Application of Machine Learning to Predict Dielectric Properties of In Vivo Biological Tissue

Abstract

In this paper we revisited a database with measurements of the dielectric properties of rat muscles. Measurements were performed both in vivo and ex vivo; the latter were performed in tissues with varying levels of hydration. Dielectric property measurements were performed with an open-ended coaxial probe between the frequencies of 500 MHz and 50 GHz at a room temperature of 25 °C. In vivo dielectric properties are more valuable for creating realistic electromagnetic models of biological tissue, but these are more difficult to measure and scarcer in the literature. In this paper, we used machine learning models to predict the in vivo dielectric properties of rat muscle from ex vivo dielectric property measurements for varying levels of hydration. We observed promising results that suggest that our model can make a fair estimation of in vivo properties from ex vivo properties.

Keywords: ex vivo and in vivo dielectric properties; machine learning modelling; tissue hydration.

Figure 1

Spread of dehydration levels and number of measurements per level per rat. The in vivo measurements are shown below the ex vivo measurements. The colour codes for the four rats are red, blue, green and purple for rats labelled 3, 4, 5 and 6, respectively. In vivo muscle measurements are represented in coloured squares (there is no muscle designator for the in vivo measurements), whereas ex vivo measurements of measured muscles 1 and 2 are represented in circles and triangles, respectively. Scatter points were plotted with an added offset to avoid their overlap.

Figure 2

Measurements of the real (top) and imaginary (bottom) part of the permittivity (ε′ and ε″, respectively) for a frequency of 500 MHz. Measurements were performed on 4 rats (labelled as 3, 4, 5 and 6, colours red, blue, green and purple, respectively); in vivo measurements were made on a single muscle (square), and ex vivo measurements were performed on two muscles (1 and 2, circle and triangle shapes, respectively).

Figure 3

Average real (top) and imaginary (bottom) parts of the relative permittivity ($${\epsilon }_r^{\prime }$$ and $${\epsilon }_r^{″}$$, respectively) across all frequencies in 3D. Note that the colour bar limits were adjusted for better contrast; the actual ranges are 7–65 for Re($${\epsilon }_r$$) and 3–68 for Im($${\epsilon }_r$$).

Figure 4

Binned and interpolated values of average real (top) and imaginary (bottom) parts of the permittivity ($${\epsilon }_r^{\prime }$$ and $${\epsilon }_r^{″}$$, respectively) across all frequencies. Note that the colour bar limits were adjusted for better contrast, the actual ranges are 7–65 for Re($${\epsilon }_r$$) and 3–68 for Im($${\epsilon }_r$$).

Figure 4

Binned and interpolated values of average real (top) and imaginary (bottom) parts of the permittivity ($${\epsilon }_r^{\prime }$$ and $${\epsilon }_r^{″}$$, respectively) across all frequencies. Note that the colour bar limits were adjusted for better contrast, the actual ranges are 7–65 for Re($${\epsilon }_r$$) and 3–68 for Im($${\epsilon }_r$$).

Figure 5

Interpolation permittivity results, average real (top) and imaginary (bottom) parts (ε′ and ε″, respectively), for data imputing for rat 3 at a frequency of 500 MHz for different interpolation methods: nearest neighbour (blue) and spline interpolation with orders of 0 (zero, orange), 1 (linear, green) and 2 (quadratic, red).

Figure 6

Feature importance across 1000 runs of the nested cross-validation loop for the extremely randomised trees regressor.