Fast 3-D Velocity Estimation in 4-D Using a 62 + 62 Row–Column Addressed Array

Abstract

This article presents an imaging scheme capable of estimating the full 3-D velocity vector field in a volume using row-column addressed arrays (RCAs) at a high volume rate. A 62 + 62 RCA array is employed with an interleaved synthetic aperture sequence. It contains repeated emissions with rows and columns interleaved with B-mode emissions. The sequence contains 80 emissions in total and can provide continuous volumetric data at a volume rate above 125 Hz. A transverse oscillation cross correlation estimator determines all three velocity components. The approach is investigated using Field II simulations and measurements using a specially built 3-MHz 62 + 62 RCA array connected to the SARUS experimental scanner. Both the B-mode and flow sequences have a penetration depth of 14 cm when measured on a tissue-mimicking phantom (0.5-dB/[<inline-formula> <tex-math notation= LaTeX >$\\text {MHz}\\cdot \\text {cm}$ </tex-math></inline-formula>] attenuation). Simulations of a parabolic flow in a 12-mm-diameter vessel at a depth of 30 mm, beam-to-flow angle of 90°, and <italic>xy</italic>-rotation of 45° gave a standard deviation (SD) of (3.3, 3.4, 0.4)% and bias of (−3.3, −3.9, −0.1)%, for (<inline-formula> <tex-math notation= LaTeX >${v_{x}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation= LaTeX >${v_{y}}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation= LaTeX >${v_{z}}$ </tex-math></inline-formula>). Decreasing the beam-to-flow angle to 60° gave an SD of (8.9, 9.1, 0.8)% and bias of (−7.6, −9.5, −7.2)%, showing a slight increase. Measurements were carried out using a similar setup, and pulsing at 2 kHz yielded comparable results at 90° with an SD of (5.8, 5.5, 1.1)% and bias of (1.4, −6.4, 2.4)%. At 60°, the SD was (5.2, 4.7 1.2)% and bias (−4.6, 6.9, −7.4)%. Results from measurements across all tested settings showed a maximum SD of 6.8% and a maximum bias of 15.8% for a peak velocity of 10 cm/s. A tissue-mimicking phantom with a straight vessel was used to introduce clutter, tissue motion, and pulsating flow. The pulsating velocity magnitude was estimated across ten pulse periods and yielded an SD of 10.9%. The method was capable of estimating transverse flow components precisely but underestimated the flow with small beam-to-flow angles. The sequence provided continuous data in both time and space throughout the volume, allowing for retrospective analysis of the flow. Moreover, B-mode planes can be selected retrospectively anywhere in the volume. This shows that tensor velocity imaging (full 3-D volumetric vector flow imaging) can be estimated in 4-D (<inline-formula> <tex-math notation= LaTeX >${x, {y}, {z},}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation= LaTeX >${t}$ </tex-math></inline-formula>) using only 62 channels in receive, making 4-D volumetric imaging implementable on current scanner hardware.