Dual-norm optimization for passive shimming in MRI with constraints on field uniformity and harmonic suppression

For high-performance MRI systems, it is crucial to achieve nearly perfect field homogeneity and minimize harmonic impurities within the imaging region. In shimming practice, the repetitive placement of iron pieces can introduce high-order components induced by the shims, along with harmonic impurities originating from the MRI magnet. This poses further challenges in reducing operational time and controlling the magnetic field characteristics.

In this study, we aimed to improve the passive shimming method that can minimize both field uniformities and harmonic impurities with enhanced operation efficiency.

To co-optimize shimming efficacy and field properties, a novel optimization algorithm is developed. This algorithm enhances shimming efficiency through dual L₀-L₁ norm minimization of shim tray usage, while preserving field quality by explicitly co-optimizing overall uniformity and specific field harmonics, particularly high-order terms.

The effectiveness of the proposed technique was numerically validated using a 7 T whole-body superconducting magnet. The peak-to-peak field homogeneity was corrected from 85.36 to 5.25 ppm while keeping high-order harmonics < 2 ppm. By employing 7.4 kg of iron, the proposed method achieved a substantial reduction in shim tray adjustments $-$ from 22 to 8, representing a 63.6% decrease.

The new method effectively ensures overall field uniformity while keeping high-order harmonic components under control during each iteration. Furthermore, compared to the standard linear programming method that requires a full set of shim trays, our method significantly reduces the need for shim tray adjustments. The simulation results indicated that the proposed method simplifies practical operations by minimizing repetitive adjustments and enhancing overall efficiency, providing a viable solution for iterative shimming optimization process.