## 3 Numerical Results
Minimum, maximum, and median values and the first and the third quartiles of the \(SAR\) distributions are shown as boxplots in Figure 4. We can see that (i) the highest \(SAR\) values were obtained for the whole head, with a maximum of 8.35 mW/kg, a median of 0.42 mW/kg and a mean value of 1.23 mW/kg; (ii) the \(SAR\) values for the whole brain were around half of those computed for the head (maximum 4.17 mW/kg, median 0.16 mW/kg and mean 0.48 mW/kg), and (iii) the lowest values were obtained for the whole body with a maximum of 1.75 mW/kg, a median of 0.12 mW/kg, and a mean value of 0.32 mW/kg. The highest \(SAR\) values obtained for the whole head and for the whole brain could be explained considering the position of the UPA antenna with respect to the model. In fact, the head was with higher probability hit by the boresight beam of the UPA antenna (that is the beam with direction orthogonal to the array and providing the highest power) and this did not happen for the lower part of the body. Furthermore, we noticed that for all the three \(SAR\) distributions mean and median values were close, while the maximum values differed by about one order of magnitude w.r.t. them, meaning that the distributions concentrated in a small range around their mean values as the boxplots show. Figure 5 shows, for each surrogate model, a map of the \(SAR\) on the plane of the 1000 combinations of azimuth angles, in the range \((-50^{\circ},+50^{\circ})\), and elevation angles, in the range \((-25^{\circ},+25^{\circ})\) (first row of Figure 5), and two graphs, extracted from the corresponding map of \(SAR\), one varying the azimuth angles of the beam, fixed the elevation angle to \(0^{\circ}\) (second row of Figure 5), and the other one varying the elevation angles, fixed the azimuth angle to \(0^{\circ}\) (third row of Figure 5). The plots highlight the high variability of the exposure levels in all the three \(SAR\) distributions depending on the beamforming patterns in the H- and E-planes. To give a quantitative idea of this variability Table 2 reports the QDC values, the percentages of values greater than 70% of the maximum value and the ranges of elevation and azimuth angles corresponding to these highest exposure levels. The table shows that QDC values vary from a maximum of 75% in the whole brain to a minimum of 72% in the whole body and the percentage of values higher that the 70% of the maximum values are really low, 7.2% for the whole-body, 4.7% for the whole head and only 3.3% for the whole brain. Looking at the \(SAR\) maps in Figure 5 and the \"Range H-plane\" values in Table 2, we realize that, for all the three \(SAR\) distributions, the highest exposure levels corresponded to beamforming patterns with the beam focused on the azimuth plane in a symmetric narrow range (about 14\({}^{\circ}\)) approximately \(0^{\circ}\), that is just the alignment direction between the antenna and [PERSON]'s body in the H-plane. On the other hand, in the E-plane, things change, and the area of higher exposure varies depending on the part of the body. The highest \(SAR\) levels in the whole body distribute on the range \((-22^{\circ},7^{\circ})\), covering the shoulder area of the model. Instead, the highest \(SAR\) levels for the whole head and for the whole brain concentrate in narrower ranges, respectively, \((-10^{\circ},7^{\circ})\) and \((0.6^{\circ},7^{\circ})\), and out of these narrow ranges the main antenna beam does not intercept these body areas. The same analysis was also conducted for the maximum \(SAR\) averaged on 10 g for the skin, the brain grey matter, and the cerebellum. The boxplot of the 1000 \(SAR_{10g}\) values obtained are reported in Figure 6.  
In this case, the highest \(SAR_{10g}\) values were obtained for the skin tissue, with a maximum value of 222.23 mW/kg, a median value equal to 9.71 mW/kg, and a mean value equal to 26.80 mW/kg. The \(SAR_{10g}\) obtained for the brain grey matter and cerebellum were