Fourier and principal component analyses of maxillary dental arch forms

Objectives: We studied the morphological character of 62 standardized maxillary dental arches by Fourier and principal component analyses of measured values. Materials and Methods: 62 maxillary dental arches having normal dentition and occlusion were selected from 396 (age: 18-26 years old; male: 257, female: 139) sets of plaster dental study models. We determined midpoints of the incisal edges, cusp tips of the canines, buccal cusp tips of the premolars, and mesiobuccal cusp tips of the molars as reference points. O point (origin, pole) was the midpoint at the line (original line) connecting mesiobuccal cusp tips of the second molars. Vectors rθn (n=1,・・・7) were represented by connecting O and the reference points. We evaluated protrusion of the canines, curvature of the anterior teeth, length-to-width ratio of the dental arch, degree of roundness of the arch and alignment of posterior teeth by six items, which were then summarized into three essential principal components. Fourier analysis was conducted on the polar coordinate system developed from the vectors rθn (n=1,・・・7). Fourier coefficient and amplitudes were analyzed for evaluation of maxillary dental arch forms. Results: 1) Significant difference of the 1 ^st Fourier coefficient representing the arch size was not observed in the analysis. In contrast, 2 ^nd , 3 ^rd and 4 ^th Fourier coefficients showed significant differences between the maxillary dentitions. 2) The 2 ^nd , 3 ^rd and 4 ^th Fourier coefficients were identified closely correlating with length-to-width ratio of the arch, width of the anterior teeth, and length-to-width ratio of the anterior teeth. Conclusions: 1) The characteristics of different maxillary dental arch forms are distinctively found in 2 ^nd , 3 ^rd and 4 ^th Fourier harmonic. 2) The present Fourier and principal component analyses obtains same results as what have been described in our previous studies (Nakatsuka et al., 2004).