Landmark-based approach to examining changes in arch shape: a longitudinal study

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2015 Landmark-based approach to examining changes in arch shape: a longitudinal study Taylor Blake Varner University of Iowa Copyright 2015 Taylor Varner This thesis is available at Iowa Research Online: Recommended Citation Varner, Taylor Blake. "Landmark-based approach to examining changes in arch shape: a longitudinal study." MS (Master of Science) thesis, University of Iowa, Follow this and additional works at: Part of the Orthodontics and Orthodontology Commons

2 LANDMARK-BASED APPROACH TO EXAMINING CHANGES IN ARCH SHAPE: A LONGITUDINAL STUDY by Taylor Blake Varner A thesis submitted in partial fulfillment of the requirements for the Master of Science degree in Orthodontics in the Graduate College of The University of Iowa May 2015 Thesis Supervisor: Assistant Professor Lina M. Moreno Uribe

3 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL MASTER'S THESIS This is to certify that the Master's thesis of Taylor Blake Varner has been approved by the Examining Committee for the thesis requirement for the Master of Science degree in Orthodontics at the May 2015 graduation. Thesis Committee: Lina M. Moreno Uribe, Thesis Supervisor Nathan E. Holton Veerasathpurush Allareddy

4 To science ii

5 ACKNOWLEDGEMENTS I wish to express my sincere appreciation to Dr. Lina Moreno, thesis supervisor, for her guidance and direction of this study. I would also like to thank Dr. Sath Allareddy and Dr. Nathan Holton for their advice throughout this endeavor, Dr. Joseph Cavanaugh and Camden Bay for statistical support, Dr. Steven Levy and Dr. John Warren for their recommendations and providing access to the Iowa Fluoride Study, and to Taylor Geyer for her assistance in cast scan classification. I am forever grateful for the invaluable insight, support and guidance of Dr. Steve Miller. This project would not have been possible without you. To my husband, Whit, for his patience, encouragement, and strength throughout my orthodontic training, a sincere thank you. iii

6 ABSTRACT Objective: Variation in dental arch shape and arch relations from the primary to the permanent dentition were studied in an untreated longitudinal sample from the Iowa Fluoride Study and Growth Study data (55 females and 63 males). Methods: 3D coordinate data from 68 landmarks located on maxillary, mandibular, and occlusal dental cast scans from ages 5, 9, and 13 were submitted to a Procrustes fit prior to a Principal Component (PC) analysis to capture symmetric and asymmetric aspects of arch shape variation. Covariance pattern models were used to determine longitudinal arch shape changes from the primary to the permanent dentition and to correlate these changes with Angle class molar classification. Results: The first 3 principal components capture 52-78% of the variation in arch shape. PC1 explains 30-44% of the variance and captures changes in overall dentoalveolar height. PC2 explains 14-22% and shows mainly variation in dentoalveolar height and width at the canines. Lastly, PC3 explains 8-12% and captures overall arch width and perimeter differences and changes in anteroposterior arch relations. Results on symmetric shape variation for the occlusal data set captured significant differences (p < ) in morphology for PC2 and PC3. For PC2, initial morphology in the deciduous dentition for an individual classified as Class II was significantly different than a Class I individual. Initial shape characteristics for the Class II features stepped down maxillary incisors and an increased curve of Spee with deep overbite. For PC3, the initial morphology for both the distocclusion and Class II individuals demonstrated characteristics such as stepped up maxillary incisors and increased overjet relative to their flush terminal plane and Class I counterparts. The rate of arch shape changes at which the distal step group transitions to the mixed dentition was also significantly different from the flush terminal plane sample. iv

7 Conclusions: Initial findings summarize the main aspects of arch shape variation throughout 3 dentition stages. The covariance pattern models estimated individual trajectories and dynamics of arch shape changes from the primary to the permanent dentition and correlated these changes with Angle molar classification. In the symmetric dataset, significant shape characteristic differences of both initial starting morphology and change in shape over time were discovered for two occlusal phenotypes highlighting differences primarily in the vertical and anteroposterior dimensions. The results found in the present study provide an excellent foundation for describing and identifying dental arch shape differences in the primary dentition that can aid in earlier detection, diagnosis, and treatment of malocclusion, or at a minimum warrant closer observation by the clinician. v

8 PUBLIC ABSTRACT Misalignment or incorrect relation between the upper and lower teeth of the maxilla and mandible is caused by discrepancies in the size and shape of the various components of the maxillamandibular complex. The functional balance and adequate spatial alignment of the upper and lower dental arches is necessary for adequate chewing, swallowing, and speech. To aid in determining the underlying causes of dental misalignments and incorrect dental bites, a shape variation analysis was performed using a geometric morphometrics approach and principal components analysis. Variation in dental arch shape and arch relations as an individual transitions from their baby teeth to permanent teeth were studied in an untreated longitudinal sample from the Iowa Fluoride Study and Growth Study data (55 females and 63 males). Results illustrated significant dental arch shape differences (p < ) between individuals who started with abnormal bites (i.e. deep bite or increased overbite) in the primary (baby teeth) dentition compared to individuals who initially had normal bites. The findings summarize detail aspects of shape variation through time that may aid in earlier detection and treatment modalities for bite problems. vi

9 TABLE OF CONTENTS LIST OF TABLES... ix LIST OF FIGURES... x INTRODUCTION... 1 CHAPTER 1 BACKGROUND... 3 Longitudinal Studies in Dental Arch Growth and Development... 3 Development of Class II and Class III Malocclusion... 3 Tooth Size-Arch Length Discrepancy... 5 Arch Length... 7 Arch Width... 8 Curve of Spee... 9 Analysis of Longitudinal Cast Data Geometric Morphometrics Shape Analysis Morphometric Analysis of the Dental Arch Form Analysis of Longitudinal 3D Coordinate Data CHAPTER 2 MATERIALS AND METHODS Classifier Data Landmark Determination GM Analyses CHAPTER 3 RESULTS Intraobserver Reliability Results Allometric Analysis Principal Component Analysis Symmetric Mandibular Principal Components Symmetric Maxillary Principal Components Symmetric Occlusal Principal Components Asymmetric Mandibular Principal Components Asymmetric Maxillary Principal Components vii

10 Asymmetric Occlusal Principal Components Covariance Pattern Models Mandibular Principal Components Maxillary Principal Components Occlusal Principal Components CHAPTER 4 DISCUSSION SUMMARY AND CONCLUSION REFERENCES viii

11 LIST OF TABLES Table 2.1. Landmark Description for Age 13 mandible Table 2.2. Landmark Description for Age 13 Maxilla Table 2.3. Landmark Description for Age 13 Occlusion Table 2.4. Classifier data information following the removal of outlier cast scans Table 3.1. Euclidean distance reliability results Table 3.2. Landmark Coordinate Data Reliability Table 3.3. Intraclass Correlation Results Table 3.4. Symmetric Allometry Regression Results Table 3.5. Asymmetric Allometry Regression Results Table 3.6. Definitions of Effects Outputted from SAS Table 3.7. Mandibular Principal Components Covariance Pattern Analysis Table 3.8. Maxillary Principal Components Covariance Pattern Analysis Table 3.9. Occlusal Principal Components Covariance Pattern Analysis ix

12 LIST OF FIGURES Figure 2.1. Age 13 Mandibular Landmarks Figure 2.2. Age 13 Maxillary Landmarks Figure 2.3. Age 13 Occlusal Landmarks Figure 3.1. Percent Variance of Symmetric Mandibular Principal Components Figure 3.2. Mandibular Principal Component 1 Symmetric Figure 3.3: Variability of Individual Cast Scans Symmetric Mandible PC Figure 3.4. Mandibular Principal Component 2 Symmetric Figure 3.5. Variability of Individual Cast Scans Symmetric Mandible PC Figure 3.6. Mandibular Principal Component 3 - Symmetric Figure 3.7. Variability of Individual Cast Scans Symmetric Mandible PC Figure 3.8: Mandibular Principal Component 4 - Symmetric Figure 3.9. Variability of Individual Cast Scans Symmetric Mandible PC Figure 3.10: Mandibular Principal Component 5 Symmetric Figure 3.11: Variability of Individual Cast Scans Symmetric Mandible PC Figure 3.12: Percent Variance of Symmetric Maxillary Principal Components Figure 3.13: Maxillary Principal Component 1 - Symmetric Figure 3.14: Variability of Individual Cast Scans Symmetric Maxillary PC Figure 3.15: Maxillary Principal Component 2 - Symmetric Figure 3.16: Variability of Individual Cast Scans Symmetric Maxillary PC x

13 Figure 3.17: Maxillary Principal Component 3 - Symmetric Figure 3.18: Variability of Individual Cast Scans Symmetric Maxillary PC Figure 3.19: Maxillary Principal Component 4 - Symmetric Figure 3.20: Variability of Individual Cast Scans Symmetric Maxillary PC Figure 3.21: Percent Variance of Symmetric Occlusal Principal Components Figure 3.22: Occlusal Principal Component 1 - Symmetric Figure 3.23: Variability of Individual Cast Scans Symmetric Occlusal PC Figure 3.24: Occlusal Principal Component 2 - Symmetric Figure 3.25: Variability of Individual Cast Scans Symmetric Occlusal PC Figure 3.26: Occlusal Principal Component 3 - Symmetric Figure 3.27: Variability of Individual Cast Scans Symmetric Occlusal PC Figure 3.28: Occlusal Principal Component 4 - Symmetric Figure 3.29: Variability of Individual Cast Scans Symmetric Occlusal PC Figure 3.30: Occlusal Principal Component 5 - Symmetric Figure 3.31: Variability of Individual Cast Scans Symmetric Occlusal PC Figure 3.32: Percent Variance of Asymmetric Mandibular Principal Components Figure 3.33: Mandibular Principal Component 1 - Asymmetric Figure 3.34: Variability of Individual Cast Scans Asymmetric Mandibular PC Figure 3.35: Mandibular Principal Component 2 - Asymmetric Figure 3.36: Variability of Individual Cast Scans Asymmetric Mandibular PC xi

14 Figure 3.37: Mandibular Principal Component 3 - Asymmetric Figure 3.38: Variability of Individual Cast Scans Asymmetric Mandibular PC Figure 3.39: Mandibular Principal Component 4 - Asymmetric Figure 3.40: Variability of Individual Cast Scans Asymmetric Mandibular PC Figure 3.41: Mandibular Principal Component 5 - Asymmetric Figure 3.42: Variability of Individual Cast Scans Asymmetric Mandibular PC Figure 3.43: Mandibular Principal Component 6 - Asymmetric Figure 3.44: Variability of Individual Cast Scans Asymmetric Mandibular PC Figure 3.45: Percent Variance of Asymmetric Maxillary Principal Components Figure 3.46: Maxillary Principal Component 1 - Asymmetric Figure 3.47: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.48: Maxillary Principal Component 2 - Asymmetric Figure 3.49: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.50: Maxillary Principal Component 3 - Asymmetric Figure 3.51: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.52: Maxillary Principal Component 4 - Asymmetric Figure 3.53: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.54: Maxillary Principal Component 5 - Asymmetric Figure 3.55: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.56: Maxillary Principal Component 6 - Asymmetric xii

15 Figure 3.57: Variability of Individual Cast Scans Asymmetric Maxillary PC Figure 3.58: Percent Variance of Asymmetric Occlusal Principal Components Figure 3.59: Occlusal Principal Component 1 - Asymmetric Figure 3.60: Variability of Individual Cast Scans Asymmetric Occlusal PC Figure 3.61: Occlusal Principal Component 2 - Asymmetric Figure 3.62: Variability of Individual Cast Scans Asymmetric Occlusal PC Figure 3.63: Occlusal Principal Component 3 - Asymmetric Figure 3.64: Variability of Individual Cast Scans Asymmetric Occlusal PC Figure 3.65: Occlusal Principal Component 4 - Asymmetric Figure 3.66: Variability of Individual Cast Scans Asymmetric Occlusal PC Figure 3.67: Mandibular Principal Component 6 - Asymmetric Figure 3.68 Mandibular Asymmetric PC6: Rate for Class II Figure 3.69: Maxillary Principal Component 5 - Asymmetric Figure 3.70 Maxillary Asymmetric PC5: y-int for Class II Figure 3.71: Occlusal Principal Component 2 - Symmetric Figure 3.72 Occlusal Symmetric PC2: y-int for Class II Figure 3.73: Occlusal Principal Component 3 - Symmetric Figure Occlusal Symmetric PC3: y-int for Distal Step Figure Occlusal Symmetric PC3: y-int for Class II Figure Occlusal Symmetric PC3: Rate for Distal Step xiii

16 INTRODUCTION Misalignment or incorrect relation between the teeth of the maxilla and mandible is caused by discrepancies in the size and shape of the various components of the craniofacial complex. The dental arches play a crucial role in orofacial functions. The functional balance and adequate spatial alignment of the maxillary and mandibular dental arches is necessary for adequate chewing, swallowing, and speech (Toro et al., 2006; Marquezin et al., 2014; Seeman, 2010). Edward Angle described three types of malocclusion based on molar positioning in 1890, which has served as the foundation of classifying malocclusion in orthodontics (Angle, 1900). Class I molar occlusion is present in about 30% of the U.S. population. There is a high prevalence of malocclusion, with Class I malocclusion being present in approximately 50-55% of the U.S. population. This form of malocclusion occurs when molars are in proper position (mesiobuccal cusp of maxillary first molar aligns with the buccal groove of the mandibular first molar) but other variables such as crowding or excess overjet and/or overbite may exist. Class II malocclusion is present in 15% of the U.S. population and occurs when the maxillary molar is ahead (more mesial) of the mandibular molar. Clinical findings often include a convex facial profile with a retrusive mandible. Lastly, Class III malocclusion occurs in only 1% of the U.S. population and clinically appears when the maxillary first molar is distal to the mandibular first molar. Clinical manifestations often found are a straight or concave profiles with a prognathic mandible. Longitudinal studies of normal and abnormal occlusions from the primary dentition toward the permanent dentition and into adulthood have provided significant insight as to the progression of dental relationships in the anteroposterior, vertical, and transverse dimensions. These studies provide understanding into the development of malocclusion and dental arch crowding, however, 1

17 the investigators utilized mostly simple linear measurements as outcome variables. Geometric morphometric techniques provide more information about the development of malocclusion, by mathematically eliminating differences in size and only focusing on shape variation within the dental arches. This methodology allows a more visual representation of the overall arch shape variation facilitating data interpretation beyond analyses of linear measurements. The purpose of this study is to examine the nature of dental arch shape and dental positional changes occurring between the deciduous and permanent dentition in an untreated sample of healthy individuals. This study will provide quantitative and qualitative representation and analysis of morphological shape differences between the dental arches using geometric coordinates instead of linear measurements. In addition, this study will evaluate between Class I and Class II subjects how such shape variation evolves in time as individuals transition between 3 different dentition stages. 2

18 CHAPTER 1 BACKGROUND Longitudinal Studies in Dental Arch Growth and Development Development of Class II and Class III Malocclusion The understanding of the three dimensional changes that occur in the occlusion between deciduous and permanent dentitions is crucial for diagnosing and treatment planning in early orthodontic treatment. Regarding anteroposterior relations, Arya et al. discovered that when primary second molars erupt into a distal or mesial step relationship, that relationship is maintained in the permanent dentition (Arya, 1973). However, of molars that initially erupt in a cusp-to-cusp (flush terminal plane) relationship, 70% developed into a Class I relationship, and the other 30% maintained their end-on relationship thus developing a Class II permanent molar relationship. Bishara describes similar changes in the molar relationship from the deciduous dentition to the permanent dentition. From the deciduous dentition, Bishara noted 61.6% developed into a Class I molar relationship, 34.3% developed into Class II, and 4.1% into a Class III malocclusion (Bishara, 1988). Essentially 100% of the deciduous dentition that started with a distal step developed into a Class II molar relationship in the permanent dentition. The presence of a mesial step in the deciduous dentition indicated a greater probability of developing a Class I molar relationship. Those that started with a flush terminal plane in the deciduous dentition, 56% developed to a Class I molar relationship and 44% progressed to Class II. (Bishara, 1988). These studies make it clear that patients exhibiting a distal step or cusp-to-cusp, end-on relationship in the primary dentition might require early orthodontic treatment intervention more often than those with a mesial step. Bishara 3

19 also studied dental arch width and length changes through time, which will be discussed later in this thesis. Longitudinal studies involving samples of Class II malocclusion during the transition from the deciduous to mixed dentition have been investigated by several authors. Frohlich reported that no improvement of Class II occlusal relationship occurs from 5 to 12 years of age (Frohlich, 1961). Moyers and co-authors (1977) concluded that a distal step in the deciduous dentition likely reflects an underlying skeletal imbalance and typically results in a Class II malocclusion in the permanent dentition (Moyers, 1977). With regards to the skeletal characteristics of Class II malocclusion, Varrela (1993) compared cephalometric values of children at the primary dentition stage with Class II occlusal development versus those children with normal occlusal development. The author concluded that children with a distal step had a shorter mandibular corpus and a larger gonial angle relative to those with normal occlusion (Varrela, 1993). Buschang noted that reduced mandibular growth rates were found in subjects with untreated Class II malocclusion when compared with normal subjects from 6 to 15 years of age (Buschang, 1988). Baccetti investigated the developmental changes in craniofacial and occlusal patterns already established in the deciduous dentition through the mixed dentition and concluded that in addition to the sagittal plane Class II relationship, there was also a transverse interarch discrepancy due to a narrower maxillary arch. Baccetti suggested that both the Class II occlusal characteristics and the transverse interarch discrepancy are maintained or made worse during the transition from the deciduous dentition to the mixed dentition (Baccetti, 1997). These findings suggest that clinical signs of Class II malocclusion are evident in the primary dentition and persist into the permanent dentition. Early 4

20 treatment can be initiated in Class II patients, but patient cooperation should be considered before early treatment is started. Tooth Size-Arch Length Discrepancy Both researchers and clinicians alike are very interested in predicting tooth size-arch length discrepancies in the growing patient (Bishara, 1989; Bishara, 1994; Bishara, 2006; Thilander, 2009). If accurate predictions can be made early on while the patient is in the mixed dentition, it would be possible for the clinician to intercept early on a developing malocclusion. Tooth size-arch length discrepancy (TSALD) studies have also been performed longitudinally. Bishara s (1989) paper is one such study that has shed light on understanding the maturational changes that occur during early childhood to early adulthood in normal untreated individuals. The author observed a significantly greater reduction in the available arch length in the group with the most tooth size-arch length discrepancy at early adulthood. This decrease in maxillary and mandibular arch lengths was significantly greater in male subjects (2.55mm in maxilla, 2.61mm in mandible) compared to females (2.33mm in maxilla, 1.25mm in mandible). The results of the author s regression analyses were used to assess the relationships between the changes in maxillary and mandibular tooth size-arch length relationship and parameters such as the mesiodistal diameter of different teeth, soft tissue and incisor angulation changes during maturation, and the changes in anterior and posterior facial heights. The results indicated a significantly greater reduction in the available arch length in the group with the most TSALD at early adulthood. No other variables were found to be significantly different. Bishara conducted a later study exploring the extent of the individual variation in the changes in the maxillary and mandibular TSALD between the time of complete eruption of the 5

21 primary dentition and the time of eruption of the second permanent molars (Bishara, 2006). The investigation indicated that 49% of subjects maintained their relative TSALD relationship ranking in the two dentitions, while 51% changed to either a more favorable or less favorable relationship in the permanent dentition. Based on his results, Bishara does not recommend early mechanical intervention in the primary dentition to influence the future TSALD in an individual, and rather to wait until the mixed dentition to take action if needed. Bishara also investigated the changes in various craniofacial and dental arch parameters between 25 and 45 years of age in an untreated normal sample. Linear measurements of the dental arches indicated that a clinically significant increase in tooth size-arch length discrepancies occurred and should be considered as part of the normal maturational process (Bishara, 1994). In both male and female subjects, interincisor and intercanine arch widths decreased, total arch lengths decreased, and anterior crowding increased. Similarly, Thilander (2009) noted that continuous changes of the dental arches occur from the primary until the adult period, with individual variations. The author interprets these changes as a biological migration of the dentition, leading to anterior crowding. Thilander also suggests that the continuous increase of palatal height up to adulthood seems to be an effect of a slow continuous eruption of teeth (Thilander, 2009). Relative to TSALD studies, retention and relapse are two of the greatest challenges orthodontists face after the completion of orthodontic treatment. Recrowding of the anterior teeth is the most post-treatment change noted if retention is not used. Even extracting premolars to alleviate the tooth size-arch length discrepancy does not ensure the stability of anterior teeth alignment (Little, 1981). The trend towards an increased incidence of mandibular incisor crowding 6

22 with age in untreated persons has been reported by many (Moorrees, 1959; Lundstrom, 1968; Cryer, 1965). These findings have important clinical implications regarding the long range stability and retention of orthodontic treatment results. When considering an adolescent orthodontic patient, it should be noted that without long term retention, various amounts of crowding in the anterior part of the dental arches can be expected as part of the normal maturation process. This increase in dental crowding as we age, even after orthodontic treatment, can be frustrating to the orthodontist and patient alike. Arch Length In 1964, Sillman performed one of the first (mixed) longitudinal studies of the dental arches from birth to age 25. Sillman observed that in both jaws the greatest incremental increase in arch length occurred between birth and 2 years. He suggested that some increase might occur during eruption of the permanent incisors, but that anterior arch length is primarily established after the eruption of the deciduous dentition, around 3 years (Sillman, 1964). Bishara evaluated longitudinally the changes in maxillary and mandibular total arch length over a 45-year span between 6 weeks and 45 years. He also observed that the greatest incremental increase occurred during the first two years of life, before the complete eruption of the deciduous dentition. Arch length continued to increase until 13 years in the maxillary arch, and until 8 in the mandible. He suggests that these changes are probably related to the eruption of the permanent incisors. Following these changes there were significant decreases in both arches mesial to the permanent first molars: maxillary arch length decreased an average of 5.7mm in males and 4.6mm in females, and mandibular arch length decreased 5.0mm in both sexes (Bishara, 1995). 7

23 Arch Width Similar longitudinal studies have been conducted with regards to dental arch width. One of the first studies to do so was DeKock in Females showed no significant change in either arch width during the 14 year time period (12 to 26). For males, there was a slight increase in each arch from 12 to 15 years (DeKock, 1972). Multiple investigators observed similar findings: that during the period of study, the arch length decreased, intercanine widths slightly decreased, and intermolar widths remained stable (DeKock, 1972; Sillman, 1964; Lundstrom, 1975). Incisor-canine circumference has been noted to decrease from 13 to 18 years of age due to a decrease in arch length rather than a narrowing in arch width (Moorrees, 1979). DeKock quantified the average reduction by 10%. Lombardo and collaborators (2013) performed a meta-analysis of several of the arch width measurements reported in the literature, and evaluated the arch widths in subjects with Class I occlusion relative to Class II individuals. They concluded that there was no statistically significant differences in arch width between Class I and Class II samples, except in the case of mandibular inter-canine width and maxillary inter-premolar width. They found that mandibular intercanine width was smaller in Class I than in Class II, Division I patients, and that maxillary inter-premolar width was smaller in Class II, Division I than Class I patients (Lombardo et al., 2013). Bishara concluded that between 6 weeks and 2 years of age, there were significant increases in the maxillary and mandibular anterior and posterior arch widths in both male and female infants (Bishara, 1997). In both jaws, between 3 and 13 years of age, intercanine and intermolar widths significantly increased. Following the complete eruption of the permanent dentition, there was a slight decrease in the dental arch width, more so in the intercanine than in 8

24 the intermolar widths. Mandibular intercanine width was established by 8 years of age, following incisor eruption. After the eruption of the permanent dentition, there was no change or only a slight decrease in arch width. Bishara suggested that based on the above findings,...the magnitude as well as the direction of these changes do not provide a scientific basis for expanding the arches in the average patient beyond its established dimension at the time of complete eruption of the canines and molars. Both patients and clinicians should be aware of these limitations... (Bishara, 1997). Similar findings are concluded by Tsujino: increases in arch width during the transitional dentition are greater in the maxilla than in the mandible, and arch widths do not change significantly from adolescence into adulthood (Tsujino, 1998). In conclusion, it can be summarized that arch width is relatively stable (or in some cases, can slightly decrease) following the complete eruption of the permanent dentition. In addition, meta-analyses of arch width measurements concluded that the only significant differences in arch width between Class I and Class II individuals are in the mandibular inter-canine and maxillary inter-premolar width. Curve of Spee A lateral view of a human mandible or dental cast usually reveals a concave curve in the mandibular teeth. This curvature, termed the curve of Spee, was first described in humans in the late 19 th century by Ferdinand Graf von Spee (Spee, 1890). Subsequent research and study has resulted in the widely accepted definition in the orthodontic literature as the arc of a curved plane in the sagittal plane that is tangent to the incisal edges and the buccal cusp tips of the mandibular dentition. Andrews described 6 characteristics of normal occlusion and reported that the curve of Spee in individuals with good occlusion ranged from flat to a mild curve (Andrews, 1972). With regards to orthodontics, Andrews proposed that flattening the occlusal plane should be an 9

25 orthodontic treatment goal since he found that the best intercuspation occurred when the occlusal plane was relatively flat. Little research has been performed on why and how the curve of Spee develops. It has been reported that once the curve of Spee is established in adolescence, the curve of Spee appears to be relatively stable (Carter, 1998; Bishara, 1989). Marshall provides the only longitudinal study to our knowledge about the development of the curve of Spee from the deciduous dentition to adulthood in a sample of untreated subjects with normal occlusion (Marshall, 2008). He concluded that in the deciduous dentition, the curve of Spee is minimal (0.24mm). As the permanent first molars and central incisors erupted transitioning into the mixed dentition, Marshall found that the curve of Spee depth increases significantly to a mean maximum depth of 1.32mm. The curve of Spee maintains this depth until the eruption of the mandibular permanent second molars to a mean maximum depth of 2.17mm. During the adolescent (permanent) dentition stage, Marshall discovered that the curve depth decreases slightly and then remains stable into early adulthood. No significant differences were found with regards to the curve of Spee development between the left and right sides of the mandibular arch or between males and females. Both a previous study in 1993 and Marshall s study support the suggestions that the deciduous dentition has a curve of Spee ranging from flat to mild, whereas the adult curve of Spee is more prominent (Ash, 1993). Analysis of Longitudinal Cast Data The studies discussed above provide an excellent foundation in longitudinal research exploring malocclusion and dental arch crowding. However, the investigators utilized mostly simple linear measurements as outcome variables in their analyses. Longitudinal cast data studies primarily evaluated subjects at two to five stages of dental development including arch 10

26 measurements before the complete eruption of the primary dentition, primary, mixed, early adulthood, and late adulthood dental stages. Variables such as molar relationship, mesiodistal crown diameters of primary and permanent teeth, dental arch widths, arch lengths, total anterior crowding or spacing, and various cephalometric dentofacial parameters were evaluated. Correlation coefficients and regression analyses were used to assess the relationships between these measurements and changes in molar relationships. Descriptive statistics were also calculated at each dental stage. Student s t-test was used to determine whether significant differences were present between genders, dental asymmetries between right and left sides, as well as subjects found with the most and least changes in TSALD. Stepwise regression analysis was used to determine which of the variables should be included in a regression model. This procedure is useful in isolating a subset of predictor variables that best explain the variation of the dependent variable. Lastly, discriminant analysis was used to supplement the findings of the regression analysis because it provides a means of assessing predictive accuracy (Bishara, 1988; 1989; 1994; 2006; Thilander, 2009). Bishara utilized the repeated measures analysis of variance to calculate arch length and width changes over time as well as individual variation in tooth size-arch length changes from the primary to permanent dentitions (Bishara, 1995; 1997; 2006). Analysis of variance general linear models procedure was also used to compare the various dental arch parameters on both a crosssectional and longitudinal basis when evaluating dental arch changes in normal and untreated Class II, Division 1 subjects (Bishara, 1996). Marshall measured the depth of the curve of Spee on dental casts at 7 time points from ages 4 with primary dentition to age 26 in the adult dentition. The Wilcoxon signed rank test was 11

27 used to compare changes in the curve of Spee depth between time points (Marshall, 2008). Adjustment for multiple comparisons was made by using the standard Bonferroni method with an overall 0.05 level of type I error. Descriptive statistics were also obtained for age at each time point. Holton et al performed a mixed longitudinal study exploring sexual dimorphism in the development of the nasal cavity utilizing geometric means with the Mann-Whitney U test and reduced major axis (RMA) regression (Holton et al., 2014). Although a linear measurement based analysis, the geometric mean technique removes size from linear measurements to evaluate shape. The authors concluded both males and females exhibit similar nasal size values early in ontogeny and that sexual dimorphism in nasal size appears during adolescence. Males also showed greater positive allometry in nasal size compared to females. The investigators conclusions described in the previous sections are limited to the findings mentioned above with linear outcome variable measurements and analyses and do not explore other aspects of dental variation such as three-dimensional dental morphology in the context of malocclusion and dental crowding etiology. Geometric morphometrics (GM), as described in the next section, is a method that allows researchers to study morphology and therefore it is a convenient approach that can be applied to characterize dental arch development, tooth size-arch length discrepancies and other occlusal irregularities. 12

28 Geometric Morphometrics While other scientific fields such as biology and engineering have used geometric morphometric (GM) techniques for the last two decades, it is a relatively new method of shape analysis for craniofacial structures in the field of dentistry. Significant developments in the instrumentation to acquire and analyze aspects of teeth such as their size and shape has led to meaningful insights into the nature and extent of morphological variation within the dentition. GM techniques can be used to identify changes in the shape of the dentofacial complex based on various biological processes that occur normally in growth and development, or due to other processes like injury or disease. In this study, we plan to characterize shape variation in a longitudinal sample in an effort to understand dental arch shape changes that occur with growth and development as individuals transition from the primary to permanent dentition. Geometric morphometric analysis allows researchers to study morphological variation and co-variation between variables beyond what is feasible using linear metric analyses, as described in the previous section. Zelditch refers to geometry as a set of rules for making sense of data about positions, distances, and angles in our ordinary three-dimensional world, while morphometrics refers to the mathematical quantification of morphology in different structures and organisms (Zelditch, 2004). The most important concept in GM analysis is shape, which Kendall has defined as all the geometric information that remains when location, scale, and rotational effects are filtered out from an object (Kendall, 1977). Using GM, the researcher is able to study the shape of objects independent of size and orientation. Differences in shape can be made by comparison with more fundamental objects, for example, the shape of an upper molar usually resembles a rhomboid. 13

29 However, to accurately describe and quantify subtle shape differences between objects, high precision modalities like GM can be employed (Bernal, 2007). GM techniques allow for complex analysis of size and shape based on coordinate landmark data in two, or three-dimensional space (Bookstein, 1991). Landmark based GM utilizes reliable coordinate data to review a large amount of information without needing a large number of coordinates. This allows the investigator to interpret information on shape independent of size or orientation of the object, minimizing the redundancy often found in traditional morphometrics with point to point distance measurements. Principal components analysis (PCA) is an example of a data reduction technique to reduce complexity and aid in interpretation of GM data (Zelditch, 2004). Earlier studies of dental morphology used univariate statistical analyses that were unable to take into account the inter-correlations between different dental dimensions and dental structures. Investigators are now able to use multivariate methods such as the PCA approach that can disclose patterns of variation not often revealed with univariate statistics alone. Prior to GM analyses, the coordinate data must be registered through generalized Procrustes analysis (GPA). GPA is a least-squares method of superimposing coordinate landmark data so that differences in shape may be examined (Rohlf, 1990). To compare the multiple shapes, the objects must be superimposed via a least squares method by translating, rotating, and uniformly scaling the objects; this is known as a Procrustes superimposition. The Procrustes distance (the square root of the sum of squared differences between the corresponding landmarks) is minimized between a reference form and all subsequent forms in the dataset (Zelditch, 2004). Once the Procrustes superimposition is complete, shape differences between dental casts can be analyzed and used to obtain in-depth information on phenotypic shape variation within our sample. 14

30 Shape Analysis Study models and intra-oral photographs of arch form are vital for the orthodontist and serve as key diagnostic tools. While diagnosing and treatment planning orthodontic patients, the clinician needs to be aware of the importance of considering arch form to attain a harmonious orthodontic occlusion. One of the earliest descriptions of the normal anatomic arrangement of human teeth was provided by Hunter (1839) in In the interest of constructing better artificial dentures, Bonwill noted the tripod shape of the lower jaw and declared that it formed an equilateral triangle with the base extending from one condyle to the other and the sides extending from each condyle to the median line of the central incisors (Bonwill, 1885). Bonwill placed great emphasis on the principle that human anatomy is in perfect consonance with geometry, physics, and mechanics. Recently, investigators as early as the late 1940s have been defining the shape and curvature of the dental arch. MacConail compared the human dental arch to a catenary curve derived by connecting loci on the teeth of both arches (MacConail, 1949). In 1952, Sved proposed the hypothesis of spherical occlusion, stating the function of mastication tends to take place on the surface of a sphere, reiterating the form is determined by function principle (Sved, 1952). Numerous researchers have reported that normal dental arches approximate certain geometric curves such as an eclipse or parabola, and attempts to find methods of arch form from predetermination have ensued (Currier, 1969; Sicher, 1952). These earlier studies were attempting to quantify the normal shape of the dental arch. Lu (1966) employed polynomials to represent dental arches, Biggerstaff (1972) and Sampson (1981) described the normal arch as conical, 15

31 whereas Begole (1980) fitted cubic spline curves to the dental arch shape. Braun (1998) concluded the beta function more accurately described the dental arch. Morphometric Analysis of the Dental Arch Form Utilization of geometric morphometrics has been applied to evaluating the orofacial complex in many studies, and specifically the dental arch form. Sampson (1981) was one of the first investigators to use geometric morphometric techniques for modeling biological dental arch shape with arcs of conic sections. Ferrario assessed maxillary and mandibular arch form differences by the Euclidean-distance matrix analysis and concluded that shape variation of the dental arch is independent of the subject s gender (Ferrario 1993, 1994). Similarly, Nie assessed incisal and gingival landmarks by Euclidean distance matrix analysis between dental arch forms of Class II, Division I and normal occlusion. He concluded that expanding the maxillary posterior arch width in Class II Division 1 subjects might be an important method to harmonize maxillary and mandibular arch forms (Nie, 2006), which is somewhat in agreement to the previous meta-analysis results on width data stating that Class II, Division I maxillas are less wide at the premolar level (Lombardo, 2013). Fourier descriptors have been used to compare the shape of crowded and uncrowded dental arches. Lestrel employed Elliptical Fourier Functions to fit normal and (anterior) crowded arches using mesial and distal incisal edge points. The author concluded that patients with crowding exhibited more variability in the overall shape of the anterior portion of the arch than did the controls (Lestrel, 2004). Geometric morphometric analysis has also been applied to investigate dental arch asymmetries. Schaefer and co-authors studied asymmetries in an isolated inbred Adriatic community versus an urban reference group from the same country. The authors concluded 16

32 fluctuating asymmetry (deviation from bilateral symmetry caused by environmental stresses or genetic developmental issues) was found to be higher in the isolated group. Their results suggest an environmental as well as genetic influence on dental arch asymmetry (Schaefer, 2006). The gingival landmarks utilized in the current study are useful for judging asymmetry of and between the dental arches. Other researchers have investigated facial architecture and dental shape in the transverse dimensions. Alarashi evaluated the dentoskeletal features of Class II malocclusion in the transverse plane by means of a thin-plate spline analysis applied to posteroanterior cephalograms. The authors concluded that Class II malocclusion subjects exhibited significant shape differences in craniofacial configuration in the frontal plane when compared with subjects with normal occlusion. A reduction in maxillary dentoskeletal width was associated with an increase in the vertical height of the maxilla (Alarashi, 2003). Another application of geometric morphometric analysis in the human dentition is the evaluation of bitemarks in forensic odontology. Kieser concluded that the incisal surfaces of the anterior dentition are unique in both shape and form and help aid in understanding of the evidential reliability of bitemark analysis (Kieser, 2007). These studies provide both the foundation and utility of shape analysis with geometric morphometric techniques. Employing incisal, gingival, mesial, and distal landmarks in both arches allows for the evaluation of inter and intra arch relations including but not limited to incisor and canine angulation, tip, rotation, crowding, overbite, overjet, and overall bodily movement of the anterior teeth. The utilization of these landmarks will allow the current study to examine the large variation in arch shape and dental relations ultimately relate to the development of malocclusion and dental misalignment. 17

33 Analysis of Longitudinal 3D Coordinate Data Very little longitudinal research in the orofacial field utilizing 3D coordinate data and GM analyses have been identified. One investigator evaluated the effects of the headgear-activator Teuscher appliance (HATA) in the treatment of Class II, Division 1 malocclusion with geometric morphometric techniques. The author tested the hypothesis that there are no gender differences in the outcomes of patients with Class II malocclusion treated with the HATA. Mean pre- and posttreatment parameters were derived from cephalometry subjected to t-tests, and finite-element scaling analysis (FESA), which localizes and quantifies differences between mean pre- and posttreatment configurations. A Procrustes method was employed to determine the variance around each landmark and express it as a root-mean square. Therefore, both groups of female and male configurations were subjected to Procrustes superimposition and each configuration was represented as a mean and variance. All configurations were co-registered, and as a result of this procedure, geometric configurations were scaled to an equivalent area, avoiding problems introduced by differences in size (Singh& Thind, 2003). Singh and Thind concluded that both male and female patients treated for Class II malocclusions with the HATA exhibited anteroposterior restraint of the maxilla, improvements in the mandible maintaining facial height as well as soft tissue profile. Similarly, Singh evaluated longitudinally craniofacial growth patterns in patients with orofacial clefts with geometric morphometrics. The purpose of his study was to demonstrate craniofacial developmental patterns in repaired cleft lip and palate using GM techniques and finiteelement analysis at three different time points. From lateral cephalograms, eight skeletal landmarks were identified and digitized using appropriate software to obtain their x, y coordinates. 18

34 Next, Procrustes superimposition was implemented to obtain a generalized rotational fit (Rohlf, 1990). That is, all configurations were scaled to an equivalent size and registered with respect to one another (Singh, 2004). Thus, the mean craniofacial morphologies were determined for all groups at the three ages to be tested, and a perturbation model (Rohlf, 1990) was used to compare the mean non-cleft and mean cleft group morphologies during two time intervals (Singh, 2004). The author concluded that noncleft patients and cleft lip/palate patients with Class I occlusion show similar craniofacial growth patterns, whereas noncleft Class III groups show excessive cranial and mandibular growth and Class III cleft lip/palate patients show deficient maxillary growth. To date, no other dental cast research has utilized GM techniques to analyze a longitudinal sample. Our study is similar to Singh s studies, in which we will implement a generalized Procrustes analysis to scale, translate, and rotate the landmark shapes to obtain the best fit, thus removing size variability in the data. Following the Procrustes superimposition, Principal Component Analysis will be applied to the data in order to explain the most variation in shape that are significant to our study, described in detail in the next section. 19

35 CHAPTER 2 MATERIALS AND METHODS Classifier Data This study examines a sample of untreated orthodontic patients, from their primary dentition to secondary dentition at three stages of time. Subjects were derived from the Iowa Fluoride Study and Iowa Growth Study. The sample included 55 females and 63 males (total n=118) that were primarily Euro-American Iowa residents. Maxillary and mandibular impressions and bite registrations were made from the individuals at ages 5, 9 and 13 years old. Subsequent dental casts were produced that provide a three-dimensional accurate representation of an individual s dentition and occlusal relationships. A 3M Lava Scan ST optical scanner was utilized to make threedimensional digital scans from the physical dental casts in which landmark-based GM techniques and analysis of dentoalveolar morphological variation were employed. Each maxillomandibular dental cast set was interdigitated into proper occlusion using a wax bite registration and photographic data when available. Each set was evaluated at three stages of dental development: stage I, completion of the deciduous dentition, stage II, during the mixed dentition with complete eruption of all permanent incisors and permanent first molars, and stage III, at the completion of eruption of the permanent dentition excluding third molars. Finally, each set was classified as distal, mesial, or flush terminal plane in the deciduous dentition stage, and Angle s classification in the permanent dentition stage. Landmark Determination After post-processing, all scans were landmarked utilizing the software package Landmark (Wiley, 2005). Landmarks were selected that yield information for overall arch shape, and other 20

36 clinical variables such as tooth size discrepancies, as well as discrepancies in the transverse, vertical, and anteroposterior dimensions. Landmark data was collected separately for the maxilla, mandible, and both arches in occlusion. Tables illustrate the landmarks collected for the permanent stage of dentition for the mandible, maxilla, and interdigitated casts in occlusion, respectively. Analogous landmarks were made for the primary and mixed dentition cast scans. Final mandibular, maxillary and occlusion datasets are summarized in Table 2.4 after removing outlier casts. Landmarks were initially placed while viewing the cast from the buccal view and then rotated so the observer was viewing the cast from an occlusal view. Cervical points were adjusted to the area of greatest convexity that represented the mesial-distal center of the tooth. Incisal points were placed at the angle between the incisal and mesial or distal surfaces which represented the width of the tooth. Landmarks on the canines were placed at the point of greatest mesiodistal width perpendicular to the long axis of the tooth. 21

37 Table 2.1. Landmark Description for Age 13 mandible Note: Analogous landmarks were made for the primary and mixed dentition cast scans of the mandible. Number Landmark Description 1 s0 Most cervical point of tooth on edge of gingiva - Lt 2nd premolar 2 s1 Most cervical point of tooth on edge of gingiva - Lt 1st premolar 3 s2 Lateral edge of Lt canine 4 s3 Most cervical point of tooth on edge of gingiva - Lt canine 5 s4 Medial edge of Lt canine 6 s5 Cusp tip - Lt canine 7 s6 Lateral incisal edge of Lt lateral incisor 8 s7 Most cervical point of tooth on edge of gingiva - Lt lateral incisor 9 s8 Medial incisal edge of Lt lateral incisor 10 s9 Lateral incisal edge of Lt central incisor 11 s10 Most cervical point of tooth on edge of gingiva - Lt central incisor 12 s11 Medial incisal edge of Lt central incisor 13 s12 Medial incisal edge of Rt central incisor 14 s13 Most cervical point of tooth on edge of gingiva - Rt central incisor 15 s14 Lateral incisal edge of Rt central incisor 16 s15 Medial incisal edge of Rt lateral incisor 17 s16 Most cervical point of tooth on edge of gingiva - Rt lateral incisor 18 s17 Lateral incisal edge of Rt lateral incisor 19 s18 Medial edge of Rt canine 20 s19 Most cervical point of tooth on edge of gingiva - Rt canine 21 s20 Lateral edge of Rt canine 22 s21 Cusp tip - Rt canine 23 s22 Most cervical point of tooth on edge of gingiva - Rt 1st premolar 24 s23 Most cervical point of tooth on edge of gingiva - Rt 2nd premolar 22

38 Table 2.2. Landmark Description for Age 13 Maxilla Note: Analogous landmarks were made for the primary and mixed dentition cast scans of the maxilla. Number Landmark Description 1 s0 Most cervical point of tooth on edge of gingiva - Rt 2nd premolar 2 s1 Most cervical point of tooth on edge of gingiva - Rt 1st premolar 3 s2 Lateral edge of Rt canine 4 s3 Most cervical point of tooth on edge of gingiva - Rt canine 5 s4 Medial edge of Rt canine 6 s5 Cusp tip - Rt canine 7 s6 Lateral incisal edge of Rt lateral incisor 8 s7 Most cervical point of tooth on edge of gingiva - Rt lateral incisor 9 s8 Medial incisal edge of Rt lateral incisor 10 s9 Lateral incisal edge of Rt central incisor 11 s10 Most cervical point of tooth on edge of gingiva - Rt central incisor 12 s11 Medial incisal edge of Rt central incisor 13 s12 Medial incisal edge of Lt central incisor 14 s13 Most cervical point of tooth on edge of gingiva - Lt central incisor 15 s14 Lateral incisal edge of Lt central incisor 16 s15 Medial incisal edge of Lt lateral incisor 17 s16 Most cervical point of tooth on edge of gingiva - Lt lateral incisor 18 s17 Lateral incisal edge of Lt lateral incisor 19 s18 Medial edge of Lt canine 20 s19 Most cervical point of tooth on edge of gingiva - Lt canine 21 s20 Lateral edge of Lt canine 22 s21 Cusp tip - Lt canine 23 s22 Most cervical point of tooth on edge of gingiva - Lt 1st premolar 24 s23 Most cervical point of tooth on edge of gingiva - Lt 2nd premolar 23

39 Table 2.3. Landmark Description for Age 13 Occlusion Note: Analogous landmarks were made for the primary and mixed dentition cast scans of the maxilla-mandibular complex Number Landmark Description 1 s0 Most cervical point of tooth on edge of gingiva - Rt 2nd premolar 2 s1 Most cervical point of tooth on edge of gingiva - Rt 1st premolar 3 s2 Most cervical point of tooth on edge of gingiva - Rt canine 4 s3 Most cervical point of tooth on edge of gingiva - Rt lateral incisor 5 s4 Most cervical point of tooth on edge of gingiva - Rt central incisor 6 s5 Most cervical point of tooth on edge of gingiva - Lt central incisor 7 s6 Most cervical point of tooth on edge of gingiva - Lt lateral incisor 8 s7 Most cervical point of tooth on edge of gingiva - Lt canine 9 s8 Most cervical point of tooth on edge of gingiva - Lt 1st premolar 10 s9 Most cervical point of tooth on edge of gingiva - Lt 2nd molar 11 s10 RT base point 12 s11 Middle base point 13 s12 LT base point 14 s13 Most cervical point of tooth on edge of gingiva - Lt 2nd premolar 15 s14 Most cervical point of tooth on edge of gingiva - Lt 1st premolar 16 s15 Most cervical point of tooth on edge of gingiva - Lt primary canine 17 s16 Most cervical point of tooth on edge of gingiva - Lt lateral incisor 18 s17 Most cervical point of tooth on edge of gingiva - Lt central incisor 19 s18 Most cervical point of tooth on edge of gingiva - Rt central incisor 20 s19 Most cervical point of tooth on edge of gingiva - Rt lateral incisor 21 s20 Most cervical point of tooth on edge of gingiva - Rt canine 22 s21 Most cervical point of tooth on edge of gingiva - Rt 1st premolar 23 s22 Most cervical point of tooth on edge of gingiva - Rt 2nd premolar 24 s23 LT base point 25 s24 Middle base point 26 s25 Rt base point 24

40 Table 2.4. Classifier data information following the removal of outlier cast scans Note: The sample included 55 females and 63 males (total n=118) that were primarily Euro- American Iowa residents. Dataset Total Number of Casts Unique Individuals MANDIBLE MAXILLA OCCLUSION Figure 2.1. Age 13 Mandibular Landmarks Note: A total of 24 landmarks were placed on each cast. Analogous landmarks were made for the primary and mixed dentition casts. The digital scans were rotated accordingly to capture each landmark. A total of 330 mandibular casts were landmarks from 110 unique individuals. 25

41 Figure 2.2. Age 13 Maxillary Landmarks Note: A total of 24 landmarks were placed on each cast. Analogous landmarks were made for the primary and mixed dentition casts. The digital scans were rotated accordingly to capture each landmark. A total of 339 maxillary casts were landmarks from 113 unique individuals. Figure 2.3. Age 13 Occlusal Landmarks Note: A total of 26 landmarks were placed on each cast. Analogous landmarks were made for the primary and mixed dentition casts. The digital scans were rotated accordingly to capture each landmark. A total of 354 occlusal casts were landmarks from 118 unique individuals. GM Analyses Landmark reliability was assessed using a sample of 20 scans that were landmarked twice by the author. Following successful completion of the reliability testing (described below in the Results section), the coordinate data was extracted and submitted to GM analyses via the software 26

42 package MorphoJ. Generalized Procrustes analysis (GPA) was first performed to remove translation, rotation, and size factors of the dataset in order to compare pure shape between individuals. Once this shape registration was complete, shape differences between dental casts were analyzed and conclusions drawn about phenotypic shape variation within the sample. The dental cast data has object symmetry, which means that the dental arches are symmetric around the median plane. With the exception of given asymmetries between the left and right sides of the dental arches (for example, an ectopically erupted canine on one side only), dental arch halves are mirror images of each other. Because the data is made of paired and unpaired landmarks, overall shape variation is composed of symmetric and asymmetric shape variation and both components were analyzed in this study. Symmetric components indicate all variation of paired landmarks in all directions of space while unpaired landmarks only vary along the midline plane. The symmetric component averaged the differences between overall left and right shape along the midline and illustrates both anteroposterior, vertical, and transverse shape variation, whereas the asymmetric component depicts shape differences between the left and the right side of the arches that is not symmetric. After the Procrustes fit of the coordinate data, covariance matrices are generated for both the symmetric and asymmetric components of shape variation and each submitted independently to a principal components analyses (PCA). PCA decomposes the variation into different independent components. The first principal component (PC1) is the main axis of variation and explains the largest amount of variance. The succeeding components in turn have the highest amount of variation that is unrelated to the preceding components. Within each axis of variation, a principal component score is calculated for each individual which represents the location of the 27

43 individual within the specific axis of variation. The spectrum of variation revolves around zero, so the designated score of variation ranges from a positive to negative extreme per component. By convention, all components that account for 5% or more of the variation were included in the analysis. Because this study is longitudinal in nature with the same individuals growing over time, it is important to characterize the effects of size on shape variation. An allometric analysis was performed with both symmetric and asymmetric datasets utilizing MorphoJ by regressing shape variables on centroid size to provide detailed information on the effects of overall size on the shape of the dental complex. Covariance pattern models were then used to determine the significance of shape variation between an individual s primary to permanent dentition. This is a type of regression model commonly used in longitudinal studies where the structure of the covariance of the repeated measures (that is, create a matrix that describes how observations from different timepoints but belonging to the same individuals are correlated with each other) is defined by the investigator in order to account for correlation between repeated observations. In the primary dentition, each maxillomandibular complex was classified as distal step, mesial step, or flush terminal plane, depending on the location of the primary maxillary second molar relative to the primary mandibular second molar. In the permanent dentition, each occlusal set was classified as Class I or Class II according to Angle s classification system. Due to insufficient sample sizes, no longitudinal Class III individuals were included in the dataset. The standard significant threshold p < 0.05 was used to indicate suggestive results. Bonferroni correction was made for the 270 tests performed to provide the adjusted p-level < for significant results. Each test compares morphological features 28

44 longitudinally between individuals classified in the mesial and distal step to those with a flush terminal plane used as the reference category for the primary dentition. Similarly, individuals classified as Class II in the permanent dentition will be compared to the Class I groups as the reference category. 29

45 CHAPTER 3 RESULTS Intraobserver Reliability Results Results for intraobserver reliability of the 26 landmarks demonstrated excellent reliability. Euclidean distance (the absolute distance in the same landmark between round one and round two) results are shown in Table 3.1. All distances recorded were less than 0.5mm. To examine the mean difference by landmark coordinate between both rounds, a t-test was performed with a Bonferroni correction of p < (see Table 3.2). No mean differences were found that were significant at this p-value of p < Intra-class correlation methods were used to evaluate whether the variability in landmarks for the same individual between round 1 and round 2 was larger than the overall variation in landmark location in the data. Table 3.3 depicts the modified ANOVA results. No measurement was greater than 20% measurement error. Therefore, the observer was deemed reliable and no additional calibration was needed before collecting the rest of the dental cast landmarks. 30

46 Table 3.1. Euclidean distance reliability results Note: The absolute distance in the same landmark was measured between rounds. Results are reliable because all distances are less than 0.5mm. LANDMARK MANDIBLE MAXILLA s s s s s s s s s s s s s s s s s s s s s s s s AVERAGE

47 Table 3.2. Landmark Coordinate Data Reliability Note: T-test of landmark coordinate data reliability for the mandible and maxilla to determine if there is a significant difference from zero after correcting for multiple comparisons. The Wilcoxon Signed-Rank Test for difference in medians is highlighted in bold text. Values which fell outside of accepted error standards (p-value of.002) are highlighted in gray boxes. MANDIBLE p-value for X X Diff from 0? p-value for Y Y Diff from 0? p-value for Z Z Diff from 0? Yes Yes No No No Yes No Yes Yes No No Yes No No No No No Yes No No No No Yes Yes No No No No No No No No No No Yes No No No No No No No No No No Yes No Yes No No Yes Yes No Yes No Yes Yes Yes No Yes No No No No No No No No Yes Yes No No 32

48 Table 3.2 Continued MAXILLA p-value for X X Diff from 0? p-value for Y Y Diff from 0? p-value for Z Z Diff from 0? No No Yes Yes No No Yes Yes No No No No Yes No Yes No No Yes No Yes No Yes Yes No Yes No No No No Yes No No No Yes No No Yes No No No No No No No No Yes No No No No No No Yes No Yes No Yes No No No No No No No No Yes No No No Yes No No 33

49 Table 3.3. Intraclass Correlation Results Note: ICC methodology was used to evaluate variability in landmarks for the same individual and then compared to the overall variation. ICC describes how strongly units in the same group resemble each other. This modified ANOVA evaluates variability in landmarks for the same individual and then compares it to the overall variation. No measurements were greater than 20% measurement error; values highlighted in bold are close to the 20% measurement error cutoff. MANDIBLE MAXILLA LMK ICC X Sig X ICC Y Sig Y ICC Z Sig Z ICC X Sig X ICC Y Sig Y ICC Z Sig Z s s s s s s s s s s s s s s s s s s s s s s s s

50 Allometric Analysis The present study explored the size-related variation in dental arch shape due to the longitudinal nature of the project with growing individuals. A simple regression was performed to determine if size had an effect on shape. The regression results are listed in Table 3.4 for symmetric data, and Table 3.5 for asymmetric data. For the symmetric component, a highly significant (p < ) effect was found in which size predicts between 14.9% to 16.8% of the shape variation of the dental arches over time as each individual transitions from deciduous to permanent dentition. For the asymmetric component, there was a very small effect (less than 1%) of size on the shape of the dental arches. The residuals were then analyzed after allometric scaling to remove size-related shape variation. The following symmetric and asymmetric shape variation results are reported below. Table 3.4. Symmetric Allometry Regression Results Note: Allometric regression results for the symmetric component of the mandible, maxilla and occlusal datasets. Total Sum of Squares Predicted Sum of Squares Residual Sum of Squares P-value Percent Predicted Mandible p < % Maxilla p < % Occlusal p < % 35

51 Table 3.5. Asymmetric Allometry Regression Results Note: Allometric regression results for the asymmetric component of the mandible, maxilla and occlusal datasets. Total Sum of Squares Predicted Sum of Squares Residual Sum of Squares P-value Percent Predicted Mandible p < % Maxilla p < % Occlusal p < % Principal Component Analysis Symmetric Mandibular Principal Components Figure 4 Figure 3.1. Percent Variance of Symmetric Mandibular Principal Components Note: Covariance results of the symmetric mandible dataset. This Principal Component Analysis (PCA) decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC5). 36

52 MANDIBLE PC1 Figure 3.2 Mandibular Principal Component 1 accounts for 23.5% variation (see Figure 3.1). The primary variation noted is change in dentoalveolar height. Positive PC scores demonstrate shorter teeth with spacing (Fig. 3.2a) in a more retroclined position (Fig. 3.2c), whereas negative PC scores illustrate larger teeth (Fig. 3.2b) that are more proclined (Fig. 3.2d). Figure 3.3 illustrates the cast scans of individuals at the extremes of the range of variation. For example, the individual with an extreme positive PC1 score demonstrates shorter, more spaced teeth (Fig. 3.3a), whereas the individual on the other end of the spectrum depicts taller teeth and in contact, that are also more proclined (Fig. 3.3b). Figure 3.2. Mandibular Principal Component 1 Symmetric Note: Principal Component 1 of the symmetric mandibular dataset. PC1 accounts for 23.5% variation. The L and R depict the left and right sides, respectively. The left and right sides noted in the figure are the same for all symmetric mandibular PC s. 37

53 Figure 3.3: Variability of Individual Cast Scans Symmetric Mandible PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and lateral views. MANDIBLE PC2 Figure 3.4 Symmetric mandibular Principal Component 2 accounts for 17.1% variation (see Figure 3.1). When transforming from positive warp values to negative warp values, it is evident that there is a change in height of the canines from small to large. There is also a decrease in dentoalveolar height for the incisors (Fig. 3.4b) and an increase in the curve of Spee (Fig. 3.4d). Figure 3.5 illustrates the cast scans of individuals at the extremes of the range of variation. The negative PC2 cast scan (Fig. 3.5b) illustrates taller canines relative to the incisors with an increased curve of Spee. 38

54 Figure Figure 3.4. Mandibular Principal Component 2 Symmetric Note: Principal Component 2 of the symmetric mandibular dataset. PC2 accounts for 17.1% variation. Figure 3.5. Variability of Individual Cast Scans Symmetric Mandible PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC2 variation from the anterior, superior and lateral views. 39

55 MANDIBLE PC3 Figure 3.6 The major change evident for 13% variation (refer to Figure 3.1) reflected in PC3 is overall alteration in arch shape from the superior view. Positive warp values illustrate a shorter, wider, and more square shaped arch form (Fig 3.6e), whereas negative warp values depict a longer, narrower, more parabolic shaped arch form (Fig 3.6f). Other variations include an increase in spacing and distal movement of the canine in the anteroposterior direction for negative PC scores (Fig. 3.6d) versus more retroclined incisors and proclined canine with an accentuated curve of Spee as depicted in Figure 3.6c. Figure 3.7 illustrates the cast scans of individuals at the extremes of the range of variation. Overall arch shape from the superior view is clearly different, with a shorter, squarer arch form for the positive PC3 individual (Fig. 3.7a) versus a longer, more parabolic dental arch form for the negative PC3 cast scan (Fig. 3.7b). 40

56 Figure 3.6. Mandibular Principal Component 3 - Symmetric Note: Principal Component 3 of the symmetric mandibular dataset. PC3 accounts for 13% variation. Figure 3.7. Variability of Individual Cast Scans Symmetric Mandible PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC3 variation from the anterior, superior and lateral views. 41

57 MANDIBLE PC4 Figure 3.8 Symmetric mandibular Principal Component 4 accounts for 8.3% of total variation (see Fig. 3.1). The primary shape change for positive warp values illustrated is the canine retrusion evident in Figure 3.8c with an additional rotational aspect (mesial in) of the canine as shown in Figure 3.8e. Similarly, the canine extrudes in nature with a more superior gingival margin in positive PC scores (Fig 3.8a, c). Curve of Spee increases when approaching negative warp values (Figure 3.8d). Figure 3.9 illustrates the cast scans of individuals at the extremes of the range of variation. The change in tip of the canines is visible when comparing positive and negative cast scans from the lateral view: the positive cast scan has more retroclined canines (Fig. 3.9a) versus proclined canines for the negative PC cast scan (Fig. 3.9b). The negative PC4 cast scan (Fig. 3.9b) also illustrates a deeper curve of Spee with the canine gingival margin much more inferior than the incisors when compared to the positive PC cast scan. 42

58 Figure 3.8: Mandibular Principal Component 4 - Symmetric Note: Principal Component 4 of the symmetric mandibular dataset. PC4 accounts for 8.3% variation. Figure 3.9. Variability of Individual Cast Scans Symmetric Mandible PC4 Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC4 variation from the anterior, superior and lateral views. 43

59 MANDIBLE PC5 Figure 3.10 The major change evident for 5.9% variation (see Figure 3.1) is canine rotation. Figure 3.10b demonstrates the canine widening in the mesiodistal direction for negative warp values, which is due to the distal-out rotation as illustrated in the superior view (Fig. 3.10e). Incisal height and proclination also increase from positive to negative warp values with a deepening of the curve of Spee (Fig. 3.10d). Figure 3.11 illustrates the cast scans of individuals at the extremes of the range of variation. Due to the partial eruption of the mandibular canines for the positive PC5 individual, the width is much smaller than the fully erupted canines for the negative PC5 individual. The rotational changes of the canines are well illustrated: Fig. 3.11a demonstrates a more extreme rotation (mesial-out) compared to the rotations of the negative canines which are more distal-out rotated (Fig. 3.11b). 44

60 Figure 3.10: Mandibular Principal Component 5 Symmetric Note: Principal Component 5 of the symmetric mandibular dataset. PC5 accounts for 5.9% variation. Figure 3.11: Variability of Individual Cast Scans Symmetric Mandible PC5 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC5 variation from the anterior, superior and lateral views. 45

61 Symmetric Maxillary Principal Components Figure 3.12: Percent Variance of Symmetric Maxillary Principal Components Note: Covariance results of the symmetric maxilla dataset. This PCA decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC4). MAXILLA PC1 - Figure 3.13 Symmetric maxillary Principal Component 1 accounts for 25.7% variation (see Figure 3.12). The most significant finding is the change in dentoalveolar height of the canines, as illustrated in Figures 3.13a-d. As the height of the canine increases from positive to negative PC scores, the gingival margin of the canine increases more apically (Fig. 3.13b, d). A decrease in the protrusion of 46

62 incisors and retrusion of the canines is also evident from the superior view (Fig 3.13f) for negative PC1 scores. Figure 3.14 illustrates the cast scans of individuals at the extremes of the range of variation. The negative PC1 cast scan (Fig. 3.14b) highlights the canine variation, with the permanent maxillary canine fully erupted with a more apically positioned gingival margin relative to the primary maxillary canine for the positive PC score individual (Fig. 3.14a). Figure 3.13: Maxillary Principal Component 1 - Symmetric Note: Principal Component 1 of the symmetric maxillary dataset. PC1 accounts for 25.7% variation. The L and R depict the left and right sides, respectively. The left and right sides noted are the same for all symmetric maxillary PC s. 47

63 Figure 3.14: Variability of Individual Cast Scans Symmetric Maxillary PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and lateral views. MAXILLA PC2 - Figure 3.15 Maxillary Principal Component 2 accounts for 19.7% variation (see Figure 3.12). There is primarily a change in dentoalveolar height of the lateral and central incisors (Fig. 3.15a, b). Also worth noting is a change in divergence of the incisors: an increase in divergence can be seen for negative PC scores (Fig. 3.15d,f). Superiorly, negative PC scores illustrate slight dental arch narrowing (Fig 3.15f). Figure 3.16 illustrates the cast scans of individuals at the extremes of the range of variation. Shorter, more spaced incisors are depicted for the positive PC2 extreme cast scan (Fig. 3.16a), whereas taller, less spaced permanent incisors are illustrated in Fig. 3.16b for the negative PC score cast scan. Similarly, the negative PC2 cast scan depicts the incisors more proclined in the lateral view and a narrower, more V-shaped dental arch from the superior view. 48

64 Figure 3.15: Maxillary Principal Component 2 - Symmetric Note: Principal Component 2 of the symmetric maxillary dataset. PC2 accounts for 19.7% variation. Figure 3.16: Variability of Individual Cast Scans Symmetric Maxillary PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and lateral views. 49

65 MAXILLA PC3 - Figure 3.17 The major change evident for 13.8% variation (refer to Figure 3.12) for symmetric Maxillary Principal Component 3 is due to shape change of the central incisors illustrated in the lateral and superior views. Central incisor proclination is evident as warp values approach the negative end of the spectrum (Fig. 3.17d, f) with increased spacing between the central and lateral incisors. The overall narrowing of the dental arch to more V-shaped is observed with central incisor proclination (Fig 3.17f). Figure 3.18 illustrates the cast scans of individuals at the extremes of the range of variation. The overall shape change from the superior view best illustrates the wire frame changes: the positive PC3 individual (Fig. 3.18a) has a more square dental arch shape since the incisors are all in a line, versus a more V-shaped arch form for the negative PC score individual (Fig. 3.18b) with proclined central incisors relative to the lateral incisors. 50

66 Figure 3.17: Maxillary Principal Component 3 - Symmetric Note: Principal Component 3 of the symmetric maxillary dataset. PC3 accounts for 13.8% variation. Figure 3.18: Variability of Individual Cast Scans Symmetric Maxillary PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and lateral views. 51

67 MAXILLA PC4 - Figure 3.19 Maxillary Principal Component 4 accounts for 6.6% variation (see Figure 3.12). The most significant change is found in dentoalveolar height and emergence profiles of all the anterior teeth. Shorter, more spaced teeth are seen for the positive warp values (Fig. 3.19a), whereas taller, wider teeth are illustrated as warp values get more negative (Fig. 3.19b). There is also an increase in the compensating curve with stepped up maxillary incisors for negative PC scores in the posterior (Fig. 3.19b) and lateral views (Fig. 3.19d). Lastly, the arch gets slightly broader with more dental retrusion (Fig. 3.19f) for negative PC scores. Figure 3.20 illustrates the cast scans of individuals at the extremes of the range of variation. As the spacing increases between the central incisors, the canines are blocked out facially, increasing their emergence profile more apically (Fig. 3.20a) compared to the negative PC individual with less spacing and a more prominent compensating curve with stepped up maxillary incisors relative to the canines (Fig. 3.20b). 52

68 Figure 3.19: Maxillary Principal Component 4 - Symmetric Note: Principal Component 4 of the symmetric maxillary dataset. PC4 accounts for 6.6% variation. Figure 3.20: Variability of Individual Cast Scans Symmetric Maxillary PC4 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and lateral views. 53

69 Symmetric Occlusal Principal Components Figure 3.21: Percent Variance of Symmetric Occlusal Principal Components Note: Covariance results of the symmetric occlusal dataset. This PCA decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC5). OCCLUSAL PC1 - Figure 3.22 The major change evident for 36% variation (see Figure 3.21) for Occlusal Principal Component 1 is due to change in vertical spacing. An increase in gingival margin interdistance as the warp values approach negative PC scores is evident in Figures 3.22a,b,c,d. Figure 3.23 illustrates the cast scans of individuals at the extremes of the range of variation. The individual at 54

70 the positive PC value extreme demonstrates shorter teeth and a deeper bite (Fig. 3.23a), whereas the negative PC score extreme has longer teeth with minimal overbite (Fig. 3.23b) with an increased gingival margin interdistance. Figure 3.22: Occlusal Principal Component 1 - Symmetric Note: Principal Component 1 of the symmetric occlusal dataset. PC1 accounts for 36% variation. The L and R depict the left and right sides, respectively. The left and right sides noted are the same for all symmetric occlusal PC s. 55

71 Figure 3.23: Variability of Individual Cast Scans Symmetric Occlusal PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior and lateral views. OCCLUSAL PC2 - Figure 3.24 Occlusal Principal Component 2 accounts for 17.5% variation (refer to Figure 3.21). Primarily there is a change in occlusal curves and inter-gingival margin distance. Stepped down maxillary incisors and stepped up mandibular incisors can be seen in Fig 3.24a, whereas the opposite findings are noted in Figure 3.24b as the interocclusal distance increases. In the lateral views, a prominent curve of Spee in the mandible is visible with an apically positioned emergence profile for the maxillary canine is illustrated in Fig 3.24c, while inter-incisal distance increases with anterior divergence in Figure 3.24d. Lastly, there is a slight decrease in overjet towards negative PC scores (Fig 3.24d,f). Figure 3.25 illustrates the cast scans of individuals at the extremes of the range 56

72 of variation. Clearly evident is the prominent curve of Spee with a deeper bite for the positive PC cast scan (Fig. 3.25a) and a flatter mandibular occlusal plane for the negative PC cast scan individual with a slight open bite (Fig. 3.25b) thus greatly increasing the inter-gingival margin distance. Figure 3.24: Occlusal Principal Component 2 - Symmetric Note: Principal Component 2 of the symmetric occlusal dataset. PC2 accounts for 17.5% variation. 57

73 Figure 3.25: Variability of Individual Cast Scans Symmetric Occlusal PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC2 variation from the anterior and lateral views. OCCLUSAL PC3 - Figure 3.26 Symmetric occlusal Principal Component 3 accounts for 10.6% variation (Fig. 3.21). Shape variation is primarily due to the interocclusal changes in the anteroposterior direction. The maxillomandibular relationship approaching positive warp values demonstrates positive overjet (Fig. 3.26c,e). This amount of overjet decreases and approaches an edge-to-edge relationship towards negative PC scores, as illustrated in Figure 3.26d,f. Similarly, arch coordination increases towards negative warp values (Fig. 3.26f). It is also worth noting there is a slight increase in interocclusal distance towards positive PC scores as the maxillary incisal gingival margin increases apically (Fig. 3.26a,c). Figure 3.27 illustrates the cast scans of individuals at the extremes of the range of variation. The positive PC cast scan (Fig. 3.27a) depicts an individual with a Class II 58

74 malocclusion with positive overjet, whereas the negative PC3 score cast (Fig. 3.27b) is a Class I malocclusion with an anterior crossbite and negative overjet. Figure 3.26: Occlusal Principal Component 3 - Symmetric Note: Principal Component 3 of the symmetric occlusal dataset. PC3 accounts for 10.6% variation. 59

75 Figure 3.27: Variability of Individual Cast Scans Symmetric Occlusal PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC3 variation from the anterior and lateral views. OCCLUSAL PC4 - Figure 3.28 The major change evident for 8.3% variation (refer to Fig. 3.21) for Occlusal Principal Component 4 is due to change in overall arch shape. Figure 3.28e illustrates the arch width increasing in the posterior with a more square shaped arch, whereas in Figure 3.28f the arches are more narrow and U-shaped. Also evident is a slight increase in inter-gingival margin distance for negative PC scores. Figure 3.29 illustrates the cast scans of individuals at the extremes of the range of variation. From the anterior views, gingival margin distance increases with the negative cast scan individual (Fig. 3.29b) as the overbite decreases, which is supported by the wire frames from the posterior and lateral views (Fig. 3.28). 60

76 Figure 3.28: Occlusal Principal Component 4 - Symmetric Note: Principal Component 4 of the symmetric occlusal dataset. PC4 accounts for 8.3% variation. Figure 3.29: Variability of Individual Cast Scans Symmetric Occlusal PC4 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC4 variation from the anterior and lateral views. 61

77 OCCLUSAL PC5 - Figure 3.30 Occlusal Principal Component 5 accounts for 6.5% variation (Fig. 3.21). There was a significant change in the anteroposterior position of the dental arches, assuming greater overjet towards positive warp values (Fig. 3.30c,e) versus a closely edge-to-edge overjet towards negative warp values (Fig. 3.30d,f). Figure 3.31 illustrates the cast scans of individuals at the extremes of the range of variation that depict greater overjet and overbite for the positive PC5 cast (Fig. 3.31a) with minimal overjet and overbite for the negative cast scan (Fig. 3.31b). Figure 3.30: Occlusal Principal Component 5 - Symmetric Note: Principal Component 5 of the symmetric occlusal dataset. PC5 accounts for 6.5% variation. 62

78 Figure 3.31: Variability of Individual Cast Scans Symmetric Occlusal PC5 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC5 variation from the anterior and lateral views. 63

79 Asymmetric Mandibular Principal Components Figure 3.32: Percent Variance of Asymmetric Mandibular Principal Components Note: Covariance results of the asymmetric mandibular dataset. This PCA decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC6). MANDIBLE PC1 Figure 3.33 Mandibular Principal Component 1 accounts for 14.7% variation (see Fig. 3.32). From the posterior view, there is primarily a change in the gingival emergence and tip of each anterior tooth from left to right (Fig. 3.33a,b). From the superior view, a rotational and proclination change is noted for all teeth. For example, in Figure 3.33d for negative PC scores, the left canine is more 64

80 retruded than the proclined left lateral incisor, whereas for positive PC scores in Figure 3.33c, the left canine is more proclined and rotated (mesial-out) than the more retruded lateral incisor. Figure 3.34 illustrates the cast scans of individuals at the extremes of the range of variation. The different emergence pattern of the canines is clearly different between the positive and negative warp values: the left canine for the negative PC cast scan has erupted in alignment with adjacent teeth (Fig. 3.34b), whereas the positive cast s left canine has erupted facially with a lingually positioned left lateral incisor, resulting in the emergence profile of the canine to be much more apical to the adjacent teeth (Fig. 3.34a). Figure 3.33: Mandibular Principal Component 1 - Asymmetric Note: Principal Component 1 of the asymmetric mandibular dataset. PC1 accounts for 14.7% variation. The L and R depict the left and right sides, respectively. The left and right sides noted are the same for all asymmetric mandibular PC s. 65

81 Figure 3.34: Variability of Individual Cast Scans Asymmetric Mandibular PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and posterior views. MANDIBLE PC2 Figure 3.35 Asymmetric mandibular Principal Component 2 accounts for 9.9% variation (see Fig. 3.32). From the posterior view, there is most notably a change in the tip of the canines and lateral incisors. Positive PC scores demonstrate the left canine and lateral incisor tipped toward each other (Fig. 3.35a), versus the right canine and lateral incisor tipped toward each other for negative PC scores (Fig. 3.35b). The change in tip from the posterior view is reflected as rotational changes in the superior view. There is a change in the overall dental arch shape superiorly. As the canine rotates more distal and the adjacent lateral incisor proclines, the arch form becomes more narrow on that side. For example, as illustrated in Figure 3.35d, the right canine rotates more mesial-out and right lateral incisor proclines, with a narrowing of the arch on the right side. The same changes 66

82 in dental movement produce similar results on the left side for positive PC scores (Fig. 3.35c). Figure 3.36 illustrates the cast scans of individuals at the extremes of the range of variation. The positive PC cast scan (Fig. 3.36a) depicts crowding and rotations for the left canine and lateral incisor, whereas the right canine and lateral incisor for the negative PC cast scan are crowded and rotated toward each other (Fig. 3.36b) similar to the wire frames described previously. Figure 3.35: Mandibular Principal Component 2 - Asymmetric Note: Principal Component 2 of the asymmetric mandibular dataset. PC2 accounts for 9.9% variation. 67

83 Figure 3.36: Variability of Individual Cast Scans Asymmetric Mandibular PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC2 variation from the anterior, superior and posterior views. MANDIBLE PC3 Figure 3.37 The major change evident for 8.1% variation (Fig. 3.32) is change in height, tip, and rotation of the canines. Positive warp values illustrate a taller left canine and shorter, more mesial tipped, rotated, and retroclined right canine (Fig. 3.37a,c). Similar findings are found for the right and left canine, respectively, for negative PC scores (Fig. 3.37b,d). Figure 3.38 illustrates the cast scans of individuals at the extremes of the range of variation. Notably there is a change in the height and rotation in the canines as described by the wire frames above. 68

84 Figure 3.37: Mandibular Principal Component 3 - Asymmetric Note: Principal Component 3 of the asymmetric mandibular dataset. PC3 accounts for 8.1% variation. Figure 3.38: Variability of Individual Cast Scans Asymmetric Mandibular PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC3 variation from the anterior, superior and posterior views. 69

85 MANDIBLE PC4 Figure 3.39 Asymmetric mandibular Principal Component 4 accounts for 6.6% of total variation (refer to Fig. 3.32). Change in rotation and tip for all teeth is the most significant finding. The left canine and lateral incisor are more distally rotated (mesial-out) for negative PC scores, versus right canine and lateral incisor for positive PC scores (Fig. 3.39c,d). The tip of all anterior teeth change as well as illustrated in the posterior views (Fig. 3.39a,b): the overall tip of the incisors for positive PC scores is to the left, versus their tip to the right for negative PC scores. The emergence profile and height of each central incisor relative to the average occlusal plane changes: for example, the positive left central incisor is proclined and has a gingival margin more apically positioned. The same finding is noted for the right central incisor in negative PC scores. Figure 3.40 illustrates the cast scans of individuals at the extremes of the range of variation. The overall tip of the incisors (left for positive PC4 and to the right for negative PC4) is well depicted. Figure 3.39: Mandibular Principal Component 4 - Asymmetric Note: Principal Component 4 of the asymmetric mandibular dataset. PC4 accounts for 6.6% variation. 70

86 Figure 3.40: Variability of Individual Cast Scans Asymmetric Mandibular PC4 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC4 variation from the anterior, superior and posterior views. MANDIBLE PC5 Figure 3.41 The major change evident for 6.2% variation (Fig. 3.32) can be seen from the superior view. Negative PC scores illustrate an arch skewness in the anterior portion of the dental arch with the teeth on the left side more proclined over rounder arch form, whereas on the right side, the teeth are more retroclined and the shape of the arch is flatter (Fig. 3.41d). The opposite is true towards positive warp values. There is also a change in the mesiodistal width of the canines from posterior view (right canine wider for negative PC scores and left canine wider for positive PC scores). This change is likely due to the rotational movements of the canines noted from the superior views. The positive PC wire frame (Fig. 3.41c) depicts the right canine distally rotated (mesial-out) and the 71

87 same rotation for the left canine in the negative PC5 wire frame (Fig. 3.41d). Figure 3.42 illustrates the cast scans of individuals at the extremes of the range of variation. Note the change in canine rotations and positional changes of the incisors as described above. Figure 3.41: Mandibular Principal Component 5 - Asymmetric Note: Principal Component 5 of the asymmetric mandibular dataset. PC5 accounts for 6.2% variation. 72

88 Figure 3.42: Variability of Individual Cast Scans Asymmetric Mandibular PC5 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and posterior views. MANDIBLE PC6 Figure 3.43 Mandibular Principal Component 6 accounts for 5.5% variation (see Fig. 3.32). Change in dentoalveolar height is noted for the canines which are reflected in their rotations and proclinations from the superior view: a shorter and wider, more retrusive left canine with distal-out rotation is evident in positive PC scores (Fig. 3.43a), whereas for negative PC scores the left canine is taller, narrower, and more upright with mesial-out rotation (Fig. 3.43b). Overall arch skewness is apparent to the right for positive PC scores and to the left for negative PC scores. Figure 3.44 illustrates the cast scans of individuals at the extremes of the range of variation. Corresponding to each shorter, wider canine is an adjacent lateral incisor that is more retroclined than its counterpart. This can be noted in both the wire frames and cast scans alike. 73

89 Figure 3.43: Mandibular Principal Component 6 - Asymmetric Note: Principal Component 6 of the asymmetric mandibular dataset. PC6 accounts for 5.5% variation. Figure 3.44: Variability of Individual Cast Scans Asymmetric Mandibular PC6 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC6 variation from the anterior, superior and posterior views. 74

90 Asymmetric Maxillary Principal Components Figure 3.45: Percent Variance of Asymmetric Maxillary Principal Components Note: Covariance results of the asymmetric maxillary dataset. This PCA decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC6). MAXILLA PC1 - Figure 3.46 Asymmetric Maxillary Principal Component 1 accounts for 15% variation (see Fig. 3.45). Similar to asymmetric mandibular PC2, from the posterior view there is most notably a change in the tip of the canines and lateral incisors. Positive PC scores demonstrate the right canine and lateral incisor tipped toward each other (Fig. 3.46a), versus the left canine and lateral incisor tipped toward each other for negative PC scores (Fig. 3.46b). From the superior view, there is variation noted in the overall dental arch shape. As the canine rotates more distal and the lateral incisor 75

91 proclines, the arch form becomes narrower on that side. For example, in Figure 3.46d, the left canine rotates more distal (mesial-out) and the left lateral incisor proclines, with a narrowing of the arch on the left side with arch elongation on the right. The same changes in dental movement produce similar results on the right side (Fig. 3.46c) for the positive PC1 scores. Figure 3.47 illustrates the cast scans of individuals at the extremes of the range of variation. It is evident to see the right canine and lateral tip toward each other with a longer arch length on the left side for the positive PC individual (Fig. 3.47a) whereas the opposite is true for the negative PC individual (Fig. 3.47b). Figure 3.46: Maxillary Principal Component 1 - Asymmetric Note: Principal Component 1 of the asymmetric mandibular dataset. PC1 accounts for 15% variation. The L and R depict the left and right sides, respectively. The left and right sides noted are the same for all asymmetric maxillary PC s. 76

92 Figure 3.47: Variability of Individual Cast Scans Asymmetric Maxillary PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior, superior and posterior views. MAXILLA PC2 - Figure 3.48 The major change evident for 9.5% variation (Fig. 3.45) for asymmetric Maxillary Principal Component 2 is due to shape change of the canines. From the posterior views, there is a high emergence profile for the left canine and lower gingival margin emergence profile for the right canine for positive warp values (Fig. 3.48a) with the opposite findings for negative warp values (Fig. 3.48b). As the canine emergence profile increases, there is an increase in canine protrusion and mesial-out rotation as well as arch narrowing on the respective side (Fig. 3.48c,d). Figure 3.49 illustrates the cast scans of individuals at the extremes of the range of variation. For example, for the negative PC3 cast scan individual, there is a higher right canine emergence profile compared to 77

93 the left. The left canine is also more proclined and rotated (mesial-out) versus the right canine (Fig. 3.49b). Figure 3.48: Maxillary Principal Component 2 - Asymmetric Note: Principal Component 2 of the asymmetric mandibular dataset. PC2 accounts for 9.5% variation. Figure 3.49: Variability of Individual Cast Scans Asymmetric Maxillary PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC2 variation from the anterior, superior and posterior views. 78

94 MAXILLA PC3 - Figure 3.50 Maxillary Principal Component 3 accounts for 7.8% variation (Fig. 3.45). The superior views illustrate a major change in proclination of the lateral incisors and rotation of the canines. Positive PC scores illustrate a proclined left lateral incisor with a retrusive right lateral incisor and canine (Fig. 3.50c). Negative PC scores demonstrate the opposite findings for the right and left side (Fig. 3.50d). Other variations include the tip and emergence of the incisors and canines from the posterior views. Figure 3.51 illustrates the cast scans of individuals at the extremes of the range of variation. The proclination and retrusion of the lateral incisors noted above is well depicted, but more difficult to note than the positional changes of the canines. Figure 3.50: Maxillary Principal Component 3 - Asymmetric Note: Principal Component 3 of the asymmetric mandibular dataset. PC3 accounts for 7.8% variation. 79

95 Figure 3.51: Variability of Individual Cast Scans Asymmetric Maxillary PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC3 variation from the anterior, superior and posterior views. MAXILLA PC4 - Figure 3.52 Asymmetric Maxillary Principal Component 4 accounts for 6.3% of total variation (see Fig. 3.45). There is a large rotational change of the canines: distal rotation (mesial-out) for the left canine in negative PC scores (Fig. 3.52d). In conjunction with this rotation, there is also evidence of the left lateral incisor rotating mesial (distal-out) and left central incisor proclination (Fig. 3.52d). Similar rotational changes can be noted on the right side for positive PC scores (Fig. 3.52c). Change in the emergence profiles and tip of the incisors and canines are evident in the posterior views with respect to the rotations noted in the superior view. The rotations of the canine and lateral incisor described above are illustrated in the cast scans of individuals at the extremes of the range of variation in Figure

96 Figure 3.52: Maxillary Principal Component 4 - Asymmetric Note: Principal Component 4 of the asymmetric mandibular dataset. PC4 accounts for 6.3% variation. Figure 3.53: Variability of Individual Cast Scans Asymmetric Maxillary PC4 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC4 variation from the anterior, superior and posterior views. 81

97 MAXILLA PC5 - Figure 3.54 Asymmetric Maxillary Principal Component 5 accounts for 5.9% variation (Fig. 3.45). Positive PC scores illustrate major tip changes: the central incisors and left lateral incisor are all tipped to the left (Fig. 3.54a) whereas negative warp values depict the central incisors and right lateral incisor tipped to the right (Fig. 3.54b). From the superior views, the arch increases skewness towards the direction the teeth are tipped (Fig. 3.54c,d): to the left for positive PC5 and to the right for negative PC5. Figure 3.55 illustrates the cast scans of individuals at the extremes of the range of variation, indicating the tip for the positive PC cast scan to the left (Fig. 3.55a) and tip of the incisors for the negative PC cast scan to the right (Fig. 3.55b). Figure 3.54: Maxillary Principal Component 5 - Asymmetric Note: Principal Component 5 of the asymmetric mandibular dataset. PC5 accounts for 5.9% variation. 82

98 Figure 3.55: Variability of Individual Cast Scans Asymmetric Maxillary PC5 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC5 variation from the anterior, superior and posterior views. MAXILLA PC6 - Figure 3.56 The major changes evident for 5.6% variation (refer to Fig. 3.45) are the change in mesiodistal width of the canines and dentoalveolar change in height and tip of the lateral incisors. Positive PC scores illustrate a wider left canine and more mesially tipped left lateral incisor compared to their contralateral distally tipped right lateral incisor and narrow right canine (Fig. 3.56a). The left canine gets wider as it rotates more distal out (Fig. 3.56c). Opposite findings are noted in Figure 3.56b. Rotational changes are illustrated from the superior views. Figure 3.57 illustrates the cast scans of individuals at the extremes of the range of variation. 83

99 Figure 3.56: Maxillary Principal Component 6 - Asymmetric Note: Principal Component 6 of the asymmetric mandibular dataset. PC6 accounts for 5.6% variation. Figure 3.57: Variability of Individual Cast Scans Asymmetric Maxillary PC6 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC6 variation from the anterior, superior and posterior views. 84

100 Asymmetric Occlusal Principal Components Figure 3.58: Percent Variance of Asymmetric Occlusal Principal Components Note: Covariance results of the asymmetric occlusal dataset. This PCA decomposes the variation present due to shape into primary components. All components accounting for 5% or more of the variation were included in the analysis (PC1-PC4). OCCLUSAL PC1 Figure 3.59 Occlusal Principal Component 1 accounts for 38.7% of total asymmetric variation (see Fig. 3.58). Positive PC scores illustrate the mandibular gingival margin plane canting inferior on the left side (Fig. 3.59a) versus negative PC scores depict the mandibular gingival margin plane canting down on the right side (Fig. 3.59b). From the superior view, arch coordination increases on the left side for positive PC scores (Fig. 3.59c) and on the right side for negative PC scores (Fig. 3.59d). Interarch midline deviations are apparent as well: maxillary midline to the left for negative PC scores and to the right for positive PC scores. Figure 3.60 illustrates the cast scans of individuals at 85

101 the extremes of the range of variation. The negative PC cast scan depicts the mandibular gingival margin plane sloping down on right from the anterior view (Fig. 3.60b). Similarly, a crossbite is evident for the negative cast scan for the right canines (Fig. 3.60b), indicating increased arch coordination as the occlusal relationship transitions into a crossbite. Figure 3.59: Occlusal Principal Component 1 - Asymmetric Principal Component 1 of the asymmetric mandibular dataset. PC1 accounts for 38.7% variation. The L and R depict the left and right sides, respectively. The left and right sides noted are the same for all asymmetric occlusal PC s. 86

102 Figure 3.60: Variability of Individual Cast Scans Asymmetric Occlusal PC1 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC1 variation from the anterior and lateral views. OCCLUSAL PC2 - Figure 3.61 The major change evident for 9.3% of the asymmetric variation (Fig. 3.58) is overall dental arch skewness in the superior view. Overjet increases towards positive PC scores on the right (Fig. 3.61c) versus an increase in overjet on the left side towards negative warp values (Fig. 3.61d). In the posterior view, there is an increase in the interocclusal distance on the left side for positive PC scores (Fig. 3.61a) and an increase on right side for negative PC scores (Fig. 3.61b). Figure 3.62 illustrates the cast scans of individuals at the extremes of the range of variation. Clearly evident is the change in the transverse dimension at each extreme: excess buccal overjet on the right side for positive PC cast scan (Fig. 3.62a) versus excess overjet (and buccal crossbite) for the negative PC cast scan on the left (Fig. 3.62b). 87

103 Figure 3.61: Occlusal Principal Component 2 - Asymmetric Note: Principal Component 2 of the asymmetric mandibular dataset. PC2 accounts for 9.3% variation. Figure 3.62: Variability of Individual Cast Scans Asymmetric Occlusal PC2 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC2 variation from the anterior and lateral views. 88

104 OCCLUSAL PC3 - Figure 3.63 Occlusal Principal Component 3 accounts for 5.6% of total variation (refer to Fig. 3.58). The most significant change is in the transverse dimension from the superior view. Similar to PC2, there is a change in the buccal overjet: increased overjet on the right side with differences in arch length on the left side for the positive PC3 wireframe (Fig. 3.63c). Increased overjet findings can be found on the left side for negative PC scores with differences in arch length on the right side (Fig. 3.63d). Interocclusal distance decreases on the left side (Fig. 3.63a) and on the right side (Fig. 3.63b) at different ends of the warp value spectrum. Figure 3.64 illustrates the cast scans of individuals at the extremes of the range of variation depicting the changes in transverse, vertical, and anteroposterior described above. For example, for the negative PC3 cast scan (Fig. 3.64b), note the interocclusal distance is smaller on the right versus the left side, as well as the change in buccal overjet and malocclusion classification on the right versus the left side. 89

105 Figure 3.63: Occlusal Principal Component 3 - Asymmetric Note: Principal Component 3 of the asymmetric mandibular dataset. PC3 accounts for 5.6% variation. Figure 3.64: Variability of Individual Cast Scans Asymmetric Occlusal PC3 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC3 variation from the anterior and lateral views. 90

106 OCCLUSAL PC4 - Figure 3.65 Asymmetric Occlusal Principal Component 4 accounts for 5.2% variation (see Fig. 3.58). Notably there exists a change in the dental arch rotations from the superior view. Positive PC scores illustrate an increase in arch length on the left side for the maxilla and on the right side for the mandible. It appears that the maxilla has rotated to the left and the mandible to the right for positive PC4 (Fig. 3.65c), thus contributing to the arch skewness. The exact opposite findings are illustrated for the negative PC4 wireframe in Figure 68d. Interocclusal distance increases on the right side for positive PC scores (Fig. 3.65a) and on the left side for negative PC scores (Fig. 3.65b). Figure 3.66 illustrates the asymmetric midlines for the cast scans of individuals at the extremes of the range of variation due to the variation in dental arch skewness described above. Figure 3.65: Occlusal Principal Component 4 - Asymmetric Note: Figure Principal Component 4 of the asymmetric mandibular dataset. PC4 accounts for 5% variation. 91

107 Figure 3.66: Variability of Individual Cast Scans Asymmetric Occlusal PC4 Note: Cast scans of two individuals illustrating the positive (a) and negative (b) extremes of PC4 variation from the anterior and lateral views. Covariance Pattern Models Tables illustrate the principal components with suggestive and significant findings for the symmetric and asymmetric mandibular, maxillary, and occlusal datasets. Two variables were evaluated: the y-intercept and the rate at which an individual s arch shape transitions from the primary to mixed to permanent dentition. The first variable evaluated differences in the y- intercept between individuals. The y-intercept represents the start point or initial morphology of the arches on an individual at age 5 in the primary dentition. The second variable tested was the rate of arch shape changes, which is evaluating the rate at which an individual s dental morphology changes over time from the primary to permanent dentition. These two variables were compared 92

108 for individuals with distal or mesial steps to those with a flush terminal plane as the reference category. Similarly, both variables were compared between Class II and Class I individuals. The graphs illustrated below represent the male findings. There is no statistical evidence to suggest that males and females have different growth rates or y-intercepts in this data. To understand the following tables and charts that were outputted from the Statistical Analysis Software (SAS), the Table 3.6 is an aid to help define each effect. Table Definitions of Effects Outputted from SAS Variable Tested Output Effect Name from SAS Definition y-intercept Age5Molar Initial shape in primary dentition compared between Mesial/Distal vs Flush individuals as reference y-intercept Age13Molar Initial shape in primary dentition compared between Class II vs Class I individuals as reference Rate Stage_Time*Age5Molar Rate of growth from primary to mixed dentition compared between Mesial/Distal vs Flush individuals as reference Rate Stage_Time*Age13Molar Rate of growth from primary to mixed dentition compared between Class II vs Class I individuals as reference Rate Rate of growth from mixed to permanent Significance Test for Spline After dentition compared between Mesial/Distal vs Knot for Distal/Mesial Age 5 Flush individuals as reference Rate Significance Test for Spline After Knot by Age 13 Molar Class Rate of growth from mixed to permanent dentition compared between Class II vs Class I individuals as reference 93

109 Mandibular Principal Components Table 3.7. Mandibular Principal Components Covariance Pattern Analysis Note: Results of the covariance pattern models suggesting (p < 0.05) the Symmetric and Asymmetric Principal Components correlated with either a mesial or distal step compared to flush or Class II compared to Class I malocclusion. The mandibular principal components did not display any truly significant results (p < after Bonferroni correction). Principal components with a p- value 0.01 will be highlighted in detail below. The estimate is correlated with positive or negative PC scores. 94

110 Mandibular Asymmetric PC6 As described in the previous section, mandibular asymmetric Principal Component 6 depicts a change in dentoalveolar height for the canines which is reflected in their rotations from the superior view: a shorter and wider left canine is evident in positive PC scores that is more rotated distal out, whereas for negative PC scores the left canine is taller, more narrow, and rotated mesial out (Fig. 3.67). Corresponding to each shorter, wider canine is an adjacent lateral incisor more retroclined than its counterpart. Also evident is overall arch skewness to the right for positive PC scores and to the left for negative PC scores. The changes noted when approaching positive warp values has been suggested (p = 0.007) to correlate with a Class II individuals rate of change from the mixed to permanent dentition (see 3.68) when compared to individuals classified as Class I. Figure 3.67: Mandibular Principal Component 6 - Asymmetric 95

111 Figure 3.68 Mandibular Asymmetric PC6: Rate for Class II Note: The x-axis Stage_Time for all y-intercept and rate figures represents the dental development stage: 0.0 = primary dentition, 1.0 = mixed dentition, 2.0 = permanent dentition. The y-axis Predicted Mean value represents PC warp values (i.e. PC scores). 96

112 Maxillary Principal Components Table 3.8. Maxillary Principal Components Covariance Pattern Analysis Note: Results of the covariance pattern models suggesting (p < 0.05) the Symmetric and Asymmetric Principal Component changes that are correlated with either a mesial or distal step compared to flush or Class II compared to Class I malocclusion. The maxillary principal components did not display any truly significant results (p < after Bonferroni correction). Principal components with a p-value 0.01 will be highlighted in detail below. The estimate is correlated with positive or negative PC scores. Maxillary Asymmetric PC5 Recall the wireframes for the asymmetric maxillary Principal Component 5 in Figure Positive PC scores illustrate major tip changes: the central incisors and left lateral incisor are all tipped to the left whereas negative warp values depict the central incisors and right lateral incisor tipped to the right. From the superior views, the arch increases skewness towards the direction the teeth are tipped: to the left for positive PC5 and to the right for negative PC5. Figure 3.70 represents the suggestive (p = 0.007) difference in initial morphology for a Class II dental cast scan compared to a Class I dental cast scan. The Class II initial arch form in the primary dentition 97

113 (approximately around age 5) closely resembles morphology characteristics for the positive PC5 wireframes described previously. Figure 3.69: Maxillary Principal Component 5 - Asymmetric Figure 3.70 Maxillary Asymmetric PC5: y-int for Class II 98

114 Occlusal Principal Components Table 3.9. Occlusal Principal Components Covariance Pattern Analysis Note: Results of the covariance pattern models illustrating the Symmetric and Asymmetric Principal Components correlated with either a mesial or distal step compared to flush or Class II compared to Class I malocclusion. Suggested correlations (p < 0.05) are displayed above with true significant results highlighted in the gray boxes (p < after Bonferroni correction). The estimate indicates positive or negative PC scores. Occlusal Symmetric PC2 Recall the PC2 wireframe. Stepped down maxillary incisors and stepped up mandibular incisors can be seen positive PC scores, whereas the opposite findings are noted for negative PC scores as the interocclusal distance increases (refer to Fig. 3.71). In the lateral views, a prominent 99