On the Performance of Time Domain Displacement Estimators for Magnetomotive Ultrasound Imaging

In magnetomotive (MM) ultrasound (US) imaging, magnetic nanoparticles (NPs) are excited by an external magnetic field and the tracked motion of the surrounding tissue serves as a surrogate parameter for the NP concentration. MMUS procedures exhibit weak displacement contrasts due to small forces on the NPs. Consequently, precise US-based displacement estimation is crucial in terms of a sufficiently high contrast-to-noise ratio (CNR) in MMUS imaging. Conventional MMUS detection of the NPs is based on samplewise evaluation of the phase of the in-phase and quadrature (IQ) data, where a low signal-to-noise ratio (SNR) in the data leads to strong phase noise and, thus, to an increased variance of the displacement estimate. This paper examines the performance of two time-domain displacement estimators (DEs) for MMUS imaging, which differ from conventional MMUS techniques by incorporating data from an axial segment. The normalized cross correlation (NCC) estimator and a recursive Bayesian estimator, incorporating spatial information from neighboring segments, weighted by the local SNR, are adapted for the small MMUS displacement magnitudes. Numerical simulations of MM-induced, time-harmonic bulk and Gaussian-shaped displacement profiles show that the two time-domain estimators yield a reduced estimation error compared to the phase-shift-based estimator. Phantom experiments, using our recently proposed magnetic excitation setup, show a 1.9-fold and 3.4-fold increase of the CNR in the MMUS images for the NCC and Bayes estimator compared to the conventional method, while the amount of required data is reduced by a factor of 100.