Numerical Simulation of Electrical Properties in Cortical and Trabecular Bone: A Simplified Model

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.

Source: arXiv:2609.31584v1 - http://arxiv.org/abs/2609.31584v1 PDF: https://arxiv.org/pdf/2609.31584v1 Original Link: http://arxiv.org/abs/2609.31584v1