Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
THE EFFECT OF FOUR FIRST PREMOLAR EXTRACTIONS ON THE POSTERIOR BOLTON RATIO Anthony D. Mongillo, B.S., D.M.D. A Thesis Presented to the Graduate Faculty of Saint Louis University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Dentistry 2015 © Copyright by Anthony David Mongillo ALL RIGHTS RESERVED 2015 i COMMITTEE IN CHARGE OF CANDIDACY: Professor Eustaquio A. Araujo, D.D.S, M.S.D. Chairperson and Advisor Assistant Clinical Professor Patrick F. Foley, D.D.S., M.S. Associate Professor Ki Beom Kim, D.D.S, M.S.D., Ph.D. ii DEDICATION “WHAT E'ER THOU ART, ACT WELL THY PART." —William Shakespeare Son. Brother. Husband. Dentist. Father. Orthodontist. I dedicate this work to All who gives role to my life. iii ACKNOWLEDGEMENTS A debt of gratitude is owed to all at Saint Louis University and the Center for Advanced Dental Education who allowed me to be a part of such a storied orthodontic program. To my thesis committee: Dr. Eustaquio Araujo, Dr. Ki Beom Kim, and Dr. Patrick Foley, I owe special thanks for your patience, encouragement, and guidance on this thesis topic. Thank you, Dr. Heidi Israel, for your assistance with the statistical analysis. Acknowledgements are due to the many faculty members who have played a role, whether major or minor, in my specialty education and professional development. May you all find contentment and satisfaction in knowing that you have touched innumerable others by sharing your time and talents with a rising generation. Thank you. iv TABLE OF CONTENTS List of Tables .................................................................................................................... vii List of Figures .................................................................................................................. viii CHAPTER 1: INTRODUCTION ....................................................................................... 1 CHAPTER 2: REVIEW OF THE LITERATURE ............................................................. 5 Seekers of Truth ...................................................................................................... 5 Occlusion ................................................................................................................ 5 Interarch Tooth Size Discrepancy........................................................................... 7 The Whole is Equal to the Sum of its Parts ............................................................ 8 Clinical Implications of an Interarch Tooth-Size Discrepancy............................... 9 The Significance of a Tooth-Size Discrepancy: ................................................... 12 The Great Debate: To Extract or Not to Extract? ................................................. 14 The Role of Extractions in A Tooth-Size Discrepancy ........................................ 16 Statement of Thesis ............................................................................................... 19 References ............................................................................................................. 22 Chapter 3: JOURNAL ARTICLE ..................................................................................... 25 Abstract ................................................................................................................. 25 Introduction ........................................................................................................... 27 Materials and Methods .......................................................................................... 30 Sample........................................................................................................... 30 Statistical Analysis ........................................................................................ 39 Reliability ...................................................................................................... 41 Results ................................................................................................................... 41 Discussion ............................................................................................................. 49 Interpretation of Results ................................................................................ 49 Present Outcomes and Past Studies .............................................................. 53 Clinical Significance and Implications ......................................................... 57 Conclusion ............................................................................................................ 62 Literature Cited ..................................................................................................... 63 Appendix A ....................................................................................................................... 65 Appendix B ....................................................................................................................... 68 Appendix C ....................................................................................................................... 69 Appendix D ....................................................................................................................... 71 Appendix E ....................................................................................................................... 74 Appendix F........................................................................................................................ 79 v Vita Auctoris ..................................................................................................................... 81 vi LIST OF TABLES Table 2.1- Ideal ratios and average tooth widths from Bolton's thesis. .............................. 9 Table 3.1- Comparison of Bolton's original thesis sample and this study’s sample. ........ 42 Table 3.2- Paired t-test comparing widths of corresponding upper and lower posterior teeth. ................................................................................ 42 Table 3.3- Ratios and measurements describing non-extraction and four first premolar extraction cases. ......................................................... 43 Table 3.4- Comparison of non-extraction and extraction Bolton ratios as well as expected and observed Bolton ratios. ............................................. 44 Table 3.5- Linear regression of variables explaining variation in net residual space. ...... 49 Table A- List of Abbreviations ......................................................................................... 65 Table B- Significant variable from NRS2Grp ANOVA ................................................... 68 Table C- Significant variables from NRS3Grp ANOVA ................................................. 69 Table D- Linear regression output of all significant variables from NRS2Grp and NRS3Grp ANOVA ................................................................. 71 Table E- Backward regression of all significant variables from NRS2Grp and NRS3Grp ANOVA. ................................................................ 74 Table F- Individual regression for U5vsL5 and U5sWidth. ............................................. 79 vii LIST OF FIGURES Figure 2.1- Ambiguity inherent in interpreting the overall Bolton ratio. ......................... 11 Figure 3.1- Measuring the mesiodistal widths and defining the clinical crown margin of each tooth. .......................................................................... 32 Figure 3.2- “Ideal 3-3" digital setup. ................................................................................ 34 Figure 3.3- Occlusion schemes for digital setups. ............................................................ 36 Figure 3.4- Example "Ideal 4's" digital setup. .................................................................. 37 Figure 3.5- Example of measuring residual space in the mandibular arch. ...................... 38 Figure 3.6- Scatterplot of NetResSpc and NetPBDiscrep for each case with the regression line and equation. ........................................................... 45 Figure 3.7- Frequency of cases grouped by net residual space......................................... 46 Figure 3.8- Two scenarios resulting from prioritizing space closure over ideal occlusion ....................................................................................... 60 Figure 3.9- Regression equation for predicting residual space ......................................... 61 Figure D- Charts from linear regression of all sig variables from NRS2Grp and NRS3Grp ANOVA ................................................................ 73 Figure E- Charts for backward regression of all sig variables from NRS2Grp and NRS3Grp ANOVA ................................................................ 78 viii CHAPTER 1: INTRODUCTION The Bolton tooth-size discrepancy analysis is a diagnostic tool employed to help identify potential limitations in detailing and finishing a patient’s final occlusion before as much as one bracket is placed. Take, for example, the anterior Bolton ratio which is most commonly used as a reference against which a patient’s anterior tooth-size ratio is compared. A mismatching anterior Bolton ratio will indicate whether the anterior teeth are too large, too small, or just right for proper anterior overjet and overbite. Armed with this knowledge, the orthodontist is able to inform the patient and plan for restorative build-ups or selective interproximal reduction in teeth of one arch or the other at the pretreatment consultation. However, little is known about the posterior Bolton ratio, how it is affected by extracting posterior teeth, and its application in the orthodontic setting. Many factors contribute to ideal dental occlusion. Perfect occlusion, as defined in textbooks, takes into account the intercuspation of maxillary and mandibular buccal and lingual cusps within the fossae or on the marginal ridges of the opposing arch. The maxillary lingual cusp tips should occlude in the fossae or on the marginal ridges of mandibular teeth. The maxillary buccal cusp tips are non-occluding, but should fit within the embrasures or buccal grooves of the mandibular teeth. Mandibular buccal cusps tips should occlude in the fossae or on the marginal ridges of maxillary teeth. While the mandibular lingual cusps are non-occluding they should fit in the lingual embrasures or lingual grooves of maxillary teeth. Prominent contributors to the orthodontic specialty, Angle and Andrews, cite the relative molar positions as “keys” to occlusion.1,2 Other major factors influencing dental 1 occlusion include rotations, tip, torque, the occlusal plane, and interdental spacing. When all factors are in harmony, textbook-perfect occlusion is possible to achieve. Studying cases deemed to have “excellent” occlusion, Bolton’s landmark study3 published in 1958 included models of 55 patients. The aim was to describe “excellent” occlusion using a mathematical ratio of the sum widths of bottom teeth versus top teeth. He found that excellent occlusion can be described as having an anterior ratio of 77.2% and an overall ratio of 91.3%. Bolton did not report a posterior ratio. Applying the ratios derived from cases with excellent occlusion to a case prior to orthodontic treatment could help indicate whether the top or bottom teeth are too large, too small, or just right for excellent occlusion. An analogy helpful for understanding the Bolton ratio would be aligning fence posts and post holes. If the posts of a prefabricated section of a fence are spaced every 10 feet, the post holes in the ground should be spaced every 10 feet for the fence posts to fit in the holes. This represents an ideal 1:1 ratio. However, if the ratio is changed to 1:1.2, for example, the fence posts are spaced every 10 feet and the post holes are spaced every 12 feet. The result is that the fence will not fit in the holes. The same goes for teeth in excellent occlusion. However, orthodontic treatment often requires extraction of teeth for various reasons. Although the popularity of extracting teeth for orthodontic purposes has varied over time, the first premolar teeth have continued to be those most commonly extracted as part of orthodontic treatment. Extracting teeth may alter the excellent occlusal relationship found in a full complement of teeth as described by Bolton’s overall ratios. One can easily understand that by extracting posterior teeth the anterior ratio would not 2 change, but the overall and posterior ratios of teeth would change—especially when the maxillary and mandibular teeth are not equal sizes. Bolton4 predicted a new expected overall ratio resulting from the extraction of four premolars. He predicted that the new overall ratio should be between 87-89% based on average premolar tooth widths. Many investigators have used the overall ratio that Bolton predicted for cases involving premolar extractions to study the effect of different extraction patterns on occlusion. However, Bolton’s predicted ratio was based on mathematical calculation that simply omits the average widths of extracted teeth. This does not take into consideration the articulation of the cusps, fossae, and marginal ridges of the remaining teeth as did his original sample. For accuracy, any newly described ratios for extraction cases should be calculated in the same way that the original anterior and overall ratios were calculated from Bolton’s non-extraction cases—that is, from cases treated with extraction and resulted in excellent occlusion. A recent study by Kayalioglu et al.5 measured 53 post-treatment models from patients treated with four first premolar extractions that resulted in good occlusion and reported a new ideal overall ratio based on this sample. The newly reported ideal overall ratio was slightly, but significantly larger than Bolton’s predicted value. This may indicate that many studies using Bolton’s predicted value for cases treated with premolar extraction may have made erroneous assumptions and/or conclusions about the occlusal consequences of different premolar extraction patterns. Using a novel method utilizing digital extractions and setups, this study seeks to add to the existing literature related to the Bolton ratios by: First, reporting a posterior Bolton ratio that can be expected from full dentition cases with excellent occlusion as 3 described by Bolton’s anterior and overall ratios; Second, describing the effect of four first premolar extractions on the posterior Bolton ratio including any compromises in the ability to finish such cases with excellent occlusion. 4 CHAPTER 2: REVIEW OF THE LITERATURE SEEKERS OF TRUTH Although the paradigms for orthodontic treatment have shifted, ebbed, and flowed from maximizing dental and oral health, masticatory efficiency, temporomandibular joint function, post-treatment stability, and simple esthetics, what is sure is that humans have been moving teeth for millennia. Some have even attributed the natural masticatory system to “the work of the great Creator, who could design and construct such a marvelous and simple piece of mechanism.”6 Many have studied the dental ‘mechanism’, searching for immutable laws in occlusal design and function. Notable contributors include Bonwill6 for using mathematics and geometry to describe the articulation of human teeth, EH Angle1 for describing the “key to occlusion” and developing the edgewise technique, Bolton3 for describing excellent occlusion using a mathematical ratio of lower versus upper tooth widths, and Andrews2 for identifying several specific variables, or keys, contributing to a normal occlusion as well as developing the straight wire appliance that is so ubiquitous today. OCCLUSION Bonwill’s contribution to dentistry includes the articulator which mimics the ginglymoarthrodial function of the mandible in the Glenoid fossa and upon which full and partial dentures are able to be constructed and adjusted extraorally. Speaking toward those dentists who failed to see his articulator’s potential, he stated, “A tooth may be elegantly shaped and colored, yet if it lacks the proper shape…and unskillfully set in the 5 arch, it is a failure.”6 Skillfully setting natural, living teeth in the arch is the task of an orthodontist. EH Angle ushered in the modern era of orthodontics. Aside from inventing the edgewise technique that is still employed in variants today, he is credited with describing the most simple and enduring dental system for classifying malocclusion and normocclusion in orthodontics. He said, “The key to occlusion is the relative position of the first molars. In normal occlusion the mesiobuccal cusp of the upper first molar is received in the sulcus between the mesial and distal buccal cusps of the lower…”1 Specifically, a normocclusion exists when the mesiobuccal cusp tip aligns with the mandibular buccal groove. When positioned anteriorly a Class II is designated, and Class III when posteriorly positioned. With the “key to occlusion” orthodontists can effectively identify, classify, communicate, and plan treatment to accomplish orthodontic correction. However, simplifying the treatment of malocclusions to the correction of merely one tooth does injustice to the complexity of treatment facing specialists daily. EH Angle recognized this, stating, “The sizes, forms, interdigitating surfaces, and positions of the teeth in the arches are such as to give one another, singly and collectively, the greatest possible support in all directions.”1 Andrews’ “The Six Keys to Normal Occlusion” is a seminal paper describing ideal dental positions.2 As did Angle, Andrews ascribed a similar importance to molar position, with the modification that the maxillary first molar’s distal slope of the distobuccal cusp should contact the mandibular second molar’s mesial slope of the mesial marginal ridge. He also listed crown angulation (tip), crown inclination (torque), rotations, spaces, and occlusal plane as the other factors affecting normal occlusion. So accurate and thorough 6 was his description of a ‘normal’ occlusion that the now-ubiquitous straight-wire appliance was developed largely from of his contributions. However, much is left to chance by assuming that all the teeth will intercuspate ideally and occlude merely by placing molars in the ideal position. For teeth to properly occlude and intercuspate each tooth must not only be in the proper position, but must also occupy the proper amount of space mesiodistally to be in proximal contact with its neighbor. INTERARCH TOOTH SIZE DISCREPANCY While acknowledging Ballard’s7 and Neff’s8 pioneering work, Dr. Wayne A. Bolton studied 55 pre and post-treatment models with ‘excellent’ occlusion as a master’s candidate at the University of Washington in 1952.9 Among other factors such as interincisal angle and overbite, he measured the mesiodistal widths of maxillary teeth and mandibular teeth and compared them in terms of a ratio. Six years later he published his thesis.3 The interarch ratios are calculated as follows from Bolton’s 1958 paper: Anterior Ratio: Sum Mandibular "1s, 2s, 3s" x 100 = Anterior Ratio Sum Maxillary "1s, 2s, 3s" Overall Ratio: Sum Mandibular 12 teeth x 100 = Overall Ratio Sum Maxillary 12 teeth Bolton found that for teeth with excellent intercuspation, the ratio of anterior mandibular tooth widths versus the anterior maxillary tooth widths has a mean proportion of 77.2 ± 0.22%, with a standard deviation of 1.65%. The average overall ratio from Bolton’s cases is 91.3 ± 0.26%, with a standard deviation of 1.91%. 7 Ratios higher than the ideal indicate that the teeth in the mandibular arch are larger (or teeth in the maxillary arch are smaller) than what is found to describe for excellent occlusion. A lower ratio indicates that teeth in the mandibular arch are smaller (or maxillary teeth are larger) than what was found to describe excellent occlusion. When anterior or overall ratios do not match the ratios Bolton found, an interarch toothsize discrepancy—hereafter referred to as an “ITSD”—can be diagnosed. THE WHOLE IS EQUAL TO THE SUM OF ITS PARTS According to Bolton, “The dental arches must be thought of as consisting of two components, the anterior and posterior.”4 It must be noted, however, that Bolton does not report in published literature a ratio that describes the proportion posterior teeth (the first and second premolars and first molars) found in excellent occlusion. He only states, The buccal segments were divided into units in an attempt to analyze the cuspal interdigitation and possibly localize tooth size discrepancy. It is felt that the findings lack clinical significance; therefore, the buccal measurements are being omitted from this paper. 3 Why this would lack clinical significance is unclear. Would not ‘excellent’ occlusion depend on the intercuspation of posterior teeth just as much as the anterior teeth? Why then, report an overall ratio for ‘excellent’ occlusion—one that includes all teeth, anterior teeth and posterior—if a possible ITSD in the posterior would “lack clinical significance”? The answer is that it does not, in fact, lack clinical significance. Bolton had the data to report an anterior and posterior ideal ratio of teeth. In his thesis9 published at the University of Washington in 1952, Bolton reports the average tooth widths and standard deviations of each tooth type from central incisors to first molars. To reveal the ideal posterior Bolton ratio from his sample of cases with ‘excellent’ occlusion, a simple calculation can be made as follows: 8 Posterior ratio: Sum Mandibular "4s, 5s, 6s" x 100 = Posterior Ratio Sum Maxillary "4s, 5s, 6s" Applying this formula to the tooth widths reported in Bolton’s thesis would have allowed him to arrive at an ideal posterior ratio (see Table 2.1 for tooth widths, and Table 3.1 for the posterior ratio). One can only speculate why Bolton failed to report the ideal posterior ratio. Perhaps he truly felt it, “lacked clinical significance.” Table 2.1- Ideal ratios and average tooth widths from Bolton's thesis. Ratios Maxillary Mandibular Bolton’s Original Sample Mean 77.20% Anterior 91.30% Overall 8.82 mm Central 6.96 mm Lateral 7.91 mm Canine 7.04 mm 1st Premolar 6.84 mm 2nd Premolar 10.4 mm 1st Molar 5.42 mm Central 5.94 mm Lateral 6.93 mm Canine 7.15 mm 1st Premolar 7.27 mm 2nd Premolar 11.14 mm 1st Molar SD 1.65 1.91 0.42 0.48 7.91 0.46 0.39 0.58 0.31 0.26 0.37 0.38 0.39 0.62 N 55 55 110 110 110 110 110 110 110 110 110 110 110 110 CLINICAL IMPLICATIONS OF AN INTERARCH TOOTH-SIZE DISCREPANCY Given an ideal anterior Bolton ratio and an ideal overall ratio, the posterior Bolton ratio must be ideal and the occlusion should be ‘excellent.’ An alternate way of looking at it is the ratio of anterior teeth resulting in excellent occlusion is equally important as 9 the ratio of posterior teeth resulting in excellent occlusion. Together, they create an overall ratio of teeth with excellent occlusion. Conversely, for any given case, an exaggerated or deficient anterior or posterior ratio can have one of two effects on the overall Bolton ratio. It could either derange the overall ratio, or compensate for the other, creating an ideal overall ratio. This begs the question, what would happen in a case with a large anterior Bolton ratio and a small posterior Bolton ratio, or small anterior and large posterior ratio, resulting in an ideal overall Bolton ratio? The answer reveals the insignificance of the overall Bolton ratio. A large anterior Bolton ratio would indicate that the maxillary anterior teeth are small in comparison to the mandibular anterior teeth—most likely due to small maxillary laterals or large mandibular centrals. Either way, when midlines are matched, canines intercuspate ideally, and the mandibular anterior teeth are ideally aligned, spacing would be evident somewhere between the maxillary anterior teeth. Now, considering the small posterior Bolton ratio in this case, one would see the maxillary first and second premolars and first molars well aligned and in proximal contact from the distal of the maxillary canine through the maxillary first molar. Yet, there would be spacing somewhere between the mandibular posterior teeth. The result of an ideal overall Bolton ratio with a large anterior and small posterior ratio is a case with spacing in the maxillary anterior and mandibular posterior teeth. The importance, then, of Bolton ratios seems to lie in the anterior segments and posterior segments separately, not collectively as the overall ratio. Figure 2.1 is a diagram illustrating three possible variations of a normal overall Bolton ratio. 10 Large anterior Small posterior Ideal overall Ideal anterior Ideal posterior Ideal overall Small anterior Large posterior Ideal overall Figure 2.1- Ambiguity inherent in interpreting the overall Bolton ratio. Reduced tooth sizes exaggerated for illustrative purposes. Darkened teeth reduced to 75% of original size. Sketch by present author. Other researchers have acknowledged the posterior segment is a factor to consider. While determining the ideal Bolton ratios for a Peruvian population, Bernabè et al.10 noticed that the anterior segment was not significantly different from Bolton’s sample but that the overall ratio was significantly different. They report that “the toothwidth discrepancy would be more of a concern in the posterior segment than in the anterior” in his population. An anterior ITSD is common. The prevalence of a clinically significant anterior ITSD has been reported to range from 22 – 33.7% in the orthodontic population.3,4,11,12 Indeed, it has long been recognized that an anterior ITSD can adversely affect finishing a case. The maxillary lateral incisors are recognized as one of the most widely varying 11 teeth in terms of width in the entire dental arch. A lateral that is looks small in comparison to the width of the central is usually the first suspect as the culprit contributing to an ITSD. However, Sharma et al.13 have shown that the visual method of screening for an ITSD has been shown to be unreliable. Options for addressing an anterior ITSD include restorative build-ups or veneers to increase the mesiodistal widths, or interproximal reduction of the incisors. Another option is to leave diastema between the laterals and centrals or laterals and canines. It may be assumed that similar options exist for cases with a posterior ITSD. Bulked restorations or prostheses can increase the mesiodistal widths of teeth if necessary. Interproximal reduction of enamel may reduce tooth mass if necessary. Alternately, intentionally leaving a diastema is an option to treat a posterior ITSD. Although the maxillary laterals are generally accepted as the cause of an anterior ITSD, the lateral incisor actually takes second place in width variability. The maxillary lateral incisors variability is preceded only by the mandibular second premolars, and followed by maxillary second premolars, then mandibular central incisors. In fact, Smith et al.14 report that these four groups of teeth account for half of the variation Bolton analyses. But, how much ITSD is too much? THE SIGNIFICANCE OF A TOOTH-SIZE DISCREPANCY There seems to be no consensus as to what magnitude, whether statistical, millimetric, or proportional, is clinically significant. Many epidemiological studies have used 2 standard deviations, or “2-3 mm,” from the normal ratios as the cutoff to describe a clinically significant proportion of patients within populations with a tooth size discrepancy.11,15-17 While this may be appropriate for determining the prevalence of 12 populations with a large deviation from what is normal for that population, it says nothing of the chairside clinical significance. Ascribing clinical significance to a linear, millimetric measurement allows the orthodontist to plan prior to treatment if restorative or operative measures may be necessary, and to what degree, in order to finish the case with excellent occlusion. Proffit et al.18 and Bernabè et al.10 claim that 1.5 mm of discrepancy is clinically significant. Othman and Harradine,19 however, claim this amounts to 0.75 mm per side—possibly “too small a potential error to be clinically significant.” They, Sharma et al.,13 and Gaidyte and Baubiniene20 offer 2 mm (or 1 mm per side) as a tooth size discrepancy more likely to cause occlusal problems. It is interesting to note that the American Board of Orthodontics, though not directly, has weighed in on the matter by assessing one point for interproximal spaces greater than 0.5 mm.21 Another method of designating clinical significance that has been proposed is to consider any ratio outside of an acceptable range from the norm as significant. After all, average tooth sizes vary from person to person. Therefore, a 1 mm discrepancy, for example, may represent a larger issue for a person with generally small teeth than someone with generally large teeth. Bolton4 recommends ± 1 standard deviation from the values he reports as a point at which re-evaluation of clinical treatment is needed. Endo et al.16 and Othman and Harradine19,22 recommend that an overall tooth-size discrepancy greater than or equal to 2 standard deviations from the norm is the threshold for the amount of discrepancy that is clinically significant enough to exhibit noticeable occlusal compromise or require treatment. 13 Though consensus is lacking, studies generally recommend 2 SD from the norm or 1.5 to 2 mm as a tooth size discrepancy significant enough to affect the occlusion and merit treatment consideration. THE GREAT DEBATE: TO EXTRACT OR NOT TO EXTRACT? Historically, trends in treating an orthodontic malocclusion with or without extractions have come full circle. The early pioneers of modern orthodontics, such as Angle,1 believed that the human jaws were capable of housing all 32 teeth within the arches. They expanded dental arches to fit teeth into ideal occlusal relationship, believing that bone would follow based on Wolff’s Law.23 Angle’s contemporary, and most ardent opponent, Case, published articles and participated in heated debates supporting extractions in orthodontic treatment.24 Among the principle reasons for extractions included crowding relief and post-treatment stability. Thus began the Great Debate of 1911 on extraction.25 Though posting a higher extraction rate, even Case rarely extracted in comparison to the height of later extractionist’s extraction rates. Tweed, a respected pupil of Angle, followed his master’s non-extraction philosophy until he came to terms with the fact that his best efforts were frustrated in post-treatment retention. Citing Brodie’s research26 demonstrating the impossibility of interstitial basal bone growth as well as his own patient’s lip fullness and bimaxillary protrusion, Tweed attributed his cases’ failure to expansion’s tendency to cause proclination of the mandibular incisors, leaving them unsupported and not upright over basal bone. Rather than flaring incisors out, his solution was to extract premolar teeth and use the space to keep the mandibular incisors upright over basal bone.27 14 In a classic story that changed orthodontic history and reversed the aversion to premolar extraction, Tweed re-treated 100 of his previous “failures” at no charge with premolar extractions and presented his work for all to see at the AAO convention. Initially regarded as heresy,28 the extraction pendulum swung the other way, and premolar extraction became the accepted norm. According to Proffit,29 extraction rates at the orthodontic residency program at UNC went from 30% of all cases in 1953 to 76% in 1968, then back down to 28% in 1993. Reasons for the decline in extraction rate after the Tweed years include improved application and acceptance of functional and extra-oral appliances,30,31 bonded brackets eliminate the thickness of bands,32 space preservation in the transitional dentition,33 as well as general risk-and litigation reduction policies.34-36 Although modern extraction rates may not be as high as they once were, Baumrind’s study37 indicates that when faced with crowding or dentoalveolar protrusion, up to 2/3rd of current orthodontists agree upon extraction treatment. Baumrind’s followup study38 asking orthodontists why they chose to extract, the four most common reasons for extracting teeth are: First, to reduce excessive crowding (49% of responses); Second, to reduce incisor protrusion (14% of responses); Third, the need to correct the profile (8% of responses; Fourth, due to Class II severity (5% of responses). Many extraction patterns can address the above problems and are employed depending on each patient’s initial diagnostic presentation. For Class II patients requiring extractions, upper first and lower second premolar extractions can optimize correction to Class I. Occasionally, molars are left in Class II and canines are corrected to Class I by extracting upper first premolars only. For Class III patients, lower first 15 premolars can be extracted to camouflage the skeletal discrepancy and achieve Class I canine relationship. According to Proffit,29 first premolar extractions are the most common extraction pattern orthodontists choose to correct excessive crowding, reduce protrusion, and to eliminate or prevent adverse profile appearances. Lopatiene39 has shown that ITSD do not show predilection to any one Angle Classification over another. Therefore, given an ITSD, extraction decisions should not be based on Angle Classification, but should be based on the ability to treat to maximum ideal intercuspation. Bolton4 advocated for the selective extraction of teeth, not based on biomechanical efficiency for treating a specific Class of malocclusion, but based on satisfying ideal a ratios found from his studies so that ‘excellent’ anterior and overall occlusion can result. In the ideal orthodontic world, teeth can be moved in any direction without side-effects. Traditionally, extra-oral and intra-oral anchorage such as headgear and elastics, and more recently, endosteal anchorage such as miniscrews have permitted orthodontists to move teeth in any direction with less anchorage loss. THE ROLE OF EXTRACTIONS IN A TOOTH-SIZE DISCREPANCY Adding intrigue to Bolton’s claim that tooth size discrepancies affecting buccal segment intercuspation may “lack clinical significance,” one of Bolton’s main conclusions in his 1958 publication is the “need for considering premolar sizes on an individual basis before the final decision is made in extraction cases.”3 He offers that the first premolars are the teeth of choice to remove because their widths are most similar. The second extraction pattern of choice is the maxillary first premolar and mandibular second premolar. The least ideal extraction pattern is the second premolars. It can be 16 inferred from these claims that maintaining ‘excellent’ occlusion of posterior teeth is only possible when similar sized teeth are extracted—the idea being that, given ideal tooth size ratios, closing similar sized extraction sites on top and bottom will maintain the ideal tooth-width ratios posterior to the extraction site and their potential for ideal occlusal relationship. Many investigators have attempted to reveal an ideal overall Bolton ratio of cases treated with extractions. In his 1962 paper, Bolton4 reported that a premolar extraction case removing equally sized premolars should result in an 89% overall ratio, while an 87% ratio should be expected in a case where extracted mandibular premolars were larger than the maxillary premolars. In fact, using the average tooth widths from his thesis as shown in Table 2.1, a four first premolar extraction case should result in an 89.67% overall Bolton ratio. This range of predicted ideal overall ratios in premolar extraction cases was derived by mathematical calculation that simply omits the average size of the extracted premolars from the overall ratio equation. It has been shown that any premolar extraction pattern results in a decreased post-treatment overall Bolton compared to the pre-treatment overall ratio.40 Gaidyte & Baubiniene,20 grouped pre-treatment cases into small, normal, and large overall Bolton categories, then simulated different premolar extraction patterns by omitting that premolar’s width in the overall Bolton ratio measurement. This was done to see which extraction pattern came closest to Bolton’s reported ideal 88% (average of 87% - 89%. They advocate that the best post-treatment results, judged by attaining an overall Bolton ratio of 88%, is attained by extracting all first premolars or maxillary first premolars and mandibular second premolars in small pre-treatment overall Bolton cases, 17 and all second premolars in normal and high pre-treatment Bolton cases. However, much hangs on the assumption that 88% is the magic number that results in ideal occlusion and that omitting premolar widths from the calculation will guarantee excellent occlusion. Also, because they don’t report the anterior ratio one cannot interpret what the reported overall Bolton ratio in this sample truly means. Perhaps the most thorough and important study of the effect of premolar extraction on the Bolton ratios was undertaken by Kayalioglu et al.5 They calculated Bolton ratios of 53 post-treatment cases treated with four first premolar extractions and good occlusion as judged by the Peer Assessment Review scores. They found that the overall Bolton ratio should be 89.28% in a four first-premolar extraction case and explained that this ratio is only achievable when the pre-treatment overall ratio was small. This closely matches the ideal overall Bolton ratio of 89.67% for a four first premolar extraction case deduced from the data in Bolton’s thesis. An overarching major weakness of all of these studies is the lack of standardizing the anterior Bolton ratios of cases included in these studies. It is unknown what factors the anterior Bolton ratio played in the calculated pre-and post-simulation overall Bolton ratios. Most of these studies simply omit a tooth measurement in calculating the overall ratio and do not take into consideration the case’s actual finished quality. To reiterate, just because an overall Bolton ratio is near the ‘ideal’ mean ratio doesn’t mean that ‘excellent’ occlusion is achieved. Excellent occlusion is most likely to be achieved with both an ideal anterior ratio and ideal posterior ratio. None of these studies report a pretreatment posterior Bolton ratio for their sample. 18 While studying gender and racial differences in the Bolton ratio, Smith et al.14 reported that the posterior Bolton ratio for a non-extraction case ranges from 104% in Caucasians to 107% in blacks. However, these describe population averages, not the posterior ratio for cases with excellent occlusion. One final study by Akinci and Uysal41 deserves mention. When evaluating cases treated with non-extraction, two, or four premolar extractions according to the ABO grading criteria,21 they noticed that four premolar extraction cases were assessed significantly more points for compromised occlusal contacts and occlusal relationships than non-extraction cases. The points assessed for compromised occlusion could be due to an ITSD created by extracting teeth, and then forcing closed the spaces resulting from the tooth-size discrepancy. STATEMENT OF THESIS The anterior and overall Bolton ratios and their clinical use are widely known. However, the overall Bolton is not as informative as the individual anterior and posterior Bolton ratios separately. Bolton did not report an ideal ratio for posterior teeth in nonextraction cases, nor did he report an ideal ratio for posterior teeth in extraction cases even though he had the data to do so. Instead, he offered a predicted overall ratio for cases with excellent occlusion based on the assumption that extracting teeth of similar size would maintain excellent occlusion. Other studies used his predicted overall ratio for extraction cases, possibly erroneously. Also, some of these studies did not ensure that their sample was similar to Bolton’s sample by selecting cases whose anterior Bolton ratios were within the range reported by Bolton to describe cases with ‘excellent’ occlusion. 19 Considering that extraction treatment is currently a viable treatment option and first premolars are the most commonly extracted teeth, one should know the effect of a treatment plan involving the extraction of first premolars on the posterior tooth ratio. Employing a novel method utilizing digitized models that undergo virtual extraction of the four first premolars and virtual setups into ‘excellent’ occlusion, this study seeks to add to the existing literature related to the Bolton ratios by: First, reporting a posterior Bolton ratio that can be expected for non-extraction cases with excellent occlusion as described by Bolton’s ideal anterior and overall ratios; Second, describing the effect of the extractions on the expected posterior Bolton ratio; Third, describing the effect of the extractions on the observed posterior Bolton ratio through performing digital setups with ‘excellent’ occlusion; Fourth, correlating discrepancies between expected and observed posterior Bolton ratios to tooth size factors. The results of this study can be used by orthodontists as follows: By simply omitting the width of the first premolars, an orthodontist can calculate his expected posttreatment posterior Bolton ratio. Then, by comparing his expected post-treatment posterior Bolton ratio to an ideal posterior Bolton ratio for first premolar extraction cases, the orthodontist should be able to gauge whether an ITSD exists in the remaining posterior dentition and judge its clinical significance. This study will also show which teeth tend to have the greatest influence on the post-extraction occlusion result. The orthodontist will be able to compare his patient’s tooth widths and ratios to the ideal widths and ratios reported herein in order to help him determine the effect of extracting four first premolars on his patient’s occlusion. 20 Armed with this diagnostic tool, the orthodontist can inform the patient of potential compromises to the final occlusion or ability to close extraction spaces, alter extraction patterns, plan for necessary interproximal reduction or restorative buildups, or opt to leave interproximal spaces. 21 REFERENCES 1. Angle EH. Classification of Malocclusion. The Dental Cosmos: a monthly record of dental science. 1899;41(3):248-64. 2. Andrews LF. The six keys to normal occlusion. Am J Orthod. 1972;62(3):296-309. 3. Bolton WA. Disharmony In Tooth Size And Its Relation To The Analysis And Treatment Of Malocclusion. Angle Orthod. 1958;28(3):113-30. 4. Bolton WA. The clinical application of a tooth-size analysis. Am J Orthod. 1962;48(7):504-29. 5. Kayalioglu M, Toroglu MS, Uzel I. Tooth-size ratio for patients requiring 4 first premolar extractions. Am J Orthod Dentofacial Orthop. 2005;128(1):78-86. 6. Bonwill WG. The Scientific Articulation of the Human Teeth as Founded on Geometrical, Mathematical, and Mechanical Laws. The Dental Cosmos: a monthly record of dental science. 1899;21:617-43. 7. Ballard ML. Asymmetry in Tooth Size: A Factor in the Etiology, Diagnosis and Treatment of Malocclusion. Angle Orthod. 1944;14(3):67-70. 8. Neff CW. Tailored occlusion with the anterior coefficient. Am J Orthod. 1949;35(4):309-13. 9. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Seatle, WA: University of Washington; 1952. 10. Bernabé E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of Peruvian adolescents. Am J Orthod Dentofacial Orthop. 2004;125(3):361-5. 11. Freeman JE, Maskeroni AJ, Lorton L. Frequency of Bolton tooth-size discrepancies among orthodontic patients. Am J Orthod Dentofacial Orthop. 1996;110(1):24-7. 12. Richardson ER, Malhotra SK. Mesiodistal crown dimension of the permanent dentition of American Negroes. Am J Orthod. 1975;68(2):157-64. 13. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North Indian orthodontic patients. Contemp Clin Dent. 2011;2(3):170-5. 14. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3 populations: “Does Bolton’s analysis apply?”. Am J Orthod Dentofacial Orthop. 2000;117(2):169-74. 15. Araujo E, Souki M. Bolton Anterior Tooth Size Discrepancies Among Different Malocclusion Groups. Angle Orthod. 2003;73(3):307-13. 16. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among different malocclusion groups. Am J Orthod Dentofacial Orthop. 1989;95(6):457-61. 17. Johe RS, Steinhart T, Sado N, Greenberg B, Jing S. Intermaxillary tooth-size discrepancies in different sexes, malocclusion groups, and ethnicities. Am J Orthod Dentofacial Orthop. 2010;138(5):599-607. 22 18. Proffit W, Ackerman J. Contemporary orthodontics. St Louis, MO: C.V. Mosby; 1986. 19. Othman S, Harradine N. Tooth Size Discrepancies in an Orthodontic Population. Angle Orthod. 2007;77(4):668-74. 20. Gaidyte A, Baubiniene D. Influence of premolar extractions on tooth size discrepancy. Part two: Analysis of Bolton values. Stomatologija. 2006;8(1):25-9. 21. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al. Objective grading system for dental casts and panoramic radiographs. Am J Orthod Dentofacial Orthop. 1998;114(5):589-99. 22. Endo T, Uchikura K, Ishida K, Shundo I, Sakaeda K, Shimooka S. Thresholds for Clinically Significant Tooth-Size Discrepancy. Angle Orthod. 2009;79(4):740-6. 23. Wolff J. The Law of bone remodelling: Berlin ; New York : Springer-Verlag, c1986.; 1986. 24. Case CS. The question of extraction in orthodontia. Am J Orthod. 1911;50(9):66091. 25. Pollock HC. The extraction debate of 1911 by Case, Dewey, and Cryer. Am J Orthod. 1964;50(9):656-8. 26. Brodie AG. Some recent observations on the growth of the face and their implications to the orthodontist. Am J Orthod Oral Surg. 1940;26(8):741-57. 27. Tweed CH. Indications for the extraction of teeth in orthodontic procedure. Am J Orthod Oral Surg. 1944;30(8):405-28. 28. Hellman M. Fundamental principles and expedient compromises in orthodontic procedures. Am J Orthod. 1944;34(1):18-26. 29. Proffit WR. Forty-year review of extraction frequencies at a university orthodontic clinic. Angle Orthod. 1994;64(6):407-14. 30. Fränkel R. The treatment of Class II, Division 1 malocclusion with functional correctors. Am J Orthod. 1969;55(3):265-75. 31. Kloehn SJ. Guiding Alveolar Growth and Eruption of Teeth To Reduce Treatment Time and Produce A More Balanced Denture and Face. Angle Orthod. 1947;17(1):10-33. 32. Oftedal B, Wisth J. Residual extraction sites after orthodontic treatment: Part 1. At debanding1982 1982-02-01 00:00:00. 11-9 p. 33. Brennan MM, Gianelly AA. The use of the lingual arch in the mixed dentition to resolve incisor crowding. Am J Orthod Dentofacial Orthop. 2000;117(1):81-5. 34. Machen DE. Orthodontic treatment and facial appearance. Am J Orthod Dentofacial Orthop. 1991;99(2):185-6. 35. Perry CK, Jr. TMJ dysfunction litigation--Pandora's Box opens up. J Mich Dent Assoc. 1988;70(11-12):533-8. 36. Wheeler PW. Risk preclusion. Am J Orthod Dentofacial Orthop. 1992;101(2):194-5. 23 37. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part 1— Interclinician agreement. Am J Orthod Dentofacial Orthop. 1996;109(3):297-309. 38. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part II. Analysis of clinicians' stated reasons for extraction. Am J Orthod Dentofacial Orthop. 1996;109(4):393-402. 39. Lopatiene K, Dumbravaite A. Relationship between tooth size discrepancies and malocclusion. Stomatologija. 2009;11(4):119-24. 40. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size discrepancies. Angle Orthod. 2004;74(4):508-11. 41. Akinci Cansunar H, Uysal T. Comparison of orthodontic treatment outcomes in nonextraction, 2 maxillary premolar extraction, and 4 premolar extraction protocols with the American Board of Orthodontics objective grading system. Am J Orthod Dentofacial Orthop. 2014;145(5):595-602. 24 CHAPTER 3: JOURNAL ARTICLE ABSTRACT Introduction: The anterior and overall Bolton ratios and their clinical use are widely known, but a normal overall Bolton ratio may be comprised of compensating interarch tooth size discrepancies between the anterior and posterior teeth. Therefore, the anterior and posterior Bolton ratios may be more useful separately. No ideal posterior ratio is reported in the literature. As four first premolars are the most commonly extracted teeth in orthodontics, it may be important to know how the posterior occlusion could be affected when they are extracted. The aim of this study is to investigate how the posterior Bolton ratio is affected by extracting four first premolars. Methods: Bolton’s sample was matched by selecting 55 Class I occlusion cases within one standard deviation of ideal anterior and overall Bolton ratios. Models were digitized, and tooth widths measured. Models underwent virtual extraction of four first premolars and setup of anterior and remaining posterior teeth in ideal occlusion. Where space closure compromised occlusion, preference was given to occlusion. Ideal setups were measured for residual interproximal spacing. ANOVA and linear regression tests were used to identify factors contributing to interproximal spacing. Results: The ideal non-extraction posterior Bolton ratio is 105.77 +/- 1.99%. The ideal expected posterior Bolton ratio for four first premolar extraction cases is 107.29 +/- 2.23%. Cases finished with an average of 1.1 mm net residual spacing between mandibular second premolars and first molars. 27% of cases finish with at least 1.5 mm of residual space and 16% of cases finish with at least 2 mm of residual space. The ratio of the upper second premolars to the lower second premolars and the width of the upper second premolars best explain residual 25 space (R = 0.554, R square = 0.307). A regression equation for predicting residual space is offered. Conclusion: A case with ideal anterior, posterior, and overall Bolton ratios treated with four first premolar extractions and ideal occlusion will likely finish with some spacing in the mandible. Closing spaces may compromise the occlusion. The best occlusion results when the maxillary second premolars are small in relation to the lower second premolars. 26 INTRODUCTION Like the ratio describing the ideal distances between fence posts versus distances between fence post holes that result in excellent post and post-hole alignment, Bolton’s1 anterior and overall ratios describe tooth proportions that result in “excellent occlusion.” Many factors contribute to ideal dental occlusion. Angle2 and Andrews,3 cite the relative molar positions as “keys” to occlusion. Other major factors influencing dental occlusion include rotations, tip, torque, the occlusal plane, and interdental spacing.3 Interdental spacing is one manifestation of an interarch tooth size discrepancy (ITSD), or “Bolton discrepancy.” While acknowledging the pioneering work accomplished by Ballard4 and Neff,5 Dr. Wayne A. Bolton developed the Bolton tooth-size discrepancy analysis as a diagnostic tool to be employed to help identify potential limitations in detailing and finishing a patient’s final occlusion before as much as one bracket is placed.6 Comparing Bolton’s ideal ratios and the ratios describing a patient’s dentition could indicate whether teeth are too large, too small, or just right for proper intercuspation, and whether treatment aimed at reducing the discrepancy may be warranted to improve the occlusion. Bolton attributes clinical significance to a discrepancy more than one standard deviation away from his reported ideal ratios.6 The American Board of Orthodontists Cast-Radiograph Examination assesses points for any spaces greater than 0.5 mm.7 Others recommend that 1.5 to 2 mm is the threshold for clinical significance.8-12 With this knowledge, the orthodontist is able to recognize an ITSD, inform the patient, and plan for restorative build-ups or selective interproximal reduction of appropriate teeth at the pre-treatment consultation. 27 Bolton’s landmark thesis study from 1952,13 later published in 1958,1 included a sample of models from 55 patients with ‘excellent’ occlusion. Using ratios of lower teeth to upper teeth, ‘excellent’ occlusion can be described as having an anterior ratio of 77.2% and an overall ratio of 91.3%. The overall ratio is comprised of the anterior and the posterior teeth. It is important to note that an anterior tooth size discrepancy may be masked by a compensating posterior tooth size discrepancy, resulting in a normal overall tooth size ratio. As the sum of its parts, the overall ratio may be less important than the anterior and posterior tooth size ratios individually. However, little is known about the posterior Bolton ratio, how it is affected by extracting posterior teeth, and its application in the orthodontic setting. According to Proffit,14 nearly 28% of current orthodontic patients undergo extractions. Orthodontists often agree on the need to utilize extraction treatment.15 Reasons for prescribing extractions as part of orthodontic treatment include the need to reduce excessive crowding and incisor protrusion, the need to correct the profile, and to correct a Class II malocclusion.16 Extracting teeth may alter the excellent occlusal relationship found in a full complement of teeth as described by Bolton’s ratios. Bolton predicted a new expected overall ratio resulting from the extraction of four premolars by omitting the average widths of the first premolars.6 He predicted that the new overall ratio should be between 87-89% based on average premolar tooth widths. Many investigators have used 88% as the ideal overall ratio based on this predicted range. Curiously, the data from his thesis13 shows that the ideal overall Bolton ratio for a four first premolar extraction case should be 89.67%. 28 Regardless, Bolton’s predicted ratio was based on mathematical calculation that simply omits the average widths of extracted teeth, but does not take into consideration the articulation of the cusps, fossae, and marginal ridges of the remaining teeth as did his original sample. For accuracy, any newly described ratios for extraction cases should be calculated in the same way that the original anterior and overall ratios were calculated from Bolton’s non-extraction cases—that is, from cases which undergo premolar extraction and result in excellent finished occlusion. A recent study by Kayalioglu et al.17 measured 53 post-treatment models from cases treated with four first premolar extractions that resulted in good occlusion and reported a new ideal overall ratio, 89.28 ± 1.07%, based on this sample. With no reported knowledge of the data included in Bolton’s thesis, the newly reported ideal overall ratio was strikingly similar to the ideal overall ratio one would expect to find (89.67%) if four first premolars were extracted in Bolton’s cases.13 However, the difference is statistically different from the 88% overall ratio predicted by Bolton for premolar extraction cases. This may indicate that many studies using Bolton’s predicted value of 87-89% for cases treated with premolar extraction may have made erroneous assumptions and/or conclusions about the occlusal consequences of different premolar extraction patterns. Employing a novel method utilizing digitized models subject to virtual extraction of the four first premolars and virtual setups into ‘excellent’ occlusion, this study seeks to add to the existing literature related to the Bolton ratios by: First, reporting a posterior Bolton ratio that can be expected for non-extraction cases with excellent occlusion as described by Bolton’s ideal anterior and overall ratios; Second, describing the effect of 29 the extractions on the expected posterior Bolton ratio; Third, describing the effect of the extractions on the observed posterior Bolton ratio through performing digital setups with ‘excellent’ occlusion; Fourth, correlating discrepancies between expected and observed posterior Bolton ratios to various combinations of tooth widths, proportions, and differences. MATERIALS AND METHODS Sample This is a retrospective study approved by the Institutional Review Board at Saint Louis University. The sample was obtained from archived physical models from patients who had completed orthodontic treatment at the Center for Advanced Dental Education at Saint Louis University. In an attempt to match Bolton’s sample, after all screening and inclusion criteria were met, a final sample of 55 cases within 1 standard deviation of Bolton’s reported ideal anterior and overall ratios were used in this study. The preliminary inclusion criteria for the physical models were: 1. Full set of permanent dentition from first molar to contralateral first-molar. 2. Post-treatment case with good Class I occlusion. 3. No obvious signs of interproximal alteration such as restorations or stripping. Physical models passing the preliminary screening were subject to the manual screening phase of the process. The manual phase of screening physical models for inclusion was performed by: 1. Measuring individual maxillary and mandibular tooth widths using an electronic digital caliper, rounded to the nearest 0.05 mm. Teeth were measured at the widest point parallel to the central groove or incisal edge when viewed from the occlusal. 30 2. Performing an anterior and overall Bolton Analysis. 3. Physical models were included in the sample a when the anterior and overall Bolton ratios were found to be within 1 standard deviation of Bolton’s reported ideal values. Physical models passing the manual screening were subject to the digital phase of the screening process. The physical models were scanned using a 3D scanner (R700, 3Shape A/S, Copenhagen, Denmark) and OrthoAnalyser (3Shape A/S) software was used for digital processing. The digital phase of screening physical models for inclusion was performed by: 1. Calibrating the scanner prior to each scanning session. 2. Scanning the physical maxillary arch, mandibular arch, articulated models, and then adding a digital base and creating a digital STL file for the model. 3. Measuring individual maxillary and mandibular tooth widths and delineating the clinical crown margin using the “Preparation” function of the software. Teeth were measured at the widest point parallel to the central groove or incisal edge when viewed from the occlusal and rounded to the nearest 0.01 mm (Figure 3.1). The tooth width data found in the “Analysis” tab (Fig 3.1) was then entered into a Microsoft Excel® 2010 spreadsheet. 4. Digital models were included in the final sample when the anterior and overall Bolton ratios were found to be within 1 standard deviation of Bolton’s reported ideal values. 31 Figure 3.1- Measuring the mesiodistal widths and defining the clinical crown margin of each tooth. 32 Models passing the digital screening were subject to the virtual treatment phase of the process using the “VirtualSetup” function of the software. The virtual treatment process included: 1. Adding a new setup, titled, “Ideal 3-3” in the list of setups. The collision detection threshold was set to 0 mm under the “Miscellaneous” tab of the “Move Teeth” function. The maxillary and mandibular anterior 3-3 teeth were moved into ideal anterior relationship, meaning coincident midlines, excellent alignment and coupling, and Class I canine position (Figure 3.2). The setup was renamed, “Ideal 3-3” setup. 33 34 Figure 3.2- “Ideal 3-3" digital setup. 2. Creating an “Ideal 4’s” setup by renaming a copy of the “Ideal 3-3” setup. Using the “Extraction” function, the four first premolars were extracted. In the “Move Teeth” function, the contact tolerance threshold was set to 0 mm under the “Miscellaneous” tab. The Virtual Setup treatment objectives for “Ideal 4’s” setup were to achieve Andrew’s six keys of occlusion3—tip, torque, rotation, flat curve of Spee, no spaces, and Class I molar position. Maxillary molars were rotated so that a ray drawn from the maxillary first molar’s distobuccal cusp tip passes through the mesiolingual cusp tip and contralateral canine. Also, the buccolingual inclinations of maxillary posterior teeth were set so that the transverse occlusal plane was flattened. The process of “Ideal 4’s” setup involved moving teeth posterior to the extraction sites mesially to be in proximal and occlusal contact in the following sequential order: mandibular second premolars, maxillary second premolars, maxillary first molars, and finally mandibular first molars. If complete space closure was not possible without compromising Class I ideal cusp-fossa or cusp-marginal ridge occlusal relationships as described by Ash18 then the final tooth position was determined by ideal occlusal intercuspation in preference over space closure. For example, if the mandibular or maxillary first molar was found to be lacking ideal occlusal intercuspation with all proximal spaces closed, then the appropriate tooth was moved distally until ideal occlusal intercuspation was achieved. See Figure 3.3 for the occlusion scheme used for the digital setups and Figure 3.4 for an example of an “Ideal 4’s” digital setup. 35 Ideal cusp-marginal ridge or cusp-fossa relationship. Figure modified from Ash, M. Wheeler’s Dental Anatomy. 8th Ed. Pg. 456, Fig. 16-36.18 Schematic of ideal occlusal contacts. Molars are rotated so that a ray drawn from the maxillary first molar’s distobuccal cusp tip passes through the mesiolingual cusp tip and contralateral canine. Figure modified from Ash, M. Wheeler’s Dental Anatomy. 8th Ed. Pg. 463, Fig 16-29.18 Transverse occlusal plane flattened. Figure 3.3- Occlusion schemes for digital setups. 36 37 Figure 3.4- Example "Ideal 4's" digital setup. 3. The “Ideal 4’s” setup was exported as a model and saved. Maxillary and Mandibular residual spaces (MaxResSpc and MandResSpc) were measured in the “Ideal 4’s” model by measuring the gap between the two teeth parallel to the alveolar ridge when viewed from the occlusal using the “Digital Calipers” option in the “Measurements” pop-up menu from the “Inspection” tools (see figure 3.5 for an example of mandibular residual space measurement). Figure 3.5- Example of measuring residual space in the mandibular arch. All measurements including individual maxillary and mandibular anterior and posterior tooth widths, interproximal spaces, and various combinations of tooth widths, proportions, and differences were recorded in a Microsoft Excel® 2010 spreadsheet for analysis. Appendix A contains a list of abbreviated variables, their definitions, and the formulas used to derive them. 38 Statistical Analysis The data recorded in Microsoft Excel® 2010 was exported into IBM SPSS Statistics 23.0 (SPSS Inc., Chicago, Illinois). The alpha level for all statistical tests was set at 0.05. To test for the accuracy of the screening process in matching the experimental sample to Bolton’s original sample,13 an independent T-test was performed comparing the anterior Bolton ratio, overall Bolton ratio, and individual posterior tooth widths between samples. The null hypothesis was that the there was no difference between the anterior ratio, overall ratio, and individual posterior tooth widths. Descriptive and frequency statistics were calculated for data in the sample. Data described, which has not been previously reported include: First, the non-extraction posterior Bolton ratio (reported as PostBolt), the overall Bolton ratio and posterior Bolton ratios that could be expected based on a mathematical calculation that omits the widths of the extracted first premolars (reported as ExpOB and ExpPB, respectively); Second, the overall Bolton ratio and posterior Bolton ratios observed after four first premolar extractions and setting the teeth in ideal occlusion (reported as NetOB and NetPB, respectively). Paired t-tests were employed to test the null hypothesis that: First, the width of the individual premolars in the upper arch are not different than the width of the corresponding premolars in the lower arch; Second, the overall and posterior Bolton ratios are not altered by extracting teeth; Third, the Bolton ratios determined by mathematical omission of first premolar widths are not different from Bolton ratios observed as determined by ideal occlusion after extracting four first premolars. 39 Correlation and regression was used to determine the relationship between the amount of residual space (NetResSpc) and the discrepancy between the posterior Bolton ratio determined by mathematical omission of the widths of the first premolars (ExpPB) and the posterior Bolton ratio observed when ideal occlusion is achieved in preference over complete space closure (NetPB). In an attempt to reduce the numerous variables describing tooth widths, proportions, and differences in each case (see Appendix A) and isolate only those which may most affect the amount of observed residual spaces after extractions and setups in ideal occlusion, one-way analysis of variance was performed. Cases were grouped according to the amount of residual spaces identified (NetResSpc) after the extractions and setup in ideal occlusion. Two variations of net residual space groupings were used. The first variant was cases with net residual space below 1.0 mm, and cases with 1.0 mm or more of net residual space, called NRS2Grps. This grouping scheme was chosen because it is close to the mean and nearly splits the sample into two equal groups. The second NetResSpc grouping variant was cases with net residual space below 0.75 mm, from 0.75 mm to 1.49 mm, and 1.5 mm and above, called NRS3Grps. This grouping scheme was chosen because some authors8,9 have suggested that the upper group’s limit, 1.5 mm, is the threshold for a clinically significant Bolton discrepancy and because the groups included generally similar numbers of cases. For each case, numerous factors, or variables, of tooth widths, proportions, and differences were recorded as listed in Appendix A. The average for each factor within a group was compared to the averages of that factor within other groups to test the null hypothesis that the averages of the variables are the same for all groups of net residual space. 40 Multiple (backward stepwise) regression analysis of factors deemed significant from each the NRS2Grp and NRS3Grp ANOVA tests was used to isolate variables with the greatest predictive power of the residual spaces. From these tests, a regression equation was derived that could be used to predict the amount of the residual space (NetResSpc) remaining in a four first premolar extraction case treated to ideal occlusion. Reliability All manual and digital measurements as well as virtual setups were performed by the same investigator. Six of the 55 cases were randomly selected using a number generator (random.org) to assess the intra-examiner reliability. Using OrthoAnalyser software, the six cases were digitally re-measured with the “Preparation” function and new setups from 3-3 and 6-6 with extraction of the four first premolars were performed as described previously. The new models were labeled “Validity Ideal 4’s”. Cronbach’s alpha set at a level of 0.8 was used to determine the measurement reliability. RESULTS Cronbach’s alpha test for intra-examiner reliability between original and repeated measurements was above 0.8 for all variables except the NRS2Grp variable (Cronbach’s alpha = 0.76), showing that, generally, the process for obtaining original measurements and repeated measurements were acceptably reliable for accuracy. The anterior Bolton ratio and overall Bolton ratio for this sample was 77.23 ± 0.93% and 91.75 ± 0.97%, respectively. Individual tooth widths for the maxillary first premolar, second premolar, and first molar , respectively, was 7.07 ± 0.48 mm, 6.88 ± 0.46 mm, and 10.42 ± 0.54 mm. Individual tooth widths for the 41 mandibular first premolar, second premolar, and first molar was 7.22 ± 0.46 mm, 7.35 ± 0.51 mm, and 11.20 ± 0.63 mm, respectively. Table 3.1 shows the descriptive statistics for the anterior Bolton ratio, overall Bolton ratio, and individual posterior tooth widths from this study’s sample and Bolton’s13 original sample. Independent t-tests comparing the mean ratios and individual tooth sizes from these samples do not differ significantly. Therefore, the null hypothesis that the tooth widths and ratios in the present study’s sample and Bolton’s sample do not differ is not rejected. Table 3.1- Comparison of Bolton's original thesis sample and this study’s sample. Anterior Ratio Overall Ratio Posterior Ratio U4 U5 U6 L4 L5 L6 Bolton’s Original Sample Mean SD N 77.20% 1.65 55 91.30% 1.91 55 105.27% a 55 7.04 mm 0.46 110 6.84 mm 0.39 110 10.40 mm 0.58 110 7.15 mm 0.38 110 7.27 mm 0.39 110 11.14 mm 0.62 110 Experimental Sample Mean SD N 77.23% 0.93 55 91.75% 0.97 55 105.77% 1.99 55 7.07 mm 0.48 110 6.88 mm 0.46 110 10.42 mm 0.54 110 7.22 mm 0.46 110 7.35 mm 0.51 110 11.20 mm 0.63 110 P-value 0.904 0.125 0.592 0.499 0.792 0.243 0.174 0.463 a Not reported by Bolton. Calculated from the average individual tooth widths reported in Bolton's original thesis. 13 When comparing widths of corresponding posterior teeth between the upper and lower arch (for example, upper first premolars versus lower first premolars), paired t-tests confirm that the widths corresponding teeth are significantly different (See Table 3.2). Therefore, the null hypothesis that corresponding tooth widths do not differ is rejected. Table 3.2- Paired t-test comparing widths of corresponding upper and lower posterior teeth. Paired Samples Test (2-tailed) U4sWidth - L4sWidth U5sWidth - L5sWidth U6sWidth - L6sWidth Mean Diff -0.29 -0.95 -1.56 SD 0.49 0.48 0.59 SEM 0.07 0.06 0.08 Widths include left and right sides. 42 Low -0.42 -1.08 -1.72 Up -0.15 -0.82 -1.40 t -4.31 -14.67 -19.74 df 54 54 54 P= 0.000 0.000 0.000 For non-extraction cases, the ideal posterior Bolton ratio is 105.77% ± 1.99 SD. For four first premolar extraction cases, the expected posterior Bolton ratio is 107.29% ± 2.23 SD and the observed posterior Bolton ratio is 110.48% ± 3.12 SD. The discrepancy between the expected and observed Bolton ratios for four first premolar extractions is 3.18% ± 2.59 SD. After extracting four first premolars and setting posterior teeth in ideal occlusion, an average of 0.04 mm of space was found between the maxillary posterior teeth (MaxResSpc), 1.16 mm of space was found between the mandibular teeth (MandResSpc), leaving 1.11 mm of net residual space (NetResSpc) in the mandible. Table 3.3 shows the various ratios derived and spaces measured from this study’s sample. Table 3.3- Ratios and measurements describing non-extraction and four first premolar extraction cases. Descriptive Statistics 1 Anterior Ratio (%) Overall Ratio (%) Posterior Ratio (%) Mean 77.23 91.75 105.77 SD 0.93 0.97 1.99 N 55 55 55 Range 3.10 3.69 8.15 2 Exp Anterior Ratio (%) Exp Overall Ratio (%) Exp Posterior Ratio (%) 3 Max Residual Space (mm) Mand Residual Space (mm) Net Residual Space (mm) Net Post Bolton Discrep (%) Net Posterior Ratio (%) Net Overall Ratio (%) 77.23 89.97 107.29 0.04 1.16 1.11 3.18 110.48 91.33 0.93 0.97 2.23 0.19 0.86 0.92 2.59 3.12 1.32 55 55 55 55 55 55 55 55 55 3.10 4.49 8.55 1.13 3.55 4.30 12.06 12.73 5.29 Minimum Maximum 75.58 78.69 89.44 93.13 102.02 110.17 75.58 87.70 103.31 0.00 0.00 -0.75 -2.25 104.15 88.59 78.69 92.19 111.86 1.13 3.55 3.55 9.80 116.88 93.88 1.Non-extraction 2.As calculated by omitting width of extracted first premolars. 3.As observed when four first premolars are extracted and teeth digitally set in ideal occlusion. Comparison of non-extraction Bolton ratios with expected and observed extraction Bolton ratios, as shown in Table 3.4 section 1, reveals that the pairs differ significantly. Therefore, the null hypothesis that the non-extraction, expected, and 43 observed ratios do not differ is rejected. Table 3.4 section 2 shows that expected and observed Bolton ratios also differ significantly. Table 3.4- Comparison of non-extraction and extraction Bolton ratios as well as expected and observed Bolton ratios. Paired Samples Test (2-tailed) Mean Difference 1.78 1 OvrlBolt - ExpOB 0.42 OvrlBolt- NetOB -1.52 PostBolt - ExpPB -4.71 PostBolt - NetPB -1.36 2 ExpOB - NetOB -3.18 ExpPB - NetPB SD SEM Low Up t df P< 0.50 1.26 1.15 2.90 1.09 2.59 0.07 0.17 0.16 0.39 0.15 0.35 1.65 0.08 -1.83 -5.49 -1.66 -3.88 1.92 0.76 -1.21 -3.92 -1.07 -2.48 26.45 2.48 -9.81 -12.06 -9.25 -9.12 54 54 54 54 54 54 0.0001 0.016 0.0001 0.0001 0.0001 0.0001 1. Comparison of non-extraction ratios and extraction ratios 2. Comparison of extraction ratios between what is expected by mathematics and what is observed after setups. Results show an extremely strong positive relationship between the net residual space and the net posterior Bolton discrepancy. The correlation is 0.997 and R-squared is 0.994. The slope of the regression equation is 2.80% and the constant is 0.06%. Figure 3.6 shows a scatterplot graph of each case’s net residual space and net posterior discrepancy along with the regression equation. 44 Relationship Between Residual Space and the Posterior Bolton Discrepancy Net Posterior Bolton Discrepancy (%) 12.0 10.0 y = 2.80x + 0.059 R² = 0.994 8.0 6.0 4.0 2.0 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 -2.0 -4.0 Net Residual Space (mm) Figure 3.6- Scatterplot of NetResSpc and NetPBDiscrep for each case with the regression line and equation. The residual spacing, whether present in the maxillary arch, mandibular arch, or both, was observed almost exclusively between the second premolar and first molar. Residual spacing in this study’s sample was observed in 54 of 55 cases. Only one case finished with no spacing in either the maxillary or mandibular arches. Although extremely infrequent, three of 55 cases finished with spacing in the maxilla. The average maxillary spacing for the sample was 0.04 mm. The majority (52 of 55, or 94.5%) of cases finished with 0 mm of or more spacing in the mandibular arch to the amount of 1.16 mm on average. When grouping the cases according to the amount of net residual space, 15 cases (27.3%) had less than 0.5 mm, and 40 cases (72.7%) had 0.5 mm or more of net spacing. 26 cases (47.3%) had less than 1 mm, and 29 cases (52.7%) of cases had 1 mm or more 45 of net spacing. 15 cases (27.3%) had 1.5 mm of spacing or more. Nine cases (16.4%) had at least 2 mm of residual spacing, and three cases (5.45%) had at least 3mm of net residual spacing. Figure 3.7 shows the frequency of cases with different amounts of net residual space. Frequency of Cases by NetResSpace 60 3 9 50 15 29 Number of Cases 40 40 30 52 52 46 20 40 26 10 15 0 NRS ≥ NRS < 3 0 mm 52 3 0.5 mm 40 15 1 mm 29 26 1.5 mm 15 40 2 mm 9 46 3 mm 3 52 Figure 3.7- Frequency of cases grouped by net residual space. The next question to be answered was which factors or variables, if any, may contribute to finishing a four first premolar extraction case with residual space when teeth are set in ideal occlusion? One-way analysis of variance (ANOVA) was used to determine if, in some cases, the observed residual spacing could be “filled in” with extra tooth mass in the mandibular posterior. Cases were divided into groups based on the size 46 of the net residual space (NRS2Grp and NRS3Grp) and tested for differences within nonextraction (PostBolt) and expected posterior Bolton ratios (ExpPB). There were no significant differences. Therefore, the null hypothesis that the mean for non-extraction and expected posterior Bolton ratios is the same for all groups of net residual space is not rejected. Various combinations of tooth widths, their proportions, and their differences were next evaluated using one-way ANOVA in an attempt to isolate factors which may contribute to or reduce net residual spacing. In the NRS2Grp ANOVA, significant differences within variables exist between the two groups. Five factors with significant differences were found. Therefore, the null hypothesis that the means of the factors is the same for all groups of net residual space is rejected. The factors with different means include the difference in width between the lower second premolar and upper second premolar (L5minU5), the upper second premolar width as a fraction of the lower second premolar width (U5vsL5), the upper second premolar as a fraction of the upper posterior tooth widths (U5PerU456), the lower second premolar as a fraction of the upper posterior tooth widths (L5PerU456), and the upper second premolar as a fraction of the lower posterior tooth widths (U5PerL456). See Appendix B for the NRS2Grp ANOVA output from SPSS. The NRS3Grp ANOVA test reveals that significant differences within four variables exist between the three groups. Therefore, the null hypothesis that the means of the factors is the same for all groups of net residual space is rejected. The four variables with significant differences include the upper second premolar width (U5sWidth), the difference in size between the lower second premolar and upper second premolar 47 (L5minU5), the upper second premolar width as a fraction of the lower second premolar width (U5vsL5), and the upper second premolar as a fraction of the lower posterior segment (U5PerL456). See Appendix C for the NRS3Grp ANOVA output from SPSS. When comparing the means of variables from cases in the smaller net residual space group to those in the larger net residual space group, it is evident that the U5sWidth, U5vsL5, U5PerU456, and U5PerL456 averages are smaller and the L5minU5 and L5PerU456 averages are greater. Refer to Appendix B and C for the SPSS output for the ANOVA tests. All six of the above-mentioned variables were entered into a multiple linear regression analysis, and it was found that R was 0.586, and R square was 0.343, and the null hypothesis that there is no significant linear correlation is rejected (See Appendix D for SPSS output of the regression analysis). Backward linear regression revealed that two of the six variables were deemed to significantly affect the variability in the observed net residual space. Again, the null hypothesis that there is no significant linear correlation is rejected. Excluding the other variables from the regression equation was statistically deemed to not alter the R square. The two variables with significant correlation were the proportion of upper second premolars to lower second premolars (U5vsL5) and the upper second premolars’ width (U5sWidth). Both variables combined for a correlation (R) of 0.554 and a regression (R square) amounting to 0.307. See Appendix E for the SPSS output of the backward regression for all significant variables from the NRS2Grp and NRS3Grp ANOVA tests). Individually, the respective R and R square for U5vsL5 was 0.474 and 0.224, and 0.337 and 0.142 for U5sWidth (see Appendix F). Table 3.5 shows a summary of the R and R square values as well as the regression equation from the 48 multiple, backward, and individual regression analyses for predicting the net residual space in a given case. Table 3.5- Linear regression of variables explaining variation in net residual space. Linear Regression of Variables from ANOVA Contributing to Net Residual Space Model R R Squared Adj R Squared Regression Equation for Predicting NetResSpc 1 0.586 0.343 0.261 139.18(a) + 0.59(b) - 4.06(c) - 621.33(d) + 589.86(e) - 13.08(f) - 132.54 2 0.554 0.307 0.281 12.43(a) + 0.29(b) - 14.56 3 0.474 0.224 0.210 14.18(a) -12.16 4 0.377 0.142 0.126 0.376(b) - 4.06 1 Multiple reg of six sig factors: U5vsL5 (a), U5sWidth (b), L5minU5 (c), U5PerU456 (d), L5PerU456 (e), U5PerL456 (f) 2 Backward regression results: U5vsL5 (a), U5sWidth (b) 3 Individual regression for U5vsL5 (a) 4 Individual regression for U5sWidth (b) DISCUSSION Interpretation of Results As the anterior ratio, posterior ratio, nor individual tooth widths from this study’s sample were not found to be significantly different from Bolton’s original sample (see Table 3.1), it can be inferred that this sample matched Bolton’s sample very closely. This attests to the accuracy of the two-step screening process utilized in obtaining the sample for this study. Table 3.2 and the significance of the statistical test indicate a high confidence that corresponding maxillary and mandibular tooth sizes are not the same. First premolars have the least difference in linear width while first molars have the greatest difference in linear width. The lower posterior teeth are wider than the corresponding upper teeth. Therefore, maintaining the ideal pre-treatment posterior ratio, and occlusion, may be impossible to maintain after extracting four corresponding teeth (four first premolars, four second premolars, or four first molars). 49 The overall Bolton ratio decreases from 91.75% in ideal non-extraction cases to an expected 89.97% after omitting the width of the four first premolars from the overall Bolton ratio equation. Even if premolars were equally sized, the expected overall Bolton is smaller than the non-extraction overall Bolton because the extracted upper premolar is just a small proportion of all of the top teeth compared with the extracted lower premolar, which is a larger proportion of all of the bottom teeth. The result is a greater reduction in the numerator and a smaller reduction in the denominator of the equation for the overall Bolton ratio. The same reason can explain the reduction from the non-extraction overall Bolton ratio to the overall Bolton ratio observed when teeth are set to ideal occlusion (91.33%). However, when comparing the non-extraction ideal posterior Bolton ratio (105.77%) and the posterior Bolton ratio expected by omitting the widths of the first four premolars (107.29%), it is evident that extracting four first premolars increases the posterior Bolton ratio. Likewise, the posterior Bolton ratio observed when teeth are set in ideal occlusion (110.48%) is also increased compared to the non-extraction ideal posterior Bolton ratio. Lower second premolars and first molars are larger than the corresponding upper premolars and molars. Even if the first premolars were similar in size, after being extracted the size discrepancy between the remaining upper and lower second premolars and first molars results in a smaller proportional reduction of the numerator and greater proportional reduction of the denominator of the equation for the posterior Bolton ratio. It is noted, however, that the expected and observed Bolton ratios are not equivalent (see Table 3.4). The discrepancy between the expected and observed ratios 50 (1.36% for overall ratios and 3.18% for posterior ratios) is due to an average of 1.11 mm of net residual spacing between the mandibular second premolar and first molar after performing digital setups in ideal occlusion (see Table 3.3). Regression analysis (see Figure 3.6) shows with an extremely strong positive relationship that each millimeter of net residual space accounts for a posterior Bolton discrepancy between the expected and the observed posterior Bolton ratios amounting to 2.8%. At 0 mm of spacing, the net posterior Bolton discrepancy is effectively 0% and the expected posterior Bolton ratio matches the observed posterior Bolton ratio. When considering the frequency at which net residual spacing or net posterior Bolton discrepancy is observed in these cases after setup, results in Figure 3.6 can be interpreted to mean that the majority of cases finished by prioritizing ideal occlusion will have least some space remaining between mandibular second premolars and first molars. The chart also shows that a large portion of these cases will finish with potentially large amounts of residual space. Therefore, many cases with ideal pre-treatment Bolton ratios undergoing four first premolar extractions cannot finish with ideal occlusion as well as complete space closure of mandibular extraction sites. The clinical tradeoff between treating to ideal occlusion versus complete space closure will be covered in greater detail in a later section. It should be noted, however, that some cases treated to ideal occlusion after extracting four first premolars finish closer to achieving complete space closure and more closely match the expected posterior Bolton ratio than other cases as is evident by the regression line in table 3.5. The regression line shows that some cases finished with less net residual spacing and less discrepancy between its expected and observed posterior 51 Bolton ratios than other cases. One-way ANOVA tests of NRS2Grp and NRS3Grp reveal that cases with larger pre-treatment or expected posterior Bolton ratios do not appear to finish with less net residual spacing. This is unexpected as one would presume that wider-than-normal mandibular teeth would occupy the net residual spaces in the mandible. Further ANOVA tests of NSR2Grp and NRS3Grp (Appendix B and C) reveal six unique factors, or variables, that appear to be different depending on the amount of net residual space. The six factors are all related to the width of the second premolars. Generally, when the upper premolars are small or the lower premolars are large, the residual spacing after ideal setups is reduced. Table 3.5 is a summary of the results of regression analysis of the variables found to be significant from the above-mentioned ANOVA tests. All six factors together show a strong positive correlation with net residual spacing in the mandible, but when adjusting for the number of variables considered and the size of the sample, the adjusted R square falls off. Some of the variables in the group may not be very good predictors of net residual space, even though they were found to be statistically significant by ANOVA. Backward regression narrowed the six variables down to only two: the proportion of the upper second premolars width versus the lower second premolars with (U5vsL5) and the linear width of the upper second premolars (U5sWidth). Although the correlation and regression coefficients are slightly lower, the adjusted R squared is higher, indicating that the two variables may be better predictors of net residual space than all six variables combined. Individually, the fraction of upper second premolars width versus lower 52 second premolars width (U5vsL5) is the strongest predictor of net residual space, followed by the width of the upper second premolars (U5sWidth). Present Outcomes and Past Studies This study is the first of its kind to report an ideal posterior Bolton ratio by matching its sample within one standard deviation of Bolton’s reported ideal anterior and overall ratios derived from 55 non-extraction cases with ‘excellent’ occlusion.1 The ideal posterior Bolton ratio calculated from average posterior tooth widths obtained from Wayne A. Bolton’s original thesis13 was found to be 105.27%. Although arguably more useful than the overall ratio when used in conjunction with the anterior ratio, Bolton never explicitly reported this posterior ratio in his thesis or in the literature he published. Smith et al.19 reported that the posterior Bolton ratio for his sample ranged from 104 – 107% while evaluating whether Bolton’s ratios could be applied equally to all genders and ethnicities. This range fits nicely around the ideal posterior Bolton ratio for nonextraction cases derived from this study, which is 105.77 ± 1.99%. Numerous past studies have investigated the effect of premolar extractions on the Bolton ratios, but only report the effect of extractions on the overall ratio.6,11,17,20-22 Generally, these studies calculate the expected overall ratio by omitting the widths of the four premolars to be extracted from the overall Bolton ratio equation. From this study, the expected overall ratio derived by omitting the widths of the extracted four first premolars is 89.97 ± 0.97%. This is larger than the 87-89% overall ratio that Bolton6 predicted and closer to the 89.28% ratio that Kayalioglu et al.17 derived from a sample of 53 post-treatment models of patients treated with four first premolars finished in ideal occlusion. Bolton’s thesis13 data, had it been published, reveals an ideal expected overall 53 ratio of 89.67% which is between the 89.28% ratio from the study by Kayalioglu et al. and the 89.79% ratio from the present study. In spite of the clinical similarity between the present study and Kayalioglu et al., an independent t-test comparing the mean overall Bolton ratios reveals that the two means are statistically different. The smaller ratio that they report could be partially explained by the fact that their study’s inclusion criteria did not require that the cases in their sample match Bolton’s pre-treatment ideal anterior and posterior ratios within one standard deviation as was the case in the present study. In fact, they report that the overall Bolton ratio from the pre-treatment models were 90.61 ± 1.08%, which is smaller than Bolton’s ideal overall ratio. The present study is the first to investigate and describe how the posterior Bolton ratio changes with the extraction of four first premolars. The present study used the mathematical methodology employed in past studies investigating the effect of extractions on the overall Bolton ratio, but applied to the posterior teeth. That is, the widths of the four first premolars were omitted from the equation used to derive the expected posterior Bolton ratio for four first premolar extraction cases. The expected posterior Bolton ratio for four first premolar extraction cases is 107.29 ± 2.99%. Unlike past studies, this study acknowledges that extracting teeth in the maxillary arch of different widths than those in the mandibular arch may derange the potentially ideal pre-treatment occlusion as defined by ideal anterior, posterior, and overall Bolton ratios and recognizes the importance of performing setups in ideal occlusion to identify ideal post-extraction ratios. This study is also the first to investigate and describe the posterior Bolton ratio when four first premolars are extracted and the remaining posterior teeth are finished with preference given to ideal occlusion rather than complete space 54 closure. The observed posterior Bolton ratio (NetPB) was 110.48 ± 3.12% when interproximal spaces remaining after ideal setups were included in the equation for calculating the posterior Bolton ratio. The 3.18% Bolton discrepancy between the expected and observed posterior Bolton ratios and 1.11 mm of net residual space in the mandible could be explained in at least three ways. First, as is shown in this study, the size differences between extracted maxillary and mandibular teeth as well as other differences between remaining teeth seem to account for at least a portion of the discrepancy. Another possibility is that ‘excellent’ occlusion could have been defined differently between Bolton and the present study’s author. The present study’s author focused on finishing each tooth with ideal cusp-fossa and cusp-marginal ridge relationship, and standardizing molar rotation as well as buccolingual inclination of each posterior tooth. Bolton may have focused, more generally, on Class I molar and canine positions. It is uncertain how the differences in defining ‘excellent’ occlusion may affect the ratios. Lastly, it is possible that although non-extraction cases with excellent occlusion are found to have an anterior ratio of 77.2%, an overall ratio of 91.3%, and a posterior ratio of 105.77%, pre-treatment cases with those ideal ratios do not necessarily have ideal occlusion due to variations in crown morphology. Using this study’s sample and performing setups to simulate non-extraction treatment resulting in ideal occlusion would be one way to improve upon this study. Comparing the residual spaces in the non-extraction group to the residual spaces from this study would make it more directly possible to isolate the effect of extracting four first premolars on the posterior Bolton ratio and validate or refute Bolton’s ideal ratios describing ‘excellent’ occlusion. 55 If the discrepancy between expected and observed posterior Bolton ratios represents an interarch tooth size discrepancy (ITSD), then the frequency at which the ITSD occurs in this sample needs to be considered. The sample had, on average, 0.04 mm of spacing between the maxillary second premolar and first molar and 1.16 mm of spacing between the mandibular second premolar and first molar. When the average spaces were closed in the maxillary arch and the average mandibular space were reduced correspondingly, 1.11 mm of net space remains in the mandibular arch between the second premolar and first molar (or 0.555 mm per side). As the most aggressive estimate of a clinically significant ITSD in the literature8,9 is 1.5 mm total (or 0.75 mm per side) it would appear that the ITSD in this sample as a whole is generally not considered clinically significant. However, the incidence of a clinically significant ITSD in this sample is not to be dismissed. In this study’s sample of 55 cases, 15 (27.3%) had at least 1.5 mm spacing—a level that some authorities deem to be at least borderline clinically significant.3,4 Nine cases (16.4%) had at least 2 mm—a level that has been described as clinically significant by several authors.8-12 Three cases had at least 3 mm of net residual spacing. The American Board of Orthodontics currently assesses one point for each 0.5 mm of interproximal space discovered in a case.7 Therefore, roughly half of the finished cases from this sample would have two points assessed on the ABO castradiograph examination for finishing with an average of 1.11 mm of spacing after extracting four first premolars and finishing with preference given to ideal occlusion. The other half of the cases would be assessed less than two points because they finished with less residual spacing in ideal occlusion. 56 Conversely, it appears that a no-win situation exists because leaving spaces is not ideal, but on the contrary, completely closing spaces can compromise the occlusion. Akinci and Uysal’s study23 provides evidence for this idea. They noticed that four premolar extraction cases were assessed significantly more points on the ABO examination for compromised occlusal contacts and occlusal relationships than nonextraction cases. The points assessed for compromised occlusion could be due to an ITSD created by extracting teeth, and then forcing closed the spaces resulting from the toothsize discrepancy. More on the clinical significance of closing net residual space is discussed in the next section. This study was also the first to investigate which tooth widths, differences, and proportions have the greatest role in finishing with less residual spacing in ideal occlusion. In these cases, expected and observed posterior Bolton ratios matched more closely. The proportion of the widths of the upper second premolars compared to the widths of the lower second premolars (U5vsL5) has the greatest influence on finishing with ideal occlusion while maximizing space closure. The next most influential factor is simply the width of the upper second premolars. Together, they account for 30% of the variation in residual spacing. Clinical Significance and Implications The interpretation of a normal overall Bolton ratio is ambiguous. A case found to have an ITSD in the anterior but normal overall ratio means that the posterior teeth compensated for the discrepancy in the anterior teeth. It is possible that the compensation is significant enough to cause occlusal discrepancies in the posterior, resulting in an anterior and posterior ITSD in spite of a normal overall ratio. A more 57 direct interpretation and more clinically useful application may be attained from knowing and applying the ideal anterior and posterior ratios to a case separately. As no ideal posterior Bolton ratio has been reported in the literature against which to check a case for a posterior ITSD, the results of this study are immediately of use to the orthodontist. Orthodontists may use 105.77% ± 1.99 SD as the ideal non-extraction posterior Bolton ratio against which to compare their patients’ posterior Bolton ratio prior to commencing treatment in order to anticipate if an ITSD may prevent their case from finishing with ideal occlusion. Two in three orthodontists agree whether a case should be treated with extractions, and currently 28% of all orthodontic cases undergo extractions.14-16 As the four first premolars are reportedly8 the most commonly chosen extraction patterns, knowing the ideal posterior ratio for four first premolar extraction cases could help an orthodontist foresee a potential posterior ITSD in their patient’s case. Also the ability to convert this posterior ITSD percentage into an actual linear, millimetric size discrepancy could help an orthodontist plan and execute appropriate corrective measures that could enable him to finish the posterior occlusion as close as possible to ideal. For a case with pre-treatment ideal anterior, posterior, and overall Bolton ratios, an orthodontist should expect the posterior Bolton ratio to be 107.29% after extracting four first premolars. However, should be aware that, based on the sample from this study, his case has a roughly 50% chance of finishing with 1.1 mm of spacing bilaterally, a 27% chance of finishing with 1.5 mm of spacing bilaterally, and 16% chance of finishing with 2 mm of spacing bilaterally between mandibular second premolars and first molars if ideal occlusion is given preference over complete space closure. 58 Conversely, if complete space closure of any net residual spacing between the lower second premolar and first molar is given preference over maintaining ideal occlusion, then a spectrum of occlusal outcomes exist with two potential extremes. On one end of the spectrum, a case could finish with the canines in ideal Class I occlusion, while the mandibular first molars would be moved mesially into the residual spacing toward Class III molar relationship. On the other end of the spectrum, a case could finish with the molars in ideal Class I occlusion, while the mandibular canine and second premolar would be moved distally into the residual spacing toward Class II relationship. Both possible outcomes could also have numerous adverse effect of varying severity including, but not limited to opening the bite, accelerating occlusal wear, or interfering with anterior guidance. Figure 3.8 shows the digital setup illustrating both extreme occlusal outcomes on the same model. This supports findings by Akinci and Uysal23 showing that cases treated with four premolar extractions were assessed significantly more points than nonextraction cases on the ABO exam due to compromised occlusal contacts and occlusal relationships. The patient’s right side shows Class I canine and premolar relationship with mesial movement of the lower first molars toward Class III. The patient’s left side shows Class I molar relationship with distal movement of the lower canine and second premolars toward Class II relationship as explained above. The occlusal markings show non-ideal contacts on the right molars and left canine and second premolars which could indicate areas of potentially accelerated tooth wear or occlusal interferences that could open the bite and/or alter anterior guidance. 59 60 Figure 3.8- Two scenarios resulting from prioritizing space closure over ideal occlusion Surprisingly, cases with a larger than ideal expected posterior Bolton ratio were not shown to finish with less interproximal spacing. Therefore, it may be advised to wait to perform interproximal reduction or buildup of proximal surfaces with the aim to alter the posterior Bolton ratio until treatment is nearing the finish and pending occlusal relationships can be assessed chairside. Or, given a case with an ideal expected posterior Bolton ratio, an orthodontist could use the regression equation in Figure 3.9 to help predict, with some caution, the amount of residual spacing present in the case at finish and then decide if interproximal reduction or buildups are indicated: 𝐍𝐞𝐭 𝐑𝐞𝐬𝐢𝐝𝐮𝐚𝐥 𝐒𝐩𝐚𝐜𝐞 = 𝟏𝟐. 𝟒𝟑( 𝐔𝟓𝐬 𝐖𝐢𝐝𝐭𝐡 ) + 𝟎. 𝟐𝟗(𝐔𝟓𝐬 𝐖𝐢𝐝𝐭𝐡) − 𝟏𝟒. 𝟓𝟔 𝐋𝟓𝐬 𝐖𝐢𝐝𝐭𝐡 Figure 3.9- Regression equation for predicting residual space. Predictive power is 0.307. A positive number indicates spacing in the mandible and a negative number indicates spacing in the maxilla. If the residual space predicted by the regression equation is deemed insignificant, then it may be possible to proceed with the treatment plan to extract four first premolars as usual without any additional treatment considerations. However, if the residual space is deemed clinically excessive, then interproximal reductions, buildups, or even an alternate extraction pattern may be indicated. If interproximal reduction is indicated, it is most likely indicated in the maxillary arch between the second premolars and first molars. If buildups or an overcontoured restoration are indicated, it is most likely needed in the mandibular arch between the second premolars and first molars. 61 CONCLUSION Based on the results obtained from this study showing the effect of four first premolar extractions on the posterior Bolton ratio, one can conclude that in a case with pre-treatment ideal anterior and overall Bolton ratios: 1. The non-extraction ideal posterior Bolton ratio is 105.77 ± 1.99%. 2. The expected ideal posterior Bolton ratio is 107.29 ± 2.23% for these cases treated with four first premolar extractions. However, this is a not a good predictor of ‘excellent’ post-treatment final occlusion. 3. Cases that undergo four first premolar extractions and are finished with preference given to occlusion over complete space closure have an average of 0.04 mm of residual spacing in the maxillary arch, 1.16 mm in the mandibular arch, resulting in 1.11 mm (0.55 mm each side) of net residual spacing between the mandibular second premolar and first molars. 4. 27% of cases may finish with at least 1.5 mm (0.75 mm each side) of residual space, and 16% of cases may finish with at least 2 mm (1 mm each side) of residual space. 5. In cases with a clinically significant posterior interarch tooth-size discrepancy, interproximal reduction, a bulked restoration, or alternative extraction pattern should be considered. Alternately, opting to completely close the residual space may compromise the finished occlusion and occlusal relationships. 6. Cases with small maxillary second premolars tend to finish with less interproximal spacing. A regression equation is offered to assist in predicting potential residual space for a given case and aid in treatment plan decisions. 62 LITERATURE CITED 1. Bolton WA. Disharmony In Tooth Size And Its Relation To The Analysis And Treatment Of Malocclusion. Angle Orthod. 1958;28(3):113-30. 2. Angle EH. Classification of Malocclusion. The Dental Cosmos: a monthly record of dental science. 1899;41(3):248-64. 3. Andrews LF. The six keys to normal occlusion. Am J Orthod. 1972;62(3):296-309. 4. Ballard ML. Asymmetry in Tooth Size: A Factor in the Etiology, Diagnosis and Treatment of Malocclusion. Angle Orthod. 1944;14(3):67-70. 5. Neff CW. Tailored occlusion with the anterior coefficient. Am J Orthod. 1949;35(4):309-13. 6. Bolton WA. The clinical application of a tooth-size analysis. Am J Orthod. 1962;48(7):504-29. 7. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al. Objective grading system for dental casts and panoramic radiographs. Am J Orthod Dentofacial Orthop. 1998;114(5):589-99. 8. Proffit W, Ackerman J. Contemporary orthodontics. St Louis, MO: C.V. Mosby; 1986. 9. Bernabé E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of Peruvian adolescents. Am J Orthod Dentofacial Orthop. 2004;125(3):361-5. 10. Othman S, Harradine N. Tooth Size Discrepancies in an Orthodontic Population. Angle Orthod. 2007;77(4):668-74. 11. Gaidyte A, Baubiniene D. Influence of premolar extractions on tooth size discrepancy. Part two: Analysis of Bolton values. Stomatologija. 2006;8(1):25-9. 12. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North Indian orthodontic patients. Contemp Clin Dent. 2011;2(3):170-5. 13. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Seatle, WA: University of Washington; 1952. 14. Proffit WR. Forty-year review of extraction frequencies at a university orthodontic clinic. Angle Orthod. 1994;64(6):407-14. 15. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part 1— Interclinician agreement. Am J Orthod Dentofacial Orthop. 1996;109(3):297-309. 16. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part II. Analysis of clinicians' stated reasons for extraction. Am J Orthod Dentofacial Orthop. 1996;109(4):393-402. 17. Kayalioglu M, Toroglu MS, Uzel I. Tooth-size ratio for patients requiring 4 first premolar extractions. Am J Orthod Dentofacial Orthop. 2005;128(1):78-86. 18. Ash MM N, SJ. Wheeler's Dental Anatomy, Physiology, and Occlusion. 8th ed. Philadelphia: W.B. Saunders; 2003. 520 p. 63 19. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3 populations: “Does Bolton’s analysis apply?”. Am J Orthod Dentofacial Orthop. 2000;117(2):169-74. 20. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size discrepancies. Angle Orthod. 2004;74(4):508-11. 21. Endo T, Ishida K, Shundo I, Sakaeda K, Shimooka S. Effects of premolar extractions on Bolton overall ratios and tooth-size discrepancies in a Japanese orthodontic population. Am J Orthod Dentofacial Orthop. 2010;137(4):508-14. 22. Saatçi P, Yukay F. The effect of premolar extractions on tooth-size discrepancy. Am J Orthod Dentofacial Orthop. 1997;111(4):428-34. 23. Akinci Cansunar H, Uysal T. Comparison of orthodontic treatment outcomes in nonextraction, 2 maxillary premolar extraction, and 4 premolar extraction protocols with the American Board of Orthodontics objective grading system. Am J Orthod Dentofacial Orthop. 2014;145(5):595-602. 64 APPENDIX A Table A- List of Abbreviations Differences, fractions, and measurements obtained from study sample 1 AntMand 2 AntMax 3 HalfL4s 4 HalfL5s 5 HalfL6s 6 HalfU4s 7 HalfU5s 8 HalfU6s 9 L4minU4 10 L4PerL456 11 L4PerU456 12 L4sWidth 13 L4vsU4 14 L5minU5 15 L5PerL456 16 L5PerL56 17 L5PerU456 18 L5PerU56 19 L5sWidth 20 L5vsU5 21 L6minU6 22 L6PerL456 23 L6PerL56 24 L6PerU456 25 L6PerU56 26 L6sWidth 27 L6vsU6 Anterior mandibular width: Sum of mandibular centrals, laterals, canines L1s + L2s + L3s Anterior maxillary width: Sum of maxillary centrals, laterals, canines U1s + U2s + U3s Half of the lower 4s width: Average width of a mandibular first premolar L4s Width / 2 Half of the lower 5s width: Average width of a mandibular second premolar L5s Width / 2 Half of the lower 6s width: Average width of a mandibular first molar L6s Width / 2 Half of the upper 4s width: Average width of a maxillary first premolar U4s Width / 2 Half of the upper 5s width: Average width of a maxillary second premolar U5s Width / 2 Half of the upper 6s width: Average width of a maxillary first molar U6sWidth / 2 Lower 4s minus upper 4s: The size difference between the premolars L4sWidth - U4sWidth Lower 4s width as a fraction of the Lower 4s, 5s, and 6s L4sWidth / L4s + L5s + L6s widths Lower 4s width as a fraction of the Upper 4s, 5s, and 6s L4sWidth / U4s + U5s + U6s widths Lower 4s width: Sum widths of both mandibular first premolars Left L4 + Right L4 Lower 4s width versus Upper 4s width: Ratio of corresponding premolars L4sWidth / U4sWidth Lower 5s minus Upper 5s: The size difference between the premolars L5sWidth - U5sWidth Lower 5s width as a fraction of the Lower 4s, 5s, and 6s L5sWidth / L4s + L5s + L6s widths Lower 5s width as a fraction of the Lower 5s, and 6s L5sWidth / L5s + L6s widths Lower 5s width as a fraction of the Upper 4s, 5s, and 6s L5sWidth / U4s + U5s + U6s widths Lower 5s width as a fraction of the Upper 5s, and 6s L5sWidth / U5s + U6s widths Lower 5s width: Sum widths of both mandibular second premolars Left L5 + Right L5 Lower 5s width versus Lower 5s width: Ratio of corresponding premolars L5sWidth / U5sWidth Lower 6s minus Upper 6s: The size difference between the premolars L6sWidth - U6sWidth Lower 6s width as a fraction of the Lower 4s, 5s, and 6s L6sWidth / L4s + L5s + L6s widths Lower 6s width as a fraction of the Lower 5s, and 6s L6sWidth / L5s + L6s widths Lower 6s width as a fraction of the Upper 4s, 5s, and 6s L6sWidth / U4s + U5s + U6s widths Lower 6s width as a fraction of the Upper 5s, and 6s L6sWidth / U5s + U6s widths Lower 6s width: Sum widths of both mandibular first molars Left L6 + Right L6 Lower 6s width versus Lower 6s width: Ratio of corresponding premolars L6sWidth / U6sWidth 65 28 OvrlMand 29 OvrlMax 30 PostMand 31 PostMax 32 U4PerL456 33 U4PerU456 34 U4sWidth 35 U4vsL4 36 U5PerL456 37 U5PerL56 38 U5PerU456 39 U5PerU56 40 U5sWidth 41 U5vsL5 42 U6PerL456 43 U6PerL56 44 U6PerU456 45 U6PerU56 46 U6sWidth 47 U6vsL6 Overall mandibular width: Sum of mandibular anterior and posterior teeth L1s + L2s + L3s + L4s + L5s + L6s Overall maxillary width: Sum of maxillary anterior and posterior teeth U1s + U2s + U3s + U4s + U5s + U6s Posterior mandibular width: Sum of mandibular first premolar, second premolar, and first molar L4s + L5s + L6s Posterior maxillary width: Sum of maxillary first premolar, second premolar, and first molar U4s + U5s + U6s Upper 4s width as a fraction of the Lower 4s, 5s, and 6s U4sWidth / L4s + L5s + L6s widths Upper 4s width as a fraction of the Upper 4s, 5s, and 6s U4sWidth / U4s + U5s + U6s widths Upper 4s width: Sum widths of both maxillary first premolars Left U4 + Right U4 Upper 4s width versus Lower 4s width: Ratio of corresponding premolars U4sWidth / L4sWidth Upper 5s width as a fraction of the Lower 4s, 5s, and 6s U5sWidth / L4s + L5s + L6s widths Upper 5s width as a fraction of the Lower 5s, and 6s U5sWidth / L5s + L6s widths Upper 5s width as a fraction of the Upper 4s, 5s, and 6s U5sWidth / U4s + U5s + U6s widths Upper 5s width as a fraction of the Upper 5s, and 6s U5sWidth / U5s + U6s widths Upper 5s width: Sum widths of both maxillary second premolars Left U5 + Right U5 Upper 5s width versus Lower 5s width: Ratio of corresponding premolars U5sWidth / L5sWidth Upper 6s width as a fraction of the Lower 4s, 5s, and 6s U6sWidth / L4s + L5s + L6s widths Upper 6s width as a fraction of the Lower 5s, and 6s U6sWidth / L5s + L6s widths Upper 6s width as a fraction of the Upper 4s, 5s, and 6s U6sWidth / U4s + U5s + U6s widths Upper 6s width as a fraction of the Upper 5s, and 6s U6sWidth / U5s + U6s widths Upper 6s width: Sum widths of both maxillary first molars Left U6 + Right U6 Upper 6s width versus Lower 6s width: Ratio of corresponding premolars U6sWidth / L6sWidth Expected: Calculated by omitting first premolar widths 48 ExpAB 49 ExpMand 50 ExpMax 51 ExpOB 52 ExpPB Anterior Bolton ratio AntBolt Expected mandibular posterior: Width of remaining mandibular posterior teeth PostMand - L4sWidth Expected maxillary posterior: Width of remaining maxillary posterior teeth PostMax - U4sWidth Expected overall Bolton ratio: Expected overall Bolton ratio after omitting first premolar widths (AntMand + PostMand - L4sWidth / AntMax + PostMand - U4sWidth) x 100 Expected posterior Bolton ratio: Expected posterior Bolton ratio after omitting first premolar widths (PostMand - L4sWidth / PostMand - U4sWidth) x 100 Non-extraction: Ideal ratios for permanent dentition from first molar to first molar 53 AntBolt 54 OvrlBolt 55 PostBolt Anterior Bolton ratio (AntMand / AntMax) x 100 Overall Bolton ratio (AntMand + PostMand / AntMax + PostMax) x 100 Posterior Bolton ratio (PostMand / AntMax) x 100 66 Observed: Four first premolar extractions and setup in ideal occlusion 56 MandResSpc 57 MaxResSpc 58 NetOB 59 NetPB 60 NetPBDisc 61 NetPMand 62 NetPMax 63 NetResSpc 64 NRS2Grp 65 NRS3Grp Mandibular residual space: Spacing between mandibular teeth Directly measured from mandibular digital model Maxillary residual space: Spacing between maxillary teeth Directly measured from maxillary digital model Net Overall Bolton Ratio: Observed overall Bolton ratio AntMand + NetPMand / AntMax + NetPMax Net Posteiror Bolton Ratio: Observed posterior Bolton ratio NetPMand / NetPMax Net Posterior Bolton Discrepancy: The difference between expected and observed posterior Bolton ratios NetPB - ExpPB Net posterior mandibular width: Widths of mandibular posterior teeth and residual spaces ExpMand + MandResSpc Net posterior maxillary width: Widths of maxillary posterior teeth and residual spaces ExpMax + MaxResSpc Net residual space: The difference between maxillary and mandibular residual space MandResSpc - MaxResSpc Net residual space in two groups Group "0", NetResSpc < 1 mm Group "1", NetResSpc ≥ 1 mm Net residual space in three groups Group "0", NetResSpce < 0.75mm Group "1", NetResSpc is from 0.75mm to < 1.5mm Group "2", NetResSpc ≥ 1.5mm Segment method: Not used in this study 66 PSegMand 67 PSegMax 68 SegOB 69 SegPDisc 70 SegPostB Posterior Segment Mandible: Length of posterior segment in the mandible Sum of direct measurements of right and left distance between distal of L3 to distal of L6 Posterior Segment Maxilla: Length of posterior segment in the maxilla Sum of direct measurements of right and left distance between distal of U3 to distal of U6 Segment Overall Bolton Ratio: AntMand + PSegMand / AntMax + PSegMax Segment Posterior Bolton Discrepancy: The difference between expected and segment posterior ratios SegPostB - ExpPB Segment Posterior Bolton Ratio: Posterior segment Bolton ratio PSegMand / PSegMax 67 APPENDIX B Table B- Significant variable from NRS2Grp ANOVA. Output modified from SPSS. Descriptives N L5minU5 U5vsL5 U5PerU456 L5PerU456 U5PerL456 Mean Minimum Maximum 26 1.1819 0.4478 0.0878 1.0011 1.3628 .130 2.010 1 29 0.7369 0.4077 0.0757 0.5818 0.8920 .050 1.500 Total 55 0.9473 0.4789 0.0646 0.8178 1.0767 .050 2.010 0 26 0.9206 0.0279 0.0055 0.9093 0.9319 .873 .990 1 29 0.9501 0.0265 0.0049 0.9401 0.9602 .904 .996 Total 55 0.9362 0.0308 0.0041 0.9279 0.9445 .873 .996 0 26 0.2800 0.0082 0.0016 0.2767 0.2833 .266 .298 1 29 0.2841 0.0063 0.0012 0.2817 0.2865 .274 .298 Total 55 0.2821 0.0075 0.0010 0.2801 0.2842 .266 .298 0 26 0.3043 0.0092 0.0018 0.3005 0.3080 .278 .319 1 29 0.2992 0.0088 0.0016 0.2958 0.3025 .285 .317 Total 55 0.3016 0.0093 0.0013 0.2991 0.3041 .278 .319 0 26 0.2641 0.0099 0.0019 0.2601 0.2681 .246 .286 1 29 0.2695 0.0086 0.0016 0.2662 0.2728 .253 .289 Total 55 0.2669 0.0096 0.0013 0.2643 0.2695 .246 .289 Between Groups Within Groups U5PerU456 L5PerU456 U5PerL456 Mean Square 2.715 1 2.715 .182 9.667 53 12.382 54 Between Groups .012 1 .012 Within Groups .039 53 .001 Total .051 54 Between Groups .000 1 .000 Within Groups .003 53 .000 Total .003 54 Between Groups .000 1 .000 Within Groups .004 53 .000 Total .005 54 Between Groups .000 1 .000 Within Groups .005 53 .000 Total .005 54 Total U5vsL5 Std. Error 0 ANOVA Sum of Squares df L5minU5 Std. Deviation 95% Confidence Interval for Mean Lower Upper Bound Bound F Sig. 14.886 .000 16.191 .000 4.413 .040 4.395 .041 4.703 .035 68 APPENDIX C Table C- Significant variables from NRS3Grp ANOVA. Output modified from SPSS Descriptives 95% Confidence Interval for Mean N U5sWidth 0 1 2 Total L5minU5 0 1 2 Total U5vsL5 0 1 2 Total U5PerL456 0 1 2 Total Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum 19 13.401 0.769 0.176 13.030 13.771 12.260 15.580 21 13.761 1.008 0.220 13.303 14.220 11.850 16.100 15 14.207 0.824 0.213 13.751 14.663 12.260 15.290 55 13.758 0.922 0.124 13.509 14.008 11.850 16.100 19 1.084 0.425 0.098 0.879 1.289 .130 1.870 21 1.059 0.432 0.094 0.862 1.256 .460 2.010 15 0.618 0.475 0.123 0.355 0.881 .050 1.500 55 0.947 0.479 0.065 0.818 1.077 .050 2.010 19 0.926 0.029 0.007 0.912 0.939 .873 .990 21 0.929 0.025 0.006 0.918 0.941 .878 .967 15 0.959 0.030 0.008 0.942 0.976 .904 .996 55 0.936 0.031 0.004 0.928 0.944 .873 .996 19 0.265 0.011 0.003 0.260 0.270 .246 .286 21 0.265 0.007 0.002 0.262 0.268 .253 .276 15 0.272 0.009 0.002 0.267 0.277 .256 .289 55 0.267 0.010 0.001 0.264 0.270 .246 .289 ANOVA U5sWidth L5minU5 U5vsL5 U5PerL456 Between Groups Within Groups Total Between Groups Within Groups Total Between Groups Within Groups Total Between Groups Within Groups Total Maximum Sum of Squares df Mean Square F Sig. 5.457 2 2.728 3.507 .037 40.455 52 .778 45.912 54 2.242 2 1.121 5.749 .006 10.140 52 .195 12.382 54 .011 2 .005 7.072 .002 .040 52 .001 .051 54 .001 2 .000 3.652 .033 .004 52 .000 .005 54 69 Multiple Comparisons Tukey HSD Mean Difference (IJ) Dependent Variable U5sWidth 95% Confidence Interval Lower Bound Upper Bound 1 -.360902 .279272 .4059 -1.03467 .31287 2 * -.806807 .304650 .0283 -1.54180 -.07181 0 .360902 .279272 .4059 -.31287 1.03467 2 -.445905 .298181 .3014 -1.16529 .27348 0 * .806807 .304650 .0283 .07181 1.54180 1 .445905 .298181 .3014 -.27348 1.16529 1 .024637 .139816 .9830 -.31268 .36196 2 * .465684 .152522 .0098 .09771 .83366 0 -.024637 .139816 .9830 -.36196 .31268 2 .441048* .149283 .0128 .08089 .80121 0 -.465684* .152522 .0098 -.83366 -.09771 1 -.441048* .149283 .0128 -.80121 -.08089 1 -.003662 .008801 .9091 -.02490 .01757 2 -.033379* .009601 .0029 -.05654 -.01022 0 .003662 .008801 .9091 -.01757 .02490 2 * .009397 .0072 -.05239 -.00705 * .009601 .0029 .01022 .05654 1 * .029716 .009397 .0072 .00705 .05239 1 -.000070 .002892 .9997 -.00705 .00691 2 -.007511 .003155 .0538 -.01512 .00010 0 .000070 .002892 .9997 -.00691 .00705 2 -.007441 .003088 .0504 -.01489 .00001 0 .007511 .003155 .0538 -.00010 .01512 1 .007441 .003088 .0504 -.00001 .01489 0 Std. Error Sig. 1 2 L5minU5 0 1 2 U5vsL5 0 1 0 -.029716 .033379 2 U5PerL456 0 1 2 *. The mean difference is significant at the 0.05 level. 70 APPENDIX D Table D- Linear regression output of all sig. variables from NRS2Grp and NRS3Grp ANOVA from SPSS. Descriptive Statistics Mean NetResSpc Std. Deviation N 1.11491 .921062 55 13.75836 .922070 55 L5minU5 .94727 .478851 55 U5vsL5 .93618 .030763 55 U5PerL456 .26694 .009573 55 U5PerU456 .28214 .007468 55 .30158 .009299 55 U5sWidth L5PerU456 Correlations Pearson Correlation Sig. (1tailed) N NetResSpc U5sWidth L5minU5 1.000 .377 -.431 U5sWidth .377 1.000 -.067 .199 L5minU5 -.431 -.067 1.000 -.988 U5vsL5 .474 .199 -.988 1.000 .666 U5PerL456 .389 .529 -.613 .666 U5PerU456 .338 .583 -.404 .470 L5PerU456 -.207 .291 .704 .002 NetResSpc NetResSpc U5vsL5 U5PerL456 U5PerU456 L5PerU456 .389 .338 -.207 .529 .583 .291 -.613 -.404 .704 .470 -.658 1.000 .860 .026 .860 1.000 .355 -.658 .026 .355 1.000 .001 .000 .002 .006 .065 .314 .072 .000 .000 .016 .000 .000 .001 .000 .000 .000 .000 .000 .424 .474 U5sWidth .002 L5minU5 .001 .314 U5vsL5 .000 .072 .000 U5PerL456 .002 .000 .000 .000 U5PerU456 .006 .000 .001 .000 .000 L5PerU456 .065 .016 .000 .000 .424 .004 NetResSpc 55 55 55 55 55 55 55 U5sWidth 55 55 55 55 55 55 55 L5minU5 55 55 55 55 55 55 55 U5vsL5 55 55 55 55 55 55 55 U5PerL456 55 55 55 55 55 55 55 U5PerU456 55 55 55 55 55 55 55 L5PerU456 55 55 55 55 55 55 55 71 .004 Variables Entered/Removed Model 1 Variables Entered Variables Removed L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, b U5vsL5 a Method Enter a. Dependent Variable: NetResSpc b. All requested variables entered. b Model Summary Change Statistics Model 1 R Adjusted R Square R Square .586a .343 Std. Error of the Estimate .261 R Square Change .791559 F Change .343 df1 4.186 6 a. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5 b. Dependent Variable: NetResSpc ANOVAa Sum of Squares Model 1 Regression Mean Square df 15.736 6 2.623 Residual 30.075 48 .627 Total 45.811 54 F Sig. 4.186 .002b a. Dependent Variable: NetResSpc b. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5 Coefficientsa Unstandardized Coefficients Model 1 (Constant) B Std. Error -132.544 99.127 .590 .301 U5sWidth L5minU5 Standardized Coefficients Beta t Sig. -1.337 .187 .590 1.958 .056 -4.052 3.748 -2.106 -1.081 .285 U5vsL5 139.178 104.827 4.648 1.328 .191 U5PerL456 -13.080 27.731 -.136 -.472 .639 U5PerU456 -621.332 423.667 -5.038 -1.467 .149 589.857 397.804 5.955 1.483 .145 L5PerU456 a. Dependent Variable: NetResSpc Residuals Statisticsa Minimum Predicted Value Residual Maximum Mean Std. Deviation N .29040 2.74836 1.11491 .539821 55 -1.613278 2.133616 .000000 .746289 55 .000 1.000 55 .000 .943 55 Std. Predicted -1.527 3.026 Value Std. -2.038 2.695 Residual a. Dependent Variable: NetResSpc 72 df2 48 Sig. F Change .002 a b c Figure D- Histogram (a), P-P Plot (b), and Scatterplot with regression (c) charts from linear regression of all sig variables from NRS2Grp and NRS3Grp ANOVA. Output from SPSS. 73 APPENDIX E Table E- Backward regression of all significant variables from NRS2Grp and NRS3Grp ANOVA. Output from SPSS. Descriptive Statistics Mean NetResSpc Std. Deviation N 1.11491 .921062 55 13.75836 .922070 55 L5minU5 .94727 .478851 55 U5vsL5 .93618 .030763 55 U5PerL456 .26694 .009573 55 .28214 .007468 55 .30158 .009299 55 U5sWidth U5PerU45 6 L5PerU456 Correlations NetResSpc Pearson NetResSpc Correlation U5sWidth L5minU5 Sig. (1tailed) N U5sWidth L5minU5 U5vsL5 U5PerL456 U5PerU456 L5PerU456 1.000 .377 -.431 .474 .389 .338 -.207 .377 1.000 -.067 .199 .529 .583 .291 -.431 -.067 1.000 -.988 -.613 -.404 .704 U5vsL5 .474 .199 -.988 1.000 .666 .470 -.658 U5PerL456 .666 1.000 .860 .026 .389 .529 -.613 U5PerU456 .338 .583 -.404 .470 .860 1.000 .355 L5PerU456 -.207 .291 .704 -.658 .026 .355 1.000 .002 .001 .000 .002 .006 .065 .314 .072 .000 .000 .016 .000 .000 .001 .000 .000 .000 .000 .000 .424 NetResSpc U5sWidth .002 L5minU5 .001 .314 U5vsL5 .000 .072 .000 U5PerL456 .002 .000 .000 .000 U5PerU456 .006 .000 .001 .000 .000 L5PerU456 .065 .016 .000 .000 .424 .004 NetResSpc 55 55 55 55 55 55 55 U5sWidth 55 55 55 55 55 55 55 L5minU5 55 55 55 55 55 55 55 U5vsL5 55 55 55 55 55 55 55 U5PerL456 55 55 55 55 55 55 55 U5PerU456 55 55 55 55 55 55 55 55 55 55 55 55 55 55 L5PerU456 74 .004 Variables Entered/Removed Variables Entered Model 1 a Variables Removed Method L5PerU456, U5PerL456, U5sWidth, U5PerU456 , L5minU5, b U5vsL5 Enter 2 U5PerL456 Backward (criterion: Probability of F-toremove >= .100). L5minU5 Backward (criterion: Probability of F-toremove >= .100). L5PerU456 Backward (criterion: Probability of F-toremove >= .100). U5PerU456 Backward (criterion: Probability of F-toremove >= .100). 3 4 5 a. Dependent Variable: NetResSpc b. All requested variables entered. Model Summaryf Change Statistics Model 1 2 R R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change df1 df2 Sig. F Change .586a .343 .261 .791559 .343 4.186 6 48 .002 b .340 .273 .785254 -.003 .222 1 48 .639 3 .583 c .571 .326 .272 .786075 -.015 1.105 1 49 .298 4 .556d .309 .268 .787922 -.017 1.240 1 50 .271 5 e .307 .281 .781160 -.002 .111 1 51 .740 .554 a. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5 b. Predictors: (Constant), L5PerU456, U5sWidth, U5PerU456, L5minU5, U5vsL5 c. Predictors: (Constant), L5PerU456, U5sWidth, U5PerU456, U5vsL5 d. Predictors: (Constant), U5sWidth, U5PerU456, U5vsL5 e. Predictors: (Constant), U5sWidth, U5vsL5 f. Dependent Variable: NetResSpc 75 a Coefficients Unstandardized Coefficients Model 1 (Constant) U5sWidth L5minU5 2 .590 .301 t Sig. -1.337 .187 .590 1.958 .056 3.748 -2.106 -1.081 .285 139.178 104.827 4.648 1.328 .191 U5PerL456 -13.080 27.731 -.136 -.472 .639 U5PerU456 -621.332 423.667 -5.038 -1.467 .149 L5PerU456 589.857 397.804 5.955 1.483 .145 (Constant) -136.469 97.990 -1.393 .170 .566 .295 .567 1.922 .060 -3.891 3.702 -2.023 -1.051 .298 U5vsL5 143.041 103.674 4.777 1.380 .174 U5PerU456 -641.180 418.214 -5.199 -1.533 .132 L5PerU456 598.433 394.223 6.042 1.518 .135 (Constant) -121.597 97.064 -1.253 .216 U5sWidth .297 .145 .297 2.043 .046 127.275 102.691 4.251 1.239 .221 U5PerU456 -383.966 339.487 -3.113 -1.131 .263 L5PerU456 357.488 321.048 3.609 1.114 .271 (Constant) -13.626 4.406 -3.093 .003 .321 .144 .321 2.229 .030 3.279 .002 U5vsL5 U5sWidth U5vsL5 5 Beta 99.127 -4.052 L5minU5 4 Std. Error -132.544 U5vsL5 U5sWidth 3 B Standardized Coefficients 13.014 3.969 .435 U5PerU456 -6.582 19.728 -.053 (Constant) -14.559 3.376 .294 .118 12.426 3.526 U5sWidth U5vsL5 a. Dependent Variable: NetResSpc 76 -.334 .740 -4.312 .000 .294 2.496 .016 .415 3.524 .001 Excluded Variables a Collinearity Statistics Model 2 U5PerL456 3 Beta In U5PerL456 Tolerance -.472 .639 -.068 .165 c -.375 .710 -.053 .166 c -1.051 .298 -.148 .004 U5PerL456 -2.023 d -.144 -.504 .617 -.071 .168 L5minU5 -.324d -.204 .839 -.029 .005 d 1.114 .271 .156 .001 -.109 e -.586 .561 -.082 .393 -.262 e -.167 .868 -.023 .006 -.051 e -.269 .789 -.038 .382 -.053 e -.334 .740 -.047 .530 L5PerU456 5 Partial Correlation Sig. -.136b -.108 L5minU5 4 t 3.609 U5PerL456 L5minU5 L5PerU456 U5PerU456 a. Dependent Variable: NetResSpc b. Predictors in the Model: (Constant), L5PerU456, U5sWidth, U5PerU456, L5minU5, U5vsL5 c. Predictors in the Model: (Constant), L5PerU456, U5sWidth, U5PerU456, U5vsL5 d. Predictors in the Model: (Constant), U5sWidth, U5PerU456, U5vsL5 e. Predictors in the Model: (Constant), U5sWidth, U5vsL5 Residuals Statisticsa Minimum Predicted Value Residual Maximum Std. Deviation Mean N .07060 2.18301 1.11491 .510632 55 -1.706587 1.986473 .000000 .766558 55 2.092 .000 1.000 55 2.543 .000 .981 55 Std. Predicted -2.045 Value Std. -2.185 Residual a. Dependent Variable: NetResSpc 77 a b c Figure E- Histogram (a), P-P Plot (b), and Scatterplot regression (c) charts for backward regression of all sig variables from NRS2Grp and NRS3Grp ANOVA. Output from SPSS. 78 APPENDIX F Table F- Individual regression for U5vsL5 and U5sWidth. Output modified from SPSS. Descriptive Statistics Std. Deviation Mean NetResSpc .921062 55 .93618 .030763 55 13.75836 .922070 55 U5vsL5 U5sWidth N 1.11491 Correlations NetResSpc Pearson Correlation Sig. (1tailed) NetResSpc .474 U5vsL5 .474 1.000 U5sWidth .377 1.000 NetResSpc .000 U5vsL5 N .000 NetResSpc 55 U5vsL5 2 55 55 Variables Entered/Removed Model 1 U5vsL5 1.000 Variables Entered 55 a Variables Removed b U5vsL5 Method Enter b U5sWidth Enter a. Dependent Variable: NetResSpc b. All requested variables entered. Model Summaryb Change Statistics Model 1 R 2 R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change .224 .210 .818810 .224 15.329 1 53 .000 a .142 .126 .861198 .142 8.768 1 53 .005 .377 b. Dependent Variable: NetResSpc ANOVAa 2 Sum of Squares Regression Mean Square df 10.277 1 10.277 Residual 35.534 53 .670 Total 45.811 54 6.503 1 6.503 39.308 53 .742 45.811 54 Regression Residual Total Sig. F Change df2 .474a a. Predictors: (Constant), U5vsL5, U5sWidth Model 1 df1 79 F Sig. 15.329 .000b 8.768 .005b a. Dependent Variable: NetResSpc, b. Predictors: (Constant), U5vsL5, U5sWidth a Coefficients Unstandardized Coefficients Model 1 B (Constant) U5vsL5 2 (Constant) U5sWidth Standardized Coefficients Std. Error -12.161 3.393 14.181 3.622 -4.063 1.753 .376 .127 Beta t .474 .377 Sig. -3.585 .001 3.915 .000 -2.318 .024 2.961 .005 a. Dependent Variable: NetResSpc Residuals Statistics Model 1 U5vsL5 Minimum Predicted Value Residual Std. Predicted Value 2 U5sWidth Std. Residual Predicted Value Residual Std. Predicted Value Maximum a Std. Deviation Mean N .22086 1.96929 1.11491 .436258 55 -1.834508 2.136065 .000000 .811193 55 -2.049 1.958 .000 1.000 55 -2.240 2.609 .000 .991 55 .39668 1.99620 1.11491 .347028 55 -1.696164 2.128661 .000000 .853186 55 -2.070 2.540 .000 1.000 55 .000 .991 55 Std. -1.970 2.472 Residual a. Dependent Variable: NetResSpc 80 VITA AUCTORIS Anthony D. Mongillo was born in Tallahassee, Florida on January 2, 1985 to Mark and Renee Mongillo. He has one younger brother, David. His early childhood years were spent mostly in Safety Harbor, Florida. Being in an adventurous family, he moved with his family to Geneva, Switzerland in 2000 where he spent his high school years learning French and playing rugby. He graduated from the International School of Geneva with an International Baccalaureate Diploma in 2003. After living in Europe, Anthony spent one year attending Brigham Young University in Provo, Utah where he met his love, Elise Tateoka. However, in 2004 they parted ways while Anthony took a two-year sabbatical to serve a church mission to Seoul, Korea where he also learned Korean. Anthony and Elise were reunited again after Elise returned from her mission to Hawaii, and they were eventually married in Bern, Switzerland in 2008. Anthony graduated with a Bachelor of Science degree in Physiology and Developmental Biology in 2009. Dr. Mongillo attended Nova Southeastern University in Ft. Lauderdale, Florida where completed his Doctor of Medicine in Dentistry degree in 2013, but not before adding two sons, Oliver and Nikolas, to his family. Dr. Mongillo plans to receive his Master of Science degree from Saint Louis University in 2015. 81