上颌第一磨牙远中移动时牙周膜应力分布的非线性三维有限元分析

目的:对上颌第一磨牙远中移动时牙周膜的应力分布进行非线性有限元分析,并与线性分析结果比较,为临床提供生物力学依据。方法:采用Mimics、Geomagic、ProE、Ansys Workbench等软件相结合的方法,建立包含上颌第一磨牙、牙周膜、牙槽骨、骨松质、骨皮质、颊面管的三维有限元模型,分别将牙周膜材料设定为非线性材料和线弹性材料,模拟临床远移上颌第一磨牙的操作,使用不同组合的负荷方式进行加载。结果:非线性模型中,牙周膜Von Mises等效应力峰值分布和压应力峰值分布均存在低应力通道：当符合条件M_t/F- M_r/F≈2时,等效应力峰值处于较低水平;当符合条件M_t/F≈M_r/F时,压应力峰值处于较低水平。线性模型中,牙周膜相关应力值均较高且变化剧烈,无低应力通道。结论:牙周膜应力分布存在低应力通道,远中移动上颌第一磨牙时,应尽量使施加的力偶矩与力比值满足低应力条件。

Analysis of stress in periodontal ligament of the maxillary first molar on distal movement by nonlinear finite element method

PURPOSE: To analyze the stress distribution in periodontal ligament of maxillary first molar during distal movement with nonlinear finite element analysis, and to compare it with the result of linear finite element analysis, consequently to provide biomechanical evidence for clinical application. METHODS: The 3-D finite element model including a maxillary first molar, periodontal ligament, alveolar bone, cancellous bone, cortical bone and a buccal tube was built up by using Mimics, Geomagic, ProE and Ansys Workbench. The material of periodontal ligament was set as nonlinear material and linear elastic material, respectively. Loads of different combinations were applied to simulate the clinical situation of distalizing the maxillary first molar. RESULTS: There were channels of low stress in peak distribution of Von Mises equivalent stress and compressive stress of periodontal ligament in nonlinear finite element model. The peak of Von Mises equivalent stress was lower when it was satisfied that M_t/F minus M_r/F approximately equals 2. The peak of compressive stress was lower when it was satisfied that M_t/F was approximately equal to M_r/F. The relative stress of periodontal ligament was higher and violent in linear finite element model and there were no channels of low stress in peak distribution. CONCLUSIONS: There are channels in which stress of periodontal ligament is lower. The condition of low stress should be satisfied by applied M/F during the course of distalizing the maxillary first molar.