Computation and prediction of sectorial arch width and arch perimeter changes of maxillary arch by graphical method of Ramanujan’s equation for the ellipse - Rishitha Gundeboina; Yamini Priyanka JS; Lekha Indukuru; Ravuru Divya; Vivek Reddy Ganugapanta; Gowri Sankar Singaraju; Prasad Mandava (Clinical and Investigative Orthodontics)
Purpose The assessment of space gain is a critical step in the non-extraction orthodontic treatment methods. This study aims to assess the arch width along the arch perimeter concurrent with the changes in the arch width due to expansion at the molar region.Material and methods The study sample included 43 models of the maxillary arch of class I patients with two data sets for computation. The initial parameters- Inter-molar width (IMW), Inter-Premolar width(IP1W), Inter-canine width (ICW), and Arch Perimeter (AP) were directly measured on the models. The measured values were utilized to calibrate the digital images of the models. The arch width changes at the premolar and canine levels for an incremental unit expansion at the second molar region of up to 5 mm were computed by Matlab®, utilizing Ramanujan’s equation of the ellipse and Adobe Photoshop®. The arch perimeter for a given change in the incisor inclination was also predicted. The calculated and measured values were correlated and compared using Pearson correlation and the student’s T-test. The Bland-Altman plots were utilized to test the reliability of the calculated values.Results Arch perimeter increases by an average of 1.8 mm for every 1 mm rise in incisor proclination and 0.66 mm for every 1 mm increase in molar expansion. The ratio of changes in canine, premolar, and molar arch width for all expansion levels is 0.6:0.8:1.Conclusion The graphical method of Ramanujan’s equation can be employed to individualize dental arches and archwires.