Matrix gradient coils consisting of many small elements offer unprecedented flexibility for spatial encoding and shimming¹. Such coils are capable of generating highly customizable nonlinear gradients as well as standard linear gradients. Applications requiring customized fields include nonlinear spatial encoding^2-4, dynamic shimming¹, and reduced field-of-view imaging⁵. In this work, we present the first imaging experiments using an actively-shielded 84 channel matrix gradient coil.

An actively-shielded matrix coil with 84 elements was designed to maximize the local gradients while reducing eddy-currents^6,7. The coil was constructed, assembled and cast in epoxy at our institution. The complexity of the power and control electronics was reduced by assigning the 84 coil elements into 12 groups, each with multiple elements connected in series. The groups were connected to 12 additional gradient power amplifiers (IECO, Helsinki, Finland). The configuration of elements in this work was obtained from combinatorial optimization to achieve linear fields in a 20cm spherical region⁸. Sequence programming was performed using the open-source environment Pulseq^9,10, while hardware execution was achieved with custom-built electronics synchronized and integrated with a 3T clinical scanner (Siemens Healthcare, Erlangen, Germany). Experiments were performed with a birdcage RF coil for transmit and either a birdcage coil or a self-built 31-channel head coil for receive.

As a first step towards imaging, field maps from the 12 gradient encoding channels were obtained using the linear gradients of the clinical system in a GRE sequence with a small gradient pulse on the additional channels. The resulting spatial encoding fields are depicted in Fig. 1. These fields were combined using constrained least-squares to produce approximately linear fields, suitable for Cartesian encoding at the desired resolution (FOV=190mm, 256x256 matrix). The currents were limited to a conservative 65A for initial experiments.

Images were acquired with a GRE sequence using the matrix coil for phase and frequency encoding and the linear z-gradient for slice-selection. Sequence parameters were FOV=190mm, 256x256 matrix, TE=18ms, TR=1000ms, slice=3mm. For comparison, reference images were acquired using linear gradients and a standard GRE sequence with similar parameters. Images were reconstructed with the conjugate gradient algorithm to correct for any field deviations.

The relative contributions of the 12 channels obtained by least-squares fitting are listed in Fig. 2a and the composite fields are shown in Fig. 2b. The X and Y fields are relatively close to linear with mean deviations of 10% and 6%, respectively. These deviations are due to the low currents used for the initial testing. It is expected these will be mitigated when higher currents of 150A are tested in the near future.

The local-k space² for imaging with the composite fields is illustrated in Fig. 3a. Field deviations alter the shape of the local k-space trajectory across the field-of-view. Consequently, a naïve reconstruction of the GRE data using a discrete Fourier transform (DFT), shown in Fig. 3b, exhibits strong distortion in areas with large field deviations.

Fig. 4 displays images from a resolution phantom for both the reference clinical system and the matrix coil approach, reconstructed using the conjugate gradient algorithm. The images are in good agreement and display the same geometry and internal structures. The conjugate gradient algorithm successfully corrects the geometric distortion since the measured fields are included in the reconstruction model. However, a slight decrease in resolution is observed and some distortion on the right side remains.

Fig. 5 presents images from a circle phantom using a 31-channel receive coil. The matrix gradient coil performs well and accurately encodes the fine structures of the phantom. Improved SNR is obtained, as expected, using the 31-channel coil compared to the reference image obtained with a birdcage coil. Some additional blurring is present, likely due to inaccurate estimation of RF sensitivities.

Compared to previous works where precise calibration was critical^2,4, very little calibration was required here to produce images almost equivalent to those from the clinical system. In particular, no compensation for eddy-currents, delays or B0 inhomogeneity was performed. Fine-tuning for these effects will further improve the results. Integration of the self-built RF coil enables investigations into novel trajectory designs with strong acceleration¹¹.

This work demonstrates successful imaging using an actively-shielded matrix coil with a large number of elements. Minimal calibration was required for the new coil, suggesting efficient active shielding and negligible eddy-currents. We anticipate this will enable the development of exciting new imaging techniques that best exploit the flexibility of a matrix gradient coil.