Finite Element Analysis of the Dynamic Response of the Maxillary Molar under Impact Loading
Finite Element Analysis of the Dynamic Response of the Maxillary Molar under Impact Loading
复制标题
冲击载荷作用下上颌磨牙动态响应的有限元分析
DOI：
10.2991/mme-16.2017.140
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
ChenYun DOU
中科院分区：
文献类型：
--
作者：
HaiTao XIN;YuLu WU;Kai LI;XiaoOu DIAO;Fan FENG;ChenYun DOU
本文通过对一个上颌磨牙牙周膜（PDL）的动力学响应进行研究，探讨了牙周膜对牙齿动力学行为的影响。利用CT图像重建技术建立了上颌磨牙牙周组织的三维有限元模型。首先对上颌磨牙在牙周系统中的模态振动进行分析，然后计算牙齿在冲击载荷下的动态响应，并与不同牙周附着体的结果进行比较，以评估牙周组织的状况。前四阶模态在模态振动中占主导地位。在模态分析中，上颌磨牙在冲击载荷作用下的共振频率接近于第二阶模态的频率。共振频率随着牙槽骨的丢失而逐渐降低，而共振振幅则呈非线性增加。上颌磨牙的共振频率和振幅可以用来描述牙槽骨的丢失和牙周组织的状况。牙周膜（PDL）是由成千上万的纤维组成的薄的软组织，其将牙骨质固定到骨窝并提供牙齿与相邻牙槽骨的附着以支撑牙齿。PDL状况的生物力学信息在临床诊断、治疗计划和预后管理中非常重要[1，2]。牙周病的评估方法很多，如X线检查、咀嚼压力、牙齿松动度等。牙齿在牙周系统中的动态行为反映了评估牙周组织状况的重要参数：牙周组织的受损状况和牙周附着水平[3，4]。当牙齿的振动特性用于描述牙周组织的状况时，具有PDL的牙齿的动态响应与施加力和激励方向密切相关[5]。瞬态动力分析是一种用于确定结构在任何一般时变载荷作用下的动态响应的技术[6，.应变能逐渐转换成另一种能量形式的机制称为阻尼。一些调查集中在计算或测量的固有频率和阻尼的牙齿受到外部激励[1，3，4]在体内和体外。但是，由冲击力激发的摩尔的动力学行为还没有得到很好的探索。为了研究上颌磨牙的动力学行为以及牙齿的共振频率与牙周附着水平之间的关系，在本研究中，对上颌磨牙在牙周系统中的动态有限元分析在冲击载荷下，以评估牙周组织的情况。994工程研究进展（AER），第105卷第三届力学和机械工程国际年会（MME 2016）版权所有© 2017，作者。出版社：Atlantis Press这是一个在CC BY-NC许可证下的开放获取文章（http：//creativecommons.org/licenses/by-nc/4.0/）。方法采用3D-DOCTOR软件（3D-DOCTOR Version3.5，Able Software Corp，列克星敦，MA，USA）进行CT图像重建，建立上颌磨牙和牙周膜的三维几何模型。建立3D模型的程序参考了我们以前的研究[8]。然后选择牙周膜附着的牙根网格面，根据牙周膜厚度向外扩张形成牙周膜组织，重建上颌磨牙牙周膜。最后，将PDL结构与上颌磨牙进行相应的网格划分。建立上颌磨牙和PDL的三维有限元模型，以进行进一步分析（图1）。在该模型中，牙齿的长度为19.3 mm，牙冠为7.1 mm，牙根为12.2 mm。PDL的厚度为0.25 mm [9]。为了模拟在体牙周附着丧失的情况，定义牙周附着高度来描述牙槽骨丧失的情况和牙周附着的水平。在分析中使用了一系列模型，每个模型的牙周附着高度从冠根之间的解剖边界减少1.0mm。牙釉质、牙本质和PDL的机械性能取自参考文献[6，10]（表1）。图1.上颌磨牙和PDL的模型表1.本研究中使用的机械性能材料杨氏模量（GPa）泊松比密度（g/cm）牙釉质77.9 0.33 3.0牙本质16.6 0.31 2.2 PDL 0.05 0.45 1.1数值方法牙齿，在本研究中，PDL和牙槽骨被假定为拉伸缓冲粘弹性系统[11-13]描述上颌磨牙在牙周系统中的动力学特性。牙槽骨被认为是不可移动的，在三个方向上对PDL的外表面施加位移限制[14，15]。为了验证模型的正确性，首先利用MSC有限元分析软件MARC-FEA对牙周系统中的上颌磨牙进行了模态分析。选取前四阶振型和频率来描述振动特性。然后计算冲击载荷下轮齿的加速度，并通过FFT分析仪将其转换为响应，以描述轮齿的动态特性。选择峰值为500 N [9]的正弦力（图2）代表咀嚼负荷，上升时间为2 ms，总持续时间为4 ms [6，9]，并沿颊舌方向施加在牙冠颊面的中心点上（图1）。加载995工程研究进展（AER），卷105
The dynamic response of a maxillary molar with periodontal ligament (PDL) was investigated to explore the dynamic behavior of the tooth. Three-dimensional (3D) finite element model of a maxillary molar with periodontium was constructed using CT image-reconstruction. The modal vibration of the maxillary molar in the periodontal system was performed at first, and then the dynamic response of the tooth under an impact loading was calculated and compared with the results of the different periodontal attachments in order to assess the condition of the periodontium. The first four modes were dominant in the modal vibration. The resonant frequency of the maxillary molar under the impact loading was close to the frequency of the second mode in the modal analysis. The resonant frequency decreased gradually with the loss of alveolar bone, while the resonant amplitude increased nonlinearly. The resonant frequency and amplitude of the maxillary molar can be used to describe the loss of alveolar bone and the condition of periodontium. Introduction The periodontal ligament (PDL) is a thin soft tissue made up of thousands of fibers which fasten tooth cementum to the bony socket and provide attachment of a tooth to the adjacent alveolar bone to support the tooth. Biomechanical information on the PDL condition is very important in clinical diagnosis, treatment planning and prognosis management [1, 2]. Many methods are used to evaluate the PDL condition, for example radiographic examination, masticatory pressure and tooth mobility. The dynamic behavior of a tooth in the periodontal system reflects the important parameters for assessing the periodontal tissue condition: the damaged condition of periodontium and the level of periodontal attachment [3, 4]. The dynamic response of a tooth with the PDL is strongly related to the application force and the excitation direction when the vibrational properties of the tooth is used to describe the condition of the periodontium [5]. Transient dynamic analysis is a technique used to determine the dynamic response of a structure under the action of any general time-dependent loads [6, . The mechanism by which the strain energy is gradually converted to another energy form is known as damping. Some investigations focus on the calculation or measuring of the natural frequency and the damping of a tooth subjected to an external excitation [1, 3, 4] in vivo and in vitro. But the dynamic behavior of a molar excited by an impact force has not been well explored. In order to investigate the dynamic behavior of a maxillary molar and the relation between the resonant frequency of the tooth and the level of periodontal attachment, dynamic finite element analysis of the maxillary molar in the periodontal system under an impact loading was performed in this study to assess the condition of periodontium. 994 Advances in Engineering Research (AER), volume 105 3rd Annual International Conference on Mechanics and Mechanical Engineering (MME 2016) Copyright © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Methods Finite Element Model To construct a 3D geometric model of a maxillary molar and the PDL, CT image-reconstruction technique was used in this study provided by the 3D-DOCTOR software (3D-DOCTOR Version3.5, Able Software Corp, Lexington, MA, USA) at first. The procedure to build the 3D model was referred to our previous study [8]. Then to rebuild the PDL of the maxillary molar, the meshed surface of the tooth root where the PDL attached was selected and expanded outwards to form the PDL tissue based on the thickness of the PDL. Finally, the PDL structure was meshed correspondingly with the maxillary molar. The 3D finite element model of the maxillary molar and the PDL was set up for further analysis (Figure 1). In this model, the length of the tooth was 19.3 mm, the crown was 7.1 mm and the root was 12.2 mm. The thickness of the PDL was 0.25mm[9]. In order to simulate periodontal attachment loss in vivo, the height of periodontal attachment was defined to describe the condition of alveolar bone loss and the level of periodontal attachment. A series of models was used in the analysis, with a decrement of 1.0mm each for the height of periodontal attachment from the anatomic boundary between the crown and the root of the tooth. The mechanical properties for enamel, dentin and the PDL were taken from the references [6, 10] (Table 1). Figure 1. The model of the maxillary molar and PDL Table 1. Mechanical properties used in the current study Material Young's modulus(GPa) Poisson’s ratio Density(g/cm) Enamel 77.9 0.33 3.0 Dentin 16.6 0.31 2.2 PDL 0.05 0.45 1.1 Numerical Approach The tooth, the PDL and the alveolar bone were assumed to be a stretch buffer viscoelastic system in this study [11-13] to describe the dynamic property of the maxillary molar in the periodontal system. The alveolar bone was considered immovable, the restrictions of displacement were applied on the exterior surface of the PDL in three-directions [14, 15]. To validate the model, the modal analysis of the maxillary molar in the periodontal system was performed at first using MSC software MARC-FEA. The first four mode shapes and frequencies were selected to describe vibration characteristics. Then the acceleration of the tooth under impact loading was calculated and converted into the response by the FFT analyser to describe dynamic property of the tooth. A sinusoidal force (Figure 2) with a peak of 500 N [9] represented masticatory load, a rise time of 2ms, and a total duration of 4 ms [6, 9], was chosen and imposed on the central point in buccal surface of the dental crown in the buccal-lingal direction (Figure 1). Load 995 Advances in Engineering Research (AER), volume 105
登录
查看更多内容
影响因子：
3.2
作者：
H. Xin;Yulong Li;Lingcheng Zhao;W. Guo
通讯作者：
H. Xin;Yulong Li;Lingcheng Zhao;W. Guo
影响因子：
3.5
作者：
Lida Shen;Haw-Ming Huang;Jun Jea Yu;S. Lee;Chi-Ming Lee;Sung-Chih Hsieh
通讯作者：
Lida Shen;Haw-Ming Huang;Jun Jea Yu;S. Lee;Chi-Ming Lee;Sung-Chih Hsieh
影响因子：
2.4
作者：
D. Noyes;C. Solt
通讯作者：
D. Noyes;C. Solt
DOI：
10.1016/j.ajodo.2006.01.046
发表时间：
2008-04-01
影响因子：
3
作者：
Nishimura, Makoto;Chiba, Mirei;Mitani, Hideo
通讯作者：
Mitani, Hideo
DOI：
10.1080/10255840290032117
发表时间：
2002-04-01
影响因子：
1.6
作者：
Pietrzak, G;Curnier, A;Belser, U
通讯作者：
Belser, U