Changes in Incisor Third-Order Inclination Resulting from Vertical Variation in Lingual Bracket Placement
Objective: To test the null hypothesis that third-order measurements are not correlated to lingual incisor features seen on radiographs.
Material and Methods: The lateral headfilms of 38 untreated, norm-occlusion subjects without incisor abrasions or restorations were used for third-order measurements of upper and lower central incisors and assessment of the inclination of four sites suitable for lingual bracket placement with reference to the occlusal plane perpendicular. Lingual sections were determined by the tangents at the incisal fossa (S1), at the transition plateau between incisal fossa and the cingulum (S2), by a constructed line reaching from the incisal tip to the cingulum (S3), and by a tangent at the cingulum convexity (S4). Third-order angles were also assessed on corresponding dental casts using an incisor inclination gauge. Regression analysis was performed using the third-order measurements of both methods as the dependent variables and the inclination of the lingual enamel sections (S1, S2, S3, S4) as the independent variables.
Results: The null hypothesis was rejected. For the most common bracket application sites located on the lingual shovel (S1 and S2), third-order inclination changes of 0.4–0.7 degrees are expected for each degree of change in the inclination of the lingual surface. The impact of bracket placement errors on third-order angulation is similar between sections S1 and S2 and the cingulum convexity (S4). Section S3 proved to be least affected by interindividual variation.
Conclusion: The third-order measurements are correlated to lingual incisor features. Accordingly, third-order changes resulting from variation in lingual bracket placement can be individually predicted from radiographic assessments.Abstract
INTRODUCTION
As the demand for esthetic dentistry has increased in recent decades, so also has the relevance of lingual orthodontic appliances. Esthetic incisor inclination constitutes both a significant issue in orthodontics, as well as a major concern, especially for those patients requiring lingual orthodontics.
Incisor inclination assessment is usually performed by estimating the inclination of the complete incisor axis on lateral headfilms (LHs) in relation to different cephalometric reference lines1 or by estimating crown inclination using the facial surface tangent (FST) at the center of the clinical crown2 (facial-axis point, or FA point). The former has the advantage of providing information about crown and root inclination, whereas the latter refers to third-order values of straight-wire appliances (SWAs) and allows prediction of the inclination of the esthetically important facial enamel surface.
Labial SWAs are usually placed on the FA point.2 Their third-order prescriptions indicate the bracket slot inclination to the bracket base perpendicular (BBP) and, consequently, the inclination of the FST with reference to the occlusal plane perpendicular (OPP), respectively, (Figure 1) after incorporation of full-size arches.
Citation: The Angle Orthodontist 79, 4; 10.2319/072308-385.1
Lingual third-order bracket prescriptions, however, do not refer to the OPP or to the inclination of the facial enamel surface as represented by the FST. They are solely representative of the angle between the slot and the BBP, and they do not explicitly refer to the site at which these brackets are supposed to be placed. There are two reasons why the lingual bracket is its own single reference plane: lingual bracket application is more complicated than labial bracketing as it needs to compensate for specific lingual features, such as (1) differing tooth diameters3 and (2) discontinuously and distinctively curved lingual incisor morphology compared with the facial enamel surface.4 Accordingly, the inclination of the lingual surface of the incisors changes relative to the occlusal plane at different bonding heights. These difficulties have created the need for customized bracket placement using setups5 or bracket placement devices,4 which both mostly coincide with varying vertical bracket positions: Applying these cast-oriented approaches, it is mainly the incisor angulation depending on the diagnostic setup that conditions the vertical position of the bracket on the lingual surface and thus its third-order property,4 in contrast to labial bracket application using the FA point.2
The distinctive features of the lingual incisor shape suggest that relatively small variations in lingual bracket positioning may result in apparent deviations from the desired first- and third-order expression,6 which has led to the recommendation of bonding lingual appliances indirectly.7 However, even when using the indirect bonding method, there is still a certain percentage of errors during bonding.7 Also, when brackets have to be reattached, they are often placed directly, a method that is more prone to error.7 Therefore, a decision may be considered initially in favor of lingual sections, which are less sensitive to bracket placement errors.
Whereas labial incisor features, bracket height variation, and their effect on torque have been the topic of a range of studies,8–10 little consideration has been given in the literature to the relationship between the inclination of the different lingual morphology features and labial enamel surface characteristics.8
Differentiation of Lingual Sections
The most common sites of the lingual enamel surface considered appropriate for bracket placement4 may be broadly divided between the lingual fossa section (S1) and the transition plateau between the incisal fossa and the cingulum convexity (S2). For compensation of different tooth diameters, it is also customary to level differences between bracket base and lingual enamel surface with a composite material,3 thereby placing brackets on an imaginary line between the incisal edge and the cingulum (S3).
Whereas labial SWAs are considered to be standard treatment, lingual SWAs have still not come of age, as the problem remains that they have to cope with the inherent problem of varying tooth diameters as a function of tooth type and bracket-bonding height, resulting in visible first-order errors6 if not compensated by excessively large anterior brackets. However, Takemoto and Scuzzo11 drew attention to the fact that diameters of different tooth types show minor variation near the gingival margin, and they proposed a lingual straight-wire approach placing brackets close to the gingival margin at the cingulum. Therefore, the most prominent part at the cingulum convexity (S4) was also considered in this study to be a possible site for lingual bracketing.
The aims of the present study were (1) to evaluate the relationship between the FST and different lingual sites (S1, S2, S3, S4) appropriate for bracket placement and (2) to assess the changes in FST or third-order inclination resulting from variation in bracket placement at these sites.
The null hypothesis was that third-order measurements on casts or radiographs do not show a significant correlation with lingual incisor features (S1, S2, S3, S4) seen in LHs; that is, the respective correlation coefficients are equal to 0. A rejection of the null hypothesis would not only allow calculation of the magnitude of changes in FST inclination resulting from varying lingual bracket placement, but it would also provide the basis for transferring established labial incisor third-order inclination standards to lingual bracket placement adjustment.
MATERIALS AND METHODS
Incisor assessments were performed on the LHs and corresponding dental casts of 38 subjects (12 males, 26 females; mean age = 19.5 years; standard deviation = 3.7) selected according to the following exclusion criteria: previous orthodontic therapy, primary teeth, missing teeth, incisor restorations or abrasions, and anomalous tooth morphology. Inclusion criteria were a neutral (Angle Class I) molar and canine relationship and a normal incisor relationship in the sagittal plane and vertically. The sample was taken from the Dentistry Center, Department of Orthodontics, at the University of Göttingen. The study received the approval of the local Ethics Committee.
Cephalometric Measurements
Each LH tracing was performed manually by two assessors. For third-order radiographic measurements (U1TR, L1TR), the FST (Figure 1) was constructed at the FA point, which was determined by measuring the midpoint of the labial enamel surface on the LH. To record the sagittal lingual characteristics incisor features with reference to their correlation with the FST, the lingual enamel surface was differentiated into three sections and one constructed line considered as suitable sites for lingual bracket application (Table 1). These were analyzed with LHs, as illustrated in Figure 2, using 11 cephalometric lines (Table 1). All measurements were assessed with reference to the OPP (Figure 1).
Citation: The Angle Orthodontist 79, 4; 10.2319/072308-385.1
Cast Measurements
In addition to estimating third-order angles from radiographs, they were also derived from corresponding dental cast pairs, as the radio-hygienic approach of assessing incisor inclination using casts and a type of incisor inclination gauge has recently proven to have sufficient accuracy and reliability.1213
The most proclined upper and lower central incisors were chosen, since these are easy to observe in lateral radiographs. They were prepared for assessment by marking the midpoint of the labial enamel surface (FA point). For these assessments, the dental casts were oriented on the gauge table according to the occlusal plane, and third-order angles were indicated by a wire-pointer that could be rotated and was adjusted according to the FST (Figure 3). The excursion of the wire-pointer on a protractor then indicated the incisor third-order angles (U1TA, L1TA, Figure 2), which were defined as positive if the FST was inclined in the posterior direction.
Citation: The Angle Orthodontist 79, 4; 10.2319/072308-385.1
Statistical and Error Analysis
The significance of differences between third-order angles determined from both methods and the distinct lingual reference angles (S1, S2, S3, S4) were tested using paired t-tests and 95% confidence intervals. Correlations between third-order angles and lingual reference angles were defined by Pearson's correlation coefficient ρ. In addition, an evaluation was made of whether these correlations were significantly different from zero. Differences and correlations between the measurements of the two assessors were evaluated in the same way.
In order to describe the relationship between the FST and lingual surface angles in more detail, single regression analysis (SRA) was used. Also, multiple regression (MRA) was used for describing third-order angles by a suitable linear combination of the lingual incisor features. Stepwise variable selection was applied to remove those radiographic angles from the linear combination that did not make a sufficient contribution to the description of third-order angles.
The significance level for all tests was α = 5%. Correlation analyses, SRA, and t-tests were made with R 2.6 software (www.r-project.org). MRA was performed using SAS 9.1 (SAS Institute, Cary, NC).
For error analysis, systematic differences between repeated measurements of the lingual reference angles were performed by examiner one for 20 arbitrarily chosen individuals on two occasions. The technical error of measurement (TEM) was assessed by the formula TEM = (Σ di2/2n)1/2, where di is the difference between the first and the second measurement on the ith subject and n is the sample size.
RESULTS
The third-order angles on casts (U1TA, L1TA) differ significantly from all lingual reference angles in radiographs but are positively correlated with each of these (Table 2a). Differences between radiographic third-order angles (U1TR, L1TR) and all lingual angles were slightly smaller but significant, whereas the correlation between these was slightly higher overall (Table 2b). Figure 4 depicts the distributions for all angle measurements.
Citation: The Angle Orthodontist 79, 4; 10.2319/072308-385.1
Differences between third-order assessments on casts and LHs were significantly different from zero but significantly correlated with each other (all P < .01). The 95% confidence intervals and Pearson's correlation coefficient are presented in Table 3.
The TEM was lowest for maxillary section S2 (TEM = 1.4) and greatest for the mandibular section S2 (TEM = 2.5) (Table 4). The proportion of observations for which the error was greater than 2, 3 or 4 degrees is given in Table 5.
Table 6 gives the interobserver correlations and differences between the various measurements. U1TA, U1TR and L1TA measurements differed significantly but were also significantly positively correlated.
Single Regression Analysis
Due to small 95% confidence intervals between the measurements of both assessors, the measurements were averaged before performing regression analysis. The estimated regression parameters for the equation a = intercept + slope × b are given for the third-order angles on casts in Table 7a and for the radiographic third-order data in Table 7b. For maxillary third-order cast angles (U1TA), the estimated regression equation means, for example, that there is an overall difference to section S2 of −21.3 degree and for each further increase of S2 by 1 degree, angle U1TA increases by 0.4 degrees.
Multiple Regression Analysis
In the maxilla, the selection procedure left only S1 and S3 angles for describing third-order cast measurements by the regression equation (R2 = 0.52): U1TA = −16.6 + 0.3 × S3 + 0.2 × S1.
This means there is an overall difference between U1TA angles and the given linear combination of −16.6 degrees. Additionally, U1TA angles increase by 0.3 and 0.2 when S3 and S1 angles increase by 1 degree, respectively. For the mandible, regression analysis yielded an equation including only S3 angles to describe L1TA angles (R2 = 0.50): L1TA = −36.0 + 0.8 × S3.
Maxillary third-order angles read from the radiographs were modeled by the following equation: U1TR = −23.5 + 0.7 × S3 (R2 = 0.70). For the lower incisors the following equation was used: L1TR = −23.7 + 0.5 × S4 + 0.3 × S1 (R2 = 0.55).
DISCUSSION
The null hypothesis of third-order measurements not showing a significant correlation with lingual incisor features seen in LHs was rejected, allowing a comparison of the inclination of lingual enamel sections to the FST. The value of this finding is that changes in third-order or FST inclination resulting from vertical variation in lingual bracket position can be individually predicted with LH assessments and the use of the regression equations presented in this study.
Relationship Between FST and Lingual Sections Appropriate for Bracket Placement
The correlation with third-order angles of both methods (U1TR-L1TA) and the distinctive lingual reference lines declined in most correlations investigated in the order S3 > S1 > S4 > S2 (Tables 2a, 2b). Section S2 showed the lowest correlation with third-order angles in both the maxilla and mandible, with P values between .49 (L1TA) and .61 (L1TR).
A possible explanation may be the fact that the construction of a line between two points (section S3) may be less error prone than that of a tangent. Moreover, it is likely that the order of decreasing correlations may reflect interindividual variation in lingual enamel section inclinations. Accordingly, the inclination of the section S2 may be subject to a more pronounced variation, as may be the case with other lingual enamel sections or the FST, whereas S3 assessments seem the most reliable maxillary lingual parameter with only 10% of errors exceeding 2 degrees (Table 5).
Changes in FST Inclination Resulting from Lingual Bracket Placement Variation
According to SRA, the results for modeling either radiographic or dental cast third-order angles from lingual surface measurements were similar (Tables 7a, 7b). The change in third-order inclination caused by a variation in the bracket site of 1 degree was smallest for section S2 (0.4 degrees U1TA or U1TR; 0.5 L1TA or L1TR) and highest for S3 in the maxilla (0.7 degrees U1TR) and S4 in the mandible (0.9 degrees L1TA); that is, per degree of individual variation at the most common bracket sites S1 and S2, which are located on the lingual shovel, maxillary third-order inclination changes of 0.4–0.5 degrees have to be expected (mandible: 0.5–0.7 degrees). This finding may be of interest in relation to directly placed lingual brackets, which are often adapted to these sites and recently have gained more relevance in less complicated orthodontic cases.14 Regarding third-order error proneness, our results (Tables 7a, 7b) also indicate that site S2 in both the maxilla and mandible may be considered the most appropriate site for a direct lingual bracket placement approach. If section S3 is considered as a constructed reference line, third-order changes of up to 0.7–0.8 degrees have to be expected per degree of variation in S3.
The cingulum convexity (site S4), which may be of value for the lingual SWA approach, showed a correlation of 0.68 (mandible: 0.74) to radiographic third-order angles and maxillary variations of 0.5 degrees (mandible: 0.7) if the FST inclination changes 1 degree (Table 7b). The third-order error proneness for direct bracket placement or rebonding on site S4 may therefore be regarded as being similar to that of the commonly used site for lingual bracket placement S1 (Tables 7a, 7b).
The MRA unravels the functional enmeshment between the FST and the inclination of the differentiated lingual enamel sections. Being most strongly correlated with FST, maxillary S1 and S3 angles contributed the most to the description of third-order angles on casts (mandible: S3 only). Also, S3 inclinations can best explain radiographic third-order (U1TR) measurements; whereas L1TR angles are better described by the lines S1 and S4. These outcomes may reflect the shape of the lingual enamel surface, the curvatures of which are obviously less pronounced in lower than in upper central incisors.
There is no point or line that can be validly defined as a general reference for lingual bracket application. However, as the lingual site with the highest correlation with FST and one that is subject to less interindividual variation than other lingual sections, the reference line S3 may be considered to be representative for lingual enamel surface inclination, similar to the FST in labial third-order assessments and, in further research, may be substantiated for all types of teeth using, for example, three-dimensional CAD/CAM methods and larger samples.
Clinical Implications
Relating labial and lingual morphologic features to one reference line, the OPP, creates a basis for comparing both lingual and labial third-order bracket prescriptions and allows the transfer of established targets in third-order corrections, as formulated in terms of labial third-order values, to the lingual side.
The cingulum convexity (S4) can be considered for the lingual straight-wire approach, as single regression indicates that the impact of bracket placement errors on third-order angulation, especially when using direct bonding techniques, is similar to commonly frequented lingual sections (S1, S2). Directly bonded lingual appliances especially may benefit from a bracket base design that adapts to lingual surface inclinations of sections S1 and S2 as much as possible with regard to minimizing bonding failures.7
The value of the regression equations presented here (Tables 7a, 7b) is that they enable the practitioner to estimate third-order changes resulting from vertical variation in lingual bracket placement and individual lingual incisor morphology on the basis of common treatment planning documents and within the limitation set by the accuracy of radiographic estimates.
CONCLUSIONS
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Using the regression equations presented in this study, third-order changes resulting from variation in lingual bracket placement can be individually predicted after radiographic assessment.
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The third-order inclination changes of 0.5 (mandible: 0.7) degrees may occur per degree of change in the most common bracket application sites located on the lingual shovel (sections S1 and S2).
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Reference line S3 seems least affected by interindividual variation and may be considered representative of the lingual enamel surface inclination.
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The cingulum convexity (S4) seems acceptable for a lingual straight-wire approach from the perspective of impact of bracket placement errors on third-order angulation.
Both bracket-slot inclination, in relation to BBP and FST at the FA point, in reference to the OPP, integrate third-order data (U1TA/U1TR, L1TA/L1TR)
Radiographic assessments of lingual sections according to Table 1 were determined from the tangents at the midpoint of the incisal fossa (S1), at the transition plateau between incisal fossa and the cingulum (S2), using a constructed line reaching from the incisal tip to the tuberculum (S3), and by a tangent at the most prominent part of the cingulum convexity (S4)
The gauge for recording third-order angles on casts
Distribution of third-order measurements on casts (U1TA, L1TA) and on radiographs (U1TR, L1TR) compared with lingual reference angles on radiographs (S1, S2, S3, S4). Values of both operators were averaged
Contributor Notes
Corresponding author: Dr Michael Knösel, Department of Orthodontics and Dentofacial Orthopedics, Center of Dentistry, Georg-August-University, Robert-Koch-Str. 40 37099 Göttingen, 37099 Germany (mknoesel@yahoo.de)