表面多点和单点受力的龋齿孔洞的无网格配点法的分析

Comparative Study on Three-dimensional Elastic Stress Analysis between Caries and Healthy Teeth

目的:用无网格配点法分析右下颌第一磨牙垂直受力和侧向受力时牙齿的形变和应力分布,并研究龋齿与健康牙齿最大应力分布的区别。方法:通过锥形束计算机断层扫描仪(CBCT)扫描一颗完整拔除的右下颌第一磨牙,获得切片图像。将切片图像导入MATLAB软件得到扫描数据,从而构建真实的牙齿计算区域。采用无网格配点法来求解三维牙齿的受力模型。在新建立的模型上,详细的分析了三维弹性牙齿的变形和应力分布,并且通过在牙齿内部设置孔洞,从最大应力分布的角度来研究并探讨龋齿与健康牙齿之间的区别。结果:磨牙的最大应力位于牙齿咬合面的窝、嵴部或牙颈部。当牙齿咬合面垂直承受荷载时,有空心球体的牙齿最大的应力位于空球体的表面。然而,在相同荷载下,没有空球体的牙齿最大应力位于牙颈部。以上结果验证了无网格配点法的有效性。结论:数据模拟结果显示,磨牙的最大应力位于牙齿咬合面的窝、嵴部或牙颈部。在龋齿中,最大应力的位置改变到牙齿内部龋坏处的表面,并且最大应力的值通常会增加,由此认为龋坏的部位很容易发生牙齿折裂。

Objective:To analyze the tooth deformation and stress distribution of right mandibular first molar under vertical and lateral forces,and to study the difference of the maximum stress distribution between caries and healthy teeth.Methods:An extracted right mandibular first molar was scanned by CBCT to obtain slice images.The data were imported into Matlab software to construct the real tooth calculation area.The meshless collocation method was used to solve the three-dimensional tooth force model.Based on the newly established model,the deformation and stress distribution of three-dimensional elastic teeth were analyzed in detail.The difference between caries and healthy teeth was studied from the perspective of maximum stress distribution by setting holes in the teeth.Results:The maximum stress is located in the pit,ridge,or neck of the occlusal surface of healthy molar.When the occlusal surface born the load vertically,the maximum stress of the tooth with hollow sphere was located on the surface of the hollow sphere.However,under the same load,the maximum stress of teeth without empty spheres was located in the tooth neck.Conclusion:The meshless collocation method is effective.It is believed that the caries site is prone to tooth fracture.