Ultrafast magnetic resonance spectroscopic imaging using SPICE with learned subspaces

Abstract

Purpose: To develop a subspace learning method for the recently proposed subspace-based MRSI approach known as SPICE, and achieve ultrafast ¹ H-MRSI of the brain.

Theory and methods: A novel strategy is formulated to learn a low-dimensional subspace representation of MR spectra from specially acquired training data and use the learned subspace for general MRSI experiments. Specifically, the subspace learning problem is formulated as learning "empirical" distributions of molecule-specific spectral parameters (e.g., concentrations, lineshapes, and frequency shifts) by integrating physics-based model and the training data. The learned spectral parameters and quantum mechanical simulation basis can then be combined to construct acquisition-specific subspace for spatiospectral encoding and processing. High-resolution MRSI acquisitions combining ultrashort-TE/short-TR excitation, sparse sampling, and the elimination of water suppression have been performed to evaluate the feasibility of the proposed method.

Results: The accuracy of the learned subspace and the capability of the proposed method in producing high-resolution 3D ¹ H metabolite maps and high-quality spatially resolved spectra (with a nominal resolution of ∼2.4 × 2.4 × 3 mm³ in 5 minutes) were demonstrated using phantom and in vivo studies. By eliminating water suppression, we are also able to extract valuable information from the water signals for data processing ( $B_0$ map, frequency drift, and coil sensitivity) as well as for mapping tissue susceptibility and relaxation parameters.

Conclusions: The proposed method enables ultrafast ¹ H-MRSI of the brain using a learned subspace, eliminating the need of acquiring subject-dependent navigator data (known as $D_1$ ) in the original SPICE technique. It represents a new way to perform MRSI experiments and an important step toward practical applications of high-resolution MRSI.

Keywords: MR spectroscopic imaging; no water suppression; rapid spatiospectral encoding; subspace learning; union-of-subspaces model.

Figure 1:

An illustration of the proposed subspace learning strategy: (a) Resonance structures for individual metabolites are obtained by QM simulations; (b) High-SNR training data are acquired and fitted to sample the distributions of spectral parameters (i.e., c_m, $T_{2,m}^{*}$, δf_m); (c) Integration of these two generates sample spectra that reside on a low-dimensional manifold. Assuming that the parameters for physiologically meaningful spectra came from an underlying distribution independent of subjects, this manifold can be accurately approximated by a low-dimensional subspace that can be learned from training data (d) and used for general MRSI experiments.

Figure 2:

Illustration of subspace approximation for spectra with parameters generated from specific distributions: 10000 metabolite spectra were synthesized using Eq. [2] with randomly distributed {c_m}, {$T_{2,m}^{*}$}and {δf_m}, and arranged into a Casorati matrix (a), which has very rapidly decaying singular values as shown in (b), indicating that these spectra can be well approximated by a low-dimensional subspace. The dash line indicates where the rank truncation error falls below 1e⁻³ (rank 14). A new spectra (not among the existing 10000) was generated and projected onto a 14-dimensional subspace (c); the projection error is negligible, further validating the subspace model.

Figure 3:

Subspace learning from in vivo data: (a) Singular value decays for the Casorati matrices formed by the fitted spatiospectral functions from all five training data (different volunteers); the rapid decays demonstrate the accuracy of low-dimensional subspace representation; (b–d) Histograms of the estimated $T_2^{*}$ parameters for three data sets. Similar distributions can be observed, supporting the concept of using training data to determine a subject-independent distribution from which a subspace can be constructed.

Figure 4:

Evaluation of the learned subspace: The first row shows the spectral basis estimated from the first training data set (the 1st, 2nd, 6th and 9th bases are shown in different columns, respectively); The second row shows the basis learned from the remaining four data; The third row compares the basis in the first row (blue) and their projections onto the subspace spanned by the basis in the second row (red). As can be seen, while individual spectra may vary, the projections match the original spectral basis very well, implying an accurate representation using the learned subspace. The project error was around 3%.

Figure 5:

High-resolution, 3D ¹H-MRSI results from the metabolite phantom using an 8 min scan: (a) Images reconstructed from the unsuppressed water signals illustrating the structural arrangement of the phantom (note that the lengths of vials are different for different rows thus the changing features across slices); (b–e) Reconstructed metabolite maps, i.e., NAA (b), Cr (c), Cho (d) and mI (e) for the corresponding slices in (a). As can be seen, the proposed method produced high-resolution, high-SNR reconstructions, allowing visualization of even the smallest vials as well as resolving the concentration differences.

Figure 6:

Spatiospectral reconstructions from a 5 min, 3D brain ¹H-MRSI acquisition. The metabolite reconstructions were produced using the learned subspace (a) and the subspace estimated from a single subject-specific ${\mathcal{D}}_1$ (b), respectively. The maps of NAA, Cr, and Cho are shown in different rows. The plots in (c) compare the reconstructed spatially-resolved spectra at selected voxels, locations indicated by the red symbols in (a). As can be seen, the two spatiospectral reconstructions are very similar to each other; but the learned subspace can achieve this result without acquiring subject-specific ${\mathcal{D}}_1$. The relative ${\mathcal{l}}_2$ errors for the NAA, Cr and Cho maps are 2.4%, 6.4%, and 8.0%, respectively.

Figure 7:

Ultrafast, 3D ¹H-MRSI of the brain from another 5 min scan without water suppression using the learned subspace: (a-d) Reconstructed metabolite maps of NAA, Cr, Cho and mI for different slices across the 3D volume; (e) anatomical images with $T_2^{*}$ contrast reconstructed from the unsuppressed water signals; (f) tissue quantitative susceptibility maps (QSM) obtained from the phase variations encoded in the water spectroscopic signals.