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.     

利用超声多普勒技术测量低速血流

利用常规的多普勒系统较难进行低速血流的测量，本文在讨论了常规的多普勒系统的局限后，就一种可测量低速血流的超声多普勒技术的原理，方法进行讨论，并通过计算机模拟实验实现了这种方法。     

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.     

A real-time ultrasound time-domain correlation blood flowmeter. I. Theory and design

A real-time ultrasound time-domain correlation (UTDC) blood flowmeter has been developed. Real-time performance has been achieved through the implementation of a custom-designed high-speed residue-number system (RNS) hardware correlator. The flowmeter is interfaced to a commercial ultrasound imager and can produce one-dimensional velocity versus range graphs at a rate of three per second. It has been validated in a blood flow phantom under a variety of conditions along with in vivo measurements in the human carotid artery. The theory of the time-domain correlation technique, design and implementation of flowmeter hardware, and the important correlation parameters which affect the performance of the flowmeter are described.     

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.     

Analysis of velocity estimation error for a multidimensional Doppler ultrasound system

The error characteristics of a single-transducer (one dimensional), dual-transducer (two-dimensional), and triple-transducer (three-dimensional) system for velocity estimation are examined. A velocity vector is completely characterized by the magnitude and the directional angles. For a single-transducer case, the velocity magnitude alone can be estimated. The variation in the directional angles for a single-transducer case cannot be accounted for in the estimation process, thus resulting in large errors. For a dual transducer, both the velocity magnitude and the angle on the x-y plane can be estimated. The use of an extra transducer provides added flexibility in the estimation process. Variation in one of the directional angles is accounted for in the estimation process, thus resulting in smaller error than the single-transducer case. For a triple-transducer case, if the normal angles between the three transducer axes are known, then the complete velocity vector with all the directional angles can be estimated.     

A new coded-excitation ultrasound imaging system. I. Basicprinciples

A new approach to ultrasound imaging with coded-excitation is presented. The imaging is performed by reconstruction of the scatterer strength on an assumed grid covering the region of interest (ROI). Our formulation is based on an assumed discretized signal model which represents the received sampled data vector as a superposition of impulse responses of all scatterers in the ROI. The reconstruction operator is derived from the pseudo-inverse of the linear operator (system matrix) that produces the received data vector. The singular value decomposition (SVD) method with appropriate regularization techniques is used for obtaining a robust realization of the pseudo-inverse. Under simplifying (but realistic) assumptions, the pseudo-inverse operator (PIO) can be implemented using a bank of transversal filters with each filter designed to extract echoes from a specified image line. This approach allows for the simultaneous acquisition of a large number of image lines. This could be useful in increasing frame rates for two-dimensional imaging systems or allowing for real-time implementation of three-dimensional imaging systems. When compared to the matched filtering approach to similar coded-excitation systems, our approach eliminates correlation artifacts that are known to plague such systems. Furthermore, the lateral resolution of the new system can exceed the diffraction limit imposed on conventional imaging systems utilizing delay-and-sum beamformers. The range resolution is compared to that of conventional pulse-echo systems with resolution enhancement (our PIO behaves as a pseudo-inverse Wiener filter in the range direction). Both simulation and experimental verification of these statements are given     

Directional velocity estimation using focusing along the flow direction. I: Theory and simulation

A new method for directional velocity estimation is presented. The method uses beam formation along the flow direction to generate data in which the correct velocity magnitude can be directly estimated from the shift in position of the received consecutive signals. The shift is found by cross-correlating the beamformed lines. The approach can find the velocity in any direction, including transverse to the traditionally emitted ultrasound beam. The velocity estimation is studied through extensive simulations using Field II. A 128-element, 7-MHz linear array is used. A parabolic velocity profile with a peak velocity of 0.5 m/s is simulated for different beam-to-flow angles and for different emit foci. At 45/spl deg/ the relative standard deviation over the profile is 1.6% for a transmit focus at 40 mm. At 90/spl deg/ the approach gave a relative standard deviation of 6.6% with a transmit focus of 80 mm, when using 8 pulse-echo lines and stationary echo canceling. Pulsatile flow in the femoral artery was also simulated using Womersley's flow model. A purely transverse flow profile could be obtained with a relative standard deviation of less than 10% over the whole cardiac cycle using 8 pulse emissions for each imaging direction, which is sufficient to show clinically relevant transverse color flow images.     

Isomorphism between pulsed-wave Doppler ultrasound anddirection-of-arrival estimation. I. Basic principles

Direction-of-arrival (DOA) estimation of signals is an important area of research in sonar and radar signal processing. Over the last few decades, numerous techniques have been developed for high-resolution DOA estimation. In this paper, we show that velocity measurement using pulsed-wave Doppler ultrasound and DOA estimation are isomorphic problems. We discuss a number of DOA methods and their potential application to flow velocity measurement using ultrasound. Wide-band DOA methods are of special interest because the pulses used for Doppler ultrasound are also wide band. These wide-band methods generally involve a preprocessing step to convert wideband signals to narrow band before applying high-resolution techniques. Application of DOA methods to Doppler ultrasound provides tools for high-resolution velocity measurement, identification of multiple velocity components within a sample volume, and clutter rejection     

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%     

Flow imaging with pulsed Doppler ultrasound and flow phantoms

The use of a multigate profiling system with steady laminar flow in plastic tubes revealed spectral artifacts not previously described. In particular, a double or split profile was often observed. In this paper, these artifacts are related to the dual mode ultrasound propagation in the plastic tube. The propagation speeds and, therefore, refraction angles and propagation paths are different for the longitudinal and the shear wave. The power transmission can be extraordinarily sensitive to small variations in the angle of incidence, and this may combine with the existence of a range of angles of incidence within any focused ultrasound beam to produce spectral distortions. The plastic tube is thus shown equivalent to a selective filter, which diminishes some frequency components in the Doppler spectrum relative to others. The spectral artifacts are explained in terms of the relative power transmitted by each mode, and the degree of beam defocusing experienced by each. Spectral distortions persist even when the beam-to-flow orientation is well away from the critical angle. The results of this study show that it is feasible to understand the acoustic transmission behavior of a flow phantom, based on a knowledge of the material properties, and to demonstrate the usefulness of doing so.     

Laser Doppler field sensor for high resolution flow velocity imaging without camera

In this paper we present a laser sensor for highly spatially resolved flow imaging without using a camera. The sensor is an extension of the principle of laser Doppler anemometry (LDA). Instead of a parallel fringe system, diverging and converging fringes are employed. This method facilitates the determination of the tracer particle position within the measurement volume and leads to an increased spatial and velocity resolution compared to conventional LDA. Using a total number of four fringe systems the flow is resolved in two spatial dimensions and the orthogonal velocity component. Since no camera is used, the resolution of the sensor is not influenced by pixel size effects. A spatial resolution of 4 microm in the x direction and 16 microm in the y direction and a relative velocity resolution of 1x10(-3) have been demonstrated up to now. As a first application we present the velocity measurement of an injection nozzle flow. The sensor is also highly suitable for applications in nano- and microfluidics, e.g., for the measurement of flow rates.     

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 technique for time-domain ultrasonic NDE of thin plates

A new time-domain ultrasonic NDE technique is reported in this paper for the measurement of the thickness (given the wavespeed) or wavespeed (given the thickness) of thin plates; by thin we mean the thickness is less than the wavelength. By introducing a retrieve function the incident field can be reconstructed from the transmitted (reflected) field by a two-term (three-term) summation. A systematic sensitivity analysis of this technique has been carried out. The new technique has been used to measure the thickness or the wavespeed of aluminum plates with thickness ranging from 0.089 to 6.426 mm using (low frequency) 1-MHz transducers: 0.014(thickness/wavelength)1.0. The measurement error was found to be about 1% for thickness and 3% for the wavespeed.     

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.     

Application of Bessel beam for Doppler velocity estimation

Limited-diffraction beams have a large depth of field and could be applied to medical imaging, tissue characterization, and nondestructive evaluation of materials. This paper reports the application of limited-diffraction beams, specifically, the Bessel beam, to Doppler velocity estimation. The Bessel beam has the advantage that velocity estimation is less subject to the depth of moving objects and the Doppler spectrum has distinct shoulders that increase the accuracy of velocity (both magnitude and Doppler angle) estimation in noisy environments. The shoulders of the Doppler spectrum might also help in solving the inverse problem, e.g., estimation of the velocity distribution in vessels     

Target velocity estimation with FM and PW echo ranging Doppler systems I. Signal analysis

The theoretical foundation is presented for velocity estimation with a pulsed wave (PW) Doppler system transmitting linear FM signals. The Doppler system possesses echo ranging capabilities and is evaluated in the context of Doppler ultrasound for blood velocity measurement. The FM excitation signal is formulated and the received signal is derived for a single moving particle. This signal is similar to the transmitted signal, but with modified parameters due to Doppler effect and range. The demodulated received signal is subsequently derived and analyzed. It is shown that, due to the Doppler effect, this is a linear sweep signal as well. The velocity and range information obtainable from one and two consecutively received signals are described. The latter case establishes the basis for an FM Doppler system for blood velocity measurements.     

Spectral velocity profiles for detailed ultrasound flow analysis

The operation of a novel ultrasound multigate instrument capable of computing in real-time the fast Fourier transform (FFT) of Doppler signals detected from 64 equally spaced range cells is presented. The new system provides up to 50 velocity profiles per second, which are displayed in such a manner that information about the full spectral content of Doppler signals at all the investigated depths is continuously monitored over a PRF-wide frequency range which can be set arbitrarily between -PRF and +PRF. Experimental results are presented, which demonstrate that the true velocity profile can be accurately detected through the computation of “local” maximum velocities obtained by properly correcting the maximum frequency of each spectrum. There is also a discussion on how the results of multigate analysis are influenced by the sample volume length, a parameter which can be usually set by modifying the duration of the transmitted burst. In particular, it is shown that, in regions close to the vessel walls, the shear rate can be measured with a spatial resolution related to the spacing between subsequent range cells and not to the sample volume length