## 2 Materials and Methods
In this frequency range the wavelength of the electromagnetic wave in the lung tissue has a dimension comparable to that of a solitary pulmonary nodule of 8 mm, which is the  
Figure 1: Dielectric properties of lung tissue taken from the Tissue Properties Database [15]. (**a**) relative dielectric permittivity \(\epsilon_{r}\) and conductance \(\sigma\) of lung tissue. (**b**) Wavelength \(\lambda\) and attenuation \(\alpha\) of a plane wave traveling through lung tissue (calculated from **a**). Figure 2: Schematic of the 3D computational domain. The violet parallelogram represents the lung medium. Inside the lung medium, the target is present (red sphere). On top of the lung medium a \(3\times 3\) antenna distribution is shown. A simulation was performed at each of these positions. The edge of the Perfectly Matched Layers (PMLs) are shown in red. threshold size for diagnosis (see Figure 1b). Note that higher frequencies would provide higher spatial resolution, but their attenuation in the lung tissue increases quickly (see Figure 1b). Ten-cells wide perfectly matched layers (PML) as highlighted in red in Figure 2 were used to truncate the computation in all the directions and the discretization was either 12 divisions per wavelength at the central frequency or 1 mm according to the smallest size. A pulmonary nodule was simulated by a spherical target with 0.5 cm of radius placed in the middle of the lung, as it is recommended that nodules larger than 8 mm should be biopsied or surgically excised for diagnosis [4,6]. Six target depths between one and six centimeters were investigated. The permittivity and conductivity of the cancer were taken from the work of [PERSON] et al. [21] where it was found that at 100 MHz, lung cancer had permittivity three times and conductivity two times larger than that of the lung medium. A monostatic antenna assembly was made of a voltage source with 50 Ohm impedance and \(z\) polarization and a simple receiver. The receiver recorded the value of the electric field at the position of the voltage source. This configuration is less effective than a real physical model of an antenna, but it allows us to study the backscattered signals independently of the antenna characteristics such as bandwidth and gain directivity. Note that, for most of the frequencies selected, the antenna would be receiving signals from within its near field, that is at a distance lower or comparable with the wavelength of the electromagnetic wave employed. Only at the higher frequencies or larger distances, the antenna operates in its far-field (see Figure 1b). The position of the antenna was changed according to a regular grid of size \(3\times 3\), \(4\times 4\), and \(5\times 5\) as shown in Figure 2. A simulation was run for every antenna position resulting in nine simulations for the \(3\times 3\) grid, 16 for the \(4\times 4\), and 25 for the \(5\times 5\). The antennas were spaced according to one wavelength of the electromagnetic wave in the lung medium. Any object as antenna and nodule target were at least thirty cells away from the end of the computation domain. The target was always located exactly under the center of the antenna grid. This represents the best configuration. Changing the alignment between the antenna grid and the target could create more realistic results, but it would also introduce additional degrees of freedom in the pool of simulations, which is not necessary as preliminary analysis. This approach was designed to mimic a series of real measurements, where either an array of antennas is positioned at the surface of the lung or a single antenna is moved at several positions on the lung surface. In the first case one single measurement is taken at every one of the antenna positions as, for example, when a physical switch would connect it to the transceiver apparatus. In the second case the same antenna would be used to perform more measurements at different locations.