Accelerated J-Resolved ¹H-MRSI with Limited and Sparse Sampling of (k, t₁, t₂)-Space

Abstract

Purpose:

To accelerate the acquisition of J-resolved ¹H-MRSI data for high-resolution mapping of brain metabolites and neurotransmitters.

Methods:

The proposed method used a subspace model to represent multidimensional spatiospectral functions, which significantly reduced the number of parameters to be determined from J-resolved ¹H-MRSI data. A semi-LASER based echo-planar spectroscopic imaging (EPSI) sequence was used for data acquisition. The proposed data acquisition scheme sampled (k, t₁, t₂)-space in variable density, where t₁ and t₂ specify the J-coupling and chemical-shift encoding times, respectively. Selection of the J-coupling encoding times (or, TE values) was based on a Cramer-Rao lower bound analysis, which were optimized for gamma-aminobutyric acid (GABA) detection. In image reconstruction, parameters of the subspace-based spatiospectral model were determined by solving a constrained optimization problem.

Results:

Feasibility of the proposed method was evaluated using both simulated and experimental data from a spectroscopic phantom. The phantom experimental results showed that the proposed method, with a factor of 12 acceleration in data acquisition, could determine the distribution of J-coupled molecules with expected accuracy. In vivo study with healthy human subjects also showed that 3D maps of brain metabolites and neurotransmitters can be obtained with a nominal spatial resolution of 3.0 × 3.0 × 4.8 mm³ from J-resolved ¹H-MRSI data acquired in 19.4 minutes.

Conclusions:

This work demonstrated the feasibility of highly accelerated J-resolved ¹H-MRSI using limited and sparse sampling of (k, t₁, t₂)-space and subspace modeling. With further development, the proposed method may enable high-resolution mapping of brain metabolites and neurotransmitters in clinical applications.

1. INTRODUCTION

The capability of ¹H-MRS/MRSI to noninvasively measure brain metabolites and neurotransmitters is desirable for investigation and assessment of various neurological (1,2), psychiatric (3–5), and oncological disorders (6,7). However, molecular quantification from ¹H-MRS/MRSI data is often difficult due to several practical problems, including spectral overlapping. The resonances of key detectable metabolites of the brain (~20 in total) lie in a very narrow chemical shift range. For instance, gamma-aminobutyric acid (GABA), the main inhibitory neurotransmitter, has significant spectral overlaps with Glutamate (Glu), Glutamine (Gln), Choline (Cho), N-acetyl aspartate (NAA) and Creatine (Cr) in one-dimensional (1D) MR spectra, making spectral decomposition and quantification difficult.

Many methods have been proposed to address the spectral overlapping problem with ¹H-MRS/MRSI using either spectral editing or multi-dimensional spectral encoding. Spectral editing methods (8) simplify ¹H spectra via a range of techniques, such as TE optimization (9), BASING (10), J-difference editing (11–13), co-editing and accelerated difference editing (14–18), and multiple quantum filtering (19–21). These methods are limited to the detection of only one or few molecules per acquisition. Multi-dimensional ¹H-MRSI methods, such as 2D correlation spectroscopy (COSY) and J-resolved spectroscopy (22–24), resolve the spectral overlap by incorporating an additional spectral dimension, capturing the distinct J-coupling pattern of each molecule. Unlike spectral editing techniques, COSY-MRSI or J-resolved MRSI can simultaneously map all detectable metabolites although at the expense of long data acquisition time. For example, 5D ¹H-MRSI needs to collect data to cover a high-dimensional (k, t₁, t₂)-space, where k represents 3 spatial encoding dimensions (k_x, k_y, k_z), t₁ represents the indirect spectral encoding dimension (J-coupling encoding time), and t₂ represents the direct spectral encoding dimension (chemical shift encoding time). As a result, 5D ¹H-MRSI experiments would increase data acquisition time by several orders of magnitude, limiting practical utility.

Over the past decades, significant advances have been made in accelerating MRSI experiments. For example, echo-planar acquisitions can significantly reduce the data acquisition time for spatiospectral encodings compared to the conventional CSI, though at the cost of SNR (25,26). Parallel data acquisition using phased array coils has become an integral part of modern MRSI methods (27). Compressed sensing further accelerates MRSI experiments by reducing the number of k-space encodings (28–32). More recently, subspace models exploiting the partial separability (PS) of high-dimensional spatiospectral signals (33) have been proposed for ultrafast MRSI using a technique known as SPectroscopic Imaging by exploiting spatiospectral CorrElation (SPICE) (34–39). Extension of SPICE to J-resolved MRSI has also been investigated, which produced encouraging results (40–42).

Building on these advances, this work investigated and demonstrated the feasibility of highly accelerated J-resolved ¹H-MRSI using: a) subspace spatiospectral models incorporating spectral prior information, b) sparse and limited sampling of (k, t₁, t₂)-space, and c) rapid acquisition of spatiospectral encodings in EPSI trajectories following semi-LASER excitations. A preliminary version of the proposed method was first described in Tang et al (43); detailed descriptions of our proposed data acquisition scheme, image reconstruction method, and experimental results are given in the subsequent sections.

2. METHODS

2.1. Data acquisition

The proposed data acquisition scheme has the following key features: a) semi-LASER excitations, b) rapid acquisition of spatiospectral encodings in EPSI trajectories, and c) sparse sampling in (k, t₂)-space and limited sampling in t₁ dimension. A pulse sequence implementing this data acquisition scheme and its corresponding sampling trajectories in (k, t₁,t₂)-space are shown in Figure 1, where k represents 3 spatial encoding dimensions (k_x, k_y, k_z). Note that for each TR, following the water suppression pulses, a semi-LASER based excitation was used to selectively excite a region of interest (Figure 1A) (44,45). During the free precession period after each semi-LASER excitation, spatiospectral encodings were acquired from the right side of an echo (i.e., half echo sampling) with EPSI trajectories using alternating gradients (Figure 1A) (46). Note that for conventional EPSI trajectories, there is a tradeoff between k-space coverage and spectral bandwidth, namely, extended k-space coverage requires longer sampling times, leading to an increased echo spacing. For example, assuming that N spatial encodings are collected with a dwell time dt in the presence of constant gradient G during each EPSI gradient pulse, then the spatial resolution along the readout direction is FOV/N = 2π/(NγGdt) and the resulting echo spacing (sampling time along t₂) is Δt₂ = 2 × (2 × t_ramp + Ndt), where t_ramp is the ramp-up or ramp-down time for the gradient. Therefore, higher resolutions would lead to larger echo spacings. For spectroscopic imaging at 3T, the frequency differences between MR detectable resonances in the human brain and water are within 600 Hz (chemical shift difference of 4.7 ppm). The corresponding Nyquist sampling interval is 0.83 ms (1/1200 Hz), which severely limits the achievable readout resolution. In this work, we used a similar strategy as reported in (34–39) to overcome this limitation. More specifically, we increased the readout size to about 60 encodings to achieve high spatial resolution; the resulting echo spacing Δt₂ was 1.2 ms, which was larger than the Nyquist interval (0.83 ms). The problem of temporal undersampling was handled through the use of pre-learned spectral basis in the subspace model. This strategy has been successfully used for accelerating basic MRSI in our previous works (34–39).

Figure 1.

Illustration of the proposed data acquisition scheme. A) Pulse sequence diagram for semi-LASER excitation and EPSI readout gradients; B) (k_x, k_y, k_z, t₁, t₂) -space sampling scheme for the optimized TE values (40 ms and 90 ms); note that outer k-space along k_y was sparsely sampled by a factor of 2 acceleration and k-space along k_z was fully sampled with conventional phase encoding.

To further accelerate data acquisition, we acquired spatiospectral encodings for very few TEs (to encode J-coupling spectral information) (Figure 1B). Selection of the TEs was based on a Cramer-Rao lower bound (CRLB) analysis to minimize GABA estimation uncertainty. In the analysis, we chose one of the conventional acquisition schemes as the reference (40–42), with TEs chosen from 40 ms to 230 ms in 10-ms intervals. To maximize SNR efficiency, we fixed the total acquisition time and calculated the CRLB for all possible combinations of TEs. More specifically, the following model was used in our CRLB analysis which decomposed the J-resolved spectroscopic signals into a linear combination of individual molecular components:

$$S\left(\text{TE},t_2\right)={\sum }_{m=1}^M{c}_m{e}^{-\frac{\text{TE}}{T_{2,m}}}{e}^{\left(i2\pi f_m-\frac{1}{T_{2,m}^{*}}\right)t_2}{\phi }_{\text{m}}\left(\text{TE},t_2\right)+\epsilon \left(\text{TE},t_2\right),$$ [1]

where φ_m(TE, t₂) denotes the two-dimensional basis function for the m^th metabolite, generated by quantum mechanics simulations; c_m, T_2,m, $T_{2,m}^{*}$, and f_m are the corresponding concentration, T₂ relaxation time constant, $T_2^{*}$ relaxation time constant, and frequency shift, obtained from literature values; ε(TE, t₂) is additive Gaussian white noise at a realistic level. With this signal model, the CRLBs for the concentration estimations were derived as follows:

$$\text{var}(\widehat{c})\ge {\sigma }^2\text{diag}{\left(V^{\text{H}}V\right)}^{-1},$$ [2]

where V contains the spectral basis functions (i.e., $v_m={\text{e}}^{-\frac{\text{TE}}{T_{2,m}}}{\text{e}}^{\left(i2\pi f_m-\frac{1}{T_{2,m}^{*}}\right)t_2}{\phi }_{\text{m}}\left(\text{TE},t_2\right)$) in matrix form and σ² is the white noise variance.

Noting the significantly reduced SNR for data at large TEs (≥ 140 ms), we only considered TEs ranging from 40 ms to 130 ms in 10-ms intervals. In addition, we fixed the acquisition time to include exactly 10 J-encodings, and multiple acquisitions at the same TE were also allowed. Then we traversed all the possible choices of TE and calculated the corresponding CRLBs for GABA estimates. As the results shown in Figure 2B, the optimal choice that gave the smallest CRLB was two TEs with repetitions. This result indicated that even if data acquisition time permits collecting J-encodings at multiple TEs, two TEs is preferred. For in vivo experiments with the proposed spatial resolution, the data acquisition time for 10 acquisitions was not practically feasible. So, with the first CRLB result, we repeated the CRLB analysis by limiting the number of acquisitions to two and then determined the optimal TE values. As the analysis results shown in Figure 2C, the optimal TE values turned out to be 40 ms and 90 ms, each now with 1 repetition. Figure 2 summarizes the results of the CRLB analysis.

Figure 2.

CRLB analysis. A) Ground truth signals; B) minimum CRLB values of GABA measurements for different numbers of TE, under a fixed acquisition time to include 10 J-encodings; the optimal number of TE turns out to be two; C) CRLB matrix of GABA estimations for combinations of two TEs, under the fixed number of acquisition to be two; TEs = 40 ms and 90 ms yields the minimum GABA CRLB.

Based on the above CRLB analysis, the sampling scheme was designed as shown in Figure 1B. Note also that we further shortened data acquisition time by sparse sampling along k_y at TE = 40 ms and 90 ms. With the total 60 phase encodings along k_y, we fully sampled central k-space with 36 encodings and sparsely sampled peripheral k-space by a factor of 2 (Figure 1B).

2.2. Data processing

The proposed data acquisition scheme requires special methods for data processing including removal of the residual water signals and spatiospectral reconstruction and quantification. The key novel features of our data processing methods are: a) use of the correlated information of the water signals from different TEs for their effective removal, b) use of a union-of-subspaces model with pre-learned spectral basis for spatiospectral reconstruction, and c) subspace-based spectral quantification using two-TE data jointly. As compared to ProFit (47) which solves a nonlinear optimization problem and requires J-resolved MRSI data from many TEs, the proposed method reformulates the problem as a linear problem by representing the spatiospectral distribution of each molecule as a subspace; the union-of-subspaces model enables efficient solution and effective incorporation of spatial constraints, which helps improve accuracy and robustness of the reconstruction and quantification results. Another subtle difference is that the proposed method works in the time domain rather than the frequency domain, which enables us to process limited and sparse data effectively. A more detailed description of our data processing methods is given below.

2.2.1. Removal of residual water signals

While lipid contamination can be adequately reduced by the semi-LASER excitation pulses, we still need to handle the residual water signals. Significant work has been done to address the water removal problem in conventional MRSI experiments (48–50). We used a modified strategy to remove the residual water signals from our J-resolved MRSI data. More specifically, since the water signal for the first TE (40 ms) had good SNR, we simply applied a subspace-based method for its removal, which was described in detail in several publications (35,36,50). The problem of removing the residual water signal for the second TE (90 ms) was more challenging due to lower SNR. To address this issue, we exploited the correlation between the water signals from different TEs using the generalized series (GS) model (51). More specifically, we modeled the water signal $d\left(k_x,k_y,k_z,t_1^{(2)},t_2\right)$ for the second TE as

$$d\left(k_x,k_y,k_z,t_1^{(2)},t_2\right)=\int \left[\widehat{\rho }\left(x,y,z,t_1^{(1)},t_2\right){\sum }_{l=1}^L{c}_l^{(2)}\left(x,z,t_2\right)e^{-i2\pi k_{l}y}\right]e^{-i2\pi \left(k_{x}x+k_{y}y+k_{z}z\right)}\text{d}x\text{d}y\text{d}z,$$ [3]

where $\widehat{\rho }\left(x,y,z,t_1^{(1)},t_2\right)$ is the estimated water signal for the first TE, and ${\left\{c_l^{(2)}\left(x,z,t_2\right)\right\}}_{l=1}^L$ are the GS model coefficients. With the model in Equation 3, the water signal for the second TE was estimated by solving the following least-squares problem:

$${\widehat{C}}_{\text{GS}}^{(2)}=\text{arg}\underset{C_{GS}}{\text{min}}\left|\right|M^{(2)}F\left\{{\widehat{\rho }}^{(1)}\circ \left(E^{(2)}{C}_{\text{GS}}\right)\right\}-d^{(2)}{\Vert }_2^2,$$ [4]

where d⁽²⁾ is the data vector acquired at $t_1^{(2)}$, ${\widehat{\rho }}^{(1)}$ is the estimated water signal at $t_1^{(1)}$, ‘o’ represents the entry-wise product operator, M⁽²⁾ is the sampling operator at $t_1^{(2)}$, F is the Fourier encoding operator, E⁽²⁾ is the matrix containing the values of $e^{-i2\pi k_{l}y}$ over the k-space sampling points, and C_GS denotes the GS model coefficients to be determined.

2.2.2. Spatiospectral reconstruction and quantification

There are three key issues in spatiospectral reconstruction from the data acquired using the proposed data acquisition scheme: a) low SNR, b) spatiospectral aliasing due to sparse sampling, and c) low spectral resolution along the J dimension due to limited sampling. First, parallel imaging (SENSE) was used to address the problem of spatial aliasing caused by sparse sampling only along k_y dimension (Figure 1B) (52,53). Then, we addressed the low SNR and spectral resolution issues by leveraging the partial separability (PS) of the J-resolved MRSI data. Leveraging the fact that multi-dimensional MRSI data reside in a low-dimensional subspace (33), we modeled the nuisance signal removed J-resolved MRSI signals with M metabolites as:

$$\rho \left(x,t_1,t_2\right)={\sum }_{m=1}^M{\sum }_{r=1}^{R_m}{u}_{r,m}(x)v_{r,m}\left(t_1,t_2\right),$$ [5]

where ${\left\{v_{r,m}\left(t_1,t_2\right)\right\}}_{r=1}^{R_m}$ are the two-dimensional temporal basis functions and ${\left\{u_{r,m}(x)\right\}}_{r=1}^{R_m}$ are the corresponding spatial coefficients, corresponding to the m^th metabolite. The model in Equation 5 represents each metabolite by a subspace and the overall J-resolved signals by a union-of-subspaces (54).

To effectively use the model in Equation 5, we pre-determined the basis functions ${\left\{v_{r,m}\left(t_1,t_2\right)\right\}}_{r=1}^{R_m}$ from specially acquired training data. The idea to use pre-learned spectral basis functions for accelerated MRSI experiments had been validated in our recent work (55). Here, we extended this concept to pre-learn the 2D spectral basis from independent training datasets, which were acquired using the standard semi-LASER CSI sequence at TE = 40, 90 ms with following parameters: FOV = 180 × 180 mm², excitation volume = 90 × 90 mm², TR = 1250 ms, matrix size = 16 × 16, slice thickness = 10 mm, and a total acquisition time of 10.84 minutes. These training datasets provided the empirical distributions of spectral parameters, especially the lineshape variations, obtained by traditional spectral quantification (56). We then generated spectral distributions for TE = 40, 50, ⋯, 230 ms using Equation 1 with the learned spectral parameters and quantum simulated resonance structures (57). Afterward, the two-dimensional temporal basis functions were determined from the synthetic J-resolved MRSI data using singular value decomposition (SVD) analysis (54). In this study, we included in our model the basis functions only for NAA, Cr, Cho, mI, Glu, Gln, and GABA; other basis functions for molecules like aspartate and glutathione were not included in our analysis due to their low concentrations and the associated difficulty in achieving reliable estimates for these molecules in our accelerated experiments at 3T (58). Note also excluding the low-concentration molecules had a negligible effect on the estimation of the other molecules considered in the paper, as described in the Supporting Information (Figure S2).

We used two separate sets of basis functions for processing the phantom and in vivo data, respectively. The basis functions used for the phantom study were generated from training data acquired from the phantom, while the basis functions used for the in vivo study were generated from training data acquired from human subjects. After the basis functions were determined, the subspace-based model in Equation 5 enabled reconstruction of the spatiospectral function from the nuisance-removed data. This was done by determining the spatial coefficients of the union-of-subspaces model via the solution of the following regularized optimization problem:

$${\widehat{U}}_m=\text{arg}\underset{\left\{U_m\right\}}{\text{min}}\left|\right|MF{B}_0\left({\sum }_{m=1}^M{U}_m{V}_m\right)-d{\Vert }_2^2+\lambda {\sum }_{m=1}^M{\Vert WD{U}_m\Vert }_2^2$$ [6]

where M, F, and B₀ are the operators accounting for sampling, Fourier encoding, and the effects of field inhomogeneity, respectively; d is the vector of nuisance signal removed (k, t₁, t₂)-space data with the methods described in subsection 2.2.1; W is an edge weight matrix; D is the spatial gradient operator which was imposed on spatial coefficients; λ is the regularization parameter which was selected using the discrepancy principle (59). ${\left\{V_m\right\}}_{m=1}^M$ are the pre-learned spectral basis functions corresponding to the m^th metabolite (in matrix form). The B₀ map and edge weights in W were predetermined from the water image obtained from the first TE signals.

After the ${\left\{U_m\right\}}_{m=1}^M$ were determined, ${\sum }_{m=1}^M{U}_m{V}_m$ or Equation 5 provided the overall spatiospectral distribution; each spectral component could also be obtained from ρ_m = U_mV_m. However, for spatiospectral reconstruction, the ranks R_m in Equation 5 were chosen relatively high so that the union-of-subspaces model was sufficient for representing any spatiospectral distributions of interest. As a consequence, the subspaces spanned by ${\left\{v_{r,m}\left(t_1,t_2\right)\right\}}_{r=1}^{R_m}$ may have significant overlaps and the resulting ρ_m = U_mV_m may not purely represent the m^th molecule. So, we used ρ_m only as an initiate estimate and performed spectral quantification on the overall spatiospectral function ${\sum }_{m=1}^M{U}_m{V}_m$ using an existing subspace-based method (54,60). To further improve the performance, we performed spectral quantification using the J-resolved data jointly; we also transferred the lineshape functions (representing the effect of intravoxel dephasing and transverse relaxation) from the molecules with high SNR (e.g., NAA) to the molecules with low SNR (e.g., GABA, Glu and Gln).

Note that in vivo data often contain non-negligible baseline signals including those from macromolecules, especially for the data collected at TE = 40 ms. Therefore, we removed all the baseline signals before spatiospectral reconstruction was done. This was accomplished using a standard strategy as in QUEST (56). More specifically, we modelled the baseline signal as a combination of B-splines in the spectral domain. To estimate the combination coefficients, we first removed the metabolite signals fitted from the FID signals with the early time points truncated (5 points were truncated in our current implementation); then we estimated the baseline signals by fitting B-splines to the residual and then removed it from the original data.

2.3. Experiments

A spectroscopic phantom was constructed in a cylindrical holder filled with NaCl doped water (configuration shown in Figure 3A). Three sets of cylindrical glass vials were positioned in parallel with the holder; each row contained three vials of different diameters and each column of vials were filled with solutions of three different combinations of NAA, Cr, Cho, myo-inositol (mI), Glu, and GABA. Concentrations of each metabolite were chosen at physiological levels (19,61–63) and described in Figure 3B.

Figure 3.

Spectroscopic phantom. A) Cross-sectional view: three sets of cylindrical vials in parallel; vials in each row were filled with the same solution; vials in each column were of the same size. B) Molecular composition of the solution in each row, indicated by I, II, and III. Note that Gln was not in the solution of the phantom, but included in the simulation study.

2.3.1. Simulation studies

Fully sampled (k, t₁, t₂)-space data with spatial matrix size of 60 × 60 × 16 and 20 TEs from a spectroscopic phantom were generated with TEs ranging from 40 ms to 230 ms, at 10-ms increments and t₂ starting from 0 to 256 ms, at 0.5-ms increments.

We compared the performance of the proposed reconstruction method to the standard Fourier reconstruction for three undersampling scenarios (Figure 4A) without noise. In the first scenario, the (k, t₁,t₂)-space data were sampled with limited TE (2/20 TEs); in the second and third scenarios, the (k, t₁, t₂)-space data were sampled with sparse TE (2/20 TEs), either uniformly or with optimal TE values as estimated by the CRLB analysis.

Figure 4.

Reconstructions from simulated data. A) Sampling patterns used to generate the J-resolved MRSI data; B) Fourier reconstructions; C) reconstructions using the proposed method. Note that the conventional Fourier method produced significant spectral artifacts with limited and sparse sampling in t₁ dimension. These artifacts were effectively removed using the proposed method.

We also added noise to the simulated spectroscopic data with SNR comparable to that of the experimental data; 100 sets of Gaussian white noise were generated to perform a Monte Carlo study. Reproducibility and reliability of the quantification results were evaluated using the coefficient of variance (COV) (63) and the intraclass correlation coefficient (ICC) (64).

2.3.2. Phantom experiments

The spectroscopic phantom was scanned on a 3T Siemens Magnetom Prisma system using a commercial 20-channel head and neck coil. The data were acquired using the proposed data acquisition scheme with the following parameters: FOV = 180 × 180 × 48 mm³, excitation volume = 90 × 90 × 40 mm³, TR = 1200 ms, nominal spatial resolution = 3.0 × 3.0 × 3.0 mm³, matrix size = 60 × 60 × 16, and 30.7 minutes scan time. The proposed method was used to reconstruct the 5D J-resolved MRSI images for spectral quantification. The metabolite concentrations of vial I were used as reference for calculating the molecule concentrations in all the other vials.

2.3.3. In vivo experiments

Four healthy volunteers were scanned (with IRB approval) on the same system using the same sequence as in the phantom scan with a resolution of 3.0 × 3.0 × 4.8 mm³, a matrix size of 60 × 60 × 10, and a scan time of 19.4 minutes. A conventional MPRAGE scan (FOV = 240 × 240 × 192 mm³, matrix size = 256 × 256 × 192, TE = 2.29 ms, TI = 900 ms, TR = 1900 ms) was also included in the protocol. The spatiospectral distributions were reconstructed using the same method as in the phantom experiments, from which brain metabolite maps of NAA, Cr, Cho, mI, Glu, Gln, and GABA were calculated.

3. RESULTS

The proposed method was able to recover the desired spatiospectral distributions from J-resolved MRSI data that had limited and sparse sampling of (k, t₁, t₂) -space, as demonstrated in simulation results (Figure 4). Note that both blurring and aliasing artifacts in the conventional Fourier reconstructions resulting from limited and sparse sampling were effectively removed using the proposed method.

In the Monte Carlo study carried out using the same simulation phantom, the concentrations of NAA, Cr, and Cho were highly reproducible, with their COVs within 0.1%; for GABA and Gln, the COVs of their concentrations ranged from 10% to 30% (Figure 5A and Table 1). The trend of their COVs, COV_GABA > COV_Gln > COV_Glu > COV_mI > COV_Cho > COV_Cr > COV_NAA, was in good agreement with the CRLB estimations (Figure 6B). For a given molecule with its intrinsic spectral line shape, the COV of estimated concentration should be inversely proportional to its concentration. Our simulation study also showed that the reliability (ICC) of the estimated concentrations for all the metabolites was above 0.99.

Figure 5.

A) Monte Carlo study using simulated data with Gaussian noise: COV maps of the estimated concentrations. B) Experimental results from a phantom: estimated concentrations for each molecule in the phantom. Note that the phantom contains no Gln, thus no Gln concentration was presented. The color bars were adjusted separately for different molecules.

Table 1.

Summary of COV and ICC in a Monte Carlo simulation study

		NAA	Cr	Cho	mI	Glu	Gln	GABA
Mean COV (%)	I	2.36	1.37	3.89	7.46	6.56	13.13	14.35
	II	3.56	2.06	3.89	7.50	7.92	13.20	14.42
	III	4.42	1.64	1.92	5.95	9.81	26.14	28.55
ICC		1.0000	1.0000	1.0000	0.9996	0.9998	0.9998	0.9998

Figure 6.

CRLB analysis of metabolite concentrations based on the ground truth signals shown in Figure 2A. A) Estimation variances are inversely proportional to the pixel SNR; B) relationship between estimation variance predicted by CRLB calculation and Monte Carlo simulations.

Our key experimental results from the spectroscopic phantom are summarized in Figure 5B and Table 2, which includes the concentrations of each metabolite. The relative error of quantification ranged from 0.28% to 27.03%.

Table 2.

Estimated molecular concentrations from a phantom

	NAA	Cr	Cho	mI	Glu	GABA
Vial I*	15.00	12.00	3.00	8.00	12.00	2.00
	Mean (Error %)
Vial II	9.29(7.17)	8.99(10.05)	2.80(6.81)	6.48(18.95)	10.31(3.07)	2.18(8.84)
Vial III	8.21(2.68)	7.67(4.14)	6.02(0.28)	11.52(15.17)	8.51(6.33)	1.27(27.03)

Note:

^*reference vial

A set of representative in vivo experimental results (2D spectra and 3D metabolic maps) using the proposed method is shown in Figures 7 and 8. For a given voxel, the main resonance lines of Cho, Cr, and NAA are clearly visible in the 2D spectra (Figure 7B), while the J-coupled resonances of Glu, Gln, and GABA are crowded within the 2.0–3.0 ppm (Figure 7C–E). Figure 8B shows the metabolite maps of NAA, Cr, Cho, mI, Glu, Gln, and GABA overlaid on top of a high-resolution structural image. All of the high-resolution metabolite and neurotransmitter maps were obtained simultaneously from a single scan (~19 minutes). Metabolite concentrations in gray matter and white matter regions were calculated from all subjects (Figure 8C). The concentration ratios between gray matter and white matter of four healthy subjects were 1.11 ± 0.03 for NAA, 1.08 ± 0.05 for Cr, 0.98 ± 0.03 for Cho, 1.06 ± 0.06 for mI, 1.07 ±0.06 for Glu, 1.06 ± 0.03 for Gln, and 1.07 ± 0.04 for GABA, which are consistent with the literature values (19,61–63).

Figure 7.

Experimental results from a healthy human subject. A) Anatomical image; B) representative 2D overall spectra from the voxel indicated by the red dot in (A); C-E) 2D spectra of Glu, Gln, and GABA from the same location.

Figure 8.

Experimental results of healthy volunteers. A) Anatomical localization image; B) representative metabolite maps of NAA, Cr, Cho, mI, Glu, Gln, and GABA in nominal spatial resolution 3.0 × 3.0 × 4.8 mm³ from the volume indicated in (A); C) white matter and gray matter metabolite concentrations of 4 healthy volunteers. GM: gray matter; WM: white matter; ***: P < 0.0001.

Note that in our experiments with TR = 1200 ms, the estimated metabolite concentrations carried a T₁-weighting effect. One can eliminate this effect, if needed, with a longer TR. For our in vivo experiments, the T1-weighting effects were relatively small. For example, for NAA, the literature T₁ values for gray matter and white matter are 1470 ms and 1350 ms, respectively (65), and the T₁-weighting effect for the estimated concentrations in gray matter and white matter was 5.4%. Note also that, with the same spatial matrix size of 60 × 60 × 10 and 20 TEs, the conventional EPSI data acquisition would require at least 240 minutes (60 × 10 × 20 × 1.2 s). Thus, the proposed scheme provided a factor of 12.5 acceleration in this particular case.

4. DISCUSSION

Our study demonstrated the feasibility of highly accelerated J-resolved MRSI using the proposed method with: a) limited and sparse sampling along t₁, and b) large echo spacings of the EPSI data (34–39). From our phantom study, the concentrations of NAA, Cr, Cho, mI, Glu, and GABA were detected with a relative error within 30% for a factor of 12 acceleration over the conventional J-resolved ¹H-MRSI method. We can reduce the estimation error, if needed, by decreasing the acceleration factor. Our in vivo study showed that the concentrations of NAA, Cr, mI, Glu, Gln, and GABA were larger in the gray matter than in the white matter (P < 0.0001) and concentration of Cho was smaller in the gray matter than in the white matter (P < 0.0001) (Figure 8C); these results were consistent with the previously published results (19,61–63). The largest inter-subject COV of gray/white matter ratio was 5.61%, which indicates that the results were reasonably reproducible. We were able to achieve a 3.0 × 3.0 × 4.8 mm³ nominal spatial resolution of a 3D volume of 180 × 180 × 48 mm³ in 19.4 minutes, which was significantly better than the previous works in accelerated J-resolved MRSI that obtained spatial resolution around 10 × 10 × 15 mm³ in a similar time (28–32). Furthermore, the proposed method was able to produce a high-resolution GABA map with 27.03% relative error in phantom (Table 2), which is rather encouraging. The ability of the proposed method to separate Glu and Gln using J-resolved MRSI data is also desirable for potential applications as conventional MRSI methods can only measure the combined signal of Glu and Gln (26,27).

The proposed method can be further improved in many aspects. Firstly, we have only optimized the sampling parameters along the t₁ dimension (via CRLB analysis). Further optimization on spatial sampling may lead to a better tradeoff in resolution, scan time and SNR. Secondly, an optimal application of spatial regularization may further improve the resulting reconstructions. For example, a transform group sparsity constraint could be imposed on the (x, t₁, t₂) data (66,67), which exploits the correlated sparse structure of the (x, t₁, t₂) data along the chemical shift and J-coupling dimensions. Utilizing the shared sparse structure in the transform domain may provide a more effective constraint than the image edge weight constraints used in our current method. Thirdly, spectral basis functions were obtained only from healthy subjects in this work. Considering the pathological differences in molecular compositions between healthy volunteers and patient groups (1–7), incorporation of additional basis functions would be helpful for clinical applications. Finally, practical issues such as subject head motion and intravoxel field inhomogeneity will also need to be addressed in future work.

5. CONCLUSIONS

This paper demonstrated the feasibility of highly accelerated J-resolved ¹H-MRSI of the brain by integrating subspace modeling, sparse sampling, parallel imaging, and semi-LASER excitation. The proposed method has been evaluated using simulated data and experimental data from which 3D maps of brain metabolites and neurotransmitters were obtained with a nominal spatial resolution of 3.0 × 3.0 × 4.8 mm³ from J-resolved ¹H-MRSI data acquired in 19.4 minutes. With further improvements, the proposed method may provide a useful tool for simultaneous mapping of NAA, Cr, Cho, mI, Glu, Gln, and GABA.

Supplementary Material

Supporting Figures

Figure S1. The generated ground truth spectra for CRLB analysis. A) Generated spectra containing 16 resonances based on their normal in vivo concentration levels at TE of 40 ms and 90 ms; B) generated spectra with added noise at TE of 40 ms and 90 ms.

Figure S2. The calculated CVBs for both estimation models. A) Estimation model including 16 resonances; B) estimation model including only the 9 resonances considered in the paper.