Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI

Abstract

High polarization of nuclear spins in liquid state through dynamic nuclear polarization has enabled the direct monitoring of 13C metabolites in vivo at very high signal-to-noise, allowing for rapid assessment of tissue metabolism. The abundant SNR afforded by this hyperpolarization technique makes high-resolution 13C 3D-MRSI feasible. However, the number of phase encodes that can be fit into the short acquisition time for hyperpolarized imaging limits spatial coverage and resolution. To take advantage of the high SNR available from hyperpolarization, we have applied compressed sensing to achieve a factor of 2 enhancement in spatial resolution without increasing acquisition time or decreasing coverage. In this paper, the design and testing of compressed sensing suited for a flyback 13C 3D-MRSI sequence are presented. The key to this design was the undersampling of spectral k-space using a novel blipped scheme, thus taking advantage of the considerable sparsity in typical hyperpolarized 13C spectra. Phantom tests validated the accuracy of the compressed sensing approach and initial mouse experiments demonstrated in vivo feasibility.

Figure 1

Double spin-echo sequence timing diagram. The RF consists of a small tip excitation followed by two adiabatic pulses (phase channel not shown). Phase encoding is along x and y while the 59-lobe flyback readout is along z. An echo is formed during the middle of the flyback readout with TE = 140ms.

Figure 2

Demonstration of wavelet compressibility of a ¹³C spectroscopic signal. A row of magnitude spectra (64×16) from a 3D-MRSI phantom data set (see Figure 5 for examples of rows of spectra) was taken as the test signal. Note that the 59 spectral points from the 59 flyback lobes were zero-padded to 64 because the wavelet software we used required dyadic numbers. a) The 16 original spectra. b) A 2D Daubechies wavelet transform was applied to the 64×16 data, after which the top 10% wavelet coefficients were retained and the inverse 2D wavelet transform taken. c) The magnitude error between a) and b). Note that a), b), and c) have the same y-axis scale. The 64×16 data were reconstructed very accurately from only 10% of their wavelet coefficients, showing that the signal of interest exhibits considerable fundamental sparsity.

Figure 3

Blipped scheme for k_f-k_x sub-sampling. Top: The only modification to the pulse sequence shown in Figure 1 is the addition of blips during the rewind portions of the flyback readout. The area of each blip is the area in an x-phase encode step. Bottom: Associated order of k-space readout. A single readout now covers two k_f-k_x lines.

Figure 4

Blipped patterns to cover 16 k_f-k_x lines, resulting coverage, and point spread function. a) Actual 8 blipped patterns used to cover 16 k_f-k_x lines in a pseudo-random manner. b) Associated k-space sampling. Because twice as much k-space is covered in the time of 8 phase encodes, half of the 59×16 k_f-k_x points are missing (missing points are black). c) 2D point spread function of pseudo-random pattern in b).

Figure 5

16×8 phantom comparison of normal vs. undersampled. a) T2-weighted image of ¹³C phantom done before spectral acquisitions. b) Spectra from normal, unblipped acquisition corresponding to the highlighted voxels from a). c) Spectra from compressed sensing reconstructed, blipped acquisition corresponding to the highlighted voxels from a).

Figure 6

Comparison of 8×8 normal mouse data and 16×8 undersampled mouse data in a region of prostate tumor. a) Normal 8×8 data. The left shows the spectrum with the highest lactate peak, the middle shows the T2-weighted anatomical image, and the right shows spectra highlighted in the anatomical image. b) Corresponding 16×8 data acquired two hours after the 8×8 data.