Maxillary central incisor crown-root relationships in Class I normal occlusions and Class II division 2 malocclusions

Transcription

1 University of Iowa Iowa Research Online Theses and Dissertations Spring 2014 Maxillary central incisor crown-root relationships in Class I normal occlusions and Class II division 2 malocclusions Thomas J. Bauer University of Iowa Copyright 2014 Thomas John Bauer This thesis is available at Iowa Research Online: Recommended Citation Bauer, Thomas J.. "Maxillary central incisor crown-root relationships in Class I normal occlusions and Class II division 2 malocclusions." MS (Master of Science) thesis, University of Iowa, Follow this and additional works at: Part of the Orthodontics and Orthodontology Commons

2 MAXILLARY CENTRAL INCISOR CROWN-ROOT RELATIONSHIPS IN CLASS I NORMAL OCCLUSIONS AND CLASS II DIVISION 2 MALOCCLUSIONS. by Thomas J. Bauer A thesis submitted in partial fulfillment of the requirements for the Master of Science degree in Orthodontics in the Graduate College of The University of Iowa May 2014 Thesis Supervisor: Professor Robert N. Staley

3 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL MASTER'S THESIS This is to certify that the Master's thesis of Thomas J. Bauer has been approved by the Examining Committee for the thesis requirement for the Master of Science degree in Orthodontics at the May 2014 graduation. Thesis Committee: Robert N. Staley, Thesis Supervisor David Jones Lina Moreno Uribe Fang Qian

4 ACKNOWLEDGMENTS I wish to thank the members of my thesis committee Drs. Robert Staley, Lina Moreno Uribe, David Jones, and Fang Qian for their assistance with this project. I also wish to express my gratitude to the faculty I have had here at the University of Iowa. They have made this residency my favorite years of all my education. A special thanks to my wife Eden, my daughter Maddy, and son Hayden for bringing me love and happiness beyond what I ever thought possible. ii

5 TABLE OF CONTENTS LIST OF TABLES... iv LIST OF FIGURES...v INTRODUCTION...1 LITERATURE REVIEW...4 The collum angle...4 The occlusal plane...7 MATERIALS AND METHODS...9 Sample selection...9 Cephalometric data...11 Description of measurements...12 Measurement reliability...17 Intra-observer agreement...18 Inter-observer agreement...20 Statistical analysis...22 RESULTS...23 Mean CA for Class I normal occlusions...23 Correlation between CA and LCRA...23 Analysis of torque measurements...29 Analysis of CA and LCRA measurements...31 Comparisons of CA and LCRA between two groups...31 Comparisons of CA and LCRA among three groups...31 DISCUSSION...36 Case report...37 Mean CA for Class I normal occlusions...42 Correlation between CA and LCRA...42 Torque...43 CA, LCRA differences between Class I normal occlusions and... Class II division 2 malocclusions...44 Limitations of the study...45 Future research...47 CONCLUSIONS...48 REFERENCES...49 iii

6 LIST OF TABLES Table 1. Interpretation of the intraclass correlation coefficient Intra-observer measurement agreement for CA, LCRA, and torque Inter-observer measurement agreement for CA, LCRA, and torque Interpretation of the Pearson s correlation coefficient Mean torque values among the three sample groups Mean CA values among the three sample groups Mean LCRA values among the three sample groups Comparisons of CA, LCRA and Torque between D.W. and expected means for a Class II division 2 malocclusion iv

7 LIST OF FIGURES Figure 1. The collum angle The labial crown-root angle The torque angle Correlation between CA and LCRA for all samples Correlation between CA and LCRA for Class I ideal samples Correlation between CA and LCRA for Class I expanded samples Correlation between CA and LCRA for Class II division 2 samples Box and whisker plot of torque among groups Box and whisker plot of CA among groups Box and whisker plot of LCRA among groups Pre-treatment radiographs of Class II division 2 patient D.W Post-treatment radiographs of patient D.W v

8 1 INTRODUCTION The practice of modern orthodontics is largely based on the use of the straightwire edgewise appliance originally described by Andrews in The advent of this technique has allowed the orthodontist to practice more efficiently by placing fewer bends in wires, particularly at the finishing stages of treatment, with more predictable results. The limitations of the straight-wire appliance become apparent, however, when one considers the variability inherent in natural crown forms, as well as the variability of root position in relation to the clinical crown. While the former may be readily visualized and compensated for by alterations in wire or bracket position, the latter is typically not addressed routinely in clinical practice. Typically, the root angulation in relation to the crown is assumed to be zero, and in fact this assumption is built in to standardized cephalometric incisor tracing templates. This is in spite of the fact that variations in the crown-root angle, or "collum angle" (CA), have been described by several authors as occurring in various types of malocclusions, particularly Class II division 2 patients, as discussed below (Bryant 1984, Delivanis 1980). Kaley and Phillips (1991) have shown that root translation or torqueing into the palatal cortex significantly increases the odds of root resorption. Thus to achieve greater predictability in root position, and to anticipate difficulties with intrusion, extrusion, or torqueing mechanics, it seems that a more thorough understanding of crown-root relationships in the bucco-lingual plane, and their application to clinical practice, is warranted. Cephalometric landmarks and measurements gain clinical acceptance not only because they yield diagnostic information, but also because they are reliable, stable, and reproducible. Nevertheless Baumrind and Frantz (1971) have shown that errors in landmark identification are too great to be ignored, and that the amount of error depends on the landmark identified. Additionally, they noted the amount of error increases when a landmark is constructed (a bisection or tangent line), interpreted (a point on a curve), or

9 2 confounded by noise of adjacent structures (superimposition). For example, the maxillary central incisor collum angle is defined by three points: U1 (central incisor) incisal edge (incision superius), the bisection point of labial and lingual cementoenamel junctions, and U1 root apex. This measurement suffers from poor reliability and limited clinical utility because it is by nature constructed, and defined in part by a point (lingual CEJ) that is often superimposed by other structures. U1 torque is another measurement that has suffered a similar fate. Intended to define the desired third order position of the clinical crown, torque has been defined by various authors as a tangent point at various levels on the clinical crown. The rigor of this definition is weakened because it requires interpretation, and as a result, incisor bracket prescriptions vary widely in their torque values, and are still debated. This investigation proposes new angular measurements of crown-root angulation and torque that are constructed of visible anatomic points, in the hope of increasing their reliability and usefulness. An analysis using these measurements will be conducted on a control sample and an experimental sample of Class II division 2 subjects to assess their merit. The purposes of the present study are several. First, this investigation proposes to establish a mean value for maxillary incisor CAs from a given sample of Class I normal occlusions. To our knowledge, mean CA values have thus far been obtained only for subjects with malocclusion. The null hypothesis states that the mean CA for Class I normal occlusions is not statistically different from zero. Second, we wish to identify a new crown-to-root angle, defined by three anatomic points: U1 incisal edge, U1 labial cementoenamel junction, and U1 root apex. We will define this angle as the "labial crown root angle" (LCRA) and attempt to correlate it with the CAs of the same sample. We believe the utility of this new angle lies in the ease with which these three points can typically be identified anatomically on lateral cephalometric radiographs, the fact that they are already used in standard cephalometric tracings, and the closer approximation

10 3 they should have with the actual position of the straight wire bracket on the labial surface of an incisor. Previous efforts to identify the surface angle on which the bracket will be placed have involved rather complex algorithms for determining the constructed tangent line or curve of the given surface. These processes may be too cumbersome for everyday practice. If the LCRA can be correlated with the CA of a given tooth, then difficulties with abnormal root positioning could be anticipated directly from this simple measurement. The null hypothesis specifies that the CA and the LCRA will not have a statistically significant correlation. Third, this investigation will measure torque using anatomic points, and use descriptive statistics to identify a mean torque angle in the Class I normal occlusion sample group in order to identity an ideal bracket prescription for incisors in normal occlusion. Fourth and finally, we will analyze the CA and LCRA for a sample of known Class II division 2 subjects to detect any differences with Class I normal occlusions, and correlate the CA and the LCRA for the Class II division 2 sample. The null hypothesis states that these measurements will be no different from those observed in Class I normal occlusions.

11 4 LITERATURE REVIEW The collum angle Although Andrews introduced the concept of the straight wire appliance as early as 1968, his description of it and the philosophy behind its use in treatment is best outlined in his 1989 book, Straight Wire: The Concept and Appliance. In it, he reiterates the well-known six keys to normal occlusion, of which crown inclination is the third. He describes the method by which crown inclination is determined, using a constructed tangent line on the facial surface of the clinical crown as it intersects with a line drawn perpendicular to the occlusal plane. Using this method, he determined average crown inclination for every tooth in the arches, and specified the maxillary incisor crown to be, on average, inclined plus seven degrees. The sample used by Andrews (1989) was comprised of 120 sets of records from patients with naturally occurring normal occlusion, collected from various sources over a period of four years. Although the modern straight wire appliance is based on these findings, Andrews never addressed the possibility that the crown and root of a given tooth may be inclined relative to each other. Indeed, in Chapter 9, entitled Fully Programmed Standard Brackets, drawings pertaining to crown inclination assume that the collum angle (CA) is zero for each tooth. One is left to wonder if Andrews originated the assumption of the zero degree CA. Carlsson and Ronnerman (1973) investigated CAs on 88 extracted teeth. They categorized their sample according to the amount of abrasion found, and it was presumed by the authors that incision superius tends to move facially as abrasion progresses. The type of malocclusion for each sample was not reported. Thirty-four teeth comprised Group I, which was characterized by enamel abrasion only and a mean CA of -0.4 degrees. Group II, consisting of 29 teeth, exhibited moderate abrasion into dentin and a mean CA of 0 degrees. Group III, 25 teeth, exhibited severe abrasion into dentin and a mean CA of 2.6 degrees. Unfortunately, the mean values ascertained in this study are not

12 5 particularly informative. First, it seems problematic to make measurements of damaged teeth on which one of the points to be measured is missing or distorted. This can hardly be expected to capture the natural prevalence of CAs in the general population. Secondly, the authors noted the large ranges in their measurements: 11 degrees, 13 degrees, and 11.5 degrees, respectively, for Groups I, II, and III. These ranges show that CAs are highly variable and warrant examination for identifiable patterns. Finally, as mentioned previously, samples were not categorized according to Angle classification and so any ability to find mean values in normal occlusion is lost. Delivanis and Kuftinec (1980) conducted a retrospective study consisting of fiftythree patients who were diagnosed clinically with Class II division 2 malocclusion, and fifty-three matched control patients who exhibited a variety of other malocclusions, excluding Class I normal occlusion and Class II division II malocclusion. No control group with normal occlusion was studied. The authors found that the mean CA for Class II division 2 patients was 6.14 ± 5.14 degrees, compared to control values of 1.52 ± 4.36 degrees. The authors concluded that the statistically significant bent character of incisors in Class II division 2 malocclusions may account for anecdotal evidence of unpredictability when intruding or torqueing these teeth. Bryant et al (1984) conducted an investigation in two phases, using two different samples. In the first phase, 98 extracted central incisors were placed into one of four categories according to the type of malocclusion from which each sample originated. Again, no sample from Class I normal occlusions was identified. Each sample was radiographed, magnified, and measured. In the second phase of the study, the authors obtained 100 cephalometric radiographs and categorized them in the same way as in the first phase. Only patients with malocclusion were sampled, and in fact the sample was chosen with preference given to patients with the most severe and readily identifiable malocclusions. Based on the combined measurements from both phases of the study, the authors concluded that crowns of incisors from patients with Class II division 2

13 6 malocclusion are "bent" lingually to a degree that is statistically greater than the other categories. No other significant differences in incisor anatomy between the four groups were noted. The problematic nature of inconsistencies in straight wire appliance theory has been addressed by some authors. Vardimon and Lambertz (1986) recorded normal torque values on models of fifty-four ideal occlusions, thirty-four treated and twenty untreated. The molar classification of the subjects was not noted, and discussion was limited only to crown position. The authors studied torque values for all teeth in each case, and noted wide variability in all cases. Of particular interest to this study, the authors noted an average torque value of 1 ± 5 degrees for the maxillary central incisor, which contrasts with Andrews (7 degrees) and Ricketts (22 degrees) data. They also acknowledged-- but did not include within the scope of their study-- the wide variability in CA, the impossibility of consistent tangent line placement on facial surfaces of crowns, and the unpredictability of treatment mechanics that may result if the first two problems are not satisfactorily addressed. Germane et al (1989) studied a sample of 600 extracted teeth, from incisors to molars, in order to determine mean facial contour values for homologous teeth from different individuals, mean faciolingual contours when viewed from the incisal/occlusal, and mean CAs. The facial contour means were calculated using multiple constructed tangent lines that intersected various points surrounding the facial midpoint of the incisogingival dimension of the clinical crown, or LA point. Importantly, the authors found that variability in facial contour increases as one proceeds posteriorly in the dentition. The authors also found no evidence that the CAs for the maxillary central incisor, maxillary second premolar, and first molar were statistically different from zero. The standard deviation for maxillary central incisors was found to be approximately ±3 degrees. No effort was made to categorize extracted teeth according to the type of

14 7 occlusion in which they were found, and the variability of CAs in different malocclusions discussed previously was not addressed. Harris et al (1993) studied cephalometric samples of central incisors from treated cases of Class I, II, and III malocclusions. The three goals of this study were to establish mean values for crown-root angulations in these three types of malocclusions, to determine if crown-root angulation predisposed to root resorption, and to discover cephalometric predictors of crown-root angulation. No attempt was made to establish a mean value for CAs found in Class I normal occlusions. He determined that Class I and II malocclusions exhibited mean CAs of 6.1 and 5.6 degrees, respectively, with no statistically significant difference between them. However, class III malocclusions were shown to have a different, statistically significant mean CA of about 12 degrees. With regard to root resorption, the study found no statistically significant relationship between molar classification and resorption, nor between CA and resorption. The relevance of this finding will be addressed in the discussion of the present study. Cephalometric prediction of CAs was related to cases of extreme Class III malocclusion, in which cephalometric prognathism was combined with a smaller U1-FH angle, indicating that the maxillary incisors were contained within the lower arch due to negative overjet. The possibility that a higher CA may cause a predisposition for anterior crossbite is not discussed. Instead, it is presumed that alterations in CA occur in situations where a tooth is deflected lingually as it erupts and its root is mineralized. The occlusal plane Downs originally defined the occlusal plane as a line drawn from the bisection of mesiobuccal cusp tips of the first molars to the bisection of the incisal edges of the most anterior central incisors. He revised this definition for cases in which incisors were severely malpositioned, limiting the occlusal plane in such cases to the bisection of overlapping cusps on the first molars and first premolars (1948, 1952, 1956). This

15 8 functional definition of the occlusal plane was later endorsed by Steiner and Ricketts (Jacobson 1985). For a malocclusion in which the incisors are stepped up or down, the occlusal plane derived from Downs original definition may be distorted, and so modifying the definition to limit the plane posteriorly is a logical step. Nevertheless, it was the original definition that was chosen for this study, since incisal edges of the most anterior central incisors are typically more readily visible on cephalometric radiographs, and indeed are already landmarked on a typical cephalometric analysis..

16 9 MATERIALS AND METHODS Sample selection This investigation was designed as a retrospective, cross-sectional study to measure the CA, LCRA, and torque angle of maxillary central incisors on patients with Class I normal occlusions and Class II division 2 malocclusions. Samples with normal occlusion, taken from the Iowa Growth Study conducted by Meredith and Knott (1973), were so designated as having Class I molars with mild crowding/spacing. The normal sample was further subdivided into two groups, an ideal sample with 1mm of crowding/spacing, and an expanded sample with 2-4mm of crowding/spacing. Both groups were utilized for this study. The Iowa Growth Study, conducted by Howard V. Meredith and L.B. Higley, began in 1946 (Meredith and Knott, 1973). It consisted of 130 subjects. Ninety-seven percent of the subjects were of northwestern European ancestry and the remaining three percent were of central or southeastern European lineage. Dental casts were made twice every year until age 12, annually until age 17 and periodically through adulthood on patients that remained in the study. The sample was described as follows, All members of the sample resided in or near Iowa City, Iowa, and were voluntary participants in a long-term research program begun in 1946 at the State University of Iowa. Enrollment for study was based on willingness to participate and likelihood of continuing residence in the community. The subjects were physically normal children unselected in respect to cephalic or faciodental characteristics (Meredith and Knott, 1973). The normal sample of subjects in the Iowa Growth Study was originally defined in a previous thesis conducted by Kuntz, in which the subjects were separated into groups based on Angle molar classification and amount of crowding/spacing (Kuntz, 1993). The subjects selected by Kuntz for the normal sample had good occlusion with a Class I

17 10 molar relationship, mild crowding/spacing, and no other skeletal or dental abnormalities of note. For the purposes of our study, the normal sample was further divided based on magnitude of crowding/spacing, with one group exhibiting 1 mm of crowding/spacing, and the other 2-4mm of crowding/spacing. Subjects that had orthodontic treatment previously were excluded, since this would confound our ability to observe ideal, naturally occurring torque values. Subjects whose cephalometric radiographs were of generally poor quality, or those for whom measurements were not easily readable, were also excluded. These limitations reduced the Class I normal occlusion sample size from 74 to 57. The sample included radiographs from 31 males and 26 females. Of those there were 33 patients (17 male and 16 female) with 1 mm of crowding/spacing and 24 patients (14 male and 10 female) with 2-4mm of crowding/spacing. The sample of Class II division 2 malocclusion subjects used for this study was obtained from two sources. Lists of previously treated patients with certain malocclusions are maintained in the University of Iowa orthodontics department for study by future residents. Thirty-seven of the Class II division 2 subjects were identified in this way. After the exclusion criteria were applied to this group, thirty-one records of high quality, for which relevant landmarks could be easily identified, remained. The second method used to populate the Class II division 2 sample was to utilize a sample previously identified in a University of Iowa master s thesis written by Huth (1988). This source yielded a further seventeen subjects, which was reduced to eleven after exclusion criteria were applied. Thus the entire sample of Class II division 2 malocclusion subjects for this study was comprised of forty-two cephalometric radiographs. Class II division 2 malocclusion subjects exhibited, at a minimum, 3mm of antero-posterior Class II discrepancy bilaterally, or 6 mm of Class II discrepancy unilaterally. This is consistent with American Board of Orthodontics standards for Class II case submission. These subjects were also previously characterized by various

18 11 providers as division 2 because of a retroclined position of maxillary central incisors. No attempt was made in this study to dispute this characterization or standardize the minimum amount of upper incisor retrusion necessary to qualify for division 2 status. Although it is relatively easy to find records of patients with Class II division 2 malocclusion in the long history of the University of Iowa orthodontics clinic, it must be reiterated that multiple methods for obtaining these records were employed to ensure that those utilized for our study were of the highest quality possible. In short, subjects were chosen that exhibited obvious landmarks. All samples were scanned, uploaded, and measured in Dolphin Imaging software (version 11.5). Paixao et al observed that measurements using Dolphin Imaging version 11 are reliable and reproducible. Measurements were recorded in Excel spreadsheets Cephalometric data Original lateral cephalometric radiographs from the Iowa Growth Study were scanned, digitized, and loaded into Dolphin for landmark identification and measurement. Scanning and basic image formatting was accomplished by the University of Iowa College of Dentistry Educational Media Department. Since all of the measurements for this study were angular, no image calibration was necessary. A customized analysis was then created to serve the needs of this investigation. Since Dolphin lacks the capability to measure the collum angle or labial crown root angle per se, landmark labels typically used for other purposes were simply re-utilized for these measurements. Prior to landmark identification, samples were subjected to our exclusion criteria for image quality and clarity. The most common reasons for exclusion were large restorations on the first molars that made identification of the occlusal plane difficult, poor visualization of the root apex due to superimposition of other structures or teeth, and generalized poor image quality due to darkness or contrast. Great emphasis was placed

19 12 on sample quality in this study in order to maximize observer agreement: landmarks on the radiographs chosen were intended to be as obvious as possible. Measurements were accomplished according to a predetermined protocol intended to ensure measurement reliability. The primary observer (T.B.) placed landmarks for all subjects and recorded all measurements in Excel spreadsheets. The statistician (F.Q.) then selected fifteen samples at random for reliability analysis. The digital records of these fifteen samples were duplicated twice, once for intra-observer reliability testing and once for inter-observer reliability testing. T.B. s original landmarks were erased from all duplicate records. The second observer (E.K.), a dental student, was trained on how to identify relevant landmarks, as well as how to utilize the custom analysis tools in Dolphin. Several weeks later, T.B. and E.K. re-accomplished landmark placement and measurement on the selected samples, and recorded their new measurements in separate spreadsheets. This procedure blinded T.B. s second measurements and E.K. s second observer measurements from T.B. s original measurements. All recorded measurements were reviewed and vetted for obvious measurement errors, typographical errors, and omissions. They were formatted to facilitate analysis and were submitted to statistician F.Q. Description of measurements The CA is traditionally measured according to three points on the most anterior maxillary central incisor: the undamaged incisal edge [incisor superius, or IS] (Rakosi 1982), the constructed bisection of the facial and lingual cementoenamel junctions (fcej and lcej, respectively), and the anatomic root apex [upper incisor apicale, or UIA] (Rakosi 1982). The CA is the supplement (180 degrees x) of this angle. A straight tooth will have a CA of zero, a lingually inclined root will have a positive angle, and a labially inclined root will have a negative angle. The traditional CA measurement, used in this study, is illustrated in Figure 1.

20 13 The labial crown root angle (LCRA), as we propose it in this writing, is constructed on a cephalometric radiograph with three points on the most anterior maxillary central incisor: IS, fcej, and UIA. The LCRA is the supplement (180 degrees x) of this angle. It may be more clinically useful than the CA, not only because the plane defined by IS and fcej more closely approximates the labial surface of the upper central incisor crown, but also because the anatomic points of the angle are already typically identified on a cephalometric analysis. The ultimate utility of this measurement, however, depends on how it correlates with the CA, since the ultimate goal of the LCRA is to describe crown-to-root angulation. The labial crown-root angle is illustrated in Figure 2. Torque is defined in this study as an angle formed by two lines. The first line is formed by fcej and IS. This differs from previous definitions of torque that have utilized a tangent line on the labial surface of the crown. The second line is drawn perpendicular to the occlusal plane through IS, where the occlusal plane is identical to that originally defined by Downs: a line from the bisection of U6 occlusal and L6 occlusal surfaces to the bisection of U1 incisal edge and L1 incisal edge (Downs 1948). A positive torque angle indicates buccal crown inclination, and a negative torque angle indicates lingual crown inclination (as was observed in some pre-treatment records of Class II division 2 subjects). The torque angle used in this investigation is illustrated in Figure 3.

21 14 UI lcej X X fcej IS Figure 1. The collum angle (CA).

22 Figure 2. The labial crown-root angle (LCRA). 15

23 Figure 3. The torque angle. 16

24 17 Measurement reliability Fifteen samples (n=5 per group) were randomly selected and used for evaluation of intra- and inter-observer agreement. Intraclass correlation coefficients were computed as a measure of agreement between two duplicate measurements of CA, LCRA, and torque, made on the same subject either by a single observer (T.B.) or by two separate observers (T.B. and E.K.). Table 1 shows an approximate guide for interpreting agreement between two measurements based on the intraclass correlation coefficient. In addition, a paired-sample t-test was used to determine whether a significant difference existed between two duplicated measurements made on the same subject by a single observer or by the two observers. All tests employed a 0.05 level of statistical significance. SAS for Windows (v9.3, SAS Institute Inc., Cary, NC, USA) was used for the data analysis. Table 1. Interpretation of the intraclass correlation coefficient. 0 No agreement Weak agreement Fair agreement Moderate agreement Good agreement Strong agreement 1.00 Perfect agreement

25 18 Intra-observer agreement Intra-observer agreement for CA measurements was evaluated to assess agreement on duplicate measurements made on the same subject by the primary observer (T.B.). Overall, there was very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.98 indicated strong agreement between the two measurements made by the primary observer. Moreover, no significant difference was found between first and second measurements of CA made by observer T.B. (p=0.8770, a paired-sample t-test). The overall mean difference between the two measurements was 0.05±1.15 (Table 2). Intra-observer agreement for LCRA measurements was evaluated similarly. Overall, there was very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.98 indicated strong agreement between the two measurements made by the primary observer. In addition, no significant differences were found between first and second measurements of LCRA made by the primary observer (p=0.3428, a paired-sample t-test). An overall mean difference between the two measurements was -0.30±1.18 (Table 2). Intra-observer agreement for torque measurements, evaluated in the same way, showed very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.99 indicated strong agreement between the two measurements made by observer T.B. Furthermore, there was no statistically significant difference between first and second measurements of torque made by the primary observer (p=0.3601, a paired sample t-test). The overall mean (or median) difference between these two measurements was -0.23±0.96 (Table 2).

26 19 Table 2. Intra-observer measurement agreement for CA, LCRA, and torque. Variable N Mean Std Dev Minimum Maximum Median 1 st CA p-value 2 nd CA CA Difference between 15 1 st and 2 nd Measurements 1 st LCRA * 2 nd LCRA LCRA Difference 15 between 1 st and 2 nd Measurements 1 st Torque * 2 nd Torque Torque Difference between 1 st and 2 nd Measurements * *Not statistically significant (p>.05) using a paired sample t-test.

27 20 Inter-observer agreement An average of the two measurements made by the primary observer (T.B.), compared with the singular measurements of the second observer (E.K.), was used to evaluate the inter-observer reliability of measurements in the study (Table 3). Inter-observer agreement for CA measurements was evaluated to assess agreement of duplicate measurements made on the same subject by the two observers. Overall, there was very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.99 indicated strong agreement between the measurements made by the two observers. Moreover, no significant difference was found between measurements of CA made by the two observers (p=0.5829, a paired sample t-test), with an overall mean (or median) difference of -0.14±0.99 (Table 3). Inter-observer agreement for LCRA measurements was evaluated to assess agreement on duplicate measurements made on the same subject by the two observers. Overall, there was very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.99 indicated strong agreement between the two measurements made by the two observers. No significant difference was found between measurements of LCRA made by the two observers (p=0.0681, a paired sample t-test), with an overall mean (or median) difference of 0.43±0.84 (Table 3). Inter-observer agreement for torque measurements was evaluated to assess agreement on duplicate measurements made on the same subject by the two observers. Overall, there was very strong evidence that the intraclass correlation differed from zero (p<0.0001), and the correlation coefficient of 0.99 indicated strong agreement between measurements made by the two observers. Additionally, there was no statistically significant difference between measurements of torque made by the two observers (p=0.8862, a paired-sample t-test), with a mean difference of -0.04±0.97 (Table 3).

28 21 Table 3. Inter-observer measurement agreement for CA, LCRA, and torque. Variable N Mean Std Dev Minimum Maximum Median 1 st Observer CA p-value 2 nd Observer CA CA Difference between Two Observers 1 st Observer LCRA * 2 nd Observer LCRA LCRA Difference 15 between Two Observers 1 st Observer Torque * 2 nd Observer Torque Torque Difference between Two Observers * *Not statistically significant (p>0.05) using a paired-sample t-test.

29 22 Statistical analysis Comparisons of CA, LCRA and torque measurements between the two groups were performed using the two-sample t-test. When the study samples were divided into three groups (i.e. Class I Ideal, Class I Expanded and Class II division 2), a one-way ANOVA with the post-hoc Tukey-Kramer test was performed to test for a difference among the three groups. Correlations between CA, LCRA and torque were assessed with the Pearson s correlation coefficient. Additionally, one-sample t-test was used to determine whether the mean collum angle was different from zero for a normal maxillary central incisor. Throughout the statistical analyses, a p-value of less than 0.05 was used as a criterion for statistical significance. SAS for Windows (v9.3, SAS Institute Inc, Cary, NC, USA) was used for the data analysis.

30 23 RESULTS Mean CA for Class I normal occlusions The first aim of this investigation was to evaluate whether the mean collum angle is different from zero for a normal maxillary central incisor. The mean CA for the Class I normal group as a whole was 1.78 degrees, which was NOT statistically different from zero at a.05 level of significance, (p=0.0657, one-sample t-test), although a p-value of.0657 is suggestive. Considered separately, the mean CA values (standard deviations) for the Class I Ideal and Expanded groups were 1.09 (3.29) and 2.73 (4.69), respectively. Correlation between CA and LCRA The second aim of this study was to determine whether the LCRA was correlated with the CA. The null hypothesis in this case specifies that there is no correlation between these two independent measurements. Pearson s correlation was used to test for a linear relationship between CA and LCRA. Table 4 illustrates an approximate guide for interpreting the strength of the relationship between two variables, based on the absolute value of the Pearson s correlation coefficient. Table 4. Interpretation of the Pearson s correlation coefficient. ±0.0 No correlation ±0.2 Weak correlation ±0.5 Moderate correlation ±0.8 Strong correlation ±1.0 Perfect correlation

31 24 When all subjects, from all groups, were combined and treated as a single sample (n=99), a significant correlation between CA and LCRA was found using Pearson s correlation (p<0.0001). A Pearson s correlation coefficient of 0.88 for the entire study indicated that there was a strong increasing relationship between the two variables (Figure 7). The sample groups were also analyzed separately. For ideal Class I normal occlusion subjects (n=33), a significant correlation between CA and LCRA was found using Pearson s correlation (p<0.0001). A Pearson s correlation coefficient of 0.76 indicated that there was a moderate increasing relationship between the two variables (Figure 8). For the expanded Class I normal occlusion subjects, (n=24), a significant correlation between CA and LCRA was found using Pearson s correlation (p<0.0001). A Pearson s correlation coefficient of 0.83 indicated that there was a strong increasing relationship between the two variables (Figure 9). For the Class I normal subjects as a whole (n=57), a significant correlation between CA and LCRA was found using Pearson s correlation (p<0.0001). A Pearson s correlation coefficient of 0.80 indicated that there was a strong increasing relationship between the two variables. For the Class II division 2 malocclusion samples (n=42), a significant correlation between CA and LCRA was found using Pearson s correlation (p<0.0001). A Pearson s correlation coefficient of 0.91 indicated that there was a strong increasing relationship between the two variables (Figure 10).

32 25 CA and LCRA Correlation, All Samples (n=99) CA and LCRA Correlation, All Samples (n=99) Linear (CA and LCRA Correlation, All Samples (n=99)) Figure 4. Correlation between CA and LCRA for all samples.* *Pearson s coefficient of 0.88.

33 26 Figure 5. Correlation between CA and LCRA for Class I ideal samples.* *Pearson s coefficient of 0.76.

34 27 Figure 6. Correlation between CA and LCRA for Class I expanded samples.* *Pearson s coefficient of 0.83.

35 28 60 Class II division 2 (n=42) Class II division 2 (n=42) Linear (Class II division 2 (n=42)) Figure 7. Correlation between CA and LCRA for Class II division 2 samples.* *Pearson s coefficient of 0.91.

36 29 Analysis of torque measurements The third aim of this investigation was to establish and evaluate mean torque values for each of the sample groups studied. Results of a one-way ANOVA test revealed that sample category had a significant effect on torque (F (2,96) = 13.56; p = ). The post-hoc Tukey-Kramer test indicated that the mean torque for Class II-2 group was significantly lower than those observed for Class I ideal and expanded groups. However, no significant differences were found between the Class I ideal and expanded groups themselves. Table 5 provides detailed results from the post-hoc Tukey-Kramer test. The data were also divided into two groups (Class I normal and Class II division 2) and analyzed. Based on the two-sample t-test, there was a significant difference in torque between the Class I and Class II-2 groups (p<0.0001). The data showed that mean torque observed in Class I group (12.54±5.82) was significantly greater than that observed in Class II-2 group (3.95±10.85). Table 5. Mean torque values among the three sample groups. Group Group N Mean Torque (SD) Comparisons Class I Ideal (5.45) A* Class I Expanded (6.11) A* Class II div (10.85) B* *Group comparisons with the same letter are not significantly different using the post-hoc Tukey-Kramer test (P > 0.05).

37 Torque angle (degrees) Class I Ideal Class I Expanded Class II div Figure 8. Box and whisker plot of torque among groups.

38 31 Analysis of CA and LCRA measurements In order to compare the CA and LCRA measurements among sample groups, descriptive statistics were calculated, and the data were analyzed in two ways. When divided into two groups (Class I normal and Class II division 2), a two-sample t-test was used to detect differences in measurements of CA and LCRA between them. When the study samples were divided into three groups (Class I ideal, Class I expanded and Class II division 2), a one-way ANOVA with the post-hoc Tukey-Kramer test was performed to detect differences among the three groups. A total of 99 subjects (51 females and 48 males), including 57 Class I normal (33 ideal and 24 expanded) and 42 Class II division 2, were included in the analysis. A mean of two duplicate measurements by the primary observer of each variable was used for the statistical analysis. Descriptive statistics are summarized below. Comparisons of CA and LCRA between two groups Based on the two-sample t-test, there was a significant difference in CA between the Class I normal and Class II division 2 groups (p = ). The data showed that mean CA observed in Class II division 2 group was significantly greater than that observed in the Class I normal group (4.29 vs ). Based on the twosample t-test, there was also a significant difference in LCRA between the Class I normal and Class II division 2 groups (p = ). The data showed that the mean LCRA observed in the Class II division 2 group was significantly greater than that observed in the Class I normal group (34.84 vs ). Comparisons of CA and LCRA among three groups Results of a one-way ANOVA revealed that sample grouping had a significant effect on the CA (F (2,96) = 4.14; p = ). The post-hoc Tukey-Kramer test indicated that the mean CA for the Class II division 2 group was significantly greater

39 32 than that observed for the Class I ideal group. However, no significant differences were found between the Class II division 2 group and the Class I expanded group, nor between the Class I ideal and expanded groups. Table 6 provides detailed results from the posthoc Tukey-Kramer test. Descriptive statistics for the CA among groups are illustrated in Figure 12. Results of a one-way ANOVA revealed that sample grouping had a significant effect on the LCRA (F (2,96) = 5.94; p = ). The post-hoc Tukey-Kramer test indicated that the mean LCRA for the Class II division 2 group was significantly greater than that observed for the Class I ideal group. However, no significant differences were found between the Class II division 2 group and the Class I expanded group, nor between the Class I ideal and expanded groups. Table 7 provides detailed results from the posthoc Tukey-Kramer test. Descriptive statistics for the LCRA among groups are illustrated in Figure 13. Table 6. Mean CA values among the three sample groups. Types of Groups N Mean CA (SD) Group Comparisons Class II (5.77) A* Class I Expanded (4.60) A, B* Class I Ideal (3.29) B* *Group comparisons with the same letter are not significantly different using the post-hoc Tukey-Kramer test (P > 0.05).

40 Collum angle (degrees) Class I Ideal Class I Expanded Class II div 2 Figure 9. Box and whisker plot of CA among groups.

41 34 Table 7. Mean LCRA values among the three sample groups. Types of Groups N Mean LCRA (SD) Group Comparisons Class II (5.95) A* Class I Expanded (4.46) A, B* Class I Ideal (3.96) B* *Group comparisons with the same letter are not significantly different using the post-hoc Tukey-Kramer test (P > 0.05).

42 LCRA (degrees) Class I Ideal Class I Expanded Class II div 2 Figure 10. Box and whisker plot of LCRA among groups.

43 36 DISCUSSION The specialty of orthodontics has historically assumed that the long axes of the crown and root of a maxillary central incisor are identical, that the collum angle is zero. As has been mentioned previously, this assumption may have originated with Andrews (1968), and, as Bryant et al. have noted, has been perpetuated in cephalometric tracing templates since that time. The results of the present study show, among other things, the wide variability of this basic morphological parameter and the difficulty inherent in assigning universally ideal values to it. In spite of the fact that the straight wire appliance has been used for nearly half a century, we have found no attempt in the literature during that time to establish a mean value for the collum angle of maxillary central incisors in Class I normal occlusions. This is perhaps due not only to assumptions about the quantitative angle of the CA, but also to the fact that it is sometimes difficult to read and measure in lateral cephalograms and is not typically included in cephalometric analysis. The basic concern surrounding the CA, and by proxy, the LCRA, is that it may offer predictive value for the susceptibility of an incisor root to be torqued into the palatal cortical plate during treatment, causing root resorption or dehiscence. Root dehiscence, depending on its severity, could compromise the periodontium around the affected tooth, or even the vitality of that tooth if its apex is moved into or through the palatal cortical plate. Root resorption, a topic reviewed comprehensively by Kaley and Phillips (1991), remains an incompletely understood phenomenon. Although it is noted to occur to some degree in most patients undergoing orthodontic treatment (DeShields 1969), it has been reported to occur more frequently and more severely in maxillary incisors whose roots are translated into the palatal cortex(ten Hoeve and Mulie 1976, Goldson 1975, and Hickham 1986). This seems intuitive, since the maxillary central incisor roots project into the most concave portion of the maxillary skeletal arch. In fact, root torqueing has been noted to be the single most predisposing factor for root resorption, with an odds

44 37 ratio of 4.5 for root torqueing in general that increases to 20 if the torqueing approximates roots against the palatal cortex (Kaley and Phillips 1991). Although root resorption has not been shown to decrease the prognosis of a tooth, preventing its occurrence, if possible, must certainly be considered a primary goal of orthodontic treatment. Several manufacturers offer a high torque version of maxillary incisor brackets that are designed to complement commonly accepted prescriptions. Anecdotally, it seems that some clinicians choose these brackets when it is anticipated that retroclined maxillary incisors will need powerful torqueing mechanics to create an ideal overbite/overjet relationship. In cases such as Class II division 2 malocclusion, for example, where retroclined incisors are a common finding, it may be argued based on the data procured in this study that it is precisely on these patients for whom torqueing mechanics may need to be moderated to avoid excessive palatal displacement of the root. In Class III patients, for whom Harris et al (1993) found higher U1 collum angle values, the decision to place large amounts of torque in an effort to create Class III dental compensation may be similarly affected. Harris et al (1993) postulated the deflection theory of the CA, whereby the crown of the incisor is deflected during the development of the root, leading to a bent tooth. In the case of Class II division 2 patients, the deflection would be caused by forces emanating from the lower lip, and in Class III cases, from the lower incisors (1993). And while it is true that not every patient in these high-risk malocclusions exhibits higher collum angles, it is our hope to offer the LCRA as a simple tool for anticipating cases such as these for which excessive torque should be avoided. Case report Analysis of the CA, LCRA, and torque angle is easily applied to both treatment planning and post-treatment case analysis. Patient D.W., illustrated in the figures below, was a 12 year 5 month old Class II division 2 patient who presented to the University of

45 38 Iowa Department of Orthodontics, for whom full treatment records of good quality exist. The initial cephalometric radiograph clearly shows a full Class II molar relationship and retroclined maxillary central incisors. The anatomic points of U1 are reasonably clear. Pre-treatment measurements of CA, LCRA, and torque, along with comparisons to expected means for Class II division 2 patients, are listed in Table 8. All measurements for patient D.W. easily fall within one standard deviation of expected means for Class II division 2 patients. Before treatment was initiated, a full mouth series of radiographs was taken to document the condition of the dentition. A periapical view of the maxillary central incisors shows normal anatomy, with fully formed apices and undamaged incisal edges. The patient was congenitally missing maxillary lateral incisors and mandibular second premolars. She was treated with canine substitution to replace lateral incisors, and prosthetic replacement of her mandibular second premolars. She had a 4 degree ANB angle. The patient was treated with standard edgewise techniques, with the exception that Unitek Victory Series TM high torque MBT brackets were used on the maxillary incisors (22 degrees on the maxillary central incisor). The post-treatment cephalogram (Figure 16) shows that the central incisors were torqued to 18.7 degrees, compared to the mean (standard deviation) torque of 13.6 (5.45) degrees for Class I Ideal subjects found in this investigation and a 17-degree torque built into a standard MBT prescription bracket. With an initial torque of -6.1 degrees, then, a total of 24.8 degrees of U1 torque was added. A closer view of the maxillary incisors (Figure 17) shows root resorption and probable dehiscence through the anterior palatal cortex. Given that the root apices are mutilated in this image, CA and LCRA are no longer measurable. The post-treatment periapical view of the maxillary central incisors (Figure 18) captures the full extent of root resorption. Note that the canines were protracted into the lateral incisor positions, not without resorption also, and restored for esthetics.

46 39 Table 8. Comparisons of CA, LCRA and Torque between D.W. (pre-treatment) and expected means for a Class II division 2 malocclusion. Patient D.W. Mean(Standard Deviation) CA (degrees) (5.77) LCRA (degrees) (5.95) Torque (degrees) (10.85)

47 40. Figure 11. Pre-treatment cephalometric radiograph of Class II division 2 patient D.W.* *Central incisor CA and LCRA in this case are 7.2 and 35.6 degrees, respectively (inset). Note the steepness of the anterior palatal cortex, which brings it into close approximation to the incisor roots. Pre-treatment torque of U1 crown was -6.1 degrees. Pre-treatment periapical radiograph of patient D.W. s maxillary central incisors (inset).

48 41 Figure 12. Post-treatment cephalometric radiograph of patient D.W.* *Central incisors were torqued to 18.7 degrees using high torque brackets (Unitek, Victory Series TM MBT high torque: 22 degrees). Note marked resorption of central incisor roots and probable dehiscence through palatal cortex (inset). The post-treatment periapical radiograph of patient D.W. s maxillary central incisors (inset) shows marked resorption of central incisor roots. Canines were protracted into lateral incisor positions (with some root resorption also) and esthetically restored.