Methods: The midpoint (O: origin, pole) at the line M2R-M2L (original line) was designated as reference point. Vectors rθn (n=1,・・・7) were represented by lines connecting O and the reference points. Fourier analysis was conducted on a polar coordinate system developed from the vectors. Fourier coefficient and amplitudes were analyzed for evaluation of mandibular dental arch forms.
Results: 1) Each mandibular dental arch form was reproduced by 1st to 4th of Fourier harmonics. 2) Significant differences of the constant value and the amplitude of the 1st Fourier harmonic (representing the arch size and form) were not observed in the analysis. In contrast, the amplitudes of the 2nd, 3rd and 4th Fourier harmonics concerning the arch forms, showed significant differences between the mandibular dentitions. 3) The amplitudes of the 2nd, 3rd, and 4th Fourier harmonics were identified closely correlating with length/width ratio, the curvature of anterior teeth and the curvilinear contour of the dental arch, respectively.
Conclusions: 1) Establishment of Fourier series is a significant method to reproduce mandibular dental arch forms. 2) Characteristics of different dental arch forms are distinctively found in each Fourier harmonic. The present analysis obtains results similar to our previous studies on characteristics of the mandibular dentitions by correlation and principal component analyses.