Harmonic analysis and optimization for closed-loop superconducting shim coils of 7 T MRI magnet

High-resolution brain imaging is crucial in clinical diagnosis and neuroscience, with ultra-high field strength MRI systems ( $\ge 7T$ ) offering significant advantages for imaging neuronal microstructures. However, achieving magnetic field homogeneity is challenging due to engineering faults during the installation of superconducting strip windings and the primary magnet.

This study aims to design and optimize active superconducting shim coils for a 7 T animal MRI system, focusing on the impact of safety margin, size, and adjustability of the second-order shim coils on the MRI system's optimization.

The study employs a nonlinear optimization method to determine the parameters of the shim coils, considering the size of the coil, the level of undesired harmonics, and the whole number approximation of the turns in each coil. The study also conducts a thorough robustness analysis, examining the effects of coil winding accuracy, former processing accuracy, and assembly angle accuracy on the harmonic intensity of each coil.

The optimization design results for the 7 T MRI system's shim coils show that the magnetic field changes are less than 0.5 %. After second-order shimming and the harmonic coupling an, the low-order harmonics are minimized, resulting in an improved magnetic field peak-to-peak uniformity from 254.47 to 8.970 ppm.

The study successfully demonstrates the creation of a set of second-order shim coils for a 7 T animal MRI system through numerical optimization. The design outputs provide essential technological support for the development of a human whole-body 7 T MRI system, ensuring high-quality imaging at the neuronal level. The project also highlights the importance of considering manufacturing and assembly flaws in the shim coil design process to achieve effective shimming in practical engineering scenarios.