# Phase Compensation Technique for Effective Heat Focusing in Microwave Hyperthermia Systems
## 3 Electromagnetic Focusing for Microwave Hyperthermia  
### Electromagnetic Focusing for Unified Breast Cancers  
Each TSA antenna radiates with precise input phase characteristics to provide effective treatment to randomly positioned cancer cells in the breast phantom. The radius of the breast tumor for microwave hyperthermia treatment was set at 5 mm. The breast tissue properties of the fat and the tumor applied to all simulations are presented in Table 1 to verify the SAR and temperature distributions. The phase delay of each antenna \((\varphi_{n})\) should be compensated to focus the E-field on the target position, thereby localizing the heat operation to a treatment area. The input phase characteristics of the TSA antenna array can be defined by compensating the phase delay caused by the different path lengths of the antennas to the target tumor. Hence, the in-phase condition of the radiated E-fields can be satisfied with an unifocal breast cancer, leading to strong constructive interference. Figure 5 presents a schematic view of the EM waves focusing on the breast phantom while the array configuration encircles the breast phantom. The phase delay of each antenna is calculated to meet the requirements for the in-phase condition of the E-field deep inside the phantom. The locations of the antennas are defined as \((\mathbf{x}_{n},y_{n})\) and the cancer location in the phantom is defined as \((\mathbf{x}_{\text{t}1},y_{\text{t}1})\). The path length from each antenna to the cancer location defined by 2D Cartesian coordinates can be defined as:  
\[\text{PL}_{n}\ =\ \sqrt{(x_{\text{t}1}-x_{n})^{2}+(y_{\text{t}1}-y_{n})^{2}} \tag{4}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Fat** & **Tumor** \\ \hline Dielectric permittivity \(\varepsilon_{r}\) & 5.14 & 55 \\ Loss tangent tan \(\delta\) & 0.137 & 0.29 \\ Density \(\rho\) (kg/m\({}^{3}\)) & 920 & 920 \\ Thermal conductivity \(\sigma\) (W/K/m) & 0.42 & 0.42 \\ Heat capacity \(C_{\text{P}}\) (J/K/kg) & 3000 & 3000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dielectric and thermal properties of breast tissues at 2.45 GHz [32]. where \(n\) is the current antenna number. The radius of the breast phantom is 50 mm, with the middle defined as (0,0), so with Cartesian coordinates, each path length between the radiating antenna and cancer location can be calculated and converted to the phase as follows:  
\[\varphi_{\text{PL}_{n}}\ =\ k\times\text{PL}_{n}\times\frac{180}{\pi}\ =\ \frac{2\pi}{\lambda_{\text{eff}}}\times\text{PL}_{n}\times\frac{180}{\pi} \tag{5}\]  
where \(k\) is the wave number, and \(\lambda_{\text{eff}}\) is the effective wavelength in the phantom (\(\varepsilon_{\text{r}}\ =\ 5.14\)) at 2.45 GHz. To determine the input phases of each antenna, the phase delay should be calculated accordingly:  
\[\varphi_{n}\ =\ \varphi_{\text{PL}_{n}}-\varphi_{\text{min}} \tag{6}\]  
where \(\varphi_{\text{min}}\) is the minimum phase value among the 12 path lengths. Therefore, the calculated final input phase \(\varphi_{n}\) is the total compensating input phase to satisfy the in-phase condition on the focusing area. Thus, \(\varphi_{n}\) of each antenna is calculated depending on the tumor position. To verify that the EM was focusing on the unifocal cancer, the input phases of each antenna when the tumor was positioned at (20,0) mm and (15,15) mm were calculated for the _xy_-plane in Table 2. These calculated input phases \((\varphi_{n})\) were aimed to enhance the constructive interference of the E-field at the focal point, which leads to a high SAR distribution on the treatment area. The maximum SAR distribution values at (20,0) mm and (15,15) mm according to the _xy_-planes presented in Figure 6a,b are 23.1 W/kg and 27.7 W/kg, respectively, at the focal points.