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PURPOSE: Slice-wise shimming can improve field homogeneity, but suffers from large noise propagation in the shim calculation. Here, we propose a robust shim current optimization for higher-order dynamic shim updating, based on Tikhonov regularization with a variable regularization parameter, λ . THEORY AND METHODS: λ was selected for each slice separately in a fully automatic procedure based on a combination of boundary constraints and an L-curve search algorithm. Shimming performance was evaluated for second order slice-wise shimming of the brain at 7T, by simulation on a database of field maps from 143 subjects, and by direct measurements in 8 subjects. RESULTS: Simulations yielded on average 36% reduction in the shim current norm for just 0.4 Hz increase in residual field SD as compared to unconstrained unregularized optimization. In vivo results yielded on average 34.0 Hz residual field SD as compared to 34.3 Hz with a constrained unregularized optimization, while simultaneously reducing the shim current norm to 2.8 A from 3.9 A. The proposed regularization also reduced the average step in the shim current between slices. CONCLUSION: Slice-wise variable Tikhonov regularization yielded reduced current norm and current steps to a negligible cost in field inhomogeneity. The method holds promise to increase the robustness, and thereby the utility, of higher-order shim updating.

Original publication




Journal article


Magn Reson Med

Publication Date



dynamic B0 shimming, higher-order shimming, regularization, shim optimization