INTRODUCTION

In the definition of orthodontic treatment, it is essential to consider the esthetic factor, since this is one of the main reasons for patient consultation. This has led researchers and clinicians to study the relationship between the anatomy and esthetics of teeth as treatment objective, with special attention to the cen- tral incisors, since they have greater exposure (^{Fredericks, 1974}). Studies as those by ^{Carlsson & Rönnerman (1973}) and ^{Mavroskoufis & Ritchie (1980}) analyzed the anatomy of central incisors. The first analyzed the inclination of the buccal long crown axis, inclination of the long root axis and the angle between these axes; the second compared the mesiodistal diameter and crown length between different patients and in the same patient. Studies conducted by Fredericks (1974) and ^{Okeson (2008}) further related this anatomy to orthodontic treatment. While the first defined the treatment objective of esthetics based on the inclination of tooth axes, the second indicated that the anatomy of central incisors has a direct implication in the active treatment phase and in its result, as well as in the retention phase.

This study recognizes the importance of considering the anatomical variables of central incisors during treatment and seeks a method that allows, in a simple manner, to determine the long crown axis, the long root axis, and the angle formed by these axes (or crown-root angle). It is relevant to consider this angle in the diagnosis, since it is directly related to the buccal surface, where the brackets are bonded in the straight arch technique. This was highlighted by ^{Andrews (1989}a), who established a relationship between the consistency of straight-wire treatment results with the consistency of crown-root angle values for central incisors.

Over time, several authors such as ^{Taylor (1969}), ^{Carlsson & Rönnerman (1973}), ^{Fredericks (1974}) and ^{Andrews (1989}b), among others, have proposed methods of varying complexity to measure the crown-root angle of central incisors. For example, Carlsson & Rönnerman (1973) used a stereograph to determine the long crown axis, and Fredericks (1974) conducted a previous study to determine the mean distance of the point of greatest crown convexity to trace the long crown axis.

However, the clinician is routinely able to visualize the crown and root inclination of incisors on a lateral radiographic image. This inherent capacity of the human eye is called visual-spatial processing, which allows identifying the position of a body, evaluating angles (^{Mandal et al., 2012}; ^{Roselli, 2015}) and estimating distances (^{Ortega et al., 2014}). The present study takes advantage of this ability to propose a simple method to determine the crown-root angle.

The objective of this study is to propose the visual-spatial processing as a method to determine the long crown axis and the long root axis, for measurement of the angle between these axes (crown-root angle) on the permanent upper and lower central incisors. For that purpose, Cone Beam Computed Tomography (CBCT) images were used, which allow controlling the over projection and distortion of anatomical structures that usually occurs in conventional radiographs (^{Adenwalla et al., 1988}; ^{Arai et al., 1999}; ^{Mah et al., 2010}).

MATERIAL AND METHOD

The study had a quantitative, descriptive, observational, and cross-sectional approach. The universe consisted of 214 maxillary and mandibular CBCT images recorded between 2014 and 2020 at the radiology center of the School of Dentistry of Universi- dad Mayor, Santiago, Chile. These records contained permanent upper and lower central incisors.

For sample size calculation, the criteria of the article "Calculation of the sample size in medical education research" were used, considering that there is not enough information on this aspect and that it is a preliminary study (^{García-García et al., 2013}). The sample size was 100 CBCT images: 50 of permanent upper central incisors (Annex 1) and 50 of permanent lower central incisors (Annex 2). Each image was obtained from a different patient, to avoid including homologous incisors that generally have similar anatomy.

The inclusion criteria were maxillary and mandibular CBCT showing erupted permanent central incisors, with complete apical formation and normal and undamaged anatomy. The exclusion criteria were patients with supernumerary teeth, cysts and/or tumors that might preclude measurement of the crown-root angle, permanent central incisors with sign(s) of dentoalveolar trauma, rhizolysis, crown and/or root frac- ture, restorations or fixed prostheses that might affect visualization of the long crown axis, dental tissue wear affecting more than the incisal third and carious lesions.

Data collection and analysis plan

Selection of CBCT. The 214 maxillary and mandibular CBCT images were obtained from the Planmeca Romexis® software database according to the aforementioned inclusion and exclusion criteria. Then, 100 CBCT images were randomly selected in Microsoft® Office 365® Excel: 50 of permanent upper central incisors and 50 of permanent lower incisors.

Calibration for determining the long crown axis and the long root axis. Calibration between examiners 1 and 2 (inter-examiner) consisted of plotting the crown- root angle axes on 30 sagittal CBCT images of permanent central incisors (15 upper and 15 lower) using Microsoft® Office 365® PowerPoint software. Subsequently, examiner 1 measured the crown-root angle considering 2 decimals, using the AutoCAD® 2015 software (Annex 3). With these measurements, the calibration between examiners was determined using the Lin Concordance test and the Bland-Altman test, yielding a correct inter-examiner calibration with a Concordance Correlation Coefficient (CCC) of 0.914 and a confidence interval (CI) of 95% of Bland-Altman between -2.450 and 3.332, p<0.0001 (Annex 4).

Before measuring the crown-root angle, examiner 1 underwent intra-examiner calibration, for which 30 permanent incisors , different from those used in the previous calibration, were selected. The angle was measured on 15 permanent upper central incisors and 15 permanent lower central incisors (Annex 5). These measurements were organized in a database using StataCorp (2015) statistical software Release 14, College Station, TX: StataCorp LP.; and were processed in the first instance by CCC, which retrieved a value of 0.995. Subsequently, the Bland- Altman test was performed, which determined a 95% CI between -0.303 and 0.499, p<0.0001. Since data were concordant, an effective intra- examiner calibration was considered.

Standardization of images. Using the Planmeca Romexis® software, a section thickness of 1mm was achieved, and the most central in the three planes of space was selected. Thus, standardized CBCT images were obtained in the sagittal plane, which allowed tracing the long crown axis and the long root axis (Annex 6).

Protocol for tracing the axes of the crown-root angle based on visual-spatial processing. To facilitate the observation of axes, the image of the sagittal section of the upper central incisor was rotated using the “move/rotate volume” tool (Planmeca Romexis® software) until the palatal plane and the true horizontal line were parallel (Fig. 1 A).

Likewise, the image of the sagittal section of the lower central incisor was rotated until the long tooth axis formed an angle of 116º to 116.50º in relation to the true horizontal line (Fig. 1 B). These values were determined based on the fact that the mandibular plane angle has an average angulation of 26° in relation to the true horizontal line; in turn, the incisor presents an angle of 90° in relation to the mandibular plane. Thus, it can be stated that the lower central incisor, in relation to the true horizontal line, presents an average angulation of 116°.

All images were copied into a Microsoft® Office 365® PowerPoint file.

Subsequently, the following protocol was followed to trace the axes of the crown- root angle of the permanent upper and lower central incisors:

- The sagittal inclination of the long root axis was observed by visual-spatial processing.

- A straight line (yellow) was drawn in the buccal area close to the root surface, copying the inclination of the long root axis (Fig. 2).

- The sagittal inclination of the long crown axis was observed by visual-spatial processing.

A straight line (yellow) was drawn in the buccal region close to the coronal surface, copying the inclination of the long crown axis (Fig. 3).

- After tracing both lines

- The line representing the long root axis (movement without inclination) was moved towards the root center.

- The line representing the long crown axis was moved until it contacted the previous line (movement without inclination).

- Both lines intersected forming an angle, which was named the crown-root angle (Fig. 4).

Then, the PowerPoint file that contained the images with traced axes was imported into the AutoCAD® 2015 software, for measurement of the crown-root angle.

Crown-root angle measurement protocol. The posterosuperior angle was measured on the upper central incisor (Figs. 5 A and B), and the posteroinferior angle was measured on the lower central incisor (Figs. 5 C and D). Two decimals were considered for both angles (Annex 7).

Fig. 1 Orientation and sagittal view of the upper and lower central incisor. A. Palatal plane parallel to the true horizontal line. B. 116º angle formed by intersection of the long axis of the lower central incisor with the true horizontal line. 

Fig. 2 Sagittal view of the upper and lower central incisor. Straight line representing inclination of the root surface: A. Upper central incisor. B. Lower central incisor. 

Fig. 3 Sagittal view of the upper and lower central incisor. Straight line representing the crown inclination: A. Permanent upper central incisor. B. Permanent lower central incisor. 

Fig. 4 Sagittal view of the permanent central incisors. A. Crown-root angle of the upper incisor. B. Crown-root angle of the lower incisor. 

Fig. 5 Sagittal view of upper and lower central incisor in AutoCAD® 2015 software. A. Legs of the crown-root angle of the upper central incisor. B. Crown-root angle: 31.05º of the upper central incisor. C. Legs of the crown-root angle of the lower central incisor. D. Crown- root angle: 24.58º of the lower central incisor 

RESULTS

From a universe of 214 CBCT of permanent central incisors, 100 met the inclusion and exclusion criteria (50 upper central incisor and 50 lower central incisor).

The angle measurements were organized in a database using the StataCorp software (2015) statistical software Release 14, College Station, TX: StataCorp LP., and processed by descriptive statistical analysis.

To determine the descriptive statistics to be used for both central tendency and dispersion, the Shapiro-Wilk test was performed, which revealed a normal distribution of data for the permanent upper central incisors (p=.866) and the permanent lower central incisors (p=.422).

Concerning the summarized measures of both groups, the upper incisors (Fig. 6) presented a slightly higher mean compared to the lower (Fig. 7), yet with similar SD between them (Table I).

The mean values, standard deviations and confidence intervals of the permanent upper and lower central incisors are shown in Table I.

Fig. 6 Scatter plot of the crown-root angle with central tendency lines in permanent upper central incisors. 

Fig. 7 Scatter plot of the crown-root angle with central tendency lines in permanent lower central incisors. 

Table I Descriptive statistics of the crown-root angle. 

^{CI. confidence interval of 95 %}.

DISCUSSION

The analysis of results allows the following discussion points: The existence of a large anatomical variability between the central incisors is confirmed, complicating the assignment of a single value to the crown-root angle. This is consistent with ^{Carlsson & Rönnerman (1973}), who concluded that the variation of this angle in the upper central incisor and that the variation of the sagittal location of the incisal edge in relation to the root are related to the different anatomical shapes of the incisor between individuals. It also agrees with ^{Fredericks (1974}), who analyzed 100 tracings of upper incisors and determined that this anatomical variation explained the different inclinations of the long crown axis and the longitudinal tooth axis between patients. Within the various implications of this anatomical variability in orthodontic therapy, ^{Andrews (1989}a) mentioned that, to use prescriptions options of straight wire brackets in different patients and to obtain similar final dental positions, it was fundamental to have low anatomical variability across the dental groups.

The crown-root angle has been assessed using multiple methodologies (^{Taylor, 1969}; ^{Carlsson & Rönnerman, 1973}; ^{Fredericks, 1974}; Andrews, 198b), precluding the comparison between studies. However, there are methodological similarities between this study and that of Carlsson & Rönnerman (1973), allowing comparison of results. Both investigations obtained similar results for the angle between the long crown axis and the long root axis of the upper central incisor: the value of their study for this angle was 21.4° with SD of 4.2°. Additionally, another point of similarity between studies is the exclusion of the root apex point. This allows a more accurate copy the inclination of the long root axis, while simultaneously avoiding difficulties related to angle measurement due to the usual variations in the position of the root apex.

Notwithstanding, there is a central difference between this study and that of ^{Carlsson & Rönnerman (1973}), in the technique to determine the long crown axis. The present study did not include the stereograph used by these authors, but used the visual-spatial processing, thus simplifying the tracing of the long crown axis. A similar simplification is observed in the tracing of this axis and thus in the measurement of the crown-root angle, when compared with the methodology used by ^{Fredericks (1974}). This last study measures the angle between the long crown axis and the long tooth axis, obtaining an average value for the upper incisor of 23.88° with a difference between the maximum and minimum values of 21°. Interestingly, to determine the inclination of the long crown axis, it uses the point of greatest crown convexity, which was located at 4.2 mm from the incisal edge towards the gingiva after a preliminary statistical study. However, it is complex to trace this inclination using this anatomical reference, since, as mentioned by the author, the curvature of the buccal surface varies widely between patients. This contrasts with the visual-spatial processing, which does not require exact location of these anatomical landmarks, thus simplifying the measurement process.

CONCLUSION

During the diagnostic and therapeutic stage, it is important to consider the inclination of the long axes of the crown and root, since they affect the results achieved using the same orthodontic straight wire therapy. This relationship between the inclination of the axes and the result of therapy is especially relevant in the central incisors since they are the teeth most exposed to evaluation by the patient.

This study suggests that the visual-spatial processing can be a valid method for determining the long crown axis and the long root, also having the advantage of not requiring specific instruments and anatomical reference points, which simplifies the tracing of axes and thus measurement of the crown- root angle.

Notwithstanding, it is suggested that the values obtained in this study, as well as the validity of the visual-spatial processing, should be analyzed in future studies on larger samples.