Mathematical definition of the shape of dental arches in human permanent healthy dentitions.

Dental arch shape was studied in 50 men and 45 women aged 20-27 years with sound dentitions. Maxillary and mandibular arches were reconstructed by a fourth-order polynomial and a 'mixed' elliptical (anterior teeth), plus parabolic (post-canine teeth) interpolation of buccal cusp tips (central incisor to second molar). The maxillary arch resulted wider than the mandibular arch regardless of gender. Gender differences were found especially in the maxillary arch, where they reflect more a size discrepancy than a shape difference. The polynomial interpolation allowed the evaluation of arch asymmetry, which resulted negligible in all the subjects. The elliptical plus parabolic interpolation gave mean plots which were well superimposable to the ones obtained by the polynomial interpolation. These curves are geometrically simple and can be used for the mathematical description of dental arch shape in non-patient subjects. Moreover, they allow separate analysis of teeth with a different functional meaning.