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

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