口腔医学研究

口腔医学研究 ›› 2018, Vol. 34 ›› Issue (1): 77-81.DOI: 10.13701/j.cnki.kqyxyj.2018.01.019

• 口腔美学研究 • 上一篇    下一篇

基于二维投影建立骨性Ⅱ类错牙合畸形数学模型研究

马艺萌1, 高辉2*, 肖丹娜2, 方姝1   

  1. 1. 天津医科大学研究生院 天津 300070;
    2. 天津市口腔医院 天津 300041
  • 收稿日期:2017-09-13 出版日期:2018-01-28 发布日期:2018-01-26
  • 通讯作者: 高辉,E-mail:keyanjiaoxue@gmail.com
  • 作者简介:马艺萌(1988~ ),女,硕士在读,主要从事口腔正畸学研究,现工作于武警后勤学院附属医院口腔科。

Establishment of Mathematical Model of Skeletal Class Ⅱ Malocclusion Based on 2D Projection Point Set

MA Yi-meng1, GAO Hui2*, XIAO Dan-na2, FANG Shu1   

  1. 1. Graduate School of Tianjin Medical University, Tianjin 300070, China;
    2. Tianjin Stomatological Hospital, Tianjin 300041, China.
  • Received:2017-09-13 Online:2018-01-28 Published:2018-01-26

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摘要： 目的:将骨性Ⅱ类错牙合牙弓及基骨弓的三维影像测量数据投影到二维平面,建立描述其形态的数学模型。方法:选取30例骨性Ⅱ类错牙合患者锥形束CT资料,确定牙弓标志点(Fa)和基骨弓标志点(Ba)并进行测量,蜂群算法确定牙合平面,Matlab 7.0软件计算二维坐标,获得消除三维值的二维投影点图。结果:建立描述骨性Ⅱ类错牙合牙弓和基骨弓形态的Beta函数模型:1)牙弓:上颌 Y=41.01[1 - (2X/61.08)2]0.73,下颌 Y=37.35[1 - (2X/59.55)2]0.717;2)基骨弓:上颌 Y=29.15[1 - (2X/65.63)2]0.721,下颌 Y=30.91[1 - (2X/79.19)2]1.242。结论:建立与骨性Ⅱ类错牙合牙弓及基骨弓形态拟合度较高的函数方程,所得函数及测量数据可指导进一步研究。

关键词: 骨性Ⅱ类错牙合, 牙弓, 基骨弓, 数学模型, 二维投影

Abstract: Objective: To describe the dental form and basal bone arch form of skeletal Class Ⅱ malocclusion patients by transforming 3D image data to 2D plane and establishing a mathematical model. Methods: CBCT data of 30 patients with skeletal Class Ⅱ malocclusion were selected. Occlusion plane with mathematical algorithm by dental form point (Fa) and basal bone arch form point (Ba) was determined. 3D image data was transformed to 2D plane with Software Matlab 7.0. Results: The mathematical model describing the dental arch and basal bone arch form of skeletal ClassⅡ malocclusion was established: 1) dental arch: maxillary Y=41.01[1- (2X/61.08)2]0.73; mandibular Y=37.35[1- (2X/59.55)2]0.717; 2) basal bone arch: maxillary Y=29.15[1- (2X/65.63)2]0.721; mandibular Y=30.91[1- (2X/79.19)2]1.24. Conclusion: A function equation which has high fitting degree with the dental form and basal bone arch form of the skeletal Class Ⅱ malocclusion patients was established. The function equation and the measurement data from it can guide further research

Key words: Skeletal class Ⅱ malocclusions, Dental arch, Basal bone arch, Mathematical model, 2D projection

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