皮质骨与松质骨电学特性的数值模拟：一种简化模型
Numerical Simulation of Electrical Properties in Cortical and Trabecular Bone: A Simplified Model
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中文总结 AI 辅助
本研究通过有限元与Bruggeman均匀化多尺度模型，模拟皮质骨与松质骨电学特性，验证各向异性并揭示微观结构变化显著影响阻抗，为骨电学测量提供基础。
中文摘要 AI 辅助
生物组织的电学特性取决于其组成和微观结构，并决定其对施加电场的响应。在骨组织中，这些特性与其组成、孔隙率和微观结构组织密切相关。然而，将骨微观结构（松质骨和皮质骨）与其有效电学特性联系起来，同时考虑皮质骨电各向异性的简化模型仍然很少。在本工作中，开发了一种多尺度方法，将有限元模拟与基于Bruggeman的均匀化模型相结合。松质骨使用基于microCT的几何结构进行建模，其有效电导率作为BV/TV和自由水含量的函数进行分析。皮质骨由哈弗斯管（轴向=z）和福尔克曼管（横向）的简化三维网络表示，通过各向异性Bruggeman公式纳入其方向性组织。这些模型捕捉到了松质骨实验报道的电导率范围（约25-200 mS/m），并再现了皮质骨有限元模拟中观察到的各向异性行为，即轴向电导率更高。在生成的皮质骨几何结构中，总孔隙率的65.5%与轴向哈弗斯管相关。在宏观尺度上，具有较低松质骨和皮质骨BV/TV以及较小皮质厚度的胫骨模型相对于参考模型表现出约38-39%的阻抗降低。这些结果表明，骨组织的微观结构变化反映在其有效电学特性和模型的宏观阻抗中，为未来研究电学测量对骨微观结构变化的敏感性提供了物理和计算基础。
英文摘要
The electrical properties of biological tissues depend on their composition and microstructure and determine their response to applied electric fields. In bone tissue, these properties are closely related to its composition, porosity, and microstructural organization. However, simplified models that link bone microstructure (trabecular and cortical) to its effective electrical properties while accounting for the electrical anisotropy of cortical bone remain scarce. In this work, a multiscale approach was developed, combining finite element simulations with Bruggeman-based homogenization models. Trabecular bone was modeled using microCT derived geometries, and its effective conductivity was analyzed as a function of BV/TV and free water content. Cortical bone was represented by a simplified three-dimensional network of Haversian canals (axial = z) and Volkmann canals (transverse), incorporating their directional organization through an anisotropic Bruggeman formulation. The models captured the conductivity range reported experimentally for trabecular bone (approximately 25-200 mS/m) and reproduced the anisotropic behavior observed in the cortical FEM simulations, with higher conductivity in the axial direction. In the generated cortical geometries, 65.5% of the total porosity was associated with axial Haversian canals. At the macroscale, the tibia model with lower trabecular and cortical BV/TV and reduced cortical thickness showed an approximately 38-39% reduction in impedance relative to the reference model. These results indicate that microstructural variations in bone tissue are reflected in its effective electrical properties and in the macroscopic impedance of the model, providing a physical and computational basis for future investigations into the sensitivity of electrical measurements to changes in bone microstructure.
发表机构
- Instituto de Física de Líquidos y Sistemas Biológicos, CONICET-UNLP（液体与生物系统物理研究所）
- Universidad Tecnológica Nacional, Facultad Regional La Plata（国立技术大学拉普拉塔地区学院）
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