Phase-sensitive lateral motion estimator for measurement of artery-wall displacement--phantom study

Artery-wall motion due to the pulsation of the heart is often measured to evaluate mechanical properties of the arterial wall. Such motion is thought to occur only in the arterial radial direction because the main source of the motion is an increase of blood pressure. However, it has recently been reported that the artery also moves in the longitudinal direction. Therefore, a 2-D motion estimator is required even when the artery is scanned in the longitudinal direction because the arterial wall moves both in the radial (axial) and longitudinal (lateral) directions. Methods based on 2-D correlation of RF echoes are often used to estimate the lateral displacement together with axial displacement. However, these methods require much interpolation of the RF echo or correlation function to achieve a sufficient resolution in the estimation of displacement. To overcome this problem, Jensen et al. modulated the ultrasonic field in the lateral direction at a designed spatial frequency to use the lateral phase for the estimation of lateral motion. This method, namely, the lateral modulation method, generates complex signals whose phases change depending on the lateral motion. Therefore, the lateral displacement can be estimated with a good resolution without interpolation, although special beamformers are required. The present paper describes a method that can be applied to ultrasonic echoes obtained by a conventional beamformer to estimate lateral displacements using the phases of lateral fluctuations of ultrasonic echoes. In the proposed method, complex signals were generated by the Hilbert transform, and the phase shift was estimated by correlation-based estimators. The proposed method was validated using a cylindrical phantom mimicking an artery. The error in the lateral displacement estimated by the proposed method was 13.5% of the true displacement of 0.5 mm with a kernel size used for calculating the correlation function of 0.6 mm in the lateral direction, which was slightly smaller than the width at -20 dB of the maximum lateral ultrasonic field (about 0.8 mm).