# Evaluation of 8-Channel Radiative Antenna Arrays for Human Head Imaging at 10.5 Tesla
## 2 Materials and Methods  
### Simulation and Numerical Analysis  
Investigating the influence of coaxial cables in detail required that the 8-channel inductor-shortened dipole antenna array was modeled without (Figure 1a) and with  
Figure 1: CAD models of the 8-channel inductor-shortened dipole antenna array without (**a**) and with (**c**) coaxial cable setups. Corresponding simulated B1\({}^{+}\) efficiency maps of the dipole antenna array are shown in (**b**,**d**), respectively. Photographs of the 8-channel inductor-shortened dipole antenna array with further (**e**) and tight (**g**) coaxial cable setups. Corresponding experimental B1\({}^{+}\) efficiency maps of the dipole antenna array are shown in (**f**,**h**), respectively.  
(Figure 1c) coaxial cables. EM simulations were performed for both arrays, and the B1+ efficiency (Figure 1b,d,f,h)), 10 g SAR (Figure 2a,b), and SAR efficiency (Figure 2c,d) maps were compared between the two models. Then, for the comparison with 8-channel end-fed antenna arrays, 8-channel monopole (Figure 3a) and sleeve antenna (Figure 3b) arrays were modeled with coaxial cables. B1+ efficiency, 10 g SAR, and SAR efficiency maps of the monopole and sleeve antenna arrays were calculated and compared with the phantom.  
A cylindrical phantom with \(\epsilon_{\mathrm{r}}\) = 49 and \(\sigma\) = 0.6 S/m was used to approximate human brain tissue properties for the performance comparison of the arrays. The diameter (=18 cm) and the length (=30.5 cm) of the phantom was chosen to emulate the comparable size of a human head and neck.  
The performance of the modeled arrays (dipole, monopole, and sleeve antenna) was compared using a human model (Duke) [22]. To closely resemble the practical coil setup, in which the coaxial feed cables are inherently part of the coil, the antenna models included the coaxial cables and the cable traps. The simulated B1+ efficiency and SAR efficiency were calculated and compared among the three antenna arrays. B1+ efficiency, 10 g SAR, and SAR efficiency of each array were summarized in Table 1.  
Simulated B- and E-fields were obtained using XFdtd (REMCOM, State College, PA, USA). By driving each of the eight elements, with relative transmit phase increasing by 45 degrees with each channel, the net B1 field generated by the array was in a circularly polarized mode. The portion of the total RF magnetic field that can induce spin excitation, the B1+ fields, were obtained with the equation below:  
\[\mathrm{B_{1}^{+}}\mathrm{=}\left|\frac{\mathrm{B_{x}+}\mathrm{iB_{y}}}{2} \right|, \tag{1}\]  
where Bx and By are the complex amplitudes of the x- and y-oriented RF magnetic fields, respectively [23]. Based on the EM simulation, B1+ efficiency and SAR efficiency maps were calculated with MATLAB (The Mathworks, Inc., Natick, MA, USA). For quantitative comparison, the highest B1+ efficiency, 10 g SAR, and SAR efficiency areas were obtained from the region of interest (ROI) in the axial plane for all arrays. The related values  
Figure 2: Simulated 10 g SAR (**a,b**) and SAR efficiency (**c,d**) maps of the 8-channel inductor-shortened dipole antenna array without and with coaxial cable setups in the axial and coronal planes.  
obtained from 2 mm isotropic voxel ROI are indicated below each of the axial images. Red dotted lines of each coronal plane indicate the location of the axial plane and display of B1+ efficiency. Red arrows indicate ROIs where these B1+ efficiency values are measured.