Mathematical ratio in defining arch form

Abstract

Introduction: The treatment of Class I malocclusion aims to arrange teeth position in a good arch form. The arch form consists of tooth size and arch dimension (intercanine width, canine depth, intermolar width, molar depth). Numerous methods have been used to describe the arch form quantitatively. The aim of this study was to develop a mathematical ratio for identifying arch form (square, oval, tapered) using arch dimension variables (intercanine width, canine depth, intermolar width, molar depth). Materials and Methods: Dental cast pre and post-orthodontic treatments from 190 Indonesian patients were scanned to obtain digital data. All data were measured using “Image Tool.” The measured data (tooth size, intercanine width, intercanine depth, intermolar width, intermolar depth, and arch perimeter) were analyzed statistically using ordered logistic to find out determining variables to the arch form. Results: The validity, reliability, and normality of all the data were analyzed using Stata. From analyzing the data using ordered logistic, intercanine width and intermolar depth showed a reverse relation to the arch form. The shape of the arch form (square, oval, and tapered) can be described quantitatively by using ratio (CD/CW)/(MD/MW); a ratio less than 45.30% indicates square, 45.30–53.37% indicates oval, and more than 53.37% indicates tapered. Conclusions: (CD/CW)/(MD/MW) ratio can be used to describe arch form quantitatively.