下颌牙列精确三维有限元模型建模及正畸过程分析
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摘要
正畸牙齿移动是牙冠受力后牙周支持组织细胞反应的结果,牙周组织应力的大小和分布对牙齿的移动具有决定作用。通过对矫治力作用下牙齿及其支持组织的应力应变分析,对研究正畸牙齿的移动规律和更好地制定矫治方案有重要的指导意义。正畸牙及牙周的应力分析在国内外都有较多的研究报道,但是目前这一领域的研究多局限于单个牙齿,缺少对牙列整体的研究。
多曲方丝弓(MEAW)技术是临床上用来矫治开颌、反颌等牙齿畸形的有效方法,它主要利用方丝弓控制牙齿的三维位置,“L”形曲的水平和垂直部分可以对需矫治的牙齿分别调整,其弓丝长,形变率低,故力量柔和且持久。
本课题运用CT三维重建技术及有限元分析方法,针对牙颌组织的解剖学和生物力学特征,建立了下中切牙及下颌牙列三维有限元模型,分别对下中切牙及下颌牙列施加不同载荷,对下颌牙列是模拟多曲方丝弓形变后对牙齿产生的反作用力等效加载到牙列上,分析比较各种矫治力作用下牙齿的位移和在牙齿及牙周组织上产生的应力,为临床上应用和发展MEAW技术治疗深覆颌做准备。
力学分析结果表明:(1)在各种矫治力作用下牙齿受到的应力值最大,牙槽骨次之,牙周膜最小;牙周膜有明显的缓冲作用且三个主应力值变化趋势一致。(2)下中切牙在垂直压入力作用下牙齿整体表现为向下移动,但在舌向出现较小位移,牙体垂直移动的同时伴有倾斜移动,说明在临床应用中要达到理想的沿牙长轴的压低移动是非常困难的。(3) 2N舌向水平力加载于牙冠不同部位,牙齿均表现出倾斜移动,要想实现牙齿的整体移动,需同时施加一个力及一个力矩。(4)下颌使用MEAW弓时,长Ⅲ类牵引在远中竖直后牙方面效果比较好,可实现压低前牙,抬高后牙,打开咬合的治疗目的。
During the Orthodontics treatment, when the force loaded on the tooth is applied to the malposed tooth, the periodontal tissues are remold and the alveolar bone moves, finally tooth moves to a new place. The stress distribution in periodontal tissue plays a very important role in determining tooth movement. Therefore, it is useful and important for making treat scheme accurately to know about the pattern of stress and strain distribution of periodontal tissues by finite element method combined with the mechanical behavior of appliance. There are many reports on periodontal tissue stress analysis, but at present stress analysis is confined to single tooth other than dentition.
Multiloop Edgewise Arch Wire (MEAW) technique, which was the valid method in the treatment of openbite and crossbite. The main characters of MEAW were: Controlling the tooth positions in three dimension (3D); The level and vertical parts of“L”can adjust the tooth respectively. Its arch wire is long, the changes of the rate is low, the power is soft and last long.
In this paper, using CT rebuilding technique , finite element method , a series geometric and finite element models of the submaxilla dentition were developed at unify coordinate including periodontal ligament and alveolar bone, for simulating the anatomy and biomechanical characters of dentognathic tissue. Then loading was loaded on the tooth and the submaxilla dentition, simulating reacting force of the MEAW loaded in brackets was loaded to dentition. By the finite element analysis, the laws of stress on the teeth and displacement of the teeth and their periodontal tissues were shown. It will help to direct the clinical uses and modify MEAW in overbite in future.
Conclusion: (1) The highest stresses were observed in the tooth surface, the lowest in the periodontal ligament, the alveolar bone between them. The periodontal ligament plays an important role in the transmission and cushion of forces acting on teeth, and its three kinds of principal stress are consistent. (2) Under vertical loading, the movement trend of tooth is downwards, appearing the smaller displacement at the direction of tongue .The clinical application ideal producing the movement along with the tooth major axis is very difficult. (3) The 2N tongue toward force add to the different part of the tooth , the tooth all expresses an inclination move. To obtain the whole movement of the tooth, a force and a moment are needed at the same time. (4) Using MEAW bow, the long elastics at MEAW the result is better, can carry out pressing the front tooth , the treatment purpose that open to bite is coming true .
多曲方丝弓(MEAW)技术是临床上用来矫治开颌、反颌等牙齿畸形的有效方法,它主要利用方丝弓控制牙齿的三维位置,“L”形曲的水平和垂直部分可以对需矫治的牙齿分别调整,其弓丝长,形变率低,故力量柔和且持久。
本课题运用CT三维重建技术及有限元分析方法,针对牙颌组织的解剖学和生物力学特征,建立了下中切牙及下颌牙列三维有限元模型,分别对下中切牙及下颌牙列施加不同载荷,对下颌牙列是模拟多曲方丝弓形变后对牙齿产生的反作用力等效加载到牙列上,分析比较各种矫治力作用下牙齿的位移和在牙齿及牙周组织上产生的应力,为临床上应用和发展MEAW技术治疗深覆颌做准备。
力学分析结果表明:(1)在各种矫治力作用下牙齿受到的应力值最大,牙槽骨次之,牙周膜最小;牙周膜有明显的缓冲作用且三个主应力值变化趋势一致。(2)下中切牙在垂直压入力作用下牙齿整体表现为向下移动,但在舌向出现较小位移,牙体垂直移动的同时伴有倾斜移动,说明在临床应用中要达到理想的沿牙长轴的压低移动是非常困难的。(3) 2N舌向水平力加载于牙冠不同部位,牙齿均表现出倾斜移动,要想实现牙齿的整体移动,需同时施加一个力及一个力矩。(4)下颌使用MEAW弓时,长Ⅲ类牵引在远中竖直后牙方面效果比较好,可实现压低前牙,抬高后牙,打开咬合的治疗目的。
During the Orthodontics treatment, when the force loaded on the tooth is applied to the malposed tooth, the periodontal tissues are remold and the alveolar bone moves, finally tooth moves to a new place. The stress distribution in periodontal tissue plays a very important role in determining tooth movement. Therefore, it is useful and important for making treat scheme accurately to know about the pattern of stress and strain distribution of periodontal tissues by finite element method combined with the mechanical behavior of appliance. There are many reports on periodontal tissue stress analysis, but at present stress analysis is confined to single tooth other than dentition.
Multiloop Edgewise Arch Wire (MEAW) technique, which was the valid method in the treatment of openbite and crossbite. The main characters of MEAW were: Controlling the tooth positions in three dimension (3D); The level and vertical parts of“L”can adjust the tooth respectively. Its arch wire is long, the changes of the rate is low, the power is soft and last long.
In this paper, using CT rebuilding technique , finite element method , a series geometric and finite element models of the submaxilla dentition were developed at unify coordinate including periodontal ligament and alveolar bone, for simulating the anatomy and biomechanical characters of dentognathic tissue. Then loading was loaded on the tooth and the submaxilla dentition, simulating reacting force of the MEAW loaded in brackets was loaded to dentition. By the finite element analysis, the laws of stress on the teeth and displacement of the teeth and their periodontal tissues were shown. It will help to direct the clinical uses and modify MEAW in overbite in future.
Conclusion: (1) The highest stresses were observed in the tooth surface, the lowest in the periodontal ligament, the alveolar bone between them. The periodontal ligament plays an important role in the transmission and cushion of forces acting on teeth, and its three kinds of principal stress are consistent. (2) Under vertical loading, the movement trend of tooth is downwards, appearing the smaller displacement at the direction of tongue .The clinical application ideal producing the movement along with the tooth major axis is very difficult. (3) The 2N tongue toward force add to the different part of the tooth , the tooth all expresses an inclination move. To obtain the whole movement of the tooth, a force and a moment are needed at the same time. (4) Using MEAW bow, the long elastics at MEAW the result is better, can carry out pressing the front tooth , the treatment purpose that open to bite is coming true .
引文
1 Russell LB ,Jones O ,Russell D . A survey of functional etiologics that produce dental open bite . Am J Orthod Dentofacial Orthop , 1993,103:9
2 Arat M , Iseri H . Orthodontic and Orthopedic approach in the treatment of skeletal open bite . Eur J Orthod , 1992,14:207~215
3 Kim YH, Treatment of malocclusions by means of multi-loop edgewise arch-wire (MEAW) technic . J Assoc Orthodontic Repubic China. 1995, 7:62~72
4 Kim YH . Anterior open bite and its treatment with multi-loop edgewise arch-wire [J] . Angle Orthod ,1987 ,57(4): 290~321
5张美超,钟世镇等.国内生物力学中有限元的应用研究进展.解剖科学进展. 2003, 9(1): 53~56
6 Farah JW, et al. Photoelastic and finite element stress analysis of a restored axisymmatic first molar. J Biomech. 1973, 6:511
7 Rubin C, Krishnamurhty N. Caiolouto G etal. Stress analysis of human tooth finite element mothod. J Dent Res, 1983, 62:8
8 Takahashi N, Kitagami T. Behavior of teeth under loading conditions with finite element method [J]. J Oral Rehab. 1980, 7:453
9周书敏,吴仲谋.应用有限单元法对下颌磨牙不同高度的牙周支持组织的应力分析.北京医学院学报. 1984, 16(4): 293
10周书敏.正常及异常牙周膜在不同载荷作用下应力分布的研究.北京医科大学学报. 1988, 20:31
11赵云凤主编.口腔生物力学北京北京医科大学.中国协和医科大学联合出版社, 1996, 7
12赵志河,房兵,赵美英.颅面骨三维有限元模型的建立.华西口腔医学杂志. 1994, 12(4): 261
13赵志河,房兵.尖牙牙周膜应力分布的研究.华西口腔医学杂志. 1994, 12(4): 301
14李俊,李清,范崇德.正畸力作用下颌磨牙的三维有限元研究.临床口腔医学杂志. 1998, 14(1): 18
15 Tanne K, Sakuda M. Initial stress induced in the periodontal tissue at the time of the application of carious types of orthodontic force 3D analysis of means offinite element method. J Osaka Univ Bull. 1983, 23:143
16洪瑾,夏文薇,朱亚勤等.有限元法建立下颌第一磨牙模型及受力分析.上海口腔医学. 2001, 10(4): 342~345
17 Williams KR, Edmundson JT. Orthodontic movement analysed by the tinite element method. Biomat, 1984, 5:347
18 Tanne K, Sakuda M. Burstone CJ .Three-dimensional finite element analysis for stress on the periodontal tissue by orthodontic forces. Am J Orthod Dentofac Orthop. 1987, 92:499~505
19卢海平,傅民魁,黄吉锋等.矫治力作用下牙周支持组织应力分布的三维有限元分析.中华口腔医学杂志. 1994, 29(6): 332彭友俭,程祥荣,胡志远.三维有限元法分析上颌支抗磨牙及其支持组织的生物力学.口腔医学纵横杂志. 1999, 15(4): 232
20吴丽萍,李洪,刘磊等.上颌尖牙远中移动的矫治力分析[J].中华口腔医学杂志. 1995, 30(6):362
21张端强,钟萍萍,石勰等.尖牙远中移动的有限元研究.福建医科大学学报. 1999, 33(3): 299
22 Peter D, Priaick K, Hong B, etal. Analysis of stress in the periondontium of the maxillary first molar a three-dimensional finite element mode [J]. Am J Orthod, 1999, 115:267~274
23陈国新,钱法汤.转矩力作用下上颌切牙及其支持组织的三维有限元分析[J].口腔医学纵横杂志. 2005, 16(1): 50~51
24周书敏.应用有限元单元法对下颌磨牙不同高度的牙周支持组织应力分析.北京医学院学报. 1984, 16 (4):293
25朱希涛等.用有限元素法分析牙槽骨吸收根长1/3得第一磨牙单独受力及作为基牙受力时的应力分布.中国生物医学工程学第三次学术会议论文汇编(摘要). 1987, 220
26 Juan cobo. Argrelles J. Puentem. Vijarde M Dentoalveolar stress from bodily tooth movement at different levels of bone loss. Am J Orthod Dentfac Orthp, 1996, 110:256~262
27陈剑虹.一种基于断层测量的快速反求系统关键技术研究[D].西安交通大学, 2005
28 Olthoff LW, Van Der Zel JM, De Ruiter WJ, etal. Computer modeling of occlusalsurfaces of posterior teeth with the CICERO CAD/CAM system. JProthet Dent 2000, 84:154~162
29李斌,马轩祥等.模型转化法构建牙齿的三维有限元模型.实用口腔医学杂志. 2005, 19(2): 151~153
30于力牛,尚鹏等.适用于口腔修复学的模块化牙列有限元建模.上海交通大学学报. 2002, 36(8):1071~1074
31 Chun-Li Lin, Huey-Er Lee. Integration of CT, CAD system and finite element method to investigate interfacial stresses of resin-bonded prosthesis. Computer Methods and Programs in Biomedicine. 2003; 72: 55~64
32 Proceedings of the 7th Symposium on the Frontiers of Massively Parallel Computation, IEEE Computer Society Press, 1999, 126
33 D W Shattuck,J Rapela etc,Internet2-based 3D PET Image Reconstruction Using a PC Cluster[J], Phys Med Biol, 2002,47:2785
34毛希平,图像重建技术在并行处理系统中的应用[J],小型微型计算机系统, 2000,21(3):289
35张如一,陆耀桢.实验应力分析.机械工业出版社, 1980:1~2
36潘少川.实验应力分析.北京:高等教育出版社,2005
37张宏伟,赵小松,张国雄等.三维曲面重构技术.天津大学学报. 2005, 35 (2): 183~186
38 Tanne K, Saknda M, Burstone CJ. Three-dimensional finite element analysis for stress on the periodontal tissue by orthodontic forces.Am J Orthod Dentofac Orthop,1987,92 :499 ~505
39卢海平,傅民魁,孙树立等.上颌“T”型曲内收弓丝矫治上颌前牙的三维有限元分析.中华口腔医学杂志,1997,32 :19~22
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57王冬梅.多曲方丝弓矫治技术及面中部牵张成骨术的三维有限元研究.上海交通大学博士后学位论文. 2006, 12
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2 Arat M , Iseri H . Orthodontic and Orthopedic approach in the treatment of skeletal open bite . Eur J Orthod , 1992,14:207~215
3 Kim YH, Treatment of malocclusions by means of multi-loop edgewise arch-wire (MEAW) technic . J Assoc Orthodontic Repubic China. 1995, 7:62~72
4 Kim YH . Anterior open bite and its treatment with multi-loop edgewise arch-wire [J] . Angle Orthod ,1987 ,57(4): 290~321
5张美超,钟世镇等.国内生物力学中有限元的应用研究进展.解剖科学进展. 2003, 9(1): 53~56
6 Farah JW, et al. Photoelastic and finite element stress analysis of a restored axisymmatic first molar. J Biomech. 1973, 6:511
7 Rubin C, Krishnamurhty N. Caiolouto G etal. Stress analysis of human tooth finite element mothod. J Dent Res, 1983, 62:8
8 Takahashi N, Kitagami T. Behavior of teeth under loading conditions with finite element method [J]. J Oral Rehab. 1980, 7:453
9周书敏,吴仲谋.应用有限单元法对下颌磨牙不同高度的牙周支持组织的应力分析.北京医学院学报. 1984, 16(4): 293
10周书敏.正常及异常牙周膜在不同载荷作用下应力分布的研究.北京医科大学学报. 1988, 20:31
11赵云凤主编.口腔生物力学北京北京医科大学.中国协和医科大学联合出版社, 1996, 7
12赵志河,房兵,赵美英.颅面骨三维有限元模型的建立.华西口腔医学杂志. 1994, 12(4): 261
13赵志河,房兵.尖牙牙周膜应力分布的研究.华西口腔医学杂志. 1994, 12(4): 301
14李俊,李清,范崇德.正畸力作用下颌磨牙的三维有限元研究.临床口腔医学杂志. 1998, 14(1): 18
15 Tanne K, Sakuda M. Initial stress induced in the periodontal tissue at the time of the application of carious types of orthodontic force 3D analysis of means offinite element method. J Osaka Univ Bull. 1983, 23:143
16洪瑾,夏文薇,朱亚勤等.有限元法建立下颌第一磨牙模型及受力分析.上海口腔医学. 2001, 10(4): 342~345
17 Williams KR, Edmundson JT. Orthodontic movement analysed by the tinite element method. Biomat, 1984, 5:347
18 Tanne K, Sakuda M. Burstone CJ .Three-dimensional finite element analysis for stress on the periodontal tissue by orthodontic forces. Am J Orthod Dentofac Orthop. 1987, 92:499~505
19卢海平,傅民魁,黄吉锋等.矫治力作用下牙周支持组织应力分布的三维有限元分析.中华口腔医学杂志. 1994, 29(6): 332彭友俭,程祥荣,胡志远.三维有限元法分析上颌支抗磨牙及其支持组织的生物力学.口腔医学纵横杂志. 1999, 15(4): 232
20吴丽萍,李洪,刘磊等.上颌尖牙远中移动的矫治力分析[J].中华口腔医学杂志. 1995, 30(6):362
21张端强,钟萍萍,石勰等.尖牙远中移动的有限元研究.福建医科大学学报. 1999, 33(3): 299
22 Peter D, Priaick K, Hong B, etal. Analysis of stress in the periondontium of the maxillary first molar a three-dimensional finite element mode [J]. Am J Orthod, 1999, 115:267~274
23陈国新,钱法汤.转矩力作用下上颌切牙及其支持组织的三维有限元分析[J].口腔医学纵横杂志. 2005, 16(1): 50~51
24周书敏.应用有限元单元法对下颌磨牙不同高度的牙周支持组织应力分析.北京医学院学报. 1984, 16 (4):293
25朱希涛等.用有限元素法分析牙槽骨吸收根长1/3得第一磨牙单独受力及作为基牙受力时的应力分布.中国生物医学工程学第三次学术会议论文汇编(摘要). 1987, 220
26 Juan cobo. Argrelles J. Puentem. Vijarde M Dentoalveolar stress from bodily tooth movement at different levels of bone loss. Am J Orthod Dentfac Orthp, 1996, 110:256~262
27陈剑虹.一种基于断层测量的快速反求系统关键技术研究[D].西安交通大学, 2005
28 Olthoff LW, Van Der Zel JM, De Ruiter WJ, etal. Computer modeling of occlusalsurfaces of posterior teeth with the CICERO CAD/CAM system. JProthet Dent 2000, 84:154~162
29李斌,马轩祥等.模型转化法构建牙齿的三维有限元模型.实用口腔医学杂志. 2005, 19(2): 151~153
30于力牛,尚鹏等.适用于口腔修复学的模块化牙列有限元建模.上海交通大学学报. 2002, 36(8):1071~1074
31 Chun-Li Lin, Huey-Er Lee. Integration of CT, CAD system and finite element method to investigate interfacial stresses of resin-bonded prosthesis. Computer Methods and Programs in Biomedicine. 2003; 72: 55~64
32 Proceedings of the 7th Symposium on the Frontiers of Massively Parallel Computation, IEEE Computer Society Press, 1999, 126
33 D W Shattuck,J Rapela etc,Internet2-based 3D PET Image Reconstruction Using a PC Cluster[J], Phys Med Biol, 2002,47:2785
34毛希平,图像重建技术在并行处理系统中的应用[J],小型微型计算机系统, 2000,21(3):289
35张如一,陆耀桢.实验应力分析.机械工业出版社, 1980:1~2
36潘少川.实验应力分析.北京:高等教育出版社,2005
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