Phase-Regularized and Displacement-Regularized Compressed Sensing for Fast Magnetic Resonance Elastography.

Liver magnetic resonance elastography (MRE) is a non-invasive stiffness measurement technique that captures the tissue displacement in the phase of the signal. To limit the scanning time to a single breathhold, liver MRE usually involves advanced readout techniques such as simultaneous multi-slice (SMS) or multi-shot methods. Furthermore, all these readout techniques require additional in-plane acceleration using either parallel imaging capabilities, such as sensitivity encoding (SENSE) or k-space undersampling, such as compressed sensing (CS). However, these methods apply a single regularization function on the complex image. This study aimed to design and evaluate methods that use separate regularization on magnitude and phase of MRE to exploit their distinct spatiotemporal characteristics. Specifically, we introduce two compressed sensing methods. The first method, termed phase regularized compressed sensing (PRCS), applies a two-dimensional total variation (TV) prior on the magnitude and two-dimensional wavelet regularization on the phase. The second method, termed displacement regularized compressed sensing (DRCS), exploits the spatiotemporal redundancy using a 3D total variation on the magnitude. Additionally, DRCS includes a displacement fitting function to apply wavelet regularization on the displacement phasor. Both DRCS and PRCS were evaluated with different levels of compression factors in three datasets: an in silico abdomen dataset, an in vitro tissue-mimicking phantom, and an in vivo liver dataset. The reconstructed images were compared with the full sampled reconstruction, zero-filling reconstruction, wavelet regularized compressed sensing, and a low rank plus sparse reconstruction. The metrics used for quantitative evaluationwere structural similarity index (SSIM) of magnitude (M-SSIM), displacement (D-SSIM), shear modulus (S-SSIM), and mean shear modulus. Results from highly undersampled in silico and in vitro datasets demonstrate that the DRCS method provides higher reconstruction quality than the conventional compressed sensing method for a wide range of stiffness values. Notably, DRCS provide 24% and 22% increase in D-SSIM compared to CS for the in silico and in vitro datasets, respectively. Comparison with liver stiffness measured from full sampled data and highly undersampled data (CR=4) demonstrates that the DRCS method provided the strongest correlation (R2=0.95), second-lowest mean bias (-0.18 kPa, lowest for CS with -0.16 kPa), and lowest coefficient of variation (CV=3.6%). Our results demonstrate the potential of using DRCS to improve the reconstruction quality of accelerated MRE.