Limits of Effective Material Properties in the Context of an Electromagnetic Tissue Model

Most calibration schemes for reflection-based tissue spectroscopy in the mm-wave/ THz-frequency range are based on homogenized, frequency-dependent tissue models where macroscopic material parameters have either been determined by measurement or calculated using effective material theory. However, as the resolution of measurement at these frequencies captures the underlying microstructure of the tissue, we will investigate the validity limits of such effective material models over a wide frequency range (10 MHz - 200 GHz). Embedded in a parameterizable virtual workbench, we implemented a numerical homogenization method using a hierarchical multiscale approach to capture both the dispersive and tensorial electromagnetic properties of the tissue, and determined at which frequency this homogenized model deviated from a full-wave electromagnetic reference model within the framework of a Monte-Carlo analysis. Simulations were carried out using a generic hypodermal tissue that emulated the morphology of the microstructure. Results showed that the validity limit occurred at surprisingly low frequencies and thus contradicted the traditional usage of homogenized tissue models. The reasons for this are explained in detail and thus it is shown how both the lower “allowed” and upper “forbidden” frequency ranges can be used for frequency-selective classification/identification of specific material and structural properties employing a supervised machine-learning approach. Using the implemented classifier, we developed a method to identify specific frequency bands in the forbidden frequency range to optimize the reliability of material classification.