Abstract

Purpose: To mathematically analyze and validate a new method to reconstruct motion from phase-contrast data and an arbitrary number of motion encoding gradients (MEGs). Theory: We compute analytically the standard deviation for single- and dual MEG methods previously reported. A multiple motion encoding method (OMME) is then derived and analyzed as an extension of the optimal dual venc method (ODV). Methods: OMME is assessed first numerically for several high/low MEG ratios. Results are compared in terms of motion-to-noise-ratio (MNR) for different image SNR. The algorithms are tested later on data coming from MR Elastography (MRE) heparin phantom and volunteer’s brain data, where also SWS maps are computed. Comparisons are performed with respect to traditional unwrapping methods. Results: For the dual MEG case, OMME performs better than the standard dual MEG method, in terms of robustness to noise and effective MNR. OMME allowed to successfully combined four MEGs in MRE, leading to SWS maps which do not loose important details (e.g. discontinuities in the stiffness) as it occurs alternative unwrapping methods. Conclusion: The OMME method presents a superior robustness with respect to noise compared standard dual encoding unwrapping for two MEGs, and allows a straightforward application to multiple encoding.