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

Abstract

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 1^st to 4^th and the 1^st to 6^th 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 2^nd 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 1^st amplitude of maxillary dentitions and in constant term and all amplitudes of mandibular dentitions. Nevertheless, the study revealed high contribution ratios of the 1^st (in mandibular dentitions) and the 2^nd (in maxillary dentitions) amplitudes essentially affecting the reproducibility of arch forms. The 1^st amplitudes demonstrated a bow-like arrangement of all arch types, while the 2^nd amplitudes adjusted the anterior-teeth curvature and in particular demonstrated the length-to-width ratio of maxillary dentitions. The 3^rd and the 4^th amplitudes were also determinants of the anterior-teeth curvature of maxillary dentitions. The 6^th 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.