Mathematical Analyses of Dental Arch Curvature in Normal Occlusion

Abstract

Abstract Objective: To present a comprehensive mathematical analysis of dental arch curvature in subjects with normal occlusion. Materials and Methods: The materials studied were 40 sets of upper and lower plaster dental casts of subjects presenting with normal occlusion. The sample was equally divided into casts from male and female subjects with an age range from 18 to 25 years. Curve-fitting analyses was carried out and four main categories of functions were considered: the beta function, natural cubic splines, polynomial equations, and Hermite cubic splines. Results: The polynomial function (fourth order) was found to be a reasonable analysis when the objective is to describe the general smooth curvature of the dental arch, while a Hermite cubic spline is more appropriate when it is desired to track arch irregularities, such as evaluating treatment changes. Conclusions: Due to its advantage in providing a more naturally smooth curve, the fourth-order polynomial function may be used as a guide to fabricate customized arch wires, or even an entire fixed orthodontic appliance system.