Multiple motion encoding in phase-contrast MRI: A general theory and application to elastography imaging.

Helge Herthum,Cristóbal Bertoglio,Ingolf Sack,Axel Osses,Sergio Uribe,Hugo Carrillo

doi:10.1016/j.media.2022.102416

Abstract

While MRI allows to encode the motion of tissue in the magnetization's phase, it remains yet a challenge to obtain high fidelity motion images due to wraps in the phase for high encoding efficiencies. Therefore, we propose an optimal multiple motion encoding method (OMME) and exemplify it in Magnetic Resonance Elastography (MRE) data. OMME is formulated as a non-convex least-squares problem for the motion using an arbitrary number of phase-contrast measurements with different motion encoding gradients (MEGs). The mathematical properties of OMME are proved in terms of standard deviation and dynamic range of the motion's estimate for arbitrary MEGs combination which are confirmed using synthetically generated data. OMME's performance is assessed on MRE data from in vivo human brain experiments and compared to dual encoding strategies. The unwrapped images are further used to reconstruct stiffness maps and compared to the ones obtained using conventional unwrapping methods. OMME allowed to successfully combine several MRE phase images with different MEGs, outperforming dual encoding strategies in either motion-to-noise ratio (MNR) or number of successfully reconstructed voxels with good noise stability. This lead to stiffness maps with greater resolution of details than obtained with conventional unwrapping methods. The proposed OMME method allows for a flexible and noise robust increase in the dynamic range and thus provides wrap-free phase images with high MNR. In MRE, the method may be especially suitable when high resolution images with high MNR are needed.

Highlights

For those reasons, it is a common practice to use low dynamic ranges and to remove the wraps afterwards
The static background phase induced by the motion encoding gradients (MEGs) δG decreased with amplitude until no difference compared to the background phase induced by the imaging gradients φ0 was visible
Toggling the MEG resulted in a different background phase which is clearly visible for MEG amplitudes

Summary

Introduction

It is a common practice to use low dynamic ranges and to remove the wraps afterwards. They cannot recover the true underlying motion and eventually fail when the aliased regions are highly heterogeneous, subject to noise or include nested wraps (i.e. when |k| > 1). In such cases, the unwrapped phase appears to be distorted and obstructs further data processing steps which leads to artifacts in the estimates of tissue properties [10]. Measurements with a reduced dynamic range (improved MNR) are unwrapped using a measurement with a larger dynamic range Those methods are performed at each voxel independently and they do not assume or enforce smoothness of the motion-encoded phase field.

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Discussion

Conclusion