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.