Evaluation of Dental Arch Form and Approximation of Dental Arch Curvature by Mathematical Functions

Abstract

AIM: To consider a possibility of using three-dimensional (3D) models for evaluation of dental arch form and approximation of dental arch curvature by mathematical functions for orthodontic treatment outcome planning. MATERIALS AND METHOD: The dental casts of 15 patients before and after orthodontic treatment (in total 60 casts) were digitized using a 3D dental scanner (VAS-38, Elintos prietaisai, Kaunas, Lithuania). The system operation is based on the laser triangulation method. All processing of raw scan data and dental cast shape reconstruction routines are performed on the scanner computer module with a multicore processor. System software developed n Borland C++ uses acquired data for automatic measurement of dental arches, to store dental cast models in 3D database. 3D model information was imported to a reverse modelling software package, Rapidform™ 2006, for additional analysis. The occlusal plane was determined using the principal component analysis (PCA) method. Curve fi tting for the lower arch on plane points was carried out by utilizing the 4th order polynomial equation, and  function was calculated using the distobuccal cusp tips of the fi rst permanent molars and the central incisors. RESULTS: The 3D scanning system is designed to achieve a total measuring depth of 60 mm, and depth and lateral resolution of 50 μm. The average correlation coeffi cient between mathematical arch shape expressed by  function and the arch shape after treatment expressed by 4th order polynomial was 0.9363. The mean square difference between arch shape expressed by  function and arch shape before treatment expressed by 4th order polynomial was 0.034 mm. CONCLUSIONS: The 4th order polynomial equation can be used to predict an individualized ideal arch for each patient when spatial coordinates of all teeth are known.  function has been shown to be an accurate representation of the human den