Ramanujan’s Equation as an Aid to Predict Arch Perimeter Changes with Precision: A Retrospective Study

Abstract

Introduction The aim of this study was to evaluate the validity of Ramanujan’s equation in measuring arch perimeter on untreated natural dentition models and their orthodontically corrected posttreatment models. The secondary objective was to apply the equation to predict the arch perimeter gained by the expansion of the molar teeth or proclination of the incisor teeth and compare it with the actual posttreatment arch perimeter changes. Methods 32 maxillary and mandibular (16 pretreatment and 16 posttreatment each) fairly aligned diagnostic casts of orthodontically treated nonextraction patients with class I molar relationships were used. The arch perimeter was measured using 0.012 mm stainless steel wire and was compared with the calculated arch perimeter obtained using Ramanujan’s equation. Pearson correlations were used to determine the correlation between the measured and predicted values. Paired t-tests were used to assess changes in different variables in the pre- and posttreatment study casts of maxilla and mandible. Results Positive correlation of 0.06 (90% CI) between predicted and measured values was found. In maxillary ( P = .04) study models, predicted arch perimeter by use of Ramanujan’s equation was more reliable than mandibular ( P = .74) study models. Conclusion Ramanujan’s equation can be an important aid to calculate the arch perimeter change by the expansion of molar teeth and proclination of incisor teeth 0.06 (90% CI). It is helpful for more accurate nonextraction treatment planning before the start of orthodontic treatment. In maxillary ( P = .04) study models, calculated arch perimeter using Ramanujan’s equation is even more reliable than mandibular study models ( P = .74).