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 phases¹, required phase reference from body coil scan², and also hampered for strongly localized B1 coil sensitivities³. 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.

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 technique⁴. To obtain the unknown susceptibility $$$χ$$$, L2-regularized QSM⁵ 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 heuristic⁶. The tissue phase ($$$ϕ$$$) was prepared prior to solving Eq.1 by applying the Laplacian phase unwrapping⁷ to the raw phase images, then the vSHARP filtering⁸ was used to remove the background phase contributions within the masked region.

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. 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 data² 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 estimation⁹. 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 approach¹.