Time-resolved spectroscopy is a potentially powerful tool for studying in vivo metabolism with/without the presence of external stimulus, e.g., understanding brain functions and characterizing tumor metabolism.^1-4 Constrained by the low SNR and low speed of conventional MRSI methods, existing studies typically use either single voxel spectroscopy or very low-resolution data, which can resolve only very limited spatially specific metabolic changes.^1-4 We propose a new subspace-based method to enable high spatiotemporal resolution MRSI for dynamic metabolic studies. In vivo brain 1H-MRSI data have been acquired to demonstrate the potential of the proposed method.

The proposed data acquisition scheme is characterized by: (a) the use of echo-planar spectroscopic imaging (EPSI) based rapid spatiospectral encoding; (b) sparse sampling of k-space but with an extended coverage; (c) sparse sampling in time; (d) time-interleaved k-space undersampling of dynamic MRSI data; (e) acquisition and use of low-resolution, high-SNR navigator signals for subspace estimation. Figure 1 shows an example of the (k,t)-space sampling pattern for this acquisition strategy.

The proposed data acquisition scheme is enabled by a subspace-based data processing and image reconstruction method that can effectively remove nuisance signals and obtain high-quality reconstruction from sparse and noisy data. More specifically, we propose a parallel imaging integrated subspace-based data processing and reconstruction scheme based on the following model

\begin{eqnarray}\rho(\mathbf{r},f,t) & = & \sum_{l_{m}=1}^{L_{m}}u_{l_{m}}(\mathbf{r},t)v_{l_{m}}(f)+\sum_{l_{ns}=1}^{L_{ns}}u_{l_{ns}}(\mathbf{r})v_{l_{ns}}(f)\quad\quad(1)\label{eq:eq_1}\end{eqnarray}

where $$$\rho(\mathbf{r},f,t)$$$ is the time-varying spatiospectral function, $$$v_{l_{m}}(f)$$$ and $$$v_{l_{ns}}(f)$$$ are the bases spanning the spectral subspaces for the metabolite and the nuisance signals (e.g., water and subcutaneous lipids), $$$u_{l_{m}}(\mathbf{r},t)$$$ are the dynamic spatial coefficients for metabolites (with $$$t$$$ denoting the time axis) while the coefficients for nuisance signals ($$$u_{l_{ns}}$$$) are assumed to be temporally unvarying. This model can be viewed as a generalization of the previously proposed subspace model;^5,6 it significantly reduces the number of degrees-of-freedom, thereby making accurate nuisance signal estimation and high-SNR reconstruction from sparse and noisy data possible. Furthermore, the model motivates the acquisition of the above described navigator data for determining $$$v_{l_{m}}(f)$$$ and $$$ v_{l_{ns}}(f)$$$.^5,6

With $$$v_{l_{m}}(f)$$$ and $$$ v_{l_{ns}}(f)$$$ determined, we formulate the reconstruction as follows (integrating parallel imaging)

\begin{eqnarray}\left\{ \hat{\mathbf{U}}_{m,t}\right\} _{t=1}^{T},\hat{\mathbf{U}}_{ns} & = & \arg\underset{\left\{ \mathbf{U}_{m,t}\right\} _{t=1}^{T},\mathbf{U}_{ns}}{\min}\sum_{t=1}^{T}\sum_{c=1}^{C}\left\Vert \mathbf{d}_{t,c}-\mathcal{F}_{\Omega_{t}}\left\{ \mathbf{B}_{t}\odot\mathbf{S}_{c}\left(\mathbf{U}_{m,t}\mathbf{V}_{m}+\mathbf{U}_{ns}\mathbf{V}_{ns}\right)\right\} \right\Vert _{2}^{2}\nonumber \\& & +\lambda_{1}\sum_{t=1}^{T}R_{1t}\left(\mathbf{U}_{m,t}\right)+\lambda_{2}R_{2}\left(\left\{ \mathbf{U}_{m,t}\right\} _{t=1}^{T}\right)+ \lambda_{3}R_{3}\left(\mathbf{U}_{ns}\right),\label{eq:recon}\\\nonumber \end{eqnarray}

where $$$\mathbf{V}_x$$$ are matrix representations of $$$v_{l_{m}}(f)$$$ and $$$ v_{l_{ns}}(f)$$$, $$$\left\{\mathbf{U}_{m,t}\right\}$$$ contain the dynamic spatial coefficients for the metabolite signals, $$$\mathbf{U}_{ns}$$$ contains the time-independent coefficients for the nuisance signals, $$$\mathbf{S}_c$$$ denotes the coil sensitivity profile, $$$\mathbf{B}_t$$$ captures the B₀ field inhomogeneity effects and $$$\mathbf{d}_{t,c}$$$ the data for all the coils and time segments. The terms $$$R_{1t}(.)$$$ apply spatial regularization for each time segment⁵ while $$$R_2(.)$$$ applies a temporal regularization jointly to all segments. $$$R_3(.)$$$ applies regularization on the nuisance signals (an $$$\ell_2$$$ penalty was used here). The sensitivity maps can be derived from either a reference scan or interleaved data from all time segments. Note that the interleaved data also facilitate accurate estimation of nuisance signals from a set of “fully-sampled” data.

In vivo brain 1H-MRSI data have been acquired on a 3T Siemens Trio equipped with a 12-channel head coil (IRB approved) to demonstrate the potential of the proposed method. The imaging parameters for the proposed acquisition were: FOV = 220x220mm², slice thickness = 8mm, matrix size = 64x64, TR/TE = 1000/30ms, and echospace = 1.74ms (for EPSI). Data were continuously acquired for approximately 25 minutes. The navigator data had 16x16 k-space encodings with 512 FID samples and a 2kHz spectral BW. B₀ field maps were acquired with a matched FOV and 128x128 matrix size. An MPRAGE image was acquired for localization and extracting edge information for regularization. Figure 2 shows a set of time-resolved reconstructions from x2 undersampled data (<1min temporal resolution) with comparison to Fourier reconstruction. A temporal total variation penalty was used for $$$R_2(.)$$$. As can be seen, the nuisance signals have been successfully removed; the proposed method yields high-resolution reconstructions with significantly higher SNR than those from the Fourier reconstruction (with noticeable aliasing artifacts). Figure 3 shows distinct dynamics for the NAA signals from one voxel in the brain and the noise signals from the background. Careful validation is needed to confirm whether there is any physiological interpretation for these variations.This paper presents a novel subspace-based acquisition and reconstruction strategy to achieve high spatiotemporal resolution for 1H-MRSI of the brain. Experimental studies have been performed to demonstrate the potential of the proposed method. With further optimizations in acquisition and reconstruction and experimental validation using known dynamic metabolism models, we expect the proposed method to provide a useful tool for in vivo metabolic studies of the brain.