Hsin-Yu Chen^{1}, Adam Autry^{1}, Jeffrey R. Brender^{2}, Shun Kishimoto^{2}, Murali C. Krishna^{2}, Maryam Vareth^{1,3}, Robert A. Bok^{1}, Galen D. Reed^{4}, Albert P. Chen^{4}, Lucas Carvajal^{1}, Jeremy W. Gordon^{1}, Mark van Criekinge^{1}, David E. Korenchan^{1}, Duan Xu^{1}, Yan Li^{1}, John Kurhanewicz^{1}, Peder E.Z. Larson^{1}, and Daniel B. Vigneron^{1}

A data-driven processing framework was proposed for dynamic hyperpolarized ^{13}C-MR Spectroscopic Imaging to maximally extract diagnostic information from existing datasets and techniques that utilized whitened-SVD^{2} to optimally combine array data, and tensor-low-rank denoising^{3,4} to enhance SNR. The framework was applied and evaluated on brain, abdomen, and pelvic datasets acquired using multi-channel arrays or single-element receivers. Substantial improvement in quality of low-SNR lactate and alanine was observed with 30+ fold apparent SNR gain, whereas high-SNR pyruvate remained largely artifact-free. Correlation of high k_{PL} with biopsy-confirmed cancer strongly indicated that this recovered important pathological information.

Patient
Studies: The patient
data (N=38) used was acquired with a 2D MRSI sequence with EPSI readout(TR/TE=130ms/3.5ms,
resolution temporal=2-5s, spatial = 1-4cc), following injection of 250mM HP-[1-^{13}C]pyruvate^{5}
polarized using a 5T SPINlab(GE Healthcare). Fig.1B summarized the ^{13}C receivers in
this study, including 8 and 32-channel brain, 16-channel and surface abdominal,
and an endorectal prostate coil^{5,6,7}. All human studies were IRB-approved
at UCSF.

Image
Processing Framework: Image
processing workflow of the 2D MRSI data is summarized in Figure 1A, where noise
decorrelation and SVD combination are unique to multichannel datasets. The
processing and visualization are realized on MATLAB and SIVIC^{8}.
Pyruvate-to-lactate conversion rate(k_{PL}) was evaluated using an inputless
kinetic model^{9}.

WSVD Array
Combination: The WSVD
algorithm^{2} first decorrelates the receiver channels, followed by SVD
decomposition to extract the voxel-wise complex coil sensitivity weighting from
a principal eigenvector. Sum-over-time was used, assuming coil profile is temporally-invariant.

Tensor Low-Rank
Denoising: TD^{3,4}
utilizes Tucker decomposition to separate the spectral-spatial-dynamic components
into factor matrices in D dimensions and a core tensor X = G×_{1}A×_{2}B×_{3}C
(conceptually similar to eigenvectors and singular values in SVD). Exploiting
the spatiotemporal correlation, noise is reduced by decreasing rank in each
dimension. Selecting the ideal set of ranks presents a classical bias-variance
tradeoff problem^{10}. One strategy is to formulate the problem as

$$\DeclareMathOperator*{\argmin}{arg\,min}\argmin_{r_{1},r_{2},..,r_{i},..,r_{D}} \frac{1}{K}\sum_k^{}|S_{pyr,orig}(k)-S_{pyr,TD}(k)|^{2}+w_{0}\cdot\sigma_{noise,TD}^2$$

where r_{i} is the rank in i^{th} dimension, S_{pyr}(k)
is the pyruvate signal from k^{th} highest SNR voxel, σ^{2}_{noise,TD} is estimated at the FID
tail or from a noise voxel outside subject, and w_{0} is a weighting
factor. An alternative strategy that the authors used, is to empirically decrease
the rank in each dimension and visually inspect the dynamic pyruvate series. Rank
should be set slightly higher before artifacts become visible on pyruvate
images, or right when reliable k_{PL} fits are attained in tumor ROI^{11},
whichever happens first.

Brain data (Figs.1C-D and 2) showed the overall framework recovered low-SNR lactate while high-SNR pyruvate remained largely artifact-free, enabling reliable quantification of cerebral metabolism in more voxels. Abdominal volunteer exam (Fig.3) highlights that WSVD array combination reduced baseline and improved noise statistics, substantially enhancing lactate and alanine in kidney/muscle over background.

Figures 4 and 5 illustrated a patient diagnosed with bilateral biopsy-confirmed prostate cancer. Dynamic spectroscopy (Fig.4A) observed 67-fold apparent SNR gain, and recovery of the otherwise undetectable pyruvate-hydrate and alanine. High k_{PL} (Fig.5B, orange and magenta) showed good agreement with T2 lesions (Fig.5B, green arrows) and the biopsy finding of bilateral midgland cancer. This strongly indicates that TD recovered quantitative pathological information rather than created artifacts.

The nature of the HP-^{13}C spectroscopy – finite and known number of discrete resonances, enables one to aggressively drive the spectral rank down and truly unleash the TD denoising power. Of note, no assumptions are made about the chemical shift or lineshape of each resonance. Recovery of low SNR resonances suggested that this framework may also benefit HP probe development^{12} where proof-of-concept studies could be made possible despite low polarization, slow conversion, or short T_{1}. One general concern of denoising methods – spatiotemporal “imprinting” of high SNR resonances onto low SNR one, was not observed. Pyruvate and lactate have distinct spatial distribution and dynamics upon detailed inspection(Figs.1C,2A&4B).

Overall, this data-driven framework is versatile across imaging targets and receiver configurations. Mean apparent SNR gain was 63-fold for arrays, and 31-fold for single-element receivers, where at least 10-fold can typically be expected for arrays (Fig.1B). The ultimate power of signal enhancement and optimal array combination will depend not only on the design/geometry of array coils, but also the anatomy, pathophysiology and pharmacokinetics of the target, which determines the spatiotemporal complexity, and therefore the rank of the underlying data.

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