Simulations providing an upper bound on ∆B0 shimming of 1096 human brains from the human connectome project with currents outside the target volume were performed and used to construct optimal n-channel shim fields. Optimal truncated shim basis performance was evaluated suggesting 70 optimal channels are required to achieve 95% of ultimate performance. Comparisons with arrays of regularly spaced circular loops suggests that under realistic current constraints, regular loop arrays with hundreds of elements only achieve 85% of ultimate performance. The ultimate ∆B 0 shim and optimal n-channel coils will be useful tools in the analysis and comparison of shim array designs.
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