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Symmetry Preserved Rectilinear Transform(SPRT): Optimized Reconstruction of Echo Planar Spectroscopic Image for Hyperpolarized [1-13C]-Pyruvate1Imaging Physics, UT MD Anderson Cancer Center, Houston, TX, United States
Synopsis
A new reconstruction method, symmetry preserved rectilinear transform (SPRT) is proposed to remove the Nyquist ghost and chemical shift artifacts from symmetric echo-planar spectroscopic imaging (EPSI) data. For each metabolite in the spectrum, an additional phase term is added to reshape the zig-zag layout of k-t space samples into a rectilinear layout with all echoes parallel to each other in k-t space. SPRT can eliminate artifacts and significantly improve SNR.
Purpose:
Magnetic resonance imaging (MRI) of hyperpolarized (HP) agents allows non-invasive assessment of physiological processes that were previously inaccessible1. While this technique provides unprecedented metabolic information and high signal-to-noise ratio (SNR), HP signals are short-lived and nonrenewable2. As an effective fast imaging approach, echo-planar spectroscopic imaging (EPSI) has been demonstrated as a versatile acquisition for HP-MRI. However, the asymmetric sampling between even and odd echo components in the raw data space, or k-t space, can result in both Nyquist ghost and aliasing artifacts. In this work, we proposed a new Fourier transform (FT) based reconstruction method: symmetry preserved rectilinear transform (SPRT). We evaluate the use of this method to improve SNR and minimize artifacts.Theory:
Theory: Imaging artifacts associated with direct FT reconstruction of raw EPSI data arise from unbalanced echo spacing between odd/even and even/odd echoes due to the zig-zag layout in k-t space. SPRT eliminates this asymmetry for individual metabolites iteratively by restoring k-t space into rectilinear Cartesian alignment, which then permits direct FT reconstruction. This is accomplished by modulating the phase of each point within an echo by the conjugate of phase evolution for that metabolite at known chemical shift offset:$${S_{SPRT}(k,t)=S(k,t)*exp^{-i\delta_{cs_{i}}(t-t_{0})}}$$ $$${S_{SPRT}}$$$ is the corrected k-t space data, $$${S}$$$ is the raw data, $$${\delta_{cs_{i}}}$$$ is the chemical shift of the metabolite to reconstruct; $$${t_{0}}$$$ is the acquisition time of the center sample of the specific echo.
The workflow of SPRT is shown in fig 1. By introducing the negative phase term, samples within the same echo will have the phase accumulation as the center sample, so that the zig-zag layout echoes will be reshaped into a rectilinear layout. This correction will counterbalance both the chemical shift artifact in the spatial dimension and the Nyquist ghost in the spectral dimension. Meanwhile, the chemical shift of the metabolite in the spectral dimension will be preserved.
Methods:
Data was acquired on a 3T GE MR750 scanner with the scanner frequency adjusted to replicate the chemical shifts of pyruvate and lactate using a thermal 13C-urea phantom by fidDall (MNS research pack,GE Healthcare) with a radial EPSI pulse sequence (TR/TE = 5000/25ms, spectral BW = 8ppm, matrix size = 16×16, in-plane resolution = 3mm, slice thickness = 8mm, 96 directions). A T1-weighted proton Image at higher resolution (1mm) was also acquired to map the location of phantom.
Data was reconstructed by four methods for comparison: even-only echoes, sum-of-square (SOS) combination of both odd-only and even-only data, direct FT, and SPRT followed by FT. Those results were evaluated by quantifying SNR, defined as the maximum peak value of the metabolite divided by the standard deviation of the background noise. Result of pyruvate only is shown in fig 2, result of pyruvate and lactate is shown in fig 3. The metabolite Images were constructed by inverse radon transform using spectral signal from all 96 directions, and overlaid with proton images (fig 4).
Results:
The SPR method resulted in the highest metabolite SNR among the methods that we compared(fig 2). Using only even echoes resulted the lowest peak spectral signal intensity, as half the data were wasted. SOS improved the peak spectral signal, but it was not optimized because the reconstructed peak of even-only echo and the peak of odd-only echo are displaced in the readout direction. After correction for chemical shift, SNR increased by roughly 40%. FT reconstruction resulted the least metabolite SNR, as the increased signal from using all the echoes was dissolved by the increased noise from the full BW. SPRT resulted both highest peak spectral signal intensity and SNR because it successfully converged all the spectral signal that the other three methods spread out in either readout or spectral direction.
SPRT removed most artifacts that resided in the other three methods. In the readout direction, the chemical shift artifact is the least in SPRT reconstructed images. In the spectral direction, SPRT also completely removed the Nyquist ghost artifact.
SPRT maximized the SNR for each metabolite at each run by loading their chemical shift values (fig 3)
SPRT precisely mapped simulated pyruvate and lactate signal to the corresponding proton image (fig 4). Image of pyruvate and lactate signal was reconstructed in two runs by adjusting $$${\delta_{x}}$$$. Images of both metabolites were free of visible artifacts, and the contour and location of metabolites images were very close to the proton image.
Conclusion:
SPRT successfully resolved artifacts in the reconstructed image of EPSI. Given the chemical shift value of certain metabolite, SPRT will maximize the spectral SNR and completely remove the Nyquist ghost.Acknowledgements
No acknowledgement found.References
1. Ardenkjaer-Larsen J, Fridlund B, Gram A, et al. Increase in signal-to-noise ratio of >10,000 times in liquid-state NMR. Proc Natl Acad Sci. 2003;100(18):10158–10163.
2. Bankson J, Walker C, Ramirez M, et al. Kinetic modeling and constrained reconstruction of hyperpolarized [1-13C]-pyruvate offers improved metabolic imaging of tumors. Cancer Res. 2015;75(22):4708–4717
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