### Synopsis

**Phase image reconstruction from multi-channel data
at high field strength becomes challenging since a volume body coil that
provides the phase offset information is generally not available. Several coil
combination techniques are still computation intensive and prone to errors for strongly
T2*-weighted data due to the requirement of spatial smoothness of image phases,
required phase reference from body coil scan, and also hampered for strongly localized
B1 coil sensitivities. These limitations lead to phase image inconsistencies
and may cause artifacts in QSMs. We demonstrated here that the coil combination
should be considered after performing individual physical and/or virtual coil
QSM.**### INTRODUCTION

Quantitative susceptibility mapping (QSM) that aims
to map the tissue susceptibility $$$(χ)$$$ based on the
measured tissue phase $$$(ϕ)$$$ has become a new
forefront of research particularly at high-field due to high SNR, CNR, and
high-resolution. For best SNR multi-channel surface coils are used. However, multi-coil phase image reconstruction becomes challenging
since a volume body coils are generally not available, which are usually required for mapping the spatial sensitivitiesof the coil array. Several combined phase techniques have been proposed, but
still computation intensive and prone to errors for strongly T2*-weighted data due
to the requirement of spatial smoothness of image phases

^{1}, required phase reference from body coil scan

^{2}, and also hampered for strongly
localized B1 coil sensitivities

^{3}.
These limitations lead to phase image inconsistencies and may cause artifacts
in QSMs. The aim of this study was to demonstrate that the coil combination
should be considered after performing individual physical and/or virtual coil
QSM.

### MATERIAL and METHOD

*Data Acquisition:* Brain data of two healthy volunteers were acquired with 3D GRE (FA = 10°, TR/TE/ = 20/9 ms, voxel sizes = 0.4x0.4x1.5
mm, and matrix size = 640x480x112) on a 7T Siemens scanner using a 32-channel
head coil. Image reconstruction and post-processing for QSM were performed offline
using Matlab 2012a.

*Data Processing:* The QSMs were
calculated from, 1. the coil combined images
of the scanner. 2. Individual coil images
(32 physical and 16, 8, 4 virtual coils). Note that k-space data from physical
coils were compressed into a small number of virtual coils using the coil
compression technique^{4}. To obtain the
unknown susceptibility $$$χ$$$, L2-regularized QSM^{5 }was implemented to
minimize Eq. 1, $$$min_χ\left\{{‖F^H DFχ-ϕ‖_2^2+λ‖Gχ‖_2^2 }\right\}---1$$$ , $$$F$$$ where is Fourier transform, $$$D$$$ is a diagonal matrix with entries $$$ 1/3-k_z^2/k^2 ,k^2=k_x^2+k_y^2+k_z^2$$$, and $$$G$$$ is the gradient operator in three dimensions.
The regularized parameter ($$$λ$$$) was chosen based on the
L-curve heuristic^{6}. The tissue phase ($$$ϕ$$$) was prepared prior to solving Eq.1 by applying
the Laplacian phase unwrapping^{7} to the raw phase images, then the vSHARP
filtering^{8} was used to remove the background phase contributions within the
masked region.

### RESULTS

Figure 1a shows that using the
scanner-combined phase, artifacts in QSMs are clearly visible in both
subjects, whereas these artifacts disappear when the individual physical or virtual
coil QSMs were combined. Note that the individual coil QSM was weighted by
magnitude of its sensitivity profile to compress noise. Weighted mean of 32 physical coil QSMs appear to have
highest SNR. They, therefore, were used as the references to calculate $$$RMSE=sqrt{∑_{k=1}^n[im(k)-ref(k)]^2/n}$$$ for the virtual coil QSMs, where $$$im$$$ is the virtual coil QSM, $$$n$$$ denotes the total number of pixels. For subject1, the QSM result is likely dependent from the
number of physical or virtual coils, they appear highly comparable to the
reference with very small RSME (3.5%, 4 virtual coils). However, for the same
number of virtual coils in subject2, artifacts become visible (red circles). This is due to higher background noise (Bgn) in
subject2, consequently, the %RSMEs of QSM from subject2 are also higher as
shown in Figure 1b. Note that the Bgn is the standard deviation of
the root-sum-of-squares magnitude image (32 coils) outside the masked region.

### DISCUSSIONS

For T2*-weighted
imaging, as e.g. required for BOLD, SWI, or QSM the B0-induced phase my become
very significant and spatially inhomogeneous, presenting considerable
complications for adaptive combination methods (1st column in figure
1a). In contrast, individual coil phase images are simply obtained since they
do not require additional data

^{2} or sophisticated reconstruction techniques

^{1, 3} rather than iFFT. Although the processing time for QSMs will become
expensive when the number of coils increases, the coil
compression technique can be a good option to speed up the computational
process. Optionally, the appropriate number of virtual coils can be
automatically selected based on noise variance estimation

^{9}. The %RSMEs in
figure 1b are more likely associated with background noise rather than the
number of virtual coils. Applying a low-pass filter to remove noise in the data
before compression into virtual coils may improve the QSM when fewer virtual
coil are used. However, the fact that coil compression is usually achieved by
singular value decomposition, where the number of virtual coils can be
determined by thresholding the singular values. Thus, using a single or very
fewer virtual coils may be equivalent to use Walsh’s approach

^{1}.

### Acknowledgements

The
study was supported by the BMBF (Forschungscampus STIMULATE, 03FO16101A), NIH (1R01-DA021146), and FP7 Marie Curie Actions of the European Commission (FP7-PEOPLE-2012-ITN-316716).### References

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