摘要
研究背景
在冠部牙体组织缺损较多的情况下，桩核技术是一种必不可少的修复手段。传统的观点认为采用桩核修复是基于两方面的原因：一方面是固位作用，可以在桩的基础上完成桩-核-冠的一体化修复；另一方面根管桩可使应力较均匀地分散，防止了无髓牙根的折裂。桩核冠修复的成功受多种因素的影响，包括剩余牙体组织的数量、桩与核的材料、桩的长度、粘接剂的种类、咬(牙合)力的大小和方向等。为了使修复体能够充分的发挥功能，用于制作桩核的材料应具有适当的弹性模量、挠曲强度以及良好的抗腐蚀、抗疲劳性能，此外还要对牙体组织起保护作用。早期使用的金属桩系统具有很多缺点：容易导致根折的发生，易腐蚀，美学性能差等。随着美学修复材料的发展，具有良好生物相容性、抗腐蚀及优良机械物理性能的非金属材料进入了牙科领域，纤维强化树脂桩系统应运而生。现在人们对桩的作用有了进一步的认识，即桩并不具有增强牙根的作用，临床工作者的关注焦点已发生变化，如何使应力更均匀的分布，防止根折的发生，达到最佳的远期修复效果已成为目前最关注的问题。为此，有必要对纤维桩对牙根的力学影响进行研究。
研究目的
本研究利用三维有限元分析法，建立上颌中切牙桩冠修复的三维有限元模型，分析不同材料、直径和深度的桩对桩冠修复体牙根组织应力分布的影响，借以为临床工作提供一些有价值的信息。
材料与方法
第一部分：
1、建模原始数据的获得：选择一颗牙体完好、形态正常的上颌中切牙，尺寸在王惠芸所报道的中国人上颌中切牙的标准值范围内。将该离体牙固定后，采用GE MEDICAL SYSTEMS(Light speed 16排CT)三维螺旋CT从牙根到牙冠进行断层扫描，断面与牙长轴垂直，层间距为0.625mm，共生成39张断面图，按顺序记录并进行数字化图像保存。
2、三维有限元模型的建立：将39张CT图像导入AUTO CAD软件。利用AUTO CAD绘图工具栏的样条曲线工具勾勒出牙断面层的内外轮廓线，即生成由点组成的横断面的封闭曲线。将生成的空间曲线导入ANSYS。利用实体建模功能将导入的各个截面曲线光滑地连结起来，即可建立上颌中切牙的实体模型。再分别建立烤瓷外冠、Ni-Cr合金底层冠、石英纤维桩、复合树脂核、牙周膜、牙胶尖和牙槽骨的模型。
3、实验假设和材料的力学参数、加载条件：实验模型中各种材料假设为连续均质的各向同性材料，材料受力变形为小变形。边界条件类型为全约束，牙槽骨固定。加载方式为静态加载。模拟临床上颌中切牙咬牙合受力情况，加载点位于牙冠舌面中1／3与切1／3交界处，大小为100牛顿(N)，与牙长轴成45°角。
第二部分：
1、采用实验(一)建立的上颌中切牙桩核修复三维有限元模型。分别建立六种桩：铸造Ni-Cr合金桩、铸造钛合金桩、铸造金合金桩、玻璃纤维树脂桩、聚乙烯纤维树脂桩、石英纤维桩修复的上颌中切牙桩冠修复三维有限元模型。
2、定义材料和边界条件同实验(一)。
3、载荷条件同实验(一)。
4、观察指标根颈1／3、根中1／3、根尖1／3牙本质横断面的Von Mises应力和最大主应力，同时观察桩／牙本质界面的应力分布。
第三部分：
1、采用实验(一)建立的上颌中切牙桩核修复三维有限元模型。参照D.T.LIGHT POST半透明双锥度石英纤维桩的外形参数，建立三种不同直径(1.5mm、1.8mm、2.2mm)的石英纤维桩，分别将每种直径的桩放置距根尖3mm、4mm、5mm三种深度。共生成九个石英纤维桩冠修复的三维有限元模型。
2、定义材料和边界条件同实验(一)。
3、载荷条件同实验(一)。
4、观察指标牙本质横断面和桩／牙本质界面的Von Mises应力。
结果
1、建立了上颌中切牙桩冠修复的三维有限元模型。建成后共生成53897个节点，形成42768个20节点的等参四面体单元。
2、六种材料的桩应力分布模式没有明显差别，牙根Von Mises应力均位于根颈1／3唇侧牙根表面，最大主应力峰值位于根颈1／3舌侧牙根表面。Von Mises应力和最大主应力从根颈1／3向根尖1／3均逐渐变小。
3、六种不同材料桩修复后牙根应力：石英纤维桩＞聚乙烯纤维树脂桩＞玻璃纤维树脂桩＞铸造金合金桩＞铸造钛合金桩＞铸造Ni-Cr合金桩，但应力值相差很小。
4、六种不同桩修复后桩／牙本质界面的应力：铸造Ni-Cr合金桩＞铸造钛合金桩＞铸造金合金桩＞玻璃纤维树脂桩＞聚乙烯纤维树脂桩＞石英纤维桩，应力值相差较大。
5、不同直径石英纤维桩牙根应力比较：桩／牙本质界面Von Mises应力：直径1.5mm＜直径1.8mm＜直径2.2mm
6、不同深度石英纤维桩牙根应力比较：桩／牙本质界面Von Mises应力：距根尖3mm＜距根尖4mm＜距根尖5mm
结论
1、将CT扫描技术与有限元方法有机结合起来，应用于建立上颌中切牙桩核修复的三维有限元模型是现实可行的，建立起的模型具有良好的几何相似性。
2、高弹性模量的材料修复后改变牙本质应力分布的情况，易产生桩／牙本质界面的应力集中，从而使牙根易与折裂。
3、弹性模量较低的纤维桩有利于应力更均匀的分布，不会产生桩／牙本质应力集中，有利于保护牙根。
4、在一定范围内，纤维桩直径越小，产生的应力越小。临床上应选用相对细小的桩进行修复。
5、在一定范围内，纤维桩放置越深，产生的应力越小。临床上可以适当的加大放置深度以减小应力。
Background
It is an essential restorative measure to restore the endodontically treated teeth andseverely defective tooth structure with internal post and core technique. There are twoconventional viewpoints: one is that posts have the retention function and support theupper restoration, the other is that posts spread the stress along the root wall, avoidingroot fractures. Successful repair of post-retain crown is affected by several factors,including residual tooth tissues, materials of post and core, the length of post, types ofcementing agents, occlusion force and direction, etc. In order to satisfy the function ofrestoration, the materials used for making post and core should have proper modulusof elasticity and flexure strength, favorable anti-corrosion and anti-fatigue capabilities,moreover, these materials must have the function to protect tooth tissues. Howeverthe early used metal post system possesses many disadvantages, such as easy to breakthe root and corrode, poor aesthetics. Along with the development of aestheticrepaired materials, non-metal materials possessing good biological compatibility, anticorrosion and excellent physical and mechanical properties have entered the dental field, thus fiber-reinforced post system comes into being. Now people have furtherunderstanding on the function of post, that is post have no function to strengthen root,what clinical workers pay attention to has changed and how to make more evendistribution of stress, how to protect roots and how to get the best repaired effect havealready become the current most attracted problem. For this purpose, it is necessary tomake a study on stress distribution of fiber post on root.
Objectives
Through three-dimensional-finite-element analysis, this article studies andestablishes three-dimensional-finite-element models of maxillary incisor teeth of postand crown repairs, analyzes the influence of post of different materials, diameters anddepths on distribution of stress of repaired root so as to provide some valuableinformation for clinical work.
Materials and Methods
PartⅠ
1. Obtainment of Primitive Data for Modeling: Choose a complete good conditionmaxillary central incisor with the size as Chinese standards reported by WangHuiyun. After fixing the tooth, scan tooth from root to dental crown using the GEMEDICAL SYSTEMS (Light speed 16 rows CT), make the section vertical tolong axis with layer distance of 0.625 mm, totally produce 39 sectional sectionpictures and save them in a numerical order.
2. Establishment of Three-dimensional-finite-element Models: Switch the 39 CTpictures into JEP format documents, introduce AUTO CADsoftware, use graphictools to draw out internal and external contour lines of tooth section, that is toproduce closed curve lines of the cross section, put the space curve lines into ANSYS, use solid modeling function to connect the introduced curve lines ofsection to rebuild the solid model of maxillary central incisor. At the same timebuild porcelain outer crown, Ni-Cr alloy base layer crown, quartz fiber-reinforcedpost, compound resin core, periodontal ligament, gutta-percha points and alveolarbone.
3. Hypothesis of Experiment, Parameters of Material Mechanics and Conditions ofloading: Various materials for experiments are supposed as continuing and evenmaterials with isotropic property, and the bearing force, deformation of materialsis small. The type of border condition is set total control and alveolar bone isfixed. As concerning clinical simulated binding condition, loading type is staticloading at the point between 1/3 of crown and tongue and 1/3 of incisor toothbeing 100N and forming an angle of 45 degrees with the long axis.
PartⅡ
1. Utilization of Experiment and Established Post and Core Repaired ThreeDimensional Finite Models. Establish six kinds of post repaired three dimensionalfinite models respectively: Ni-Cr alloy post, titanium alloy post, gold alloy post,glass fiber-reinforced post, polyethylene fiber-reinforced post and quartzfiber-reinforced post.
2. Defined Materials and Border Conditions: The Same with partⅠ
3. Conditions of Loading: The Same with partⅠ
4. Observation of Indexes: Observe Von Mises stress and the 1 st Principal Stress ofcervix 1/3 of root, middle 1/3 of root, cusp 1/3 of root, at the same time observethe distribution of stress of post and root section.
PartⅢ
1. Utilization of Experiment and Established Post and core Repaired ThreeDimensional Finite Models: Establish 3 quartz fiber-reinforced posts withdifferent diameters (1.5mm、1.8mm、2.2mm),and place them at 3 differentdepth: 3mm、4mm、5mm from root cusp. Totally establish ninethree-dimensional-finite-element models repaired with post and core.
2. Defined Materials and Border Conditions: The Same with partⅠ
3. Conditions of Loading: The Same with partⅠ
4. Observation of Indexes: Observe the Von Mises stress of the root of tooth and thesection of post and root.
Results
1. Establishment of the three dimensional finite models of maxillary central incisor.Upon establishment, 53897 nodes and dots were produced and formed 42768tetrahedrons each of which has 20 nodes.
2. There are no obvious differences of stress distribution of post in the 6 types ofmaterials. The pea.k value ofVon Mises stress is located at the labial surface of thedental cervix. The peak value of 1st Principal Stress is located at the lingualsurface of the dental cervix. The stress of Von Mises and the 1st Principal Stressreduce from the place of 1/3 of dental cervix to the place of 1/3 of root cusp.
3. Six materials were used to repair the stress of root: quartz fiber-reinforced post＞polyethylene fiber-reinforced post＞glass fiber-reinforced post t＞cast gold alloypost＞cast titanium alloy post＞cast Ni-Cr alloy post. But the different is small.
4. Six types of stresses of repaired post/dentin section: cast Ni-Cr alloy post＞casttitanium alloy post＞cast gold alloy post＞glass-reinforced fiber post＞polyethylene fiber-reinforced resin post＞quartz fiber-reinforced post. Thedifferent is large.
5. Comparison of different diameters: post/dentin section Von Mises stresses:diameter 1.5＜diameter 1.8＜diameter2.2
6. Comparison of different depth: post/dentin section Von Mises stresses: 3 mm fromroot cusp＜4 mm from root cusp＜5mm from root cusp
Conclusion
1. It is possible to combine CT scanning technology with the method of finitemethod and apply it to the repair model of Establishment maxillary central incisorof three-dimensional-finite-element models has fine similarity.
2. Use high modulus of elasticity materials to repair teeth can change the situation ofdistribution of tooth essential stress and can easily concentrate on the stress ofpost/dental section, thus making root easy to be broken.
3. Lower modulus of elasticity post benefits even distribution of stress andprotection of root.
4. In certain extent, the smaller diameter of fiber post, the smaller stress is. Smallpost should be selected for clinical use.
5. In certain extent, the post was put deeper, the smaller stress is.
引文
[1] Fauchard P. The surgeon dentist or treatise on the teeth,Vol 2.Translated from the 2nd ed. 1746 by Londsay L ,London: Butterworth and Company Ltd; 1946
[2] Bergman B, Lundquist P, Sjogren U, et al. Restorative and endodontic results after treatment with cast posts and cores[J].J Prosthet Dent,1989,61:10-5
[3] Assif D, Bitenski S, Pilo R, et al. Effect of post design on resistance of endodontically treated teeth with complete crowns [J].J Prosthet Dent, 1993,69:36-40
[4] Bex RT, Parker MW. Effects of dentinal bonded resin post-core preparations on resistance to vertical root fracture [J]. J Prosthet Dent, 1992, 67:769
[5] 张玉幸，陆支越，王科力．CELAY全瓷桩核强度的研究[J]．华西口腔医学杂志，2002，20(1)：39-44
[6] Raigrodski AJ, Chiche GJ. The safety and efficacy of anterior ceramic fixed partial dentures: A review of the literature [J]. J Prosthet Dent, 2002, 86(5):520-525
[7] 铁征骑主编．新型陶瓷材料手册[M]．江苏：江苏科学技术出版社，1996：P447-448
[8] Piconi C, Maccanco G. Zirconia as a ceramic biomaterial [J]. Biomaterials,1999,20(1):21-25
[9] 刘亦洪．全瓷桩核与镍铬合金桩核在前牙修复中的受力比较[J]．现代口腔医学杂志，2004，18(6)：546-548
[10] Ichikawa Y, Akagawa Y, Nikai H,et al.Tissue coMPatibility and stability of a new zirconia in vivo[J]. J Prosthet Dent, 1992, 68(2):322-326
[11] Butz F, Lennon AM, Heydeeke G et al. Survival rate and fracture strength of endodontically treated maxillary incisors with moderate defects restored with different post-and-core systems:an in vitro study[J].Int J Prosthodont, 2001,14(1):58-64
[12] Wegner SM, Kem M. Long-term resin bond strength to zirconia ceramic[J].J Adhes Dent,2000,2(2); 139-147
[13] Edelhoff D, Sorensen JA. Retention of selected core materials to zirconia posts [J].Oper Dent, 2002, 27(5):455-461
[14] Fredriksson M, Astback J, Pamenius M, et al. A retrospective study of 236 patients with teeth restored by carbon fiber-reinforced epoxy resin posts[J].J Prosthet Dent, 1998,80; 151-157
[15] Isidor F, Odman P, Brondum K. Intermittent loading of teeth restored using prefabricated carbon fiber posts. Int J Prosthodont, 1996, 9(2), 131-136
[16] Asmussen E, Peutzfeldt A, Heitmann T. Stiffness, elastic limit, and strength of newer types of endodontic posts. J Dent, 1999, 27:275-278
[17] Ottl P,Hahn L,Lauer H.Fracture characteristics of carbon fiber, ceramic and non-palladium endodontic post systems at monotonously increasing loads [J].J Oral Rehabil,2002,29(2): 175-183
[18] Fredriksson M,Astback J,Pamenius M,et al.A retrospective study of 236 patients with teeth restored by carbon fiber-reinforced epoxy resin post[J].J Prosthet Dent, 1998,80:151-155
[19] Akkayan.Resistance to fracture of endodontically treated teeth restored with different post systems [J]J Prosthet Dent, 2002, 87(4)431-437
[20] Mannocci F, Qualtrough AJ, Worthington HV, Watson TF, Pitt Ford TR. Randomized clinical comparison of endodontically treated teeth restored with amalgam or with fiber posts and resin composite: five-year results. Oper Dent. 2005, 30(1):9-15
[21] Ferrari M,Vichi A,Maanocci F, et al.Am J Dent,2000,13:9B-13B
[22] 曹颖，孙少宣．纤维桩树脂核修复前牙牙体缺损的美学评价．中国美容医 学，2006，15(5)：574-575
[23] Sirrimai S,Riis DN,Morgano SM.An in vivo study of the fracture resistance and the incidence ofvertical root fracture of pulpless teeth restored with six post-and-coresystems[J]. J Prosthet Dent, 1999,8(3):262-269
[24] 张胜民．基于有限元软件ANSYS7.0的结构分析M．北京：清华大学出版社，2003
[25] 叶先磊，史亚杰．ANSYS工程分析软件应用实例M．北京：清华大学出版社，2003．
[26] 皮昕．口腔解剖生理学．第5版．北京：人民卫生出版社，2003，40
[27] 吴红霞，吴友农，陈培生。纤维桩外形和深度对牙根应力分布影响的三维有限元分析[J]．牙体牙髓牙周病学杂志2004，20(4)：382-385
[28] Pierrisnard L, Bohin F, Renault P, et al. Corono-radicular reconstruction of pulpless teeth: a mechanical study using finite element analysis [J]. J Prosthet Dent, 2002; 88(4):442-448.
[29] Eskitascioglu G, Belli S, Kalkan M. Evaluation of two post core systems using two different methods (fracture strength test and a finite elemental stress analysis). J Endod. 2002, 28(9):629-633
[30] Chang KH, Magdum S, Khera SC. An advanced approach for computer modeling and prototyping of the human tooth J. Ann Biomed Eng, 2003; 31(5):621-631
[31] 贾安琦，骆小平，徐君伍．不同载荷方向下游离端附着体义齿基牙牙周及粘膜的有限元应力分析[J]．第四军医大学学报，1998，19(1)：5-7
[32] 薄斌，周树夏，曹建广，等．下颌骨在撞击载荷作用下的应力分布[J]。第四军医大学学报，1999，20(2)：119-120
[33] 王懿，张少锋，李世俊．三维有限元方法建立下颌磨牙模型[J]．第四军医大学学报，2004；25(7)：603-605
[34] 翁维民，李玲，张富强等．不同材料桩核冠系统修复上中切牙后的三维有限元分析[J]。口腔材料器械杂志2004，13(2)：79-81
[35] 唐高妍，巢永烈，文志红，等．四种桩材料对牙本质应力分布的影响的三维有限元分析[J]．华西口腔医学杂志，1998，16：259-262
[36] Yang HS,Lang LA,Guckes AD,et al. The effect of thermal change on various dowel-and-core restorative materials. J prosthet Dent, 2001,86:74-80
[37] Heydecke G, Peter MC. The restoration of endodontically treated single-rooted teeth with cast or direct posts and cores: A systematic review[J].J prosthet Dent,2002,87:380-386
[38] AlbuquerqueL -Rde C, Polletol T, Fontana R H. Stress analysis of an upper central incisor restored with different posts J .J Oral Rehabil, 2003,30:936-943
[39] Toksavul S, Zor M, Toman M,et al. Analysis ofdentinal stress distribution of maxillary central incisors subjected to various post-and-core applications [J]. Oper Dent. 2006, 31(1):89-96
[40] Holmes DC, Diaz- Arnold AM, Leary JM. Influence of post dimension on stress distribution in dentin[J]. J Prostht Dent ,1996,75 (2): 140-147
[41] 周峰，盛祖立，刘鹏飞．不同材料桩核修复后的牙本质应力分析[J]．浙江医学，2004，26(12)：903-907
[42] Manning KE, Yu DC, et al. Factors to consider for predictable post and core build-ups of endodontically treated teeth .Part: Clinical application of basic concepts [J].J Can Dent Assoc, 1995,61 (8):696-699,701-707
[43] Love RM, Purton DG. The effect of serrations on carbon fiber posts-retention within the root canal, core retention, and post rigidity[J]. Int J rosthodont, 1996, 9(5):484-488
[44] 张文云，施长溪，陈吉华等．新型美容牙科纤维／树脂复合材料桩钉的研制[J]．中国美容医学杂志，2001，10(1)：13-15
[45] Ottl P, Hahn L, Lauer HCH, et al. Fracture characteristics of carbon fibrer ceramic and non-palladium endodontic post systems at monotonously increasing loads. J Oral Rehabil, 2002, 29(2):175-183
[46] M. Gordon I, Metzger. Resistance to horizontal forces of dowel and amalgam core restorations: a comparative study. Journal of Oral Rehabilitaion1987; 47:337
[47] 鲁洁。石英纤维强化树脂桩修复严重缺损上颌中切牙的机械力学评价．硕士学位论文．2005：p33