A noise-robust post-processing pipeline for accelerated phase-cycled ²³Na Multi-Quantum Coherences MRI

To develop an improved post-processing pipeline for noise-robust accelerated phase-cycled Cartesian Single (SQ) and Triple Quantum (TQ) sodium (²³Na) Magnetic Resonance Imaging (MRI) of in vivo human brain at 7 T.

Our pipeline aims to tackle the challenges of ²³Na Multi-Quantum Coherences (MQC) MRI including low Signal-to-Noise Ratio (SNR) and time-consuming Radiofrequency (RF) phase-cycling. Our method combines low-rank k-space denoising for SNR enhancement with Dynamic Mode Decomposition (DMD) to robustly separate SQ and TQ signal components. This separation is crucial for computing the TQ/SQ ratio, a key parameter of ²³Na MQC MRI. We validated our pipeline in silico, in vitro and in vivo in healthy volunteers, comparing it with conventional denoising and Fourier transform (FT) methods. Additionally, we assessed its robustness through ablation experiments simulating a corrupted RF phase-cycle step.

Our denoising algorithm doubled SNR compared to non-denoised images and enhanced SNR by up to 29% compared to Wavelet denoising. The low-rank approach produced high-quality images even at later echo times, allowing reduced signal averaging. DMD effectively separated the SQ and TQ signals, even with missing RF phase cycle steps, resulting in superior Structural Similarity (SSIM) of 0.89±0.024 and lower Root Mean Squared Error (RMSE) of 0.055±0.008 compared to conventional FT methods (SSIM=0.71±0.061, RMSE=0.144±0.036). This pipeline enabled high-quality 8x8x15mm³ in vivo ²³Na MQC MRI, with a reduction in acquisition time from 48 to 10 min at 7 T.

The proposed pipeline improves robustness in ²³Na MQC MRI by exploiting low-rank properties to denoise signals and DMD to effectively separate SQ and TQ signals. This approach ensures high-quality MR images of both SQ and TQ components, even in accelerated and incomplete RF phase-cycling cases.