Ensemble tracking for 2D vector velocity measurement: Experimental and initial clinical results

Velocity vector comparison between vector flow imaging and computational fluid dynamics in the carotid bifurcation

It has been largely documented that local hemodynamic conditions, characterized by low and oscillating wall shear stresses, play a key role in the initiation and progression of vascular atherosclerotic lesions. Thus, investigation of the flow field in the carotid bifurcation can lead to early identification of vulnerable plaques. In this scenario, the development of novel non-invasive imaging tools that can be used in routine clinical practice to identify disturbed and recirculating blood flow becomes crucial. In this context, Vector Flow Imaging is becoming a relevant tool as it provides an angle independent assessment of blood flow velocity and multidimensional flow vector visualization. The purpose of the present study was to validate, in several locations of the carotid bifurcation, the high-frame rate vector flow imaging (HiFR-VFI) technique by comparing with computational fluid dynamic simulations (CFD). In all eight carotid bifurcations, HiFR-VFI accurately detected regions of laminar flow as well as recirculation and unsteady flow areas. An accurate and statistically significant agreement was observed between velocity vectors obtained by HiFR-VFI and those computed by CFD, both for vector magnitude (R = 0.85) and direction (R = 0.74). Our study demonstrated that HiFR-VFI is a valid technique for rapid and advanced visual representation of velocity field in large arteries. Thus, it has a great potential in research-based clinical practice for the identification of flow recirculation, low and oscillating velocity gradients near vessel wall. The use of HiFR-VFI may provide a great improvement in the investigation of the role of local hemodynamics in vascular pathologies, as well in the assessment of the effect of pharmacological treatments.

Measurement of flow velocity vectors in carotid artery using plane wave imaging with repeated transmit sequence

PURPOSE

Doppler-based methods are widely used for blood flow imaging in clinical settings. However, they inherently estimate the velocity component only in the axial direction. Therefore, various studies of angle-independent methods have been conducted. The multi-angle Doppler method is one such angle-independent method, in which the velocity vector is estimated using axial velocities obtained from multiple directions by steering an ultrasonic beam. Recently, plane wave imaging, which realizes a very high frame rate of several thousand frames per second, was applied to the multi-angle Doppler method. However, the maximum detectable velocity, i.e., the aliasing limit, was reduced depending on the number of steering angles. In the present study, the feasibility of a specific transmit sequence, namely, the repeated transmit sequence, was examined using the plane-wave multi-angle Doppler method.

METHOD

In the repeated transmit sequence, plane waves were emitted to the same direction twice, after which the steering angle was changed. By repeating the same procedure, a pair of beamformed radio-frequency (RF) signals could be obtained under each beam steering angle. By applying the autocorrelation method to each pair of RF signals, the time interval between the RF signals could be kept as the pulse repetition interval (PRI). The feasibility of such a transmit sequence was examined by numerical simulation and in vivo measurement of a human carotid artery.

RESULTS

The simulation results showed that the maximum steering angles of over 10 degrees were not feasible with the linear array used in the present study. The feasible maximum steering angle would depend on the element pitch of the probe relative to the ultrasonic wavelength. By limiting the maximum steering angles to 5 and 10 degrees, bias errors were 9.2% and 11.3%, respectively, and root mean squared errors were 21.5% and 16.9%, respectively. Also, flow velocity vectors in a human carotid artery could be visualized with the proposed method.

CONCLUSION

The multi-angle Doppler method was implemented in plane wave imaging with the repeated transmit sequence, and the proposed method was shown to be feasible through numerical simulation and in vivo measurement of a carotid artery.

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.

Efficient Two-Pass 3-D Speckle Tracking for Ultrasound Imaging

Speckle tracking based on block matching is the most common method for multi-dimensional motion estimation in ultrasound elasticity imaging. Extension of two-dimensional (2-D) methods to three dimensions (3-D) has been problematic because of the large computational load of 3-D tracking, as well as performance issues related to the low frame (volume) rates of 3-D images. To address both of these problems, we have developed an efficient two-pass tracking method suited to cardiac elasticity imaging. PatchMatch, originally developed for image editing, has been adapted for ultrasound to provide first-pass displacement estimates. Second-pass estimation uses conventional block matching within a much smaller search region. 3-D displacements are then obtained using correlation filtering previously shown to be effective against speckle decorrelation. Both simulated and in vivo canine cardiac results demonstrate that the proposed two-pass method reduces computational cost compared to conventional 3-D exhaustive search by a factor of 10. Moreover, it outperforms one-pass tracking by a factor of about 3 in terms of root-mean-square error relative to available ground-truth displacements.

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.

Performance study of a new time-delay estimation algorithm in ultrasonic echo signals and ultrasound elastography

Time-delay estimation has countless applications in ultrasound medical imaging. Previously, we proposed a new time-delay estimation algorithm, which was based on the summation of the sign function to compute the time-delay estimate (Shaswary et al., 2015). We reported that the proposed algorithm performs similar to normalized cross-correlation (NCC) and sum squared differences (SSD) algorithms, even though it was significantly more computationally efficient. In this paper, we study the performance of the proposed algorithm using statistical analysis and image quality analysis in ultrasound elastography imaging. Field II simulation software was used for generation of ultrasound radio frequency (RF) echo signals for statistical analysis, and a clinical ultrasound scanner (Sonix® RP scanner, Ultrasonix Medical Corp., Richmond, BC, Canada) was used to scan a commercial ultrasound elastography tissue-mimicking phantom for image quality analysis. The statistical analysis results confirmed that, in overall, the proposed algorithm has similar performance compared to NCC and SSD algorithms. The image quality analysis results indicated that the proposed algorithm produces strain images with marginally higher signal-to-noise and contrast-to-noise ratios compared to NCC and SSD algorithms.

Quantification of ultrasound correlation-based flow velocity mapping and edge velocity gradient measurement

This study investigated the use of ultrasound speckle decorrelation- and correlation-based lateral speckle-tracking methods for transverse and longitudinal blood velocity profile measurement, respectively. By studying the blood velocity gradient at the vessel wall, vascular wall shear stress, which is important in vascular physiology as well as the pathophysiologic mechanisms of vascular diseases, can be obtained. Decorrelation-based blood velocity profile measurement transverse to the flow direction is a novel approach, which provides advantages for vascular wall shear stress measurement over longitudinal blood velocity measurement methods. Blood flow velocity profiles are obtained from measurements of frame-to-frame decorrelation. In this research, both decorrelation and lateral speckle-tracking flow estimation methods were compared with Poiseuille theory over physiologic flows ranging from 50 to 1000 mm/s. The decorrelation flow velocity measurement method demonstrated more accurate prediction of the flow velocity gradient at the wall edge than the correlation-based lateral speckle-tracking method. The novelty of this study is that speckle decorrelation-based flow velocity measurements determine the blood velocity across a vessel. In addition, speckle decorrelation-based flow velocity measurements have higher axial spatial resolution than Doppler ultrasound measurements to enable more accurate measurement of blood velocity near a vessel wall and determine the physiologically important wall shear.

Volumetric Flow Measurement Using an Implantable CMUT Array

This paper describes volumetric-flow velocity measurement using an implantable capacitive micromachined ultrasonic transducer (CMUT) array. The array is comprised of multiple-concentric CMUT rings for ultrasound transmission and an outmost annular CMUT array for ultrasound reception. Microelectromechanical-system (MEMS) fabrication technology allows reception CMUT on this flowmeter to be implemented with a different membrane thickness and gap height than that of transmission CMUTs, optimizing the performance of these two different kinds of devices. The silicon substrate of this 2-mm-diameter CMUT ring array was bulk micromachined to approximately 80 to 100 μm thick, minimizing tissue disruption. The blood-flow velocity was detected using pulse ultrasound Doppler by comparing the demodulated echo ultrasound with the incident ultrasound. The demodulated ultrasound signal was sampled by a pulse delayed in time domain from the transmitted burst, which corresponds to detecting the signal at a specific distance. The flow tube/vessel diameter was detected through the time-flight delay difference from near and far wall reflections, which was measured from the ultrasound pulse echo. The angle between the ultrasound beam and the flow was found by using the cross-correlation from consecutive ultrasound echoes. Artificial blood flowing through three different polymer tubes was experimented with, while keeping the same volumetric flow rate. The discrepancy in flow measurement results between this CMUT meter and a calibrated laser Doppler flowmeter is less than 5%.

Two-dimensional flow imaging in the carotid bifurcation using a combined speckle tracking and phase-shift estimator: a study based on ultrasound simulations and in vivo analysis

A two-dimensional (2-D) blood velocity estimator is presented combining speckle tracking (ST) and phase-shift estimation (PE) to measure lateral (vx) and axial (vz) velocities respectively. Estimator properties were assessed in a carotid bifurcation using ultrasound simulations based on computational fluid dynamics, allowing validation toward a ground truth. Simulation results were supported with in vivo data of a healthy carotid. ST and PE estimates were combined as: (1) vx from 2D-ST and vz from PE, (2) vx from 2D-ST and vz from PE with aliasing correction based on ST and (3) vz from PE and only lateral ST for vx. Regression analysis showed a 35% to 77% decrease in standard deviation for vz for PE compared with ST. Aliasing correction based on ST improved results but also introduced spurious artifacts. A marginal decrease in performance was observed when only tracking laterally. Further work will focus on in vivo trials in patients with carotid plaques.

3-D phantom and in vivo cardiac speckle tracking using a matrix array and raw echo data

Cardiac motion has been tracked using various methods, which vary in their invasiveness and dimensionality. One such noninvasive modality for cardiac motion tracking is ultrasound. Three-dimensional ultrasound motion tracking has been demonstrated using detected data at low volume rates. However, the effects of volume rate, kernel size, and data type (raw and detected) have not been sufficiently explored. First comparisons are made within the stated variables for 3-D speckle tracking. Volumetric data were obtained in a raw, baseband format using a matrix array attached to a high parallel receive beam count scanner. The scanner was used to acquire phantom and human in vivo cardiac volumetric data at 1000-Hz volume rates. Motion was tracked using phase-sensitive normalized cross-correlation. Subsample estimation in the lateral and elevational dimensions used the grid-slopes algorithm. The effects of frame rate, kernel size, and data type on 3-D tracking are shown. In general, the results show improvement of motion estimates at volume rates up to 200 Hz, above which they become stable. However, peak and pixel hopping continue to decrease at volume rates higher than 200 Hz. The tracking method and data show, qualitatively, good temporal and spatial stability (for independent kernels) at high volume rates.

Two-dimensional blood velocity estimation with ultrasound: speckle tracking versus crossed-beam vector Doppler based on flow simulations in a carotid bifurcation model

Detailed imaging of complex blood flow may improve early diagnosis of cardiovascular disease. In clinical practice, non-invasive flow imaging has been limited to one-dimensional Doppler techniques. Searching for multi-dimensional estimators, research has given attention to speckle tracking (ST) and vector Doppler (VD). However, these techniques have yet to be validated for complex flow patterns as may arise in diseased arteries. In this work, the properties of ST and crossed-beam VD are compared with a ground truth for clinically relevant flow using an ultrasonic simulation environment coupled with the output from computational fluid dynamics (CFD). The statistical properties (n = 80) of ST and VD were first evaluated for stationary flow in a tube for varying vessel positions and angles, and for varying noise levels. The parameter study demonstrated VD to be a more robust axial velocity estimator, and similar results were obtained overall for the lateral velocity component. As an example, the relative standard deviation was 15% and 8% for ST compared with 3% and 10% for VD, for the axial and lateral velocity component, respectively. Further, performance was evaluated for pulsatile flow conditions in a stenosed carotid bifurcation model. A linear regression analysis showed that both methods overall had a good agreement to the CFD reference, however VD suffered from more spurious artifacts and was severely hampered by aliasing in parts of the cardiac cycle. ST was less accurate in estimating the axial component, but prevailed in estimating velocities well beyond the Nyquist range. Based on our simulations, both methods may be used to image complex flow behavior in the carotid bifurcation, however, considering also the scanning limitations of VD, ST may provide a more consistent and practical approach. Future work will entail in vitro and in vivo validation of these results.

Mean volume flow estimation in pulsatile flow conditions

To verify a previously reported three-dimensional (3D) ultrasound method for the measurement of time-average volumetric blood flow, experiments were performed under pulsatile flow conditions, including in vivo investigations, and results were compared with accepted, but invasive, "gold standard" techniques. Results showed that volume averaging results in the correct time-average volume flow without the need for cardiac gating. Unlike other currently employed methods, this method is independent of Doppler angle, flow profile and vessel geometry. A GE Logiq 9 ultrasound system (GE Medical Systems, Milwaukee, WI, USA) and a four-dimensional (4D) 10L and 4D 16L probe were used to acquire 3D Doppler measurements in the femoral and carotid arteries of four canines. Two invasive blood flow meters were used (electromagnetic for one canine and ultrasonic for three canines) as the gold standard techniques. Transcutaneous color flow measurements were taken to obtain 3D volume data sets encompassing the vessel. Constant depth planes were used to integrate color flow pixels encompassing the entire vessel cross-section. Power Doppler data were used to correct for partial volume effects. An artificial stenosis was induced to vary the ambient volume flow. Unrestricted, bidirectional flow was measured as high as 400 mL min(-1). Several flow restrictions were imposed that decreased the measured volumetric flow rate to as low as 30 mL min(-1). All flow rate estimates (n=38) were plotted against results obtained via the gold standards. A general line fit resulted in y = 0.926 x - 0.87 (r(2) = 0.95), which corresponds to a 0.6% flow offset relative to the average flow rate of 142 mL min(-1), as well as a 7.4% error in the linearity of our estimate. A secondary curve fit was performed that required the slope to be 1 and the intercept to be 0, which yielded an r(2)-value of 0.93. The percent-error distribution was computed and fitted to a Gaussian function, which yielded mu=-7.04% and sigma=9.52%. Theoretical studies were conducted to estimate the expected error in our volume flow measurements as a function of number of samples (N) used for averaging pulsatile waveforms. Experiments showed the same 1/N dependence as theory. Direct comparisons of volume flow rate estimates using volumetric color Doppler and independent standards showed that our method has good accuracy under in vivo pulsatile blood flow conditions.

Haemodynamics and blood flow measured using ultrasound imaging

Visualization of, and measurements related to, haemodynamic phenomena in arteries may be made using ultrasound systems. Most ultrasound technology relies on simple measurements of blood velocity taken from a single site, such as the peak systolic velocity for assessment of the degree of lumen reduction caused by an arterial stenosis. Real-time two-dimensional (2D) flow field visualization is possible using several methods, such as colour flow, blood flow imaging, and echo particle image velocimetry; these have applications in the examination of the flow field in diseased arteries and in heart chambers. Three-dimensional (3D) and four-dimensional ultrasound systems have been described. These have been used to provide 2D velocity profile data for the estimation of volumetric flow. However, they are limited for haemodynamic evaluation in that they provide only one component of the velocity. The provision of all seven components (three space, three velocity, and one time) is possible using image-guided modelling, in which 3D ultrasound is combined with computational fluid dynamics. This method also allows estimation of turbulence data and of relevant quantities such as the wall shear stress.

MUlti-Dimensional Spline-Based Estimator (MUSE) for motion estimation: algorithm development and initial results

Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multi-dimensional displacements/strain components from multi-dimensional data sets. We describe the mathematical formulation for two- and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 x 10(-4) samples in range and 2.2 x 10(-3) samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 x 10(-3) samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE is broadly applicable across imaging applications.

High frame-rate blood vector velocity imaging using plane waves: simulations and preliminary experiments

Conventional ultrasound methods for acquiring color images of blood velocity are limited by a relatively low frame-rate and are restricted to give velocity estimates along the ultrasound beam direction only. To circumvent these limitations, the method presented in this paper uses 3 techniques: 1) The ultrasound is not focused during the transmissions of the ultrasound signals; 2) A 13-bit Barker code is transmitted simultaneously from each transducer element; and 3) The 2-D vector velocity of the blood is estimated using 2-D cross-correlation. A parameter study was performed using the Field II program, and performance of the method was investigated when a virtual blood vessel was scanned by a linear array transducer. An improved parameter set for the method was identified from the parameter study, and a flow rig measurement was performed using the same improved setup as in the simulations. Finally, the common carotid artery of a healthy male was scanned with a scan sequence that satisfies the limits set by the Food and Drug Administration. Vector velocity images were obtained with a frame-rate of 100 Hz where 40 speckle images are used for each vector velocity image. It was found that the blood flow approximately followed the vessel wall, and that maximum velocity was approximately 1 m/s, which is a normal value for a healthy person. To further evaluate the method, the test person was scanned with magnetic resonance (MR) angiography. The volume flow derived from the MR scanning was compared with that from the ultrasound scanning. A deviation of 9% between the 2 volume flow estimates was found.

An improved spectral width Doppler method for estimating Doppler angles in flows with existence of velocity gradients

Doppler angle (i.e., beam-to-flow angle) is an important parameter for quantitative flow measurements. With known Doppler angles, volumetric flows can be obtained by the mean flow velocity times the cross-section area of the vessel. The differences or changes between prestenotic and poststenotic volumetric flows have been quantified as an indicator for assessing the clinical severity of the stenosis. Therefore, several research groups have dedicated themselves to developing user-independent methods to determine automatically the Doppler angle. Nevertheless, most of these methods were developed for narrow ultrasound beam measurements. For small vessels, where the beam width is a significant fraction of the diameter of the vessel, the effect of velocity gradients plays an important role and should not be ignored in the Doppler angle estimations. Accordingly, this paper is concerned with a method for improving the estimation of Doppler angles from spectral width Doppler (SWD) method, but correcting for velocity-gradient broadening that may arise when the beam has a nonzero width. In our method, Doppler angles were firstly calculated by SWD and then were corrected by an artificial neural network (ANN) method to neutralize the contribution of velocity gradient broadening (VGB). This SWD and ANN conjoint method has been successfully applied to estimate Doppler angles from 50 degrees to 80 degrees for constant flows in 10 mm, 4 mm and 1 mm diameter tubes, whose mean flow velocities were 15.3, 19.9 and 25.5 cm/s, respectively, and the achieved mean absolute errors of the estimated Doppler angles were 1.46 degrees , 1.01 degrees and 1.3 degrees.

Ultrasound imaging

Ultrasound imaging is now in very widespread clinical use. The most important underpinning technologies include transducers, beam forming, pulse compression, tissue harmonic imaging, contrast agents, techniques for measuring blood flow and tissue motion, and three-dimensional imaging. Specialized and emerging technologies include tissue characterization and image segmentation, microscanning and intravascular scanning, elasticity imaging, reflex transmission imaging, computed tomography, Doppler tomography, photoacoustics and thermoacoustics. Phantoms and quality assurance are necessary to maintain imaging performance. Contemporary ultrasonic imaging procedures seem to be safe but studies of bioeffects are continuing. It is concluded that advances in ultrasonic imaging have primarily been pushed by the application of physics and innovations in engineering, rather than being pulled by the identification of specific clinical objectives in need of scientific solutions. Moreover, the opportunities for innovation to continue into the future are both challenging and exciting.

Vector-velocity estimation in swept-scan using a K-space approach

The swept-scan technique (i.e., continuously moving a single-crystal transducer during pulse-echo data acquisition) is used in high-frequency, ultrasonic flow imaging. Relative to the conventional step-scan technique, swept scanning improves the rate of data acquisition and enables near-real-time, high-frequency color flow mapping. However, the continuous transducer movement may have non-negligible effects on accuracy of velocity estimation. This paper introduces a spatial frequency domain (i.e., k-space) approach that quantifies the effects of both lateral and axial motions in a swept scan. It is shown that the k-space representation is equivalent to a Doppler-radio frequency (RF) frequency domain representation, and that transducer movement in the swept-scan technique results in a change in Doppler bandwidth. In addition, a vector velocity estimator is developed based on the proposed k-space approach. Both simulations and flow-phantom experiments were performed to evaluate the performance of the proposed vector velocity estimator. A 45-MHz transducer was scanned at 20 mm/s. The Doppler angle ranged from 29 degrees to 90 degrees, and the flow velocities ranged from 15 to 30 mm/s. The results show that the proposed k-space vector velocity estimator exhibited a mean error of 2.6 degrees for flow-direction estimation, with the standard deviation ranging from 2.2 degrees to 8.2 degrees. In comparison, for the conventional spectral-broadening-based vector velocity estimator ignoring the swept-scan effect, the mean error became 15 degrees and the standard deviations were from 2.7 degrees to 6.6 degrees.

A spline-based algorithm for continuous time-delay estimation using sampled data

Time delay estimation (TDE) lies at the heart of signal processing algorithms in a broad range of application areas, including communications, coherent imaging, speech processing, and acoustics. In medical ultrasound for example, TDE is used in blood flow estimation, tissue motion measurement, tissue elasticity estimation, phase aberration correction, and a number of other algorithms. Because of its central significance, TDE accuracy, precision, and computational cost are of critical importance. Furthermore, because TDE is typically performed on sampled signals-and delay estimates are usually desired over a continuous domain-time delay estimator performance should be considered in conjunction with associated interpolation. In this paper we present a new time-delay estimator that directly determines continuous time-delay estimates from sampled data. The technique forms a spline-based, piecewise continuous representation of the reference signal then solves for the minimum of the sum squared error between the reference and the delayed signals to determine their relative time delay. Computer simulation results clearly show that the proposed algorithm significantly outperforms other algorithms in terms of jitter and bias over a broad range of conditions. We also describe a modified version of the algorithm that includes companding with only a minor increase in computational cost.

Effects of swept scanning on velocity estimation

The swept-scan technique adopted in high-frequency ultrasound involves mechanically scanning a single-element transducer to acquire image data. Unlike conventional step scanning, where the image data are acquired at discrete positions, the swept-scan technique acquires the image data while the transducer is continuously moving. Such a scanning method is particularly advantageous for Doppler flow estimation because its frame rate is higher than that for the step-scan technique. However, the effects of the transducer motion on the accuracy of velocity estimation have not been studied comprehensively. This study employed a k-space approach to experimentally investigate the effects of swept scanning on both conventional Doppler axial velocity estimation and spectral-broadening-based lateral velocity estimation using a 45-MHz transducer. The results indicate that such effects must be corrected in order to obtain an accurate estimation of flow velocities.

Sample volume misregistration in linear array-based dual beam Doppler ultrasound systems

Large velocity estimation errors can occur in dual beam Doppler ultrasound velocity measurement systems when there is left/right sample volume misregistration, particularly when the interbeam angle is small. Such misregistration will occur when there is tissue inhomogeneity. This is investigated for a typical type of inhomogeneity--a layer of fat--by calculating the amount of both angle and translation misregistration occurring in such a system realized using a single linear array transducer. The complex sample volume sensitivity is calculated using a modified time domain approach, combining the spatial impulse response method with ray tracing. The effects on these misregistrations of altering the aperture sizes and their relative positions on the array is then investigated to derive an improved aperture configuration for dual beam velocity estimation. Arrangements with transmit apertures wider than the receive apertures are shown to be preferable in this context.

A new method of ultrasound color flow mapping

Conventional ultrasound color flow mapping systems estimate and visualize only the axial velocity component. To obtain the transverse velocity component a modification of a multiple-beam method is proposed. The new two-dimensional color flow mapping system has a small size and consists of three transducers. The central transducer is an appodized and focused phased array. The other transducers are unfocused probes. Three transducers act as receivers and the central transducer operates as a transmitter. All receivers acquire rf scan lines that are then processed to estimate three axial velocity components using an autocorrelation method. These estimates are then combined to estimate the transverse velocity component, taking into account the geometric relationships among three transducers. Two algorithms for transverse velocity estimation are proposed. The first uses the Doppler angle estimate for calculation of the transverse velocity component. The other algorithm calculates the transverse velocity component directly from the axial components. The accuracy of the flow velocity estimators is estimated by simulations. Analysis of accuracy allows choosing the more effective algorithm for two-dimensional velocity estimation, which is insensitive to variations of the Doppler angle.

Ultrafast compound imaging for 2-D motion vector estimation: application to transient elastography

This paper describes a new technique for two-dimensional (2-D) imaging of the motion vector at a very high frame rate with ultrasound. Its potential is experimentally demonstrated for transient elastography. But, beyond this application, it also could be promising for color flow and reflectivity imaging. To date, only axial displacements induced in human tissues by low-frequency vibrators were measured during transient elastography. The proposed technique allows us to follow both axial and lateral displacements during the shear wave propagation and thus should improve Young's modulus image reconstruction. The process is a combination of several ideas well-known in ultrasonic imaging: ultra-fast imaging, multisynthetic aperture beamforming, 1-D speckle tracking, and compound imaging. Classical beamforming in the transmit mode is replaced here by a single plane wave insonification increasing the frame rate by at least a factor of 128. The beamforming is achieved only in the receive mode on two independent subapertures. Comparison of successive frames by a classical 1-D speckle tracking algorithm allows estimation of displacements along two different directions linked to the subapertures beams. The variance of the estimates is finally improved by tilting the emitting plane wave at each insonification, thus allowing reception of successive decorrelated speckle patterns.

Adaptive clutter filtering via blind source separation for two-dimensional ultrasonic blood velocity measurement

A method for adaptive clutter rejection via blind source separation (BSS) using principal and independent component analyses is presented in application to blood velocity measurement in the carotid artery. In particular, the filtering method's efficacy for eliminating clutter and preserving lateral blood flow signal components is presented. The performance of IIR filters is compromised by shorth data ensembles (10 to 20 temporal samples) as implemented for color-flow and high frame-rate imaging due to initialization requirements. Further, the ultrasonic imaging system's transfer function maps axial wall and lateral blood motion to overlapping spectra. As such, frequency domain-based approaches to wall filtering are ineffective for distinguishing wall from blood motion signals. Rather than operating in the frequency domain. BSS performs clutter rejection by decomposing the input data ensemble into N constitutive source signals in time, where N is the ensemble length. Source signal energy coupled with respective signal depth and time course profiles reveal which source signals correspond to blood, noise and clutter components. Clutter components may then be removed without disruption of lateral blood flow information needed for two-dimensional blood velocity measurement. A simplistic data simulation is employed to offer an intuitive understanding of BSS methods for signal separation. The adaptive BSS filter is further demonstrated using a Field II simulation of blood flow through the carotid artery including tissue motion. BSS clutter filter performance is compared to the performance of FIR, IIR and polynomial regression clutter filters. Finally, the filter is employed for clinical application using a Siemens Elegra scanner, carotid artery data with lateral blood flow collected from healthy volunteers, and Speckle Tracking; velocity magnitude and angle profiles are shown. Once again, the BSS clutter filter is contrasted to FIR, IIR and polynomial regression clutter filters using clinical examples. Velocities computed with Speckle Tracking after BSS wall filtering are highest in the center of the artery and diminish to low velocities near the vessel walls, with velocity magnitudes consistent with physiological expectations. These results demonstrate that the BSS adaptive filter sufficiently suppresses wall motion signal for clinical lateral blood velocity measurement using data ensembles suitable for color-flow and high frame-rate imaging.

Doppler angle estimation of pulsatile flows using AR modeling

In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 3o degrees to 78 degrees) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50 degrees compared to an average error of 7.08 degrees for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.

2-D motion estimation using two parallel receive beams

We describe a method for estimating 2-D target motion using ultrasound. The method is based on previous ensemble tracking techniques, which required at least four parallel receive beams and 2-D pattern matching. In contrast, the method described requires only two parallel receive beams and 1-D pattern matching. Two 1-D searches are performed, one in each lateral direction. The direction yielding the best match indicates the lateral direction of motion. Interpolation provides sub-pixel magnitude resolution. We compared the two beam method with the four beam method using a translating speckle target at three different parallel beam steering angles and transducer angles of 0, 45, and 90 degrees. The largest differences were found at 90 degrees, where the two beam method was generally more accurate and precise than the four beam method and also less prone to directional errors at small translations. We also examined the performance of both methods in a laminar flow phantom. Results indicated that the two beam method was more accurate in measuring the flow angle when the flow velocity was small. Computer simulations supported the experimental findings. The poorer performance of the four beam method was attributed to differences in correlation among the parallel beams. Specifically, center beams 2 and 3 correlated better with each other than with the outer beams. Because the four beam method used a comparison of a kernel region in beam pair 2-3 with two different beam pairs 1-2 and 3-4, the 2-to-1 and 3-to-4 components of this comparison increased the incidence of directional errors, especially at small translations. The two beam method used a comparison between only two beams and so was not subject to this source of error. Finally, the two beam method did not require amplitude normalization, as was necessary for the four beam method, when the two beams were chosen symmetric to the transmit axis. We conclude that two beam ensemble tracking can accurately estimate motion using only two parallel receive beams.

A novel interpolation strategy for estimating subsample speckle motion

Multidimensional, high-resolution ultrasonic imaging of rapidly moving tissue is primarily limited by sparse sampling in the lateral dimension. In order to achieve acceptable spatial resolution and velocity quantization, interpolation of laterally sampled data is necessary. We present a novel method for estimating lateral subsample speckle motion and compare it with traditional interpolation methods. This method, called grid slopes, requires no a priori knowledge and can be applied to data with as few as two samples in the lateral dimension. Computer simulations were performed to compare grid slopes with two conventional interpolation schemes, parabolic fit and cubic spline. Results of computer simulations show that parabolic fit and cubic spline performed poorly at translations greater than 0.5 samples, and translations less than 0.5 samples were subject to an estimation bias. Grid slopes accurately estimated translations between 0 and 1 samples without estimation bias at high signal-to-noise ratios. Given that the grid slopes interpolation technique performs well at high signal-to-noise ratios, one pertinent clinical application might be tissue motion tracking.

Speckle tracking for multi-dimensional flow estimation

Speckle tracking methods overcome the major limitations of current Doppler methods for flow imaging and quantification: angle dependence and aliasing. In this paper, we review the development of speckle tracking, with particular attention to the advantages and limitations of two-dimensional algorithms that use a single transducer aperture. Ensemble tracking, a recent speckle tracking method based upon parallel receive processing, is described. Experimental results with ensemble tracking indicate the ability to measure laminar flow in a phantom at a beam-vessel angle of 60 degrees, which had not been possible with previous 2D speckle tracking methods. Finally, important areas for future research in speckle tracking are briefly summarized.

Doppler angle estimation using correlation

Conventional Doppler techniques can only detect the axial component of blood flow. To obtain the transverse flow component, an approach based on the dependence of Doppler bandwidth on Doppler angle has been widely investigated. To compute the bandwidth, a full Doppler spectrum is often required. Therefore, this approach has not been applied to real-time, two-dimensional Doppler imaging because of the long data acquisition time. To overcome this problem, a correlation-based method is proposed. Specifically, variance of the Doppler spectrum is used to approximate the square of the Doppler bandwidth. Because variance is computed efficiently and routinely in correlation-based color Doppler imaging systems, implementation of this method is straightforward. In addition, the two-dimensional velocity vector can be calculated and mapped to different colors using the color mapping function of current systems. Simulations were performed, and experimental data were also collected using a string phantom with the Doppler angle varying from 23 degrees to 82 degrees . Results indicate that the correlation-based method may produce significant errors if only a limited number of flow samples are available. With averaging, however, the Doppler angles estimated by the correlation-based method can achieve good agreement with the true angles by using only four flow samples with proper variance averaging.

Angle-independent motion measurement by correlation of ultrasound signals assessed with a single circular-shaped transducer

In medicine, pulsed ultrasound is a widespread noninvasive technique that measures motion in the direction of the ultrasound beam, i.e., axial motion. The magnitude of the actual motion can be determined only if the angle between the ultrasound beam and the direction of motion (transducer-to-motion angle) is known. For blood flow measurements, current pulsed ultrasound systems assume this angle to be equal to the angle between the ultrasound beam and the longitudinal direction of the vessel, as can be estimated from a two-dimensional brightness-mode (B-mode) image that is obtained prior to the blood flow measurement. For tissue motion measurements, current pulsed ultrasound systems are mostly unable to determine the transducer-to-motion angle. Recently, a model has been derived for the correlation of(analytic) radiofrequency (rf) signals, assessed with a circular-shaped ultrasound transducer along the same line of observation. In the present paper, this model is used to derive estimators, requiring only the calculation of a few correlation coefficients, for the motion components (axial, lateral and actual) and for some of the signal parameters (center frequency, bandwidth and signal-to-noise ratio) of the assessed rf signals. The transducer-to-motion angle can be derived from the estimated motion components. For the evaluation of the estimators, rf signals were acquired with a motion-controlled experimental arrangement. The results of the evaluation study show that the transducer-to-motion angle can be estimated with a mean standard deviation of less than 2 degrees.