Chung David D, Wolfgramm Richard
Program director, Division of Orthodontics and Dentofacial Orthopedics, Department of Dentistry, Maimonides Medical Center, Brooklyn, NY.
Private practice, Vancouver, Wash.
Am J Orthod Dentofacial Orthop. 2015 Feb;147(2):235-41. doi: 10.1016/j.ajodo.2014.10.022.
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.
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.
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.
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.
在正畸治疗拔牙与不拔牙治疗方案的决策中，预测扩弓或前牙唇倾时牙弓周长的增加尤为重要。
使用30副未经治疗的上颌牙弓诊断模型，评估上颌牙弓测量周长与应用拉马努金椭圆周长公式计算出的周长之间的相关性。在这些上颌牙弓的颊面中部直接进行线性和圆周测量。
使用双尾t检验，在比较上颌牙弓测量周长与计算周长时，拉马努金公式在0.01水平（误差1.2%）具有高度相关性。将结果应用于拉马努金公式，以预测扩弓或前牙唇倾时上颌牙弓周长的增加。
椭圆是上颌牙弓形态的精确几何模型。每毫米磨牙间扩弓增加的上颌牙弓周长平均为0.73毫米，每毫米切牙前突增加的上颌牙弓周长平均为1.66毫米。
