0925

Low-rank reconstruction for simultaneous Double-Half-Echo ²³Na and undersampled ²³Na Multi-Quantum Coherences MRI

Christian Licht^1,2, Simon Reichert^1,2, Mark Bydder³, Jascha Zapp^1,2, Shirley Corella^3,4, Maxime Guye^3,4, Lothar R Schad^1,2, and Stanislas Rapacchi^3,4
¹Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, ²Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, ³CNRS, CRMBM, Aix-Marseille Université, Marseille, France, ⁴APHM, Hôpital Universitaire Timone, CEMEREM, Marseille, France

Synopsis

Keywords: Non-Proton, Non-Proton, low-rank matrix completion, sequence optimization

Motivation: Sodium (²³Na) Multi-Quantum Coherences (MQC) MRI potentially provides richer tissue information. However, 3D ²³Na multi-quantum coherences imaging lacks conventional ²³Na MRI resolution and requires multiple radiofrequency phase-cycling limiting spatial resolution.

Goal(s): We propose an efficient sequence to simultaneously acquire Cartesian double-half echo (DHE) ²³Na and accelerated ²³Na MQC MRI.

Approach: Leveraging advanced low-rank matrix completion frameworks to enable simultaneous DHE ²³Na and ²³Na MQC MRI were tested on numerical simulations, retro- and prospectively undersampled phantom and in vivo brain data acquired at 7T.

Results: Simultaneous Cartesian ²³Na and higher resolution 3-fold prospectively undersampled ²³Na MQC brain MRI of 4 volunteers were obtained.

Impact: The new sequence, in combination with the low-rank reconstruction frameworks, enables efficient ²³Na and higher resolution ²³Na MQC MRI while supporting conventional ¹H-based acceleration techniques and offers, therefore, a convenient sequence for the sodium MRI community.

Introduction

Conventional sodium (²³Na) MRI is an emerging tool to probe tissue ionic homeostasis by quantifying tissue sodium concentration (TSC) associated with cell vitality. However, thanks to its 3/2 spin, ²³Na multi-quantum coherences MRI enables disentangling the underlying multi-quantum coherences (MQC) and therefore, holds potentially richer sodium tissue characterization. Nevertheless, ²³Na MQC MRI is slow due to the necessity of RF phase-cycling, limiting spatial resolution. Furthermore, ²³Na MQC MRI lacks conventional ²³Na MRI resolution. However, ²³Na MQC MRI consists of a 3D volumetric acquisition sampled along the echo time by leveraging phase-cycling, creating highly redundant signal subspaces.
Herein, we aim to tackle two major challenges of ²³Na MQC MRI. First, we developed an efficient sequence to obtain conventional ²³Na and ²³Na MQC MRI simultaneously. The sequence is based on Cartesian sampling. For the first time, we demonstrate the DHE technique to acquire conventional Cartesian sodium images with very short echo times and simultaneously higher resolution, prospectively undersampled Cartesian ²³Na MQC MRI. ²³Na and ²³Na MQC MRI were reconstructed by leveraging the data's intrinsic redundancy.

Methods

All measurements were performed on a 7T MRI (Siemens Terra) with a bird-cage dual-tuned ²³Na/¹H head coil (RapidBiomedical). ²³Na MQC MR images were obtained using a modified CRISTINA¹ sequence with the following parameters.
For brain in-vivo, 3 healthy volunteers, FoV 240x240x210mm³, ²³Na DHE: matrix size 40x40x40mm³, TE=0.6ms; ²³Na MQC: matrix size 30x30x26, τ=10ms, BW=330Hz/px, TE/ΔTE/nTE=1.1/4.2ms/10,TR=200ms resulting in TA=2x23min.
Image reconstruction: For ²³Na MRI, the DHE technique leverages strong asymmetric echoes to start sampling at the k-space center. However, the DHE² technique requires two k-space halves (forward and reverse) to obtain a full k-space line. A low-rank coupling constraint concatenates both lines to form a fully sampled k-space matrix by solving the following optimization problem $$\overset{min}{u} ||\varPhi_F(u) - f||^2 + \lambda_{WT}||\varPsi_F(u)||_1 s.t. rank(A_H)= k', u=H^*(A_H)$$ ²³Na MQC data was prospectively undersampled via variable density, by a factor R=3. ²³Na MQC MRI exhibits a 5D multi-dimensional space, which is highly redundant. Projecting this signal matrix onto a structured 2D matrix enables efficient exploitation of coherent information. ²³Na MQC MRI was reconstructed utilizing the SAKE³ framework solving the following optimization problem $$ \overset{min}{u} ||\varPhi_F(D_{TE,φ}(u)) - f||^2 s.t. rank(A_H)= k', u=H^*(A_H)$$ with $$$\varPhi_F$$$ being the structured Fourier sampling operator with the extension of $$$D_{TE,φ}$$$ that relates the 5D MQC signal structure to the 4D k-space that is exploited for coherent information. $$$\varPsi_F$$$ is the Wavelet transform with the sparsity weighting $$$\lambda_{WT}$$$, $$$u$$$ is the image to reconstruct and $$$f$$$ is the sampled k-space data in the fidelity term. Prior rank $$$k'$$$ is chosen to enforce low-rankness and $$$H^*$$$ is the inverse matrix operator to invert the Hankel-like structured matrix, $$$A_H$$$. SAKE reconstructed images were compared with 5D CS⁴. The sequence and image reconstruction workflow are given in Figure 1. Phase-cycled ²³Na MQC raw data were processed as Fleysher et al⁵proposed and in vivo TSC estimation was based on the CSF⁶.

Results

Fig.2: Simulations of DHE reconstruction revealed an optimal echo fraction (EF) of 52% with SSIM=0.90, RMSE=0.029 and improved SNR by 14% when compared to fully sampled noisy data, with TSC values being on par. SAKE improved ²³Na TQ signal reconstruction, especially for later echoes (TE₅=20 ms to TE₁₀=46 ms), SAKE improved SSIM by 80% and reduced RMSE by 3-fold on average. Fig.3: The phantom study revealed accurate TSC (DHE image), SQ and TQ signal intensities, and SAKE increased SNR for the TQ image by ~10% compared to 5D CS. Linear regression confirmed accurate signal intensity versus prior known NaCl (DHE, R²=0.99) and agar concentrations (TQ/SQ, R²=0.92) for retro- and prospectively undersampled data. Fig.4: In vivo study revealed accurate ²³Na and prospectively undersampled ²³Na MQC image reconstruction. TSC was 37±11 in WM, 41±9 in GM and 134±23 in CSF, respectively. TQ/SQ ratio was found to be 0.11±0.03 in WM, 0.09±0.02 in GM and 0.05±0.01 in CSF, respectively.

Discussion & Conclusion

Maintaining Cartesian acquisitions, which are reliable and reproducible, a dual conventional and multi-quantum coherence sodium MRI sequence was proposed using low-rank approaches. First, double-half echoes for conventional ²³Na MRI can be combined by exploiting correlations along the rows due to the low-rankness projection. Second, due to the MQC signal's intrinsic redundancy, the SAKE framework is well suited to reconstruct undersampled ²³Na MQC data. We have further demonstrated that despite prospective undersampling, reliable TQ/SQ ratio maps were reconstructed, which shows the potential of TQ/SQ representing an additional quantitative parameter besides TSC.
Conclusively, we demonstrated simultaneous Cartesian ²³Na DHE and ²³Na MQC MRI, with ²³Na MQC MRI prospectively undersampled by leveraging two low-rank reconstruction frameworks.

Acknowledgements

Lothar R Schad and Stanislas Rapacchi contributed equally to this work.

This work was supported by ISMRM Research Exchange 2022.

This work was supported by PROCOPE Mobility 2022.

This study received funding from the French government under the “Programme d'Investissement d'Avenir”, Excellence Initiative of Aix-Marseille University-A*MIDEX (AMX-19IET-004), 7 TEAMS Chair.

References

1. Hoesl, MAU, Schad, LR, Rapacchi, S. Efficient 23Na triple-quantum signal imaging on clinical scanners: Cartesian imaging of single and triple-quantum 23Na (CRISTINA). Magn Reson Med. 2020; 84: 2412–2428.

2. Bydder, M, Ali, F, Ghodrati, V, Hu, P, Yao, J, Ellingson, BM. Minimizing echo and repetition times in magnetic resonance imaging using a double half-echo k-space acquisition and low-rank reconstruction. NMR in Biomedicine. 2021; 34:e4458.

3. Shin, P.J., Larson, P.E.Z., Ohliger, M.A., Elad, M., Pauly, J.M., Vigneron, D.B. and Lustig, M. (2014), Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion. Magn. Reson. Med., 72: 959-970.

4. Licht, C., Reichert, S., Guye, M., Schad, LR, Rapacchi, S. Multidimensional compressed sensing to advance 23Na multi-quantum coherences MRI. Magn Reson Med. 2023; 1-16.

5. Fleysher, L., Oesingmann, N. and Inglese, M. (2010), B0 inhomogeneity-insensitive triple-quantum-filtered sodium imaging using a 12-step phase-cycling scheme. NMR Biomed., 23: 1191-1198.

6. Adlung, A. et al. Quantification of tissue sodium concentration in the ischemic stroke: A comparison between external and internal references for 23Na MRI. Journal of neuroscience methods vol. 382 (2022): 109721.

Figures

Fig1. Three-pulse sequence with an additional readout during the evolution time and the proposed workflow for image reconstruction. (1) Forward and reverse k-space halves are reconstructed by a low-rank coupling constraint exploiting coherences along the k-space rows. (2) Undersampled Multi-Quantum Coherences MRI is reconstructed using the SAKE framework. Therefore, the multi-dimensional signal is reshaped into a structured 2D matrix, exploiting coherence across the multi-dimensional k-space. Singular Value Thresholding (SVT) is used to enforce low-rankness.

Fig2. (A) Numerical simulations of ²³Na DHE reconstruction for varying echo fractions and corresponding echo times. Quantifying low-rank reconstruction performance revealed an optimal echo fraction of around 52%, which minimizes TE and maximizes SSIM and RMSE. (B) Numerical simulations of 3-fold undersampled ²³Na MQC MRI reconstructed with 5D CS and the SAKE framework. (B) Quantitative evaluation of reconstruction performance via SSIM, RMSE and SNR along the echo time, TE, for R=3. SAKE leverages the coherent information along TE.

Fig3. Phantom consisted of 9 different vials (350-mL each) with varying NaCl (50, 100, 150-mM) and agar concentrations (0, 2 and 4%). Comparison of 5D CS and SAKE for 3-fold retro- and prospectively undersampled ²³Na MQC MRI. Additionally, the ²³Na DHE image is shown, which was obtainable without and with prospective undersampling of ²³Na MQC MRI. Linear regression evaluated the relationship of the signal intensity (SI) of ²³Na and TQ/SQ ratio, and the prior known TSC or agar gel concentration. Solid lines correspond to retrospectively, dashed lines to prospectively undersampled.

Fig4. Prospective in-vivo undersampling study. Reconstructed MP2RAGE, DHE and prospectively undersampled (R=3) ²³Na MQC MRI reconstructed with the SAKE framework shown for three volunteers in sagittal, transverse and coronal planes. For all shown volunteers, TQ signal intensity mostly arose from the brain parenchyma, whereas SQ signal intensity was predominantly concentrated in the CSF. The TQ/SQ ratio was consistent throughout the volunteers and exhibits, thus, the potential to be an additional quantitative parameter to obtain and inform about tissue besides TSC.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

0925

DOI: https://doi.org/10.58530/2024/0925