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.     

Optimal velocity estimation in ultrasound color flow imaging in presence of clutter

In color flow imaging (CFI), the rejection of tissue clutter signal is treated separately from blood velocity estimation by high-pass filtering the received Doppler signal. The complete suppression of clutter is then difficult to achieve without affecting the subsequent velocity estimates. In this work, a different approach to velocity estimation is investigated, based on a statistical model of the signal from both clutter and blood. An analytic expression for the Cramer-Rao lower bound (CRLB) is developed, and used to determine the existence of an efficient maximum likelihood estimator (MLE) of blood velocity in CFI when assuming full knowledge of the clutter statistics. We further simulate and compare the performance of the MLE to that of the autocorrelation method (ACM) using finite-impulse response (FIR) and polynomial regression clutter filters. Two signal scenarios are simulated, representing a central and peripheral vessel. Simulations showed that, by including 3-9 (independent) spatial points, the MLE variance approached the CRLB in both scenarios. The ACM was approximately unbiased only for the central scenario in the clutter filter pass band, then with a variance of up to four times the CRLB. The ACM suffered from a severe bias in the filter transition region, and a significant performance gain was achieved here using the MLE. For practical use, the clutter properties must be estimated. We finally replaced the known clutter statistics with an estimate obtained from low-rank approximations of the received sample correlation matrix. Used in the model-based framework, this method came close to the performance of the MLE, and it may be an important step toward a practical model-based estimator, including tissue clutter with optimal performance.     

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.     

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.     

Ultrasound three-dimensional velocity measurements by featuretracking

This article describes a new angle-independent method suitable for three-dimensional (3-D) blood flow velocity measurement that tracks features of the ultrasonic speckle produced by a pulse echo system. In this method, a feature is identified and followed over time to detect motion. Other blood flow velocity measurement methods typically estimate velocity using one- (1-D) or two-dimensional (2-D) spatial and time information. Speckle decorrelation due to motion in the elevation dimension may hinder this estimate of the true 3-D blood flow velocity vector. Feature tracking is a 3-D method with the ability to measure the true blood velocity vector rather than a projection onto a line or plane. Off-line experiments using a tissue phantom and a real-time volumetric ultrasound imaging system have shown that the local maximum detected value of the speckle signal may be identified and tracked for measuring velocities typical of human blood flow. The limitations of feature tracking, including the uncertainty of the peak location and the duration of the local maxima are discussed. An analysis of the expected error using this method is given     

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: preliminary results

This paper describes a new ultrasound-based system for high-frame-rate measurement of periodic motion in 2-D for tissue elasticity imaging. Similarly to conventional 2-D flow vector imaging, the system acquires the RF signals from the region of interest at multiple steering angles. A custom sector subdivision technique is used to increase the temporal resolution while keeping the total acquisition time within the range suitable for real-time applications. Within each sector, 1-D motion is estimated along the beam direction. The intra- and inter-sector delays are compensated using our recently introduced delay compensation algorithm. In-plane 2-D motion vectors are then reconstructed from these delay-compensated 1-D motions. We show that Young's modulus images can be reconstructed from these 2-D motion vectors using local inversion algorithms. The performance of the system is validated quantitatively using a commercial flow phantom and a commercial elasticity phantom. At the frame rate of 1667 Hz, the estimated flow velocities with the system are in agreement with the velocity measured with a pulsed-wave Doppler imaging mode of a commercial ultrasound machine with manual angle correction. At the frame rate of 1250 Hz, phantom Young's moduli of 29, 6, and 54 kPa for the background, the soft inclusion, and the hard inclusion, are estimated to be 30, 11, and 53 kPa, respectively.     

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     

Single-ensemble-based eigen-processing methods for color flow imaging--Part I. The Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).     

A new wideband spread target maximum likelihood estimator for blood velocity estimation. I. Theory

The derivation and theoretical evaluation of new wideband maximum-likelihood strategies for the estimation of blood velocity using acoustic signals are presented. A model for the received signal from blood scatterers, using a train of short wideband pulses, is described. Evaluation of the autocorrelation of the signal based on this model shows that the magnitude, periodicity, and phase of the autocorrelation are affected by the mean scatterer velocity and the presence of a velocity spread target. New velocity estimators are then derived that exploit the effect of the scatterer velocity on both the signal delay and the shift in frequency. The wideband range spread estimator is derived using a statistical model of the target. Based on the point target assumption, a simpler wideband maximum-likelihood estimator is also obtained. These new estimation strategies are analyzed for their local and global performance. Evaluation of the Cramer-Rao bound shows that the bound on the estimator variance is reduced using these estimators, in comparison with narrowband strategies. In order to study global accuracy, the expected estimator output is evaluated, and it is determined that the width of the mainlobe is reduced. In addition, it is shown that the height of subsidiary velocity peaks is reduced through the use of these new estimators.     

Coherent array imaging using phased subarrays. Part II: simulations and experimental results

The basic principles and theory of phased subarray (PSA) imaging imaging provides the flexibility of reducing the number of front-end hardware channels between that of classical synthetic aperture (CSA) imaging--which uses only one element per firing event--and full-phased array (FPA) imaging-which uses all elements for each firing. The performance of PSA generally ranges between that obtained by CSA and FPA using the same array, and depends on the amount of hardware complexity reduction. For the work described in this paper, we performed FPA, CSA, and PSA imaging of a resolution phantom using both simulated and experimental data from a 3-MHz, 3.2-cm, 128-element capacitive micromachined ultrasound transducer (CMUT) array. The simulated system point responses in the spatial and frequency domains are presented as a means of studying the effects of signal bandwidth, reconstruction filter size, and subsampling rate on the PSA system performance. The PSA and FPA sector-scanned images were reconstructed using the wideband experimental data with 80% fractional bandwidth, with seven 32-element subarrays used for PSA imaging. The measurements on the experimental sector images indicate that, at the transmit focal zone, the PSA method provides a 10% improvement in the 6-dB lateral resolution, and the axial point resolution of PSA imaging is identical to that of FPA imaging. The signal-to-noise ratio (SNR) of PSA image was 58.3 dB, 4.9 dB below that of the FPA image, and the contrast-to-noise ratio (CNR) is reduced by 10%. The simulated and experimental test results presented in this paper validate theoretical expectations and illustrate the flexibility of PSA imaging as a way to exchange SNR and frame rate for simplified front-end hardware.     

Multi-frequency encoding for fast color flow or quadroplex imaging

Ultrasonic color flow maps are made by estimating the velocities line by line over the region of interest. For each velocity estimate, multiple repetitions are needed. This sets a limit on the frame rate, which becomes increasingly severe when imaging deeper lying structures or when simultaneously acquiring spectrogram data for triplex imaging. This paper proposes a method for decreasing the data acquisition time by simultaneously sampling multiple lines for color flow maps, using narrow band signals with approximately disjoint spectral support. The signals are separated in the receiver by filters matched to the emitted waveforms, producing a number of data sets with different center frequencies. The autocorrelation estimator is then applied to each of the data sets. The method is presented, various side effects are considered, and the method is tested on data from a recirculating flow phantom. A mean standard deviation across the flow profile of 3.1, 2.5, and 2.1% of the peak velocity was found for bands at 5 MHz, 7 MHz, and 9 MHz, respectively. Alternatively, the method can be used for simultaneously sampling data for a color flow map and for multiple spectrograms using different spectral bands. Using three spectral bands, data for a color flow map and two independent spectrograms can be acquired at the time normally spent on acquiring data for a color flow map only. This yields an expansion of triplex imaging called multifrequency quadroplex imaging, which enables study of the flow over an arterial stenosis by simultaneously acquiring spectrograms on both sides of the stenosis, while maintaining the color flow map. The method was tested in vivo on data from the common carotid artery of a healthy male volunteer, both for fast color flow mapping and for multifrequency quadroplex imaging.     

An extended autocorrelation method for estimation of blood velocity

The conventional autocorrelation method (AM) to estimate the blood velocity for color flow imaging (CFI) is based on the phase estimation of the autocorrelation function. In this paper, a new extended autocorrelation method (EAM) that uses both phase and magnitude of the two dimensional (depth and temporal direction) autocorrelation function for estimating the blood velocity is presented. It is shown that the EAM has similar performance as the cross-correlation method (CCM). Both of them have smaller estimation variance than the AM and have the ability to estimate velocities beyond the Nyquist velocity, but the EAM is more computationally efficient than the CCM. A 2-D blood flow signal with rectilinear velocity including the transit time effect has also been simulated and the results are presented in this paper. For comparison, the EAM and the CCM have been applied to the simulated signals in which the flow velocities are up to four times the Nyquist velocity. The EAM has been further verified by experimental RF data from the subclavian artery     

Clutter filter design for ultrasound color flow imaging

For ultrasound color flow images with high quality, it is important to suppress the clutter signals originating from stationary and slowly moving tissue sufficiently. Without sufficient clutter rejection, low velocity blood flow cannot be measured, and estimates of higher velocities will have a large bias. The small number of samples available (8 to 16) makes clutter filtering in color flow imaging a challenging problem. In this paper, we review and analyze three classes of filters: finite impulse response (FIR), infinite impulse response (IIR), and regression filters. The quality of the filters was assessed based on the frequency response, as well as on the bias and variance of a mean blood velocity estimator using an autocorrelation technique. For FIR filters, the frequency response was improved by allowing a non-linear phase response. By estimating the mean blood flow velocity from two vectors filtered in the forward and backward direction, respectively, the standard deviation was significantly lower with a minimum phase filter than with a linear phase filter. For IIR filters applied to short signals, the transient part of the output signal is important. We analyzed zero, step, and projection initialization, and found that projection initialization gave the best filters. For regression filters, polynomial basis functions provide effective clutter suppression. The best filters from each of the three classes gave comparable bias and variance of the mean blood velocity estimates. However, polynomial regression filters and projection-initialized IIR filters had a slightly better frequency response than could be obtained with FIR filters     

Blood flow images by a SAW-based multigate Doppler system

Multigate operation of an ultrasound pulsed Doppler flowmeter, providing Doppler frequency detection in a number of adjacent sample volumes, is capable of displaying the instantaneous blood velocity distribution along the cross section of a sonified vessel. Real-time serial Doppler processing of 32 range cells has been implemented in a novel system using fast spectral analysis based on surface-acoustic wave (SAW) dispersive filters. The basic architecture and first in vitro experiments were reported previously. The in vivo application of the system is described here, and images of human carotid artery and jugular vein are presented. Appropriate display formats are introduced to use the great amount of information known on spatial and temporal behavior of flow profiles. Digital postprocessing of spectral Doppler data allows velocity profiles to be displayed at selected times to correlate spatial and temporal evolution. A color code can be used to represent different velocity strengths. The potential application of the system to two-dimensional (2-D) flow imaging is discussed.     

Single-ensemble-based eigen-processing methods for color flow imaging--Part II. The matrix pencil estimator

Parametric spectral estimators can potentially be used to obtain flow estimates directly from raw slow-time ensembles whose clutter has not been suppressed. We present a new eigen-based parametric flow estimation method called the matrix pencil, whose principles are based on a matrix form under the same name. The presented method models the slow-time signal as a sum of dominant complex sinusoids in the slow-time ensemble, and it computes the principal Doppler frequencies by using a generalized eigen-value problem-formulation and matrix rank reduction principles. Both fixed rank (rank-one, rank-two) and adaptive-rank matrix pencil flow estimators are proposed, and their potential applicability to color flow signal processing is discussed. For the adaptive-rank estimator, the nominal rank was defined as the minimum eigen-structure rank that yields principal frequency estimates with a spread greater than a prescribed bandwidth. In our initial performance evaluation, the fixed-rank matrix pencil estimators were applied to raw color flow data (transmit frequency: 5 MHz; pulse repetition period: 0.175 ms; ensemble size: 14) acquired from a steady flow phantom (70 cm/s at centerline) that was surrounded by rigid-tissue-mimicking material. These fixed-rank estimators produced velocity maps that are well correlated with the theoretical flow profile (correlation coefficient: 0.964 to 0.975). To facilitate further evaluation, the matrix pencil estimators were applied to synthetic slow-time data (transmit frequency: 5 MHz; pulse repetition period: 1.0 ms; ensemble size: 10) modeling flow scenarios without and with tissue motion (up to 1 cm/s). The bias and root-mean-squared error of the estimators were computed as a function of blood-signal-to-noise ratio and blood velocity. The matrix pencil flow estimators showed that they are comparatively less biased than most of the existing frequency-based flow estimators like the lagone autocorrelator.     

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.     

Real-time rectilinear 3-D ultrasound using receive mode multiplexing

In previous work, we developed two generations of a real-time rectilinear volumetric scanner operating at 5 MHz for abdominal, breast, or vascular imaging using a Mills cross two-dimensional (2-D) array and a rectilinear periodic 2-D array. To improve spatial resolution performance and sensitivity, we developed a new design using 4:1 receive mode multiplexing. With 4:1 multiplexing, the new 65,000 element 2-D array has 4 x 256 = 1024 receivers so that 256 receivers can be used on any image line. The two major benefits of using receive mode multiplexing are an increase in receive sensitivity due to a greater number of receive elements, and a decrease in grating lobe and clutter levels due to increased receive element density. Theoretical simulations and analysis show an increase of about 13 dB in sensitivity compared to our previous work. With these encouraging results, a new 65,000 element 5-MHz, 2-D array having 1024 receivers and 169 transmitters was prototyped. In addition, the multiplexer and control circuitry were designed, built, and interfaced with both the transducer and volumetric scanner. Images of tissue-mimicking phantoms and in vivo targets were obtained. Using a spherical cyst phantom, experimental results showed a +12 dB improvement in signal-to-noise ratio and a +6 dB improvement in contrast compared to our previous work.