## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Tumor Size**} & \multicolumn{3}{c}{**Tumor Size**} \\  & \(r\) = 10 mm & & & \(r\) = 12 mm & \\ \hline \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** & \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** \\  & \(P_{i}\) (W) & \(\phi_{i}\) (\(\circ\)) & & \(P_{i}\) (W) & \(\phi_{i}\) (\(\circ\)) \\ \hline
1 & 0.4054 & 14.6487 & 1 & 0.3320 & 23.0597 \\
2 & 3.7182 & \(-\)52.4283 & 2 & 4.3765 & \(-\)43.1907 \\
3 & 2.4654 & 8.4417 & 3 & 2.4697 & 11.1388 \\
4 & 0.4516 & 140.2195 & 4 & 0.2764 & 148.3518 \\
5 & 0.0036 & \(-\)125.5640 & 5 & 0.0077 & \(-\)99.0500 \\
6 & 0.0066 & 12.1489 & 6 & 0.0456 & \(-\)37.1462 \\
7 & 0.1896 & 18.0303 & 7 & 0.0842 & \(-\)42.1068 \\
8 & 0.7596 & 0 & 8 & 0.4079 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 6: Normalized specific absorption rate (SAR) distributions in the \(xy\) plane from an eight-dipole antenna array after the optimization procedure (sum \(P_{i}\) = 8W) for various tumor radii: (**a**) \(r\) = 4 mm; (**b**) \(r\) = 6 mm; (**c**) \(r\) = 8 mm; (**d**) \(r\) = 10 mm; (**e**) \(r\) = 12 mm; (**f**) \(r\) = 12 mm—before the optimization procedure (\(\phi_{i}\) = 0 and \(P_{i}\) = 1 W). Figure 6f shows an example of SAR distribution for a tumor radius \(r=12\) mm; however, this was before applying the optimization algorithm (all antennas operate with the same \(P_{i}\) and \(\phi_{i}\) values). In this case, the SAR values within the breast tissues around the applicators were similar and had values below 207 W/kg, which illustrates the advantage of warm colors. On the other hand, with optimized SAR distributions, warm colors were concentrated in the immediate vicinity of the breast cancer, which corresponds to an increased power dissipation and heat accumulation in this area. Figure 7 depicts the distributions for the heat source (\(Q=\rho\)SAR) in the \(xy\) plane of the breast model passing through the tumor center (\(z=0\)) after the optimization procedure. Similar distributions for temperature are presented in Figure 8. Additionally, the cross sections in the \(zy\) plane for the female breast phantom passing through the tumor center (\(x=0\)) are included in Figure 8. It should be noted from the given drawings that the optimization algorithm used is good at dealing with tumors of various sizes. However, for larger tumors with radii greater than \(r=6\) mm, its reliability is much better. Figures 9 and 10 present the heat source (\(Q=\rho\)SAR) and temperature dependencies through the tumor along the \(y\)- and \(x\)-axes, respectively. All curves are referred to the tumor center and compare the distributions for tumors of different sizes. Larger changes in the analyzed parameters are observed along the \(x\)-axis than the \(y\)-axis of the tumor, which results from the arrangement of various tissues around breast cancer and different perfusion rates characterizing breast tissues. Additionally, the character of \(Q\)-profiles strongly depends on the density of the tumor and neighboring tissues. This implies that homogeneous temperature distribution inside the whole tumor volume cannot be achieved in practice by using the described optimization procedure. However, a specific carcinoma's behavior can be seen in the performed in silico simulation, namely, for tumors of larger size, higher temperature levels are induced in the tumor. Figure 7: The distributions of power dissipation (\(Q=\rho\)SAR) in the \(xy\) plane for various tumor radii: (**a**) \(r=2\) mm; (**b**) \(r=4\) mm; (**c**) \(r=6\) mm; (**d**) \(r=8\) mm; (**e**) \(r=10\) mm; (**f**) \(r=12\) mm—derived from the eight–dipole antenna array after the optimization procedure (sum \(P_{i}=8\) W). Figure 11 illustrates radius-dependent heat accumulation inside the analyzed breast tumors, according to the modified [PERSON] bioheat equation (Equation (1)).