Estimation of the Parameters of the Havriliak-Negami Model for Breast Phantoms

This article is devoted to determining the parameters of the Havriliak- Negami dielectric model for breast phantoms using dielectric impedance spectroscopy. Experimental studies of homogeneous and inhomogeneous breast phantoms were conducted using a two-electrode capacitive sensor. The impedance components of the sensor with phantoms were measured using a precision RLC meter in the frequency range of up to 2 MHz. The original technique for processing the results of breast phantom bioimpedance measurements is based on the analytical solution of the inverse problem for the Havriliak-Negami model obtained by the authors and the use of the least squares method to optimize the parameters. The applicability of the model and the method for numerically finding its parameters was experimentally confirmed. The obtained model data coincide quite accurately with the experimental data. A number of statistical parameters, including the Hausdorff metric, were used for the assessment. The difference in the frequency response curves of the target inhomogeneous phantom by the MAEP parameter was about 0.2% for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{E}^{\prime}$</tex> component and about 3.5% for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{E}^{\prime\prime}$</tex> component, by the Hausdorff distance about 0.2 and about 0.007 for the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{E}^{\prime}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{E}^{\prime\prime}$</tex> components respectively.