Optimized Design of Microwave Tomography Techniques for Breast Cancer Detection

Microwave tomography aims at achieving a quantitatively accurate description of the electrical and geometrical characteristics of an assigned domain from the knowledge of incident fields and measures of the corresponding total or scattered fields. Due to the wide range of possible applications, the development of accurate and reliable techniques for solving the corresponding inverse scattering problem is nowadays a still important challenge. Recently, several contributions have suggested the use of microwave tomography based procedures in biomedical applications, such as breast cancer imaging. Breast cancer is still a common cause of death in women and early detection is an important part of effective treatments. The state-of-the-art screening technique is X-ray mammography which, while sensitive to tumors, has indeed limitations in distinguishing amongst malignant and benign tumors. Because of the very high difference, at microwave frequencies, of the electromagnetic properties of the malignant tissues with respect to the normal ones, microwave tomography appear as a possible effective tool in this context. As a matter of fact, microwave tomography can provide information that is complementary to mammography, as the resulting images indicate the differences in the electrical properties of the breast tissues, which also allows, at least in principle, to discriminate amongst the different types of tumors. On the other side, it is simple to understand that the reconstruction capabilities of the inverse scattering procedure (which is the core of a microwave tomography problem) play a key role, as a non accurate reconstruction may lead to either false alarms or lack of detection. With respect to this framework, in this communications, we show the usefulness of some theoretical tools which allow a somehow optimal design of the measurement set-up for an accurate imaging. In particular, by reasoning on the electromagnetic characteristics of the coupling medium, the desired space resolution and the degree of non-linearity of the underlying inverse scattering problem, useful criteria are derived for an optimal choice of the working frequency and of the electromagnetic characteristics of the matching liquid. Then, we exploit the reconstruction capabilities of two inversion methods: the recently introduced Contrast Source-Extended Born inversion method and the traditional and widely used Contrast Source inversion scheme. Preliminary numerical examples show how, by properly acting on the degrees of freedom of the problem (type of immersion liquid, working frequency and so on), it is possible to achieve good reconstructions and to accurately discriminate between different types of tumors when they are contemporary present.