人工骨支架多场耦合力学数值仿真

A Simulation Study of Artificial Bone Scaffolds Based on Multi-Physics Coupling Model

建立多孔骨支架重组的多物理场耦合数值分析模型,研究了多孔骨组织支架在流固耦合情况下,骨架间隙营养液和骨架颗粒随外载变化规律。仿照自然骨解剖结构建立了具有哈福氏(Haversian)和福克曼(Volkmann)管道的人工骨支架模型和用于数值分析的1/16简化模型,根据力学平衡条件推出应力场方程,建立动态孔隙率和渗透率数学模型;考虑骨架变形和营养液具有可压缩特性,根据流体力学连续性方程,推导出孔隙流体的连续性方程-渗流方程。辅以控制方程和定解条件,建立人工骨饱和多孔介质流-固全耦合渗流的数学模型;进而分析多孔人工骨支架应力场、孔隙间骨液压力场及渗流速度场在各种载荷下的分布规律。

Through establishing the fully coupling mathematical model of the fluid-structure of the artificial bone scaffolds under the saturated porous medium and using finite element method, we analyze the stress, strain trends of the artificial bone scaffolds under several load constraints so that we can predict the biodegradation and regeneration of the artificial bone scaffolds under optimization growth situations. We demonstrated the stress equation in multi-physics according to the mechanical equilibrium condition, and established the dynamic coefficient model of porosity （Eq. 6） and permeability （Eq. 11） in Section 2. Section 3 describes seepage dynamical equation deduction procedure and Eq. 21 is the dynamical seepage equation. Meanwhile, based on the hydromechanics continuity equation and considering the deformation of the skeleton and the compressibility of the fluid, we obtained the full fluid flow constitutive equation （Eq. 30） in Section 4. We put Eq. 21 into COMSOL simulation platform as the seepage governing equation and input Eq. 30 as constitutive equation. In addition, in Section 5.1 we put forward the initial and constraint conditions. We then analyzed the distributed rule between stresses, displacement under interstitial fluid flow pressure based on this fluid-structure coupling seepage theory. Figs. 4 and 5 demonstrate that the density of nutrition fluid flow and bone scaffolds increases with the external loads and interstitial fluid flow pressure; Fig. 6 demonstrates that the seepage velocity of nutrition fluid flow increases sharply with the depth of bone scaffolds Figs. 7 and 8 show that the coupling stress is bigger than the non-coupling stress; Fig. 9 shows that the nutrition fluid flow velocity increases with bone scaffolds porosity.