Williams and Andersen, 1986).

Despite these limitations, for a comparison between the two studies, Nanda’s results are

consistent with the finding in this study in that females with vertical dysplasia seemed to

have the earliest peak in the adolescent growth spurt among all the groups. In Nanda’s study,

the mean age at peak growth for female open bite subjects occurred as early as 11.3 +/- 1.1

years for total anterior face height. The timing of peak growth for female open bite subjects

seemed to be the earliest to reach maximum growth in all five facial dimensions he studied

and was up to 1.7 years earlier than female deep bite subjects. In the present study, the

female vertical facial growth pattern group reached their PMG 1.18 years earlier than the

65

group with the next earliest age at PMG, the female horizontal group. However, although this

difference is clinically relevant, as will be discussed, statistical significance was not found.

To create a more clinically meaningful comparison, subjects whose Y-axis opened were

compared to those subjects whose Y-axis closed between the ages of 10 and 16 years.

Therefore, the average and horizontal growth pattern groups were combined and this larger

group was compared to the vertical group. As noted previously, there was an overall gender

effect in the timing of peak mandibular growth (p<0.001). In addition, there was a

significant interaction effect between growth pattern and gender (p<0.05). This interaction

could be attributed in part to the earlier attainment of PMG in vertically growing females

compared with the average and horizontal growing subjects. Given the clinically relevant

difference in the timing of PMG, if the clinician plans to target the peak mandibular growth,

orthodontic and dentofacial orthopedic treatment may need to be instituted in females with

vertical facial growth patterns according to this age of PMG

Males had a significantly higher peak mandibular growth rate than females (p<0.005). Peak

mandibular growth rate was 5.31 +/- 1.4 mm/yr for males and 4.2+/- 0.9 mm/yr for females.

The gender difference in yearly maximum mandibular growth increments is consistent with

investigations by Harris (Harris, 1962), Tracy and Savara (Savara and Tracy, 1967; Tracy

and Savara, 1966), and Lewis and Roche (Lewis et al., 1985). They found the peak rate of

mandibular growth in males to be 6.69 mm/yr, 4.6 + 1.0 mm/yr, and 3.26 + 1.47 mm/yr,

respectively. For females, the rate of peak mandibular growth was significantly lower

(p<0.05). They found the growth rate for females to be 4.5 mm/yr, 2.43 + 1.31 mm/yr, and

2.90 + 1.32 mm/yr, respectively. These differences explain why facial and mandibular

dimensions in males are generally larger than in females.

Peak mandibular growth rates were not found to be significantly different between the

different growth patterns among the males and females. A study by Chung and Mongiovi

(Chung and Mongiovi, 2003) who studied longitudinal craniofacial growth changes in

skeletal class I subjects with low, average and high mandibular plane angles also showed

similar findings. They found significant sex differences in linear measurements whereby

males had larger overall values than females (p<0.05). However, they did not find significant

66

differences in measurements such as mandibular body length among the male and female

low, average, and high angle groups.

To resemble a potential clinical scenario of treatment targeting PMG being commenced a

year too soon or a year too late relative to the age at PMG, this study found that it may not be

as efficient as treatment that were to commence just prior to and included the PMG. If

initiated too early, dentofacial orthopedic treatment would be unnecessarily prolonged in

order to benefit from the peak in mandibular growth or if it is initiated after the peak, the

treatment response may not be as much. A systematic review of functional appliance

treatment by Cozza et al. (Cozza et al., 2006) found that the average duration of active fixed

or removable functional appliance treatment is approximately 17 months. However, given

that many studies did not ideally time the initiation of dentofacial orthopedic treatment

relative to the adolescent growth spurt, active treatment duration can be as little as 6 to 9

months (Illing et al., 1998; Pancherz, 1982; Pancherz and Hägg, 1985; Tümer and Gültan,

1999).

To examine the difference from the rate at PMG, the mean mandibular growth rate for each

facial growth pattern group was calculated for the year preceding PMG (PMG-1 yr) and for

the year following PMG (PMG+1 yr). Comparison between growth pattern groups at all

three time points using two-way ANOVA showed no significant differences. Within each

growth pattern group, these mandibular growth rates were also compared to their respective

peak growth rates. For all three facial growth pattern groups, the mandibular growth rates

one year prior to the peak and one year following the peak were significantly lower

compared to the mean growth rates at PMG (p<0.0001). The rates at PMG-1 year and

PMG+1 year were approximately half the rate observed at the peak of the adolescent growth

spurt, which ranged from 4.6 – 5.0 mm/yr. The mean difference in the growth rate at PMG

and the rates in the year preceding and following peak growth was between 2.2 – 2.4 mm/yr

+/- 1.5 mm/yr. According to Cozza et al. (Cozza et al., 2006), an incremental difference of 2

mm in mandibular growth is clinically significant (p<0.05). This highlights the importance of

knowing the age of PMG in different facial growth patterns if the spurt is to be targeted

during treatment.

67

Since the female vertical group in this study reached PMG 1.18 years (14 months) earlier

than the next closest group, this timing, coupled with the PMG rates is clinically relevant.

The age at PMG between the growth pattern groups was not statistically significant.

Therefore, if female patients with a vertical facial growth pattern undergoing functional jaw

orthopedics had their treatment initiated according to the mean age at PMG for horizontally

growing females, then those patients may be starting treatment 14 months past their peak

mandibular growth. Any benefit from the maximal growth rate would have surpassed and

treatment time would be prolonged in order to produce the same clinical result due to the

significantly lower rate of growth one year following peak growth (p<0.0001). Growth past

the adolescent growth spurt would also be rapidly decelerating to adult levels, further

increasing active treatment time and decreasing the likelihood of successful treatment.

Furthermore, if females with a horizontal facial growth pattern initiated orthopedic treatment

according to the timing of PMG for vertically growing females, these patients would be

prematurely initiating treatment by 14 months. Since active treatment duration is on average

17 months, these patients would end treatment soon after reaching peak mandibular growth.

Terminating treatment at this time would minimize the potential benefit obtained from a

significantly increased rate of growth, and if treatment was extended it would be

unnecessarily prolonged thereby increasing the burden of treatment for these patients. On the

other hand, if active orthopedic treatment duration was 6 to 9 months such as in the studies

by Pancherz, Illing et al., and Tümer and Gültan (Illing et al., 1998; Pancherz, 1982;

Pancherz and Hägg, 1985; Tümer and Gültan, 1999), orthopedic treatment would not include

the period of maximal growth and end at a prepubertal stage of growth when there is a

significantly decreased rate of mandibular growth (p<0.0001).

The clinical significance of a measured increase in mandibular length also needs to be

considered in terms of chin projection. The growth and position of the mandible has an effect

on an individual`s profile and facial esthetics. An increase in length may be negated by

vertical facial growth whereas horizontal facial growth may enhance chin projection.

Dongieux and Sassouni (Dongieux and Sassouni, 1980) studied mandibular positional

variation and assessed its contribution to facial esthetics. They found that the anteroposterior

and vertical variation in mandibular position does influence the opinion of observers with

respect to facial esthetics (p<0.05).

68

In the present study, chin projections were examined relative to the anterior cranial base. A

two way repeated measures ANOVA was used to test differences in the horizontal and

vertical projections of the mandible between the different growth pattern groups from age 9

to 18 years. Both sella and nasion were used as reference points to measure mandibular

projection. Sella is a stable craniofacial landmark and is widely used as a point of reference

for cephalometric analysis. Nasion, although less stable due to its forward growth over time,

is a visible landmark used by an observer to better assess chin position and thereby an

individual’s profile. The difference in the vertical projection of the mandible relative to both

of these reference points was not shown to be statistically significant between the growth

pattern groups at any age within the male and female samples. However, a significant gender

related difference was found where males had a significantly greater vertical chin projection

relative to sella compared to females from age 15 to 18 years (p<0.0001). For vertical chin

projection relative to nasion the gender difference was significant from age 14 to 18 years

(p<0.0001).

The difference in horizontal chin projection between the growth pattern groups increased

continuously from age 9 to 18 years. In comparing the two extreme facial growth pattern

groups, the horizontal group had an increasingly larger horizontal chin projection compared

to the vertical group. This difference ranged from 0.3 +/- 7.4 mm to 6.6 +/- 7.5 mm in

relation to nasion and from 0.3 +/- 8.1 mm to 6.9 +/- 8.2 mm in relation to sella. Although

these differences were not statistically significant, a trend towards statistical significance was

evident over time. In relation to nasion, the p-value was as high as 0.97 at age 10 years and

continuously decreased to 0.04 by age 17 years. Similarly, in relation to sella, the p-value

was as high as 0.88 at age 10 years and decreased to 0.03 by age 17 years. The difference in

the horizontal chin projection between the growth pattern groups over time was expected

since the sample was divided according to the direction of growth of the mandible (Y-axis).

However, a statistical significance was not found due in part to the small number of subjects

in each group thereby decreasing the statistical power to detect significant differences

between these groups. The standard deviations of the mean chin projection was also large

and was likely due to the combined effect of small sample size and large individual

variations in facial size. Overall, the sex differences in relation to both sella and nasion also

69

were not significant, except at age 17 and 18 years for horizontal chin projection relative to

sella, which was greater in males (p<0.0001).

Although the cranial base has been shown to lengthen during growth (Lewis et al., 1985;

Nanda, 1990; Roche and Lewis, 1974), horizontal and vertical growth of nasion did not

significantly affect the results. In males, vertical chin projection increased by 17.6 +/- 2.3

mm relative to sella compared to 18.6 +/- 2.3 mm relative to nasion between the ages 9 to 18

years. For females, this projection increased by 12.8 +/- 2.3 mm relative to sella and by 13.3

+/- 2.3 mm relative to nasion. Since the vertical projections relative to both landmarks were

similar, vertical growth of nasion had very little effect on the vertical projection of the

mandible relative to cranial base. In contrast, horizontal projection in males increased by

12.0 +/- 2.4 mm relative to sella between ages 9 to 18 years, however due to the concomitant

forward growth of nasion, the effective increase in horizontal mandibular projection relative

to nasion was 3.9 +/- 2.3 mm. Similarly, in females, the projection increased by 8.9 +/- 2.4

mm relative to sella compared to an increase in horizontal projection of 4.3 +/- 2.3 mm

relative to nasion during growth. The horizontal growth of nasion, therefore, seemed to have

a more pronounced effect on horizontal chin projection due to the relatively greater

difference in horizontal mandibular projection between sella and nasion in both the male and

female samples.

The inclusion of the pubertal growth spurt in the treatment period can be regarded as a key

factor in the attainment of clinically significant supplementary mandibular growth with

functional jaw orthopedics. Variations in facial growth patterns amongst the population

imply that variations may also exist in the timing of the pubertal growth spurt. However, the

results of this investigation suggest that an adjustment in the timing of orthodontic and

dentofacial orthopedic treatment according to an individual`s facial growth pattern alone is

not necessary. Despite this, further investigation is warranted due the significant interaction

that was found between growth pattern and gender when those subjects with predominantly

vertical facial growth (Y-axis opened) were compared to those with predominantly

horizontal growth (Y-axis closed). Considering females with a vertical growth pattern

reached peak mandibular growth earlier than males and females with an average or

horizontal growth pattern, this clinically relevant difference in timing could explain, in part,

70

the interaction between growth pattern and gender. If the clinician is attempting to time

orthodontic and dentofacial orthopedic treatment to the age of peak mandibular growth, then

this earlier timing in vertically growing females should be considered.

71

Future Directions

Digital scanning of records from all the growth centers in North America is currently in

progress to compile a North America wide growth legacy collection of normative

cephalometric facial growth data. When this becomes available, the number of subjects

available for inclusion and analysis in future investigations will be significantly increased

allowing for detection of significant differences among the different facial growth patterns.

Based on the findings of this study and the data regarding the timing and rate of PMG

presented on pages 34 and 39, a sample size of more than 250 subjects per group would be

required to achieve 80% power to detect a significant difference of 0.5 yrs (the difference

noted between the timings of PMG in the vertical and horizontal growth pattern groups) with

an estimated standard deviation of 1.8yrs at the 0.05 level of significance, using a two-sided

2 sample t-test. Similarly, to detect a significant difference of the magnitude of difference

noted in the peak mandibular growth rates between these groups, more than 1200 subjects

would be required per group. These findings should be kept in mind while planning future

studies with larger samples.

The present study examined the timing of peak mandibular growth according to chronologic

age. Future studies may consider examining differences in the timing of peak mandibular

growth in subjects with vertical, average, and horizontal growth patterns according to

skeletal age and/or maturation.

72

Study Limitations

Due to an administrative error at the time when the Burlington Growth records were being

compiled, 51 subjects (23 M, 28 F) did not have records taken at age 15 yrs. Therefore, data

for missing 15 year records were extrapolated from data collected at ages 14 and 16 years.

All other subjects had consecutive annual records.

The results of this study apply only to those individuals of Caucasian descent due to the

ethnic origin of the study sample as described previously.

The sample size for this study was limited to those individuals whose cephalograms were

available from the Burlington Growth Center.

73

Conclusions

The following conclusions can be made with respect to the timing and rate of peak

mandibular growth in skeletal class I Caucasian subjects with vertical, average, and

horizontal facial growth patterns and their resultant mandibular projections:

1. Individuals with vertical, average and horizontal growth patterns do not significantly

differ in the timing of peak mandibular growth. The null hypothesis was accepted.

2. Females reach their peak mandibular growth earlier than males (p<0.0001) and males

have a significantly higher peak mandibular growth rate than females (p=0.003). The

null hypothesis was rejected.

3. The female vertical growth pattern group had a mean age at PMG of 11.68 +/- 0.81

years in comparison to the other groups which had a mean age at PMG which ranged

from 12.86 +/- 0.80 years to 14.39 +/- 1.39 years. This difference was clinically

relevant although not statistically significant.

4. Individuals with vertical, average and horizontal growth patterns do not significantly

differ in the rate of peak mandibular growth. The null hypothesis was accepted.

5. Vertical projections of the mandible do not significantly differ between different

growth patterns. The null hypothesis was accepted.

6. Differences in horizontal mandibular projection approached significance with growth.

74

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Appendix

Appendix 1 Age at Peak Mandibular Growth PMG Time at Peak Interaction with Gender The GLM Procedure Dependent Variable: Age_at_PMG Sum of Source DF Squares Mean Square F Value Pr > F Model 5 48.8116007 9.7623201 8.61 <.0001 Error 57 64.5960639 1.1332643 Corrected Total 62 113.4076646 R-Square Coeff Var Root MSE Age_at_PMG Mean 0.430408 7.850847 1.064549 13.55967 Source DF Type I SS Mean Square F Value Pr > F Growth_Pattern 2 2.06427279 1.03213639 0.91 0.4080 Gender 1 41.35610872 41.35610872 36.49 <.0001 Growth_Patter*Gender 2 5.39121923 2.69560961 2.38 0.1018 Source DF Type III SS Mean Square F Value Pr > F Growth_Pattern 2 3.23823488 1.61911744 1.43 0.2481 Gender 1 43.52108220 43.52108220 38.40 <.0001 Growth_Patter*Gender 2 5.39121923 2.69560961 2.38 0.1018

81

PMG Time at Peak Interaction with Gender The GLM Procedure Least Squares Means Growth_ Age_at_PMG Standard LSMEAN Pattern LSMEAN Error Pr > |t| Number 1 13.6044907 0.2509166 <.0001 1 2 13.0326736 0.2874610 <.0001 2 3 13.5689067 0.1937352 <.0001 3 Least Squares Means for effect Growth_Pattern Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: Age_at_PMG i/j 1 2 3 1 0.1395 0.9110 2 0.1395 0.1274 3 0.9110 0.1274 Growth_ Age_at_PMG Pattern LSMEAN 95% Confidence Limits 1 13.604491 13.102039 14.106943 2 13.032674 12.457043 13.608304 3 13.568907 13.180959 13.956855 Least Squares Means for Effect Growth_Pattern Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 0.571817 -0.192257 1.335891 1 3 0.035584 -0.599208 0.670376 2 3 -0.536233 -1.230390 0.157924 NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

82

PMG Time at Peak Interaction with Gender The GLM Procedure Least Squares Means H0:LSMean1= Age_at_PMG Standard H0:LSMEAN=0 LSMean2 Gender LSMEAN Error Pr > |t| Pr > |t| 0 14.2859954 0.1916407 <.0001 <.0001 1 12.5180520 0.2113370 <.0001 Age_at_PMG Gender LSMEAN 95% Confidence Limits 0 14.285995 13.902241 14.669749 1 12.518052 12.094857 12.941247 Least Squares Means for Effect Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 1.767943 1.196663 2.339224 Growth_ Age_at_PMG Standard LSMEAN Pattern Gender LSMEAN Error Pr > |t| Number 1 0 14.1834259 0.3548496 <.0001 1 1 1 13.0255556 0.3548496 <.0001 2 2 0 14.3927083 0.3763749 <.0001 3 2 1 11.6726389 0.4346003 <.0001 4 3 0 14.2818519 0.2509166 <.0001 5 3 1 12.8559615 0.2952527 <.0001 6

83

Age at PMG for Combined Average + Horizontal and Vertical Groups

PMG Time at Peak Interaction with Gender The GLM Procedure Dependent Variable: Age_at_PMG Sum of Source DF Squares Mean Square F Value Pr > F Model 3 48.6005125 16.2001708 14.75 <.0001 Error 59 64.8071521 1.0984263 Corrected Total 62 113.4076646 R-Square Coeff Var Root MSE Age_at_PMG Mean 0.428547 7.729232 1.048058 13.55967 Source DF Type I SS Mean Square F Value Pr > F new_Growth_pattern* 1 1.99246742 1.99246742 1.81 0.1832 Gender 1 41.39677097 41.39677097 37.69 <.0001 new_Growth_pa*Gender 1 5.21127412 5.21127412 4.74 0.0334 Source DF Type III SS Mean Square F Value Pr > F new_Growth_pattern 1 3.28727976 3.28727976 2.99 0.0889 Gender 1 43.70367342 43.70367342 39.79 <.0001 new_Growth_pa*Gender 1 5.21127412 5.21127412 4.74 0.0334 NOTE: * Combined Average + Horizontal groups vs. Vertical group

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PMG Time at Peak Interaction with Gender The GLM Procedure Least Squares Means H0:LSMean1= new_Growth_ Age_at_PMG Standard H0:LSMEAN=0 LSMean2 pattern LSMEAN Error Pr > |t| Pr > |t| 1 13.5871921 0.1505082 <.0001 0.0889 2 13.0326736 0.2830081 <.0001 new_Growth_ Age_at_PMG pattern LSMEAN 95% Confidence Limits 1 13.587192 13.286026 13.888358 2 13.032674 12.466376 13.598972 Least Squares Means for Effect new_Growth_pattern Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 0.554518 -0.086882 1.195919 H0:LSMean1= Age_at_PMG Standard H0:LSMEAN=0 LSMean2 Gender LSMEAN Error Pr > |t| Pr > |t| 0 14.3208758 0.2109418 <.0001 <.0001 1 12.2989899 0.2413501 <.0001 Age_at_PMG Gender LSMEAN 95% Confidence Limits 0 14.320876 13.898782 14.742969 1 12.298990 11.816049 12.781930 Least Squares Means for Effect Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 2.021886 1.380485 2.663286

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PMG Time at Peak Interaction with Gender The GLM Procedure Least Squares Means new_Growth_ Age_at_PMG Standard LSMEAN pattern Gender LSMEAN Error Pr > |t| Number 1 0 14.2490432 0.2016989 <.0001 1 1 1 12.9253409 0.2234468 <.0001 2 2 0 14.3927083 0.3705446 <.0001 3 2 1 11.6726389 0.4278680 <.0001 4 Least Squares Means for effect new_Growth_pa*Gender Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: Age_at_PMG i/j 1 2 3 4 1 <.0001 0.7347 <.0001 2 <.0001 0.0012 0.0119 3 0.7347 0.0012 <.0001 4 <.0001 0.0119 <.0001 new_Growth_ Age_at_PMG pattern Gender LSMEAN 95% Confidence Limits 1 0 14.249043 13.845445 14.652642 1 1 12.925341 12.478225 13.372457 2 0 14.392708 13.651250 15.134166 2 1 11.672639 10.816477 12.528801 Least Squares Means for Effect new_Growth_pa*Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 1.323702 0.721370 1.926035 1 3 -0.143665 -0.987852 0.700522 1 4 2.576404 1.629882 3.522927 2 3 -1.467367 -2.333204 -0.601531 2 4 1.252702 0.286821 2.218583 3 4 2.720069 1.587474 3.852665 NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

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Appendix 2 Rate at Peak Mandibular Growth PMG Rate Time at Peak Interaction with Gender The GLM Procedure Dependent Variable: PMG_rate Sum of Source DF Squares Mean Square F Value Pr > F Model 5 27.2708422 5.4541684 3.54 0.0074 Error 57 87.8538904 1.5412963 Corrected Total 62 115.1247327 R-Square Coeff Var Root MSE PMG_rate Mean 0.236881 25.85774 1.241490 4.801229 Source DF Type I SS Mean Square F Value Pr > F Growth_Pattern 2 1.32971459 0.66485730 0.43 0.6517 Gender 1 21.32417336 21.32417336 13.84 0.0005 Growth_Patter*Gender 2 4.61695427 2.30847714 1.50 0.2323 Source DF Type III SS Mean Square F Value Pr > F Growth_Pattern 2 1.63364833 0.81682417 0.53 0.5915 Gender 1 14.86385487 14.86385487 9.64 0.0030 Growth_Patter*Gender 2 4.61695427 2.30847714 1.50 0.2323

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PMG Rate Time at Peak Interaction with Gender The GLM Procedure Least Squares Means Growth_ PMG_rate Standard LSMEAN Pattern LSMEAN Error Pr > |t| Number 1 4.98789981 0.29262190 <.0001 1 2 4.56666178 0.33524050 <.0001 2 3 4.67798025 0.22593629 <.0001 3 Least Squares Means for effect Growth_Pattern Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: PMG_rate i/j 1 2 3 1 0.3478 0.4054 2 0.3478 0.7840 3 0.4054 0.7840 Growth_ PMG_rate Pattern LSMEAN 95% Confidence Limits 1 4.987900 4.401935 5.573865 2 4.566662 3.895354 5.237969 3 4.677980 4.225551 5.130410 Least Squares Means for Effect Growth_Pattern Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 0.421238 -0.469834 1.312310 1 3 0.309920 -0.430383 1.050222 2 3 -0.111318 -0.920853 0.698216 NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

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PMG Rate Time at Peak Interaction with Gender The GLM Procedure Least Squares Means H0:LSMean1= PMG_rate Standard H0:LSMEAN=0 LSMean2 Gender LSMEAN Error Pr > |t| Pr > |t| 0 5.26078042 0.22349366 <.0001 0.0030 1 4.22758081 0.24646368 <.0001 PMG_rate Gender LSMEAN 95% Confidence Limits 0 5.260780 4.813242 5.708319 1 4.227581 3.734046 4.721116 Least Squares Means for Effect Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 1.033200 0.366966 1.699433 Growth_ PMG_rate Standard LSMEAN Pattern Gender LSMEAN Error Pr > |t| Number 1 0 5.74329500 0.41382985 <.0001 1 1 1 4.23250463 0.41382985 <.0001 2 2 0 4.64247563 0.43893284 <.0001 3 2 1 4.49084793 0.50683599 <.0001 4 3 0 5.39657064 0.29262190 <.0001 5 3 1 3.95938986 0.34432725 <.0001 6

89

Rate at PMG for Combined Average + Horizontal and Vertical Groups

PMG Rate Interaction with Gender The GLM Procedure Dependent Variable: PMG_rate Sum of Source DF Squares Mean Square F Value Pr > F Model 3 26.1528435 8.7176145 5.78 0.0016 Error 59 88.9718892 1.5079981 Corrected Total 62 115.1247327 R-Square Coeff Var Root MSE PMG_rate Mean 0.227170 25.57690 1.228006 4.801229 Source DF Type I SS Mean Square F Value Pr > F new_Growth_pattern* 1 0.90104601 0.90104601 0.60 0.4426 Gender 1 20.80835659 20.80835659 13.80 0.0005 new_Growth_pa*Gender 1 4.44344086 4.44344086 2.95 0.0913 Source DF Type III SS Mean Square F Value Pr > F new_Growth_pattern 1 0.54107172 0.54107172 0.36 0.5515 Gender 1 6.77934630 6.77934630 4.50 0.0382 new_Growth_pa*Gender 1 4.44344086 4.44344086 2.95 0.0913 NOTE: * Combined Average + Horizontal groups vs. Vertical group

90

PMG Rate Interaction with Gender The GLM Procedure Least Squares Means H0:LSMean1= new_Growth_ PMG_rate Standard H0:LSMEAN=0 LSMean2 pattern LSMEAN Error Pr > |t| Pr > |t| 1 4.79163203 0.17634990 <.0001 0.5515 2 4.56666178 0.33159945 <.0001 new_Growth_ PMG_rate pattern LSMEAN 95% Confidence Limits 1 4.791632 4.438757 5.144507 2 4.566662 3.903133 5.230191 Least Squares Means for Effect new_Growth_pattern Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 0.224970 -0.526556 0.976496 H0:LSMean1= PMG_rate Standard H0:LSMEAN=0 LSMean2 Gender LSMEAN Error Pr > |t| Pr > |t| 0 5.07731053 0.24715964 <.0001 0.0382 1 4.28098328 0.28278896 <.0001 PMG_rate Gender LSMEAN 95% Confidence Limits 0 5.077311 4.582745 5.571876 1 4.280983 3.715124 4.846843 Least Squares Means for Effect Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 0.796327 0.044801 1.547853

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PMG Rate Interaction with Gender The GLM Procedure Least Squares Means new_Growth_ PMG_rate Standard LSMEAN pattern Gender LSMEAN Error Pr > |t| Number 1 0 5.51214543 0.23632982 <.0001 1 1 1 4.07111863 0.26181171 <.0001 2 2 0 4.64247563 0.43416560 <.0001 3 2 1 4.49084793 0.50133125 <.0001 4 Least Squares Means for effect new_Growth_pa*Gender Pr > |t| for H0: LSMean(i)=LSMean(j) Dependent Variable: PMG_rate i/j 1 2 3 4 1 0.0001 0.0837 0.0704 2 0.0001 0.2643 0.4610 3 0.0837 0.2643 0.8199 4 0.0704 0.4610 0.8199 new_Growth_ PMG_rate pattern Gender LSMEAN 95% Confidence Limits 1 0 5.512145 5.039251 5.985040 1 1 4.071119 3.547235 4.595003 2 0 4.642476 3.773712 5.511239 2 1 4.490848 3.487686 5.494009 Least Squares Means for Effect new_Growth_pa*Gender Difference Between 95% Confidence Limits for i j Means LSMean(i)-LSMean(j) 1 2 1.441027 0.735276 2.146777 1 3 0.869670 -0.119461 1.858800 1 4 1.021297 -0.087739 2.130334 2 3 -0.571357 -1.585854 0.443140 2 4 -0.419729 -1.551448 0.711990 3 4 0.151628 -1.175430 1.478686 NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

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Appendix 3 Rate at PMG +/- 1 year MG rate The Mixed Procedure Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Gender 1 59 8.64 0.0047 GrowthPattern 2 59 0.98 0.3822 time 2 124 97.11 <.0001 Least Squares Means Growth Standard Effect Gender Pattern time Estimate Error DF t Value Pr > |t| Alpha GrowthPattern 1 3.3279 0.1847 59 18.02 <.0001 0.05 GrowthPattern 2 2.9705 0.2099 59 14.15 <.0001 0.05 GrowthPattern 3 3.2829 0.1417 59 23.17 <.0001 0.05 Gender 0 3.4865 0.1374 59 25.37 <.0001 0.05 Gender 1 2.9010 0.1513 59 19.17 <.0001 0.05 time 1 2.5519 0.1527 124 16.71 <.0001 0.05 time 2 4.7361 0.1527 124 31.01 <.0001 0.05 time 3 2.2933 0.1527 124 15.01 <.0001 0.05 Least Squares Means Growth Effect Gender Pattern time Lower Upper GrowthPattern 1 2.9583 3.6976 GrowthPattern 2 2.5504 3.3905 GrowthPattern 3 2.9994 3.5664 Gender 0 3.2116 3.7615 Gender 1 2.5982 3.2038 time 1 2.2495 2.8542 time 2 4.4338 5.0385 time 3 1.9910 2.5957 Differences of Least Squares Means Growth Growth Standard Effect Gender Pattern time Gender Pattern time Estimate Error DF t Value GrowthPattern 1 2 0.3575 0.2796 59 1.28 GrowthPattern 1 3 0.04498 0.2328 59 0.19 GrowthPattern 2 3 -0.3125 0.2524 59 -1.24 Gender 0 1 0.5856 0.1992 59 2.94 time 1 2 -2.1843 0.1926 124 -11.34 time 1 3 0.2585 0.1926 124 1.34 time 2 3 2.4428 0.1926 124 12.68

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MG rate The Mixed Procedure Differences of Least Squares Means Growth Growth Effect Gender Pattern time Gender Pattern time Pr > |t| Alpha GrowthPattern 1 2 0.2061 0.05 GrowthPattern 1 3 0.8475 0.05 GrowthPattern 2 3 0.2205 0.05 Gender 0 1 0.0047 0.05 time 1 2 <.0001 0.05 time 1 3 0.1819 0.05 time 2 3 <.0001 0.05 Differences of Least Squares Means Growth Growth Effect Gender Pattern time Gender Pattern time Lower Upper GrowthPattern 1 2 -0.2021 0.9170 GrowthPattern 1 3 -0.4208 0.5108 GrowthPattern 2 3 -0.8175 0.1925 Gender 0 1 0.1869 0.9842 time 1 2 -2.5654 -1.8031 time 1 3 -0.1227 0.6397 time 2 3 2.0616 2.8240

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Appendix 4 Cumulative Mandibular Length and Projections

Cumulative Mandibular Length ML

Type 3 Tests of Fixed Effects

Num Den Effect DF DF F Value Pr > F

Gender_ 1 57 6.92 0.0109 GrowthPattern 2 57 0.54 0.5876 Gender_*GrowthPatter 2 57 1.52 0.2264 Time 9 497 965.77 <.0001 Gender_*Time 9 497 43.80 <.0001 GrowthPattern*Time 18 497 1.11 0.3343 Gender_*GrowthP*Time 18 497 1.15 0.2964

Tests of Effect Slices

Num Den Effect Gender Time DF DF F Value Pr > F

Gender_*GrowthP*Time 0 1 2 497 0.12 0.8833 Gender_*GrowthP*Time 0 2 2 497 0.35 0.7030 Gender_*GrowthP*Time 0 3 2 497 0.63 0.5308 Gender_*GrowthP*Time 0 4 2 497 1.48 0.2284 Gender_*GrowthP*Time 0 5 2 497 0.99 0.3727 Gender_*GrowthP*Time 0 6 2 497 2.14 0.1189 Gender_*GrowthP*Time 0 7 2 497 2.17 0.1147 Gender_*GrowthP*Time 0 8 2 497 2.40 0.0916 Gender_*GrowthP*Time 0 9 2 497 2.08 0.1259 Gender_*GrowthP*Time 0 10 2 497 1.86 0.1568 Gender_*GrowthP*Time 1 1 2 497 0.68 0.5066 Gender_*GrowthP*Time 1 2 2 497 0.65 0.5219 Gender_*GrowthP*Time 1 3 2 497 1.47 0.2320 Gender_*GrowthP*Time 1 4 2 497 1.67 0.1900 Gender_*GrowthP*Time 1 5 2 497 1.33 0.2651 Gender_*GrowthP*Time 1 6 2 497 0.61 0.5415 Gender_*GrowthP*Time 1 7 2 497 0.55 0.5795 Gender_*GrowthP*Time 1 8 2 497 0.48 0.6166 Gender_*GrowthP*Time 1 9 2 497 0.21 0.8096 Gender_*GrowthP*Time 1 10 2 497 0.38 0.6814

Tests of Effect Slices

Num Den Effect Time DF DF F Value Pr > F

Gender_*Time 1 1 497 1.65 0.1995 Gender_*Time 2 1 497 1.63 0.2016 Gender_*Time 3 1 497 0.35 0.5540 Gender_*Time 4 1 497 0.03 0.8574 Gender_*Time 5 1 497 0.00 0.9944 Gender_*Time 6 1 497 2.48 0.1157 Gender_*Time 7 1 497 11.71 0.0007 Gender_*Time 8 1 497 23.41 <.0001 Gender_*Time 9 1 497 31.55 <.0001 Gender_*Time 10 1 497 38.88 <.0001

95

Differences of Least Squares Means

Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha

Gender_*Time 0 1 1 1 1.5504 1.2068 497 1.28 0.1995 0.05 Gender_*Time 0 2 1 2 1.5431 1.2068 497 1.28 0.2016 0.05 Gender_*Time 0 3 1 3 0.7146 1.2068 497 0.59 0.5540 0.05 Gender_*Time 0 4 1 4 -0.2170 1.2068 497 -0.18 0.8574 0.05 Gender_*Time 0 5 1 5 -0.00840 1.2068 497 -0.01 0.9944 0.05 Gender_*Time 0 6 1 6 1.9016 1.2068 497 1.58 0.1157 0.05 Gender_*Time 0 7 1 7 4.1304 1.2068 497 3.42 0.0007 0.05 Gender_*Time 0 8 1 8 5.8390 1.2068 497 4.84 <.0001 0.05 Gender_*Time 0 9 1 9 6.9897 1.2445 497 5.62 <.0001 0.05 Gender_*Time 0 10 1 10 7.5410 1.2093 497 6.24 <.0001 0.05

96

Vertical Projection Relative to Nasion (N-Gn) N-GN The Mixed Procedure Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Gender 1 57 6.28 0.0151 GrowthPattern 2 57 0.49 0.6123 Gender*GrowthPattern 2 57 2.28 0.1118 Time 9 497 764.14 <.0001 Gender*Time 9 497 35.71 <.0001 GrowthPattern*Time 18 497 0.54 0.9368 Gender*GrowthPa*Time 18 497 1.09 0.3597 Tests of Effect Slices Num Den Effect Gender Time DF DF F Value Pr > F Gender*GrowthPa*Time 0 1 2 497 1.15 0.3189 Gender*GrowthPa*Time 0 2 2 497 1.23 0.2943 Gender*GrowthPa*Time 0 3 2 497 0.99 0.3725 Gender*GrowthPa*Time 0 4 2 497 0.82 0.4401 Gender*GrowthPa*Time 0 5 2 497 0.72 0.4862 Gender*GrowthPa*Time 0 6 2 497 1.12 0.3282 Gender*GrowthPa*Time 0 7 2 497 0.88 0.4160 Gender*GrowthPa*Time 0 8 2 497 1.53 0.2183 Gender*GrowthPa*Time 0 9 2 497 1.59 0.2051 Gender*GrowthPa*Time 0 10 2 497 1.70 0.1831 Gender*GrowthPa*Time 1 1 2 497 0.72 0.4886 Gender*GrowthPa*Time 1 2 2 497 1.08 0.3408 Gender*GrowthPa*Time 1 3 2 497 1.35 0.2602 Gender*GrowthPa*Time 1 4 2 497 1.67 0.1886 Gender*GrowthPa*Time 1 5 2 497 1.57 0.2081 Gender*GrowthPa*Time 1 6 2 497 1.30 0.2747 Gender*GrowthPa*Time 1 7 2 497 1.52 0.2198 Gender*GrowthPa*Time 1 8 2 497 1.77 0.1708 Gender*GrowthPa*Time 1 9 2 497 1.54 0.2158 Gender*GrowthPa*Time 1 10 2 497 1.68 0.1868 Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F Gender*Time 1 1 497 1.61 0.2058 Gender*Time 2 1 497 1.79 0.1819 Gender*Time 3 1 497 1.30 0.2544 Gender*Time 4 1 497 0.42 0.5167 Gender*Time 5 1 497 0.67 0.4143 Gender*Time 6 1 497 4.12 0.0428 Gender*Time 7 1 497 11.77 0.0007 Gender*Time 8 1 497 18.28 <.0001 Gender*Time 9 1 497 20.67 <.0001 Gender*Time 10 1 497 21.90 <.0001

97

N-GN Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 1 1 1.9603 1.5472 497 1.27 0.2058 0.05 Gender*Time 0 2 1 2 2.0683 1.5472 497 1.34 0.1819 0.05 Gender*Time 0 3 1 3 1.7653 1.5472 497 1.14 0.2544 0.05 Gender*Time 0 4 1 4 1.0041 1.5472 497 0.65 0.5167 0.05 Gender*Time 0 5 1 5 1.2642 1.5472 497 0.82 0.4143 0.05 Gender*Time 0 6 1 6 3.1423 1.5472 497 2.03 0.0428 0.05 Gender*Time 0 7 1 7 5.3073 1.5472 497 3.43 0.0007 0.05 Gender*Time 0 8 1 8 6.6144 1.5472 497 4.28 <.0001 0.05 Gender*Time 0 9 1 9 7.1618 1.5754 497 4.55 <.0001 0.05 Gender*Time 0 10 1 10 7.2488 1.5491 497 4.68 <.0001 0.05

N-GN Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 0 10 -18.6222 0.3895 497 -47.81 <.0001 0.05 Gender*Time 1 1 1 10 -13.3337 0.4363 497 -30.56 <.0001 0.05

N-GN Differences of Least Squares Means Growth Growth Standard Diff Effect Pattern Gender Time Pattern Gender Time Estimate Error DF Mean s.d. Gender*GrowthPa*Time A 0 2 A 0 8 -14.4333 0.7212 497 14.43 2.1636 Gender*GrowthPa*Time H 0 2 H 0 8 -14.9333 0.5100 497 14.93 2.1637 Gender*GrowthPa*Time V 0 2 V 0 8 -15.1875 0.7650 497 15.18 2.1637 Gender*GrowthPa*Time A 1 2 A 1 8 -11.0222 0.7212 497 11.02 2.1636 Gender*GrowthPa*Time H 1 2 H 1 8 -9.3769 0.6001 497 9.38 2.1637 Gender*GrowthPa*Time V 1 2 V 1 8 -10.5167 0.8833 497 10.52 2.1636

98

Vertical Projection Relative to Sella (S-S`)

S_S The Mixed Procedure Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Gender 1 57 4.67 0.0348 GrowthPattern 2 57 0.55 0.5786 Gender*GrowthPattern 2 57 2.27 0.1121 Time 9 497 724.75 <.0001 Gender*Time 9 497 31.89 <.0001 GrowthPattern*Time 18 497 0.54 0.9362 Gender*GrowthPa*Time 18 497 1.09 0.3632 Tests of Effect Slices Num Den Effect Gender Time DF DF F Value Pr > F Gender*GrowthPa*Time 0 1 2 497 1.15 0.3189 Gender*GrowthPa*Time 0 2 2 497 1.23 0.2943 Gender*GrowthPa*Time 0 3 2 497 0.99 0.3725 Gender*GrowthPa*Time 0 4 2 497 0.82 0.4401 Gender*GrowthPa*Time 0 5 2 497 0.72 0.4862 Gender*GrowthPa*Time 0 6 2 497 1.12 0.3282 Gender*GrowthPa*Time 0 7 2 497 0.88 0.4160 Gender*GrowthPa*Time 0 8 2 497 1.53 0.2183 Gender*GrowthPa*Time 0 9 2 497 1.59 0.2051 Gender*GrowthPa*Time 0 10 2 497 1.70 0.1831 Gender*GrowthPa*Time 1 1 2 497 0.72 0.4886 Gender*GrowthPa*Time 1 2 2 497 1.08 0.3408 Gender*GrowthPa*Time 1 3 2 497 1.35 0.2602 Gender*GrowthPa*Time 1 4 2 497 1.67 0.1886 Gender*GrowthPa*Time 1 5 2 497 1.57 0.2081 Gender*GrowthPa*Time 1 6 2 497 1.30 0.2747 Gender*GrowthPa*Time 1 7 2 497 1.52 0.2198 Gender*GrowthPa*Time 1 8 2 497 1.77 0.1708 Gender*GrowthPa*Time 1 9 2 497 1.54 0.2158 Gender*GrowthPa*Time 1 10 2 497 1.68 0.1868 Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F Gender*Time 1 1 497 1.10 0.2943 Gender*Time 2 1 497 1.21 0.2711 Gender*Time 3 1 497 0.86 0.3534 Gender*Time 4 1 497 0.23 0.6288 Gender*Time 5 1 497 0.37 0.5459 Gender*Time 6 1 497 2.99 0.0844 Gender*Time 7 1 497 9.09 0.0027 Gender*Time 8 1 497 14.43 0.0002 Gender*Time 9 1 497 16.37 <.0001 Gender*Time 10 1 497 17.17 <.0001

99

S-S Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 1 1 1.6426 1.5647 497 1.05 0.2943 0.05 Gender*Time 0 2 1 2 1.7240 1.5647 497 1.10 0.2711 0.05 Gender*Time 0 3 1 3 1.4532 1.5647 497 0.93 0.3534 0.05 Gender*Time 0 4 1 4 0.7569 1.5647 497 0.48 0.6288 0.05 Gender*Time 0 5 1 5 0.9455 1.5647 497 0.60 0.5459 0.05 Gender*Time 0 6 1 6 2.7053 1.5647 497 1.73 0.0844 0.05 Gender*Time 0 7 1 7 4.7177 1.5647 497 3.02 0.0027 0.05 Gender*Time 0 8 1 8 5.9426 1.5647 497 3.80 0.0002 0.05 Gender*Time 0 9 1 9 6.4387 1.5913 497 4.05 <.0001 0.05 Gender*Time 0 10 1 10 6.4918 1.5664 497 4.14 <.0001 0.05

S-S Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 0 10 -17.6083 0.3809 497 -46.23 <.0001 0.05 Gender*Time 1 1 1 10 -12.7592 0.4266 497 -29.91 <.0001 0.05

S-S Differences of Least Squares Means Growth Growth Standard Diff Effect Pattern Gender Time Pattern Gender Time Estimate Error DF Mean s.d. Gender*GrowthPa*Time A 0 2 A 0 8 -14.4333 0.7212 497 13.70 2.1636 Gender*GrowthPa*Time H 0 2 H 0 8 -14.9333 0.5100 497 14.13 2.1637 Gender*GrowthPa*Time V 0 2 V 0 8 -15.1875 0.7650 497 14.48 2.1637 Gender*GrowthPa*Time A 1 2 A 1 8 -11.0222 0.7212 497 10.54 2.1636 Gender*GrowthPa*Time H 1 2 H 1 8 -9.3769 0.6001 497 8.95 2.1637 Gender*GrowthPa*Time V 1 2 V 1 8 -10.5167 0.8833 497 10.17 2.1636

100

Horizontal Projection Relative to Nasion (Gn-Gn`)

GN-GN Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Gender 1 57 1.35 0.2509 GrowthPattern 2 57 0.93 0.4010 Gender*GrowthPattern 2 57 1.38 0.2607 Time 9 497 51.37 <.0001 Gender*Time 9 497 1.71 0.0847 GrowthPattern*Time 18 497 6.37 <.0001 Gender*GrowthPa*Time 18 497 2.10 0.0051 Tests of Effect Slices Num Den Effect Gender Time DF DF F Value Pr > F Gender*GrowthPa*Time 0 1 2 497 0.56 0.5732 Gender*GrowthPa*Time 0 2 2 497 0.80 0.4520 Gender*GrowthPa*Time 0 3 2 497 0.21 0.8123 Gender*GrowthPa*Time 0 4 2 497 0.26 0.7707 Gender*GrowthPa*Time 0 5 2 497 0.80 0.4510 Gender*GrowthPa*Time 0 6 2 497 1.06 0.3466 Gender*GrowthPa*Time 0 7 2 497 1.65 0.1932 Gender*GrowthPa*Time 0 8 2 497 2.15 0.1174 Gender*GrowthPa*Time 0 9 2 497 2.14 0.1187 Gender*GrowthPa*Time 0 10 2 497 2.10 0.1240 Gender*GrowthPa*Time 1 1 2 497 0.84 0.4344 Gender*GrowthPa*Time 1 2 2 497 0.39 0.6742 Gender*GrowthPa*Time 1 3 2 497 0.98 0.3776 Gender*GrowthPa*Time 1 4 2 497 1.24 0.2909 Gender*GrowthPa*Time 1 5 2 497 1.77 0.1722 Gender*GrowthPa*Time 1 6 2 497 1.87 0.1551 Gender*GrowthPa*Time 1 7 2 497 1.77 0.1707 Gender*GrowthPa*Time 1 8 2 497 1.71 0.1814 Gender*GrowthPa*Time 1 9 2 497 2.74 0.0652 Gender*GrowthPa*Time 1 10 2 497 1.97 0.1406 Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F GrowthPattern*Time 1 2 497 0.08 0.9269 GrowthPattern*Time 2 2 497 0.03 0.9719 GrowthPattern*Time 3 2 497 0.22 0.8043 GrowthPattern*Time 4 2 497 0.38 0.6871 GrowthPattern*Time 5 2 497 0.63 0.5315 GrowthPattern*Time 6 2 497 1.29 0.2771 GrowthPattern*Time 7 2 497 1.68 0.1875 GrowthPattern*Time 8 2 497 2.23 0.1082 GrowthPattern*Time 9 2 497 3.32 0.0369 GrowthPattern*Time 10 2 497 2.82 0.0605

101

Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F Gender*Time 1 1 497 0.44 0.5096 Gender*Time 2 1 497 0.59 0.4414 Gender*Time 3 1 497 1.61 0.2058 Gender*Time 4 1 497 1.58 0.2097 Gender*Time 5 1 497 2.41 0.1214 Gender*Time 6 1 497 2.43 0.1198 Gender*Time 7 1 497 1.77 0.1842 Gender*Time 8 1 497 1.65 0.1995 Gender*Time 9 1 497 0.40 0.5287 Gender*Time 10 1 497 0.88 0.3497

GN-GN Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 1 1 -1.0717 1.6239 497 -0.66 0.5096 0.05 Gender*Time 0 2 1 2 -1.2511 1.6239 497 -0.77 0.4414 0.05 Gender*Time 0 3 1 3 -2.0574 1.6239 497 -1.27 0.2058 0.05 Gender*Time 0 4 1 4 -2.0397 1.6239 497 -1.26 0.2097 0.05 Gender*Time 0 5 1 5 -2.5194 1.6239 497 -1.55 0.1214 0.05 Gender*Time 0 6 1 6 -2.5303 1.6239 497 -1.56 0.1198 0.05 Gender*Time 0 7 1 7 -2.1595 1.6239 497 -1.33 0.1842 0.05 Gender*Time 0 8 1 8 -2.0860 1.6239 497 -1.28 0.1995 0.05 Gender*Time 0 9 1 9 -1.0411 1.6514 497 -0.63 0.5287 0.05 Gender*Time 0 10 1 10 -1.5219 1.6258 497 -0.94 0.3497 0.05

GN-GN Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 0 10 -3.8903 0.3938 497 -9.88 <.0001 0.05 Gender*Time 1 1 1 10 -4.3405 0.4411 497 -9.84 <.0001 0.05

GN-GN Differences of Least Squares Means Growth Growth Standard Diff Effect Pattern Gender Time Pattern Gender Time Estimate Error DF Mean s.d. Gender*GrowthPa*Time A 0 2 A 0 8 -3.4111 0.7292 497 3.41 2.1876 Gender*GrowthPa*Time H 0 2 H 0 8 -5.9000 0.5156 497 5.90 2.1875 Gender*GrowthPa*Time V 0 2 V 0 8 0.4250 0.7734 497 -0.42 2.1875 Gender*GrowthPa*Time A 1 2 A 1 8 -2.8000 0.7292 497 2.80 2.1875 Gender*GrowthPa*Time H 1 2 H 1 8 -5.2077 0.6067 497 5.21 2.1875 Gender*GrowthPa*Time V 1 2 V 1 8 -3.3833 0.8931 497 3.38 2.1876

102

Horizontal Projection Relative to Sella (S`-Gn)

S-GN Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F Gender 1 57 1.31 0.2569 GrowthPattern 2 57 1.29 0.2839 Gender*GrowthPattern 2 57 1.45 0.2434 Time 9 497 294.15 <.0001 Gender*Time 9 497 15.66 <.0001 GrowthPattern*Time 18 497 7.27 <.0001 Gender*GrowthPa*Time 18 497 2.24 0.0026 Tests of Effect Slices Num Den Effect Gender Time DF DF F Value Pr > F Gender*GrowthPa*Time 0 1 2 497 0.62 0.5386 Gender*GrowthPa*Time 0 2 2 497 1.07 0.3449 Gender*GrowthPa*Time 0 3 2 497 0.37 0.6880 Gender*GrowthPa*Time 0 4 2 497 0.49 0.6110 Gender*GrowthPa*Time 0 5 2 497 1.30 0.2734 Gender*GrowthPa*Time 0 6 2 497 1.71 0.1811 Gender*GrowthPa*Time 0 7 2 497 2.37 0.0944 Gender*GrowthPa*Time 0 8 2 497 2.73 0.0664 Gender*GrowthPa*Time 0 9 2 497 2.32 0.0993 Gender*GrowthPa*Time 0 10 2 497 2.39 0.0923 Gender*GrowthPa*Time 1 1 2 497 1.06 0.3484 Gender*GrowthPa*Time 1 2 2 497 0.56 0.5690 Gender*GrowthPa*Time 1 3 2 497 0.94 0.3899 Gender*GrowthPa*Time 1 4 2 497 1.12 0.3269 Gender*GrowthPa*Time 1 5 2 497 1.70 0.1839 Gender*GrowthPa*Time 1 6 2 497 1.86 0.1564 Gender*GrowthPa*Time 1 7 2 497 1.84 0.1606 Gender*GrowthPa*Time 1 8 2 497 1.85 0.1583 Gender*GrowthPa*Time 1 9 2 497 2.61 0.0748 Gender*GrowthPa*Time 1 10 2 497 2.15 0.1176 Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F GrowthPattern*Time 1 2 497 0.25 0.7800 GrowthPattern*Time 2 2 497 0.13 0.8768 GrowthPattern*Time 3 2 497 0.26 0.7688 GrowthPattern*Time 4 2 497 0.40 0.6735 GrowthPattern*Time 5 2 497 0.96 0.3845 GrowthPattern*Time 6 2 497 1.84 0.1594 GrowthPattern*Time 7 2 497 2.41 0.0909 GrowthPattern*Time 8 2 497 3.05 0.0481 GrowthPattern*Time 9 2 497 3.50 0.0308 GrowthPattern*Time 10 2 497 3.27 0.0387

103

Tests of Effect Slices Num Den Effect Time DF DF F Value Pr > F Gender*Time 1 1 497 0.72 0.3972 Gender*Time 2 1 497 0.72 0.3962 Gender*Time 3 1 497 0.04 0.8349 Gender*Time 4 1 497 0.00 0.9702 Gender*Time 5 1 497 0.00 0.9524 Gender*Time 6 1 497 0.29 0.5903 Gender*Time 7 1 497 1.95 0.1627 Gender*Time 8 1 497 3.49 0.0622 Gender*Time 9 1 497 7.38 0.0068 Gender*Time 10 1 497 6.70 0.0099

S-GN

Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 1 1 1.5067 1.7780 497 0.85 0.3972 0.05 Gender*Time 0 2 1 2 1.5099 1.7780 497 0.85 0.3962 0.05 Gender*Time 0 3 1 3 0.3708 1.7780 497 0.21 0.8349 0.05 Gender*Time 0 4 1 4 0.06645 1.7780 497 0.04 0.9702 0.05 Gender*Time 0 5 1 5 0.1062 1.7780 497 0.06 0.9524 0.05 Gender*Time 0 6 1 6 0.9579 1.7780 497 0.54 0.5903 0.05 Gender*Time 0 7 1 7 2.4860 1.7780 497 1.40 0.1627 0.05 Gender*Time 0 8 1 8 3.3232 1.7780 497 1.87 0.0622 0.05 Gender*Time 0 9 1 9 4.9011 1.8044 497 2.72 0.0068 0.05 Gender*Time 0 10 1 10 4.6052 1.7798 497 2.59 0.0099 0.05

S-GN Differences of Least Squares Means Standard Effect Gender Time Gender Time Estimate Error DF t Value Pr > |t| Alpha Gender*Time 0 1 0 10 -11.9671 0.4038 497 -29.63 <.0001 0.05 Gender*Time 1 1 1 10 -8.8686 0.4524 497 -19.61 <.0001 0.05

S-GN Differences of Least Squares Means Growth Growth Standard Effect Pattern Gender Time Pattern Gender Time Estimate Error DF Std Dev Gender*GrowthPa*Time A 0 2 A 0 8 -9.4556 0.7478 497 2.2434 Gender*GrowthPa*Time H 0 2 H 0 8 -12.3833 0.5287 497 2.2431 Gender*GrowthPa*Time V 0 2 V 0 8 -5.1750 0.7931 497 2.2432 Gender*GrowthPa*Time A 1 2 A 1 8 -6.5444 0.7478 497 2.2434 Gender*GrowthPa*Time H 1 2 H 1 8 -8.6462 0.6222 497 2.2434 Gender*GrowthPa*Time V 1 2 V 1 8 -6.3833 0.9158 497 2.2432