## 2 Materials and Methods
### Numerical and Experimental Phantoms  
The original MRI-derived Zubal head phantom [45] comprises 256 \(\times\) 256 \(\times\) 128 voxels with size of 1.1 mm \(\times\) 1.1 mm \(\times\) 1.4 mm. First, we imported the phantom into CST Microwave Studio to obtain the numerical \"measured\" data (S-parameters) of the full-wave 3-D interaction of the experimental antenna array with the phantom, which is used to test the 3-D algorithm. We then resized the model to fit the FDTD's grid of 2 mm for each side. We have also transformed the original Zubal head model from dozens of materials into an eight-material head model. The permittivity of the materials used in CST was obtained from the IT'IS foundation database [52]. These data were also used to develop single-pole Debye models for our FDTD code by curve fitting. As these two approaches are not identical, there are discrepancies between the CST and FDTD Debye models. The 3-D structure of the Zubal head phantoms in CST is shown in Figure 2.  
As for the 2-D cases, a slice of the Zubal head phantom inside the brain is used in FDTD as shown in Figure 2d. The model includes eight layers with tissue types, color codes and respective Debye parameters (for our FDTD models) shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Resolution** & **Grid Size** & **Time** \\ \hline
2 mm & \(150\times 150\times 100\) & 31 s \\
1.5 mm & \(225\times 225\times 150\) & 59 s \\
1 mm & \(300\times 300\times 200\) & 176 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average running time for each antenna. Figure 2: Views of the Zubal phantom in CST: (**a**) 3-D side-view, (**b**) cross-sectional top-down view, (**c**) 3-D view with blood target inserted, (**d**) cross-sectional slice used in the 2-D experiments (93 th slice of the original model, where the center of the target is placed). These phantoms are used for the “Case I” imaging scenario described in Section 3. The head models are surrounded by 90-10% glycerol-water mixture, which we have used previously as immersion liquid in our recent experiment work [53; 54]. The permittivity of the glycerol-water mixture is \(\varepsilon_{r}\approx 15.9-14.2j\) at 1.0 GHz. The Debye parameters \(\varepsilon_{\infty}=6.566\), \(\Delta\varepsilon=16.86\) and \(\sigma_{\mathrm{s}}=0.3231\). The relaxation time \(\tau\) is fixed as 0.14288 ns for all the materials. Starting from this head model, we have studied various different imaging scenarios, which will be discussed in next section. Moreover, we have used a simplified experimental head phantom [54] shown in Figure 3 to validate our algorithm with more realistic data. The phantom is made of a 3D-printed plastic mould and is filled with an \"average brain tissue\" material with \(\varepsilon_{r}\approx 41.6-5.9j\) at 1.0 GHz. We should note that the permittivity of the brain tissue differs at different positions, i.e., the permittivity near the different surface, in the inner parts or near the bottom has different values [54]. The brain phantom is immersed in the 90-10% glycerol-water mixture inside an imaging tank, which is made of acrylic and is surrounded by absorbing material ECCOSORB MCS covered by a metallic shield. A printed monopole triangular patch antenna is used, as shown in Figure 3c, which operates well in the frequency range 0.5-2 GHz [55]. An eight-antenna array inside the tank captures MWT data with the help of an eight-port VNA system embedded in the Keysight M9019A PXIe Chassis connected to a desktop, shown in Figure 3d,e. Further details of the experimental system and the process of making the phantom can be found in [54].