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

Purpose: To develop a new sequence to simultaneously acquire Cartesian sodium (Na-23) 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 Na-23 MRI and acquires two k-space halves, reconstructed by a low-rank coupling constraint. Additionally, three-dimensional (3D) Na-23 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 Na-23 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 Na-23 MRI while leveraging prospective undersampling for Na-23 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 Na-23 MQC MRI was enhanced from 8 x 8 x 15 mm(3) to 8 x 8 x 8 mm(3) while reducing acquisition time from 2 x 31 min to 2 x 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 Na-23 MQC MRI, allowing for accelerated acquisition or enhanced spatial resolution.