Low Frequency Electrical Conductivity of Trabecular Bone: Insights from In Silico Modeling

Abstract

Background: Electrical conductivity of trabecular bone at 100 kHz was recently reported as a good predictor of bone volume fraction. However, to quantify its relationship with the free water (or physiological solution) content and between the conductivities of its constituents, is still unclear. Methods: In this contribution, in silico models inspired by microCT images of trabecular bovine samples were used to build realistic geometries. Finite Element Method was applied to solve the electrical problem and to robustly fit the conductivity of the constituents with literature data. The obtained effective electrical conductivity was compared to Bruggeman three media mixture model: physiological solution, bone marrow and bone matrix. Results: The values for physiological solution plus bone marrow and bone matrix that captured better the bone volume fraction in the two media Finite Element model were: σps+bm = 298.4 mS/m and σb = 21.0 mS/m, respectively. Additionally, relative good results were obtained by a three media Bruggeman mixture model with σbm= 103 mS/m, σb= 21.0 mS/m, and σps= 1200 mS/m. Simple linear relationships between the proportions of constituents depending on bone volume fraction were tested. Degree of anisotropy and fractal dimension do not show detectable changes in effective conductivity. Conclusions: These results provided some useful findings for simulation purposes: first, a higher value of electrical conductivity of bone marrow has to be used in order to obtain similar values to those experimental published data. Second, anisotropy is not detectable by conductivity measurements for small trabecular samples (cube 5 mm). Finally, the simulations presented here showed a relatively good fitting of the mixture Bruggeman model which potentially would allow both, accounting for the free water content and re-scaling the model for whole bone electrical simulations.