口腔正畸中三维有限元法的发展

doi:10.3969/j.issn.1674-490X.2015.03.017

摘要/Abstract

摘要： 正畸过程就是作用力的体现过程，所以正畸的研究离不开生物力学分析。随着计算机技术的普及和发展，三维有限元分析这种力学分析方法日趋成熟。因其模型具有良好的几何相似性，以及可以进行复杂几何形态的分析被广泛的应用于生物力学领域。本文主要讲述了三维有限元法的定义、运算步骤和在口腔正畸领域的牙体、牙周、种植体等多个方面的应用和进展以及今后三维有限元分析法在正畸生物力学中的发展方向。

关键词: 三维有限元, 正畸, 生物力学

Abstract: The action force is usually reflected during orthodontic process, so the study of orthodontic cannot be separated with the biomechanics analysis. With the development and popularization of the computer technology, the mechanical analysis method, for example, the three dimensional finite element analysis method has become more and more mature. Because its model has good geometry similarity, as well as the analysis of complex geometry is widely used in the field of biomechanics. This paper is mainly about the definition, operation steps of the three dimensional finite element analysis method, and the application and development of this method in many aspects of the orthodontics field, such as teeth body, periodontal tissue, dental implant etc. Besides, the development direction of the three dimensional finite element analysis method (3D-FEM) in orthodontic biomechanics is also introduced.

Key words: three dimensional finite element, orthodontics, biomechanics

中图分类号:

张婉君，李金源，马永平，高林清. 口腔正畸中三维有限元法的发展[J]. 医学研究与教育, 2015, 32(3): 75-81.

ZHANG Wanjun, LI Jinyuan, MA Yongping, GAO Linqing. The development of orthodontics in the three dimensional finite element method[J]. Medical Reserch and Education, 2015, 32(3): 75-81.

参考文献

[1] YU W, PARK H S, KYUNG H M, et al. Dynamic simulation of the self-tapping insertion process of orthodontics: a 3-dimensional finite element method[J]. Am J Orthod Dentofacial Orthop, 2012,142(6): 834-841.
[2] HUANG Y W, CHANG C H, WONG T Y, et al. Bone stress when miniplates are used for orthodontic anchorage: finite element analysis[J]. Am J Orthod Dentofacial Orthop, 2012,142(4): 466-472.
[3] GAINSFORT B L, HIGLEY L B. A study of orthodontic anchorage Possibilities in basal bone[J]. Am J Drthod Oral Surg, 1945,31(8): 406-416.
[4] 王翰章, 周学东. 中华口腔医学-基础总论卷[M]. 2 版. 北京: 人民卫生出版社, 2009: 727-735.
[5] 蒋孝煜. 有限元基础[M]. 2 版. 北京: 清华大学出版社, 1992: 11-13.
[6] HUISKES R, CHAO E Y. A survey of finite element analysis : northopedic biomechanics, the first decade [J]. Biomech, 1998,16(6): 385-391.
[7] COURANT R. Variational Method for Solutions of Problems of Equilibrium and Vibrations [J]. Bull AmMath Soc, 1943, 49(1): 1-23.
[8] TURNER M S, CLOUGH R W, MARTIN H C. Stiffness and deflection analysis complex structure [J]. J Aero Sic, 1956, 23: 805-809.
[9] CLOUGH R W. The Finite Element Method in Plane Stress Analysis [C]// Proceeding of the 2nd ASCE Conference on Electronic Computation. Pittsburg: [s.n.], 1960: 345.
[10] THRESHER R W. The stress analysis of human teeth [J]. J Biomech, 1973, 6(5): 443-449.
[11] FARAH J W. Photoelastic and finite element stress analysis of a restoted arisymmetric first molar [J]. J Biomech, 1973, 6(5): 551.
[12] 周书敏. 有限元法研究牙周韧带的应力分布[J]. 中华口腔医学杂志, 1989, 24(6): 334-337, 385.
[13] 魏洪涛, 张天夫, 曾晨光, 等. 牙颌三维有限元模型生成方法的探讨[J]. 白求恩医科大学学报, 2000, 26(2): 150-151.
[14] BHASKER P, MOHAMMED C, OMAR F. Effective elastic properties of nanocomposites using a novel atomistic-continuum interphase model [J]. Comptes Rendus Mecanique, 2012, 340(4-5): 296-306.
[15] MAGNE P, OGANESYAN J. CTscan-based finite element analysis of premolar cuspal deflection following operative procedures [J]. Int J Periodont Rest, 2009, 29(4): 361-369.
[16] TAJIMA K, CHEN K K, TAKAHASHI N. Three-dimensional finite element modeling from CT images of tooth and its validation [J]. Dent Mater J, 2009, 28(2): 219-226.
[17] 李志华, 陈天云, 刘剑, 等. 上颌第一磨牙的三维有限元模型建立[J]. 实用临床医学，2001, 2(1): 31-33.
[18] 彭佳美, 严斌, 王林, 等. 三维数字化牙颌模型在口腔正畸学中的应用[J]. 中国实用口腔科杂志，2008, 24(2): 236-239.
[19] 林川, 杜莉, 沈颉飞. 建立三种桩核系统修复下颌第一磨牙的三维有限元模型[J]. 实用口腔医学杂志，2008, 24(2): 236-239.
[20] 牟雁东, 樊瑜玻, 刘展. 不同基牙牙周状况下双侧游离缺损冠外附着体义齿的三维有限元分析[J]. 中华老年口腔医学杂志, 2009, 7(4): 241-252.
[21] OLSZEWSKI R, COSNARAL G, MACQ B, et al. 3DCT-based cephalometric analysis : 3D Cephalometric theoretical concept and software [J]. Neuroradiology, 2006, 48(1): 853-862.
[22] PARK S H, YU H S, KIM K D, et al. A proposal for a new analysis of craniofacial morphology by 3-dimensional computed tomography [J]. Am J Orthod dentofacial Orthop, 2006, 129(5): 657-660.
[23] LAGRAVERE M, MAJOR P W. Proposed reference point for 3-dimensianal cephalometric analysis with cone-bean computerized tomography [J]. Am J Orthod Dentofacial Orthod, 2005, 128(5): 657-660.
[24] 狄婧, 孙哲, 尹新芹, 等. 基于CBCT图像构建下颌第一前磨牙三维有限元模型[J]. 临床口腔医学杂志, 2013, 29(9): 530-533.
[25] ZHANG S, LIU X, XU Y, et al. Applicationg of rapid prototyopng for temporomandibular joint reconstruction [J]. J Oral Maxillofacsurg, 2011, 69(2): 432-438.
[26] 于力牛, 常伟, 王成焦, 等. 基于实体模型的牙颌组织三维有限元建模问题讨论[J]. 机械设计与研究, 2002, 18(2): 59-61.
[27] CATTANEO P M, DALSTRA M, MELSEM B. The finite element method: a Tool to Study Orthodontic Tooth Movement [J]. J Dent Res, 2005, 84(5): 428-433.
[28] 王慧媛, 张玉梅, 丁向东, 等. 下颌前牙金属烤瓷桥三维有限元模型的建立[J]. 牙体牙髓牙周病学杂志, 2006,16(1): 34-37.
[29] 李九军, 张静. 下颌牙列直丝弓矫治器三维有限元模型的建立[J]. 口腔医学, 2013, 33(10): 653-656.
[30] 张莹, 彭惠. 三维有限元法在正畸生物力学中的研究进展[J]. 齐齐哈尔医学院学报，2013, 343(2): 249-251.
[31] RODOLPH D J, WILLES P M, SAMESHINA G T. A finite element model of apical force distribution from orthodontic tooth movement [J]. Angle Orthod, 2001, 71(2): 127-131.
[32] 黄跃, 卫晓霞, 袁水平, 等.上颌尖牙及矫治器三维有限元模型的建立[J]. 泸州医学院学报, 2008, 31(4): 370-372.
[33] 左凯, 珂杰, 赵桂芝, 等. 滑动法关闭下颌第一磨牙拔牙间隙三维有限元模型的建立及验证[J]. 牙体牙髓牙周病学杂志，2013, 23(5): 319-322.
[34] CATTANEO P M, DALSTRA M, MELSEN B. Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyed by finite element [J]. Orthod Craniofac Res, 2009, 12(2): 120-128.
[35] 陈文静, 许文翠, 郑仕中. 牙周支持骨高度对垂直向力下牙周应力分布有限元分析[J]. 口腔正畸学, 2004, 11(4): 151. [36] 孙红丽, 杨建军, 徐国皓, 等. 三维有限元分析不同生物力作用的上颌第一前磨牙[J]. 中国组织工程研究, 2013, 17(24):4451-4456.
[37] LIN C L, CHANG S H, CHANG W J, et al. Factorial analusis of variables influencing mechanical characteristics of a single tooth implant placed in the maxilla using finite element analysis and the statistics-based Taguehi method[J]. Ear J Oral Sci, 2007,115(5): 408-416.
[38] 丁煕, 朱形好, 廖胜辉, 等. 牙种植体即刻负载骨界面应力分布的三维有限元分析[J]. 中国口腔种植学杂志, 2007, 12(2):60-64.
[39] MOTOYOSHI M, INABA M, UENO S, et al. Mechanical anisotropy of orthodontic mini-implants[J]. Int J Oral Maxillofac Surg,2009, 38(9): 972-977.
[40] 邵玶, 闫伟军, 宋冰, 等. 基于CT扫描图像的上颌牙列的三维重建及有限元模型建模研究[J]. 中国美容医学, 2012, 21(13): 1773-1775.
[41] 张晓娟, 郭宏铭, 白玉兴, 等. 舌侧矫治种植支抗关闭拔牙间隙阶段三维有限元模型的建立[J]. 北京口腔医学, 2014, 22(4):214-217.
[42] 赵刚, 魏佳佳, 张晓平, 等. 两种颌间牵引对下颌骨微种植体及周围影响的三维有限元分析[J]. 中国组织工程研究, 2013,(24): 4444-4450.
[43] 丁锐, 满云娜, 吴佩玲, 等. 传动直丝弓矫治器三维有限元模型的建立[J]. 中国组织工程研究, 2013, 17(33): 5942-5948.
[44] HUANG Y, KEILIG L, RAHIMI A, et al. Numeric modeling of torque capabilities of self-ligating and conventional brackets[J].Am J Orthod Dentofacial Orthop, 2009, 136(5): 638-643.
[45] 朱亚玲, 李闻颖, 张翼, 等. 上颌前牙舌侧差动力内收系三维有限元模型的建立[J]. 第三军医大学学报, 2014, 36(5): 466-469.
[46] 林铭, 符志峰, 陈涛, 等. Twin-block 矫治器系统三维有限元模型的建立[J]. 华南国防医学杂志, 2014, 28(1): 30-33.
[47] 刘畅, 朱宪春, 张星台, 等. 颌面骨三维有限元模型中骨缝实体模型的建立[J]. 华西医学杂志, 2011, 29(1): 75-78.
[48] GAUTAN P, VALIATHAN A, ADHIKARI R. Marillary protraction with and without maxillary expansion : a finite element
analysis of sutural stresses[J]. Am J Orthod Dentofaccial Orthop, 2009, 136(3): 361-366.
[49] GAUTAN P, VALIATHSN A, ADHIKARI R. Skeletal response to narillary protraction with and without maxillary
expansion: a finite element study[J]. Am J Orthod Dentofacial Orthop, 2009, 136(6): 728.
[50] LAPEER R J, GASSON P D, KARRI V. Simulating plastic surgery: From human skin tensile tests, through by perelastic finite element models to real-time haptics[J]. Praq Biophys Mol Biol, 2010, 103(2/3): 208-216.
[51] AMMAR H H, NGAN P, CROUT R J, et al. Three-dimensional modeling and finite element analysis in treatment platning for orthodomtic tooth movement [J]. Am J Orthod Dentofacial Orthop, 2011, 139(1): e59-e71.
[1] YU W, PARK H S, KYUNG H M, et al. Dynamic simulation of the self-tapping insertion process of orthodontics: a 3-dimensional finite element method[J]. Am J Orthod Dentofacial Orthop, 2012,142(6): 834-841.
[2] HUANG Y W, CHANG C H, WONG T Y, et al. Bone stress when miniplates are used for orthodontic anchorage: finite element analysis[J]. Am J Orthod Dentofacial Orthop, 2012,142(4): 466-472.
[3] GAINSFORT B L, HIGLEY L B. A study of orthodontic anchorage Possibilities in basal bone[J]. Am J Drthod Oral Surg, 1945,31(8): 406-416.
[4] 王翰章, 周学东. 中华口腔医学-基础总论卷[M]. 2 版. 北京: 人民卫生出版社, 2009: 727-735.
[5] 蒋孝煜. 有限元基础[M]. 2 版. 北京: 清华大学出版社, 1992: 11-13.
[6] HUISKES R, CHAO E Y. A survey of finite element analysis : northopedic biomechanics, the first decade [J]. Biomech, 1998,16(6): 385-391.
[7] COURANT R. Variational Method for Solutions of Problems of Equilibrium and Vibrations [J]. Bull AmMath Soc, 1943, 49(1): 1-23.
[8] TURNER M S, CLOUGH R W, MARTIN H C. Stiffness and deflection analysis complex structure [J]. J Aero Sic, 1956, 23: 805-809.
[9] CLOUGH R W. The Finite Element Method in Plane Stress Analysis [C]// Proceeding of the 2nd ASCE Conference on Electronic Computation. Pittsburg: [s.n.], 1960: 345.
[10] THRESHER R W. The stress analysis of human teeth [J]. J Biomech, 1973, 6(5): 443-449.
[11] FARAH J W. Photoelastic and finite element stress analysis of a restoted arisymmetric first molar [J]. J Biomech, 1973, 6(5): 551.
[12] 周书敏. 有限元法研究牙周韧带的应力分布[J]. 中华口腔医学杂志, 1989, 24(6): 334-337, 385.
[13] 魏洪涛, 张天夫, 曾晨光, 等. 牙颌三维有限元模型生成方法的探讨[J]. 白求恩医科大学学报, 2000, 26(2): 150-151.
[14] BHASKER P, MOHAMMED C, OMAR F. Effective elastic properties of nanocomposites using a novel atomistic-continuum interphase model [J]. Comptes Rendus Mecanique, 2012, 340(4-5): 296-306.
[15] MAGNE P, OGANESYAN J. CTscan-based finite element analysis of premolar cuspal deflection following operative procedures [J]. Int J Periodont Rest, 2009, 29(4): 361-369.
[16] TAJIMA K, CHEN K K, TAKAHASHI N. Three-dimensional finite element modeling from CT images of tooth and its validation [J]. Dent Mater J, 2009, 28(2): 219-226.
[17] 李志华, 陈天云, 刘剑, 等. 上颌第一磨牙的三维有限元模型建立[J]. 实用临床医学，2001, 2(1): 31-33.
[18] 彭佳美, 严斌, 王林, 等. 三维数字化牙颌模型在口腔正畸学中的应用[J]. 中国实用口腔科杂志，2008, 24(2): 236-239.
[19] 林川, 杜莉, 沈颉飞. 建立三种桩核系统修复下颌第一磨牙的三维有限元模型[J]. 实用口腔医学杂志，2008, 24(2): 236-239.
[20] 牟雁东, 樊瑜玻, 刘展. 不同基牙牙周状况下双侧游离缺损冠外附着体义齿的三维有限元分析[J]. 中华老年口腔医学杂志, 2009, 7(4): 241-252.
[21] OLSZEWSKI R, COSNARAL G, MACQ B, et al. 3DCT-based cephalometric analysis : 3D Cephalometric theoretical concept and software [J]. Neuroradiology, 2006, 48(1): 853-862.
[22] PARK S H, YU H S, KIM K D, et al. A proposal for a new analysis of craniofacial morphology by 3-dimensional computed tomography [J]. Am J Orthod dentofacial Orthop, 2006, 129(5): 657-660.
[23] LAGRAVERE M, MAJOR P W. Proposed reference point for 3-dimensianal cephalometric analysis with cone-bean computerized tomography [J]. Am J Orthod Dentofacial Orthod, 2005, 128(5): 657-660.
[24] 狄婧, 孙哲, 尹新芹, 等. 基于CBCT图像构建下颌第一前磨牙三维有限元模型[J]. 临床口腔医学杂志, 2013, 29(9): 530-533.
[25] ZHANG S, LIU X, XU Y, et al. Applicationg of rapid prototyopng for temporomandibular joint reconstruction [J]. J Oral Maxillofacsurg, 2011, 69(2): 432-438.
[26] 于力牛, 常伟, 王成焦, 等. 基于实体模型的牙颌组织三维有限元建模问题讨论[J]. 机械设计与研究, 2002, 18(2): 59-61.
[27] CATTANEO P M, DALSTRA M, MELSEM B. The finite element method: a Tool to Study Orthodontic Tooth Movement [J]. J Dent Res, 2005, 84(5): 428-433.
[28] 王慧媛, 张玉梅, 丁向东, 等. 下颌前牙金属烤瓷桥三维有限元模型的建立[J]. 牙体牙髓牙周病学杂志, 2006,16(1): 34-37.
[29] 李九军, 张静. 下颌牙列直丝弓矫治器三维有限元模型的建立[J]. 口腔医学, 2013, 33(10): 653-656.
[30] 张莹, 彭惠. 三维有限元法在正畸生物力学中的研究进展[J]. 齐齐哈尔医学院学报，2013, 343(2): 249-251.
[31] RODOLPH D J, WILLES P M, SAMESHINA G T. A finite element model of apical force distribution from orthodontic tooth movement [J]. Angle Orthod, 2001, 71(2): 127-131.
[32] 黄跃, 卫晓霞, 袁水平, 等.上颌尖牙及矫治器三维有限元模型的建立[J]. 泸州医学院学报, 2008, 31(4): 370-372.
[33] 左凯, 珂杰, 赵桂芝, 等. 滑动法关闭下颌第一磨牙拔牙间隙三维有限元模型的建立及验证[J]. 牙体牙髓牙周病学杂志，2013, 23(5): 319-322.
[34] CATTANEO P M, DALSTRA M, MELSEN B. Strains in periodontal ligament and alveolar bone associated with orthodontic tooth movement analyed by finite element [J]. Orthod Craniofac Res, 2009, 12(2): 120-128.
[35] 陈文静, 许文翠, 郑仕中. 牙周支持骨高度对垂直向力下牙周应力分布有限元分析[J]. 口腔正畸学, 2004, 11(4): 151. [36] 孙红丽, 杨建军, 徐国皓, 等. 三维有限元分析不同生物力作用的上颌第一前磨牙[J]. 中国组织工程研究, 2013, 17(24):4451-4456.
[37] LIN C L, CHANG S H, CHANG W J, et al. Factorial analusis of variables influencing mechanical characteristics of a single tooth implant placed in the maxilla using finite element analysis and the statistics-based Taguehi method[J]. Ear J Oral Sci, 2007,115(5): 408-416.
[38] 丁煕, 朱形好, 廖胜辉, 等. 牙种植体即刻负载骨界面应力分布的三维有限元分析[J]. 中国口腔种植学杂志, 2007, 12(2):60-64.
[39] MOTOYOSHI M, INABA M, UENO S, et al. Mechanical anisotropy of orthodontic mini-implants[J]. Int J Oral Maxillofac Surg,2009, 38(9): 972-977.
[40] 邵玶, 闫伟军, 宋冰, 等. 基于CT扫描图像的上颌牙列的三维重建及有限元模型建模研究[J]. 中国美容医学, 2012, 21(13): 1773-1775.
[41] 张晓娟, 郭宏铭, 白玉兴, 等. 舌侧矫治种植支抗关闭拔牙间隙阶段三维有限元模型的建立[J]. 北京口腔医学, 2014, 22(4):214-217.
[42] 赵刚, 魏佳佳, 张晓平, 等. 两种颌间牵引对下颌骨微种植体及周围影响的三维有限元分析[J]. 中国组织工程研究, 2013,(24): 4444-4450.
[43] 丁锐, 满云娜, 吴佩玲, 等. 传动直丝弓矫治器三维有限元模型的建立[J]. 中国组织工程研究, 2013, 17(33): 5942-5948.
[44] HUANG Y, KEILIG L, RAHIMI A, et al. Numeric modeling of torque capabilities of self-ligating and conventional brackets[J].Am J Orthod Dentofacial Orthop, 2009, 136(5): 638-643.
[45] 朱亚玲, 李闻颖, 张翼, 等. 上颌前牙舌侧差动力内收系三维有限元模型的建立[J]. 第三军医大学学报, 2014, 36(5): 466-469.
[46] 林铭, 符志峰, 陈涛, 等. Twin-block 矫治器系统三维有限元模型的建立[J]. 华南国防医学杂志, 2014, 28(1): 30-33.
[47] 刘畅, 朱宪春, 张星台, 等. 颌面骨三维有限元模型中骨缝实体模型的建立[J]. 华西医学杂志, 2011, 29(1): 75-78.
[48] GAUTAN P, VALIATHAN A, ADHIKARI R. Marillary protraction with and without maxillary expansion : a finite element
analysis of sutural stresses[J]. Am J Orthod Dentofaccial Orthop, 2009, 136(3): 361-366.
[49] GAUTAN P, VALIATHSN A, ADHIKARI R. Skeletal response to narillary protraction with and without maxillary
expansion: a finite element study[J]. Am J Orthod Dentofacial Orthop, 2009, 136(6): 728.
[50] LAPEER R J, GASSON P D, KARRI V. Simulating plastic surgery: From human skin tensile tests, through by perelastic finite element models to real-time haptics[J]. Praq Biophys Mol Biol, 2010, 103(2/3): 208-216.
[51] AMMAR H H, NGAN P, CROUT R J, et al. Three-dimensional modeling and finite element analysis in treatment platning for orthodomtic tooth movement [J]. Am J Orthod Dentofacial Orthop, 2011, 139(1): e59-e71.