## Introduction

The aim of this study was to investigate the vestibular anatomy of teeth in samples of adult Italian and Mozambican subjects in ideal occlusion and permanent dentition and identify any anatomic characteristics that may influence bonding in the straight-wire technique.

## Methods

Linear measurements and coordinates of each curve representing the clinical crown height and width of each tooth were acquired from digital models of each subject categorized to 1 of 2 groups: Italian (18 males, 22 females; mean age, 29.6 ± 5.7 years) or Mozambican (14 males, 15 females; mean age, 23.4 ± 5.9 years). All subjects had normal dentition and no previous orthodontic treatment, fillings, or prostheses. Method error and systematic error were calculated according to the Dahlberg formula (S ^{2} = ∑ d ^{2} /2n) and dependent Student *t* test ( *P* <0.05), respectively. Tooth symmetry was investigated through a paired-samples *t* test ( *P* <0.05) and sex difference via an independent-samples *t* test ( *P* <0.05). After neither asymmetry nor sexual dimorphism was found, all data were pooled, inverting the signs of the X coordinates and then mirroring data. Subsequently, a 2-samples *t* test ( *P* <0.05) and a multivariate cluster analysis were performed on the mirrored data to compare the 2 groups and to identify any within-group diversity for number of clusters for each tooth. Means of all linear measurements and coordinates (crown height and width) calculated for each cluster were reported and compared using a standard 2-samples *t* test ( *P* <0.05).

## Results

Two clusters were identified for the maxillary second premolars and molars in Italian subjects, whereas in the Mozambican subjects, there were 2 clusters for the maxillary first premolars and lateral incisors and 3 clusters for the maxillary canines and central incisors. The mandibular arch was remarkably homogeneous, with only 1 cluster per tooth in each group. In the mandibular arch, statistical differences were recorded between ethnic groups in crown height at the central incisors and second molars and in crown width in the sector from the second premolar to the second molar.

## Conclusions

There were considerable differences both between and within racial groups in crown height, crown width, and numbers of clusters, which should be taken into account during bonding. Although single-bracket placement guides specific for ethnicity may be feasible for the mandibular arch, the significant diversity in number of clusters in the maxillary arch indicates that more accurate bracket placement guides that take into account such heterogeneity are required.

## Highlights

- •
To measure crown height and width in the natural permanent dentition digitally using 3-dimensional mapping software.

- •
To quantify differences in clinical crown sizes between Italian and Mozambican samples.

- •
To use cluster analysis to assess within-group diversity in the optimal bonding height for each tooth.

- •
To reflect on the suitability of current bracket placement guides in light of our findings.

The straight-wire technique is currently the most used in orthodontics, and over the years, many researchers and clinicians have helped to improve the technique. Improvements have been made to prescription type and bracket shape and material and manufacture making outcomes ever more predictable. However, despite these innovations, the single most influential factor to the success of the straight-wire technique remains the accurate positioning of the brackets at the mid of the clinical crown.

The correct position in the mid position of the crowns depends on both the correct vertical position of the bracket and the construction of the brackets themselves. For accurate positioning, bases must closely conform to the coronal surfaces of the teeth. This issue was initially identified by Andrews, who stated that an ill-fitting bracket would be not only more difficult to position but also unstable, increasing the risk of transverse and vertical displacement. This led to unwanted rotations, intrusions, and extrusions and therefore, considerably increased treatment times in the finishing phase. With a view to determining the optimal bracket base, Andrews set out to study the superficial morphology and height of teeth.

Despite his efforts, however, his conclusions were hampered by the technology available at the time. He did not have the benefit of today’s digital analysis techniques, which provide simple, precise, and repeatable measurements.

Furthermore, his sample was composed entirely of white North Americans. We now know that there are considerable differences in tooth size and morphology between ethnicities.

In addition, the Boley gauge he used reduced the crown height to a straight line rather than a convex surface. Therefore, the measurements he obtained were considerable underestimations of the actual clinical dimensions. Moreover, Andrews was unable to avail himself of cluster analysis, which enables individuals in a particular sample to be grouped on the basis of a certain feature and therefore, provides the most accurate description of a population, taking into account its intrinsic heterogeneity. ^{,}

Later studies sought to overcome these limitations, first by measuring the angles formed by straight lines tangent to 1 or more points along the facial axis of the clinical crown (FACC). However, studying the convex dental surface by means of a straight line is reductive, and studies that relied on several tangents were only conducted on certain teeth rather than the full dentition. ^{,}

Therefore, Miethke and Melson sought to examine dental morphology by describing the shape of each tooth as a parabola on sagittal sections that were mesial, distal, and central to the bracket. This approach enabled them to highlight considerable morphologic differences between the teeth and individuals.

Other authors studied erroneous torque expression following vertical bracket displacement owing to labial curvature, and eventually Smith et al investigated the surface curvature (FACC) of the maxillary incisors and canines. They concluded that this curve is asymmetrical and that the most prominent point is often slightly displaced toward the incisal margin, whereas the flattest areas are found at the extremes, especially toward the gingival side.

Using the Finite Element Method, Papageorgiou et al showed that the vertical displacement of the bracket along the clinical crown has a huge influence on crown movement and, to a lesser extent, on root displacement. This was due to the nonhomogeneous curvature of the FACC.

However, with the exception of the study by Papageorgiou et al, the measurements in the literature are based entirely on analogical mathematical measurements; there have been no attempts to use cluster analysis together with digital techniques—which the scientific community now recognizes as precise and reliable—to describe the morphology of individual teeth. ^{,} Moreover, no authors have yet specifically investigated tooth morphology with a view to resolving the issue of bracket base conformity and precise height of bracket positioning.

We, therefore, set out to conduct a preliminary study to investigate tooth surface morphology in 2 groups of subjects, Mozambicans and Italians. After testing for tooth symmetry and sex-based differences, our goal was to compare the measurements obtained for the groups and then identify any homogeneous subgroups for digital measurements of the height and width of each type of tooth using cluster analysis. This type of analysis provides a detailed description of a sample by identifying distinct subgroups or clusters for each type of tooth analyzed and by identifying a medoid (mean value) and standard deviation (SD) for them.

The ultimate aim of the study was to provide clinicians with important information not only on racial differences, but also any within-race subgroups identified for each tooth with a view to providing indications for new bonding strategies, focusing on the teeth that display more intrinsic heterogeneity (ie, more than 1 cluster).

## Material and methods

Tooth measurements were made on a total of 85 virtual models (standard triangulation language files) taken from the University of Ferrara Postgraduate School of Orthodontics Clinic’s electronic database. Models had been acquired via direct and indirect scanning using a 3Shape R700 scanner (Great Lakes Orthodontics, Tonawanda, NY) or an orthodontic 3-dimensional (3D) scanner (3Shape D700/710; 3Shape, Copenhagen, Denmark) ( Fig 1 ).

The sample was divided into 2 groups based on ethnicity: 1 composed of Italians (18 males, 22 females; mean age, 29.6 ± 6.7 years) and the other of Mozambicans (14 males, 15 females; mean age, 23.4 ± 5.9 years). Ethnicity was verified to 3 previous generations.

Patients were subjected to the following inclusion criteria: complete permanent dentition except the third molars, Class I molar relationship, minimal crowding (< 1.5 mm, considering both arches), ^{,} and no previous orthodontic, conservative, or prosthetic treatment. Any teeth showing signs of wear, surface defects, altered, passive or active eruption, or rotation sufficient to prevent measurement of their mesial or distal points were excluded from the analysis.

According to these exclusion criteria, 16 models (all belonging to the Italian group) were excluded entirely because of extensive and marked surface anomalies; 25 individual teeth from the Italian group and 37 from the Mozambican group were also excluded because they failed to meet the inclusion criteria.

The analysis was conducted using Rhinoceros 3D version 5.0 software (Robert McNeel & Associates, Seattle, Wash). Specifically, each model was orientated in 3D space according to a reference plane passing through the following 3 lingual points: the tip of the retroincisal papilla and the most gingival points on the maxillary and mandibular second molars. The model was orientated in such a way that (1) the plane XZ coincided with the reference plane, (2) the plane YZ divided the model into 2 halves, and (3) the plane XY (plane C on the Rhinoceros rendering) was tangent to the distal surfaces of the sevenths ( Fig 2 ). This enabled precise measurements of each tooth to be performed as follows:

- •
On a vestibular view, the FACC was traced in an apical-coronal direction through the

*PolylineOnMesh*command, according to Andrews’ criteria ( Fig 3 ). After detecting the start point (gingival zenith) and the end point (most occlusal point), this command enables a polyline to be traced on the clinical crown surface. - •
After identifying the central facial axis point of this curve (

*Divide>Curve>Number of segments>2*tool), the curve representing the mesiodistal width passing through FA point was traced with the*PolylineOnMesh*command and the Object Snap function*Mid*activated ( Fig 4 ). - •
The

*Divide>Curve>Number of segments>99*(parameter: SelectEnd = Yes and GroupOutput = Yes) tool was used to mark 100 equidistant points on each of the 2 lines (equivalent to the crown height and mesiodistal width) traced on each tooth ( Fig 5 ). It was arbitrarily considered that these 100 points and their respective coordinates would be sufficient to accurately describe the previously traced polylines. - •
The group of points describing each curve was identified using the tooth number, and the

*Report*command was used to obtain the respective 3D coordinates, which were saved in .txt files (Microsoft, Redmond, Wash) specific for each curvature.

The procedure described had the aim of simplifying the complex anatomy of the tooth crown into 2 linear values (crown height and width) that would enable comparative statistical analysis between the 2 groups to be performed.

The data obtained (linear measurements and point coordinates for each curve) were imported into an Excel file (Microsoft) using OsmaniConverter software 1.0 (O. Osmani, Ferrara, Italy). An Excel file was created for each patient model, and the coordinates pertaining to each tooth were reported on separate spreadsheets. The coordinates were orientated that the sagittal curve was described by the coordinates orientated in a coronoapical direction and the transverse curve by the coordinates orientated in a mesiodistal direction. A single operator trained in the use of Rhinoceros software made all measurements.

After 4 weeks, measurements on 14 randomized models were repeated by the same operator, and the method error was calculated according to Dahlberg’s formula (S ^{2} = ∑ d ^{2} /2n). Dahlberg values ranged between 0.004 mm and 0.062 mm. The systematic error was calculated via the dependent Student *t* test with *P* <0.05 considered significant. The mean *P* value was 0.407, and no statistically significant differences were found in any case, with the exception of the maxillary right lateral incisor height ( *P* = 0.019). Despite this, the analysis confirmed the reliability of our measurements.

## Statistical analysis

Statistical analysis was performed to investigate both tooth symmetry and sexual dimorphism in both samples. First, a paired-samples *t* test, with a significance threshold of α = 0.05 (5%), was performed on the digitally-acquired data. No significant differences between the right and left side were detected in either sample. Hence, the measurements made on each side of the digital models were mirrored by inverting the signs of the X coordinates on the Excel file, as described previously in the literature. This mirroring process enabled us to expand the sample, effectively doubling the number of Italian and Mozambican models available to analyze to 80 and 58, respectively. A *t* test for independent samples ( *P* <0.05 considered significant) was then performed on both samples to check for any differences in tooth measurements between sexes. No sexual dimorphism was found in either sample, except for the mandibular lateral incisor width in the Mozambican group ( *P* = 0.02). So, effect size and minimum detectable effect size (assuming a required statistical power of 80%) were calculated together with the *P* value for both ethnic groups. No estimated effect size for sex was greater than the minimum detectable effect sizes of 0.914 (Italian group) and 1.08 (Mozambican group), and this difference was not considered clinically significant. Therefore, based on these results, no distinctions were made between sex or sides in the statistical comparison between groups or in the subsequent multivariate cluster analysis.

To detect any racial differences between the Italian and Mozambican groups, a standard 2-samples *t* test was performed on the 2 sets of crown heights and widths, with a *P* <0.05 considered significant. Then, multivariate cluster analysis was performed for each tooth in both samples using R software (R Core Team, Vienna, Austria), with a statistical hypothesis confidence level (error I level) set to 1 − α = 95%. Essentially, this type of statistical analysis enables detection of any subgroups or clusters within a known dataset. These subgroups consist of subjects that are very similar to each other but different to members of the other subgroups or clusters. It can sort a group into several subgroups, each described by a medoid (mean value) and SD, with minimal mean dissimilarity between members.

The algorithm for identifying clusters was applied as follows:

- •
Clusters were identified on the clinical crown width and height variables. These were point-to-point curves (100 points describing each curve). Gaussian mixture modeling was used to assign each sampled tooth to the appropriate cluster using the approach implemented by the mclust R package.

- •
Assuming normal distribution, the number of clusters was determined within each subgroup. In particular, a maximum number of cluster K equal to 5 was selected, clustering was performed in the 1, 2, . . . K range, and the Bayesian information criterion statistic, appropriate for Gaussian mixture modeling, was computed. The optimal number of clusters for each tooth was taken as the K corresponding to the minimum Bayesian information criterion.

- •
Missing values from the teeth excluded by the exclusion criteria were substituted with mean values for statistical purposes.

After the clusters had been detected, further comparisons of clinical crown height and width were performed for those teeth in both groups that displayed the same number of clusters. A standard 2-samples *t* test with a significance threshold of *P* <0.05 was used for this purpose.

The mean coordinates for the curves pertaining to each tooth were then calculated based on the number of clusters, previously centered at Cartesian 0, and exported into an Excel file. MATLAB R2013a (MathWorks, Natick, Mass) was used to plot curves from these data.

## Results

Owing to the fact that neither sexual dimorphism nor differences between right and left side were recorded, a 2-samples *t* test and a subsequent cluster analysis were performed on both clinical crown height and width, without sex or side distinctions. As expected, the comparative 2-samples analysis revealed differences in both crown and height values between the 2 groups ( Table I ). Specifically, the Italian group displayed higher values for both measurements with respect to the Mozambican group. These differences were statistically significance ( *P* <0.05) for 7 crown-height measurements and 4 crown-width measurements.

Measure | Arch | Tooth | Italians mean | Italians SD | Mozambicans mean | Mozambicans SD | t test |
P value |
---|---|---|---|---|---|---|---|---|

Height | Maxilla | 1 | 10.1 | 1 | 9.6 | 0.9 | 2.7 | <0.05 ^{∗ } |

2 | 8.4 | 1.1 | 8.4 | 1 | 0.3 | 0.76 | ||

3 | 9.6 | 1.1 | 9.5 | 0.8 | 0.8 | 0.45 | ||

4 | 8.2 | 0.9 | 7.9 | 0.9 | 1.7 | 0.09 | ||

5 | 7.2 | 1 | 6.7 | 0.9 | 2.7 | <0.05 ^{∗ } |
||

6 | 6.0 | 0.9 | 5.1 | 0.8 | 5.7 | <0.001 ^{∗ } |
||

7 | 5.4 | 0.8 | 4.5 | 0.9 | 5.8 | <0.001 ^{∗ } |
||

Mandible | 1 | 8.0 | 1 | 7.8 | 0.9 | 1.5 | 0.14 | |

2 | 8.3 | 0.8 | 8.2 | 1 | 0.6 | 0.57 | ||

3 | 9.8 | 1.2 | 9.9 | 1.1 | −0.2 | 0.82 | ||

4 | 8.5 | 0.9 | 8.3 | 0.9 | 1.1 | 0.29 | ||

5 | 7.7 | 0.8 | 7.3 | 0.9 | 2.6 | <0.05 ^{∗ } |
||

6 | 6.8 | 0.8 | 5.7 | 0.7 | 7.9 | <0.001 ^{∗ } |
||

7 | 5.8 | 1.1 | 5.0 | 0.8 | 5.1 | <0.001 ^{∗ } |
||

Width | Maxilla | 1 | 8.5 | 0.7 | 8.1 | 0.7 | 2.9 | <0.001 ^{∗ } |

2 | 6.5 | 0.7 | 6.4 | 0.7 | 0.6 | 0.57 | ||

3 | 8.0 | 0.7 | 7.6 | 0.5 | 3.8 | <0.001 ^{∗ } |
||

4 | 7.0 | 0.7 | 7.2 | 0.5 | −1.8 | 0.07 | ||

5 | 6.8 | 0.6 | 6.9 | 0.5 | −1.1 | 0.25 | ||

6 | 10.2 | 0.8 | 10.2 | 0.7 | 0.4 | 0.68 | ||

7 | 10.3 | 0.9 | 9.8 | 0.7 | 3.9 | <0.001 ^{∗ } |
||

Mandible | 1 | 5.0 | 0.5 | 4.8 | 0.4 | 1.6 | 0.11 | |

2 | 5.4 | 0.6 | 5.3 | 0.4 | 1.2 | 0.22 | ||

3 | 7.0 | 0.6 | 7.0 | 0.5 | −0.4 | 0.70 | ||

4 | 7.5 | 0.8 | 7.4 | 0.7 | 1.2 | 0.22 | ||

5 | 7.4 | 0.7 | 7.3 | 0.7 | 0.7 | 0.51 | ||

6 | 11.8 | 0.8 | 11.8 | 0.8 | −0.2 | 0.86 | ||

7 | 10.8 | 0.9 | 10.5 | 0.8 | 2.1 | <0.05 ^{∗ } |