Multidimensional compressed sensing to advance 23 Na multi‐quantum coherences MRI

Purpose Sodium ( 23 Na) multi‐quantum coherences (MQC) MRI was accelerated using three‐dimensional (3D) and a dedicated five‐dimensional (5D) compressed sensing (CS) framework for simultaneous Cartesian single (SQ) and triple quantum (TQ) sodium imaging of in vivo human brain at 3.0 and 7.0 T. Theory and Methods 3D 23 Na MQC MRI requires multi‐echo paired with phase‐cycling and exhibits thus a multidimensional space. A joint reconstruction framework to exploit the sparsity in all imaging dimensions by extending the conventional 3D CS framework to 5D was developed. 3D MQC images of simulated brain, phantom and healthy brain volunteers obtained from 3.0 T and 7.0 T were retrospectively and prospectively undersampled. Performance of the CS models were analyzed by means of structural similarity index (SSIM), root mean squared error (RMSE), signal‐to‐noise ratio (SNR) and signal quantification of tissue sodium concentration and TQ/SQ ratio. Results It was shown that an acceleration of three‐fold, leading to less than min of scan time with a resolution of at 3.0 T, are possible. 5D CS improved SSIM by 3%, 5%, 1% and reduced RMSE by 50%, 30%, 8% for in vivo SQ, TQ, and TQ/SQ ratio maps, respectively. Furthermore, for the first time prospective undersampling enabled unprecedented high resolution from to MQC images of in vivo human brain at 7.0 T without extending acquisition time. Conclusion 5D CS proved to allow up to three‐fold acceleration retrospectively on 3.0 T data. 2‐fold acceleration was demonstrated prospectively at 7.0 T to reach higher spatial resolution of 23 Na MQC MRI