Analysis of microstructural parameters of trabecular bone based on electrical impedance spectroscopy and deep neural networks

Abstract

The potential of electrical impedance spectroscopy (EIS) was demonstrated for the investigation of microstructural properties of osseous tissue. Therefore, a deep neural network (DNN) was implemented for a sensitive assessment of different structural features that were derived on the basis of dielectric parameters, especially relative permittivities, recorded over a frequency range from 40 Hz to 5 MHz. The advantages of the developed method over conventional approaches, including equivalent circuit models (ECMs), linear regression and effective medium approximation (EMA), is the comprehensive quantification of bone morphologies by several microstructural parameters simultaneously, such as bone volume fraction (BV/TV), bone surface-volume-ratio (BS/BV), structure model index (SMI), trabecular number (Tb.N) and trabecular thickness (Tb.Th). The comparison of predictions of the DNN with an analysis of µCT-images confirmed a high accuracy for different microstructural parameters, which was indicated by corresponding Pearson correlation coefficients, especially for Tb.Th (r = 0.89) and BS/BV (r = 0.80). Concurrently, the approach was able to unambiguously discriminate anatomically similar bone regions (femoral head, greater trochanter and femoral neck) and therefore was capable to determine the morphological status of osseous tissue in detail. The classification was more discriminative than one based on classical linear discriminant analysis (LDA), due to the distinguishing features extracted by the DNN model. Accordingly, the method and model can serve as a potential tool for evaluating bone quality and bone status.

Keywords: Deep neural network; Electrical impedance spectroscopy; Microstructural parameters; Osseous tissue; Permittivity.