This paper presents an imaging scheme capable of estimating the full 3-D velocity vector field in a volume using rowcolumn addressed (RCA) arrays 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 crosscorrelation 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/[MHz•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 xyrotation 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 v v x x x , v v v y y y , v v v z z z ). Decreasing the beam-to-flow angle to 60 • gave a 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 a 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 a pulsating flow. The pulsating velocity magnitude was estimated across 10 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 x x

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Row-column (RC) arrays have the potential to yield full three-dimensional ultrasound imaging with a greatly reduced number of elements compared to fully populated arrays. They, however, have several challenges due to their special geometry. This review paper summarizes the current literature for RC imaging and demonstrate that full anatomic and functional imaging can attain a high quality using synthetic aperture (SA) sequences and modified delay-and-sum beamforming. Resolution can approach the diffraction limit with an isotropic resolution of half a wavelength with low side-lobe levels, and the field-ofview can be expanded by using convex or lensed RC probes. GPU beamforming allows for 3 orthogonal planes to be beamformed at 30 Hz, providing near real time imaging ideal for positioning the probe and improving the operator's workflow. Functional imaging is also attainable using transverse oscillation and dedicated SA sequence for tensor velocity imaging for revealing the full 3-D velocity vector as a function of spatial position and time for both blood velocity and tissue motion estimation. Using RC arrays with commercial contrast agents can reveal super resolution imaging with isotropic resolution below 20 µm. RC arrays can, thus, yield full 3-D imaging at high resolution, contrast, and volumetric rates for both anatomic and functional imaging with the same number of receive channels as current commercial 1-D arrays.

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This study presents a method for non-invasive pressure gradient estimation, which allows the detection of small pressure differences with a higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier-Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256 elements, 6.5 MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture interleaved sequence with 2×12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields a R-square of 0.985 and a RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from -59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flow rate of 12.9 mL/s. The double cross-correlation approach revealed no improvement compared to a normal differential operator. The method's strength, thus, lies primarily in the ultrasound sequence, which allows precise and accurate velocity estimations, at which acceleration and pressure differences can be acquired.