We seek to reduce the acquisition time of 3D 1H-MRSI by leveraging the complementary strengths of parallel imaging^1-4 and subspace-based imaging^5,6. The integration of parallel imaging into 1H-MRSI presents a unique challenge because removal of water and lipids, which are 10² to 10⁴ times larger than the metabolic signals of interest, requires much higher reconstruction accuracy than in conventional parallel imaging applications (especially for short TE whole brain 1H-MRSI). We solve this problem (illustrated in Fig. 1) by incorporating both spatial and spectral constraints as well as sensitivity encoding into a Union-of-Subspace (UoS) model⁶.

We model the 1H-MRSI signal as$$\rho \left( {\bf x}, f \right) = W_M\left( {\bf x}\right) \sum_{p=1}^{P_M} u_{M,p}\left( {\bf x}\right) v_{M,p}\left( f \right) + W_W\left( {\bf x}\right) \sum_{p=1}^{P_W} u_{W,p}\left( {\bf x}\right) v_{W,p}\left( f \right) + W_L\left( {\bf x}\right) \sum_{p=1}^{P_L} u_{L,p}\left( {\bf x}\right) v_{L,p}\left( f \right),$$ where $$$W_M$$$, $$$W_W$$$, $$$W_L$$$ specify the respective spatial supports of the metabolite, water, and lipid signals, and $$$\{u_{M,p}\}_{p=1}^{P_M}$$$, $$$\{u_{W,p}\}_{p=1}^{P_W}$$$, $$$\{u_{L,p}\}_{p=1}^{P_L}$$$, $$$\{v_{M,p}\}_{p=1}^{P_M}$$$, $$$\{v_{W,p}\}_{p=1}^{P_W}$$$, $$$\{v_{L,p}\}_{p=1}^{P_L}$$$ are the corresponding spatial and spectral bases. A major benefit of this model lies in its flexibility to directly incorporate spatial and subspace constraints for each signal component. These constraints reduce the number of degrees of freedom in the reconstruction problem. Combining this model with sensitivity encoding enables accurate reconstructions from data sampled sparsely in both k-space and time, thereby providing for a better combination of speed, resolution, and SNR than can be achieved using parallel or subspace-based imaging alone.

Our algorithm for reconstruction begins with UoS-based nuisance signal removal by solving$$\hat{U} = \arg \min\limits_U \sum_{c=1} \parallel {\bf d}_c - {\bf F}\{{\bf S}_c \circ {\bf W}U{\bf \hat{V}} \} \parallel_2^2,$$where $$${\bf d_c}$$$ and $$${\bf S_c}$$$ are the data and sensitivity map from the $$$c$$$^th coil, $$${\bf F}$$$ is the Fourier sampling operator including the effects from $$$B_0$$$ field inhomogeneity, and $$${\bf W}U{\bf \hat{V}}$$$ is the matrix form of the UoS model ($$${\bf W}$$$ and $$${\bf \hat{V}}$$$ are obtained as described in Ref. 6). The subtraction of the water and lipid signals estimated in this step will remove the majority of the nuisance signals; however, there will remain sparse residual nuisance signals due to inaccuracies in the sensitivity maps. We remove these remaining residual components coil-by-coil by solving$$\hat{U}_c = \arg \min\limits_{U_c} \parallel {\bf d}_c - {\bf F}\{{\bf W}U_c{\bf \hat{V}} \} \parallel_2^2 + R(U_c),$$where explicit spatial support constraints are imposed with $$${\bf W}$$$, and $$$R(\cdot)$$$ is a regularization term enforcing spatial sparsity. After the nuisance signals have been removed, we reconstruct the metabolite signal from the residual by following the recently proposed SPICE framework⁵, but with the sensitivity maps included in the forward model.

We tested our method using 3D in vivo 1H-MRSI data acquired on a 3T Siemens Trio scanner from a healthy (IRB approved) human subject. WET water suppression and outer volume suppression bands were used to reduce the levels of nuisance signals prior to UoS removal. The field of view for the experiment was $$$240 \times 240 \times 72~mm^3$$$ and the matrix size was $$$80 \times 80 \times 20$$$ yielding a nominal voxel size of $$$3 \times 3 \times 3.6~mm^3$$$. The data was acquired in 23 minutes using a customized spin echo EPSI sequence. We retrospectively under-sampled the data along the $$$k_y$$$ direction with a reduction factor of 2 and 8 ACS lines (Fig. 2), simulating an effective scan time of 13 minutes. As described in Ref. 5, we used auxiliary scans to acquire a data set for subspace estimation, $$$B_0$$$ field inhomogeneity map, and an anatomical image. For the purpose of feasibility evaluation, we estimated the sensitivity maps from the fully-sampled data. In practice, however, they would be estimated from an auxiliary scan.^1,3,4

Figure 3(a) shows several adjacent slices of the anatomical image. The NAA maps (obtained via peak integration) for the corresponding slices reconstructed from the fully-sampled and under-sampled data are shown in Figs. 3(b and c). Notice that while the visual quality is similar between Figs. 3(b) and 3(c), the effective acquisition time of Fig. 3(c) is approximately half that of Fig. 3(b). Fig. 3(d) shows spectra from each reconstruction, demonstrating that the spectral quality between the reconstructions is also similar.

This paper presents a novel method that integrates parallel imaging with subspace-based imaging for 1H-MRSI. The method successfully removes nuisance signals and reconstructs high-resolution metabolite distributions from rapidly acquired, sparsely-sampled data. These capabilities should prove useful in a variety of practical applications.