2.3. Permittivity Estimation

Because qualitative radar imaging does not directly provide dielectric property values, the next step of our approach is the estimation of relative permittivity and effective conductivity in the region of interest from the reconstructed UWB radar images. We assume that the image values I(r0,T) in the region of treatment are depending on two parts: the dielectric contrast between background material and tumor tissue, as well as on the aggregation of all other temperature independent influencing parameters (e.g., the radar cross section of the tumor, signal path attenuation, impulse response of radar and antennas, etc.) which we do not know exactly, and we cannot quantify separately, especially because the treatment area is located in the near field. Therefore, they are summarized within the parameter F:

Since all parameters included in F remain constant during hyperthermia treatment, only the dielectric contrast between background and tumor will change [29]. For the sake of simplicity, specular reflection is assumed at the boundary between the background medium and the tumor and approximate the effect of dielectric contrast in (Equation (7)) by means of the complex reflection coefficient Γ:

where ε_bg and ε_t are the complex relative permittivities of the background and tumor region to be heated, respectively.

From the initial clinical imaging and the database of tissue specific dielectric properties (see Figure 1), we know the correct localization and size of the tumor and can specify the permittivity of tumor and background at the beginning of treatment. The reflection coefficient and the corresponding UWB image at the starting time T = 0 are used as reference and refer to Γ_ref(r0,ω)=Γ_(r0,ω,T=0) and Iref(r0)=I(r0,T=0), respectively. During the treatment, we relate the ongoing images to this reference image:

In this way, the effect of F_(r0) is eliminated, and the changing permittivity ε^_t(r0,ω,T) can be estimated:

It has to be emphasized that this approach is only able to estimate the permittivity and temperature, respectively, inside the target to be treated. This is because outside this area Γ_ref(r0,ω)=0, Equation (10) yields ε^_t(r0,ω,T)=ε_bg(ω) independently from I(r0,T).