Bronsen Schliep D.D.S.

Transcription

1 Longitudinal Assessment of Maxillary and Mandibular Molar and Incisor Dentoalveolar Heights and Growth Rates in Class I Subjects with Varied Craniofacial Growth Patterns as Classified by Directional and Proportionate Methods by Bronsen Schliep D.D.S. A thesis submitted in conformity with the requirements for the degree of Master of Science (Orthodontics) Graduate Department of Orthodontics Faculty of Dentistry, University of Toronto Copyright by Bronsen Schliep 2014

2 Longitudinal Assessment of Maxillary and Mandibular Molar and Incisor Dentoalveolar Heights and Growth Rates in Class I Subjects with Varied Craniofacial Growth Patterns as Classified by Directional and Proportionate Methods Bronsen Schliep Master of Science Degree, 2014 Discipline of Orthodontics, Faculty of Dentistry, University of Toronto Toronto, Ontario, Canada Abstract Objective: To determine if significant differences exist in dentoalveolar heights and dentoalveolar height growth rates, among skeletal Class I subjects that exhibit differing craniofacial growth patterns. Methods: One hundred and five subjects with cephalograms available at 9, 12, 14, and 16 years were categorized into directional (change in Y-axis angle) and proportionate (UFH:LFH) growth pattern groups. Maxillary and mandibular molar and incisor dentoalveolar heights and dentoalveolar height growth rates were determined. Comparisons were made by mixed model and ANOVA. Results: Neither dentoalveolar heights, nor growth rates differed significantly among directional classification groups in either gender. All dentoalveolar heights differed significantly among all proportionate classification groups at all ages in both male and female subjects. Conclusions: No statistically significant differences were found in dentoalveolar heights or dentoalveolar height growth rates of different directional growth pattern groups. Statistically significant differences were found in all dentoalveolar heights of different proportionate growth pattern groups. ii

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

4 Table of Contents Page Abstract.....ii Acknowledgements.....iii List of Tables......v List of Figures.... vi List of Appendices.....vii List of Abbreviations...viii I. Introduction and Statement of the Problem...1 II. Significance of the Problem....2 III. Review of the Literature....3 a. Craniofacial Growth Patterns.3 b. Determination of Craniofacial Growth Patterns..4 c. Assessment of Dentoalveolar Heights and Dentoalveolar Height Growth Rates..10 d. Summary 15 IV. Purpose of the study.. 16 V. Research Objectives...17 VI. Hypotheses 18 VII. Materials and Methods 19 a. Sample Description 19 b. Cephalometric Analysis..22 c. Growth Pattern Classification d. Reliability Analysis..30 e. Analysis of Results..31 VIII. Results..32 a. Dentoalveolar Heights.32 b. Dentoalveolar Height Growth Rates..49 c. Evaluation of the effect of gender on dentoalveolar height growth rates...82 IX. Discussion..90 X. Study Limitations..100 XI. Future Directions..102 XII. Conclusions 103 XIII. References..105 XIV. Appendices. 111 iv

5 List of Tables Table I: Table II. Table III. Table IV. Table V. Table VI. Table VII. Table VIII. Table VIII. Page Application of Exclusion Criteria phase I Application of Exclusion Criteria phase II 21 Directional Classification: Change in Y-axis angle (9 to 16 y) Directional growth pattern classification Directional groups: mean and standard deviation of Y-axis change (9 to 16 years) Proportionate Classification: UFH:LFH ratio (16 y) Proportionate growth pattern classification Proportionate groups: mean and standard deviation of UFH:LFH (16 years).29 Reliability Analysis..30 v

6 List of Figures Figure 1. Figure 2. Figure 3. Figure 4. Figures 5-12 Figure Figures Figures Figures Page Final Sample Flowchart Craniofacial and Dental Landmarks Craniofacial Reference Planes Maxillary and Mandibular Dentoalveolar Height Measurements...25 Directional Classification: Dentoalveolar heights at the maxillary and mandibular first molar and central incisor sites in females and males Proportionate Classification: Dentoalveolar heights at the maxillary and mandibular first molar and central incisor sites in females and males Directional Classification: Dentoalveolar height growth rates at the maxillary and mandibular first molar and central incisor sites in females and males in the 9 to 12 year, 12 to 14 year, and 14 to 16 year periods Proportionate Classification: Dentoalveolar height growth rates at the maxillary and mandibular first molar and central incisor sites in females and males in the 9 to 12 year, 12 to 14 year, and 14 to 16 year periods Evaluation of the effect of gender on dentoalveolar height growth rates: Dentoalveolar height growth rates at the maxillary and mandibular first molar and central incisor sites in females and males in the 9 to 12 year, 12 to 14 year, and 14 to 16 year periods vi

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

8 List of Abbreviations AFH AFT ANS ANS' Ar' BGC FH FMA Gn Go LFH LFT MP Me N OP PMG PFH S SN SFT TFH UFH anterior facial height average facial type anterior nasal spine anterior nasal spine prime articulare prime Burlington Growth Centre Frankfort horizontal Frankfort horizontal to mandibular plane angle gnathion gonion lower facial height long facial type mandibular plane menton nasion occlusal plane peak mandibular growth posterior facial height sella sella to nasion plane short facial type total facial height upper facial height viii

9 Introduction and Statement of the Problem Orthodontists are routinely tasked with the responsibility of managing malocclusions in the transverse, sagittal, and vertical dimensions. Of these three, the vertical dimension often presents the greatest difficulty, allowing the least margin of error in a clinical sense. Though vertical dysplasias typically present in certain fashions, they can take many forms, owing to dental compensation mechanisms at both the molar and incisor levels. For example, in hyperdivergent patients with open bite tendencies, dentoalveolar compensation occurring in the anterior region may significantly limit the typical presentation of a negative overbite. In fact, these patients may even present with an excessive dental overbite (Beckmann et al., 1998). Thus, dentoalveolar mechanisms have great potential in compensating vertical skeletal deviations resulting from inherent craniofacial growth patterns. Regarding craniofacial growth patterns, Bishara and Jakobsen (1985) conducted a longitudinal evaluation from ages 5 to 25 years of subjects categorized according to three facial types: relatively long, average, and relatively short faces. Of these, 77% had the same facial type at 5 years and 25 years of age. There was a strong tendency to maintain the original face type with age. Other studies have agreed that the morphogenetic craniofacial growth pattern is established early in life and subsequent growth increments tend to follow that initial pattern (Sassouni and Nanda, 1964; Nanda, 1988; Jacob and Buschang, 2011). Though the overall pattern is generally maintained, craniofacial growth has been found to proceed at a variety of rates in differing directions (Lande, 1952; Subtelny, 1959) with alveolar development exhibiting regional differences during pubertal growth (Arat and Rubenduz, 2005). Therefore, changes in facial projection and occlusion may result from the relative motion of the various parts of the dentofacial complex with growth (Sinclair and Little, 1985), which would disguise easily recognizable dentoalveolar patterns. Therefore, the following question arises: Is there a statistically significant difference in molar and incisor dentoalveolar heights and dentoalveolar height growth rates in skeletal Class I subjects exhibiting various craniofacial growth patterns evaluated longitudinally? 1

10 Significance of the Problem Dentoalveolar heights can be modified, to a certain extent, by orthodontic treatment (Martina et al., 2005), and adolescents undergo dramatic changes in maxillary and mandibular dentoalveolar heights that hold important clinical implications. The vast majority of patients treated orthodontically are children, and the period between 8 and 14 years of age is the stage at which corrective orthodontic treatment is most frequently applied (Chen et al., 2007). Therefore, an evaluation of the dentoalveolar height growth changes normally occurring during this period may provide valuable information. The amount of growth of the mandible and concurrent eruption of the dentition seems to have posttreatment stability implications. Alexander (1996) found that Class I extraction cases with the greatest mandibular vertical growth post-treatment displayed the greatest increases of incisor irregularity during the retention phase. Increased vertical ramal growth leads to increased dentoalveolar eruption, which in turn creates the potential for instability. Furthermore, Naumann et al. (2000) evaluated the multidimensional nature of overbite changes that occur during adolescence. Their multivariate model suggested that mandibular changes, specifically vertical growth and rotation, are more important than maxillary changes in determining overbite variations. The large amount of eruption of the lower incisors that normally occurs over 7 mm on average during adolescence provides enormous potential for modifying the overbite (Naumann et al., 2000). Thomas Creekmore noted that if it were possible to control the vertical growth of the face, it would be possible to solve nearly all orthodontic problems (Creekmore, 1967). An understanding of the typical dentoalveolar height presentations and dentoalveolar height growth rates for patients presenting with extremes in the vertical dimension may aid the clinician in making proper biomechanical decisions for both treatment and stability concerns. On the other hand, failure to recognize and manage the vertical dimension of a challenging case may leave the clinician and patient with few options other than orthognathic surgery to correct the resulting dentofacial deformity. Consequently, a thorough understanding of the consequences of an individual s growth pattern and potential differences between methods of assessment (e.g. directional versus proportionate) may aid the clinician in recognizing significant craniofacial and dentoalveolar inter-relationships and implementing the most ideal orthodontic mechanotherapy to achieve proper overbite, overjet, and dental relations within such constraints. 2

11 Review of the Literature A. Craniofacial Growth Patterns Orthodontists have long placed considerable attention on the significance of interrelationships between craniofacial growth and the development of the occlusion (Hellman, 1933; Bjork, 1951). From the lateral perspective, facial growth direction is determined by the amount of both horizontal and vertical components. The proportion of facial height to facial depth has not only a direct bearing upon facial type but also a direct influence upon vertical overbite and dental function (Schudy, 1964). As a result, one would reasonably expect that dentoalveolar heights are influenced by the vertical facial development, or lack thereof. Due to the complexity of the vertical craniofacial dimension, skeletal and dental tendencies have been extensively studied for correlations with various growth patterns or facial types. In general, individuals with a predominantly vertical growth pattern are associated with: short posterior and long anterior facial heights (i.e. long facial type) a high mandibular plane angle (i.e. hyper-divergent, high-angle) open bite tendencies On the other hand, individuals with a horizontal facial growth pattern are associated with: long posterior and short anterior facial heights (i.e. short facial type) a low mandibular plane angle (i.e. hypo-divergent, low-angle) deep bite tendencies Bishara and Jakobsen (1985) conducted a longitudinal evaluation from 5 to 25 years of age of 35 subjects, who were categorized into three facial types: relatively long, average, and relatively short faces. Their results showed that 77% of subjects had the same facial type at 5 years and 25 years of age. Consequently, they concluded that a strong tendency exists to maintain the original face type with age. Other researchers have also corroborated this finding (Sassouni and Nanda, 1963; Cangialosi, 1984; Nanda, 1988; Jacob and Buschang, 2011). As a result, multiple quantitative cephalometric measures have been proposed to identify various craniofacial growth patterns with the intention of aiding the clinician in prospectively identifying future types of craniofacial growers or simply identifying the craniofacial region to be addressed in a non-growing individual. 3

12 B. Determination of Craniofacial Growth Patterns Methods to determine the vertical or horizontal nature of craniofacial growth patterns are primarily constrained to soft or hard tissue assessment of either frontal or lateral profile images. Regarding lateral cephalometric radiographs, the osseous craniofacial measurements generally consist of three types: angular, linear, or proportionate. Concerning vertical facial parameters, the following measures are routinely used: Angular measures o Mandibular plane angle SN-MP (sella-nasion plane to mandibular plane) FH-MP (Frankfort horizontal plane to mandibular plane) o Y-Axis angle NSGn (sella-nasion plane to sella-gnathion plane FH-SGn (Frankfort horizontal plane to sella-gnathion plane) Linear measures o N-ANS (nasion to anterior nasal spine) o N-ANS' (nasion to anterior nasal spine prime) o N-Me (nasion to menton) o ANS-Me (anterior nasal spine to menton) o Ar'-Go (articulare prime to gonion) o S-Go (sella to gonion) Proportions (ratios) o N-ANS:ANS-Me % (nasion to anterior nasal spine : ANS to menton) Interpretation: Upper facial height : lower facial height (anterior) o N-ANS :N-Me % (nasion to anterior nasal spine prime : nasion to menton) Interpretation: Upper facial height : total facial height (anterior) o Ar-Go:S-Go % (articulare to gonion : sella to gonion) Interpretation: Lower facial height : total facial height (posterior) o S-Go:N-Me % (sella to gonion : nasion to menton) Interpretation: Posterior facial height : anterior facial height 4

13 Angular measurements In predicting the craniofacial growth pattern of a young patient, the clinician will often consider the inclination of the mandibular plane (MP). According to Schudy (1964, 1965) and Isaacson et al. (1971), the degree of inclination of the MP to the anterior cranial base (SN) has an effect on the degree of mandibular rotation with growth. A greater SN-MP angle causes the mandible to become steeper and the chin to move backward, which would indicate a vertical growth tendency. A smaller angle indicates a greater tendency of the mandible to become flatter and the chin to grow forward, indicating more of a horizontal growth pattern. When investigating the interaction of anteroposterior and vertical facial dysplasias, Schudy (1964) used the SN-MP angle to determine the proportions that produced average versus extreme facial types. He divided his sample of 120 patients into three groups based on their SN-MP angle and coined the phrase facial divergence as a method of indicating vertical variation. The two extremes of facial divergence were described as hyperdivergent for individuals with a large mandibular plane angle and hypodivergent for individuals with a small mandibular plane angle. His description of facial divergence resounded well in the orthodontic profession and has withstood the test of time. A variety of SN-MP angle cutoff points for hypodivergent and hyperdivergent classifications have been used in previous studies. For 120 patients aged 11 to 14 years, Schudy (1964) divided the sample into average (31-34 ), hyperdivergent/retrognathic (>34 ), and hypodivergent/prognathic (<31 ) groups. Isaacson (1971) studied 60 young adolescents with extreme variations in vertical facial growth and stipulated a cutoff point for hyperdivergency of >38 and hypodivergency of <26. On a sample of 129 subjects, Bishara and Augspurger (1975) used the cutoff of ±1 standard deviation from the sample mean, which resulted in a definition of high-angle cases as those with values 34.8 and low-angle cases as those with Rather than utilizing SN as the plane of reference, the FMA (Frankfort horizontal to mandibular plane angle) is formed by the intersection of the Frankfort horizontal plane and the mandibular plane. From clinical research, Tweed (1966) concluded that the normal variations of FMA are with an average angle of According to DiPietro and Moergeli (1976), the rule of thumb is that an FMA of 25 ± 5 is within normal range. A high-angle patient is considered to have an FMA of 30 or more, whereas a low angle patient is one with an FMA of 20 or less. With respect to vertical facial types, a high FMA is 5

14 characterized by an open-bite skeletal pattern while a low FMA is characterized by a closed-bite skeletal pattern. However, one must be cognizant that variations from this mean are known to exist among races, age, and sex. In addition, the skeletal patterns should not be confused with open- and closed-bite dental patterns (DiPietro and Moergeli, 1976), as variations of anterior dental presentation do not imply a specific type of skeletal pattern. For example, an individual with a vertical skeletal pattern may present with a deep, open, or normal dental overbite. Though FMA and SN-MP angle measurements have been and continue to be widely used, the variability between subjects in the orientation of the Frankfort horizontal plane and sella-nasion plane can be quite large. Consequently, their validity has come under scrutiny due to the potential for substantial differences among individuals (Bjerin, 1957; Lundström and Lundström, 1995) that may cause the cutoff points between mandibular plane divisions to become very sample specific and quite variable. Furthermore, assessment of the mandibular plane does not come without caution. Using metallic implants as reference points in the maxilla and mandible, Bjork and Skieller (1972) found a general feature of facial development was forward rotation of both jaws but greater for the mandible. There was a strong association between facial rotation and condylar growth. At the lower border of the mandible, approximately one half of the rotation was masked by compensatory remodeling. At the posterior border of the ramus, approximately four fifths of the mandibular rotation was masked by compensatory remodeling. Likewise, the rotation of the maxilla was masked by remodeling of the nasal floor, which remained almost unchanged in inclination. Interestingly, they found that only 2 of 21 subjects had backward mandibular rotation. Most subjects (19 of 21) showed forward rotation, including some with a high SN-MP angle. Consequently, the maxillomandibular growth pattern may be masked by a higher or lesser degree of compensatory osseous remodeling among individuals, and those variations create the potential for common correlations to falter in outliers of the human population. Rather than utilizing the mandibular plane, craniofacial growth patterns have also been described in terms of the Y-axis angle, of which there are two methods used. The original Y-axis angle referred to a line connecting sella to gnathion and the angle it creates with the Frankfort horizontal plane. The second uses the reference plane of sella to nasion, assuming the anterior cranial base is relatively more stable intra-individually than the Frankfort horizontal plane during growth and development. In 1948, Downs published one of the first cephalometric analyses to quantify variation in facial relationships and 6

15 described the term Y-axis to analyze the growth direction of the face and mandible. In a control group of 20 individuals equally divided by gender, he found the Y-axis to range from 53 to 66 with a mean value of Therefore, as the face swings out from under the cranium during its growth and development from birth to maturity, it grows in a downward and forward direction. In 1982, Rakosi found the Y-axis angle to decrease as a normally growing individual matures; therefore, the growth of the face is in a slightly more forward than downward direction (i.e. horizontal growth). Conversely, the Y-axis angle increases if growth of the face is in a more downward than forward direction (i.e. vertical growth). Schudy s (1965) research on facial growth corroborates this account. In a sample of 50 subjects from 11 to 14 years of age, the relationship of facial height to depth was found to have a very high correlation with the Y-axis. In other words, as an individual matures, the more the growth in anterior face height exceeds the individual s growth in face depth, the more the Y-axis will increase and vice versa. However, Schudy also noted that the Y-axis is not sensitive enough to relate information on the vertical growth of the posterior to anterior dental heights, gonion angle, ramus height, or the relative position of the mandibular molars within the body of the mandible. Linear measurements Although several linear dimensions have been studied pertaining to the vertical development of the face, the exclusive use of linear measurements for craniofacial growth pattern classification is not justified. In 1948, Downs noted that a comparison of two or more individuals on the basis of linear measurements is of little value due to differences expected between genders and for growth over time. Comparing mixed- to permanent-dentition groups, Cangialosi (1984) found that ratios and angles remained relatively constant over time, indicating that only size (but not facial proportion) changes with age. Consequently, it is more appropriate to evaluate individuals on the basis of proportions and angles of linear measurements rather than absolute values. Proportionate measures (ratios) In determining the cause of vertical malocclusion relationships, the proportions of the face are far more important than absolute measurements (Khouw et al., 1970). The same logic applies to the description of facial or skeletal types and by extension to the determination of craniofacial growth patterns. In other words, skeletal open bite or vertically growing subjects are characterized by an excessive lower 7

16 anterior face height relative to the upper anterior face height, while skeletal deep bite or horizontally growing subjects are characterized by a decreased lower anterior face height (Nanda, 1988). Nahoum (1971, 1975, and 1977) extensively evaluated UFH:LFH ratios as an indication of open bite tendency. He reported that in patients with an acceptable, untreated Angle Class I occlusion, the UFH:LFH ratio averaged Open bite patients had an average UFH:LFH ratio of 0.69 while deep bite patients exhibited UFH:LFH ratios of Similarly, Wylie and Johnson (1952) examined 57 attractive individuals from a sample of mixed normal subjects between the ages of 11 to 13 years and found the mean value of the UFH:LFH ratio to be In lieu of utilizing the UFH:LFH ratio for facial growth pattern classification, Nanda (1988, 1990) determined the LFH:TFH (lower face height : total face height) ratio. Subjects with a relatively larger LFH:TFH ratio were considered to have a skeletal open-bite tendency, while a smaller LFH:TFH ratio indicated a skeletal deep-bite tendency. Rather than comparing upper, lower, or total facial heights to one another, the posterior facial height (S- Go) can be compared to the total anterior facial height (N-Me) in a manner called the Facial Height Ratio or Jarabak quotient (Jarabak and Fizzell, 1972). Jarabak and co-workers (Jarabak and Fizzell, 1972; Siriwat and Jarabak, 1985) defined subjects in the following manner: Hyperdivergent growth pattern = PFH:AFH ratio < o Face rotates downward and posteriorly with growth. o Anterior facial height increases more rapidly than posterior height. o Down s Y-axis angle tends to open. Neutral growth pattern = PFH:AFH ratio of o Growth direction is downward and forward along Down s Y-axis with about the same increments anteriorly and posteriorly and no progressive change in most angular relationships. Hypodivergent growth pattern = PFH:AFH ratio > o Growth direction is predominantly horizontal. o Down s Y-axis tends to close. Variations in Method Assessment In general, the Y-axis angle, upper to lower facial height ratio, and the mandibular plane angle tend to differ significantly between skeletal open- and deep-bite subjects. However, the literature has shown that various measurements used to classify vertical malocclusions (i.e. overbite, UFH:LFH, PFH:AFH, SN- 8

17 MP angle, SN-PP angle, PP-MP angle, gonial angle, etc.) do not necessarily always have strong intercorrelations as one might expect (Jacob and Buschang, 2011). Furthermore, Dung and Smith (1988) found that different measures of open bite tendency identified different patients. Due to the complex nature of the vertical craniofacial dimension and variety of landmarks used within various classification methods, conflicting growth pattern determinations is not uncommon. In 1985, Bishara and Jakobsen studied the range of variation in craniofacial relationships in a population with normal occlusion. A sample of 20 males and 15 females was divided into long, average, and short facial types (LFT, AFT, SFT) based on the adult ratio of posterior to anterior facial height (PFH:AFH) and mandibular plane angle (FH-MP). Lateral cephalograms were obtained biennially between the ages of 4.5 to 12 years and then annually through age 17 years with an additional record set at 25.5 years. Descriptive statistics of the Y-axis (NSGn ) absolute values were provided. The absolute Y-axis (NSGn ) values at ages 5, 10, 15, and 25 years for the males followed the expected pattern (i.e. LFT Y-axis > AFT Y-axis > SFT Y-axis); however, the female Y-axis values at all four age points did not (e.g. AFT Y-axis > LFT Y-axis). As predicted by Schudy (1965), SFT subjects evaluated longitudinally should exhibit the greatest amount of Y-axis closure, followed by AFT subjects, with the LFT subjects potentially having an opening of the angle. Interestingly, the overall Y-axis angle closure of the Bishara and Jakobsen (1985) sample between 5 to 25 years of age followed the expected pattern for male groups, but not for female groups. However, the male groups did not follow the expected pattern for the period between 5 to 10 years of age. In 2003, Chung and Mongiovi investigated longitudinal craniofacial growth changes in untreated skeletal Class I subjects with low, average, and high angle facial types. For a sample of 36 males and 32 females, cephalograms at ages 9 and 18 years were measured. Subjects were divided based on the presence of low ( 27 ), average (>27 -<37 ), or high ( 37 ) mandibular plane (SN-MP) angles at age 9 years. The cross-sectional data at age 9 years of both males and females was provided and showed agreement with expectations: low-angle facial types had the smallest absolute Y-axis angle (FH-SGn ) while high-angle facial types had the largest Y-axis angle. However, the longitudinal changes from age 9 to 18 years exhibited patterns that were not congruent with the expected results. In males, the high-angle group closed while the low-angle group closed ; conversely, the average-angle group opened In females, all groups opened but not in the expected pattern: low (+2.02 ), high (+1.52 ), and 9

18 average (+0.69 ). Consequently, different methods of craniofacial growth pattern assessment may result in conflicting growth pattern determinations. C. Assessment of Dentoalveolar Heights and Dentoalveolar Height Growth Rates The inherent craniofacial growth pattern influences the rotation of the maxillomandibular complex, which necessitates compensatory adaptation in the eruption paths of the dentition. Although the relationship is extremely important to orthodontists, very little longitudinal research has been performed to explicitly compare the absolute value of molar and incisor dentoalveolar heights or their growth rates in subjects grouped according to various growth patterns. According to Bishara and Jakobsen (1985), longitudinal analysis of the data provides more consistent and therefore more meaningful results than cross-sectional comparisons when craniofacial growth trends are evaluated. This occurs because growth changes are often subtle and of magnitudes not readily observed when the data is evaluated cross-sectionally (Bishara and Jakobsen, 1985). Furthermore, with cross-sectional studies, there may be interchange and crossover of the subjects between various types of growth patterns (Worms et al., 1971), which goes unnoticed. Reference data for longitudinal vertical growth of adolescents is inconsistent and limited (Jacob and Buschang, 2011). Such a scarcity is not surprising, since longitudinal studies are, by their nature, lengthy, costly, and dependent upon the cooperation of the subjects. The following longitudinal and cross sectional studies were retrieved in the published literature that did have partial relevance regarding evaluation of dentoalveolar heights between various growth craniofacial growth patterns: Longitudinal studies Karlsen (1995) evaluated craniofacial and dentoalveolar dimensions longitudinally in two groups of males with low ( 26, n=15) and high ( 35, n=15) SN-MP angles for two periods: age 6 to 12 years and age 12 to 15 years. Maxillary and mandibular molar dentoalveolar heights were not statistically different between low- and high-angle groups in either growth period. However, both maxillary and mandibular incisor dentoalveolar heights exhibited larger growth rate values (mm/yr) in the high-angle subjects but only during the 6 to 12 year period. Buschang et al. (2008) conducted a mixed longitudinal study on 227 French-Canadians (119 males, 108 females) with cephalograms taken annually between 10 to 15 years of age. The individuals were chosen 10

19 at random from a pool of untreated normal occlusion and malocclusion subjects. Dentoalveolar heights increased from 10 to 15 years of age, with the anterior and posterior dentoalveolar heights showing the smallest and greatest changes, respectively. Male adolescents exhibited larger dentoalveolar heights than female adolescents with a reduction or lack of sex difference around 12 and 13 years of age. The greatest difference in dentoalveolar heights between the 10- and 15-year old age groups was for the maxillary first molar while the maxillary central incisor dentoalveolar height showed the smallest age effects. The coefficients of variation were greater for the maxillary than the mandibular dentoalveolar heights, indicating a greater variation of maxillary dentoalveolar height means than the mandibular dentoalveolar height means. Arat and Rübendüz (2005) examined the alveolar height dimensions (rather than dentoalveolar) in 62 subjects with normal facial patterns and acceptable occlusions during early and late growth periods, as determined by Gruelich and Pyle skeletal maturation criteria. During the early stage, the mandibular anterior alveolar height showed the highest increase in the vertical dimension, while the maxillary anterior alveolar height exhibited the least increase. Conversely, in the late stage, whereas a substantial increase occurred in the maxillary posterior alveolar height, no change was observed in maxillary anterior alveolar height. The authors concluded that alveolar development exhibits regional differences during pubertal growth, which is crucial for establishing normal occlusal relations during mandibular growth rotation. Cross-sectional studies: Though longitudinal assessment is certainly the gold standard for assessing craniofacial growth and development correlations, cross-sectional studies do provide valuable information. However, these snap shots in time create difficulty in visualizing the overall influence of growth patterns, and extrapolation to different age ranges must be made cautiously. Multiple cross-sectional studies evaluating correlations between dentoalveolar heights and craniofacial dimensions do exist, in which the subjects are typically categorized according to facial type, mandibular plane angle, or overbite characteristics (i.e. open vs. deep). As noted previously, their relevance is based on the assumption that these measures accurately classify the growth pattern present and that pattern remains consistent over time. 11

20 Janson et al. (1994) cross-sectionally examined the maxillary and mandibular first molar and central incisor dentoalveolar height dimensions in 12-year old male and female subjects (188 males, 156 females) who had long, normal, and short lower face height ratios (UFH:LFH). The dentoalveolar heights were significantly different between faces with long, normal, and short lower face heights, except for the mandibular molar dentoalveolar height, which showed no difference between short and normal face height subjects. All dentoalveolar heights were larger for male subjects except for the maxillary molar dentoalveolar height. The maxillary molars presented a higher correlation to the UFH:LFH ratio than the lower dentition. Stepwise regression analysis showed that 22% of the variation in the UFH:LFH ratio was explained by the maxillary and mandibular molar dentoalveolar heights and 41% was explained by the maxillary and mandibular incisor dentoalveolar heights. Betzenberger et al. (1999) assessed the dentoskeletal morphology in 191 untreated children with hyperdivergent mandibular plane angles (> 40 ). The subjects were divided into mixed and permanent dentition groups then further divided into subgroups based on the amount of overbite (OB) as a measure of dentoalveolar compensation of jaw base hyperdivergency. Regarding the mixed dentition, deep bite subjects exhibited relative increases of maxillary and mandibular incisor dentoalveolar heights when compared to open bite subjects. In the molar region, no group differences in dentoalveolar heights existed. However, in the permanent dentition, deep bite subjects exhibited relative decreases in maxillary and mandibular molar dentoalveolar heights compared with open bite subjects. In the anterior region, no group differences in dentoalveolar heights were found. Ceylan and Eroz (2001) investigated the differences in the maxillary and mandibular morphology related to overbite. A total of 80 untreated subjects aged 13 to 15 years were divided into 4 groups with normal overbite, edge-to-edge bite, open bite, or deep bite. Maxillary and mandibular dentoalveolar heights were greater in the open-bite group than in the other groups. The subjects with open bite showed a long and narrow symphysis morphology, while the subjects with deep bite had a short and broad symphysis form. Martina et al. (2005) tested the hypothesis that molar dentoalveolar heights are positively related to vertical craniofacial features in a sample of 82 untreated, adult subjects. Females were of age 15 years or greater while males were of age 18 years or greater. Approximately 70% of the total molar dentoalveolar height variance was explained by lower facial height (ANS-Me) and the palatal to 12

21 mandibular plane angle (PP-MP). Increases in the lower face height had a positive correlation with the molar dentoalveolar heights; conversely, the molar dentoalveolar heights were negatively influenced by increasing divergency of the jaws (PP-MP angle). Martina et al. (2009) evaluated a sample of 79 children younger than 9 years of age for the relationship between posterior dentoalveolar heights and vertical craniofacial patterns. Approximately 54% of the total variability in molar dentoalveolar heights was explained by the variability in lower facial height (ANS-Me) and the palatal to mandibular plane angle (PP-MP). Both maxillary and mandibular dentoalveolar heights were significantly influenced by the length of the lower facial height and mandibulopalatal plane angle. Increases of ANS-Me and PP-MP had opposite effects on the amount of molar dentoalveolar heights; thus, an inverse relationship between molar dentoalveolar heights and jaw divergence was determined to be present when vertical growth is still incomplete. Kucera et al. (2011) evaluated the skeletal and dentoalveolar components in 69 adult female subjects with skeletal open bite (SN-MP > 40 ) in the presence or absence of dental compensation. As opposed to previous findings (Martina et al., 2005 and 2009), increased maxillary and mandibular molar dentoalveolar height was a common finding in adult skeletal open bite subjects. In addition, incisor dentoalveolar height was significantly greater in both skeletal open bite groups. Overdevelopment of lower facial height was compensated by significant elongation of the incisal dentoalveolar heights of both jaws, with lower incisors playing a more important role. Nahoum et al. (1972) evaluated the lateral cephalograms of 128 male patients categorized into three groups: a) good occlusion (n=92); b) Angle Class II anterior open-bite (n=18); and c) Angle Class III anterior open-bite (n=18). On the average, persons with an open bite had a longer LFH, a shorter posterior face height, a short maxillary incisor to S-N distance, a smaller mandibular molar to MP distance, and a smaller UFH:LFH ratio than did normal control subjects. Kuitert et al. (2006) investigated the vertical dentoalveolar compensation in untreated adults (ages 17 to 56 years) with excessive (long-face, n=112) and deficient (short-face, n=95) lower anterior facial heights. Subjects were grouped according to both overbite and lower face height (mm) measurements. Dentoalveolar height compensation occurred in both short-face (SF) and long-face (LF) groups mainly by adaptations in mandibular incisor alveolar and basal heights. Lower dentoalveolar compensation was 13

22 found to maintain a normal overbite in long-face subjects to a limited extent. In SF and LF subjects, overbite was independent of vertical molar dentoalveolar dimensions; consequently, molar dentoalveolar height was unrelated to overbite. Haralabakis et al. (1994) evaluated the morphogenetic characteristics that contribute to the development of open bite in adults. Cephalograms of 22 males and 34 females who exhibited an anterior open bite of at least 2 mm were compared against a control group. In both male and female groups with open bites, the total facial height (N-Me) and three dentoalveolar heights (maxillary incisor, mandibular incisor, and maxillary molar) were significantly greater than control groups. Tsai (2000) investigated the facial morphologic characteristics in children with long (n=46) and short (n=42) faces as determined by the ratio of PFH:AFH (S-Go:N-Me) and inclination of the mandibular plane to Frankfort horizontal (FH-MP angle). Long-face girls had significantly greater maxillary molar and incisor dentoalveolar heights but not mandibular molar or incisor dentoalveolar heights, as compared to the short-face group. Similarly, long-face boys had significantly greater maxillary dentoalveolar heights and mandibular incisor dentoalveolar heights as compared to the short-face group. Anwar and Fida (2009) evaluated the dental compensation patterns in 186 orthodontic patients (120 females and 66 males; mean age: 15 years, 11 months) as classified by the following SN-MP angle criteria: a) hyperdivergent (> 36 ); b) normal (28-36 ); and c) hypodivergent (< 28 ). Significant differences were found for only the mandibular incisor dentoalveolar height between the three vertical facial types. All dentoalveolar height measurements, except for upper anterior incisor dentoalveolar height, were significantly correlated with the skeletal parameters and showed compensation. Weak correlation coefficients for the maxillary incisor dentoalveolar height suggested limited compensation for vertical skeletal relationships. The mandibular incisor dentoalveolar height was found to be the most likely parameter to compensate for different skeletal vertical dysplasias, while maxillary incisor dentoalveolar height showed the least tendency to change according to vertical skeletal relationships. Han et al. (2013) investigated the relationship between craniofacial growth patterns and mandibular posterior dentoalveolar complex morphology in a Chinese sample (23 males, 22 females) aged 21 to 41 years with normal occlusion. The subjects were divided into different growth pattern types based on their Frankfort horizontal to mandibular plane angle (FH-MP) and facial height index (FHI), which 14

23 resulted in 20 horizontal growth pattern patients (FMA<27, FHI>65 ) and 20 vertical growth pattern patients (FMA>37, FHI<62 ). The inclination of the molars, the thickness of cortical bone, and the height of the mandibular alveolus differed significantly between patients with the horizontal growth pattern and those with the vertical growth pattern. The alveolar height at the first and second molars and second premolar of subjects with the horizontal growth pattern was greater than that of those with the vertical growth pattern. D. Summary Overall, the orthodontic literature has a void in regards to longitudinal evaluations of dentoalveolar heights and dentoalveolar height growth rates in relation to various types of facial growth patterns. The multitude of cross-sectional studies certainly aids the orthodontist in determining correlations between skeletal markers and dentoalveolar compensation at specific ages, but a longitudinal investigation may provide more information concerning the overall growth and development process. Although Janson et al. (1994) did investigate the dentoalveolar height dimensions cross-sectionally at age 12 years, one cannot extrapolate their results to other ages due to the potential for growth occurring in unequal amounts and in varying directions (i.e. relative motion of the various parts of the dentofacial complex). Furthermore, Arat and Rübendüz s (2005) finding that alveolar development exhibits regional differences during pubertal growth testifies to the necessity of longitudinal evaluation of the dentition s vertical dimension, as a cross-sectional evaluation may miss important compensations in time. 15

24 Purpose of the Study The purpose of this longitudinal study is: To determine if significant differences in maxillary and mandibular molar and incisor dentoalveolar heights and dentoalveolar height growth rates exist between skeletal Class I subjects classified into 3 different craniofacial growth patterns by a directional method (Y-Axis angle change). To determine if significant differences in the maxillary and mandibular molar and incisor dentoalveolar heights and dentoalveolar height growth rates exist between skeletal Class I subjects classified into 3 different craniofacial growth patterns by a proportionate method (UFH:LFH ratio). To determine if there are significant gender related differences in dentoalveolar height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I individuals. 16

25 Research Objectives The objectives of this study are to: Longitudinally evaluate the dentoalveolar heights and dentoalveolar height growth rates of maxillary and mandibular molars and incisors of skeletal Class I subjects as classified by directional and proportionate methods. Determine whether the dentoalveolar height growth rates of skeletal Class I subjects exhibit sexual dimorphism. 17

26 Hypotheses To address the research objectives, the following hypotheses were framed: Hypothesis #1 Within each gender, there is a significant difference in the dentoalveolar heights and dentoalveolar height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I subjects classified into vertical, average, and horizontal growth patterns, as determined by change in Y-axis angle. Hypothesis #2 Within each gender, there is a significant difference in the dentoalveolar heights and dentoalveolar height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I subjects classified into long, average, and short facial type growth patterns, as determined by the UFH:LFH ratio. Hypothesis #3 There are significant gender related differences in the dentoalveolar height growth rates of the maxillary and mandibular molars and incisors in skeletal Class I subjects. 18

27 Materials & Methods A. Sample Description Established in 1952, the Burlington Growth Centre (BGC) data is a collection of longitudinal craniofacial growth records from the town of Burlington, Ontario, Canada. In 1994, the sample was extended to 40 years for a portion of the original sample. The BGC records are currently located in the Burlington Orthodontic Research Centre at the University of Toronto. The predominant racial group was Caucasian and mostly Anglo Saxon. The original sample consisted of 1258 children separated into a serial experimental group and 4 control groups, as follows: Serial Experimental (SE) records taken every year from ages 3 to 20 years. Control at age 6 (C-6) records were taken at ages 6, 9, 12, 14, 16, and 20 years. Control at age 8 (C-8) records were taken at age 8 years, but some other ages were obtained. Control at age 10 (C-10) records were taken at age 10 years, with a few other ages. Control at age 12 (C-12) records were taken at age 12 years and again at age 20 on approximately half of the individuals. For the current investigation, an initial sample of 242 subjects (111 males, 131 females) was collected from the serial experimental and C6 groups, which were expected to have records available at 9, 12, 14, and 16 years of age. Radiographs used from the study were lateral cephalometric images taken in the centric occlusion position. The original film-based lateral cephalograms had an enlargement factor of 9.84% as the anode to center of subject distance was cm, and the distance from the center of the subject to the film was 15.0 cm. Recently, all film-based cephalograms have been digitally converted (Epson Perfection V700 Photo scanner) and stored as a TIFF (Tagged Image File Format) for long-term preservation. Using Adobe Photoshop 6 (San Jose, CA, USA), each image was converted to JPEG (Joint Photographic Experts Group) format and resampled at a resolution of 300 pixels per inch. The images were imported into version 11.7 of the Dolphin imaging software (Dolphin Imaging and Management Systems, Chatsworth, CA, USA) program for cephalometric tracing. 19

28 Phase I Exclusion criteria For each individual, all lateral cephalometric radiographs were examined, and subjects were excluded according to the following criteria: Dental agenesis of any permanent tooth (excluding 2 nd or 3 rd molars) Failure of eruption of a 1 st molar or central incisor Extraction of any permanent tooth (excluding 2 nd or 3 rd molars) Generalized or localized (i.e. 1 st molar or central incisor) severe dental wear pattern Restoration of central incisor incisal edge or 1 st molar mesiobuccal cusp tip Radiographs not of diagnostic quality Any orthodontic treatment (including lingual holding arches) Incomplete occlusion (maximum intercuspation) at either age 9 or 16 year cephalogram In total, 83 subjects (39 males, 44 females) were excluded during phase I. Table I contains the specific details of each applied criterion. Table I. Exclusion Criteria phase I # Excluded Male Female Dental agenesis of any permanent tooth (excluding 2 nd or 3 rd molars) 2 1 Failure of eruption of a 1st molar or central incisor 1 0 Extraction of any permanent tooth (excluding 2 nd or 3 rd molars) Generalized or localized (i.e. 1st molar or central incisor) severe dental wear pattern 3 0 Restoration of central incisor incisal edge or 1st molar mesiobuccal cusp tip 3 1 Radiographs not of diagnostic quality 1 0 Any orthodontic treatment (including lingual holding arches) 9 14 Incomplete occlusion (maximum intercuspation) at either age 9 or 16 year cephalogram 9 12 Total Excluded: Table I. Application of Exclusion Criteria phase I 20

29 Phase II Exclusion criteria In an effort to constrain the residual sample (72 males, 87 females) to include skeletal Class I subjects at age 16 years with minimal changes in dental inclination from ages 9 to 16 years, the following secondary exclusion criteria were applied: Age 16 years: Skeletal Class II pattern o ANB > 4.5 o McNamara s unit length difference < 20.0 mm Age 16 years: Skeletal Class III pattern o ANB < 0.5 o McNamara s unit length difference > 30.0 mm Age 9 to 16 years: > 10 change of incisor inclination In total, 54 subjects (23 males, 31 females) were excluded during phase II. Table II contains the specific details of each applied criterion: Table II. Exclusion Criteria phase II: Male # Excluded Female Skeletal Class II pattern ANB > McNamara s unit length difference < 20.0 mm 6 7 Skeletal Class III pattern ANB < McNamara s unit length difference > 30.0 mm 2 1 > 10 change of incisor inclination 4 1 Total Excluded: Table II. Application of Exclusion Criteria phase II 21

30 The final study sample included 105 subjects (49 males, 56 females). Of those, three female subjects were missing their age 14 lateral cephalogram while complete records for the male subjects were available. Subjects with one missing lateral cephalogram at either age 12 or 14 were decided to be included in the sample since the missing data would not influence the directional classification, which is dependent upon the age 9 and 16 cephalograms, or the statistical analyses. 242 BGC subjects 111 males 131 females Phase I Exclusion Criteria applied 72 males 87 females Phase II Exclusion Criteria applied 49 males 56 females Figure 1. Final Sample Flowchart B. Cephalometric Analysis Using the Dolphin Imaging program, a custom cephalometric analysis was created, which utilized the following craniofacial and dental landmarks (definitions used from Daskalogiannakis, 2000): A point the deepest (most posterior) midline point on the curvature between the ANS and prosthion. Anterior nasal spine (ANS) the tip of the bony anterior nasal spine at the inferior margin of the piriform aperture in the midsagittal plane. B point the deepest (most posterior) midline point on the bony curvature of the anterior mandible, between infradentale and pogonion, in the midsagittal plane. Condylion (Co) the most superior posterior point on the head of the mandibular condyle (bilateral) 22

31 Gnathion (Gn) the most anterior inferior point on the bony chin in the midsagittal plane Gonion (Go) the most posterior inferior point on outline of the angle of the mandible L1 Root root apex of the most labially placed mandibular central incisor (unilateral) L1 Tip incisal tip of the most labially placed mandibular incisor (unilateral) L6 Occlusal mesial buccal cusp tip of the mandibular 1st molars (midsagittal) Menton (Me) the most inferior point of the mandibular symphysis, in the midsagittal plane Nasion (N) the intersection of the internasal and frontonasal suture, in the midsagittal plane Pogonion (Pg) the most anterior point on the contour of the bony chin, in the midsagittal plane Posterior nasal spine (PNS) the most posterior point on the bony hard palate in the midsagittal plane Sella (S) the geometric center of the pituitary fossa (sella turcica) constructed in the midsagittal plane U1 Root root apex of the most labially placed maxillary central incisor (unilateral) U1 Tip incisal tip of the most labially placed maxillary central incisor (unilateral) U6 Occlusal mesial buccal cusp tip of the maxillary 1st molars (midsagittal) Figure 2. Craniofacial and Dental Landmarks The following reference planes were constructed (definitions used from Daskalogiannakis, 2000): 23

32 Mandibular plane (MP) a line representing the plane passing through the mandibular borders (Go-Me) bilaterally. Palatal plane (PP) a line joining PNS and ANS. Y-axis (Growth axis) a line connecting points sella and gnathion. Sella-nasion a line connecting points sella and nasion. Figure 3. Craniofacial Reference Planes The following linear, angular, and proportionate measurements were recorded: ANB angle the difference between angles SNA and SNB, as introduced by R.A. Riedel, aimed at providing an evaluation of the anteroposterior relationship between the maxillary and mandibular apical bases. Lower facial height (LFH) the linear millimetric distance between the ANS and menton measured directly. L1 MP ( MP, mm) the linear millimetric distance (perpendicular to MP) from the mandibular central incisor tip to the mandibular plane. L6 MP ( MP, mm) the linear millimetric distance (perpendicular to MP) from the mandibular 1st molar mesial buccal cusp tip to the mandibular plane. Maxillary (midface) length the linear measurement from condylion to A point. Mandibular length the linear measurement from condylion to gnathion. 24

33 McNamara s unit length difference (Co-Gn minus Co-A point) the maxillomandibular differential as determined by the mandibular length minus the mid-face (maxillary) length. Upper facial height (UFH) the linear millimetric distance between nasion and the ANS. Upper facial height to Lower facial height ratio (UFH:LFH) U1 PP ( PP, mm) the linear millimetric distance (perpendicular to PP) from the maxillary central incisor tip to the palatal plane. U6 PP ( PP, mm) the linear millimetric distance (perpendicular to PP) from the maxillary 1st molar mesial buccal cusp tip to the palatal plane. Y-axis angle (NSGn) the anteroinferior angle between the Y-axis (S-Gn) and S-N plane. Figure 4. Maxillary and Mandibular Dentoalveolar Height Measurements The dentoalveolar heights (mm) were recorded from the age 9, 12, 14, and 16 year cephalograms. The maxillary dentoalveolar heights were calculated based on the perpendicular distances of the central incisor tip and the first molar mesial buccal cusp tip to the palatal plane (ANS-PNS). The mandibular dentoalveolar heights were calculated based on the perpendicular distance of the central incisor tip and the first molar mesial buccal cusp tip to the mandibular plane (Go-Me). The dentoalveolar height growth rates were recorded for three time periods (9 to 12 years, 12 to 14 years, and 14 to 16 years). Each respective dentoalveolar height growth rate value was calculated by subtracting the dentoalveolar height recorded at the earlier time point from the later time point (e.g. dentoalveolar height at age 12 years minus dentoalveolar height at age 9 years), then dividing by the number of years between the two time points (i.e. 2 or 3 years), which resulted in a measurement of millimeters per year (mm/yr). 25

34 C. Growth Pattern Classification Classification of the male and female samples was performed according to both the directional (change in Y-axis angle) and proportionate (UFH:LFH) methods. The gender means and standard deviation of the means of both the Y-axis angle change between ages 9 to 16 years and the UFH:LFH ratio at age 16 years were calculated. The average range was considered to be within 1 standard deviation of each gender s mean. Subjects exhibiting values greater or lesser than 1 standard deviation were considered to be in the horizontal or vertical group for the Y-axis classification method and the short or long LFH group for the proportionate classification method. Directional Classification: Change in Y-axis angle The final sample was classified according to the directional growth pattern (Table III) as follows: Y-axis measurements at age 9 and 16 years were recorded. Change in Y-axis measurement between 9 and 16 years was determined for each individual. The mean change in Y-axis: o For the entire sample was calculated to be with a standard deviation of o For the female sample was calculated to be with a standard deviation of o For the male sample was calculated to be with a standard deviation of Table III. Directional Classification: Change in Y-axis angle (9 to 16 y) Range Mean Standard Deviation Entire Sample +3.4 to Males +3.4 to Females +3.1 to Note: (+) opening of Y-axis angle = Vertical growth pattern (-) closure of Y-axis angle = Horizontal growth pattern Subjects were classified into vertical, average, or horizontal growth pattern groups as follows: o Males Vertical subjects whose change in Y-axis was > (greater than +1 standard deviation from the male sample mean). 26

35 Average subjects whose change in Y-axis was and (within ±1 standard deviation from the male sample mean). Horizontal subjects whose change in Y-axis was < (less than -1 standard deviation from the male sample mean). o Females Vertical subjects whose change in Y-axis was > (greater than +1 standard deviation from the female sample mean). Average subjects whose change in Y-axis was and (within ±1 standard deviation from the female sample mean). Horizontal subjects whose change in Y-axis was < (less than -1 standard deviation from the female sample mean). As a result, the directional growth pattern classification method grouped the 49 male and 56 female subjects as follows (Table IV): Table IV. Directional growth pattern classification Vertical Average Horizontal Males Females The mean and standard deviations of the Y-axis change for each directional group are listed as follows (Table V): Table V. Directional groups: means and standard deviations of Y-axis change (9 to 16 years) Vertical Average Horizontal Mean (SD) Mean (SD) Mean (SD) Males (±0.64) (±1.02) (±0.78) Females (±0.87) (±0.82) (±0.73) 27

36 Proportionate Classification: UFH:LFH ratio The final sample was classified according to the proportionate growth pattern (Table VI) as follows: UFH:LFH measurements at age 16 were recorded. The mean UFH:LFH value: o For the entire sample was calculated to be 0.80 with a standard deviation of o For the female sample was calculated to be 0.81 with a standard deviation of o For the male sample was calculated to be 0.80 with a standard deviation of Table VI. Proportionate Classification: UFH:LFH ratio (16 y) Range Mean Standard Deviation Entire Sample 0.96 to Males 0.96 to Females 0.96 to Subjects were classified into short, average, and long facial height growth pattern groups as follows: o Males Short subjects whose UFH:LFH ratio was > 0.86 (greater than +1 standard deviation from the male sample mean). Average subjects whose UFH:LFH ratio was 0.86 and 0.74 (within ±1 standard deviation from the male sample mean). Long subjects whose UFH:LFH ratio was < 0.74 (less than -1 standard deviation from the male sample mean). o Females Short subjects whose UFH:LFH ratio was > 0.88 (greater than +1 standard deviation from the female sample mean). Average subjects whose UFH:LFH ratio was 0.88 and 0.74 (within ±1 standard deviation from the female sample mean). Long subjects whose UFH:LFH ratio was < 0.74 (less than -1 standard deviation from the female sample mean). 28

37 As a result, the proportionate growth pattern classification method grouped the 49 male and 56 female subjects as follows (Table VII): Table VII. Proportionate growth pattern classification Long Average Short Males Females The mean and standard deviations of the UFH:LFH ratio for each proportionate group are listed as follows (Table VIII): Table VIII. Proportionate groups: means and standard deviations of UFH:LFH (16 years) Long Average Short Mean (SD) Mean (SD) Mean (SD) Males 0.71 (±0.03) 0.80 (±0.02) 0.90 (±0.03) Females 0.73 (±0.02) 0.79 (±0.03) 0.92 (±0.05) 29

38 D. Reliability Analysis After a period of four months, intra-rater reliability was determined by having the primary investigator (B.S.) re-trace and measure the lateral cephalograms of twenty subjects (10 males, 10 females) as determined by a random number generator using Microsoft Excel (Redmond, WA, USA). Inter-rater reliability was determined by a secondary investigator (K.K.) tracing and measuring the lateral cephalograms of the same twenty randomly selected subjects. The following measurements were assessed: ANB angle, Y-Axis angle, U1 dentoalveolar height, U6 dentoalveolar height, L1 dentoalveolar height, L6 dentoalveolar height, and McNamara s unit length difference. The intraclass correlation coefficients (ICC) analysis was used to determine intra-rater reliability of the 7 measurements and the measurement error (Table IX) was calculated by using Dahlberg s formula (Dahlberg, 1940). Results of the ICC showed excellent reliability with minimal measurement error. Table IX. Reliability Analysis Intraclass Correlation Coefficient Measurement Error* (mm) BS 1 -BS 2 BS 1 -KK BS 1 -BS 2 BS 1 -KK ANB Y-Axis U U L L ULD ICC =(σ 2 s) / (σ 2 s + σ 2 i) * = Method error = ( d²/2n), where D is the difference between the repeated measurements, and N is the number of C. paired Analysis measurements of Results 30

39 E. Analysis of Results As described, male and female subjects were placed into Y-axis groups (vertical, average, horizontal) and UFH:LFH groups (long, average, short) according to their sample means (Y-axis change between 9 to 16 years, or UFH:LFH at 16 years) and standard deviations. The following descriptive statistics were calculated and recorded: o Means, standard deviations, and standard error of the means for the dentoalveolar heights in each of the four sites (U1, U6, L1, and L6) at ages 9, 12, 14, and 16 years. o Means, standard deviations, and 95% confidence limits for the dentoalveolar height growth rates (mm/year) of U1, U6, L1, and L6 for three time periods, as follows: 9 to 12 years 12 to 14 years 14 to 16 years For each classification method, mixed models were constructed for males and females separately to test for between group differences in dentoalveolar heights at all four ages evaluated together. Predictors were age and craniofacial growth group. Interactions between age and group were also assessed. o The dentoalveolar heights were assessed for significant differences for all four dentoalveolar sites (U1, U6, L1, and L6) within each gender. For each classification method, mixed models were constructed in order to test for between group differences in dentoalveolar heights at each of the four ages individually. Predictors were gender and craniofacial growth group. Interactions between gender and group were also assessed. o The dentoalveolar heights (U1, U6, L1, L6) at each specific age were assessed for significant differences. For each classification method, between group one-way ANOVA analyses were used to test for significant differences of the dentoalveolar height growth rates among the classified groups within the male and female samples for three time periods (9 to 12 years, 12 to 14 years, and 14 to 16 years) for all four dentoalveolar sites (U1, U6, L1, and L6). Tukey post-hoc comparisons were used for further evaluation of inter-group differences where the initial mixed model or ANOVA analysis resulted in a finding of statistically significant differences (p<0.05). If the mixed model or ANOVA analysis did not reveal statistically significant inter-group differences, further statistical analyses were not required. 31

40 Independent t-tests were used to evaluate for gender differences in dentoalveolar height growth rates for each dentoalveolar site and time period. The level of significance for comparisons of the dentoalveolar heights and dentoalveolar height growth rates was set at p<0.05 throughout the analysis. Results Overview A. Dentoalveolar heights Directional Classification o U1, U6, L1, L6 Proportionate Classification o U1, U6, L1, L6 B. Dentoalveolar height growth rates Directional Classification o U1, U6, L1, L6 Proportionate Classification o U1, U6, L1, L6 C. Evaluation of the effect of gender on dentoalveolar height growth rates Dentalveolar height growth rates o U1, U6, L1, L6 A. Dentoalveolar heights Mixed model analyses were used to test for significant differences in dentoalveolar heights (U1, U6, L1, and L6) between the three different growth patterns within each gender at ages 9, 12, 14, and 16 years, evaluated both together and separately (i.e. at each of the four time points). The following results describe the dentoalveolar heights of the different groups within the sample for each site, age and gender, and can be found in table format in Appendices 1 and 2. 32

41 Directional classification a. Maxillary Central Incisor (U1) i. Females The maxillary central incisor dentoalveolar heights (U1) for the three female directional growth pattern groups are as follows. For females at age 9 years, the maxillary central incisor dentoalveolar height was 22.6 ± 1.8 mm for the vertical group, 21.9 ± 2.0 mm for the average group, and 22.7 ± 1.8 mm for the horizontal group. For females at age 12 years, the maxillary central incisor dentoalveolar height was 24.2 ± 2.3 mm for the vertical group, 23.1 ± 2.1 mm for the average group, and 23.8 ± 2.7 mm for the horizontal group. For females at age 14 years, the maxillary central incisor dentoalveolar height was 25.0 ± 2.4 mm for the vertical group, 23.7 ± 2.3 mm for the average group, and 24.0 ± 2.8 mm for the horizontal group. For females at age 16 years, the maxillary central incisor dentoalveolar height was 25.4 ± 2.4 mm for the vertical group, 24.2 ± 2.3 mm for the average group, and 24.6 ± 2.8 mm for the horizontal group (Figure 5). Dentoalveolar height differences at the maxillary central incisor, found between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 5. Directional Classification: Dentoalveolar heights at the maxillary central incisor site in females 33

42 ii. Males The maxillary central incisor dentoalveolar heights (U1) for the three male directional growth pattern groups are as follows. For males at age 9 years, the maxillary central incisor dentoalveolar height was 23.0 ± 1.2 mm for the vertical group, 23.2 ± 2.1 mm for the average group, and 23.8 ± 1.5 mm for the horizontal group. For males at age 12 years, the maxillary central incisor dentoalveolar height was 24.5 ± 1.6 mm for the vertical group, 24.4 ± 2.4 mm for the average group, and 25.1 ± 2.1 mm for the horizontal group. For males at age 14 years, the maxillary central incisor dentoalveolar height was 25.4 ± 1.3 mm for the vertical group, 25.2 ± 2.5 mm for the average group, and 26.2 ± 2.4 mm for the horizontal group. For males at age 16 years, the maxillary central incisor dentoalveolar height was 26.4 ± 1.5 mm for the vertical group, 25.9 ± 2.7 mm for the average group, and 26.9 ± 2.6 mm for the horizontal group (Figure 6). Dentoalveolar height differences at the maxillary central incisor, found between the male directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 6. Directional Classification: Dentoalveolar heights at the maxillary central incisor site in males 34

43 b. Maxillary first molar (U6) i. Females The maxillary first molar dentoalveolar heights (U6) for the three female directional growth pattern groups are as follows. For females at age 9 years, the maxillary molar dentoalveolar height was 16.1 ± 1.2 mm for the vertical group, 15.7 ± 1.2 mm for the average group, and 15.9 ± 1.9 mm for the horizontal group. For females at age 12 years, the maxillary first molar dentoalveolar height was 18.3 ± 1.3 mm for the vertical group, 17.7 ± 1.4 mm for the average group, and 17.8 ± 2.2 mm for the horizontal group. For females at age 14 years, the maxillary first molar dentoalveolar height was 20.0 ± 1.5 mm for the vertical group, 19.2 ± 1.5 mm for the average group, and 19.1 ± 2.7 mm for the horizontal group. For females at age 16 years, the maxillary first molar dentoalveolar height was 20.4 ± 1.7 mm for the vertical group, 19.8 ± 1.5 mm for the average group, and 19.8 ± 2.8 mm for the horizontal group (Figure 7). Dentoalveolar height differences at the maxillary first molar, found between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 7. Directional Classification: Dentoalveolar heights at the maxillary first molar site in females 35

44 ii. Males The maxillary first molar dentoalveolar heights (U6) for the three male directional growth pattern groups are as follows. For males at age 9 years, the maxillary first molar dentoalveolar height was 15.8 ± 1.3 mm for the vertical group, 16.1 ± 1.8 mm for the average group, and 16.1 ± 1.4 mm for the horizontal group. For males at age 12 years, the maxillary first molar dentoalveolar height was 17.9 ± 1.4 mm for the vertical group, 18.1 ± 2.1 mm for the average group, and 18.1 ± 1.6 mm for the horizontal group. For males at age 14 years, the maxillary first molar dentoalveolar height was 20.1 ± 2.2 mm for the vertical group, 19.8 ± 2.7 mm for the average group, and 19.7 ± 2.1 mm for the horizontal group. For males at age 16 years, the maxillary first molar dentoalveolar height was 21.3 ± 1.6 mm for the vertical group, 21.2 ± 2.3 mm for the average group, and 21.1 ± 1.7 mm for the horizontal group (Figure 8). Dentoalveolar height differences at the maxillary first molar, found between the male directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 8. Directional Classification: Dentoalveolar heights at the maxillary first molar site in males 36

45 c. Mandibular central incisor (L1) i. Females The mandibular central incisor dentoalveolar heights (L1) for the three female directional growth pattern groups are as follows. For females at age 9 years, the mandibular central incisor dentoalveolar height was 31.1 ± 1.3 mm for the vertical group, 30.6 ± 1.7 mm for the average group, and 31.0 ± 1.9 mm for the horizontal group. For females at age 12 years, the mandibular central incisor dentoalveolar height was 32.9 ± 1.0 mm for the vertical group, 32.4 ± 1.9 mm for the average group, and 32.4 ± 2.2 mm for the horizontal group. For females at age 14 years, the mandibular central incisor dentoalveolar height was 34.2 ± 1.1 mm for the vertical group, 33.2 ± 2.0 mm for the average group, and 33.2 ± 2.3 mm for the horizontal group. For females at age 16 years, the mandibular central incisor dentoalveolar height was 34.8 ± 1.3 mm for the vertical group, 33.8 ± 2.1 mm for the average group, and 33.5 ± 2.4 mm for the horizontal group (Figure 9). Dentoalveolar height differences at the mandibular central incisor, found between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 9. Directional Classification: Dentoalveolar heights at the mandibular central incisor site in females 37

46 ii. Males The mandibular central incisor dentoalveolar heights (L1) for the three male directional growth pattern groups are as follows. For males at age 9 years, the mandibular central incisor dentoalveolar height was 31.0 ± 1.6 mm for the vertical group, 31.7 ± 1.8 mm for the average group, and 31.7 ± 2.7 mm for the horizontal group. For females at age 12 years, the mandibular central incisor dentoalveolar height was 33.4 ± 1.8 mm for the vertical group, 33.4 ± 2.2 mm for the average group, and 33.4 ± 2.9 mm for the horizontal group. For males at age 14 years, the mandibular central incisor dentoalveolar height was 34.7 ± 2.4 mm for the vertical group, 35.0 ± 2.4 mm for the average group, and 35.3 ± 3.4 mm for the horizontal group. For males at age 16 years, the mandibular central incisor dentoalveolar height was 36.3 ± 2.4 mm for the vertical group, 36.5 ± 2.4 mm for the average group, and 36.7 ± 3.0 mm for the horizontal group (Figure 10). Dentoalveolar height differences at the mandibular central incisor, found between the male directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 10. Directional Classification: Dentoalveolar heights at the mandibular central incisor site in males 38

47 d. Mandibular first molar (L6) i. Females The mandibular first molar dentoalveolar heights (L6) for the three female directional growth pattern groups are as follows. For females at age 9 years, the mandibular first molar dentoalveolar height was 23.4 ± 1.2 mm for the vertical group, 23.2 ± 1.3 mm for the average group, and 23.6 ± 2.4 mm for the horizontal group. For females at age 12 years, the mandibular first molar dentoalveolar height was 25.0 ± 1.1 mm for the vertical group, 24.5 ± 1.6 mm for the average group, and 24.5 ± 2.2 mm for the horizontal group. For females at age 14 years, the mandibular first molar dentoalveolar height was 26.0 ± 1.7 mm for the vertical group, 25.5 ± 1.7 mm for the average group, and 25.4 ± 3.1 mm for the horizontal group. For females at age 16 years, the mandibular first molar dentoalveolar height was 26.7 ± 1.9 mm for the vertical group, 26.1 ± 1.8 mm for the average group, and 25.9 ± 3.2 mm for the horizontal group (Figure 11). Dentoalveolar height differences at the mandibular first molar, found between the female directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 11. Directional Classification: Dentoalveolar heights at the mandibular first molar site in females 39

48 ii. Males The mandibular first molar dentoalveolar heights (L6) for the three male directional growth pattern groups are as follows. For males at age 9 years, the mandibular first molar dentoalveolar height was 23.3 ± 1.9 mm for the vertical group, 23.4 ± 1.5 mm for the average group, and 24.3 ± 2.7 mm for the horizontal group. For males at age 12 years, the mandibular first molar dentoalveolar height was 24.4 ± 2.0 mm for the vertical group, 24.5 ± 1.6 mm for the average group, and 24.8 ± 3.2 mm for the horizontal group. For males at age 14 years, the mandibular first molar dentoalveolar height was 26.0 ± 2.1 mm for the vertical group, 26.1 ± 2.1 mm for the average group, and 26.6 ± 3.4 mm for the horizontal group. For males at age 16 years, the mandibular first molar dentoalveolar height was 27.7 ± 2.3 mm for the vertical group, 27.8 ± 2.1 mm for the average group, and 28.5 ± 3.0 mm for the horizontal group (Figure 12). Dentoalveolar height differences at the mandibular first molar, found between the male directional growth pattern groups at ages 9, 12, 14, or 16 years were not significant, both in the overall analysis as well as at any of these time points. Figure 12. Directional Classification: Dentoalveolar heights at the mandibular first molar site in males 40

49 Proportionate classification a. Maxillary Central Incisor (U1) i. Females The maxillary central incisor dentoalveolar heights (U1) for the three female proportionate growth pattern groups are as follows. For females at age 9 years, the maxillary central incisor dentoalveolar height was 20.1 ± 1.6 mm for the short group, 22.4 ± 1.7 mm for the average group, and 23.6 ± 1.3 mm for the long group. For females at age 12 years, the maxillary central incisor dentoalveolar height was 21.0 ± 1.6 mm for the short group, 23.7 ± 1.9 mm for the average group, and 25.2 ± 1.8 mm for the long group. For females at age 14 years, the maxillary central incisor dentoalveolar height was 21.4 ± 1.5 mm for the short group, 24.3 ± 2.0 mm for the normal group, and 25.8 ± 1.6 mm for the long group. For females at age 16 years, the maxillary central incisor dentoalveolar height was 21.7 ± 1.4 mm for the short group, 24.8 ± 2.0 mm for the average group, and 26.5 ± 1.6 mm for the long group (Figure 13). Dentoalveolar height differences at the maxillary central incisor, found between the female proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 13. Proportionate Classification: Dentoalveolar heights at the maxillary central incisor site in females 41

50 ii. Males The maxillary central incisor dentoalveolar heights (U1) for the three male proportionate growth pattern groups are as follows. For males at age 9 years, the maxillary central incisor dentoalveolar height was 22.1 ± 1.3 mm for the short group, 22.9 ± 1.5 mm for the average group, and 25.2 ± 1.1 mm for the long group. For males at age 12 years, the maxillary central incisor dentoalveolar height was 23.0 ± 1.5 mm for the short group, 24.2 ± 1.6 mm for the average group, and 26.9 ± 1.1 mm for the long group. For males at age 14 years, the maxillary central incisor dentoalveolar height was 23.6 ± 1.2 mm for the short group, 25.0 ± 1.6 mm for the normal group, and 28.1 ± 1.2 mm for the long group. For males at age 16 years, the maxillary central incisor dentoalveolar height was 24.4 ± 1.1 mm for the short group, 25.9 ± 1.7 mm for the average group, and 28.9 ± 1.3 mm for the long group (Figure 14). Dentoalveolar height differences at the maxillary central incisor, found between the male proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 14. Proportionate Classification: Dentoalveolar heights at the maxillary central incisor site in males 42

51 b. Maxillary first molar (U6) i. Females The maxillary first molar dentoalveolar heights (U6) for the three female proportionate growth pattern groups are as follows. For females at age 9 years, the maxillary molar dentoalveolar height was 14.9 ± 1.3 mm for the short group, 15.9 ± 1.2 mm for the average group, and 16.6 ± 1.4 mm for the long group. For females at age 12 years, the maxillary first molar dentoalveolar height was 16.6 ± 1.2 mm for the short group, 17.9 ± 1.4 mm for the average group, and 18.9 ± 1.6 mm for the long group. For females at age 14 years, the maxillary first molar dentoalveolar height was 17.9 ± 1.3 mm for the short group, 19.4 ± 1.6 mm for the average group, and 20.5 ± 1.5 mm for the long group. For females at age 16 years, the maxillary first molar dentoalveolar height was 18.4 ± 1.2 mm for the short group, 20.0 ± 1.7 mm for the average group, and 21.6 ± 1.2mm for the long group (Figure 15). Dentoalveolar height differences at the maxillary first molar, found between the female proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 15. Proportionate Classification: Dentoalveolar heights at the maxillary first molar site in females 43

52 ii. Males The maxillary first molar dentoalveolar heights (U6) for the three male proportionate growth pattern groups are as follows. For males at age 9 years, the maxillary molar dentoalveolar height was 14.7 ± 1.1 mm for the short group, 16.3 ± 1.6 mm for the average group, and 16.7 ± 1.3 mm for the long group. For males at age 12 years, the maxillary first molar dentoalveolar height was 16.2 ± 1.2 mm for the short group, 18.2 ± 1.8 mm for the average group, and 19.1 ± 1.1 mm for the long group. For males at age 14 years, the maxillary first molar dentoalveolar height was 17.6 ± 1.5 mm for the short group, 19.7 ± 1.9 mm for the average group, and 20.8 ± 1.2 mm for the long group. For males at age 16 years, the maxillary first molar dentoalveolar height was 19.3 ± 1.5 mm for the short group, 21.3 ± 1.9 mm for the average group, and 22.4 ± 1.2 mm for the long group (Figure 16). Dentoalveolar height differences at the maxillary first molar, found between the male proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 16. Proportionate Classification: Dentoalveolar heights at the maxillary first molar site in males 44

53 c. Mandibular central incisor (L1) i. Females The mandibular central incisor dentoalveolar heights (L1) for the three female proportionate growth pattern groups are as follows. For females at age 9 years, the mandibular central incisor dentoalveolar height was 29.2 ± 1.4 mm for the short group, 30.8 ± 1.4 mm for the average group, and 32.1 ± 1.5 mm for the long group. For females at age 12 years, the mandibular central incisor dentoalveolar height was 31.1 ± 1.8 mm for the short group, 32.5 ± 1.6 mm for the average group, and 33.9 ± 1.6 mm for the long group. For females at age 14 years, the mandibular central incisor dentoalveolar height was 31.8 ± 1.9 mm for the short group, 33.4 ± 1.6 mm for the average group, and 35.2 ± 1.4 mm for the long group. For females at age 16 years, the mandibular central incisor dentoalveolar height was 32.1 ± 1.8 mm for the short group, 34.0 ± 1.8 mm for the average group, and 35.7 ± 1.4 mm for the long group (Figure 17). Dentoalveolar height differences at the mandibular central incisor, found between the female proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 17. Proportionate Classification: Dentoalveolar heights at the mandibular central incisor site in females 45

54 ii. Males The mandibular central incisor dentoalveolar heights (L1) for the three male proportionate growth pattern groups are as follows. For males at age 9 years, the mandibular central incisor dentoalveolar height was 30.4 ± 1.5 mm for the short group, 31.3 ± 1.7 mm for the average group, and 33.1 ± 2.0 mm for the long group. For males at age 12 years, the mandibular central incisor dentoalveolar height was 31.8 ± 1.4 mm for the short group, 33.1 ± 2.0 mm for the average group, and 35.4 ± 1.9 mm for the long group. For males at age 14 years, the mandibular central incisor dentoalveolar height was 32.9 ± 1.6 mm for the short group, 34.9 ± 2.4 mm for the average group, and 37.1 ± 2.1 mm for the long group. For males at age 16 years, the mandibular central incisor dentoalveolar height was 34.4 ± 1.4 mm for the short group, 36.3 ± 2.2 mm for the average group, and 38.6 ± 2.2 mm for the long group (Figure 18). Dentoalveolar height differences at the mandibular central incisor, found between the male proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 18. Proportionate Classification: Dentoalveolar heights at the mandibular central incisor site in males 46

55 d. Mandibular first molar (L6) i. Females The mandibular first molar dentoalveolar heights (L6) for the three female proportionate growth pattern groups are as follows. For females at age 9 years, the mandibular first molar dentoalveolar height was 22.4 ± 0.8 mm for the short group, 23.2 ± 1.4 mm for the average group, and 24.6 ± 1.6 mm for the long group. For females at age 12 years, the mandibular first molar dentoalveolar height was 23.6 ± 1.4 mm for the short group, 24.6 ± 1.5 mm for the average group, and 25.8 ± 1.4 mm for the long group. For females at age 14 years, the mandibular first molar dentoalveolar height was 24.4 ± 1.5 mm for the short group, 25.5 ± 1.8 mm for the average group, and 27.4 ± 1.5 mm for the long group. For females at age 16 years, the mandibular first molar dentoalveolar height was 25.0 ± 1.6 mm for the short group, 26.2 ± 2.0 mm for the average group, and 28.0 ± 1.7 mm for the long group (Figure 19). Dentoalveolar height differences at the mandibular first molar, found between the female proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 19. Proportionate Classification: Dentoalveolar heights at the mandibular first molar site in females 47

56 ii. Males The mandibular first molar dentoalveolar heights (L6) for the three male proportionate growth pattern groups are as follows. For males at age 9 years, the mandibular first molar dentoalveolar height was 22.7 ± 1.3 mm for the short group, 23.0 ± 1.6 mm for the average group, and 25.4 ± 1.4 mm for the long group. For males at age 12 years, the mandibular first molar dentoalveolar height was 23.8 ± 1.3 mm for the short group, 24.2 ± 2.0 mm for the average group, and 26.5 ± 1.3 mm for the long group. For males at age 14 years, the mandibular first molar dentoalveolar height was 24.8 ± 1.0 mm for the short group, 25.8 ± 2.3 mm for the average group, and 28.1 ± 1.8 mm for the long group. For males at age 16 years, the mandibular first molar dentoalveolar height was 26.2 ± 1.4 mm for the short group, 27.6 ± 2.2 mm for the average group, and 29.8 ± 1.9 mm for the long group (Figure 20). Dentoalveolar height differences at the mandibular first molar, found between the male proportionate growth pattern groups at ages 9, 12, 14, and 16 years were significant, both in the overall analysis and at all four time points. Figure 20. Proportionate Classification: Dentoalveolar heights at the mandibular first molar site in males 48

57 B. Dentoalveolar height growth rates Between group one-way ANOVA analyses were used to test for significant differences of the dentoalveolar height growth rates among the classified groups within each gender for three time periods (9 to 12 years, 12 to 14 years, and 14 to 16 years) for all four dentoalveolar sites (U1, U6, L1, and L6). The following results describe the dentoalveolar height growth rates of the different groups within the sample for each site, time period and gender, and can be found in table format in Appendices 3 and 4. Directional classification a. Maxillary Central Incisor (U1) i. Females The maxillary central incisor (U1) dentoalveolar height growth rates for the three female directional growth pattern groups are as follows. For females during the 9 to 12 year period, the maxillary central incisor dentoalveolar height growth rate was 0.38 ± 0.31 mm/yr for the horizontal group, 0.41 ± 0.24 mm/yr for the average group, and 0.53 ± 0.25 mm/yr for the vertical group. For females during the 12 to 14 year period, the maxillary central incisor dentoalveolar height growth rate was 0.26 ± 0.2 mm/yr for the horizontal group, 0.3 ± 0.21 mm/yr for the average group, and 0.42 ± 0.25 mm/yr for the vertical group. For females during the 14 to 16 year period, the maxillary central incisor dentoalveolar height growth rate was 0.19 ± 0.21 mm/yr for the horizontal group, 0.22 ± 0.19 mm/yr for the average group, and 0.19 ± 0.16 mm/yr for the vertical group. No statistically significant differences in maxillary central incisor dentoalveolar height growth rates were found between the female directional growth pattern groups for any of the three time periods. 49

58 Figure 21. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in females in the 9 to 12 year period Figure 22. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in females in the 12 to 14 year period 50

59 Figure 23. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in females in the 14 to 16 year period 51

60 ii. Males The maxillary central incisor (U1) dentoalveolar height growth rates for the three male directional growth pattern groups are as follows. For males during the 9 to 12 year period, the maxillary central incisor dentoalveolar height growth rate was 0.43 ± 0.31 mm/yr for the horizontal group, 0.43 ± 0.28 mm/yr for the average group, and 0.59 ± 0.27 mm/yr for the vertical group. For males during the 12 to 14 year period, the maxillary central incisor dentoalveolar height growth rate was 0.5 ± 0.27 mm/yr for the horizontal group, 0.42 ± 0.29 mm/yr for the average group, and 0.3 ± 0.31 mm/yr for the vertical group. For males during the 14 to 16 year period, the maxillary central incisor dentoalveolar height growth rate was 0.36 ± 0.31 mm/yr for the horizontal group, 0.4 ± 0.27 mm/yr for the average group, and 0.53 ± 0.3 mm/yr for the vertical group. No statistically significant differences in maxillary central incisor dentoalveolar height growth rates were found between the male directional growth pattern groups for any of the three time periods. Figure 24. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in males in the 9 to 12 year period 52

61 Figure 25. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in males in the 12 to 14 year period Figure 26. Directional Classification: Dentoalveolar height growth rate at the maxillary central incisor site in males in the 14 to 16 year period 53

62 b. Maxillary first molar (U6) i. Females The maxillary first molar (U6) dentoalveolar height growth rates for the three female directional growth pattern groups are as follows. For females during the 9 to 12 year period, the maxillary first molar dentoalveolar height growth rate was 0.63 ± 0.3 mm/yr for the horizontal group, 0.66 ± 0.23 mm/yr for the average group, and 0.72 ± 0.19 mm/yr for the vertical group. For females during the 12 to 14 year period, the maxillary first molar dentoalveolar height growth rate was 0.65 ± 0.23 mm/yr for the horizontal group, 0.74 ± 0.26 mm/yr for the average group, and 0.83 ± 0.24 mm/yr for the vertical group. For females during the 14 to 16 year period, the maxillary first molar dentoalveolar height growth rate was 0.33 ± 0.37 mm/yr for the horizontal group, 0.34 ± 0.27 mm/yr for the average group, and 0.27 ± 0.27 mm/yr for the vertical group. No statistically significant differences in maxillary first molar dentoalveolar height growth rates were found between the female directional growth pattern groups for any of the three time periods. Figure 27. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in females in the 9 to 12 year period 54

63 Figure 28. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in females in the 12 to 14 year period Figure 29. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in females in the 14 to 16 year period 55

64 ii. Males The maxillary first molar (U6) dentoalveolar height growth rates for the three male directional growth pattern groups are as follows. For males during the 9 to 12 year period, the maxillary first molar dentoalveolar height growth rate was 0.69 ± 0.3 mm/yr for the horizontal group, 0.65 ± 0.33 mm/yr for the average group, and 0.62 ± 0.3 mm/yr for the vertical group. For males during the 12 to 14 year period, the maxillary first molar dentoalveolar height growth rate was 0.76 ± 0.36 mm/yr for the horizontal group, 0.73 ± 0.23 mm/yr for the average group, and 0.91 ± 0.46 mm/yr for the vertical group. For males during the 14 to 16 year period, the maxillary first molar dentoalveolar height growth rate was 0.72 ± 0.52 mm/yr for the horizontal group, 0.84 ± 0.35 mm/yr for the average group, and 0.82 ± 0.47 mm/yr for the vertical group. No statistically significant differences in maxillary first molar dentoalveolar height growth rates were found between the male directional growth pattern groups for any of the three time periods. Figure 30. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in males in the 9 to 12 year period 56

65 Figure 31. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in males in the 12 to 14 year period Figure 32. Directional Classification: Dentoalveolar height growth rate at the maxillary first molar site in males in the 14 to 16 year period 57

66 c. Mandibular central incisor (L1) i. Females The mandibular central incisor (L1) dentoalveolar height growth rates for the three female directional growth pattern groups are as follows. For females during the 9 to 12 year period, the mandibular central incisor dentoalveolar height growth rate was 0.47 ± 0.15 mm/yr for the horizontal group, 0.6 ± 0.25 mm/yr for the average group, and 0.62 ± 0.12 mm/yr for the vertical group. For females during the 12 to 14 year period, the mandibular central incisor dentoalveolar height growth rate was 0.27 ± 0.25 mm/yr for the horizontal group, 0.47 ± 0.29 mm/yr for the average group, and 0.61 ± 0.32 mm/yr for the vertical group. For females during the 14 to 16 year period, the mandibular central incisor dentoalveolar height growth rate was 0.24 ± 0.15 mm/yr for the horizontal group, 0.24 ± 0.15 mm/yr for the average group, and 0.32 ± 0.12 mm/yr for the vertical group. No statistically significant differences in mandibular central incisor dentoalveolar height growth rates were found between the female directional growth pattern groups for any of the three time periods. Figure 33. Directional Classification: Dentoalveolar height growth rate at the mandibular central incisor site in females in the 9 to 12 year period 58

67 Figure 34. Directional Classification: Dentoalveolar height growth rate at the mandibular central incisor site in females in the 12 to 14 year period Figure 35. Directional Classification: Dentoalveolar height growth rate at the mandibular central incisor site in females in the 14 to 16 year period 59