Electromagnetic simulation of a 16-channel head transceiver at 7 T using circuit-spatial optimization

Abstract

Purpose: With increased interest in parallel transmission in ultrahigh-field MRI, methods are needed to correctly calculate the S-parameters and complex field maps of the parallel transmission coil. We present S-parameters paired with spatial field optimization to fully simulate a double-row 16-element transceiver array for brain MRI at 7 T.

Methods: We implemented a closed-form equation of the coil S-parameters and overall spatial $B_1^{+}$ field. We minimized a cost function, consisting of coil S-parameters and the $B_1^{+}$ homogeneity in brain tissue, by optimizing transceiver components, including matching, decoupling circuits, and lumped capacitors. With this, we are able to compare the in silico results determined with and without $B_1^{+}$ homogeneity weighting. Using the known voltage range from the host console, we reconstructed the $B_1^{+}$ maps of the array and performed RF shimming with four realistic head models.

Results: As performed with $B_1^{+}$ homogeneity weighting, the optimized coil circuit components were highly consistent over the four heads, producing well-tuned, matched, and decoupled coils. The mean peak forward powers and $B_1^{+}$ statistics for the head models are consistent with in vivo human results (N = 8). There are systematic differences in the transceiver components as optimized with or without $B_1^{+}$ homogeneity weighting, resulting in an improvement of 28.4 ± 7.5% in $B_1^{+}$ homogeneity with a small 1.9 ± 1.5% decline in power efficiency.

Conclusion: This co-simulation methodology accurately simulates the transceiver, predicting consistent S-parameters, component values, and $B_1^{+}$ field. The RF shimming of the calculated field maps match the in vivo performance.

Keywords: EM simulation; RF shimming; co-simulation; parallel transmission; transformer decoupling; ultrahigh-field MRI.

Figure 1.

A: The array set up. A slotted RF shield is placed outside the array. The dual row coil array is made with a former and covered with copper clad board. The simulated human models are positioned in the array center, with the eyes aligned with the eye portals on the array former, mimicking the real scanning scenario. B: The 1-V, 50-Ω voltage feeds’ orientations in the XFdtd setup for the ℂ^208×208 S-parameters calculation. The green arrows indicate the direction of current flow. The circuit diagrams of the top and bottom row loop coil elements are shown in C. The RID and TD circuits are shown in D. In total, 16 RID circuits are applied to decouple neighboring coil elements in the horizontal direction, 8 vertical TD circuits are applied to decouple neighboring elements in the vertical direction, and 16 diagonal TD circuits are applied to decouple neighboring elements in the diagonal direction.

Figure 2.

The 208-port array as a network system. The 8 forward waves from the RF amplifiers are split to 16 forward waves by the splitter to feed the 16 matching circuits which are connected to the array elements. The array elements are also connected with lumped capacitors and transformer decoupling circuits.

Figure 3.

A: Magnitude (dB) and phase of the S-parameter matrix at 298 MHz, and frequency sweep determined from the cost function in Eq. 11 (with $B_1^{+}$ homogeneity optimization) for the Louis model. Panel B shows these equivalent data for Louis but determined with Eq. 15, without $B_1^{+}$ homogeneity optimization.

Figure 4.

A: $B_1^{+}$ field magnitude for 16 channels, with each coil element fed with 65.5 V peak forward voltage. The field maps are from the axial plane at the center of each coil element. The channel index is labeled in Figure 1B. B: The standard deviation over mean ($B_1^{+}$ homogeneity) for inter-row coil element phase shifts from 0 to 80°.

Figure 5.

A: $B_1^{+}$ magnitude profiles of eight channels on one axial slice of the Louis model (first and second rows) and in vivo head (third and fourth rows). B: $B_1^{+}$ phase profiles are presented in the same order as in A. The phase map of each channel is relative to the first channel. In both simulation and experiment, each coil element is fed with 65.5 V peak forward voltage. The absolute magnitude (C) and phase (D) difference between the Louis model and in vivo heads for each of the eight channels’ $B_1^{+}$ profiles.

Figure 6.

A: The sagittal $B_1^{+}$ profiles of the RF shimmed homogeneous distributions for the Ella (top left), Louis (top right), Hanako (bottom left), and Duke (bottom right) models. The nine ROI slices indicated with dashed red lines are evenly spaced across the head. The axial views are shown in Supporting Information Figure S2. B: The corresponding coronal $B_1^{+}$ profiles for the four head models.

Figure 7.

RF shimmed $B_1^{+}$ profiles from 10 volunteers. Each column includes seven evenly spaced axial slices from one volunteer.

Figure 8.

Seven evenly spaced, RF shimmed $B_1^{+}$ axial profiles of the Hanako model (first column) and in vivo heads (second column); the corresponding tissue maps for the Hanako model and in vivo heads are shown in the third and fourth columns, respectively.