BACKGROUND Bone is a hierarchically structured composite material, and different hierarchical levels exhibit diverse material properties and functions. The stress and strain distribution and fluid flow in bone play an important role in the realization of mechanotransduction and bone remodeling. METHODS To investigate the mechanotransduction and fluid behaviors in loaded bone, a multiscale method was developed. Based on poroelastic theory, we established the theoretical and FE model of a segment bone to provide basis for researching more complex bone model. The COMSOL Multiphysics software was used to establish different scales of bone models, and the properties of mechanical and fluid behaviors in each scale were investigated. RESULTS FE results correlated very well with analytical in macroscopic scale, and the results for the mesoscopic models were about less than 2% different compared to that in the macro-mesoscale models, verifying the correctness of the modeling. In macro-mesoscale, results demonstrated that variations in fluid pressure (FP), fluid velocity (FV), von Mises stress (VMS), and maximum principal strain (MPS) in the position of endosteum, periosteum, osteon, and interstitial bone and these variations can be considerable (up to 10, 8, 4 and 3.5 times difference in maximum FP, FV, VMS, and MPS between the highest and the lowest regions, respectively). With the changing of Young's modulus (E) in each osteon lamella, the strain and stress concentration occurred in different positions and given rise to microscale spatial variations in the fluid pressure field. The heterogeneous distribution of lacunar-canalicular permeability (klcp) in each osteon lamella had various influence on the FP and FV, but had little effect on VMS and MPS. CONCLUSION Based on the idealized model presented in this article, the presence of endosteum and periosteum has an important influence on the fluid flow in bone. With the hypothetical parameter values in osteon lamellae, the bone material parameters have effect on the propagation of stress and fluid flow in bone. The model can also incorporate alternative material parameters obtained from different individuals. The suggested method is expected to provide dependable biological information for better understanding the bone mechanotransduction and signal transduction.

中文翻译：

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通过多尺度多孔弹性有限元分析研究加载骨的宏观和细观生物力学响应。

背景技术骨是一种层次结构的复合材料，不同层次表现出不同的材料性能和功能。骨内的应力应变分布和流体流动对于实现力传导和骨重塑具有重要作用。方法 为了研究负载骨中的力传导和流体行为，开发了一种多尺度方法。基于多孔弹性理论，建立了节段骨的理论和有限元模型，为研究更复杂的骨模型提供了基础。利用COMSOL Multiphysics软件建立不同尺度的骨模型，并研究各尺度下的力学和流体行为特性。结果有限元结果与宏观尺度的解析结果有很好的相关性，细观模型的结果与宏观-细观模型的结果相差约小于2%，验证了模型的正确性。在宏观-中观尺度上，结果表明，内膜、骨膜、骨和间质骨位置的流体压力（FP）、流体速度（FV）、冯米塞斯应力（VMS）和最大主应变（MPS）的变化和这些变化可能相当大（最高区域和最低区域之间的最大 FP、FV、VMS 和 MPS 分别高达 10、8、4 和 3.5 倍）。随着各骨板杨氏模量（E）的变化，应变和应力集中发生在不同位置，并引起流体压力场的微观空间变化。各骨板腔隙小管通透性(klcp)的不均匀分布对FP和FV有不同的影响，但对VMS和MPS影响不大。结论基于本文提出的理想化模型，内膜和骨膜的存在对骨中的液体流动具有重要影响。根据骨板的假设参数值，骨材料参数对骨中应力和流体流动的传播有影响。该模型还可以结合从不同个体获得的替代材料参数。建议的方法有望为更好地理解骨力转导和信号转导提供可靠的生物学信息。