Introduction

There have been a considerable amount of work conducted to design multi-coil arrays (MCA) for human brain shimming at 3T^1-7. Menese, et al. has proposed a numerical method to find optimal geometry and positions of shimming coils, although they are difficult to be implemented⁸. In this work, we proposed an optimization algorithm to identify the redundancy in a surface shimming coil system. The algorithm utilized mathematical models, such as singular value decomposition (SVD) and principle component analysis (PCA) to derive the importance of each surface shimming coils in a realistic shimming environment. We tested the algorithm using a set of evenly distributed surface shimming coils with a cylindrical coverage. Brain field maps from the Human Connectome Project (HCP) were used to test the efficacy of the algorithm. We successfully demonstrated that 95% of the shimming capability can be preserved with 30% reduction in shimming channels using the proposed algorithm.

Methods

Field maps of human heads (N=500) from the HCP were used for the optimization process. 100 surface shimming coils were placed around the targeted field-of-view in a cylindrical fashion. The corresponding shim field of each coil was derived using Biot-Savart Law. After proper alignment and masking of the HCP field maps, the field maps were decomposed using a SVD model to identify the key elements in human brain field variation. To further identify the efficacy of each surface shimming coils and reduce system redundancy, the shim field were derived using a least square mean regression model for each key element using the surface shimming coils. Consequently, a PCA analysis were performed iteratively to identify the key components from the cylindrical shimming system, which helps decide the contribution of each coil to the shimming field matrix. By ranking the contributions, the redundant coil can be identified and removed. A worth noting component in the algorithm is to determine if the convergence condition is satisfied. If not, the algorithm loops back to the current solving step for the set of newly truncated multi-coil array. This iterative process essentially ensures that we carefully remove the least contributing coils and leverage the dynamics among the coils’ radiated fields by exploring different current compositions.

Results

Fig. 1 shows the 3-dimensional view of the initial single-layer 100 4-cm-radius circular coils around a 0.15-m-radius cylinder. 34 redundant coils are being removed from the algorithm, plotted in Fig. 2. A comparison, shown in Fig.3, is regarding the 72 slices of the human brain field maps before and after the shimming of the truncated multi-coil array. Whole brain shimming is applied to both cases with 100 coils before truncation and 66 coils after truncation. Then the standard deviation of frequencies across the whole brain was compared between before and after shimming. As shown in Fig. 4, the shimming performance remains almost the same when 100 coils are being reduced to 66 coils.

Discussion and Conclusion

The numerical results have proven that the proposed algorithm has successfully identified and removed redundant coils. The final 66-channel multi-coil array has demonstrated to maintain a shimming performance comparable to that for the original 100 coils. It suggests a significant number of coils is essentially redundant. Also the reserved coils are nearly symmetric with respect to the central plane and the results agree with the intuition that the coils farther away from the isocenter are less critical than the ones closer. Further works on this topic include 1) considering the variations in subject location and motions 2) adding shim coil geometry, and placement into the optimization routine and algorithm architecture, and 3) using the Eigen brains generated from the dataset instead of raw data to obtain a more generalized results.

Acknowledgements

No acknowledgement found.