Variation in arch shape and dynamics of shape change from infancy to early childhood

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2017 Variation in arch shape and dynamics of shape change from infancy to early childhood Gisela Lilian Borget University of Iowa Copyright 2017 Gisela Lilian Borget This thesis is available at Iowa Research Online: Recommended Citation Borget, Gisela Lilian. "Variation in arch shape and dynamics of shape change from infancy to early childhood." MS (Master of Science) thesis, University of Iowa, Follow this and additional works at: Part of the Orthodontics and Orthodontology Commons

2 Variation in Arch Shape and Dynamics of Shape Change From Infancy to Early Childhood by Gisela Lilian Borget 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 2017 Thesis Supervisor: Professor Steven F. Miller

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 Gisela L. Borget has been approved by the Examining Committee for the thesis requirement for the Master of Science degree in Orthodontics at the May 2017 graduation. Thesis Committee: Steven F. Miller, Thesis Supervisor Lina M. Moreno Uribe Nathan E. Holton Thomas E. Southard

4 ACKNOWLEDGEMENTS I would like to express my gratitude to Steve Miller, my thesis supervisor, for his guidance throughout this process. I would also like to thank Drs. Nathan Holton, Lina Moreno Uribe, and Thomas Southard for their invaluable input. Finally, I would like to thank my husband, Parker and son, Jett for their patience, support and encouragement throughout my residency. ii

5 ABSTRACT Introduction: In order to properly diagnose and treatment plan, an orthodontist needs to be knowledgeable about the changes that occur to the maxillary and mandibular dental arches throughout growth. The purpose of this study is to provide an analysis of morphological shape change as a function of growth seen in the maxillary and mandibular dental arches from birth to 3 years of age. Methods: Dental casts from the Iowa Infant Growth study ranging from 2 months to age 4 were photographed in the occlusal plane. The images were landmarked with 3 standard landmarks and 10 sliding semi-landmarks along the curvature of the maxillary and mandibular arches. TpsRelW was used to slide the semi-landmarks and superimpose the data to facilitate shape analysis. MorphoJ was used to determine the degree to which size influences dental arch shape. Once the effects of allometry had been removed, a principal component analysis was run on the residuals to display major features of shape variation in the dataset. Finally, a two block partial least squares analysis was run to determine the degree to which the maxillary and mandibular arches were integrated throughout early growth. Results: Allometry accounts for 9.63% (p<0.0001) of symmetric shape variation in the maxilla, while it accounts for 56% (p<0.0001) of symmetric shape variation in the mandible. Asymmetric shape variation is independent of allometry as it only affects 0.34% (p=0.783) of the maxillary and 1.46% (p=0.0001) of the mandibular shape variation. Principal component one accounts for over 60% of all shape variation seen in maxillary and mandibular residuals. Principal component one of the symmetric residuals results in a longer, wider dental arch. Principal component one of asymmetric residuals results in a dental arch with one posterior side being longer and wider iii

6 while the contralateral side is shorter and narrower. The first three time points (2 months - 1 year) show no significant integration or very weak integration between the maxillary and mandibular arches. Integration increases with age, displaying significant integration at the last three time points, with the most integration being displayed at 2.5 years. Conclusions: Allometry affects very little of the symmetric shape variation in the maxilla, indicating its shape is very stable at birth. In contrast, over half of the symmetric shape variation in the mandible is affected by allometry, indicating its shape is not as stable at birth. The asymmetric components are independent of allometric effects. Integration of the maxillary and mandibular arches increase with age from 2 months to 3 years, peaking at a time point of 2.5 years, correlating with the eruption of the posterior primary dentition. We conclude that the developing dentition plays an instrumental role in the integration of the maxillary and mandibular arch shapes. iv

7 PUBLIC ABSTRACT An orthodontist needs to know what occurs to the maxillary and mandibular arches as a person grows in order to properly diagnose problems and determine an adequate treatment plan. The purpose of this study was to evaluate those changes in each arch separately and together from birth to 3 years of age. This was done using dental casts of children in the Iowa Infant Growth study from 2 months to 4 years of age. The casts were photographed and landmarked. The data were then analyzed in MorphoJ to see the effect that size has on shape variation. These size effects were then removed and further analyses were run to determine the principal components of shape variation in each arch as well as the similarities in growth of both arches together, or integration, as the individual got older. Results indicate that size affects the shape variation of the symmetric component for the maxilla and mandible, but does not affect the shape variation of the asymmetric components. It was also found that as the arches are growing from 2 months to 3 years, the integration, or the amount that arch shapes covary, increases with age. v

8 TABLE OF CONTENTS LIST OF TABLES... vii LIST OF FIGURES... viii INTRODUCTION... 1 REVIEW OF THE LITERATURE ARCH LENGTH... 3 ARCH WIDTH...5 MATERIALS AND METHODS SAMPLE... 9 DATA COLLECTION DATA ANALYSIS...12 RESULTS MAXILLARY AND MANDIBULAR SYMMETRIC ALLOMETRY ANALYSIS...14 MAXILLARY AND MANDIBULAR ASYMMETRIC ALLOMETRY ANALYSIS.15 PCA: MAXILLARY SYMMETRIC RESIDUALS...16 PCA: MAXILLARY ASYMMETRIC RESIDUALS 19 PCA: MANDIBULAR SYMMETRIC RESIDUALS..22 PCA: MANDIBULAR ASYMMETRIC RESIDUALS.. 25 TWO BLOCK PARTIAL LEAST SQUARES ANALYSIS...28 DISCUSSION...37 CONCLUSIONS REFERENCES...45 vi

9 LIST OF TABLES Table 1. Landmarks used by Bishara to measure arch length Landmarks used by Bishara to measure arch width Age of individuals and number of dental casts at each time point Landmarks for maxillary and mandibular casts RV coefficients and p-values from two block partial squares analysis. 29 vii

10 LIST OF FIGURES Figure 1. Landmarks used by Bishara to measure arch length Landmarks used by Bishara to measure arch width Landmarks placed along maxillary and mandibular dental arches Maxillary symmetric component allometry Mandibular symmetric component allometry PCA: PC 1 of maxillary symmetric residuals PCA: PC 2 of maxillary symmetric residuals PC 1 vs. PC 2 of maxillary symmetric residuals PCA: PC 1 of maxillary asymmetric residuals PCA: PC 2 of maxillary asymmetric residuals PCA: PC 3 of maxillary asymmetric residuals PCA: PC 1 of mandibular symmetric residuals PCA: PC 2 of mandibular symmetric residuals PC 1 vs. PC 2 of mandibular symmetric residuals PCA: PC 1 of mandibular asymmetric residuals PCA: PC 2 of mandibular asymmetric residuals PCA: PC 3 of mandibular asymmetric residuals Confidence ellipses for all 6 time points Two Block PLS for maxillary and mandibular time point Two Block PLS for maxillary and mandibular time point Two Block PLS for maxillary and mandibular time point viii

11 INTRODUCTION As an orthodontist treats patients, their goals involve correcting malocclusions that are oftentimes related to abnormal growth patterns. For this reason, an orthodontist has a special interest in dental development and facial growth. Specifically, they are interested in the dimensional changes that occur in the maxillary and mandibular arches of a patient throughout their lives. Understanding changes that occur in the dental arches as a function of growth can help the orthodontist in many ways. If normal growth patterns are understood, improper growth can be properly identified (Andrews 1972). Accurate and early identification can allow for early intervention (Das, 2008; DeVries, 1917; Karjalainen, 1999). There are many abnormal growth patterns that if addressed early enough, can be treated with more conservative orthopedic treatments. Once a patient s growth is complete, those same cases may require more complex treatment, including extractions or possibly maxillofacial surgery (Kluemper and Spalding, 2001). Finally, adequate knowledge of a person s growth pattern allows an orthodontist to explain expected growth to a patient and/or their parents during and after treatment. Patients can be better informed about the changes expected and about relapse potential. Because dental development and facial growth patterns are so critical to proper diagnosis and treatment planning in orthodontics, a large extent of research has been dedicated to this field. There are many longitudinal studies that have researched the growth patterns of different populations from birth into late adulthood. While these studies have provided significant insight into the growth that is expected as a patient ages, they have focused on changes associated with linear measurements, such as length and width. Geometric morphometrics provides several 1

12 advantages over linear morphometrics, including a means to directly analyze shape variation (with and without size effects) as well as the ability to quantify very minor aspects of shape variation that traditional morphometrics cannot. Despite these advantages, few studies have attempted to describe shape changes employing geometric morphometrics within dental research. The purpose of this study is to provide an analysis of morphological shape differences seen in the maxillary and mandibular dental arches individually, as well as the arches evaluated together, from birth to 3 years of age. Identifying growth patterns in this sample will allow detection of problems in dental arch development that may manifest as malocclusion in the future. Additionally, we are trying to understand patterns of morphological integration to see how strongly (or weakly) the maxillary and mandibular arches covary with one another throughout the first couple years of life. 2

13 REVIEW OF THE LITERATURE Arch Length In 1964, Sillman completed the first longitudinal group study looking at dimensional changes of the dental arches from birth to 25 years. He concluded that in both the maxillary and mandibular arches, the greatest incremental increase in arch length occurred between birth and 2 years. By age 3 (after eruption of the primary dentition) anterior arch length is essentially established, but some increase may occur during eruption of the permanent incisors. Between 3 years of age and adulthood, there is a mean 1.5 mm decrease in maxillary arch length and a mean 2.0 mm decrease in the mandibular arch length (Sillman, 1964). Bishara et al. (1995) also evaluated maxillary and mandibular total arch length on a longitudinal basis. He evaluated two samples, 6 weeks to 2 years and 3 to 45 years. The 6 week to 2 year sample was from the Iowa infant growth study and consisted of 28 female and 33 male individuals. The 3 year to 45 year sample was derived from the Iowa facial growth study and included 16 females and 15 males. Bishara identified five maxillary and mandibular landmarks. They include a single central point and bilateral lateral and posterior points in each arch. The landmarks are listed (Table 1) and shown below (Figure 1). These landmarks were originally defined by Sillman in his longitudinal study (Sillman, 1964; Moorrees et al, 1979) and were used as a guide for landmark placement in this study. 3

14 Maxillary Landmarks A Incisive Point Most anterior point of the incisive papilla B Lateral Sulcus Point Where the lateral sulcus crosses the crest of the alveolar ridge C Postgingival Point Posterior border of the gum pad at the crest of the alveolar ridge Mandibular Landmarks D Incisive Point Midline on the crest of the alveolar ridge E Lateral Sulcus Point Where the lateral sulcus crosses the crest of the alveolar ridge F Posterior Border of the Pad Point Posterior margin of the pad where it drops to the posterior ridge Table 1. Landmarks use by Bishara et al. (1995) to measure arch length in the pre-eruptive stage. Figure 1. Landmarks used by Bishara et al. (1995) to measure arch length in the pre-eruptive stage. 4

15 Maxillary arch length was measured as the sum of the right and left A-B and B-C measurements. Mandibular arch length was measured as the sum of the right and left F-E and E- D measurements. Bishara s study concluded that from 6 weeks to 2 years, maxillary arch length increased significantly. He agreed with Sillman in that the greatest incremental increase in the maxillary and mandibular arch length occurred during the first two years of life. Bishara also found that males have significantly greater total arch length than females in both arches (Bishara, 1995). The maxillary arch length continues to increase until the age of 13 years, while the mandibular arch length only continues to increase until 8 years. Finally, he found that there is a significant decrease in arch length until 45 years of age (Bishara, 1989; Bishara, 1995). Arch Width In a mixed longitudinal study, Sillman also evaluated arch width in a sample of patients from birth to 25 years. From birth to 2 years, he noted an increase in intercanine width of 5.0 mm in the maxillary arch and 3.5 mm in the mandibular arch. After 2 years, intercanine width increased until 13 years of age in the maxillary arch and 12 years of age in the mandibular arch (Sillman, 1964). From the primary dentition to early adulthood, both Sillman and Knott found that intercanine width either remained unchanged, increased, or decreased by 1 mm. However, there was considerable individual variation, where the average change in mandibular intercanine width was 3.2 mm but ranged between 0 and 6.0 mm (Sillman, 1964; Knott, 1972). Moorrees and co-authors found that arch width increases markedly (3.0 mm) during eruption of the maxillary and mandibular permanent incisors and then stabilized shortly after (Moorrees et al, 1969). Additionally, Moyers et al. found that between 4 years and 17 years, 5

16 intercanine width increased 3.5 mm in both the maxillary and mandibular arches. He also found that there was greater sexual dimorphism in the maxillary intercanine width than mandibular intercanine width, with males having a significantly greater maxillary intercanine width (Moyers et al, 1976). Bishara et al. (1997) also evaluated arch width changes from 6 weeks to 45 years of age in a longitudinal study. He evaluated two samples, 6 weeks to 2 years and 3 to 45 years. The 6 week to 2 year sample was from the Iowa infant growth study and consisted of 28 female and 33 male individuals. The 3 year to 45 year sample was derived from the Iowa facial growth study and included 15 females and 15 males. In this study, Bishara identified two bilateral landmarks in each arch. The landmarks included bilateral lateral and posterior points. They are listed (Table 2) and shown below (Figure 2). Maxillary Landmarks A Lateral Sulcus Point Where the lateral sulcus crosses the crest of the alveolar ridge B Postgingival Point Point on the posterior ridge of the gum pad at the crest of the alveolar ridge Mandibular Landmarks E Lateral Sulcus Point Where the lateral sulcus crosses the crest of the alveolar ridge F Posterior Border of the Pad Point Point on the posterior margin of the pad, where it drops to the posterior ridge Table 2. Landmarks used by Bishara et al. (1997) to measure arch width in the pre-eruptive stage. 6

17 Figure 2. Landmarks used by Bishara et al. (1997) to measure arch width in the pre-eruptive stage. Arch width changes in the pre-eruptive stage were measured from the point on one side to the other contralateral point (A-A). When the dentition was present, the distances between the cusps tips of the canines and the mesial cusp tips of the second deciduous molar (age 3 and 5) or the mesiobuccal cusp tips of the first permanent molar (all subsequent ages) were measured. Bishara found that between 6 weeks and 2 years of age (before eruption of the deciduous dentition) there is a significant increase in intercanine and intermolar width for males and females. There was also a significant increase in intercanine and intermolar widths in both maxillary and mandibular arches in males and females between the ages of 3 and 13 years. After complete eruption of the permanent dentition there was a slight decrease in dental arch widths. This was more evident in the intercanine width than in the intermolar width. Finally, he found that on average, mandibular intercanine width was established by 8 years of age (after eruption of the 4 incisors). The eruption of the permanent dentition did not produce any significant 7

18 changes in intercanine width. Thus a clinician should not expect any significant increases in intercanine width after the age of 8 (Bishara et al, 1997). Burdi and Moyers conducted a similar study and found that dimensional increases in width are almost completely due to alveolar process growth and have very little to do with skeletal growth. This is true, particularly in the mandible. They also found that the direction of vertical alveolar growth differs significantly between the maxillary and mandibular arches. The maxillary alveolar processes diverge as the teeth erupt, while the mandibular alveolar processes remains more parallel. This difference in growth may allow for a greater change in maxillary arch width during treatment (Burdi and Moyers, 1988). Other authors have found similar results and have concluded that an increase in intercanine width during treatment is far more stable in the maxillary arch (Burdi and Moyers, 1988; Moyers et al, 1976; Walter 1953). In contrast, an increase in intercanine width in the mandibular arch is not stable. Pretreatment canine width dimensions should not be violated if a stable result is wanted. Instead, the pretreatment mandibular intercanine width should be used as a guide to build both the maxillary and the mandibular arch form (Herberger, 1981; Little et al, 1981). 8

19 MATERIALS AND METHODS Sample This study employs dental casts from the Iowa Infant Growth Study, a longitudinal cast series ranging from 2 months post-birth up to age 4, to examine changes in dental arch shape throughout growth. Infants were recruited from the obstetric and pediatric departments at the University of Iowa Hospitals and Clinics and from private pediatric practices in Iowa City, Iowa. The criteria for selection were healthy full-term babies with no apparent congenital anomalies and availability of the family for evaluation over an eight-year period. The infants were evaluated and dental impressions were taken at 6 month intervals. These impressions were then poured into dental casts and trimmed appropriately. Records for 8 time points are available, however, very few patients returned for the 7 th and 8 th time point. For this study, only the initial 6 time points are used. The ages of the individuals and number of dental cast sets available at each time point are found in Table 1. Time Point Age of Individual Dental Casts Available 1 2 months months year years years years 97 Table 3. Ages of individuals and number of dental casts available at each time point used in this study. 9

20 Data Collection The dental casts were photographed in the occlusal plane using a Nikon D7100 digital SLR camera. A scale bar was present in each image for scaling purposes. The images were then imported into TPSDIG2 in order to place 13 landmarks along the curvature of the maxillary and mandibular arches. Three landmarks (1, 7, 13) are two-dimensional Type 2 standard landmarks. These had been identified and marked on the dental casts prior to being photographed, thus ensuring accurate landmarking in TPSDIG2. These landmarks were selected based on similar landmarks used by Sillman and Bishara in their growth analyses to establish where the most posterior, anterior, and central positions of the maxillary and mandibular arches were located (Sillman, 1964; Bishara et al, 1995). The other landmarks (2-6 and 8-12) are two-dimensional Type 3 sliding semi-landmarks. They were placed along the alveolar ridge spaced out between the standard landmarks. The landmarks used for the maxillary and mandibular arches are shown in Figure 3 and listed in Table 4. 10

21 Figure 3. Landmarks placed along the maxillary (left) and mandibular (right) dental arches. Circled landmarks (1, 7, 13) are standard Type 2 landmarks. All others are Type 3 semi-landmarks. Landmark Maxillary Arch Mandibular Arch 1 Left post-gingival point on the posterior border of the gum pad at the crest of the alveolar ridge Left posterior border of the pad point at the posterior margin of the alveolar ridge points placed equidistantly along the left side of the alveolar ridge 7 Incisive point at the most anterior part of the incisive papilla points placed equidistantly along the right side of the alveolar ridge 13 Right post-gingival point on the posterior border of the gum pad at the crest of the alveolar ridge 5 points placed equidistantly along the left side of the alveolar ridge Incisive point at the midline on the crest of the alveolar ridge 5 points placed equidistantly along the right side of the alveolar ridge Right posterior border of the pad point at the posterior margin of the alveolar ridge Table 4. Landmarks for maxillary and mandibular arches. 11

22 All casts were landmarked by one investigator (Borget). Landmark reliability was assessed by using a small sample of 20 images that were landmarked twice by the investigator at two separate occasions. Only standard Type 2 landmarks were used in the reliability test. The results indicated consistent landmarking at all three sites. Data Analysis Once all images had been landmarked, TPSRELW was used to slide the semi-landmarks along the curvature of the dental arches in order to superimpose the landmark data and facilitate shape analysis. The files were then imported into MorphoJ for the remainder of the statistical analyses. In MorphoJ, the degree to which size influences dental arch shape was calculated via a test of allometry. Allometry is the study of shape as a function of change in size. This test was used to determine the amount of variance that was due to size (growth) in this longitudinal dataset. To accomplish this, linear regression was used to separate the component of variation in the dependent variable (shape) that is predicted by the independent variable (centroid size). Results from this regression were used to demonstrate how dental arch shape changes throughout growth in the sample. Additionally, the residual component of shape variation; which is uncorrelated with the independent (size) variable was calculated and used in subsequent shape analyses in order to also investigate shape variation that is not attributed to arch size (and therefore growth). Once the effects of allometry had been removed, a principal component analysis was run on the residuals. A principal component analysis (PCA) is a statistical procedure that uses an 12

23 orthogonal transformation to convert shape variation into different independent components. This is used as a data reduction method to allow for direct examination of the largest (and therefore most important) components of shape variation present in the sample. Both the symmetric and asymmetric components of shape variation were submitted and independently analyzed. This analysis is used to display the major features of shape variation in the dataset across the components that account for the largest amount of the total variance. In PCA, the first component always explains the largest amount of variance, with each succeeding component explaining less of the total variance. Only components explaining more than 5% of the shape variation were included in this study. Finally, a two block partial least squares analysis (2B PLS) was run to determine the degree to which the maxillary and mandibular arches were integrated throughout early growth. A two block partial least squares analysis allows us to examine the co-variation between two sets of variables. For this study, the two variables or blocks are the maxillary and mandibular arches. The null hypothesis of the analysis is complete independence between the two blocks of variables. A significant p-value rejects the null hypothesis and indicates that the two blocks are not independent (and therefore integrated). RV coefficients were employed in order to determine the strength of integration between the blocks. Higher RV coefficients indicate that there is a stronger association between the maxillary and mandibular blocks. The 2B PLS analysis was repeated for each time point (1-6) in order to determine changes in the strength of integration found between the dental arches during growth. 13

24 RESULTS Maxillary and Mandibular Symmetric Allometry Analysis The maxillary symmetric component allometry results show that 9.63% (p<0.0001) of the shape variation in the maxillary arch is due to size. While there appears to be a significant relationship between centroid size and maxillary arch shape, the majority of the shape variation is independent of allometry. In contrast, the mandibular symmetric component allometry results show that 56.00% (p<0.0001) of the variation seen in mandibular arch shape is due to size. This indicates that allometry plays a role in over half the shape variation seen in this arch. The morphological changes seen in both arches during these analyses are similar. There is a narrowing of the arch in the transverse dimension, while the anterior segment lengthens in the anterior-posterior dimension. The changes are seen more prominently in the mandibular arch. (Figures 4 and 5). Figure 4. Maxillary symmetric component allometry with a scale factor of 25. Percent of variation predicted: 9.63%. P-value: p< Light blue line represents the average arch shape in the dataset. Dark blue line demonstrates the shape variation due to the allometry. 14

25 Figure 5. Mandibular symmetric component allometry with a scale factor of 25. Percent predicted: 56.00%. P-value: p< Light blue line represents the average arch shape in the dataset. Dark blue line demonstrates the shape variation due to the allometry. Maxillary and Mandibular Asymmetric Allometry Analysis The maxillary asymmetric component allometry results show that only 0.34% (p=0.783) of the shape variation seen in the maxillary arch is due to size. Thus, there is no significant relationship between the maxillary asymmetric component of variation and size. Similarly, the mandibular asymmetric component allometry results show that only 1.46% (p=0.0001) of the shape variation seen in the mandible are due to size. While more significant than the relationship seen in the maxillary arch, the relationship in the mandibular arch is still very weak. Essentially all of the asymmetric components of variation in the maxillary and mandibular arches are either independent of size or demonstrate less than 2% variation due to size. 15

26 Principal Component Analysis: Maxillary Symmetric Residuals The results of the principal component analysis of the maxillary symmetric residuals showed two principal components that accounted for more than 5% of the shape variation. Principal component one, which explains 73.04% of the shape variation, demonstrates that an individual s maxillary arch shape can vary between being wider than average in the posterior segment and shorter in the anterior-posterior dimension or being narrower than average in the posterior segment and longer in the anterior-posterior dimension (Figure 6). Figure 6. Principal component one of maxillary symmetric component allometric residuals. Percent of variance explained: 73.04%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

27 Principal component two, which explains 22.05% of the shape variation, demonstrates that an individual s maxillary arch shape can vary between being narrower than average in the posterior segment, wider in the middle segment and slightly shorter in the anterior-posterior dimension or being wider in the posterior segment, narrower in the middle segment, and slightly longer in the anterior-posterior dimension (Figure 7). Figure 7. Principal component two of maxillary symmetric component allometric residuals. Percent of variance explained: 22.05%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

28 When principal components 1 and 2 of the maxillary symmetric residuals are graphed against one another, it illustrates the changes that occur as an individual ages. As the individual gets older, PC 1 scores tend to move toward the negative side of the graph for the first 5 time points, then it moves toward the positive side of the graph for the remaining time points. PC 2 moves steadily in a negative direction (Figure 8). Figure 8. Principal component one of the maxillary symmetric residuals on the X-axis vs. Principal component two of the maxillary symmetric residuals on the Y-axis. 18

29 Principal Component Analysis: Maxillary Asymmetric Residuals The results of the principal component analysis of the maxillary asymmetric residuals showed three principal components that accounted for more than 5% of the shape variation. Principal component one, which accounts for 63.39% of the shape variation, demonstrates slight asymmetries that can be present in the posterior segments of the maxillary arches. The asymmetries can vary between being slightly longer and wider than average on the left side, while being narrower and shorter on the right or being slightly shorter and narrower on the left, while being longer and wider in the posterior segments on the right (Figure 8). Figure 9. Principal component one of maxillary asymmetric component allometric residuals. Percent of variance explained: 63.39%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

30 Principal component two, which accounts for 19.26% of the shape variance, displays an asymmetry where the maxillary arch growth is angled toward one side. When the arch growth is angled toward the right, the most posterior left section is wider than average, then narrows significantly until it reaches the midpoint. The arch shape then widens again, but becomes narrow at the most posterior right section. When the arch growth is angled toward the left, the same growth pattern is observed in the opposite direction (Figure 9). Figure 10. Principal component two of maxillary asymmetric component allometric residuals. Percent of variance explained: 19.26%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

31 Principal component three, which accounts for 8.93% of the shape variance, displays an asymmetry that is noticeable in both the anterior and posterior segments. As an individual grows toward the positive side of the scale, they display a very straight left side of the arch instead of the average arch curvature. This changes as the midline is approached and the individual displays a much more curved right side. The left side is narrower than average in the posterior and longer than average in the anterior segment. The right side is shorter than average in the anterior segment and wider than average in the posterior segment. The same growth pattern in the opposite direction is observed in individuals growing toward the negative side of the scale (Figure 10). Figure 11. Principal component three of maxillary asymmetric component allometric residuals. Percent of variance explained: 8.93%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

32 Principal Component Analysis: Mandibular Symmetric Residuals The results of the principal component analysis of the mandibular symmetric residuals showed two principal components that accounted for more than 5% of the shape variation. Principal component one, which accounts for 82.59% of the shape variation, shows that a mandible can either grow wider than average in the posterior segments and shorter in the anterior-posterior dimension or narrower than average in the posterior segments and longer in an anterior-posterior dimension (Figure 11). Figure 12. Principal component one of mandibular symmetric component allometric residuals. Percent of variance explained: 82.59%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

33 Principal component two, which accounts for 11.74% of the shape variance, displays that a mandible can grow wider than average in the most posterior segments and become narrower bilaterally until the midline is reached or it can be narrower than average and become wider bilaterally as the midline is approached. The first will display a more V-shaped mandibular arch while the second will display a more square-shaped mandibular arch (Figure 12). Figure 13. Principal component two of mandibular symmetric component allometric residuals. Percent of variance explained: 11.74%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

34 When principal components 1 and 2 of the mandibular symmetric residuals are graphed against one another, we can see some of the changes that occur as an individual ages. PC 1 scores consistently move in a more negative direction, while PC 2 stays in the center of the graph over time (Figure 14). Figure 14. Principal component one of mandibular symmetric residuals (x-axis) vs. Principal component 2 of mandibular symmetric residuals (y-axis). 24

35 Principal Component Analysis: Mandibular Asymmetric Residuals The results of the principal component analysis of the mandibular asymmetric residuals showed three principal components that accounted for more than 5% of the shape variation. Principal component one, which accounts for 60.67% of the shape variation, displays an asymmetry where the left side of the mandibular arch is longer than average in the anteriorposterior dimension and slightly wider in the transverse dimension while the right side of the mandibular arch is slightly shorter in the anterior-posterior dimension and slightly narrower in the transverse. The asymmetry may also present in a growth pattern where the left side is shorter and slightly narrower and the right side is longer and slightly wider (Figure 15). Figure 15. Principal component one of mandibular asymmetric component allometric residuals. Percent of variance explained: 60.67%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

36 Principal component two, which accounts for 20.52% of the shape variation, displays an asymmetry where growth is angled toward the right side of the mandibular arch or where growth is angled toward the left side of the mandibular arch. The side that the growth is angled toward has a straighter arch form whereas the opposite side is very angled (Figure 16). Figure 16. Principal component two of mandibular asymmetric component allometric residuals. Percent of variance explained: 20.52%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

37 Principal component three, which accounts for 10.88% of the shape variation, displays a very drastic asymmetry where the left side of the mandibular arch is very concave while the right side is very convex or where the right side of the mandibular arch is very convex while the right side is very concave. In both cases anterior-posterior length of the mandibular arch and midlines are very close to average (Figure 17). Figure 17. Principal component three of mandibular asymmetric component allometric residuals. Percent of variance explained: 10.88%. Figure on left has a positive scale factor of 0.1. Figure on right has a negative scale factor of

38 Two Block Partial Least Squares Analysis The results of the two-block partial least squares analysis produced an RV coefficient with an associated p-value for each time point. These values are listed in Table 3. The RV coefficient for the first time point is (p-value: ). This is very low and not significant, indicating that there is independence between the maxillary and mandibular blocks. There is no evidence of any meaningful morphological integration between the maxilla and the mandible at this time point. Time point two has an RV coefficient of (p-value: ), while time point three has an RV coefficient of (p-value: ). These values are both significant, but also very low. This indicates that there is evidence of very weak integration between the maxilla and mandible at these two time points. Time points 4, 5, and 6 have higher and more significant RV coefficients of , , and (p<0.0001) respectively. These last three time points indicate that integration between the upper and lower arches increases with age. While the RV coefficient at time point 6 is lower than at time point 5, it is still significantly higher than any of the initial time points. A confidence ellipse was generated for each time point and it is evident that the slopes of the ellipses become increasingly positive (Figure 18). This supports the conclusion that the maxillary and mandibular arches become more integrated as the individual gets older. 28

39 Time Point RV Coefficient P-values 1 (2 months) (6 months) (1 year) (1.5 years) < (2.5 years) < (3 years) < Table 5. RV coefficients and p-values for each time point that resulted from the two block partial squares analysis. 29

40 Figure 18. Confidence ellipses generated for each of the 6 time points. Graphs are in chronological order from upper left to lower right. The slopes of the ellipses become increasingly positive with age of the individual. 30

41 PLS component one of the two block partial squares analysis at time point four displays that as the individual grows in the positive direction of the scale, their maxilla and mandible both grow longer in the anterior-posterior dimension and gradually narrower as the posterior is reached. The mandible narrows less in the most posterior segment than the maxilla (Figure 19 top row). As the individual grows in the negative direction of the scale, their maxilla and mandible both grow shorter in the anterior-posterior dimension and wider in the transverse. The most posterior segments of the mandible expand less than the most posterior segments of the maxilla (Figure 19 bottom row). The RV coefficient is and the p-value (p<0.0001) is highly significant so there is relatively strong evidence of integration between the arches at this time point. 31

42 Figure 19. Two block partial least squares analysis for maxilla (left) and mandible (right) at time point 4 (1.5 years). Scale factor used: 0.1 for top row and -0.1 for bottom row. Light blue line represents the average arch shape in the dataset. Dark blue line demonstrates the shape variation due to the analysis. RV coefficient: P-value <

43 Principal component one of the two block partial squares analysis at time point five indicates that as the individual grows in the positive direction of the scale, their maxilla and mandible both grow longer in the anterior-posterior dimension and narrower as the posterior is reached. The mandible, however, begins to narrow further posteriorly than the maxilla (Figure 20 top row). As the individual grows in the negative direction of the scale, their maxilla and mandible both grow shorter in the anterior-posterior dimension and wider in the transverse. The mandible begins to expand only in the most posterior segments (Figure 20 bottom row). The RV coefficient is and the p-value (p<0.0001) is highly significant so there is strong evidence of integration between the arches at this time point. PLS results for the time points prior to 2.5 years of age show a steady increase in RV coefficients from 2 months after birth (with no significant evidence of integration) up until the maximum RV value at 2.5 years. 33

44 Figure 20. Two block partial least squares analysis for maxilla (left) and mandible (right) at time point 5 (2.5 years). Scale factor used: 0.1 for top row and -0.1 for bottom row. Light blue line represents the average arch shape in the dataset. Dark blue line demonstrates the shape variation due to the analysis. RV coefficient: P-value <

45 Principal component one of the two block partial squares analysis at time point six indicates that as the individual grows in the positive direction of the scale, their maxilla and mandible both grow longer in the anterior-posterior dimension and narrow gradually as the posterior segment is reached. The mandible expands slightly more than the maxilla at the most posterior aspect (Figure 21 top row). As the individual grows in the negative direction of the scale, their maxilla and mandible both grow shorter in the anterior-posterior dimension and gradually wider in the transverse. The mandible expands slightly more than the maxilla does in the most posterior aspect (Figure 21 bottom row). The RV coefficient is and the p-value (p<0.0001) is highly significant so there is evidence of integration between the arches at this time point. Note the RV coefficient at this time point is slightly lower than the previous time point (2.5 years). This indicates that integration between the mandible and maxilla is slightly weaker at 3 years of age compared to 2.5 years of age. 35

46 Figure 21. Two block partial least squares analysis for maxilla (left) and mandible (right) at time point 6 (3 years). Scale factor used: 0.1 for top row and -0.1 for bottom row. Light blue line represents the average arch shape in the dataset. Dark blue line demonstrates the shape variation due to the analysis. RV coefficient: P-value <

47 DISCUSSION In order to properly treatment plan and diagnose a patient, an orthodontist needs to have an understanding of the changes that will occur in the shape of the dental arches. The findings from this study provide insight into the changes that the maxillary and mandibular arches undergo from birth to 3 years of age. The allometry analysis of the symmetric components of the maxilla and mandible reveals that some of their shape change is due to growth. The maxillary arch s shape variation is more independent of size (9.63% of variation due to allometry), while the mandible is strongly influenced by it (56.00% of variation due to allometry). The morphological changes seen in both arches are similar. As an individual grows, their maxillary and mandibular arches get narrower in the transverse dimension and longer in the anterior-posterior dimension (Figures 4 and 5). An individual with that growth pattern would display a more prognathic facial appearance. The changes seen in the anterior-posterior dimension in this section of the study are similar to those found by Sillman (1964) and Bishara (1995) in their growth analyses. They both agreed that between birth and 2 years of age, there is a significant increase in the length of the maxillary and mandibular arches. After the age of 2, Bishara found that the maxillary arch continues to grow in length until the age of 13 and the mandibular arch continues to grow in length until the age of 8 (Bishara et al, 1995). Sillman s findings disagreed, stating that after age 3, both dental arches begin to decrease in length until adulthood (Sillman 1964). Between birth and the age of 3, the same growth pattern is exemplified in our sample. However, since our data only accounted for the first three years of age, it cannot be determined if the arch length for this population would increase or decrease after that time frame. 37

48 The changes seen in the transverse dimension in this section of the study are different from those found by previous authors. Both Bishara et al. (1997) and Sillman (1964) found that there was a significant increase in intercanine and intermolar width from birth to adolescence. Our study found that the maxillary arch stays the same in the anterior and most posterior regions, but narrows slightly in the middle. The mandibular arch, however, narrows significantly from the canine area to the most posterior region of the arch. The allometry analysis of the asymmetric components of the maxillary and mandibular arches reveals that the shape variation seen here is independent of allometry. This indicates that asymmetries seen in these arches are not related to size (and therefore are not a function of growth). This finding is similar to those found in other studies involving dental and facial asymmetries. Palmer and Strobeck (1986) discuss how multiple genetic studies have confirmed that there is little or no measurable heritability to small, random deviations from bilateral symmetry. Bishara et al. (1994) states that an asymmetry in the face and dentition is a naturally occurring phenomenon. He presents that etiology to asymmetries include genetic or congenital malformations (e.g. hemifacial macrosomia, clefts of lip and palate, etc.), environmental factors (e.g. habits and trauma), or functional deviations (mandibular shifts as a result of tooth interferences). The principal component analyses show that for all residuals, principal component one accounts for more than 60% of the shape variation. Principal component one of the maxillary symmetric residuals accounts for 73.04% of variation. The morphological changes seen in this component involve changes in the anterior-posterior length of the maxilla and changes in the transverse in the posterior segments (Figure 6). Principal component 2 accounts for 22.05% of the shape variation seen in the maxillary arch. The morphological changes seen for this 38

49 component involve transverse differences in the middle and most posterior segments, as well as minimal anterior-posterior length changes (Figure 7). When PC 1 and PC 2 are plotted together and data points for each time point are distinguished, we are able to identify specific changes that occur over time (Figure 8). Since both components show discernable differences as the time points change, it can be interpreted that growth is a factor in both component variations. As time passes, PC 1 gradually becomes more negative for the initial 5 time points. This means that the maxilla gets increasingly longer and narrower in the posterior segments. At time point 6, PC 1 shifts to the positive side of the graph. At this time point, the maxilla is becoming shorter and wider in the posterior segments. PC 2 becomes increasingly negative as time goes by. This means that over time the maxilla is becoming narrower in the middle segments and wider in the most posterior aspects. Principal component one of the mandibular symmetric residuals accounts for 82.59% of shape variations. The morphological changes seen in this component involve changes in the length of the arch and transverse dimensions in the posterior segments (Figure 12). Principal component two accounts for 11.74% of the shape variation seen in the mandibular symmetric residuals. The morphological changes seen for this component involve changes in the transverse dimension both in the middle and most posterior segments (Figure 13). When PC 1 and PC 2 are plotted together and the data points for each time point are distinguished we see that PC 1 as it becomes increasingly negative over time, but PC 2 stays in the middle of the graph (Figure 14). This indicates that PC 1 is a function of growth, but PC 2 is not. This also indicates that over time, the mandibular arch becomes longer in the anteriorposterior dimension and narrower in the transverse. 39

50 The growth patterns in this section of the study are similar to those found in the allometry analyses with both arches becoming longer and narrower. The growth in length correlates with what was found in similar growth studies (Bishara et al. 1995; Sillman, 1964), while the growth in the transverse dimension is different. Principal component one of the maxillary asymmetric residual accounted for 63.39% and principal component one of the mandibular asymmetric residual accounted for 60.67% of shape variation present. This component displayed morphological changes in which the dental arches were longer and wider on one side, while being shorter and narrower on the contralateral side. This indicates that asymmetric shape variations seen in these arches will most likely involve small anterior-posterior and transverse changes limited to the most posterior segments. The two block partial least squares analyses revealed that there is a trend of increasing integration between the maxillary and mandibular arches as an individual ages from birth to 3 years of age, with the most integration seen at 2.5 years of age. Lack of integration at the initial three time points (2 months, 6 months, 1 year) could be due to a lack of a dentition. According to the American Dental Association, primary central and lateral incisors normally erupt between 8-12 months. Primary canines erupt between months, and first and second primary molars erupt between months of age (Lunt and Law, 1974). During the initial three time points, a child would be expected to have only central and lateral incisors. Without posterior teeth to develop an occlusion, the arches are likely to grow in their own pattern, with minimal integration. During the last three time points, a child would have primary canines and molars present. A more established dentition would allow the maxillary and mandibular arches to better interdigitate, leading to a better integration of the dental arches as the child ages. It is unknown 40