Ultrafast ultrasound is a promising imaging modality that enabled, inter alia, the development of pulse wave imaging and the local velocity estimation of the so-called pulse wave for a quantitative evaluation of arterial stiffness. However, this technique only focuses on the propagation of the axial displacement of the artery wall, and most techniques are not specific to the intima-media complex and do not take into account the longitudinal motion of this complex. Within this perspective, this paper presents a study of two-dimensional tissue motion estimation in ultrafast imaging combining transverse oscillations, which can improve motion estimation in the transverse direction, i.e., perpendicular to the beam axis, and a phase-based motion estimation. First, the method was validated in simulation. Two-dimensional motion, inspired from a real data set acquired on a human carotid artery, was applied to a numerical phantom to produce a simulation data set. The estimated motion showed axial and lateral mean errors of 4.2 ± 3.4 μm and 9.9 ± 7.9 μm, respectively. Afterward, experimental results were obtained on three artery phantoms with different wall stiffnesses. In this study, the vessel phantoms did not contain a pure longitudinal displacement. The longitudinal displacements were induced by the axial force produced by the wall's axial dilatation. This paper shows that the approach presented is able to perform 2-D tissue motion estimation very accurately even if the displacement values are very small and even in the lateral direction, making it possible to estimate the pulse wave velocity in both the axial and longitudinal directions. This demonstrates the method's potential to estimate the velocity of purely longitudinal waves propagating in the longitudinal direction. Finally, the stiffnesses of the three vessel phantom walls investigated were estimated with an average relative error of 2.2%.

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We present a new method to estimate 4-D (3-D + time) tissue motion. The method used combines 3-D phase based motion estimation with an unconventional beamforming strategy. The beamforming technique allows us to obtain full 3-D RF volumes with axial, lateral, and elevation modulations. Based on these images, we propose a method to estimate 3-D motion that uses phase images instead of amplitude images. First, volumes featuring 3-D oscillations are created using only a single apodization function, and the 3-D displacement between two consecutive volumes is estimated simultaneously by applying this 3-D estimation. The validity of the method is investigated by conducting simulations and phantom experiments. The results are compared with those obtained with two other conventional estimation methods: block matching and optical flow. The results show that the proposed method outperforms the conventional methods, especially in the transverse directions.