Research summary: The role of the concentration and distribution of water in the complex permittivity of breast fat tissue

Tarek Said and Vasundara V. Varadan

Microwave and Optics Laboratory for Imaging & Characterization, University of Arkansas, Fayetteville, Arkansas, 72701 USA

Summary of research published in Biolelectromagnetics, Vol. 30, No. 8, pp. 669-677.

This paper is a theoretical study of a complex problem, predicting the dielectric properties of breast fat tissue in terms of its gross composition. Currently, microwave imaging has offered hope for safer diagnostic and tumor detection; however further experimental work is still needed.

Experimental studies of breast tissue permittivity in literature are available only at frequencies below 20 GHz and only at a few discrete selected frequencies. Debye and Cole-Cole relaxation models are frequently used to extrapolate the measurement to provide continuous data at higher microwave frequencies. Relaxation models serve essentially to parameterize the dielectric data without interpreting wide variations in the measurement data from one sample to another.

The approach used in this paper is an attempt to partly explain the wide variations in the measured complex permittivity data for breast fat tissue at microwave frequencies. In the microwave  frequency region, tissue permittivity can be determined mainly using the data on the free water. Past research has focused on the variation of dielectric properties of a biological tissue as a function of its water content. But the distribution of water in the tissue is also a strong contributor to the effective permittivity of the tissue. In this study we take into account both the concentration and distribution of water to model the dielectric permittivity of the tissue. This is an important area of study because water content and distribution is an indicator of tissue health.

Motivated by the overall need to improve breast cancer detection and characterization and our standing interest in advancing medical microwave imaging, we have proposed computational models of the dielectric permittivity of breast fat tissue varying with water content and distribution. In our study, we look at 1-D (fat layers interspersed with layers of water), 2-D (water tubules and fat tubules coated with water), and 3-D (water globules and fat globules coated with water) all of which show variations in dielectric permittivity for the same volume content of water. The 1-D and 2-D models may find application for different types of tissues such as skin, muscle or collagenous tissues.

The T-matrix multiple scattering formalism has been successful to compute effective properties of inhomogeneous media for arbitrary inclusion geometry. It is a good method to predict the effective permittivity of a heterogeneous material when either the concentration or the size of the suspended constituents is large. It has not been applied to model the dielectric permittivity of biological tissues. This paper proposes an application of this theory to fat/water mixtures to explain the dependence of the complex permittivity on water content as well as water distribution. The effective permittivity, obtained for different shape of water inclusions, is compared with experimental data from literature. Our results indicate that water distribution is another factor that contributes to the differences in the dielectric permittivity of samples of fat that have the same water content. Our model is a small but positive step to develop robust models for microwave biomedical diagnostics.