Recently, matrix coils (MCs, also called 'multi-coils') design was demonstrated based on Halbach magnet structure.

Chinese scientists at the Suzhou Institute of Biomedical Engineering and Technology (SIBET) of the Chinese Academy of Sciences proposed a high efficiency MCs optimization technology and a simplified current optimization algorithm to implement the MCs shimming, which was applicable for limited space applications.

Halbach array magnet is of great potential in desktop NMR applications. Due to the stringent requirements of field homogeneity in MR application, active shimming is mandatory. Traditional shimming executions with groups of coils is limited in the compact magnet, for which MCs technology is especially appropriate.

With multi-target Spherical Harmonics (SHs) of the 1^st, 3^rd, and mixed 1^st & 2^nd degrees in Halbach magnet shimming, MCs structure optimizations were successfully performed in this study.

Comparisons with regular interleaved MCs showed the optimized coil structure provides better performance, including reduction of power dissipation, maximum current amplitude, and total current requirement.

The research article "A Spherical Harmonics Decomposition Method (SHDM) for irregular Matrix Coils design" was published in IEEE Transactions on Biomedical Engineering.

In traditional magnetic resonance (MR) active shimming, the main magnetic field is decomposed using an SH orthogonal basis characterized, and shimming coils are designed for each SH term. However, impurities exist within these SH shimming coil groups.

Besides, a displacement between multiple sets of coils during assembly may also introduce high-degree magnetic field residuals, which may result in a time-consuming shimming process. Furthermore, tens of layered SH shimming coils may also occupy too much magnet inner space.

MCs technique utilizes a set of coils distributed on a cylindrical surface to directly generate a target magnetic field distribution. In ordinary applications, number and positions of MCs based on regular type of coil elements, such as circular or saddle structures were optimized to improve its performance. However, the actual applications may more focus on some specified components. Thus, MCs geometrical shape optimizations are necessary for given scenarios.

This work proposes a simple and intuitive way of irregular MCs optimization, which is of high benefits in compact MR systems based on permanent magnets. The methodology may also be translated into local gradient & shimming matrix coils designs for conventional magnetic resonance device.

Implementation for SH (1, -1/0/1) target field coils. a) the 3D printed MCs prototype, b) field distribution of SH (1, -1) degree on R2.5 mm sphere, and the field on yoz and xoy plane are illustrated in b.2-3; c)-d were results of SH (1,0) and SH (1,1) target field, and their corresponding orthogonal slice field distributions. (Image by SIBET)