For the assessment of primary arch form, different methods have been used including qualitative classifications, inter-canine and inter-molar widths and quantitative and numerical methods using mathematical models. The purpose of this study was to compare the validity and reliability of Cast Analyzer X Iranian software with those of Curve Expert Professional version 1.1 for arch form construction based on mathematical models.

This diagnostic, in-vitro study was performed on 18 sets of dental casts with normal Class I occlusion. The clinical buccal points (bracket attachment sites)(CBPs) were marked on each tooth and their spatial coordinates were digitized using a three-dimensional (3D) laser scanning system. These coordinates were entered in Cast Analyzer X and Curve Expert software programs. Arch forms were constructed by the software programs using Brown’s beta function, Noroozi’s beta function and fourth order polynomial equation. The root mean square (RMS) of the distance from reference points to their corresponding points on the curve was calculated. The RMS values in the two software programs were compared.

The RMS values in Brown’s beta function, Noroozi’s beta function and fourth order polynomial equation were significantly different in the Cast Analyzer X software (P<0.001) and the fourth order polynomial equation had the lowest RMS. The difference in RMS values between the two software programs was not clinically considerable and was 0.45 and 0.68 mm for the fourth order polynomial equation and Brown’s beta function, respectively. 

  Conclusion: 

Considering the RMS values, the fourth order polynomial equation is the most suitable analysis for describing normal dental arch forms best fitted with the CBPs. Although the difference between the two software programs was statistically significant, this difference was not clinically noticeable. The RMS value was lower in Cast Analyzer X and consequently the fitting of curves with the landmarks (CBP) was better in the Iranian software.