Abstract: Objective　To explore the influencing factors of the growth potential of mandibular retromolar region in adolescents，and analyze the accuracy of non-linear equation based on genetic algorithms（GAS）optimization. Methods　A total of 306 patients were selected according to the inclusion criteria，who were treated at the Department of Orthodontics in Jilin University Stomatological Hospital from 2017 to 2019. The lateral cephalometric radiographs were used to obtain the mandibular retromolar space and cervical vertebrae measurements. Multiple linear regression analysis was used to evaluate the correlation between retromolar space and age，dental age of the third mandibular molar，cervical vertebral maturation，etc. The strongest correlation factor was selected to construct a linear regression equation and a non-linear equation based on GAS optimization，and the accuracy of the two prediction equations were compared. Results　（1）The retromolar space was different in different antero-posterior skeletal facial types. There was no statistically significant difference between the skeletal class Ⅰ malocclusion group ［（9.99 ± 2.53）mm］ and the skeletal class Ⅲ malocclusion group ［（10.53 ± 3.53）mm］（P > 0.05）. In the skeletal class Ⅱ malocclusion group ［（8.98 ± 2.71）mm］ it was smaller than the skeletal class Ⅰ and class Ⅲ malocclusion group，the difference being statistically significant （all P < 0.05）. Therefore，all patients were divided into skeletal class Ⅰ+Ⅲ malocclusion group and skeletal class Ⅱ malocclusion group.（2）The retromolar space（RMS）was positively correlated with the third molar age（YL）. The linear regression equations and nonlinear equations based on GAS optimization were constructed respectively：for skeletal class Ⅰ+Ⅲ group：RMS = 1.489YL + 3.891，and RMS = 2.36YL0.81 + 2.686；for skeletal class Ⅱ group：RMS = 1.464YL + 1.961，and RMS = 2.36YL0.81 + 0.723. The error value of the nonlinear equation optimized based on GAS was lower than the linear regression equation，but the difference was not statistically significant（P > 0.05）. Conclusion　Clinical orthodontists should take the third molar age and antero-posterior skeletal facial types into account when designing orthodontic programs for adolescent  patients. The precision and accuracy is higher in the nonlinear equations based on GAS optimization to predict the growth potential of mandibular retromolar region.

Key words: retromolar space, genetic algorithm, dental age, cervical vertebral maturation, antero-posterior skeletal facial types

摘要： 目的　探讨影响青少年下颌磨牙后区生长潜力的因素，并分析基于遗传算法（genetic algorithms，GAS）优化青少年下颌磨牙后区生长潜力非线性预测方程的准确性。方法　选取2017—2019年于吉林大学口腔医院正畸科就诊的符合纳入标准的初诊患者306例。通过头颅定位侧位片测量下颌磨牙后间隙及颈椎测量指标，采用多元线性回归分析下颌磨牙后间隙与年龄、下颌第三磨牙牙龄、颈椎骨龄等的相关性，选取最强相关因子构建线性回归方程和基于GAS优化的非线性方程，并比较两个预测方程的准确性。结果　（1）不同矢状骨面型患者下颌磨牙后间隙不同，骨性Ⅰ类错牙合畸形组［（9.99 ± 2.53）mm ］与骨性Ⅲ类错牙合畸形组［（10.53 ± 3.53）mm ］比较，差异无统计学意义（P > 0.05）；而骨性Ⅱ类错牙合畸形组患者下颌磨牙后间隙［（8.98 ± 2.71）mm］小于骨性Ⅰ类和Ⅲ类错牙合畸形组，差异均有统计学意义（均P < 0.05）。故将所有患者分为骨性Ⅰ+Ⅲ类错牙合畸形组和骨性Ⅱ类错牙合畸形组。（2）下颌磨牙后间隙（RMS）与下颌第三磨牙牙龄（YL）呈正相关关系，两组分别构建线性回归方程和基于GAS优化的非线性方程如下。骨性Ⅰ+Ⅲ类错牙合畸形组：RMS = 1.489YL + 3.891；RMS = 2.36YL0.81 + 2.686。骨性Ⅱ类错牙合畸形组：RMS = 1.464YL + 1.961；RMS = 2.36YL0.81 + 0.723。基于GAS优化的非线性方程误差值低于线性回归方程，但其差异无统计学意义（P > 0.05）。结论　临床正畸医生进行青少年患者正畸方案设计时，应着重结合患者第三磨牙牙龄及矢状骨面型。应用基于GAS优化的非线性方程预测下颌磨牙后区生长潜力具有较高的预测精度和准确性。

关键词: 磨牙后间隙, 遗传算法, 牙龄, 颈椎骨龄, 矢状骨面型