Dental arch form in three Pacific populations: a comparison with Japanese and Australian aboriginal samples

Human evaluation in association to the mathematical analysis of arch forms: Two-dimensional study

OBJECTIVES

To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation.

MATERIALS AND METHODS

This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated.

RESULTS

Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable.

CONCLUSION

The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch.

Is arch form influenced by sagittal molar relationship or Bolton tooth-size discrepancy?

Background

Orthodontic patients show high prevalence of tooth-size discrepancy. This study investigates the possible association between arch form, clinically significant tooth-size discrepancy, and sagittal molar relationship.

Methods

Pretreatment orthodontic casts of 230 Saudi patients were classified into one of three arch form types (tapered, ovoid, and square) using digitally scanned images of the mandibular arches. Bolton ratio was calculated, sagittal molar relationship was defined according to Angle classification, and correlations were analyzed using ANOVA, chi-square, and t-tests.

Results

No single arch form was significantly more common than the others. Furthermore, no association was observed between the presence of significant Bolton discrepancy and the sagittal molar relationship or arch form. Overall Bolton discrepancy is significantly more prevalent in males.

Conclusions

Arch form in a Saudi patient group is independent of gender, sagittal molar relationship, and Bolton discrepancy.

Comparison of mandibular arch forms of Korean and Vietnamese patients by using facial axis points on three-dimensional models

Objective

This study was aimed at comparing the mandibular arch forms of Korean and Vietnamese patients by using facial axis (FA) points on three-dimensional (3D) models.

Methods

Mandibular casts of 68 Korean (Class I malocclusion, 30; Class II malocclusion, 38) and 78 Vietnamese (Class I malocclusion, 41; Class II malocclusion, 37) patients were scanned in their occluded positions and grouped according to arch form (tapered, ovoid, and square). The FA point of each tooth was digitized on the 3D mandibular models. The measurements and frequency distributions of the arch forms were compared between the ethnic groups.

Results

The Vietnamese patients had significantly greater intercanine depth and intercanine and intermolar width-to-depth ratios than the Korean patients (p < 0.05). The frequency distributions of the arch forms were also significantly different (p = 0.038), but no sexual dimorphism was found.

Conclusions

Vietnamese people tend to have deeper and wider arches than Korean people. The three arch forms are evenly distributed in Korean people, but Vietnamese people frequently have square arches. Clinicians should identify the correct arch form of an ethnic group before initiating orthodontic treatment.

Comparison of maxillary and mandibular dental arch forms by studying Fourier series developed from mathematically estimated dentitions

We conducted a Fourier analysis on data obtained using correlation and principal component analyses of parallel-standardized dental study models; both maxillary and mandibular dental arches were predominantly round square in shape. The present study compared and determined the contribution ratio and reproducible coefficients of amplitudes (factors affecting dental arch forms), and demonstrated that the 1st to 4th and the 1st to 6th Fourier harmonics reproduced maxillary and mandibular dental arch forms, respectively. The correlation analyses of the constant term and amplitudes demonstrated that significant differences in the 2nd harmonic amplitude was strongly correlated with the curvature of anterior teeth and the length-to-width ratio in maxillary dentitions. By comparison of the constant term and amplitudes between different arch types, we did not observe significant differences in the constant term and the 1st amplitude of maxillary dentitions and in constant term and all amplitudes of mandibular dentitions. Nevertheless, the study revealed high contribution ratios of the 1st (in mandibular dentitions) and the 2nd (in maxillary dentitions) amplitudes essentially affecting the reproducibility of arch forms. The 1st amplitudes demonstrated a bow-like arrangement of all arch types, while the 2nd amplitudes adjusted the anterior-teeth curvature and in particular demonstrated the length-to-width ratio of maxillary dentitions. The 3rd and the 4th amplitudes were also determinants of the anterior-teeth curvature of maxillary dentitions. The 6th amplitude was necessary for reproduction, but showed no difference between varying mandibular dental arch types. Collectively, we conclude that the establishment of a Fourier series significantly reproduced maxillary but not mandibular dental arch forms.