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Multi-layered radiofrequency coil design for X-nuclei Imaging
Tony Zhou1,2, Justin Lau1,2, Andrew Tyler1,2, Chris Randell3, Jack Miller1,2,4, and Damian Tyler1,2

1Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, United Kingdom, 2Oxford Centre for Clinical Magnetic Resonance Research, University of Oxford, Oxford, United Kingdom, 3Pulse Teq Ltd, Woking, United Kingdom, 4Department of Physics, University of Oxford, Oxford, United Kingdom

### Synopsis

A novel multi-layered radiofrequency coil for X-nuclei imaging is presented which implements stacked layers for improved B1+ and SNR. The multi-layer design increased B1+ by 27% in 23Na phantom experiments and 19% in electromagnetic simulations compared to a single layer coil. Transmit-receive efficiency for a 13C multi-layer coil was double that of a quadrature coil, requiring half the power to achieve a 90° flip. An averaged SNR map from CSI indicated receive sensitivity gain of 33% from the quadrature to multi-layer design.

### Introduction

X-nuclei imaging presents unique opportunities, for example dynamic nuclear polarization can be used to enhance the signal of 13C allowing monitoring of in-vivo metabolic changes in organs, such as the healthy and diseased heart1. However, all X-nuclei coils are inherently power limited owing to the wideband requirements of X-nuclei radiofrequency (RF) amps. Improved RF coil transmit and receive performance would allow for more ambitious pulse sequence designs and increased SNR. Recent developments in X-nuclear coils have followed two general directions: either dense arrays with high SNR near the surface at the expense of depth penetration, or volume coils with excellent transmit homogeneity that are B1+ limited.

We present a multi-layer RF coil design that may replace standard single loop coils. The design principle follows the linear scaling of B1+ in a solenoid with the number of turns. To minimize resistance from both the skin and proximity effects at high frequency, conductive copper tracks from overlapping layers are offset and separated by a dielectric. The design superimposes the B1 field generated from each layer for overall improved transmit/receive (T/R) efficiency.

### Coil Comparisons

A 23Na multi-layer T/R coil was built for a 7T (Varian) preclinical MRI system at 79.5 MHz (Q loaded/Q unloaded: $\text{Q}_\text{L}/\text{Q}_\text{U}\,=\,0.805$). For this prototype, straight copper tracks tracing the path of an octagram were used; overlapping layers are separated by a $100\,\text{µm}$ polytetrafluoroethylene (PTFE) strip. Transmit improvements were quantified with a B1+ map of the 23Na multi-layer coil, a small single-layer coil ( $\text{Q}_\text{L}/\text{Q}_\text{U}\,=\,0.891$) with a congruent local B1+ field profile and a large single-layer coil ( $\text{Q}_\text{L}/\text{Q}_\text{U}\,=\,0.785$) tracing the outer track for comparable volume coverage (Figure 1).

A second 13C multi-layer T/R coil was built at 75.5 MHz ( $\text{Q}_\text{L}/\text{Q}_\text{U}\,=\,0.723$) to demonstrate transmit-receive efficiency and receive chain improvements for hyperpolarized 13C imaging studies. Power-calibrations were performed to determine RF power required for a 90° flip-angle on a fiducial. SNR maps at this power for the multi-layer coil were compared to a commercially available preclinical quadrature surface coil (RAPID Biomedical GmbH, Rimpar, Germany).

### Methods

Transmit efficiency was determined from phantom experiments and electromagnetic (EM) simulation. B1+ maps were obtained using Gradient Echo (GRE, $160\,\text{ms}\,\text{TR}$, $1.9\,\text{ms}\,\text{TE}$, $0.78\,\times0.78\,\times100\,\text{mm}$3 voxel size, $1\,\text{ms}$ Gaussian pulse, 1024 averages) images of aqueous NaCl (5 M) performed at increasing transmit powers supplied by the RF amplifier, from 0 to 90 W in steps of 10 W. 2D flip-angle projection maps at 100 W were calculated via sinusoidal curve fit for each voxel to produce B1+ field profiles2 (Figure 2, top row).

EM simulations were performed on CST Microwave Studio, (Computer Simulation Technology AG, Darmstadt, Germany) using a frequency domain (FEM) solver3 with tetrahedral meshing to reproduce the curvature of the coil (≈ 400,000 mesh cells). The H-field was simulated until steady state and decomposed into right (B1+) and left (B1-) circularly polarized fields, (Figure 2, bottom row) assuming linear materials with constant permeabilities.

Receive sensitivity was determined by performing a power calibration on a 9 M [13C]urea fiducial for peak signal intensity representing a 90° flip-angle. Chemical Shift Imaging (CSI, $600\,\text{ms}\,\text{TR}$, $2\,\text{ms}\,\text{TE}$, $3.125\,\times\,3.125\,\times\,20\,\text{mm}$3 voxel size, 2 ms Gaussian pulse, 32 averages) at this optimal transmit power was run on natural abundance ethylene glycol (0.39 M of 13C) to provide an SNR map.

### Results

The multi-layer design indicates B1+ improvements of 27% from phantom experiments and 19% from EM-simulations averaged over a specified ROI, when compared to the small single layer coil (Figure 2). Greater B1+ improvements of 66% from phantom experiments and 37% from EM-simulations are observed when compared to the large single layer coil. The 1D vertical plot though B1+ maps are consistent with expected $1/r^3$ drop off, where $r$ is distance from the coil (Figure 3). For receive efficiency, the multi-layer coil achieved a 90° flip-angle on the urea fiducial at 35 dB RF transmit power, with the quadrature coil requiring 41 dB transmit power. The multi-layer design requires half the power of a quadrature coil to achieve a 90° flip-angle, being twice as efficient. For receive sensitivity in the specified region, axial CSI data for the multi-layer coil and quadrature coil are converted into SNR maps. Quadrature coil designs theoretically improve SNR by 41.4% over a standard single loop; the multi-layer coil improves SNR by a further 33% compared to the quadrature coil (Figure 4).

### Future Directions

Multi-layer designs are inherently high in inductance; however, they boost transmit efficiency and receive sensitivity for X-nuclei experiments. Future work will implement the multi-layer 13C coil for preclinical in-vivo hyperpolarized 13C studies. We will further investigate the feasibility of exchanging standard loops for multi-layer designs on volume transmit/surface receive and quadrature coils as well as upscaling to clinical sizes.

### Acknowledgements

This work was supported by funding from the British Heart Foundation, Medical Research Council industrial CASE studentship and Pulse Teq Ltd.

### References

1. Apps A, Lau J, Peterzan M, et al. Hyperpolarised magnetic resonance for in vivo real-time metabolic imaging. Heart. 104, 1484-1491 (2018).

2. Insko EK, Bolinger L. J Magn Reson. 103, 82-85 (1993).

3. Computer Simulation Technology AG. CST Microwave Studio Technical Specifications (2016).

### Figures

Figure 1. 23Na (79.5 MHz) RF-coils and corresponding CST EM-simulation models.

Left to Right: Photos of (a) Multi-Layer coil, (b) Small Single-Layer coil and (c) Large Single-Layer coil; EM model of (d) Multi-Layer coil, (e) Small Single-Layer coil and (f) Large Single-Layer coil.

Figure 2. Axial 2D projections of B1+ field profiles normalized for 100 W RF power input. B1+ was averaged over circular ROI as indicated, in µT.

Top: Experimental GRE B1+ field maps for (a) Multi-Layer coil, (b) Small Single-Layer coil and (c) Large Single-Layer coil.

Bottom: EM-Simulated B1+ field maps for (d) Multi-Layer coil, (e) Small Single-Layer coil and (f) Large Single-Layer coil.

Figure 3. Vertical 1D plot through ROI of B1+ map following red line shown in Figure 2, in μT.

Left to Right: (a) B1+ measured from experimental GRE with $1/r^3$ curve fit, (b) B1+ generated from EM-simulations with $1/r^3$ curve fit.

Figure 4. Axial 2D CSI and SNR maps at 90° flip-angle on [13C]urea fiducial.

Top: CSI maps for (a) Multi-Layer coil, (b) Quadrature coil.

Bottom: Normalized SNR maps for (c) Multi-Layer coil, (d) Quadrature coil.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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