Evaluation of Dental Arch Characters by Analysis of a Fourier Series Developed from Mathematically Estimated Maxillary Dentitions

Our previous principal component analysis conducting on reference points, lines and angles, and a vector-developed polar coordinate system has elucidated that the components of eigenvectors had positive relationships in the curvature of anterior teeth segment, between the protrusion of canines and degree of arch roundness, and in the length-to-width ratio of 62 maxillary dentitions, which were preliminarily classified with reference to the conventional Thompson's morphological descriptions for dental arch forms. In the present study on morphological characters of the maxillary dentitions, we conducted a Fourier analysis on the previously obtained data. We observed that the amplitude of 2nd, 3rd and 4th Fourier harmonics were closely correlated with the length-to-width ratio, curvature of the anterior teeth segment, and the curvilinear contour of maxillary dental arches. In addition, the relationships between previously estimated data and the constant value and the amplitude of the Fourier series were examined by analysis of correlation coefficients (p＜0.01). The results of the present study suggest that the morphology of maxillary dentitions consists of three essentials the length-to-width ratio, the curvature of anterior teeth, and the curvilinear contour of dental arches.