Low-rank reconstruction for simultaneous double half-echo 23Na and undersampled 23Na multi-quantum coherences MRI

Christian Licht; Simon Reichert; Mark Bydder; Jascha Zapp; Shirley Corella; Maxime Guye; Frank G Zöllner; Lothar R Schad; Stanislas Rapacchi

doi:10.1002/mrm.30132

Low-rank reconstruction for simultaneous double half-echo ²³Na and undersampled ²³Na multi-quantum coherences MRI

Magn Reson Med. 2024 May 10. doi: 10.1002/mrm.30132. Online ahead of print.

Authors

Christian Licht^{1

2}, Simon Reichert^{1

2}, Mark Bydder³, Jascha Zapp^{1

2}, Shirley Corella^{3

4}, Maxime Guye^{3

4}, Frank G Zöllner^{1

2}, Lothar R Schad^{1

2}, Stanislas Rapacchi^{3

4}

Affiliations

¹ Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany.
² Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany.
³ Aix-Marseille Univ, CNRS, CRMBM, Marseille, France.
⁴ APHM, CEMEREM, Hôpital Universitaire Timone, Marseille, France.

PMID: 38725430
DOI: 10.1002/mrm.30132

Abstract

Purpose: To develop a new sequence to simultaneously acquire Cartesian sodium (²³Na) MRI and accelerated Cartesian single (SQ) and triple quantum (TQ) sodium MRI of in vivo human brain at 7 T by leveraging two dedicated low-rank reconstruction frameworks.

Theory and methods: The Double Half-Echo technique enables short echo time Cartesian ²³Na MRI and acquires two k-space halves, reconstructed by a low-rank coupling constraint. Additionally, three-dimensional (3D) ²³Na Multi-Quantum Coherences (MQC) MRI requires multi-echo sampling paired with phase-cycling, exhibiting a redundant multidimensional space. Simultaneous Autocalibrating and k-Space Estimation (SAKE) were used to reconstruct highly undersampled ²³Na MQC MRI. Reconstruction performance was assessed against five-dimensional (5D) CS, evaluating structural similarity index (SSIM), root mean squared error (RMSE), signal-to-noise ratio (SNR), and quantification of tissue sodium concentration and TQ/SQ ratio in silico, in vitro, and in vivo.

Results: The proposed sequence enabled the simultaneous acquisition of fully sampled ²³Na MRI while leveraging prospective undersampling for ²³Na MQC MRI. SAKE improved TQ image reconstruction regarding SSIM by 6% and reduced RMSE by 35% compared to 5D CS in vivo. Thanks to prospective undersampling, the spatial resolution of ²³Na MQC MRI was enhanced from $8 \times 8 \times 15$ mm³ to $8 \times 8 \times 8$ mm³ while reducing acquisition time from $2 \times 31$ min to $2 \times 23$ min.

Conclusion: The proposed sequence, coupled with low-rank reconstructions, provides an efficient framework for comprehensive whole-brain sodium MRI, combining TSC, T2*, and TQ/SQ ratio estimations. Additionally, low-rank matrix completion enables the reconstruction of highly undersampled ²³Na MQC MRI, allowing for accelerated acquisition or enhanced spatial resolution.

Keywords: compressed sensing; double half‐echo; low‐rank matrix completion; neuroimaging; single and triple quantum imaging; sodium multi‐quantum coherences.

Abstract

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