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# Finding the optimal 8-TxRx array for a tight shielded brain coil at 11.7T: a simulation study

Paul-François Gapais, Michel Luong, Alexis Amadon

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Paul-François Gapais, Michel Luong, Alexis Amadon. Finding the optimal 8-TxRx array for a tight shielded brain coil at 11.7T: a simulation study. ISMRM, May 2025, Honolulu, United States. hal-05090052

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# Finding the optimal 8-TxRx array for a tight shielded brain coil at 11.7T: a simulation study

Paul-François Gapais¹, Michel Luong², and Alexis Amadon¹

¹Université Paris-Saclay, CEA, CNRS, Joliot, NeuroSpin, BAOBAB, Gif-sur-Yvette, France, ²Université Paris-Saclay, CEA, DRF, IRFU, DACM, Gif-sur-Yvette, France

## Synopsis:

**Motivation:** To fit inside a shielded $B_0$ shimming system and overcome $B_1^+$ inhomogeneities, an 8-channel parallel transmit array for human brain studies needs to be developed at 11.7T.

**Goal(s):** Using various metrics, find the optimal 8-Tx array for a 27-cm diameter shielded coil at 11.7T. Meanwhile, consider it for reception supplementing a tighter Rx-array.

**Approach:** Relying on full wave electromagnetic simulations, six different 8-channel arrays types were compared at 500 MHz in terms of $B_1^+$ efficiency, homogeneity, sum-of-magnitudes, SAR-constrained $k_T$-points design, and SNR.

**Results:** Accounting for all presented metrics, the full-length dipoles provide the best compromise.

**Impact:** Our parallel arrays benchmarking of the different Tx-Rx types at 11.7T provides new insights for UHF coil development. It confirms previous findings claiming the superiority of dipole-like elements over loops at UHF.

## Introduction:

The ultra-high magnetic field of 11.7T¹ is associated with several challenges, in particular in terms of $B_0$ and transmit field ($B_1^+$) shimming. To mitigate $B_0$ inhomogeneities related to magnetic susceptibility gradients causing EPI distortions and signal losses, a $B_0$ shimming system was developed (SCOTCH)², made of three layers of coils. To be efficient, its internal diameter is only 27 cm and thus restrict the transmit coil size. Moreover, to limit the interaction of the transmit and receive arrays on the $B_0$ shimming insert (and vice-versa), an RF shield is considered. Since $B_1^+$ is strongly inhomogenous at UHF, parallel transmission and pulse design³,⁴,⁵ have provided significant gains in excitation homogeneity. Also, in combination with an inner Rx-array, it was shown that it is particularly advantageous to use the Tx-elements in reception in order to gain SNR at the center of the brain⁶,⁷. In this abstract, we compare six types of elements arranged for an 8-TxRx brain-focused array at 11.7T in terms of $B_1^+$ efficiency, homogeneity, sum-of-magnitudes, SAR-constrained $k_T$-points design⁴. We also evaluate them in terms of SNR for a future use with a close-to-subject receive array.

## Methods:

Six different transceiver types were studied (Figure 1):

* Low-impedance dipole: "full" dipole made of two quarter-wavelength copper blades (total length = 276 mm), without tuning component.

* High-impedance dipole: microstrip linear resonator with two gaps on the outer conductor making the dipole resonate at the Larmor frequency with an intrinsic impedance of about 600 Ω, without tuning component (length = 300 mm).

* Anatomical dipole: inductively-shortened (~50nH each) copper wire dipole following the patient's head curvature.

* Meander dipole: meander-shortened dipole, without tuning component.

* Low-impedance loop: standard copper wire loop with 13 tuning capacitors (3.1pF each) equally distributed along its perimeter.

* High-impedance loop: stripline loop with 5 gaps on the outer conductors and 4 gaps on the inner conductor to make it resonant at the Larmor frequency and present an impedance of about 1.4kΩ, without tuning component.

For all configurations but the anatomical dipoles, the transceivers were placed at 15mm from the shield, and the azimuthal angle between neighbouring elements was 45°. The loops in the last two presented configurations were optimally overlapped to mitigate coupling lower than -10dB in each case. Transceivers were matched to 50Ω using either LC baluns (for dipole-like elements) or PI matching networks (for loop elements), in the presence of a 10-layer female head and shoulders model. The tuning and matching components were modelled with realistic losses using their quality factors. Relying on the reciprocity theorem⁸, the complex field maps were exported with a 5-mm voxel resolution, injecting 1W in each port. The $B_1^+$ and $B_1^-$ maps could then be computed for Tx and Rx assessment. The noise covariance matrix was computed using Bosma's equation⁹, then used to reconstruct the noise-covariance-weighted root-sum-of-square SNR¹⁰. Virtual observation points (VOPs) were computed for each 8-Tx array and used to compute power and SAR-constrained pulse design for different schemes of $k_T$-points and target flip angles (maximum average power per channel of 6W, and maximum 10g-SAR limit of 10W/kg). The simulations were performed with HFSS (Ansys Inc., PA, USA) at 500MHz. The pseudo-CP combined $B_1^+$, pulse design, and SNR maps were computed using custom Matlab routines (Mathworks, MA, USA).
**Results:**

The $B_1^+$ computed using a pseudo-CP mode shows the best efficiency for the low-impedance dipoles, and the best homogeneity for the high-impedance loops (Figure 2). The sum-of-magnitudes maps (Figure 3) also demonstrate the superiority of dipoles over loops in terms of median, but more specifically of low- and high-impedance dipoles over the shortened dipoles when considering the first decile of the distribution. $K_T$-points design, in any of the presented schemes (Figure 4), is in favour of the two kinds of full-length dipoles and of the high-impedance loops when computing the normalized-root-mean-squared-error (NRMSE) over the brain. The SNR maps (Figure 5) show the superiority of dipoles over any kind of loop arrays. In this specific study, the elements are placed close to the shield, which could spoil the SNR performance, especially for the loop arrays¹¹.

**Conclusion:**

In this study, the full-length dipoles outperform the other types of elements in every aspect. The performance of the low- and high-impedance dipoles are close but the high-impedance dipole is particularly interesting as the values needed to create an LC balun are more convenient (i.e., the inductor value is greater and therefore less sensitive to PCB effects). Moreover, the possibility to rely on the gap size and location to fine-tune the dipole makes it an interesting candidate for transmit and receive performance at 500MHz.

**Acknowledgements:**

This work was funded by the French Research Agency (ANR) and the German Research Foundation (DFG), under grant agreement n°ANR-2023-CE19-0033-01 (UHF NeuroBOOST: Novel Parallel-Transmit Head/Neck RF Array Coils for Ultra-High Field MRI at 7T, 9.4T, and 11.7T).

**References:**

1) Boulant, N., Mauconduit, F., Gras, V. et al. In vivo imaging of the human brain with the Iseult 11.7-T MRI scanner. Nat Methods 2024.

2) Meneses, B. P., Stockmann, J. P., Arango N., et al., Shim coils tailored for correcting B0 inhomogeneity in the human brain (SCOTCH): Design methodology and 48-channel prototype assessment in 7-Tesla MRI, Neuroimage 2022.

3) Williams, S. N., McElhinney, P., Gunamony, S., Ultra-high field MRI: parallel-transmit arrays and RF pulse design. Phys. Med. Biol. 2023.

4) Cloos, M. A., Boulant, N., Luong, M. et al. $K_T$-Points: Short Three-Dimensional Tailored RF Pulses for Flip-Angle Homogenization Over an Extended Volume. Magn Reson Med. 2012.

5) Gras, V., Vignaud, A., Amadon, A., Le Bihan, D., Boulant, N., Universal pulses: A new concept for calibration-free parallel transmission. Magn Reson Med. 2017.

6) Waks, M., Lagore, R. L., Grand, A., RF coil design strategies for improving SNR at the ultrahigh magnetic field of 10.5T. Magn Reson Med. 2024.

7) Avdievich, N. I., Nikulin, A., Ruhm, L., A 32-element loop/dipole hybrid array for human head imaging at 7 T. Magn Reson Med. 2022.

8) Hoult, D. I., The Principle of Reciprocity in Signal Strength Calculations, Concepts in Magnetic Resonance 2000.

9) Gapais P-F, Luong M, Nizery F, et al. Efficiently building receive arrays with electromagnetic simulations and additive manufacturing: A two-layer, 32-channel prototype for 7T brain MRI. Magn Reson Med. 2024.

10) Roemer, P.B., Edelstein, W.A., Hayes, C.E., Souza, S.P., Mueller, O.M., The NMR Phased Array. Magn Reson Med. 1990.

11) Zhang, B., Adriany, G., Delabarre, L. et al. Effect of radiofrequency shield diameter on signal-to-noise ratio at ultra-high field MRI. Magn Reson Med. 2020.
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*Capacitors are equally distributed along the LIC

**Gaps on the inner and outer conductors are
equally distributed along the HIC

**Figure 1:** Six different 8-Tx arrays are considered. The full model is presented in each case (top) and a focus on each transmitter type is shown with the ports and components locations (bottom). Simulations are made using a female multi-layer head and shoulders phantom at 11.7T (Larmor Frequency = 500 MHz). The shield diameter is equivalent between all setups, but the length is different depending on the transmitter type and length.

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**Figure 2:** B1+ maps computed using a pseudo-CP mode at the center of the brain (Left). Bar plots of the B1+ standard deviations and mean value for each case, only computed inside the model's brain.

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**Figure 3:** Sum of B1+ magnitude maps for each case (left). First decile and median, along with the histogram distribution (right).
<figure><img src="image_6.png" /><figcaption>Figure 4: Example of pulse design simulation result for 5 k<sub>T</sub>-points and a target flip angle of 90° (left), and several pulse designs (right) with computed NRMSE and first percentile divided by the target flip angle.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: Signal-to-noise ratio computed with a noise covariance-weighed root sum-of-square. SNR maps (left) with their mean and standard deviation (right).</figcaption></figure>

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5 k<sub>T</sub>-points, target FA = 90°

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