不同力系统下的上中切牙位移、转动中心及牙周应力的三维有限元研究

FEM Study on Displacement, Position of Rotation Center and Stress Distribution of PDL under Various Loading Force Systems

目的 研究不同力系统 (力矩 /后退力 )下的上中切牙位移、转动中心及牙周应力分布。方法 建立包括牙齿、牙周膜、硬骨板、松质骨、皮质骨的上中切牙三维有限元模型 ,采用 8节点三维六面体单元 ,共包括 94 5个单元 ,12 4 5个节点。计算 13种力系统下的上中切牙位移、转动中心及牙周应力分布。结果 ①牙齿表现为三种典型位移性质 ,力矩 /后退力比值为_9 15∶1、_10 30～_10 5 0∶1及_10 90∶1时 ,牙齿分别出现以根尖点为中心转动、平行移动及以切缘为中心转动 ;②转动中心曲线以横坐标_10 5 0、纵坐标 6 75两直线为渐进线 ,力矩 /后退力比值在_9 15至_10 90之间变化时 ,其转动中心变化较大 ;③以根尖点为转动中心时牙周最大牵张力、压应力分别为 1 4 7× 10 -2MPa和_2 81× 10 _2 MPa;平行移动时牙周最大牵张力、压应力分别为 1 10× 10 _2 MPa和_1 86× 10 _2 MPa ;以切缘为转动中心时牙周最大牵张力、压应力分别为 0 96× 10 _2 MPa和_2 5 8× 10 _2 MPa。结论 ①牙齿的位移与力矩 /后退力比值有关 ;②力矩 /后退力比值在_9 15∶1至_10 90∶1之间变化时 ,应仔细调整力系统 ,以获得确定的牙齿位移方式 ;③平行移动时 ,牙周膜应力分布较均匀 ,最大应力值较小 ;当上中切牙受到 1N水平力及转?

Objective To investigate the displacement, the position of rotation center and the stress distribution of PDL under different loading force system (Moment/Force ,M/F) by simulating clinical loading force system.Methods A three-dimensional finite element model of upper central incisor, which consists of 945 isoparametric elements and 1 245 nodes was developed. The displacement, the position of the rotation center and the stress distribution of PDL were analyzed under 13 types of loading force system.Results 1.Different force system led to different types of tooth movement. When M/F= -9.15∶1, -10.30～-10.50∶1 and -10.90∶1, it brought the result of controlled tipping movement, the bodily movement and the root movement; 2. The graph of the center rotation was a hyperbolic asymptotic line:Mx/Fy= -10.50 (horizontal axis) and L=6.75(vertical axis). Moreover, a little change of M/F between -9.15 and -10.90 led to apparent change of the position of rotation center. 3. The maximum strain and stress during the tipping movement were 1.47×10+{-2} MPa and -2.81×10+{-2} MPa, and during the bodily movement the results were 1.10×10+{-2} MPa and -1.86×10+{-2} MPa, while during the root movement were 0.96×10+{-2} MPa and -2.58×10+{-2} MPa.Conclusion 1. Different force system (M/F) leads to different types of tooth movement. 2. It is necessary to adjust the force system accurately to obtain prescient tooth movement, especially when M/F changes between -9.15∶1 and -10.90∶1. 3. This study suggested that the tooth movement style and the force system (M/F) should be controlled to protect the periodontal tissue.