## 2 Materials and Methods
### Electrical and Thermal Characteristics of Biological Tissues  
Each biological component of the breast (see Figure 5) has its own values of physical parameters. The main characteristics include the thermal conductivity \(\lambda\), the heat capacity \(C\), the mass density of matter \(\rho\), the heat source power density due to metabolic processes \(Q^{(met)}\), the electrical conductivity \(\sigma\), and the permittivity \(\varepsilon\). Our analysis of these characteristics from the scientific literature is shown in Table 1, which allowed us to determine the ranges in which the values of such parameters vary. Moreover, the value of \(Q^{(can)}\) for tumors varies widely at different stages of disease development (see Figure 4). It should be emphasized that the electromagnetic parameters of various components may depend on the radiation frequency \(\
u\) (the data in Table 1 are given for the frequency \(\
u=1.5\) GHz). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\lambda\)**, W/(m\(\cdot\)K)** & \(C\)**, J/(kg\(\cdot\)K)** & \(\rho\)**, kg/m\({}^{3}\)** & \(Q^{(met)}\)**, W/m\({}^{3}\)** & \(\sigma\)**, S/m** & \(\varepsilon\) \\ \hline Skin & 0.21–0.54 & 3391–3690 & 1180–1215 & 380–410 & 1.1–2.4 & 40–50 \\ Muscles & 0.4–0.56 & 3421–3790 & 1070–1100 & 675–690 & 0.44–0.7 & 54–56 \\ Fat & 0.18–0.34 & 2348–2690 & 900–915 & 356–370 & 0.03 & 4–4–6 \\ Blood & 0.45–0.6 & 3800–4200 & 1046–1058 & 0 & 0.9–1.2 & 64–85 \\ Glands & 0.4–0.5 & 3700–3790 & 1035–1041 & 450–610 & 0.56–0.61 & 10.6–12 \\ Connective tissue & 0.44–0.5 & 3340–3400 & 1006–1020 & 604–620 & 0.3–0.36 & 38–40 \\ Cancers & 0.45–0.58 & 3710–3800 & 1045–1054 & 3000–71,000 & 0.79–1.5 & 42–50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The range of natural variability in the physical properties of the main components of the breast [62; 75; 76; 77; 78]. Figure 7: Procedure to construct a 3D breast model of different components in Blender: steps for constructing a single breast lobe model (**a–c**), system of the laciferous sinus and breast lobes (**d–e**), the blood flow includes arteries (red) and veins (blue) (**f**), the skin (g), the subcutaneous fat pad (**h**), and the section of the final 3D model of the breast with textures (**i**). The set of physical parameters of the breast model is determined by the vector \(\vec{\mathcal{F}}\), the meaning of which is similar to the vector \(\vec{\mathcal{G}}\) (see (2)):  
\[\vec{\mathcal{F}}=(\vec{F}_{A},\vec{F}_{C},\vec{F}_{\rho},\vec{F}_{Q},\vec{F}_{ \sigma},\vec{F}_{\epsilon},T_{air},T_{core}), \tag{5}\]  
where the dimension of each of the \(\vec{F}_{A,\ldots,\epsilon}\) vectors is equal to the total number of objects (\(K\)) that make up the entire model, \(T_{air}\) is the air temperature in the room during measurements, and \(T_{core}\) is the human core temperature (see Section 2.3 for detailed discussion). Each physical quantity is characterized by a corresponding possible deviation (see Table 1), for example, the heat capacity of fat varies within \(\delta C=\pm 171\) J/(kg\(\cdot\)K). We distribute the values of the components of the vector \(\vec{\mathcal{F}}\) according to the normal law similar to the geometric characteristics (see Section 2.1, Formulas (3) and (4)), which allows generating samples of models with random characteristics, each of which is determined by its own tuple \(\left\langle\vec{\mathcal{G}},\vec{\mathcal{F}}\right\rangle\). Physical characteristics vector  
\[\vec{\mathcal{F}}=\left\{f_{1}^{(1)},f_{2}^{(1)},\ldots,f_{k_{1}}^{(1)},f_{1 }^{(2)},f_{2}^{(2)},\ldots,f_{k_{2}}^{(2)},\ldots,f_{1}^{(K)},f_{2}^{(K)}, \ldots,f_{k_{K}}^{(K)},f^{(air)},f^{(core)}\right\}, \tag{6}\]  
is defined similarly to the vector \(\vec{\mathcal{G}}\) (see (2)), \(f_{j}^{(i)}\) is the \(j\)th physical characteristic (thermal conductivity, heat capacity, mass density, heat release rate, electrical conductivity, dielectric constant) for \(i\)th object, \(f^{(air)}=T_{air}\), \(f^{(core)}=T_{core}\).