Penetration Depth Quantification of Open-ended Coaxial Probes for Dielectric Spectroscopy of Layered Media

Dielectric spectroscopy using open-ended coaxial probes is a powerful tool for biological tissue classification. It measures the complex permittivity of a medium as a function of frequency by applying an electromagnetic field and observing the energy reflected back. In heterogeneous tissue, a critical parameter that defines the accuracy of permittivity measurement is the penetration depth (PD) of the electromagnetic field for a given probe geometry, however, it is still unclear how the tissue characteristics affect the PD and the accuracy of the measurements. This paper evaluates the effect of various tissue and probe parameters on the PD in the context of dielectric spectroscopy through an open-ended coaxial probe. The PD is evaluated under different simulation conditions considering a probe inserted into a 2-layered tissue with different dielectric characteristics in 54,000 different simulations. A model for extracting the permittivity from the simulated reflection coefficient is also described. The results show for the first time that the PD increases as the difference in permittivity and conductivity between the layers increases, suggesting that measurement accuracy is sensitive to changes of contrast in the layer's characteristics. The results also show that the PD decreases with the excitation frequency but increases with the diameter of the coaxial probe. These findings can greatly aid in quantifying and understanding the sensitivity of biological tissue classification using dielectric spectroscopy.