## 3 Results  
Figure 5 contains the results of the test calculations for the liver tissue exposed to microwave frequency of 2.45 GHz and the input power of 10 W by using (a) 2D axial-symmetric and (b) full 3D simulation models. As can be observed, the temperature distributions obtained by both models are in an excellent agreement, confirming that the full 3D model that we developed could provide correct results and could be useful for realistic modelling of the effect of MWA on early-stage HCC. To determine the proper value of the input power that leads to the minimal tissue damage, calculations were carried out for a frequency of 2.45 GHz, ablation time of 600 s, and three values of the input power (10 W, 13 W, and 15 W). The optimal input power that causes minimal healthy tissue damage can be estimated from the isocontours related to the fraction of damage equal to 1, shown in Figure 6. For the input power of 10 W, tumoral tissue is not treated completely with MWA. When the input power is 15 W, the ablation zone encompasses the whole tumor, but some parts of healthy tissue are also damaged. The isocontour that best fits the necrotic tissue corresponds to the input power of 13 W, where the tumor is totally treated with minimal damage to the healthy tissue. Since the proper choice of the input power strongly depends on the size and the shape of the tumor, they have to be determined before any procedure in order to achieve the desired ablation margin. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \hline
**Tissue properties** & \\ \hline Density & 1079 kg/m3 \\ \hline Thermal conductivity & 0.52 W/m \({}^{\circ}\)C \\ \hline Specific heat & 3540 J/kg \({}^{\circ}\)C \\ \hline
**Tumor properties** & \\ \hline Density & 1040 kg/m3 \\ \hline Thermal conductivity & 0.57 W/m \({}^{\circ}\)C \\ \hline Specific heat & 3960 J/kg \({}^{\circ}\)C \\ \hline
**Blood properties** & \\ \hline Density & 1060 kg/m3 \\ \hline Thermal conductivity & 0.5 W/m \({}^{\circ}\)C \\ \hline Specific heat & 3600 J/kg \({}^{\circ}\)C \\ \hline Temperature & 37 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of biological materials (healthy liver tissue, tumoral liver tissue, and blood) were collected from the literature [68] and used in numerical simulations. Figure 7 shows (a) \(x\)-\(y\), (b) \(y\)-\(z\), and (c) \(x\)-\(z\) cut planes of the microwave power density absorbed in tumoral liver tissue during MWA at 2.45 GHz and input power of 13 W at the end of the 600 s ablation process. A microwave field oscillates rapidly, causing rotation of polar molecules, primarily water, and some amount of electromagnetic energy is absorbed. Close to the antenna, absorbed power density is large, and this decreases with distance. The energy emitted from the antenna through the tissue is converted into heat that destroys cancer cells. The majority of the heat is due to the excitement of polar water particles, while ionic polarization contributes to a minor part of the generated heat. The heated zone is almost spherical and encompasses the tumoral tissue. The input power and ablation time are chosen so that a very small area of healthy tissue around the tumor is heated. The absorbed energy converted into thermal energy leads to an increase in the tissue temperature, as shown in Figure 8. The boundary of the tumoral tissue is designated by the black line, while the white line represents the 60 \({}^{\circ}\)C isothermal contours. It was reported that cell death occurs instantly above 60 \({}^{\circ}\)C [54], so the 60 \({}^{\circ}\)C isothermal contour is linked to the lesion size and shape of the ablated tissue. The perfusion of blood restricts the extent of the heated area.