Accelerated high-bandwidth MR spectroscopic imaging using compressed sensing

Abstract

Purpose: To develop a compressed sensing (CS) acceleration method with a high spectral bandwidth exploiting the spatial-spectral sparsity of MR spectroscopic imaging (MRSI).

Methods: Accelerations were achieved using blip gradients during the readout to perform nonoverlapped and stochastically delayed random walks in kx -ky -t space, combined with block-Hankel matrix completion for efficient reconstruction. Both retrospective and prospective CS accelerations were applied to (13) C MRSI experiments, including in vivo rodent brain and liver studies with administrations of hyperpolarized [1-(13) C] pyruvate at 7.0 Tesla (T) and [2-(13) C] dihydroxyacetone at 3.0 T, respectively.

Results: In retrospective undersampling experiments using in vivo 7.0 T data, the proposed method preserved spectral, spatial, and dynamic fidelities with R(2) ≥ 0.96 and ≥ 0.87 for pyruvate and lactate signals, respectively, 750-Hz spectral separation, and up to 6.6-fold accelerations. In prospective in vivo experiments, with 3.8-fold acceleration, the proposed method exhibited excellent spatial localization of metabolites and peak recovery for pyruvate and lactate at 7.0 T as well as for dihydroxyacetone and its metabolic products with a 4.5-kHz spectral span (140 ppm at 3.0 T).

Conclusions: This study demonstrated the feasibility of a new CS approach to accelerate high spectral bandwidth MRSI experiments. Magn Reson Med 76:369-379, 2016. © 2016 Wiley Periodicals, Inc.

Keywords: Hankel matrix completion; MR spectroscopic imaging; calibrationless parallel imaging; compressed sensing; hyperpolarized carbon-13; random blip gradients.

Figure 1

CS MRSI sequence, random walk and time delay scheme and undersampling pattern. (a) CS MRSI sequence for a single acquisition. Blip gradients with random amplitudes and time delays were applied on G_x and G_y during the readout period, which facilitated a random walk trajectory in the k_x-k_y plane. (b) The initial phase encoding locations followed a random spiral-out order. During the readout, some phase encodings were performing random walks, and some were not, due to the random time delays or the full sampling at the center. Random walks moved slower near the center, creating variable density sampling. Four phase encodings in the center were fully sampled along t dimension. (c) The probability distribution of undersampling at various time points. The central peak indicated full sampling. The sampling distribution due to the random walks in peripheral k-space became increasingly flat from t = 0 to 3.1 ms, and was relatively stationary with t > 3.1 ms. (d) The 3D k_x-k_y-t undersampling pattern (3.8-fold) for the first frame, with the cylindrical sampling boundary (dashed line).

Figure 2

Illustration of the singular value thresholding method used to reconstruct CS datasets. Y is the undersampled k-space; X is the estimated or reconstructed k-space data; X’ the k-space data at measured locations extracted from X; A is the accumulative sum of the difference between Y and X’; H is the block-Hankel matrix of A and the input of the singular value thresholding operation; and I_max for maximum iteration number. Hankel matrices for FIDs (red windows) are first stacked in a column-wise order for all voxels within a k_x-k_y window (green window). Then, the column-wise block matrices for all k_x-k_y windows and frames (blue window indicates one frame) are concatenated along each row to form a large block-Hankel matrix, H.

Figure 3

A typical full k-space in vivo hyperpolarized [1-¹³C] pyruvate MRSI dataset, reordered as a block-Hankel matrix with size of 1000 × 30000 (via sliding window and reordering as illustrated in Fig. 2). (a) The T₂-weighted MRI depicts the field of view for the 2D 8 × 8 MRSI. (b) The first 200 singular values from the singular value decomposition of original block-Hankel matrix (red solid line) and its low-rank approximation (blue dash line) are plotted. Low-rank approximation (by Cadzow denoising on block-Hankel matrix) iteratively extracted the top 100 singular values and vectors, and was repeated 300 times. (c) Singular values and vectors from the block-Hankel matrix decomposition after low-rank approximation, showing distinct spectral, dynamic and spatial features.

Figure 4

Retrospective CS experiment on a full k-space ¹³C mouse brain MRSI dataset following intravenous administration of hyperpolarized [1-¹³C] pyruvate (same as Fig. 3). The reconstructed dynamic spectra with undersampling factors of 2, 2.7, 3.8 and 6.6 were compared with full k-space ground truth. (a) Fully sampled k-space spectra are overlaid on top of a reference ¹H image. Voxel A was selected as a high SNR voxel, and B was a low SNR voxel. (b) Dynamic spectra and metabolic maps with different undersampling factors. PEs stands for phase encodings. The pyruvate (Pyr) and lactate (Lac) peaks and their spatial features were well-preserved in all undersampled datasets. (c) The pyruvate and lactate time courses from the sum of six voxels on brain. CS largely preserved dynamic features as well.

Figure 5

Prospectively 3.8-fold accelerated CS MRSI on mouse brain, following intravenous administration of hyperpolarized [1-¹³C] pyruvate. (a) A mosaic view of spectra and T₂ weighted MRI. Spectra were spatially localized within the head area. (b) Dynamic spectra from the sum of six voxels marked by the solid box in (a). Lactate (Lac) and pyruvate (Pyr) peaks were clearly observed. (c) Time courses of pyruvate and lactate from the marked area. (d) The ¹³C metabolic maps showed pyruvate and lactate dynamics, with the majority of signal localized to the brain.

Figure 6

Prospectively 3.8-fold accelerated CS MRSI on rat liver, following intravenous administration of hyperpolarized [2-¹³C] dihydroxyacetone (DHAc), which results in a 140-ppm (4.5 kHz at 3T) range of metabolite chemical shifts. (a) A mosaic view of spectra and abdominal T₂-weighted MRI. Spectra were spatially localized primarily within the liver as expected. (b) Dynamic spectra from the marked area in (a). The three peaks in the dynamic spectra are DHAc (≤0.3° flip, 213 ppm), DHAc hydrate (DHAc-hyd, 2.3° flip, 96 ppm) and glycerol 3-phosphate (G3P, 20° flip, 73 ppm), all of which were recovered by the proposed method. (c) Time courses of DHAc, DHA-hyd and G3P from the marked liver area. (d) The ¹³C metabolic map showed that G3P generated from DHAc was primarily distributed within the liver, indicating accurate reconstruction by our method.

Figure 7

Retrospectively 4-fold accelerated 2D MRSI on a thermal ¹³C phantom (containing 99.8% ethylene glycol) including calibrationless parallel imaging. (a) For reconstruction incorporating calibrationless parallel imaging, Hankel matrices for FIDs (red windows) are stacked in a column-wise order, and k_x-k_y windows (green windows) are concatenated along each row, as done when not using parallel imaging (Fig. 2). Then, block-Hankel matrices for coils (blue windows) are concatenated along column. (b) Full k-space and CS accelerated spectra after the sum of squares coil combination. Bright bold lines indicate eight elements of the surface ¹³C RF receiver coil. The bottom panel shows the comparison of spectra from marked area (solid boxes). The triplet spectra of ethylene glycol (J_C-H = 150 Hz) were well recovered by the combined CS and calibrationless parallel imaging, with most obvious differences occurring in the low SNR region in the middle of the phantom. (c) Integrated spectra maps comparison. The combined CS and parallel imaging acceleration generally preserved the most of spectral and spatial features of the ¹³C MRSI phantom dataset.