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.     

Estimating the blood velocity vector using aperture domain data

Most conventional blood flow estimation methods measure only the axial component of the blood velocity vector. In this study, we developed a new method for two-dimensional (2-D) velocity vector estimation in which time shifts resulting from blood motion are calculated for the individual channels using aperture domain data. This allows the construction of a time-shift profile along the array direction as a function of channel index, which is approximated by a first-order polynomial whose zeroth-order and first-order terms can be used to determine the axial and lateral velocity components, respectively. The efficacy of the proposed method was verified by simulations and experiments in which the transducer array had 64 elements, an aperture size of 1.96 cm, and a center frequency of 5 MHz. The flow velocity ranged from 5 to 35 cm/s and the Doppler angle ranged from 0 degrees to 90 degrees. The experimental results show that the accuracy of axial velocity estimation is higher for the new method than for the autocorrelation-based conventional method when the signal-to-noise ratio is larger than 0 dB. The mean estimation error for the axial velocity component is 2.18% for the new method, compared to 4.51% for the conventional method. The mean estimation error for the lateral velocity component is 15%, which is comparable to existing methods.     

Estimating 2-D vector velocities using multidimensional spectrum analysis

Wilson (1991) presented an ultrasonic wideband estimator for axial blood flow velocity estimation through the use of the 2-D Fourier transform. It was shown how a single velocity component was concentrated along a line in the 2-D Fourier space, where the slope was given by the axial velocity. Later, it was shown that this approach could also be used for finding the lateral velocity component by also including a lateral sampling. A single velocity component would then be concentrated along a plane in the 3-D Fourier space, tilted according to the 2 velocity components. This paper presents 2 new velocity estimators for finding both the axial and lateral velocity components. The estimators essentially search for the plane in the 3- D Fourier space, where the integrated power spectrum is largest. The first uses the 3-D Fourier transform to find the power spectrum, while the second uses a minimum variance approach. Based on this plane, the axial and lateral velocity components are estimated. Several phantom measurements, for flow-to-depth angles of 60, 75, and 90 degrees, were performed. Multiple parallel lines were beamformed simultaneously, and 2 different receive apodization schemes were tried. The 2 estimators were then applied to the data. The axial velocity component was estimated with an average standard deviation below 2.8% of the peak velocity, while the average standard deviation of the lateral velocity estimates was between 2.0% and 16.4%. The 2 estimators were also tested on in vivo data from a transverse scan of the common carotid artery, showing the potential of the vector velocity estimation method under in vivo conditions.     

Lateral blood flow velocity estimation based on ultrasound speckle size change with scan velocity

Conventional (Doppler-based) blood flow velocity measurement methods using ultrasound are capable of resolving the axial component (i.e., that aligned with the ultrasound propagation direction) of the blood flow velocity vector. However, these methods are incapable of detecting blood flow in the direction normal to the ultrasound beam. In addition, these methods require repeated pulse-echo interrogation at the same spatial location. A new method has been introduced which estimates the lateral component of blood flow within a single image frame using the observation that the speckle pattern corresponding to blood reflectors (typically red blood cells) stretches (i.e., is smeared) if the blood is moving in the same direction as the electronically-controlled transducer line selection in a 2-D image. The situation is analogous to the observed distortion of a subject photographed with a moving camera. The results of previous research showed a linear relationship between the stretch factor (increase in lateral speckle size) and blood flow velocity. However, errors exist in the estimation when used to measure blood flow velocity. In this paper, the relationship between speckle size and blood flow velocity is investigated further with both simulated flow data and measurements from a blood flow phantom. It can be seen that: 1) when the blood flow velocity is much greater than the scan velocity (spatial rate of A-line acquisition), the velocity will be significantly underestimated because of speckle decorrelation caused by quick blood movement out of the ultrasound beam; 2) modeled flow gradients increase the average estimation error from a range between 1.4% and 4.4%, to a range between 4.4% and 6.8%; and 3) estimation performance in a blood flow phantom with both flow gradients and random motion of scatterers increases the average estimation error to between 6.1% and 7.8%. Initial attempts at a multiple-scan strategy for estimating flow by a least-squares model suggest the possibility of increased accuracy using multiple scan velocities.     

A new method for estimation of velocity vectors

The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.     

Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of the cross-correlation function

A widely used time-domain technique for motion or delay estimation between digitized ultrasound RF signals involves the maximization of a discrete pattern-matching function, usually the cross-correlation. To achieve sub-sample accuracy, the discrete pattern-matching function is interpolated using the values at the discrete maximizer and adjacent samples. In prior work, only 1-D fit, applied separately along the axial, lateral, and elevational axes, has been used to estimate the sub-sample motion in 1-D, 2-D, and 3-D. In this paper, we explore the use of 2-D and 3-D polynomial fitting for this purpose. We quantify the estimation error in noise-free simulations using Field II and experiments with a commercial ultrasound machine. In simulated 2-D translational motions, function fitting with quartic spline polynomials leads to maximum bias of 0.2% of the sample spacing in the axial direction and 0.4% of the sample spacing in the lateral direction, corresponding to 38 nm and 1.31 μm, respectively. The maximum standard deviations were approximately 1% of the sample spacing in both the axial and the lateral directions, corresponding to 193 nm axially and 4.43 μm laterally. In simulated 1% axial strain, the same function fitting leads to mean absolute displacement estimation errors of 255 nm in the axial direction and 4.77 μm in the lateral direction. In experiments with a linear array transducer, 2-D quartic spline fitting leads to maximum bias of 458 nm and 6.27 μm in the axial and the lateral directions, respectively. These results are more than one order of magnitude smaller than those obtained with separate 1-D fit when applied to the same data set. Simulations and experiments in 3-D yield similar results when comparing 3-D polynomial fitting with 1-D fitting along the axial, lateral, and elevational directions.     

A new time-domain narrowband velocity estimation technique for Doppler ultrasound flow imaging. II. Comparative performance assessment

For pt.I see ibid., vol.45, no.4, pp.939-54 (1998). The statistical performance of the new 2-D narrowband time-domain root-MUSIC blood velocity estimator described previously is evaluated using both simulated and flow phantom wideband (50% fractional bandwidth) ultrasonic data. Comparisons are made with the standard 1-D Kasai estimator and two other wideband strategies: the time domain correlator and the wideband point maximum likelihood estimator. A special case of the root-MUSIC, the "spatial" Kasai, is also considered. Simulation and flow phantom results indicate that the root-MUSIC blood velocity estimator displays a superior ability to reconstruct spatial blood velocity information under a wide range of operating conditions. The root-MUSIC mode velocity estimator can be extended to effectively remove the clutter component from the sample volume data. A bimodal velocity estimator is formed by processing the signal subspace spanned by the eigenvectors corresponding to the two largest eigenvalues of the Doppler correlation matrix. To test this scheme, in vivo common carotid flow complex Doppler data was obtained from a commercially available color flow imaging system. Velocity estimates were made using a reduced form of this data corresponding to higher frame rates. The extended root-MUSIC approach was found to produce superior results when compared to both 1- and 2-D Kasai-type estimators that used initialized clutter filters. The results obtained using simulated, flow phantom, and in vivo data suggest that increased sensitivity as well as effective clutter suppression can be achieved using the root-MUSIC technique, and this may be particularly important for wideband high frame rate imaging applications.     

3-D flow velocity vector estimation with a triple-beam lens transducer-experimental results

Current commercial ultrasound blood flow measurement systems only measure the axial component of the true blood flow velocity vector. In order to overcome this limitation, a technique which tracks blood cell scatterers as they move between three ultrasound beams has been developed. With this technique, the entire 3-D blood flow velocity vector can be estimated. Previous work has presented the theory behind the technique, lens transducer design and construction, as well as results of computer simulations and preliminary experimental results. This work presents the first experimental results obtained with a prototype system for continuous, fully developed flow in a flow phantom under a wide range of flow rates and flow directions. The results indicate that the accurate measurement of the 3-D flow velocity vector using this technique is possible.     

A new estimator for vector velocity estimation

A new estimator for determining the two-dimensional velocity vector using a pulsed ultrasound field is derived. The estimator uses a transversely modulated ultrasound field for probing the moving medium under investigation. A modified autocorrelation approach is used in the velocity estimation. The new estimator automatically compensates for the axial velocity when determining the transverse velocity. The estimation is optimized by using a lag different from one in the estimation process, and noise artifacts are reduced by averaging RF samples. Further, compensation for the axial velocity can be introduced, and the velocity estimation is done at a fixed depth in tissue to reduce the influence of a spatial velocity spread. Examples for different velocity vectors and field conditions are shown using both simple and more complex field simulations. A relative accuracy of 10.1% is obtained for the transverse velocity estimates for a parabolic velocity profile for flow transverse to the ultrasound beam and a SNR of 20 dB using 20 pulse-echo lines. The overall bias in the estimates was -4.3%     

Comparison between 2-D cross correlation with 2-D sub-sampling and 2-D tracking using beam steering

We have previously presented multi-dimensional sub-sample motion estimation techniques that use multi-dimensional polynomial fitting to the discrete cross-correlation function to jointly estimate the sub-sample motion in all three spatial directions. Previous simulation and experimental results showed that these estimators significantly improve the performance of the motion estimation in 2-D and 3-D. In this short communication, we present additional simulation results and compare these techniques to 2-D tracking using beam steering. The results show that beam steering technique performs better in estimating the motion vector especially the lateral component.     

Maximum likelihood blood velocity estimator incorporating properties of flow physics

The aspect of correlation among the blood velocities in time and space has not received much attention in previous blood velocity estimators. The theory of fluid mechanics predicts this property of the blood flow. Additionally, most estimators based on a cross-correlation analysis are limited on the maximum velocity detectable. This is due to the occurrence of multiple peaks in the cross-correlation function. In this study a new estimator (CMLE), which is based on correlation (C) properties inherited from fluid flow and maximum likelihood estimation (MLE), is derived and evaluated on a set of simulated and in vivo data from the carotid artery. The estimator is meant for two-dimensional (2-D) color flow imaging. The resulting mathematical relation for the estimator consists of two terms. The first term performs a cross-correlation analysis on the signal segment in the radio frequency (RF)-data under investigation. The flow physic properties are exploited in the second term, as the range of velocity values investigated in the cross-correlation analysis are compared to the velocity estimates in the temporal and spatial neighborhood of the signal segment under investigation. The new estimator has been compared to the cross-correlation (CC) estimator and the previously developed maximum likelihood estimator (MLE). The results show that the CMLE can handle a larger velocity search range and is capable of estimating even low velocity levels from tissue motion. The CC and the MLE produce incorrect velocity estimates due to the multiple peaks, when the velocity search range is increased above the maximum detectable velocity. The root-mean square error (RMS) on the velocity estimates for the simulated data is on the order of 7 cm/s (14%) for the CMLE, and it is comparable to the RMS for the CC and the MLE. When the velocity search range is set to twice the limit of the CC and the MLE, the number of incorrect velocity estimates are 0, 19.1, and 7.2% for the CMLE, CC, and MLE, respectively. The ability to handle a larger search range and estimating low velocity levels was confirmed on in vivo data.     

Estimation of blood velocity with high frequency ultrasound

In order to map blood velocity in small regions near the transducer, we evaluate the performance of the wideband maximum likelihood (WMLE) strategy and infinite impulse response (IIR) filters for blood velocity estimation with a transducer center frequency of 38 MHz. Using a short transmitted pulse and the narrow lateral beam width obtained using this frequency, we show that velocities smaller than 1 mm/s can be estimated reliably. In addition, using both changes in the location and magnitude of the peak of the RF correlation, vessels as small as 40 μm can be visualized in the RF signal and distinguished from stationary tissue. The experimental system also provides the opportunity to examine changes in flow and in the vessel wall over a cardiac cycle     

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.     

Comparison of 2-D speckle tracking and tissue Doppler imaging in an isolated rabbit heart model

Ultrasound strain imaging has been proposed to quantitatively assess myocardial contractility. Cross-correlation-based 2-D speckle tracking (ST) and auto-correlation-based tissue Doppler imaging (TDI) [often called Doppler tissue imaging (DTI)] are competitive ultrasound techniques for this application. Compared with 2-D ST, TDI, as a 1-D method, is sensitive to beam angle and suffers from low strain signal-to-noise ratio because a high pulse repetition frequency is required to avoid aliasing in velocity estimation. In addition, ST and TDI are fundamentally different in the way that physical parameters such as the mechanical strain are derived, resulting in different estimation accuracy and interpretation. In this study, we directly compared the accuracy of TDI and 2-D ST estimates of instantaneous axial normal strain and accumulated axial normal strain using a simulated heart. We then used an isolated rabbit heart model of acute ischemia produced by left descending anterior artery ligation to evaluate the performance of the two methods in detecting abnormal motion. Results showed that instantaneous axial normal strains derived using TDI (0.36% error) were less accurate with larger variance than those derived from 2-D ST (0.08% error) given the same spatial resolution. In addition to poorer accuracy, accumulated axial normal strain estimates derived using TDI suffered from bias, because the accumulation method for TDI cannot trace along the actual tissue displacement path. Finally, we demonstrated the advantage 2-D ST has over TDI to reduce dependency on beam angle for lesion detection by estimating strains based on the principal stretches and their corresponding principal axes.     

Directional velocity estimation using a spatio-temporal encoding technique based on frequency division for synthetic transmit aperture ultrasound

This paper investigates the possibility of flow estimation using spatio-temporal encoding of the transmissions in synthetic transmit aperture imaging (STA). The spatial encoding is based on a frequency division approach. In STA, a major disadvantage is that only a single transmitter (denoting single transducer element or a virtual source) is used in every transmission. The transmitted acoustic energy will be low compared to a conventional focused transmission in which a large part of the aperture is used. By using several transmitters simultaneously, the total transmitted energy can be increased. However, to focus the data properly, the signals originating from the different transmitters must be separated. To do so, the pass band of the transducer is divided into a number of subbands with disjoint spectral support. At every transmission, each transmitter is assigned one of the subbands. In receive, the signals are separated using a simple filtering operation. To attain high axial resolution, broadband spectra must be synthesized for each of the transmitters. By multiplexing the different waveforms on different transmitters over a number of transmissions, this can be accomplished. To further increase the transmitted energy, the waveforms are designed as linear frequency modulated signals. Therefore, the full excitation amplitude can be used during most of the transmission. The method has been evaluated for blood velocity estimation for several different velocities and incident angles. The program Field II was used. A 128-element transducer with a center frequency of 7 MHz was simulated. The 64 transmitting elements were used as the transmitting aperture and 128 elements were used as the receiving aperture. Four virtual sources were created in every transmission. By beamforming lines in the flow direction, directional data were extracted and correlated. Hereby, the velocity of the blood was estimated. The pulse repetition frequency was 16 kHz. Three different setups were investigated with flow angles of 45, 60, and 75 degrees with respect to the acoustic axis. Four different velocities were simulated for each angle at 0.10, 0.25, 0.50, and 1.00 m/s. The mean relative bias with respect to the peak flow for the three angles was less than 2%, 2%, and 4%, respectively.     

Investigation of transverse oscillation method

Conventional ultrasound scanners can display only the axial component of the blood velocity vector, which is a significant limitation when vessels nearly parallel to the skin surface are scanned. The transverse oscillation (TO) method overcomes this limitation by introducing a TO and an axial oscillation in the pulse echo field. The theory behind the creation of the double oscillation pulse echo field is explained as well as the theory behind the estimation of the vector velocity. A parameter study of the method is performed, using the ultrasound simulation program Field II. A virtual linear-array transducer with center frequency 7 MHz and 128 active elements is created, and a virtual blood vessel of radius 6.4 mm is simulated. The performance of the TO method is found around an initial point in the parameter space. The parameters varied are: flow angle, transmit focus depth, receive apodization, pulse length, transverse wave length, number of emissions, signal-to-noise ratio (SNR), and type of echo-canceling filter used. Using an experimental scanner, the performance of the TO method is evaluated. An experimental flowrig is used to create laminar parabolic flow in a blood mimicking fluid, and the fluid is scanned under different flow-to-beam angles. The relative standard deviation on the transverse velocity estimate is found to be less than 10% for all angles between 50 degrees and 90 degrees. Furthermore, the TO method is evaluated in the flowrig using pulsatile flow, which resembles the flow in the femoral artery. The estimated volume flow as a function of time is compared to the volume flow derived from a conventional axial method at a flow-to-beam angle of 60 degrees. It is found that the method is highly sensitive to the angle between the flow and the beam direction. Also, the choice of echo canceling filter affects the performance significantly.     

Experimental evaluation of velocity and power estimation forultrasound blood flow imaging, by means of a two-dimensionalautocorrelation approach

This paper evaluates experimentally the performance of a novel axial velocity estimator, the 2D autocorrelator, and its Doppler power estimation counterpart, the 2D zero-lag autocorrelator, in the context of ultrasound color flow mapping. The evaluation also encompasses the well-established 1D autocorrelation technique for velocity estimation and its corresponding power estimator (1D zero-lag autocorrelator), to allow performance comparisons under identical conditions. Clutter-suppressed in vitro data sets from a steady-flow system are used to document the effect of the range gate and ensemble length, noise level and angle of insonation on the precision of the velocity estimates. The same data sets are used to examine issues related to the estimation of the Doppler signal's power. The first-order statistics of power estimates from regions corresponding to flow and noise are determined experimentally and the ability of power-based thresholding to separate flow signals from noise is characterized by means of ROC analysis. In summary, the results of the in vitro evaluation show that the proposed 2D-autocorrelation form of processing is consistently better than the corresponding 1D-autocorrelation techniques, in terms of both velocity and power estimation. Therefore, given their relatively modest implementation requirements, the 2D-autocorrelation algorithms for velocity and power estimation appear to represent a superior, yet realistic, alternative to conventional Doppler processing for color flow mapping     

A new time-domain narrowband velocity estimation technique for Doppler ultrasound flow imaging. I. Theory

A significant improvement in blood velocity estimation accuracy can be achieved by simultaneously processing both temporal and spatial information obtained from a sample volume. Use of the spatial information becomes especially important when the temporal resolution is limited. By using a two-dimensional sequence of spatially sampled Doppler signal "snapshots" an improved estimate of the Doppler correlation matrix can be formed. Processing Doppler data in this fashion addresses the range-velocity spread nature of the distributed red blood cell target, leading to a significant reduction in spectral speckle. Principal component spectral analysis of the "snapshot" correlation matrix is shown to lead to a new and robust Doppler mode frequency estimator. By processing only the dominant subspace of the Doppler correlation matrix, the Cramer-Rao bounds on the estimation error of target velocity is significantly reduced in comparison to traditional narrowband blood velocity estimation methods and achieves almost the same local accuracy as a wideband estimator. A time-domain solution is given for the velocity estimate using the root-MUSIC algorithm, which makes the new estimator attractive for real-time implementation.     

Autocorrelation techniques in color flow imaging: signal model andstatistical properties of the autocorrelation estimates

A review of the scattering theory for moving blood, and a model for the signal in a multigated pulsed wave Doppler system is presented. The model describes the relation between a general time-variable velocity field and the signal correlation in space and time, including the effect of movement of the ultrasonic beam for color flow imaging systems with mechanical scanning. In the case of a constant and rectilinear velocity field, a parametric model for the autocorrelation function is deduced. General formulas for a full second order characterization of the set of autocorrelation estimates, with arbitrary lags in the spatial and temporal directions, are developed. The formulas are applied to the parametric model, and numerical results for the estimator variance are presented. A qualitative evaluation of the theoretical results has been performed by offline-processing of 2-D Doppler signals from a color flow imaging scanner. The benefit of spatial and temporal averaging is demonstrated by using different averaging filters to the same set of recorded data