A Spherical Harmonics Decomposition Method (SHDM) for Irregular Matrix Coils Design

With advantages of reduced coupling and compact structure, Matrix Coils (MCs) design extension to approximate multiple target inhomogeneities is necessary to improve its performance in shimming applications.A Spherical Harmonics Decomposition Method (SHDM) is proposed for the multi-target MCs optimization problem. The magnetic field generated by the MCs is represented in form of SHs' orthogonal basis, based on which the MCs pattern is optimized to adapt to multiple SH targets.With multi-target SHs of the 1st, 3rd, and mixed 1st&2nd degrees in Halbach magnet shimming, MCs structure optimizations were successfully performed. Comparisons with regular interleaved MCs show the optimized coil structure provides better performance, including reduction of power dissipation, maximum current amplitude, and total current requirement.This work proposed a simple and intuitive way of irregular MCs optimization, which is of high benefits in compact MR systems based on permanent magnets.This methodology may also be translated into local gradient & shimming matrix coils designs for conventional magnetic resonance device.