## 3 Results  
### Computational Analysis to Determine the Optimum Phantom Size  
The minimum phantom size that reliably represents a whole body for implant communication and EM attenuation is addressed in this subsection according to the model described in Section 2.1. An iterative increase of its size was performed until field convergence.  
In order to set the direction for the size increment, a general scenario was analyzed. The electric field distribution in vertical polarization when a 1 V/m (peak) plane wave impinges upon one side of a 355 \(\times\) 160 \(\times\) 255 mm\({}^{3}\) phantom with muscle theoretical properties [25; 26; 27] is shown in Figure 4. It illustrates with the same scale the reflection at the boundaries (outside and inside) and the penetration into the phantom at the different commercial frequencies present in this study.  
Figure 4: _Cont._  
It was observed that, at 402 MHz and at 868 MHz, internal reflections became significant and the dimensions of the phantom should be increased to obtain a representative size of the whole body. However, the top view in Figure 4 is already considered a limit for the cross section of a representative human torso. Therefore, the geometrical dimension to be increased to pursue convergence will be done in the y direction (height). The chosen step was 100 mm. On the other hand, for the upper frequencies, at 2.45 GHz and at 5.8 GHz, the convergence was expected to happen before reaching this condition, and a cubical increment with a step of 50 mm will be performed in the three dimensions at the same time, as long as 355 mm and 255 mm limits are not overcome for x and z directions. By truncating at a certain size defined by a convergence criterion, computational and experimental resources will be saved.  
Figures 5 and 6 represent the simulated normalized electric field amplitudes with insertion distance at the four frequencies with tissue theoretical characteristics [25; 26; 27]. In all cases, the incident field was along the z direction, as mentioned. The difference between horizontal and vertical polarization was negligible due to the cubical symmetry of the phantom for the higher frequency cases (Figure 6), as expected.  
The size reductions with respect to a full body model estimated as 65 dm\({}^{3}\)[34; 35] are summarized in Table 3. It can be observed that important savings of manufacturing resources for phantom implementation was achieved in all cases and this reduction increased with frequency. A minimum volume reduction of 49.8% at 402 MHz for deep implants and up to a maximum of 99.8% at 5.8 GHz for subcutaneous systems with respect to the entire body was obtained.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Freq [GHz]**} & \multicolumn{3}{c}{**Size [mm]**} & \multirow{2}{*}{**Absorption [dB/mm]**} \\ \cline{2-3}  & x & y & z \\ \hline
0.402 & 355 & 260 & 255 & 0.16 \\
0.868 & 355 & 260 & 255 & 0.2 \\
2.45 & 200 & 200 & 200 & 0.4 \\
5.8 & 150 & 150 & 150 & 1.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Minimum phantom size that reliably represents an entire body for implant communication at a 10 mm to 50 mm insertion depth and corresponding absorption rate.  
Figure 5: Normalized electric field vs. insertion distance (z axis) computation using CST for a phantom dimension of (355 \(\times\) Y \(\times\) 255) mm. H polarization (continuous line) and V polarization (dashed line): (**a**) f = 402 MHz and (**b**) f = 868 MHz.  
Figure 6: Normalized electric field vs. insertion distance (z axis) computation using CST for a phantom dimension of (size mm \(\times\) size mm \(\times\) size mm. (**a**) f = 2.45 GHz and (**b**) f = 5.8 GHz.