Estimation of High Velocities in Synthetic Aperture Imaging: I: Theory

The Effect of Spatial Velocity Gradients on Block-Matching Accuracy for Ultrasound Velocimetry

OBJECTIVE

Block matching serves as the foundation for ultrasound velocimetry techniques such as blood speckle tracking and echo-particle image velocimetry. Any spatial velocity gradients (SVGs) inside a block-matching pair will result in tracking error, due to both the finite block size and the ultrasound point-spread-function. We assess, using an in silico sinusoidal flow phantom, the effect of SVG magnitude and beam-to-flow angle on block-matching bias and precision. Secondarily we assess the effect that SVGs have on velocimetry bias when using angled plane-wave compounding.

METHODS

The magnitude and angle of SVGs were varied by adjusting the wavelength and direction of a sinusoidal flow profile. Scatterers displaced by this flow profile were used for simulating ultrasound radio frequency data at discrete time points. After beamforming, the 2-D flow field was estimated using block matching. Two imaging sequences were tested, a single plane-wave and a three-angled plane-wave.

RESULTS

Smaller sinusoidal flow wavelengths resulted in increased bias and reduced precision, revealing an inverse relationship between sinusoidal flow wavelength and tracking error, with median errors ranging from 69%-90% for the smallest flow wavelengths (highest SVGs) down to 3%-5% for the largest (lowest SVGs). The SVG angle was also important, in which lateral SVGs (with axially oriented flows) resulted in significant speckle decorrelation and high tracking errors in regions with high SVGs. Conversely, axial SVGs (laterally oriented flow) experienced higher bias in the peak velocity regions of the flow profile. Coherent compounding resulted in higher velocity errors than using a single transmission for lateral SVGs but not for axial SVGs.

CONCLUSION

The highest SVGs that could be measured with ≤10% error was when the sinusoidal flow wavelength was less than 20 times the ultrasound pulse wavelength. The clinical significance is that the high SVGs present in high kinetic energy flows, such as severe carotid stenosis and aortic regurgitation, will limit the ability to accurately quantify the velocities in these flow structures.

A Transverse Velocity Spectral Estimation Method for Ultrafast Ultrasound Doppler Imaging

A novel transverse velocity spectral estimation method is proposed to estimate the velocity component in the direction transverse to the beam axis for ultrafast imaging. The transverse oscillation was introduced by filtering the envelope data after the axial oscillation was removed. The complex transverse oscillated signal was then used to estimate the transverse velocity spectrum and mean velocity. In simulations, both steady flow with a parabolic flow profile and temporally varying flow were simulated to investigate the performance of the proposed method. Next, the proposed approach was used to estimate the flow velocity in a phantom with pulsatile flow, and finally, this method was applied in vivo in a small animal model. Results of the simulation study indicate that the proposed method provided an accurate velocity spectrogram for beam-to-flow angles from 45° to 90°, without significant performance degradation as the angle decreased. For the simulation of temporally varying flow, the proposed method had a reduced bias ( % versus 73.3%) and higher peak-to-background ratio (PBR) (>15.6 versus 10.5 dB) compared to previous methods. Results in a vessel phantom show that the temporally varying flow velocity can be estimated in the transverse direction obtained using the spectrogram produced by the proposed method operating on the envelope data. Finally, the proposed method was used to map the microvascular blood flow velocity in the mouse spinal cord, demonstrating the estimation of pulsatile blood flow in both the axial and transverse directions in vivo over several cardiac cycles.

A GPU-Based, Real-Time Dealiasing Framework for High-Frame-Rate Vector Doppler Imaging

Vector Doppler is well regarded as a potential way of deriving flow vectors to intuitively visualize complex flow profiles, especially when it is implemented at high frame rates. However, this technique's performance is known to suffer from aliasing artifacts. There is a dire need to devise real-time dealiasing solutions for vector Doppler. In this article, we present a new methodological framework for achieving aliasing-resistant flow vector estimation at real-time throughput from precalculated Doppler frequencies. Our framework comprises a series of compute kernels that have synergized: 1) an extended least squares vector Doppler (ELS-VD) algorithm; 2) single-instruction, multiple-thread (SIMT) processing principles; and 3) implementation on a graphical processing unit (GPU). Results show that this new framework, when executed on an RTX-2080 GPU, can effectively generate aliasing-free flow vector maps using high-frame-rate imaging datasets acquired from multiple transmit-receive angle pairs in a carotid phantom imaging scenario. Over the entire cardiac cycle, the frame processing time for aliasing-resistant vector estimation was measured to be less than 16 ms, which corresponds to a minimum processing throughput of 62.5 frames/s. In a human femoral bifurcation imaging trial with fast flow (150 cm/s), our framework was found to be effective in resolving two-cycle aliasing artifacts at a minimum throughput of 53 frames/s. The framework's processing throughput was generally in the real-time range for practical combinations of ELS-VD algorithmic parameters. Overall, this work represents the first demonstration of real-time, GPU-based aliasing-resistant vector flow imaging using vector Doppler estimation principles.

Transverse oscillation tensor velocity imaging using a row-column addressed array: Experimental validation

Tensor velocity imaging (TVI) performance with a row-column probe was assessed for constant flow in a straight vessel phantom and pulsatile flow in a carotid artery phantom. TVI, i.e., estimating the 3-D velocity vector as a function of time and spatial position, was performed using the transverse oscillation cross-correlation estimator, and the flow was acquired with a Vermon 128+128 row-column array probe connected to a Verasonics 256 research scanner. The emission sequence used 16 emissions per image, and a TVI volume rate of 234 Hz was obtained for a pulse repetition frequency (f_prf) of 15 kHz. The TVI was validated by comparing estimates of the flow rate through several cross-sections with the flow rate set by the pump. For the constant 8 mL/s flow in the straight vessel phantom with relative estimator bias (RB) and standards deviation (RSD) was found in the range of -2.18% to 0.55% and 4.58% to 2.48% in measurements performed with an f_prf of 15, 10, 8, and 5 kHz. The pulsatile flow in the carotid artery phantom the was set to an average flow rate of 2.44 mL/s, and the flow was acquired with an f_prf of 15, 10, and 8 kHz. The pulsatile flow was estimated from two measurement sites: one at a straight section of the artery and one at the bifurcation. In the straight section, the estimator predicted the average flow rate with an RB value ranging from -7.99% to 0.10% and an RSD value ranging from 10.76% to 6.97%. At the bifurcation, RB and RSD values were between -7.47% to 2.02% and 14.46% to 8.89%. This demonstrates that an RCA with 128 receive elements can accurately capture the flow rate through any cross-section at a high sampling rate.

Precise Estimation of Intravascular Pressure Gradients

This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with 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-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) 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 an R -square of 0.985 and an 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.

Advanced Fourier migration for Plane-Wave vector flow imaging

Ultrafast ultrasound imaging modalities have been studied extensively in the ultrasound community. It breaks the compromise between the frame rate and the region of interest by imaging the whole medium with wide unfocused waves. Continuously available data allow monitoring fast transient dynamics at hundreds to thousands of frames per second. This feature enables a more accurate and robust velocity estimation in vector flow imaging (VFI). On the other hand, the huge amount of data and real-time processing demands are still challenging in VFI. A solution is to provide a more efficient beamforming approach with smaller computation complexity than the conventional time-domain beamformer like delay-and-sum (DAS). Fourier-domain beamformers are shown to be more computationally efficient and can provide equally good image quality as DAS. However, previous studies generally focus on B-mode imaging. In this study, we propose a new framework for VFI which is based on two advanced Fourier migration methods, namely, slant stack migration (SSM) and ultrasound Fourier slice beamform (UFSB). By carefully modifying the beamforming parameters, we successfully apply the cross-beam technique within the Fourier beamformers. The proposed Fourier-based VFI is validated in simulation studies, in vitro, and in vivo experiments. The velocity estimation is evaluated via bias and standard deviation and the results are compared with conventional time-domain VFI using the DAS beamformer. In the simulation, the bias is 6.4%, -6.2%, and 5.7%, and the standard deviation is 4.3%, 2.4%, and 3.9% for DAS, UFSB, and SSM, respectively. In vitro studies reveal a bias of 4.5%, -5.3%, and 4.3% and a standard deviation of 3.5%, 1.3%, and 1.6% from DAS, UFSB, and SSM, respectively. The in vivo imaging of the basilic vein and femoral bifurcation also generate similar results using all three methods. With the proposed Fourier beamformers, the computation time can be shortened by up to 9 times and 14 times using UFSB and SSM.

Anatomic and Functional Imaging Using Row-Column Arrays

Row-column (RC) arrays have the potential to yield full 3-D 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 article summarizes the current literature for RC imaging and demonstrates 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 sidelobe levels, and the field of view can be expanded by using convex or lensed RC probes. GPU beamforming allows for three 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 (SRI) with isotropic resolution below [Formula: see text]. 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.

Forward-viewing estimation of 3D blood flow velocity fields by intravascular ultrasound: Influence of the catheter on velocity estimation in stenoses

Coronary artery disease is the most common type of cardiovascular disease, affecting > 18 million adults, and is responsible for > 365 k deaths per year in the U.S. alone. Wall shear stress (WSS) is an emerging indicator of likelihood of plaque rupture in coronary artery disease, however, non-invasive estimation of 3-D blood flow velocity and WSS is challenging due to the requirement for high spatial resolution at deep penetration depths in the presence of significant cardiac motion. Thus we propose minimally-invasive imaging with a catheter-based, 3-D intravascular forward-viewing ultrasound (FV US) transducer and present experiments to quantify the effect of the catheter on flow disturbance in stenotic vessel phantoms with realistic velocities and luminal diameters for both peripheral (6.33 mm) and coronary (4.74 mm) arteries. An external linear array ultrasound transducer was used to quantify 2-D velocity fields in vessel phantoms under various conditions of catheter geometry, luminal diameter, and position of the catheter relative to the stenosis at a frame rate of 5000 frames per second via a particle imaging velocimetry (PIV) approach. While a solid catheter introduced an underestimation of velocity measurement by > 20% relative to the case without a catheter, the hollow catheter introduced < 10% velocity overestimation, indicating that a hollow catheter design allowing internal blood flow reduces hemodynamic disturbance. In addition, for both peripheral and coronary arteries, the hollow catheter introduced < 3% deviation in flow velocity at the minimum luminal area compared to the control case. Finally, an initial comparison was made between velocity measurements acquired using a low frequency, catheter-based, 3-D intravascular FV US transducer and external linear array measurements, with relative error < 12% throughout the region of interest for a flow rate of 150 mL/min. While further system development is required, results suggest intravascular ultrasound characterization of blood flow velocity fields in stenotic vessels could be feasible with appropriate catheter design.

Tensor Velocity Imaging With Motion Correction

This article presents a motion compensation procedure that significantly improves the accuracy of synthetic aperture tensor velocity estimates for row-column arrays. The proposed motion compensation scheme reduces motion effects by moving the image coordinates with the velocity field during summation of low-resolution volumes. The velocity field is estimated using a transverse oscillation cross-correlation estimator, and each image coordinate's local tensor velocity is determined by upsampling the field using spline interpolation. The motion compensation procedure is validated using Field II simulations and flow measurements acquired using a 3-MHz row-column addressed probe and the research scanner SARUS. For a peak velocity of 25 cm/s, a pulse repetition frequency of 2 kHz, and a beam-to-flow angle of 60°, the proposed motion compensation procedure was able to reduce the relative bias from -27.0% to -9.4% and the standard deviation from 8.6% to 8.1%. In simulations performed with a pulse repetition frequency of 10 kHz, the proposed method reduces the bias in all cases with beam-to-flow angles of 60° and 75° and peak velocities between 10 and 150 cm/s.

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

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/[ [Formula: see text]] 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.

Effects of motion on correlations of pulse-echo ultrasound signals: Applications in delay estimation and aperture coherence

The correlation between two pulse-echo ultrasound signals is used to achieve a wide range of ultrasound techniques, such as Doppler imaging and elastography. Prior theoretical descriptions of pulse-echo correlations were restricted to stationary scatterers. Here, a theory for the correlation of moving scatterers is presented. An expression is derived for the correlation of two pulse-echo signals with arbitrary transmit and receive apertures acquired from a medium undergoing bulk motion using the Fresnel approximation. The derivation is shown to coincide with prior derivations in the absence of scatterer motion. The theory was compared against simulations in applications of phase-shift estimation and aperture coherence measurements. The phase-shift estimate and jitter were accurately predicted under axial and transverse motion for focused transmit apertures and for sequential and interleaved synthetic transmit apertures. The theory also accurately predicted how motion affects the correlation coefficient between receive aperture elements for a synthetic transmit aperture. The presented theory provides a framework for analyzing the correlations of arbitrary pulse-echo configurations for applications in which scatterer motion is expected.

Estimation of High Velocities in Synthetic Aperture Imaging: II: Experimental Investigation

The paper describes the performance of a new pulse sequence design and estimation approach for increasing the maximum detectable velocity in synthetic aperture (SA) velocity imaging. Measurements are conducted for conventional imaging for comparing the velocity range detectable by a directional Transverse Oscillation (TO) autocorrelation estimator to a new cross-correlation estimator. For conventional focused emissions a 192-elements, 3 MHz convex array transducer is used together with the SARUS experimental scanner on a flow rig at beam-to-flow angles of 60°, 70° and 90°. Here the new estimator always yields a higher precision, and the aliasing limit is increased by a factor 3. The new SA inter-spaced scheme was investigated using Field II simulations and SARUS measurements. A 3 MHz, 128-elements phased array was employed with a 5 virtual source emissions scheme for flow estimation and 15 emissions for B-mode imaging. The scheme was interleaved three times for a positive, negative, and positive transmission, so that non-linear pulse inversion also could be made. The experiments were conducted at three angles and for 4 different pulse repetition frequencies. A peak transverse velocity of 0.51 m/s could be estimated at fprf=450 Hz, translating to 5.6 m/s at fprf=5 kHz showing the theoretical increase of a factor 10 predicted in the accompanying theory paper.