基于边光滑有限元法的骨重建力电效应

目的 针对骨重建压电效应仿真分析时传统有限元法(finite element method, FEM)数值解精度差的问题，提出了一种基于边的光滑有限元法(edged-based smoothed FEM, ES-FEM)模型。方法 基于三角形背景网格构建光滑域，依托梯度光滑技术获得光滑应变梯度与光滑电场梯度，在光滑伽辽金弱形式的框架下构造系统离散方程。结果 采用上述模型能反映压电效应下骨重建过程中骨密度变化和电势分布，相比于FEM,ES-FEM能够在一定程度上提高骨重建仿真结果的精度。结论 提出的边光滑有限元模型能够更准确地模拟出骨重建过程，该方法对骨重建压电效应问题的准确预测为骨类疾病临床研究提供有效的理论依据。

Electromechanical Effects of Bone Remodeling Based on Edge Smoothed Finite Element Method

Objective Aiming at solving the problem of poor accuracy for numerical solution of traditional finite element method (FEM) in numerical analysis on piezoelectric effects of bone remodelling, a model with an edge-based smoothed FEM (ES-FEM) was proposed. Methods The bone model was discretized by triangular elements, and the smoothing domain was constructed based on edges of the existing mesh element. Based on gradient smoothing technique, the smoothed strain gradient and the smoothed electric field gradient were obtained, and the discrete equations of the system were constructed under the framework of smoothed Galerkin weakform. Results The changes of bone mineral density (BMD) and the distributions of electric potential under piezoelectric effects in the process of bone remodelling were reflected by using the above model. Compared with FEM, ES-FEM could improve the accuracy of simulation result for bone remodelling to a certain extent. Conclusions The proposed ES-FEM can simulate the process of bone remodelling more accurately. The accurate prediction for piezoelectric effect of bone reconstruction by this method provides an effective theoretical basis for clinical research of bone diseases.