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In this work, the accuracy of row–column tensor velocity imaging (TVI), i.e., 3-D vector flow imaging (VFI) in 3-D space over time, is quantified on a complex, clinically relevant flow. The quantification is achieved by transferring the flow simulated using computational fluid dynamics (CFD) to a Field II simulation environment, and this allows for a direct comparison between the actual and estimated velocities. The carotid bifurcation flow simulations were performed with a peak inlet velocity of 80 cm/s, nonrigid vessel walls, and a flow cycle duration of 1.2 s. The flow was simulated from two observation angles, and it was acquired using a 3-MHz 62+62 row–column addressed array (RCA) at a pulse repetition frequency (${f}_{prf}$) of 10 and 20 kHz. The tensor velocities were obtained at a frame rate of 208.3 Hz, at ${f}_{prf} = {10} ~\mathrm{kHz}$ , and the results from two velocity estimators were compared. The two estimators were the directional transverse oscillation (TO) cross correlation estimator and the proposed autocorrelation estimator. Linear regression between the actual and estimated velocity components yielded, for the cross correlation estimator, an ${R}$ 2 value in the range of 0.89–0.91, 0.46–0.77, and 0.91–0.97 for the ${x}$ -, ${y}$ -, and ${z}$ -components, and 0.87–0.89, 0.40–0.83, and 0.91–0.96 when using the autocorrelation estimator. The results demonstrate that an RCA can, with just 62 receive channels, measure complex 3-D flow fields at a high volume rate. [ABSTRACT FROM AUTHOR]

A method for volumetric Tensor Velocity Imaging employing row-column (RC) addressed array with low computational complexity is investigated in simulations. An interleaved and non-interleaved sliding aperture sequence with 11 rows and 11 columns emissions by a 62 + 62 RC addressed array was used. The 3D velocities were estimated by a transverse oscillation (TO) cross-correlation estimator. Parabolic profiles at six different orientations corresponding to combinations of 0, 45 degrees azimuth angles and 90, 75, 60 beam-to-flow angles were investigated with 5 kHz pulse repetition frequencies. The Field II simulations were performed at a depth of 30 mm with peak velocity of 0.3 m/s. Across all vessel orientations, the relative mean bias varied from 2.3% to −14.26%, and the relative standard deviation varied from 0.43% to 5.5%. The best and worst performance was found at beam to flow angles of 90 degrees with 0 degrees rotation angle and 60 degrees beam-to-flow angle with 45 degrees rotation angle respectively. Due to the low channel count of the RC array and the low computational complexity, real-time implementation is feasible on conventional ultrasound systems. [ABSTRACT FROM AUTHOR]

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/[ $\text {MHz}\cdot \text {cm}$ ] 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 xy-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 (${v_{x}}$ , ${v_{y}}$ , and ${v_{z}}$). 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 (${x, {y}, {z},}$ and ${t}$) using only 62 channels in receive, making 4-D volumetric imaging implementable on current scanner hardware. [ABSTRACT FROM AUTHOR]

The objective of the study described here was to investigate the accuracy and precision of a plane wave 2-D vector flow imaging (VFI) method in laminar and complex blood flow conditions in the healthy carotid artery. The approach was to study (i) the accuracy for complex flow by comparing the velocity field from a computational fluid dynamics (CFD) simulation to VFI estimates obtained from the scan of an anthropomorphic flow phantom and from an in vivo scan; (ii) the accuracy for laminar unidirectional flow in vivo by comparing peak systolic velocities from VFI with magnetic resonance angiography (MRA); (iii) the precision of VFI estimation in vivo at several evaluation points in the vessels. The carotid artery at the bifurcation was scanned using both fast plane wave ultrasound and MRA in 10 healthy volunteers. The MRA geometry acquired from one of the volunteers was used to fabricate an anthropomorphic flow phantom, which was also scanned using the fast plane wave sequence. The same geometry was used in a CFD simulation to calculate the velocity field. Results indicated that similar flow patterns and vortices were estimated with CFD and VFI in the phantom for the carotid bifurcation. The root-mean-square difference between CFD and VFI was within 0.12 m/s for velocity estimates in the common carotid artery and the internal branch. The root-mean-square difference was 0.17 m/s in the external branch. For the 10 volunteers, the mean difference between VFI and MRA was -0.17 m/s for peak systolic velocities of laminar flow in vivo. The precision in vivo was calculated as the mean standard deviation (SD) of estimates aligned to the heart cycle and was highest in the center of the common carotid artery (SD = 3.6% for velocity magnitudes and 4.5° for angles) and lowest in the external branch and for vortices (SD = 10.2% for velocity magnitudes and 39° for angles). The results indicate that plane wave VFI measures flow precisely and that estimates are in good agreement with a CFD simulation and MRA. [ABSTRACT FROM AUTHOR]