天津医药

天津医药 ›› 2017, Vol. 45 ›› Issue (1): 30-35.doi: 10.11958/20161031

• 实验研究 • 上一篇    下一篇

骨性Ⅲ类错牙合牙弓与基骨弓的三维数学模型研究

方姝 1， 肖丹娜 2△， 高辉 2   

  1. ： 1 天津医科大学研究生院 （邮编 300070）； 2 天津市口腔医院
  • 收稿日期:2016-09-23 修回日期:2016-11-29 出版日期:2017-01-15 发布日期:2017-01-15
  • 基金资助:
    国家临床重点专科建设项目（口腔正畸专业）

The mathematical model of the dental and basal bone arch form of skeletal class Ⅲ malocclusions in three-dimensional space

FANG Shu1, XIAO Dan-na2△, GAO Hui2 #br# #br#   

  1. 1 Graduate School of Tianjin Medical University, Tianjin 300070, China;
    2 Orthodontic Department of Tianjin Stomatological Hospital

  • Received:2016-09-23 Revised:2016-11-29 Published:2017-01-15 Online:2017-01-15

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摘要： 摘要： 目的 建立描述骨性Ⅲ类错 患者牙弓及基骨弓形态的数学模型， 为后期进一步研究提供数据参考和依 据。方法 本实验选用 35 例骨性Ⅲ类错 患者的计算机重组断层影像 （CBCT） 为研究对象， 分析三维影像资料， 对 牙弓标志点 （Fa） 和基骨弓标志点 （Ba） 进行定点测量， 以最小二乘法确定参考平面， 用 Matlab 7.0 软件计算二维坐标， 在此基础上建立描述骨性Ⅲ类错 患者上、 下颌牙弓和基骨弓形态的数学模型， 并对该模型进行验证分析。结果 （1）描述骨性Ⅲ类错 牙弓形态的数学模型。上颌： Y=46.12［1-（2X/70.99） 2］ 1.052； 下颌： Y=39.16［1-（2X/64.51） 2］ 1.038。 （2）描述骨性 Ⅲ类错 基骨弓形态的数学模型。上颌： Y=43.14［1-（2X/75.09） 2］ 1.061； 下颌： Y=39.03［1-（2X/ 60.63） 2］ 1.021。（3） 骨性Ⅲ类错 患者的上颌 Fa’ 点均位于 Ba’ 点唇侧， 其距离为正值； 下颌 Fa’ 点均位于 Ba’ 点舌侧， 其 距离为负值。（4） Beta 函数曲线与骨性Ⅲ类错 上、 下颌牙弓与基骨弓在各个牙位上拟合相关系数均大于 0.7（P＜ 0.05）。结论 本实验所建立的 Beta 函数数学模型可用于描述骨性Ⅲ类错 患者上、 下颌牙弓和基骨弓形态， 所得 函数及测量结果可指导进一步研究。

关键词: 骨性Ⅲ类错 , 牙弓, 基骨弓, 数学模型, 计算机重组断层影像, Beta 函数

Abstract: Abstract: Objective To establish a mathematical model to describe the skeletal class Ⅲ malocclusion of patient dental and basal bone arch form, for providing a data reference and basis for further study. Methods Thirty-five patients with skeletal class Ⅲ malocclusion were selected in this study for computed tomography CBCT. The data of 3-D image were analyzed, and dental arch marker (Fa) and base bone arch marker (Ba) were determined. The reference plane was determined by least square method. Software Matlab 7.0 was used to calculate two- dimensional coordinate system. Based on this, a mathematical model was established to describe the dental and basal bone arch form and then to validate the mathematical model. Results (1) The mathematical model can be used to describe the dental arch form of skeletal class Ⅲ malocclusion, maxillary: Y=46.12 [1- (2X/70.99)2]1.052; mandibular: Y=39.16 [1- (2X/64.51)2]1.038. (2) The mathematical model can be used to describe the basal bone arch form of skeletal class Ⅲ malocclusion, maxillary: Y=43.14 [1- (2X/75.09)2]1.061; mandibular: Y=39.03 [1- (2X/60.63)2]1.021. (3) Fa was located at Ba labial side in the maxilla, the distance was positive. Fa was located at Ba lingual side in the mandibular, and the distance was negative. (4) The fitting correlation coefficient of beta-function curve and each tooth on the dental and basal bone arch of skeletal class Ⅲ malocclusion were greater than 0.7 (P＜0.05). Conclusion In this study, the mathematical model can be used to describe the dental and basal bone arch form of the skeletal class Ⅲ malocclusion, which can guide further research.

Key words: skeletal class Ⅲ malocclusion, dental arch, basal bone arch, mathematical model, cone-beam computed tomography, Beta-function