A Guideline for Complex Permittivity Retrieval of Tissue-Mimicking Phantoms From Open-Ended Coaxial Probe Response With Deep Learning

In this work, we proposed a general guideline and a technique for retrieving the complex permittivities (CPs) of material under test (MUT) from the measured reflection coefficients (RCs) obtained with the open-ended coaxial probe (OECP) through a deep learning model (DLM). Particularly, lossy materials such as phantoms mimicking the biological tissues are considered as MUT in this study. The dataset used to design (train, validate, and test) the DLM is synthetically generated using the relationship between the CPs of the MUT, namely, admittance model, and the four-pole Cole-Cole relaxation model. Moreover, the technique is implemented to accurately predict the CPs of biological tissues with real measured RCs' data from 0.5 to 20 GHz with a 50-MHz resolution. This technique eliminates the need to physically perform measurements required to create the dataset for DLM and it can be easily implemented for real-time CPs' measurement of biological tissues. The designed DLM is initially trained, validated, and tested with 80%, 10%, and 10% of the total generated synthetic dataset, respectively. A percent relative error of 1.5 ± 0.88% is obtained for CPs' prediction at the test stage. Furthermore, DLM is tested with real RCs' data measured from four different tissue-mimicking phantoms: skin, muscle, blood, and fat. Predicted CPs from DLM are compared with the CPs' results obtained from a commercially available OECP measurement kit. A (mean) ± (std.dev) percent relative error ranging from 2.08 ± 0.4 to 10.84 ± 2.43 within the frequency band of interest was obtained after comparison.