Optimization of Multi-Coil
Array Design for Efficient Human Brain Shimming at 3T
Yubin Cai1, Hsin-Jung Yang1, Xinqi Li2, Tianshi Hu2, Yuheng Huang2, Yujie Shan2, Meng Lu1, Wai Shing Liu2, Debiao Li1, and Hui Han11Biomedical Imaging Research Institute, Cedars-Sinai Medical Center, Los Angeles, CA, United States, 2Cedars-Sinai Medical Center, Los Angeles, CA, United States
Synopsis
An algorithm is proposed
to optimize a multi-coil array for efficient human brain shimming at 3T.
Numerically, the algorithm relies on singular value decomposition (SVD) and
iterative principle component analysis (PCA) to truncate spurious or redundant
coils. For proof of concept, it is demonstrated that a set of individually
driven shim coils, after truncation through the proposed optimization, has a
shimming performance comparable to that before the truncation.
IntroductionThere have been a
considerable amount of work conducted to design multi-coil arrays (MCA) for
human brain shimming at 3T1-7. 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. MethodsField 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.ResultsFig. 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 ConclusionThe 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.AcknowledgementsNo acknowledgement found.ReferencesJuchem C., Nixon T. W., McIntyre S.et al.J Magn Reson.2010;204:281-289.Juchem C., Green D. & de Graaf R. A.J Magn Reson.2013;236:95-104.Juchem C. & de Graaf R. A.Magn Reson Med.2017;78:2042-2047.Hui Han, Allen W Song, and Trong-Kha Truong. Integrated parallel reception, excitation, and shimming(ipres). Magnetic resonance in medicine, 70(1):241–247, 2013.Truong TK, Darnell D, and Song AW. Integrated RF/shim coil array for parallel reception and localized B0 shimming in the human brain. NeuroImage 2014;103:235–240.Stockmann JP, Witzel T, Keil B, et al. A 32-channel combined RF and B0 shim array for 3T brain imaging. Magn Reson Med 2016;75:441-451.
Han Hui, John Stager, Hsin-Jung Yang, Na Zhang, Sizhe Guo, Zhuoqi Li, Yicheng Wang, and Debiao Lil. Unified coils (unic) for simultaneous RF reception and
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B.P. Meneses, A. Amadon. Optimized multi-coil array design for human brain shimming at Ultra-High Field. ISMRM 2019

^{1}Biomedical Imaging Research Institute, Cedars-Sinai Medical Center, Los Angeles, CA, United States, ^{2}Cedars-Sinai Medical Center, Los Angeles, CA, United States

An algorithm is proposed
to optimize a multi-coil array for efficient human brain shimming at 3T.
Numerically, the algorithm relies on singular value decomposition (SVD) and
iterative principle component analysis (PCA) to truncate spurious or redundant
coils. For proof of concept, it is demonstrated that a set of individually
driven shim coils, after truncation through the proposed optimization, has a
shimming performance comparable to that before the truncation.

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