Comprehensive characterization of osseous tissues from impedance measurements by effective medium approximation

Abstract

A unified mixing (UM) model was developed to derive microstructural information of trabecular bone, i.e., bone volume fraction (BV/TV), from electrical impedance spectroscopy. A distinct advantage of the UM-model over traditional methods, such as equivalent circuit models and multivariate analysis, is that the influence of both the environment (hydroxyapatite) and different inclusions (water, fat, and air) can be taken into account simultaneously. In addition, interactions between the different components such as interfacial polarization can be addressed by a dedicated fitting parameter v. Accordingly, values of BV/TV for different bone samples, e.g., including or not including water, were determined in the higher frequency range of 1–5 MHz. Results showed good agreement with experimental data obtained by micro-computer tomography. In particular, predictions for dielectric parameters that were derived for 3 and 4 MHz were found most promising for the assessment and distinction of osteopathic conditions and differences. This was shown by a clear differentiation of osseous tissues, e.g., the greater trochanter, femoral head, and femoral neck.

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

“…The results of this paper focused on the electrical conductivity of trabecular bone at 100 kHz. At this frequency, there is a consensus in the literature that bone can be considered a purely resistive medium because the phase shift is almost zero [10,19,22]. Considering this, we have studied the role of the microstructure and physiological solution (or free water that can flow within the pores) on the effective electrical conductivity of samples.…”

“…For bone marrow, the problem is more difficult, and the proportion of free water is not clearly known. Wei and collaborators measured the volume fraction of water in porcine trabecular bone by fitting a unified mixing dielectric model, but they obtained confusing results [19]. Instead of volume fraction, the authors considered mass fraction, arriving at mean values from 0.13 to 0.18, when the BV/TV was between 0.29 and 0.40.…”

“…Most of these potential medical applications of DP imply numerical simulation of the electromagnetic problem [4,[13][14][15][16][17]. Then, there is an interest in modeling and quantifying the influence of both composition and structure on the DP [10,11,[18][19][20]. For example, Balmer et al measured and modeled at the macro scale the correlation between bovine bone microstructure and electrical conductivity in the physiological state [10].…”

“…As an alternative, mixing theories from the effective medium theory has been used to homogenize the electrical properties of materials, which also allow for model rescaling [23]. Wei et al proposed a dielectric model considering fat, water content and BV/TV in porcine non-physiological trabecular samples [18,19]. The authors proposed the unified mixing (UM) model [23] and obtained good results, which are unfortunately not applicable to in vivo conditions.…”