Achieving High Spatiotemporal Resolution for 1H-MRSI of the Brain

Fan Lam^{1}, Chao Ma^{1}, Qiegen Liu^{1}, Bryan Clifford^{1,2}, and Zhi-Pei Liang^{1,2}

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 B_{0} 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 segment^{5} 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.

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Figure 1: The proposed sparse sampling strategy. The dots with different colors denote the samples for different time segments, while the gray dots denote the calibration data repetitively sampled. All the interleaves form a fully-sampled data set (Combined) from which sensitivity maps and accurate nuisance signal estimates can be obtained.

Figure 2: Time-resolved reconstructions from the dynamic data. Left: T1-weighted anatomical image (T1w); Middle: NAA maps for four different time segments, from the conventional Fourier reconstruction (top row) and the proposed method (bottom row); Right: the spectra from the voxel identified by the red dot in the anatomical image.

Figure 3: Temporal variations for NAA signals from one voxel within the brain (red dot, red curve) and noise signals from one voxel in the background (blue dot, blue curve). Distinct dynamics can be observed, although careful investigations are needed to interpret these changes. $$$t$$$ denotes the time segment index.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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