Human evaluation in association to the mathematical analysis of arch forms: Two-dimensional study

To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation.

This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated.

Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable.

The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch.