Microwave tomography with phaseless data on the calcaneus by means of artificial neural networks.

The aim of this study is to use a multilayer perceptron (MLP) artificial neural network (ANN) for phaseless imaging the human heel (modeled as a bilayer dielectric media: bone and surrounding tissue) and the calcaneus cross-section size and location using a two-dimensional (2D) microwave tomographic array. Computer simulations were performed over 2D dielectric maps inspired by computed tomography (CT) images of human heels for training and testing the MLP. A morphometric analysis was performed to account for the scatterer shape influence on the results. A robustness analysis was also conducted in order to study the MLP performance in noisy conditions. The standard deviations of the relative percentage errors on estimating the dielectric properties of the calcaneus bone were relatively high. Regarding the calcaneus surrounding tissue, the dielectric parameters estimations are better, with relative percentage error standard deviations up to ≈ 15%. The location and size of the calcaneus are always properly estimated with absolute error standard deviations up to ≈ 3 mm. Microwave tomography of the calcaneus using phaseless data. Simulations were inspired in Computed Tomography images from real heels (above). Inverse problem was solved using Multilayer Perceptron Artificial Neural Network (below).

Is there any information on micro-structure in microwave tomography of bone tissue?

In this work, two-dimensional simulations of the microwave dielectric properties of models with ellipses and realistic models of trabecular bone tissue are performed. In these simulations, finite difference time domain methodology has been applied to simulate two-phase structures containing inclusions. The results presented here show that the micro-structure is an important factor in the effective dielectric properties of trabecular bone. We consider the feasibility of using the dielectric behaviour of bone tissue to be an indicator of bone health. The frequency used was 950 MHz. It was found that the dielectric properties can be used as an estimate of the degree of anisotropy of the micro-structure of the trabecular tissue. Conductivity appears to be the most sensitive parameter in this respect. Models with ellipse shaped-inclusions are also tested to study their application to modelling bone tissue. Models with ellipses that had an aspect ratio of a/b=1.5 showed relatively good agreement when compared with realistic models of bone tissue. According to the results presented here, the anisotropy of trabecular bone must be accounted for when measuring its dielectric properties using microwave imaging.