# Phase Compensation Technique for Effective Heat Focusing in Microwave Hyperthermia Systems
## 3 Electromagnetic Focusing for Microwave Hyperthermia
### Electromagnetic Focusing for Multifocal Breast Cancer  
In the case of multifocal breast cancer, time and costs can be reduced by treating multiple tumors simultaneously rather than sequentially. Unlike for a single tumor, the calculation method for the input phases \((\varphi_{n})\) for multiple targets should be modified to deliver precise EM energy deposition. In deep-seated tumors, the TSA antennas should transfer adequate energy to necrotize the tumor cells without harming the normal tissue. To enhance the thermal focusing, an exquisite phase control technique should be applied to each microwave antenna, and unwanted electric field focusing should be avoided. Thus, the multiple E-field focusing technique with a sub-array antenna configuration and phase compensation technique will be discussed. The configuration of the E-field focused on two breast tumors with an antenna sub-array is presented in Figure 7. The radii of the two breast tumors for multifocal breast cancer were set at 5 mm as well. The magnitude of the radiated E-field is decreased due to the dielectric loss component of the breast phantom. Therefore, in terms of the tumor positions, designating the antennas that are closest to the tumor cell as a sub-array ensures E-field concentration on each breast tumor. Therefore, as shown in Figure 7, sub-arrays #1 and #2 consist of antennas #1-6 and #7-#12, respectively. Tumor cells #1 and #2 are located at positions \((x_{\text{t1}},\ y_{\text{t1}})\) and \((x_{\text{t2}},y_{\text{t2}})\) in the phantom, respectively. To focus the E-field on two breast tumors at the same time, each antenna sub-array radiates the E-field onto tumor cells #1 and #2. The input phase of each antenna sub-array should be calculated separately to provide optimal focusing depending on the multiple targets. The phase delay of each antenna is calculated to meet the requirement of the in-phase condition of the E-field deep inside the phantom. Hence, the path length from each antenna sub-array to the tumor cells using 2D Cartesian coordinates can be defined as follows:  
\[\text{PL}_{n1}\ =\ \sqrt{\left(x_{\text{t1}}-x_{n1}\right)^{2}+\left(y_{\text{t1} }-y_{n1}\right)^{2}}\text{PL}_{n2}\ =\ \sqrt{\left(x_{\text{t2}}-x_{n2}\right)^{2}+\left(y_{\text{t2}}-y_{n2}\right)^{2}} \tag{7}\]  
where \(n_{1}\) and \(n_{2}\) are the antenna numbers of sub-arrays #1 and #2, respectively. The calculated path lengths can be converted to the phases of each sub-arrays accordingly:  
\[\varphi_{\text{PL}_{n1}}\ =\ k\times\text{PL}_{n1}\times\frac{180}{\pi}\ =\ \frac{2\pi}{\lambda_{\text{eff}}}\times\text{PL}_{n1}\times\frac{180}{\pi} \varphi_{\text{PL}_{n2}}\ =\ k\times\text{PL}_{n2}\times\frac{180}{\pi}\ =\ \frac{2\pi}{\lambda_{\text{eff}}}\times\text{PL}_{n2}\times\frac{180}{\pi} \tag{8}\]  
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, and \(\varphi_{\text{PL}_{n1}}\) and \(\varphi_{\text{PL}_{n2}}\) are the calculated phases of antenna sub-arrays #1 and  
Figure 6: The 2D section of SAR distributions focused at different tumor positions: (**a**) (20,0) mm and (**b**) (15,15) mm. #2, respectively. To decide the input phases of each antenna, the phase delay should be calculated as follows:  
\[\varphi_{n1}\ =\ \varphi_{\text{PL}_{n1}}-\varphi_{\text{min1}}\varphi_{n2}\ =\ \varphi_{\text{PL}_{n2}}-\varphi_{\text{min2}} \tag{9}\]  
where \(\varphi_{\text{min1}}\) and \(\varphi_{\text{min2}}\) are the minimum phase values of the phases in sub-array #1 and #2, respectively. Therefore, the calculated final input phases \(\varphi_{n1}\) and \(\varphi_{n2}\) are the total compensating input phases to satisfy the in-phase condition of each tumor. Thus, \(\varphi_{n1}\) and \(\varphi_{n2}\) of each antenna are calculated and applied depending on the position of the tumor cells. The positions of two tumor cells at (15,10) mm and (\(-15,-10\)) mm on the \(xy\)-plane are presented in Figure 8a.