Maxillary arch perimeter prediction using Ramanujan's equation for the ellipse.

Introduction: The prediction of arch perimeter gained when expanding the arch or proclining the anterior incisors is particularly important in the decision of tooth extraction vs nonextraction therapy for orthodontic treatment.

Methods: Correlation of the measured perimeter of the maxillary dental arch and the calculated perimeter applying Ramanujan's equation for the perimeter of an ellipse was evaluated with 30 diagnostic casts of untreated maxillary dental arches. Both linear and circumferential measurements were made directly on the midbuccal surface of these maxillary arches.

Results: Ramanujan's equation had a high level of correlation when comparing the measured perimeter of the maxillary dental arch and the calculated perimeter with the 0.01 level (1.2% error) using a 2-tailed t test. The results were applied to Ramanujan's equation to predict maxillary arch perimeter gained by expansion or proclination of the incisors.

Conclusions: The ellipse is an accurate geometric model of the maxillary arch form. The average amounts of maxillary arch perimeter gained were 0.73 mm per millimeter of intermolar expansion and 1.66 mm per millimeter of incisor protrusion.