Suchit Kumar^{1}, Young-Seung Jo^{2,3}, Jeong-Hee Kim^{4}, Chulhyun Lee^{3}, and Chang-Hyun Oh^{1,2,3,4,5}

In ultra-high-field magnetic resonance imaging (UHF-MRI), body imaging suffers from B1 inhomogeneity due to relatively short wavelength. A range of new radio frequency (RF) coil designs has been proposed to overcome this problem. As previously reported, dipole antenna had been proposed to address this B1+ inhomogeneity problem for body imaging. In this paper, structural adjustment of dipole antenna has been tried for parallel transmission to improve overall B1+ homogeneity. Surface dipole antennas with several structures are tried and compared with our top-hat dipole antenna array reported previously. Also, static RF shimming was employed to evaluate the B1 uniformity.

Conventional dipole antenna consists of two conductive lines such as microstrips or rods, which are symmetric in both sides (arms), with the source feed at its center. A top-hat dipole antenna is a combination of conventional dipole antenna and pieces of copper [2]. The first structural adjustment refers to the rotation of dipole antenna and the second adjustment is the dipole antenna with curved and rotated shape, like a spiral shape. We will call it a spiral dipole antenna. A surface loop coil of rectangular shape (10 cm W x 50 cm L) is also considered for comparison. Figure 1 shows the top view of these antennas described.

EM simulation analysis based on FDTD method was performed using Sim4Life [3]. For 8-channel configuration, the 8 elements are equally distributed in radial direction (52 cm D) identical to inner diameter of the Achieva 7 T (Philips, The Netherlands) magnet bore. A uniform digital phantom (46 cm D × 52 cm H) with the dielectric properties of oil was used (relative permittivity of 11.74 and the conductivity of 0.764 S/m).

The RF shimming optimization method was previously proposed to improve the B1 uniformity in a selected region of interest (ROI) by optimizing the relative magnitude and phase of RF power delivered to each transmit element [4,5]. To obtain the complex weight of each element, the superposition of linear system was used to solve the optimization equation using the conjugate gradient method [6]. The least square method is implemented in MATLAB as follows:

**Solve Ax = b **

**
Or
minimize ǁ Ax – b ǁ **

**
Or solve (A ^{T}A +sI)x = A^{T}b**

where A = B1 from individual coil, s = regularization parameter for maximizing uniformity (must be positive), x = magnitude of power delivered to individual coil, AT = transpose of matrix A, I = identity matrix, and b = desired B1 field from combined coil.

After the optimization for shimming, the power values applied to each element were normalized to produce a rectangular excitation pulse with a duration of 1 msec at the center of the coil and resultant 90° ﬂip angle (B1+ field value of 5.87 μT). The RF shimming optimization was evaluated in both 2D and 3D ROI’s. The 2D ROI in axial plane is 21 cm and coronal plane is 29 cm in diameter, respectively and 3D ROI is in a cylindrical shape with 21 cm in height and 29 cm in diameter (Fig. 2).

1. Raaijmakers, A. J. E. et al. Design of a radiative surface coil array element at 7 T: The single-side adapted dipole antenna. Magnetic Resonance in Medicine. 2011; 66(5): 1488-1497.

2. Kumar, S. et al. Improved B1+ along Z-direction using top-hat dipole antenna pTX array for body imaging at 7 Tesla. ISMRM. 2016; 1801.

3. Sim4Life by ZMT, <http://www.zurichmedtech.com>

4. Metzger, G.J. et al. Local B1+ shimming for prostate imaging with transceiver arrays at 7T based on subject-dependent transmit phase measurements. Magnetic resonance in medicine. 2008; 59(2): 396-409.

5. Collins, C. M. and Smith, M. B. Signal-to-noise ratio and absorbed power as functions of main magnetic field strength, and definition of “90°” RF pulse for the head in the birdcage coil. Magnetic Resonance in Medicine. 2001; 45(4): 684-691.

6. Hestenes, M. R. and Stiefel, E. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards. 1952; 49(6): 409–43.

Figure 3. B1+ uniformity (%), B1 efficiency, 10g Average SAR for a) 2D ROI axial plane, b) 2D ROI coronal plane, and c) 3D ROI based RF shimming optimization.