High-resolution mapping of brain metabolites and neurotransmitters using 1H-MRSI has many potential applications ranging from basic neuroscience inquiries to the study of various neurological disorders.^1,2 However, this imaging problem is very challenging because of: a) long imaging time due to the inherently low sensitivity of MRSI (low concentrations of the molecules of interest), and b) difficulty in separating the spectral components corresponding to different molecules in conventional 1D spectrum (e.g., glutamate, glutamine, and the multiplets of NAA have significant spectral overlap). We present a new subspace-based sparse sampling method with multiple-TE (mTE) encoding capability to address these problems. Subspace-based acquisition and reconstruction enable high-resolution, high-SNR reconstruction from sparse and noisy data,³ and mTE encoding enables the separation between metabolite and neurotransmitter signals by incorporating J-resolved spectral prior information.^4-6

The proposed sampling strategy acquires a hybrid of: (1) a set of low-resolution, high-SNR training data ($$$\mathcal{D}_1$$$) and (2) a set of sparse, high-resolution imaging data ($$$\mathcal{D}_2$$$), to achieve accelerated acquisition with multiple TEs. Unlike conventional J-resolved spectroscopy with many TEs, the proposed acquisition aims at acquiring a limited number of arbitrarily spaced TEs chosen for the metabolites of interest (e.g., based on theoretical analysis).⁵ Figure 1 illustrates the proposed sampling strategy for $$$\mathcal{D}_2$$$. Specifically, a 3D spin-echo echo-planar spectroscopic imaging (EPSI) sequence with J-resolved encoding ability is developed. $$$\mathcal{D}_1$$$ is acquired using a low-bandwidth (BW) fully-sampled EPSI scan. This special acquisition strategy is based on the following subspace model

\begin{eqnarray*} \rho(\mathbf{r},t_2,t_1) & = & \sum_{l_{m}=1}^{L_{m}}u_{l_{m}}(\mathbf{r})v_{l_{m}}(t_2,t_1)+\sum_{l_{nt}=1}^{L_{nt}}u_{l_{nt}}(\mathbf{r})v_{l_{nt}}(t_2,t_1)\end{eqnarray*}

where $$$\rho(\mathbf{r},t_2,t_1)$$$ is the image function of interest (with $$$t_2$$$ and $$$t_1$$$ denoting the FID and TE dimensions), $$$\sum_{l_{m}=1}^{L_{m}}u_{l_{m}}(\mathbf{r})v_{l_{m}}(t_2,t_1)$$$ and $$$\sum_{l_{nt}=1}^{L_{nt}}u_{l_{nt}}(\mathbf{r})v_{l_{nt}}(t_2,t_1)$$$ the low-dimensional subspace models for the metabolite (e.g., NAA and choline) and the neurotransmitter (e.g., glutamate and glutamine) components, and $$$L_m$$$ and $$$L_{nt}$$$ the model orders. In contrast to compressed sensing based approaches that require high-SNR data for joint subspace pursuit and reconstruction, this explicit subspace model enables high-resolution, high-SNR reconstruction from the above described data through determining the metabolite and neurotransmitter signal subspaces ($$$\left\{v_{l_{m}}(t_2,t_1)\right\}$$$ and $$$\left\{v_{l_{nt}}(t_2,t_1)\right\}$$$) from the high-SNR $$$\mathcal{D}_1$$$ and the coefficients ($$$\left\{u_{l_{m}}(\mathbf{r})\right\}$$$ and $$$\left\{u_{l_{nt}}(\mathbf{r})\right\}$$$) from the sparse $$$\mathcal{D}_2$$$.

Nuisance signal removal was first performed using the method in 7. B₀ field inhomogeneity was corrected for the nuisance-removed $$$\mathcal{D}_{1}$$$.⁸ The following spectral quantification model was then used to separate the neurotransmitter component from the metabolite component in $$$\mathcal{D}_{1}$$$:

\begin{eqnarray}\rho_{1}(\mathbf{r},t_{2},t_{1}) & = & \sum_{m=1}^{M}a_{m,t_{1}}(\mathbf{r})e^{-t_2/T_{2,m}^{*}(\mathbf{r})}\phi_{m}\left(t_{2},t_{1}\right)\label{eq:quant_subspace}\\ \nonumber \end{eqnarray}

where $$$\phi_{m}\left(t_{2},t_{1}\right)$$$ was generated using quantum mechanical simulation (NAA, creatine, choline, myoinositol, glutamate and glutamine were considered here while more basis can be included).⁹ The quantified glutamate+glutamine ($$$\rho_{1,nt}(\mathbf{r},t_{2},t_{1})$$$) component was then subtracted from $$$\rho_{1}(\mathbf{r},t_{2},t_{1})$$$ to generate the metabolite component $$$(\rho_{1,m}(\mathbf{r},t_{2},t_{1}))$$$. $$$v_{l_{m}}(t_2,t_1)$$$ and $$$v_{l_{nt}}(t_2,t_1)$$$ were obtained by SVD analysis of each component.

With $$$v_{l_{m}}(t_2,t_1)$$$ and $$$v_{l_{nt}}(t_2,t_1)$$$ determined, a joint reconstruction from $$$\mathcal{D}_{2}$$$ can be formulated as follows:

\begin{eqnarray}\hat{\mathbf{U}}_{m},\hat{\mathbf{U}}_{nt} & = & \arg\underset{\mathbf{U}_{m},\mathbf{U}_{nt}}{\min}\sum_{t_{1}=1}^{N_{TE}}\left\Vert \mathbf{d}_{2,t_{1}}-\mathcal{F}_{\Omega_{t_{1}}}\left\{ \mathbf{B}\odot\left(\mathbf{U}_{m}\mathbf{V}_{m}+\mathbf{U}_{nt}\mathbf{V}_{nt}\right)\right\} \right\Vert _{2}^{2}\nonumber \\ & & +\lambda_{1}\left\Vert \mathbf{D}_{w}\mathbf{U}_{m}\right\Vert _{F}^{2}+\lambda_{2}\left\Vert \mathbf{D}_{w}\mathbf{U}_{nt}\right\Vert _{F}^{2},\label{eq:recon}\\\nonumber \end{eqnarray}

where $$$\mathbf{V}_{m}$$$ and $$$\mathbf{V}_{nt}$$$ are matrix representations of each subspace, $$$\mathbf{U}_{m}$$$ and $$$\mathbf{U}_{nt}$$$ the corresponding spatial coefficients, $$$\mathbf{B}$$$ contains linear phase terms modeling the field inhomogeneity effects, $$$\mathcal{F}_{\Omega_{t_{1}}}$$$ represents the Fourier encoding operators with different sampling patterns for different TEs, $$$\mathbf{d}_{2,t_{1}}$$$ denote the data for each TE and $$$N_{TE}$$$ the number of TEs encoded. $$$\mathbf{D}_{w}$$$ is an edge-weighted finite difference operator for spatial regularization. The metabolite and neurotransmitter maps can be obtained by performing quantification to $$$\mathbf{\hat{\rho}}_{m}=\hat{\mathbf{U}}_{m}\mathbf{V}_{m}$$$ and $$$\hat{\mathbf{\rho}}_{nt}=\hat{\mathbf{U}}_{nt}\mathbf{V}_{nt}$$$ separately with reduced model orders.

Data were acquired from healthy volunteers using the above described mTE acquisition on a 3T Siemens Trio scanner. An MPRAGE image was acquired for localization and extracting spatial prior information for data processing. Figure 2 shows the brain coverage of the MRSI volume. The imaging FOV is 220x220x72mm³ and TR = 1s. $$$\mathcal{D}_1$$$ has a matrix size of 16x16x10 and 4TEs (20ms,60ms, 80ms and 100ms).⁵ $$$\mathcal{D}_2$$$ has a matrix size of 60x60x20 and 3 TEs (20ms, 60ms, and 80ms). B₀ maps were obtained for field inhomogeneity correction. Figures 3-5 show some representative results from the data with a total x2.5 undersampling. The proposed subspace estimation method effectively separates the spectral components for different molecules (Fig. 3). The proposed reconstruction yields high-quality spectra (Fig. 4), and high-SNR metabolite and glutamate+glutamine maps (Fig. 5), while those from Fourier reconstruction of the fully sampled mTE EPSI data are too noisy to be useful.We have developed a new subspace-based sparse sampling strategy and reconstruction method for 3D mapping of brain metabolites and neurotransmitters using multiple-TE MRSI. Initial experimental results demonstrate the capability of the proposed method in producing high-resolution and high-SNR spatiospectral distributions of both metabolites and neurotransmitters.