Sensing volume of open-ended coaxial probes for dielectric characterization of breast tissue at microwave frequencies

We have used open-ended coaxial probes to determine the dielectric properties of freshly excised normal and diseased breast tissue specimens. The considerable variability in size and composition of these specimens predicates the need for determining the minimum surgical specimen size that yields accurate measurements for a given probe diameter. We investigate the sensing volume of 2.2- and 3.58-mm-diameter flange-free coaxial probes for both lowand high-water-content tissue using standard liquids that exhibit dielectric properties similar to breast tissue over the microwave frequency range from 1 to 20 GHz. We also present an innovative graphical technique based on the use of Cole-Cole diagrams to determine the error thresholds in the magnitude and phase of the reflection coefficient, which bound the errors in the measured complex permittivity to an acceptable level. Results from self-consistent experiments and finite-difference time-domain simulations indicate that a tissue specimen with a thickness of 3.0 mm and a transverse dimension of 1.1 cm is the minimum size that yields accurate measurements with the 3.58-mm-diameter probe. For the 2.2-mm-diameter probe, the specimen's thickness and width should be at least 1.5 and 5 mm, respectively. These conclusions are relevant not only to breast tissue characterization, but also more generally to the dielectric characterization of a variety of low- and high-water-content biological tissues.