Staggered Multiple-PRF Ultrafast Color Doppler

Nonlinear beamforming for intracardiac echocardiography: a comparative study

Intracardiac echocardiography (ICE) enables cardiac imaging with a wide field of view, deep imaging depth, and high frame rate during surgery. However, strong sidelobe and grating lobe artifacts created by the ultra-compact transducer degrade its image quality, making diagnosis and monitoring of treatment difficult. Conventionally, aperture apodization algorithms are often used to suppress sidelobe and grating lobe artifacts at the expense of lateral resolution, which is undesirable in ICE. In this study, we present comparative results of the beamforming methods specifically in ICE application. We demonstrate and compare five nonlinear beamforming algorithms in ICE: nonlinear pth root delay and sum (NL-p-DAS), nonlinear pth root spectral magnitude scaling (NL-p-SMS), delay-and-sum with coherence factors (DAS + SCF), delay and sum with apodization (DAS + apodization) and delay and sum (DAS). Phantom and ex-vivo experiment compare the performance of each algorithm in static and dynamic conditions. DAS + SCF shows the best lateral resolution, and all four algorithms improve the image contrast and sidelobe suppression over conventional DAS. NL-p-SMS stands out for the best axial resolution and suppression of grating lobe artifacts. For motion tracking, NL-p-SMS shows better temporal resolution than other methods. Overall, all the beamforming algorithms other than DAS showed improved image quality. Among them, NL-p-SMS, which has a high temporal resolution, showed the potential for providing more accurate information regards movement tracking.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13534-024-00352-9.

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.

Deep-learning-assisted and GPU-accelerated vector Doppler imaging with aliasing-resistant velocity estimation

Vector flow imaging is a diagnostic ultrasound modality that is suited for the visualization of complex blood flow dynamics. One popular way of realizing vector flow imaging at high frame rates over 1000 fps is to apply multi-angle vector Doppler estimation principles in conjunction with plane wave pulse-echo sensing. However, this approach is susceptible to flow vector estimation errors attributed to Doppler aliasing, which is prone to arise when a low pulse repetition frequency (PRF) is inevitably used due to the need for finer velocity resolution or because of hardware constraints. Existing dealiasing solutions tailored for vector Doppler may have high computational demand that makes them unfeasible for practical applications. In this paper, we present the use of deep learning and graphical processing unit (GPU) computing principles to devise a fast vector Doppler estimation framework that is resilient against aliasing artifacts. Our new framework works by using a convolutional neural network (CNN) to detect aliased regions in vector Doppler images and subsequently applying an aliasing correction algorithm only at these affected regions. The framework's CNN was trained using 15,000 in vivo vector Doppler frames acquired from the femoral and carotid arteries, including healthy and diseased conditions. Results show that our framework can perform aliasing segmentation with an average precision of 90 % and can render aliasing-free vector flow maps with real-time processing throughputs (25-100 fps). Overall, our new framework can improve the visualization quality of vector Doppler imaging in real-time.

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.

Requirements and Hardware Limitations of High-Frame-Rate 3-D Ultrasound Imaging Systems

The spread of high frame rate and 3-D imaging techniques has raised pressing requirements for ultrasound systems. In particular, the processing power and data transfer rate requirements may be so demanding to hinder the real-time (RT) implementation of such techniques. This paper first analyzes the general requirements involved in RT ultrasound systems. Then, it identifies the main bottlenecks in the receiving section of a specific RT scanner, the ULA-OP 256, which is one of the most powerful available open scanners and may therefore be assumed as a reference. This case study has evidenced that the “star” topology, used to digitally interconnect the system’s boards, may easily saturate the data transfer bandwidth, thus impacting the achievable frame/volume rates in RT. The architecture of the digital scanner was exploited to tackle the bottlenecks by enabling a new “ring“ communication topology. Experimental 2-D and 3-D high-frame-rate imaging tests were conducted to evaluate the frame rates achievable with both interconnection modalities. It is shown that the ring topology enables up to 4400 frames/s and 510 volumes/s, with mean increments of +230% (up to +620%) compared to the star topology.

Signal-to-noise ratio of diverging waves in multiscattering media: Effects of signal duration and divergence angle

In this paper, SNR maximization in coded diverging waves is studied, and experimental verification of the results is presented. Complementary Golay sequences and binary phase shift keying modulation are used to code the transmitted signal. The SNR in speckle and pin targets is maximized with respect to chip signal length. The maximum SNR is obtained in diverging wave transmission when the chip signal is as short a duration as the array permits. We determined the optimum diverging wave profile to confine the transmitted ultrasound energy in the imaging sector. The optimized profile also contributes to the SNR maximization. The SNR performances of the optimized coded diverging wave and conventional single-focused phased array imaging are compared on a single frame basis. The SNR of the optimized coded diverging wave is higher than that of the conventional single-focused phased array imaging at all depths and regions.

Physics-constrained intraventricular vector flow mapping by color Doppler

Color Doppler by transthoracic echocardiography creates two-dimensional fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved ouriVFM numerical scheme by imposing physical constraints. TheiVFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific computational fluid dynamics (CFD) model. The numerical evaluations showed that theiVFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3% and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrainediVFM and CFD. The capability of physics-constrainediVFM was finally tested within vivocolor Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrainediVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

An Angle Independent Depth Aware Fusion Beamforming Approach for Ultrafast Ultrasound Flow Imaging. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:3399-3402. [PMID: 34891969 DOI: 10.1109/embc46164.2021.9630742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In the case of vector flow imaging systems, the most employed flow estimation techniques are the directional beamforming based cross correlation and the triangulation-based autocorrelation. However, the directional beamforming-based techniques require an additional angle estimator and are not reliable if the flow angle is not constant throughout the region of interest. On the other hand, estimates with triangulation-based techniques are prone to large bias and variance at low imaging depths due to limited angle for left and right apertures. In view of this, a novel angle independent depth aware fusion beamforming approach is proposed and evaluated in this paper. The hypothesis behind the proposed approach is that the peripheral flows are transverse in nature, where directional beamforming can be employed without the need of an angle estimator and the deeper flows being non-transverse and directional, triangulation-based vector flow imaging can be employed. In the simulation study, an overall 67.62% and 74.71% reduction in magnitude bias along with a slight reduction in the standard deviation are observed with the proposed fusion beamforming approach when compared to triangulation-based beamforming and directional beamforming, respectively, when implemented individually. The efficacy of the proposed approach is demonstrated with in-vivo experiments.

Real-Time High Frame Rate Color Flow Mapping System

Plane wave (PW) transmission (TX) can be profitably used to improve the performance of color flow mapping (CFM) systems by increasing the autocorrelation ensemble length (EL) and/or the frame rate (FR). Although high-end scanners tend to include imaging schemes using PW TX and parallel receive beams, high frame rate (HFR) CFM has been so far experimentally implemented mostly through research platforms that transmit PWs and beamform/process the received channel data off-line. In this article, full real-time implementation of PW CFM with continuous-time clutter filtering and extended FR/EL is reported. The field-programmable gate arrays (FPGAs) and digital signal processors (DSPs) onboard the ULA-OP 256 research scanner were programmed to perform high-speed parallel beamforming and autocorrelation-based CFM processing, respectively. Different strategies were tested, in which the TX of PWs for CFM is either continuous or interleaved with the TX of packets of B-mode pulses. A fourth-order Chebyshev continuous-time high-pass filter with programmable cutoff frequency was implemented and its clutter rejection performance was positively compared with that obtained when operating on packet data. CFM FRs up to 575 were obtained. The possibility of programming the autocorrelation EL up to 64 permitted to detect flow with high sensitivity and accuracy (average relative errors down to 0.4% ± 8.4%). In vivo HFR movies are presented, showing the dynamics of flow in the common carotid artery, which highlight the presence of secondary flow components.

Dealiasing High-Frame-Rate Color Doppler Using Dual-Wavelength Processing

Doppler ultrasound is the premier modality to analyze blood flow dynamics in clinical practice. With conventional systems, Doppler can either provide a time-resolved quantification of the flow dynamics in sample volumes (spectral Doppler) or an average Doppler velocity/power [color flow imaging (CFI)] in a wide field of view (FOV) but with a limited frame rate. The recent development of ultrafast parallel systems made it possible to evaluate simultaneously color, power, and spectral Doppler in a wide FOV and at high-frame rates but at the expense of signal-to-noise ratio (SNR). However, like conventional Doppler, ultrafast Doppler is subject to aliasing for large velocities and/or large depths. In a recent study, staggered multi-pulse repetition frequency (PRF) sequences were investigated to dealias color-Doppler images. In this work, we exploit the broadband nature of pulse-echo ultrasound and propose a dual-wavelength approach for CFI dealiasing with a constant PRF. We tested the dual-wavelength bandpass processing, in silico, in laminar flow phantom and validated it in vivo in human carotid arteries ( n = 25 ). The in silico results showed that the Nyquist velocity could be extended up to four times the theoretical limit. In vivo, dealiased CFI were highly consistent with unfolded Spectral Doppler ( r²=0.83 , y=1.1x+0.1 , N=25 ) and provided consistent vector flow images. Our results demonstrate that dual-wavelength processing is an efficient method for high-velocity CFI.

Virtual Real-Time for High PRF Multiline Vector Doppler on ULA-OP 256

The recent development of high-frame-rate (HFR) imaging/Doppler methods based on the transmission of plane or diverging waves has proposed new challenges to echographic data management and display. Due to the huge amount of data that need to be processed at very high speed, the pulse repetition frequency (PRF) is typically limited to hundreds hertz or few kilohertz. In Doppler applications, a PRF limitation may result unacceptable since it inherently translates to a corresponding limitation in the maximum detectable velocity. In this article, the ULA-OP 256 implementation of a novel ultrasound modality, called virtual real-time (VRT), is described. First, for a given HFR RT modality, the scanner displays the processed results while saving channel data into an internal buffer. Then, ULA-OP 256 switches to VRT mode, according to which the raw data stored in the buffer are immediately reprocessed by the same hardware used in RT. In the two phases, the ULA-OP 256 calculation power can be differently distributed to increase the acquisition frame rate or the quality of processing results. VRT was here used to extend the PRF limit in a multiline vector Doppler (MLVD) application. In RT, the PRF was maximized at the expense of the display quality; in VRT, data were reprocessed at a lower rate in a high-quality display format, which provides more detailed flow information. Experiments are reported in which the MLVD technique is shown capable of working at 16-kHz PRF, so that flow jet velocities higher up to 3 m/s can be detected.

Characterization of Vortex Flow in a Mouse Model of Ventricular Dyssynchrony by Plane-Wave Ultrasound Using Hexplex Processing

The rodent heart is frequently used to study human cardiovascular disease (CVD). Although advanced cardiovascular ultrasound imaging methods are available for human clinical practice, application of these techniques to small animals remains limited due to the temporal and spatial-resolution demands. Here, an ultrasound vector-flow workflow is demonstrated that enables visualization and quantification of the complex hemodynamics within the mouse heart. Wild type (WT) and fibroblast growth factor homologous factor 2 (FHF2)-deficient mice (Fhf2 ^KO/Y ), which present with hyperthermia-induced ECG abnormalities highly reminiscent of Brugada syndrome, were used as a mouse model of human CVD. An 18-MHz linear array was used to acquire high-speed (30 kHz), plane-wave data of the left ventricle (LV) while increasing core body temperature up to 41.5 °C. Hexplex (i.e., six output) processing of the raw data sets produced the output of vector-flow estimates (magnitude and phase); B-mode and color-Doppler images; Doppler spectrograms; and local time histories of vorticity and pericardium motion. Fhf2 ^WT/Y mice had repeatable beat-to-beat cardiac function, including vortex formation during diastole, at all temperatures. In contrast, Fhf2 ^KO/Y mice displayed dyssynchronous contractile motion that disrupted normal inflow vortex formation and impaired LV filling as temperature rose. The hexplex processing approach demonstrates the ability to visualize and quantify the interplay between hemodynamic and mechanical function in a mouse model of human CVD.

A Deep Learning Approach to Resolve Aliasing Artifacts in Ultrasound Color Flow Imaging

Despite being used clinically as a noninvasive flow visualization tool, color flow imaging (CFI) is known to be prone to aliasing artifacts that arise due to fast blood flow beyond the detectable limit. From a visualization standpoint, these aliasing artifacts obscure proper interpretation of flow patterns in the image view. Current solutions for resolving aliasing artifacts are typically not robust against issues such as double aliasing. In this article, we present a new dealiasing technique based on deep learning principles to resolve CFI aliasing artifacts that arise from single- and double-aliasing scenarios. It works by first using two convolutional neural networks (CNNs) to identify and segment CFI pixel positions with aliasing artifacts, and then it performs phase unwrapping at these aliased pixel positions. The CNN for aliasing identification was devised as a U-net architecture, and it was trained with in vivo CFI frames acquired from the femoral bifurcation that had known presence of single- and double-aliasing artifacts. Results show that the segmentation of aliased CFI pixels was achieved successfully with intersection over union approaching 90%. After resolving these artifacts, the dealiased CFI frames consistently rendered the femoral bifurcation's triphasic flow dynamics over a cardiac cycle. For dealiased CFI pixels, their root-mean-squared difference was 2.51% or less compared with manual dealiasing. Overall, the proposed dealiasing framework can extend the maximum flow detection limit by fivefold, thereby improving CFI's flow visualization performance.

Flow Complexity Estimation in Dysfunctional Arteriovenous Dialysis Fistulas using Vector Flow Imaging

Non-invasive assessment is preferred for monitoring arteriovenous dialysis fistulas (AVFs). Vector concentration assesses flow complexity, which may correlate with stenosis severity. We determined whether vector concentration could assess stenosis severity in dysfunctional AVFs. Vector concentration was estimated in four stenotic phantoms at different pulse repetition frequencies. Spectral Doppler peak velocity and vector concentration were measured in 12 patients with dysfunctional AVFs. Additionally, 5 patients underwent digital subtraction angiography (DSA). In phantoms, vector concentration exhibited an inverse relationship with stenosis severity and was less affected by aliasing in severe stenoses. In nine stenoses of 5 patients undergoing DSA, vector concentration correlated strongly with stenosis severity (first stenosis: r = -0.73, p = 0.04; other stenoses; r = -0.69, p = 0.02) and mid-stenotic diameter (first stenosis: r = 0.87, p = 0.006; other stenoses: r = 0.70, p = 0.02) as opposed to peak velocities (p > 0.05). Vector concentration is less affected by aliasing in severe stenoses and correlates with DSA in patients with dysfunctional AVF.

4-D Echo-Particle Image Velocimetry in a Left Ventricular Phantom

Left ventricular (LV) blood flow is an inherently complex time-varying 3-D phenomenon, where 2-D quantification often ignores the effect of out-of-plane motion. In this study, we describe high frame rate 4-D echocardiographic particle image velocimetry (echo-PIV) using a prototype matrix transesophageal transducer and a dynamic LV phantom for testing the accuracy of echo-PIV in the presence of complex flow patterns. Optical time-resolved tomographic PIV (tomo-PIV) was used as a reference standard for comparison. Echo-PIV and tomo-PIV agreed on the general profile of the LV flow patterns, but echo-PIV smoothed out the smaller flow structures. Echo-PIV also underestimated the flow rates at greater imaging depths, where the PIV kernel size and transducer point spread function were large relative to the velocity gradients. We demonstrate that 4-D echo-PIV could be performed in just four heart cycles, which would require only a short breath-hold, providing promising results. However, methods for resolving high velocity gradients in regions of poor spatial resolution are required before clinical translation.

Imaging Heart Dynamics With Ultrafast Cascaded-Wave Ultrasound

The heart is an organ with highly dynamic complexity, including cyclic fast electrical activation, muscle kinematics, and blood dynamics. Although ultrafast cardiac imaging techniques based on pulsed-wave ultrasound (PUS) have rapidly emerged to permit mapping of heart dynamics, they suffer from limited sonographic signal-to-noise ratio (SNR) and penetration due to insufficient energy delivery and inevitable attenuation through the chest wall. We hereby propose ultrafast cascaded-wave ultrasound (uCUS) imaging to depict heart dynamics in higher SNR and larger penetration than conventional ultrafast PUS. To solve the known tradeoff between the length of transmitted ultrasound signals and spatial resolution while achieving ultrafast frame rates (>1000 Hz), we develop a cascaded synthetic aperture (CaSA) imaging method. In CaSA, an array probe is divided into subapertures; each subaperture transmits a train of diverging waves. These diverging waves are weighted in both the aperture (i.e., spatial) and range (i.e., temporal) directions with a coding matrix containing only +1 and -1 polarity coefficients. A corresponding spatiotemporal decoding matrix is designed to recover backscattered signals. The decoded signals are thereafter beamformed and coherently compounded to obtain one high-SNR beamformed image frame. For CaSA with M subapertures and N cascaded diverging waves, sonographic SNR is increased by 10× log ₁₀ (N ×M) (dB) compared with conventional synthetic aperture (SA) imaging. The proposed uCUS with CaSA was evaluated with conventional SA and Hadamard-encoded SA (H-SA) methods in a calibration phantom for B-mode image quality and an in vivo human heart in a transthoracic setting for the quality assessment of anatomical, myocardial motion, and chamber blood power Doppler images. Our results demonstrated that the proposed uCUS with CaSA (4 subapertures, 32 cascaded waves) improved SNR (+20.46 dB versus SA, +14.83 dB versus H-SA) and contrast ratio (+8.44 dB versus SA, +7.81 dB versus H-SA) with comparable spatial resolutions to and at the same frame rates as benchmarks.

Ultrasonic Vascular Vector Flow Mapping for 2-D Flow Estimation

A vascular vector flow mapping (VFM) method visualizes 2-D cardiac flow dynamics by estimating the radial component of flow from the Doppler velocities and wall motion velocities using the mass conservation equation. Although VFM provides 2-D flow, the algorithm is applicable only to bounded regions. Here, a modified VFM algorithm, vascular VFM, is proposed so that the velocities are estimated regardless of the flow geometry. To validate the algorithm, a phantom mimicking a carotid artery was fabricated and VFM velocities were compared with optical particle image velocimetry (PIV) data acquired in the same imaged plane. The validation results indicate that given optimal beam angle condition, VFM velocitiy is fairly accurate, where the correlation coefficient R between VFM and PIV velocities is 0.95. The standard deviation of the total VFM error, normalized by the maximum velocity, ranged from 8.1% to 16.3%, whereas the standard deviation of the measured input errors ranged from 8.9% to 12.7% for color flow mapping and from 4.5% to 5.9% for subbeam calculation. These results indicate that vascular VFM is reliable as its accuracy is comparable to that of conventional Doppler-flow images.

4D simultaneous tissue and blood flow Doppler imaging: revisiting cardiac Doppler index with single heart beat 4D ultrafast echocardiography

The goal of this study was to demonstrate the feasibility of semi-automatic evaluation of cardiac Doppler indices in a single heartbeat in human hearts by performing 4D ultrafast echocardiography with a dedicated sequence of 4D simultaneous tissue and blood flow Doppler imaging. 4D echocardiography has the potential to improve the quantification of major cardiac indices by providing more reproducible and less user dependent measurements such as the quantification of left ventricle (LV) volume. The evaluation of Doppler indices, however, did not benefit yet from 4D echocardiography because of limited volume rates achieved in conventional volumetric color Doppler imaging but also because spectral Doppler estimation is still restricted to a single location. High volume rate (5200 volume s^-1) transthoracic simultaneous tissue and blood flow Doppler acquisitions of three human LV were performed using a 4D ultrafast echocardiography scanner prototype during a single heartbeat. 4D color flow, 4D tissue Doppler cineloops and spectral Doppler at each voxel were computed. LV outflow tract, mitral inflow and basal inferoseptal locations were automatically detected. Doppler indices were derived at these locations and were compared against clinical 2D echocardiography. Blood flow Doppler indices E (early filling), A (atrial filling), E/A ratio, S (systolic ejection) and cardiac output were assessed on the three volunteers. Simultaneous tissue Doppler indices e' (mitral annular velocity peak), a' (late velocity peak), e'/a' ratio, s' (systolic annular velocity peak), E/e' ratio were also estimated. Standard deviations on three independent acquisitions were averaged over the indices and was found to be inferior to 4% and 8.5% for Doppler flow and tissue Doppler indices, respectively. Comparison against clinical 2D echocardiography gave a p  value larger than 0.05 in average indicating no significant differences. 4D ultrafast echocardiography can quantify the major cardiac Doppler indices in a single heart beat acquisition.

Live Ultrasound Color-Encoded Speckle Imaging Platform for Real-Time Complex Flow Visualization In Vivo

Complex flow patterns are prevalent in the vasculature, but they are difficult to image noninvasively in real time. This paper presents the first real-time scanning platform for a high-frame-rate ultrasound technique called color-encoded speckle imaging (CESI) and its use in visualizing arterial flow dynamics in vivo. CESI works by simultaneously rendering flow speckles and color-coded flow velocity estimates on a time-resolved basis. Its live implementation was achieved by integrating a 192-channel programmable ultrasound front-end module, a 4.8-GB/s capacity data streaming link, and a series of computing kernels implemented on the graphical processing unit (GPU) for beamforming and Doppler processing. A slow-motion replay mode was also included to offer coherent visualization of CESI frames acquired at high frame rate [3000 frames per second (fps) in our experiments]. The live CESI scanning platform was found to be effective in facilitating real-time image guidance (at least 20 fps for live video display with 55-fps GPU processing throughout). In vivo pilot trials also showed that live CESI, when running in replay mode, can temporally resolve triphasic flow at the brachial bifurcation and can reveal flow dynamics in the brachial vein during a fist-clenching maneuver. Overall, live CESI has potential for use in routine investigations in vivo that seek to identify complex flow dynamics in real time and relate these dynamics to vascular physiology.

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

The paper describes a new pulse sequence design and estimation approach, which can increase the maximum detectable velocity in synthetic aperture (SA) velocity imaging. In SA N spherical or plane waves are emitted, and the sequence is repeated continuously. The N emissions are combined to form a High Resolution Image (HRI). Correlation of HRIs is employed to estimate velocity, and the combination of N emissions lowers the effective pulse repetition frequency by N. Inter-leaving emission sequences can increase the effective pulse repetition frequency to the actual pulse repetition frequency, thereby increasing the maximum detectable velocity by a factor of N. This makes it possible to use longer sequences with better focusing properties. It can also increase the possible interrogation depth for vessels with large velocities. A new cross-correlation vector flow estimator is also presented, which can further increase the maximum detectable velocity by a factor of three. It is based on Transverse Oscillation (TO), a pre-processing stage, and cross-correlation of signals beamformed orthogonal to the ultrasound propagation direction. The estimator is self-calibrating without estimating the lateral TO wavelength. This paper develops the theory behind the two methods. The performance is demonstrated in the accompanying paper for convex and phased array probes connected to the SARUS scanner for parabolic flow for both conventional and SA imaging.

A Dual Tissue-Doppler Optical-Flow Method for Speckle Tracking Echocardiography at High Frame Rate

A coupled computational method for recovering tissue velocity vector fields from high-frame-rate echocardiography is described. Conventional transthoracic echocardiography provides limited temporal resolution, which may prevent accurate estimation of the 2-D myocardial velocity field dynamics. High-frame-rate compound echocardiography using diverging waves with integrated motion compensation has been shown to provide concurrent high-resolution B-mode and tissue Doppler imaging (TDI). In this paper, we propose a regularized least-squares method to provide accurate myocardial velocities at high frame rates. The velocity vector field was formulated as the minimizer of a cost function that is a weighted sum of: 1) the ${\ell }^{{2}}$ -norm of the material derivative of the B-mode images (optical flow); 2) the ${\ell }^{{2}}$ -norm of the tissue-Doppler residuals; and 3) a quadratic regularizer that imposes spatial smoothness and well-posedness. A finite difference discretization of the continuous problem was adopted, leading to a sparse linear system. The proposed framework was validated in vitro on a rotating disk with speeds up to 20 cm/s, and compared with speckle tracking echocardiography (STE) by block matching. It was also validated in vivo against TDI and STE in a cross-validation strategy involving parasternal long axis and apical three-chamber views. The proposed method based on the combination of optical flow and tissue Doppler led to more accurate time-resolved velocity vector fields.

CColor and Vector Flow Imaging in Parallel Ultrasound with Sub-Nyquist Sampling

RF acquisition with a high-performance multi-chan-nel ultrasound system generates massive datasets in short periods of time, especially in "ultrafast" ultrasound when digital receive beamforming is required. Sampling at a rate four times the carrier frequency is the standard procedure since this rule complies with the Nyquist-Shannon sampling theorem and simplifies quadrature sampling. Bandpass sampling (or undersampling) outputs a band-pass signal at a rate lower than the maximal frequency without harmful aliasing. Advantages over Nyquist sampling are reduced storage volumes and data workflow, and simplified digital signal processing tasks. We used RF undersampling in color flow imag-ing (CFI) and vector flow imaging (VFI) to decrease data volume significantly (factor of 3 to 13 in our configurations). CFI and VFI with Nyquist and sub-Nyquist samplings were compared in vitro and in vivo. The estimate errors due to undersampling were small or marginal, which illustrates that Doppler and vector Doppler im-ages can be correctly computed with a drastically reduced amount of RF samples. Undersampling can be a method of choice in CFI and VFI to avoid information overload and reduce data transfer and storage.

Vector Flow Visualization of Urinary Flow Dynamics in a Bladder Outlet Obstruction Model

Voiding dysfunction that results from bladder outlet (BO) obstruction is known to alter significantly the dynamics of urine passage through the urinary tract. To non-invasively image this phenomenon on a time-resolved basis, we pursued the first application of a recently developed flow visualization technique called vector projectile imaging (VPI) that can track the spatiotemporal dynamics of flow vector fields at a frame rate of 10,000 fps (based on plane wave excitation and least-squares Doppler vector estimation principles). For this investigation, we designed a new anthropomorphic urethral tract phantom to reconstruct urinary flow dynamics under controlled conditions (300 mm H₂O inlet pressure and atmospheric outlet pressure). Both a normal model and a diseased model with BO obstruction were developed for experimentation. VPI cine loops were derived from these urinary flow phantoms. Results show that VPI is capable of depicting differences in the flow dynamics of normal and diseased urinary tracts. In the case with BO obstruction, VPI depicted the presence of BO flow jet and vortices in the prostatic urethra. The corresponding spatial-maximum flow velocity magnitude was estimated to be 2.43 m/s, and it is significantly faster than that for the normal model (1.52 m/s) and is in line with values derived from computational fluid dynamics simulations. Overall, this investigation demonstrates the feasibility of using vector flow visualization techniques to non-invasively examine internal flow characteristics related to voiding dysfunction in the urethral tract.

Intracardiac Vortex Dynamics by High-Frame-Rate Doppler Vortography-In Vivo Comparison With Vector Flow Mapping and 4-D Flow MRI

Recent studies have suggested that intracardiac vortex flow imaging could be of clinical interest to early diagnose the diastolic heart function. Doppler vortography has been introduced as a simple color Doppler method to detect and quantify intraventricular vortices. This method is able to locate a vortex core based on the recognition of an antisymmetric pattern in the Doppler velocity field. Because the heart is a fast-moving organ, high frame rates are needed to decipher the whole blood vortex dynamics during diastole. In this paper, we adapted the vortography method to high-frame-rate echocardiography using circular waves. Time-resolved Doppler vortography was first validated in vitro in an ideal forced vortex. We observed a strong correlation between the core vorticity determined by high-frame-rate vortography and the ground-truth vorticity. Vortography was also tested in vivo in ten healthy volunteers using high-frame-rate duplex ultrasonography. The main vortex that forms during left ventricular filling was tracked during two-three successive cardiac cycles, and its core vorticity was determined at a sampling rate up to 80 duplex images per heartbeat. Three echocardiographic apical views were evaluated. Vortography-derived vorticities were compared with those returned by the 2-D vector flow mapping approach. Comparison with 4-D flow magnetic resonance imaging was also performed in four of the ten volunteers. Strong intermethod agreements were observed when determining the peak vorticity during early filling. It is concluded that high-frame-rate Doppler vortography can accurately investigate the diastolic vortex dynamics.

Extension of Fourier-Based Techniques for Ultrafast Imaging in Ultrasound With Diverging Waves

Ultrafast ultrasound imaging has become an intensive area of research thanks to its capability in reaching high frame rates. In this paper, we propose a scheme that allows the extension of the current Fourier-based techniques derived for planar acquisition to the reconstruction of sectorial scan with wide angle using diverging waves. The flexibility of the proposed formulation was assessed through two different Fourier-based techniques. The performance of the derived approaches was evaluated in terms of resolution and contrast from both simulations and in vitro experiments. The comparisons of the current state-of-the-art method with the conventional delay-and-sum technique illustrated the potential of the derived methods for producing competitive results with lower computational complexity.

Ultrasound Vector Flow Imaging-Part I: Sequential Systems

This paper gives a review of the most important methods for blood velocity vector flow imaging (VFI) for conventional sequential data acquisition. This includes multibeam methods, speckle tracking, transverse oscillation, color flow mapping derived VFI, directional beamforming, and variants of these. The review covers both 2-D and 3-D velocity estimation and gives a historical perspective on the development along with a summary of various vector flow visualization algorithms. The current state of the art is explained along with an overview of clinical studies conducted and methods for presenting and using VFI. A number of examples of VFI images are presented, and the current limitations and potential solutions are discussed.

Least-Squares Multi-Angle Doppler Estimators for Plane-Wave Vector Flow Imaging

Designing robust Doppler vector estimation strategies for use in plane-wave imaging schemes based on unfocused transmissions is a topic that has yet to be studied in depth. One potential solution is to use a multi-angle Doppler estimation approach that computes flow vectors via least-squares fitting, but its performance has not been established. Here, we investigated the efficacy of multi-angle Doppler vector estimators by: 1) comparing its performance with respect to the classical dual-angle (cross-beam) Doppler vector estimator and 2) examining the working effects of multi-angle Doppler vector estimators on flow visualization quality in the context of dynamic flow path rendering. Implementing Doppler vector estimators that use different combinations of transmit (Tx) and receive (Rx) steering angles, our analysis has compared the classical dual-angle Doppler method, a 5-Tx version of dual-angle Doppler, and various multi-angle Doppler configurations based on 3 Tx and 5 Tx. Two angle spans (10°, 20°) were examined in forming the steering angles. In imaging scenarios with known flow profiles (rotating disk and straight-tube parabolic flow), the 3-Tx, 3-Rx and 5-Tx, 5-Rx multi-angle configurations produced vector estimates with smaller variability compared with the dual-angle method, and the estimation results were more consistent with the use of a 20° angle span. Flow vectors derived from multi-angle Doppler estimators were also found to be effective in rendering the expected flow paths in both rotating disk and straight-tube imaging scenarios, while the ones derived from the dual-angle estimator yielded flow paths that deviated from the expected course. These results serve to attest that using multi-angle least-squares Doppler vector estimators, flow visualization can be consistently achieved.

Spread-Spectrum Beamforming and Clutter Filtering for Plane-Wave Color Doppler Imaging

Plane-wave imaging is desirable for its ability to achieve high frame rates, allowing the capture of fast dynamic events and continuous Doppler data. In most implementations of plane-wave imaging, multiple low-resolution images from different plane wave tilt angles are compounded to form a single high-resolution image, thereby reducing the frame rate. Compounding improves the lateral beam profile in the high-resolution image, but it also acts as a low-pass filter in slow time that causes attenuation and aliasing of signals with high Doppler shifts. This paper introduces a spread-spectrum color Doppler imaging method that produces high-resolution images without the use of compounding, thereby eliminating the tradeoff between beam quality, maximum unaliased Doppler frequency, and frame rate. The method uses a long, random sequence of transmit angles rather than a linear sweep of plane wave directions. The random angle sequence randomizes the phase of off-focus (clutter) signals, thereby spreading the clutter power in the Doppler spectrum, while keeping the spectrum of the in-focus signal intact. The ensemble of randomly tilted low-resolution frames also acts as the Doppler ensemble, so it can be much longer than a conventional linear sweep, thereby improving beam formation while also making the slow-time Doppler sampling frequency equal to the pulse repetition frequency. Experiments performed using a carotid artery phantom with constant flow demonstrate that the spread-spectrum method more accurately measures the parabolic flow profile of the vessel and outperforms conventional plane-wave Doppler in both contrast resolution and estimation of high flow velocities. The spread-spectrum method is expected to be valuable for Doppler applications that require measurement of high velocities at high frame rates.

An Extended Least Squares Method for Aliasing-Resistant Vector Velocity Estimation

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit-receive setups. Furthermore, it is demonstrated that careful design of the transmit-receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At -5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers.