## 2 Numerical Method and Simulation Conditions
Black, green, light blue, and brown colors correspond to conducting material, Teflon, air, and dielectric, respectively. The width of the slot is 0.6 mm, while the spacing between slots is 0.8 mm. Figure 2: Three-dimensional (**a**) simulation model of the liver (triangulated surface) and an early-stage HCC (solid surface) corresponding to patient 16 in the 3D-IRCADb-01 database [70] and (**b**) configuration of the antenna inserted into biological tissue and positions of four test points (A, B, C, D). During MWA, the elevated temperatures reached by the tissue close to the antenna cause structural modifications of treated tissue, resulting in changes in the dielectric and thermal properties that affect the electromagnetic power distribution. Since dielectric properties of the tissue are temperature-dependent [78; 79], we used the expressions [68; 80]:  
\[\epsilon_{\rm r}(T)=s_{\rm 1}\left[1-\frac{1}{1+\exp(s_{2}-s_{\rm 3}T)}\right], \tag{2}\]  
\[\sigma(T)=r_{\rm 1}\left[1-\frac{1}{1+\exp(r_{2}-r_{\rm 3}T)}\right], \tag{3}\]  
with coefficients taken from [68]. Figure 3 displays the sigmoidal temperature-dependent model of (a) relative permittivity and (b) electric conductivity for healthy and tumoral tissues. As expected, relative permittivity and conductivity of liver tumors are around 24% and 11% higher than those corresponding to healthy liver tissue [81]. Due to the water evaporation during the MWA, dielectric properties of tissue decrease with increasing the temperature [82]. Additionally, the change rate of dielectric properties with temperature is the same in both healthy and tumoral tissues. Heat transfer during the MWA process can be accurately described by the Pennes bioheat equation [83]:  
\[\rho c\frac{\partial T}{\partial t}=\
abla\times(k\
abla T)+\rho_{\rm b}W_{\rm b }c_{\rm b}(T_{\rm b}-T)+Q_{\rm ext}+Q_{\rm m}, \tag{4}\]  
where \(t\) is time, \(\rho\), \(c\), and \(T\) are the density, the heat capacity, and the temperature of the tissue, respectively, and \(\rho_{\rm b}\), \(c_{\rm b}\), \(T_{\rm b}\), and \(W_{\rm b}\) are the density, the heat capacity, the temperature, and the perfusion rate of the blood, respectively. The heat source from metabolism \(Q_{\rm m}\) is neglected in our calculation, while the external heat source \(Q_{\rm ext}\) describes coupling with electromagnetic field and is given by:  
\[Q_{\rm ext}=\frac{\sigma\left|\mathbf{E}\right|^{2}}{2}. \tag{5}\]  
The tissue thermal conductivity \(k\) varies with the temperature [68; 84]:  
\[k(T)=\kappa_{0}+\Delta k|T-T_{0}|, \tag{6}\]  
Figure 3: The temperature dependence of (**a**) relative permittivity and (**b**) electric conductivity of the healthy (red circles) and tumoral liver tissue (blue diamonds). Plots are obtained by using expressions (2) and (3) with coefficients taken from the literature [68]. where \(k_{0}\)_is_ the thermal conductivity measured at temperature \(T_{0}\), while \(\Delta k\) represents the change in \(k\) due to temperature. Blood perfusion dictates the bioheat transfer in living tissues. The difference in temperature between blood and tissue leads to convective heat transfer, so the blood perfusion rate \(\omega_{\text{b}}\) is also a function of temperature [68]:  
\[\omega_{\text{b}}=2.1\times 10^{-5}T+3.5\times 10^{-3}. \tag{7}\]  
Another important temperature-dependent parameter is water vaporization, which influences specific heat. The water content \(W\) is given by the expression [85]:  
\[W(T)=\left\{ \begin{array}{l}0.778\cdot\left(1-\text{e}^{\frac{T-100}{3.42}} \right),\ 70\ ^{\circ}\text{C}\leq T<100\ ^{\circ}\text{C}\\ 7.053-0.064096\cdot T,\ 100\ ^{\circ}\text{C}\leq T<104\ ^{\circ}\text{C}\\ 0.778\cdot\text{e}^{-\frac{T+30}{3.57}},\ \ T\geq 104\ ^{\circ}\text{C}\end{array} \right. \tag{8}\]  
At steady state, the water content of liver tissue is around 78% water by mass, as depicted in Figure 4a.