Lihong Tang^{1}, Yibo Zhao^{2,3}, Yudu Li^{2,3}, Rong Guo^{2,3}, Bryan Clifford^{2,3}, Chao Ma^{4}, Zhi-Pei Liang^{2,3}, and Jie Luo^{1}

J-resolved 1H-MRSI is a powerful tool for mapping brain molecules, especially those with large spectral overlaps (e.g., glutamate, glutamine _{J}*in vivo *experiments which have yielded very encouraging results.

Data acquisition

In this work, data were acquired using semi-LASER localization, which is robust to $$$B_1$$$ inhomogeneity, combined with echo-planar spectroscopic imaging readouts (Fig.1 a). The water signal is only weakly suppressed, enabling the tracking and correction of field inhomogeneity, field variations, and eddy current effects. Data acquisition was further accelerated by limited and sparse sampling in (k, t_{J})-space (Fig.1 b-e). The $$$t_J$$$ dimension was highly undersampled, where the optimal selection of $$$t_J$$$ was found by CRLB analysis. To this end, we calculated the CRLB of measurement GABA concentration with all possible $$$t_J$$$_{ }combinations (from 40 – 230 ms) and chose the one that lead to the minimal CRLB. In this work, we found the optimal $$$t_J$$$ combination ($$$t_J$$$ = 40, 90, and 110 ms). The scan FOV was 180x180 mm^{2} with a slice thickness of 10 mm and excitation volume of 90x90x10 mm^{3}, leading to the in-plane resolution of 2.3x1.6 mm^{2}. Other parameters were: TR=1250 ms, total acquisition time = 3.43 mins.

Data processing

For the data acquired at the very first $$$t_J$$$ value with high-resolution and high-SNR, nuisance signals can be effectively removed using a union-of-subspaces method^{4}. For later $$$t_J$$$ values, the limited k-space coverage and poor SNR makes nuisance removal rather challenging. We address this challenge by using generalized series model^{5} to exploit the correlation between nuisance signals from different $$$t_J$$$ acquisitions to remove nuisance signal in later $$$t_J$$$'s. After nuisance signals removal, a physics-based spectral model is used to reconstruct the spatiospectral distribution of metabolites. The image function can be written as a partially separable (PS) function^{6} to perform spectral quantification directly from the (k, t_{J})-space data:

$$\rho(x,t_J,t_2 )=\sum_{l=1}^{L}c_l(x)v_l(t_J,t_2),$$

where $$$t_J$$$ is the $$$TE$$$ time, $$$t_2$$$ is the chemical shift time, $$$\{c_l(x)\}$$$ are spatial coefficients, and $$$\{v_l(t_J,t_2)\}_{l=1}^{L}$$$ are the basis functions determined by quantum mechanical simulations and training data. The spatial coefficients are estimated from the solution to the following regularized least-squares problem

$$\hat{C}=\arg\min_{C}\| M\mathcal{F}B_0CV-d\|_2^2+\lambda\| WD(CV)\|_2^2,$$

where $$$M$$$, $$$\mathcal{F}$$$, and $$$B_0$$$ are the sampling, Fourier encoding, and the field inhomogeneity operators, $$$V$$$ is a row matrix of the basis functions, $$$d$$$ is the vector of water removed k-space data, $$$W$$$ is the edge weight matrix, $$$D$$$ is the gradient operator, and $$$\lambda$$$ is the regularization parameter. The $$$B_0$$$ map and edge weights in $$$W$$$ are predetermined using the data from the first $$$t_J$$$ encoding.

1. Wilson NE, Iqbal, Z., Burns B.L, et al., et al. Accelerated five-dimensional echo planar J-resolved spectroscopic imaging: Implementation and pilot validation in human brain. Magn. Reson. Med., 2016; 75(1):42-51.

2. Ma C, Lam F, and Liu Q, et al. Accelerated high-resolution multidimensional 1H_MRSI using low-rank tensors. Proc. Intl. Soc. Mag. Reson. Med., 2016.

3. Lam F, Cheng B, and Christodoulou, A. G. et al., Accelerated J-resolved MRSI using joint subspace and sparsity constraints. Proc. Intl. Soc. Mag. Reson. Med., 2017.

4. Ma C, Lam F, Johnson C. L, et al., Removal of nuisance signals from limited and sparse 1H MRSI data using a union‐of‐subspaces model. Magn. Reson. Med., 2015.

5. Liang ZP, Lauterbur PC. A generalized series approach to MR spectroscopic imaging. IEEE Trans on Med Imaging. 1991 Jun;10(2):132-7.

6. Liang ZP. Spatiotemporal imaging with partially separable functions. In Proc. IEEE Int Symp Biomed Imaging, USA, 2007; 988-991

7. Lam, Fan, and Liang ZP. A subspace approach to high‐resolution spectroscopic imaging. Magn. Reson. Med., 2014; 71:1349-1357.

Fig. 1 The J-resolved semi-LASER sequence diagram is shown in (a). The delay time controls the J-coupling encoding, $$$t_J$$$. (b-e) depict the proposed sparse sampling strategy which is enabled by the partially separable model.

Fig. 2. Simulation results demonstrating the proposed method’s ability to produce accurate reconstructions from sparsely sampled, noisy data. (a) shows the ground truth, estimated values, and estimation standard deviation. (b)-(d) show 1D spectra for GABA, Glu, and NAA from one of the 40 realizations. The spectra from the ground truth and reconstruction are shown in green and blue, respectively.

Fig. 3. In vivo results using the proposed method. (a) Shows the metabolite signal energy map estimated at 2.3 mm x 1.6 mm x10 mm nominal resolution, and (b) shows a representative localized 2D spectra from the position indicated by the black dot.

Fig. 4. In vivo results using the proposed method, (a) Glu, Gln, and GABA map (norm to 0-1individually, 2.3 mm x 1.6 mm x10 mm nominal resolution), (b), (c) Representative 2D spectra of black dot position.