基于两相多孔介质模型的骨组织力学响应数值分析

Mechanical Response Numerical Analysis of Bone Tissue Based on Liquid Saturated Biphasic Porous Medium Model

引入基于混合物理论的流 -固两相多孔介质模型来描述骨组织在承受各种动载荷时 ,其骨质应力场、变形场以及孔间骨液压力场的分布规律。模型中考虑固体骨质为横观各向同性的液饱和多孔材料 ,研究骨质变形、骨液流动以及流动电位间的耦合关系。采用 Galerkin加权残值法 ,导出了骨组织流 -固耦合动力响应的罚有限元公式和流动电位计算式 ,编制了相应的有限元程序。算例表明 ,骨组织特别是松质骨组织的表观黏弹性行为和能量耗散性质 ,很大程度上是由于骨孔间液体扩散和流动引起的 ;同时 ,由于骨组织固 -液两相界面间双电层的存在 ,当液体组分扩散时 ,引起流动电位 ,从而促进骨的生长和吸收。

A biphasic porous medium model based on the mixture theory in continuum mechanics frame was used to depict the distributions of osseous stress field, distortion field and pore pressure when the bone tissue was subject to various dynamic loads. In the model, the bone tissue was considered as a transversely isotropic, liquid saturated porous material. The coupling relationship among the distortion, fluid flow and the streaming potential is studied. The Galerkin weighted residual method was used to derive the finite element formulation for dynamic response and the streaming potential calculating formulation of bone tissue, the penalty finite element formulation was obtained via introducing the ratio term of pressure p and penalty parameter β in the continuity equation and, in turn, eliminated the pressure term in governing equation sets. The computational results show that the viscoelastic behavior and the energy dissipation property in the bone tissue, especially in the cancellous bone, is caused to a great extent by the pore liquid flow and diffusion. Meanwhile, because of the existence of electrical double layer between the solid phase and liquid phase, when the liquid constituents in the pore diffuse, the streaming potential appears, and the growth and absorption of bone tissue is expedited.