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Radial Flyback Echo-Planar Spectroscopic Imaging with Golden Angle Sampling and Total Variation-based Compressed Sensing Reconstruction
Andres Saucedo1, Manoj Sarma1, and M. Albert Thomas1
1Radiological Sciences, University of California, Los Angeles, Los Angeles, CA, United States

Synopsis

In this pilot study, we implement a radial echo-planar spectroscopic imaging (rEPSI) sequence and compare its performance to the Cartesian (EPSI) sequence under multiple rates of retrospective undersampling, for the case of 2D acquisitions in which a single phase-encoded direction is undersampled for EPSI, and a reduced number of radial profiles using golden angle view ordering are reconstructed for rEPSI. Fully sampled data from a healthy volunteer brain and from a brain phantom are acquired. The retrospectively undersampled data is reconstructed using compressed sensing with Total Variation regularization, and the performance of both methods are compared.

Introduction

Magnetic resonance spectroscopic imaging (MRSI) is a powerful tool for measuring biochemical concentrations and spatial distribution of various metabolites. However, long acquisitions times hinder the practical use of conventional MRSI techniques. Echo-planar trajectories, in which one spatial and one spectral dimension are sampled simultaneously, have been implemented to reduce acquisition time by an order of magnitude1.Other echo-planar-based approaches utilizing non-Cartesian sampling, such as concentric circular rings, rosettes, and spirals, have also been applied for efficient and fast MRSI2,3,4. Recently, radial sampling techniques have gained more widespread use for MRI applications, due to their increased motion robustness, inherent SNR advantage, and potential for high acceleration5,6,7. In this pilot study, we implement a radial echo-planar spectroscopic imaging (rEPSI) sequence and compare its performance to the Cartesian (EPSI) sequence under multiple rates of retrospective undersampling, in the case of 2D acquisitions in which a single phase-encoded direction is undersampled for EPSI, and a reduced number of radial profiles from golden angle sampling8 is used for rEPSI. A flyback trajectory approach, as opposed to alternating bi-polar readout gradients, is implemented for both sequences due to its increased spectral width, simpler post-processing, less T2*-weighting, and relative insensitivity to timing errors9. Fully sampled data from a healthy volunteer brain and from a brain phantom are acquired. The 2D retrospectively undersampled data for both EPSI and rEPSI are reconstructed using compressed sensing with Total Variation regularization, and we compare the performance of both methods.

Methods

The flyback EPSI and rEPSI (Figure 1) sequences were implemented on a 3T clinical scanner. One healthy 26 year-old healthy volunteer was recruited with IRB approval for the acquisition of in vivo brain data. Data from a brain phantom containing metabolites at physiological concentrations was also acquired. Both data sets were acquired with a 32×32 matrix size, a 32×32×1.5 cm3 slab using volumetric semi-LASER localization, TE = 40 ms, TR = 1.5s, and a spectral width of 1351.35 Hz, with 512 t2 points. With 10 averages each, acquisition time for fully sampled water-suppressed data totaled 6.5 minutes for EPSI (32 ky phase-encoding steps) and 10 minutes for rEPSI (50 radial spokes). A separate water scan was also acquired for eddy-current phase correction. The radial spokes were acquired and undersampled using a golden-angle view ordering scheme. For EPSI undersampling masks in the ky direction were implemented using a Gaussian probability distribution with a fully-sampled central region of 4 ky lines. Acceleration factors (AF) for EPSI were 1.5, 2.0, 2.5, 2.9, 4, and 5.3, corresponding to 21, 16, 13, 11, 8, and 6 ky phase-encodes, respectively. For rEPSI, AF = 2.4, 3.1. 3.8, 4.5, 6.25, and 8.3, corresponding to 21, 16, 13, 11, 8, and 6 radial spokes, so that EPSI and rEPSI were compared on a time-equivalent basis, although higher AF’s are technically feasible for rEPSI. Total Variation (TV)-based compressed sensing reconstructed was implemented using the MFISTA10 framework to solve the following minimization problem: $$ \min_{u} \frac{1}{2} \| Fu - y \|_2^{2} + \lambda TV(u) $$
where F is the Fourier transform, or non-uniform Fourier transform11 (NUFFT) for radial data, u is the spatial-spectral data, y is the undersampled data, and λ is a regularization parameter empirically chosen as 𝜎 · 10-1, where 𝜎 is an estimate of the noise standard deviation. Coil-by-coil reconstruction was performed with 80 outer iterations and 20 inner iterations of the TV proximal mapping. The fully-sampled and reconstructed data was used to compute spectral normalized root mean square error (nRMSE) maps, absolute difference images, and metabolite maps of N-acetylaspartate (NAA), Creatine 3.0 (Cre 3.0), and Choline (Cho), as a function of increasing acceleration factor.

Results

The NAA metabolite maps in Figure 2 and Figure 3 show that radial sampling results in greater reconstruction accuracy and is more robust to increasing undersampling rates. Even at a high acceleration of 8.3, rEPSI still outperforms EPSI in terms of the fidelity of the reconstructed map. The absolute difference maps of NAA display reduced differences within the VOI for rEPSI compared to EPSI. Reconstructed spectra from rEPSI also appear more consistent with the fully-sampled spectra (Figure 4), whereas spectra reconstructed from EPSI data loses SNR at a greater rate than those from the radially sampled data, in agreement with earlier results in radial MRI. In terms of imaging fidelity, the nRMSE of the NAA, Creatine 3.0, and Choline maps are lower than those from the EPSI acquisition (Table 5), particularly at high undersampling rates.

Discussion and Conclusion

Radial EPSI is shown to be more robust to acceleration for undersampled 2D spatial acquisitions. For MRSI applications, in which the resolutions are relatively low, radial acquisitions can provide a good trade-off between acquisition speed and spectroscopic image quality. While 2D Cartesian EPSI undersampling is limited to one phase-encoding dimension, rEPSI offers greater flexibility by allowing undersampling across the entire k-space plane, while still preserving spectral and imaging quality. Streaking artifacts can be a limitation in rEPSI, but this is true outside the region of interest only, and this effect can be further reduced through more optimized reconstruction schemes. Furthermore, golden angle view ordering offers a further potential for motion-robust and temporally resolved spectroscopic imaging.

Acknowledgements

Authors acknowledge grant support from DoD CDMRP Breakthrough I Award #W81XWH-16-1-0524.

References

[1] Posse, S., et al., High speed 1H spectroscopic imaging in human brain by echo planar spatial-spectral encoding. Magnetic Resonance in Medicine. 1995; 33(1): 34-40.

[2] Furuyama, J.K., et al. Spectroscopic imaging using concentrically circular echo-planar trajectories in vivo. Magnetic Resonance in Medicine. 2012; 67(6): 1515-1522.

[3] Schirda, C.V., et al. Rosette spectroscopic imaging: optimal parameters for alias-free, high-sensitivity spectroscopic imaging. Journal of Magnetic Resonance Imaging. 2009; 29(6): 1375-1385.

[4] Adalsteinsson, E., et al. Volumetric spectroscopic imaging with spiral-based k-space trajectories. Magnetic Resonance in Medicine. 1998; 889-898.

[5] Ramirez, M.S., et al. Radial spectroscopic MRI of hyperpolarized [1-13C] pyruvate at 7T. Magnetic Resonance in Medicine. 2014; 72(4): 986-995.

[6] Block, K.T., et al. Undersampled radial MRI with multiple coils. Iterative reconstruction using a total variation constraint. Magnetic Resonance in Medicine. 2007; 57(6): 1086 – 1098.

[7]. Feng, L., et al. Golden-angle radial sparse parallel MRI: combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI. Magnetic Resonance in Medicine. 2014; 72(3):707-717.

[8] Winkelmann, S., et al. An optimal radial profile order based on the Golden Ratio for time-resolved MRI. IEEE Transactions on Medical Imaging. 2006; 26(1): 68-76.

[9] Cunningham, C.H., et al. Design of flyback echo-planar readout gradients for magnetic resonance spectroscopic imaging. Magnetic Resonance in Medicine. 2005; 54(5): 1286 – 1289.

[10] Beck, A. and Teboulle, M. Fast gradient-based algorithms for contrained total variation image denoising and deblurring problems. IEEE Transactions on Image Processing. 2009; 18(11): 2419 – 2434.

[11] Fessler, J.A. and Sutton, B.P. Nonuniform fast Fourier transforms using min-max interpolation. IEEE Transactions on Signal Processing. 2003; 51(2): 560-574.

Figures

Figure 1: Schematic diagram of the flyback radial EPSI sequence, in which ½n spectral points are acquired from the readout train. A pair of adiabatic full passage (AFP) pulses are played after the 90° excitation pulse to achieve PRESS-based localization in a 2D plane.

Figure 2: NAA metabolite maps from a healthy brain, computed using data from the EPSI (A, top row) and rEPSI sequence (A, bottom row), as a function of increasing acceleration factor (AF). Note that rEPSI results in NAA maps with greater similarity to the fully-sampled NAA map (leftmost column). Maps of the absolute difference between the fully-sampled and reconstructed NAA maps are shown in (B). Within the volume-of-interest (red box), EPSI reconstructions result in more differences with respect to the fully-sampled data, compared to rEPSI.

Figure 2: NAA metabolite maps from a phantom containing representative brain metabolites at physiological concentrations. In (A, top row) the EPSI reconstructions degrade more rapidly as a function of increasing acceleration factor (AF), compared to the rEPSI reconstructions (A, bottom row). Similarly, the absolute difference maps between the fully-sampled and reconstructed NAA maps indicates greater reconstruction accuracy of data from rEPSI acquisitions, particularly within the volume-of-interest (red box).

Figure 4: (A) Maps of the normalized root mean square error (nRMSE) for spectra within the volume-of-interest. As the acceleration factor (AF) increases, reconstructed rEPSI spectra retains more fidelity to the fully-sampled spectrum. (B) Top row – representative spectra from EPSI reconstructions, where the spectrum clearly degrades rapidly as the AF increases. Bottom row – the reconstructed spectra from rEPSI retain good lineshape and fidelity to the fully-sampled spectrum (in blue). The reconstructed spectrum from EPSI data loses SNR at a greater rate as the AF increases.

Table 1: nRMSE values for metabolite maps of N-acetylaspartate (NAA), Creatine 3.0 (Cre3.0), and Choline (Cho), reconstructed from data sampled with EPSI and rEPSI, in both the in vivo brain and phantom acquisitions. Note that rEPSI has lower values for all acceleration factors (AF) above 2.4 for rEPSI and 1.5 for EPSI. The lower nRMSE's from the rEPSI data show that radial sampling is more robust to greater acceleration than Cartesian sampling.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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