Mathematical Beta Function Formulation for Maxillary Arch Form Prediction in Normal Occlusion Population

The aim of this study was to assess the dental arch curvature in subjects with normal occlusion in an Iranian population and propose a beta function formula to predict maxillary arch form using the mandibular intermolar widths (IMW) and intermolar depths (IMD). The materials used were study casts of 54 adolescents with normal occlusion and mean age of 14.1 years (25 males, 29 females, age range 12–16 years). Curve-fitting analyses were carried out and the curves passing through the facial-axis point of the canines, premolars, first molars, and the incisal edges of the anterior teeth were studied using a 3D laser scanner. Using the measured IMW and IMD of the dental arches at the maxillary and mandibular first molar region, a beta function formula proposed for predicting maxillary arch form. The accuracy of the proposed formula was assessed on 10 randomly selected dental casts. The mean (SD) of the maxillary and mandibular IMW and IMD were 57.92 (4.75), 54.19 (5.31), and 31.59 (2.90) and 28.10 (2.59) mm, respectively. There was no gender dimorphism (P > 0.05) for both variables (IMW, IMD). There was a strong positive association (n = 10, Pearson r = 0.98, P < 0.05) between the measured (actual) maxillary arch length and proposed arch length derived from generated formula. The goodness of fit (whole arch) for the proposed beta function formula, using adjusted r square measure and root mean square in 10 patients averaged 0.97 and 1.49 mm, respectively. The corresponding figures for the maxillary anterior arch (canine to canine) were 0.90 and 0.92 mm, respectively. The proposed beta function formula used for predicting maxillary arch form based on two mandibular measures (IMW, IMD) was found to have a high accuracy for maxillary arch prediction in the Iranian population and may be used as a guide to fabricate customized arch wires or as an aid in maxillary reconstructive surgery.