## 2 Methods
### Simulation Setup  
We performed EM simulations using the commercial software Sim4 Life (Zurich med tech, [[https://zmt.swiss/sim4](https://zmt.swiss/sim4) life/]([https://zmt.swiss/sim4](https://zmt.swiss/sim4) life/), accessed on 10 March 2021). Sim4 Life is an FDTD based software to solve Maxwell's equations and for electromagnetic analysis, it also provides computation of the temperature based on the RF excitation from an antenna. Two types of EM simulations were performed, one for acquiring a \(\mid\)B\(\mid\) -field operating at 300 MHz for MRI applications and the other to produce an electric field at 1.06 GHz which was consequently used to compute the temperature rise in the target cancer-mimicking tissue. We used the antennas shown in Figure 4, and the dielectric material selected was a Rogers  
Figure 3: (**a**) The reduced patch antenna in the vertical and horizontal directions, (**b**) the ground plane meandering pattern and (**c**) the patch (**top**) plane meandering pattern. Figure 2: The design of the patch antenna (**a**) with reduction in the horizontal direction, (**b**) the ground plate showing the meandering pattern and (**c**) the diagram of the meandering pattern and dimensions. RT duroid 6006 with a conductivity of 0.0015 S/m and permittivity of 6.45 at 300 MHz and 1.06 GHz. We excited the antennas with a Gaussian pulse with a central frequency of 300 MHz and 600 MHz bandwidth, and the second simulation using a central frequency of 1.06 GHz with a bandwidth of 2 GHz. To produce a uniform magnetic field, we used two patch antennas positioned along the \(z\)-axis and exited with a phase difference such that the field between them was highly uniform. For this purpose, we placed a second patch antenna and rotated it by 90\({}^{\circ}\) phase with around the \(z\)-axis. By having two antennas in the \(x\)-\(y\) plane and applying a 90\({}^{\circ}\) phase difference, a uniform circular polarized magnetic field can be produced. Using this configuration, a circular magnetic field was produced in the middle of the antennas. With this configuration, a focused \(|\) E\(|\)-field can be achieved. Figure 4 shows the arrangement of the double patch antennas. In Figure 4a the cylindrical phantom is shown with the patch antennas. Figure 4b shows the rat model with the orientation between the patch antennas, and also indicating in highlighted red color the cancer-mimicking voxels. A cylindrical phantom with a radius of 30 mm and a length of 80 mm was positioned along the \(z\)-axis to demonstrate the capabilities of the patch antenna arrangement, with electrical properties equivalent to the tissues of the large intestine with an electrical conductivity and permittivity of 0.77 S/m and 58.20, respectively, at 300 MHz. The spherical cancer-mimicking tissue is a sphere of 5 mm radius that was placed in the middle of the cylinder phantom. The cancer-mimicking tissue had a conductivity of 1.05 S/m and permittivity of 62.85, these values were based on previously reported results on electrical properties measurements of rodent's cancers [32]. For RF heating, the electrical properties were updated using the database and model provided by the Sim4 life. The values set at 1.06 GHz for the cylindrical phantom were 1.0 S/m and 54.7 for electrical conductivity and permittivity, respectively. To update the values of the spherical cancer-mimicking tissue we used the ref. [32] for which the conductivity was set to 1.2 S/m and the permittivity to 59.6. Furthermore, we used the computed \(|\) E\(|\)-field to estimate the temperature change inside the phantom. The changes in the induced temperature (\(T\)) of a tissue over time (t) are described by the Pennes bioheat equation (PBE) [21; 33], which is given by  
\[\rho C_{p}\frac{\partial T}{\partial t}=\
abla\cdot(k\
abla T)+Q_{m}+SAR+\rho_ {b}C_{p,b}\rho\omega_{b}(T_{a}-T) \tag{2}\]  
Figure 4: The arrangement of the double patch antenna (a) for a cylindrical phantom and (b) a rat model, showing the cancer-mimicking tissue.