Flow velocity profile via time-domain correlation: error analysis and computer simulation

An ultrasonic human-blood-flow velocity profile measurement method using time-domain correlation of consecutive echo pairs has been developed. The time shift between a pair of range gated echoes is estimated by searching for the shift that results in the maximum correlation. The time shift indicates the distance a group of scatterers has moved, from which flow velocity is estimated. The basis for the computer simulations and error analyses of the scheme includes a band-passed white Gaussian noise signal model for an echo from a scattering medium, the estimate of flow velocity from both a single scatterer and multiple scatterers, and a derived precision estimation. The error analysis via computer simulation includes an evaluation of errors associated with the correlation method. For a uniform flow velocity profile, beamwidth modulation represents the greatest error source. However, for a nonuniform flow velocity profile, the jitter caused by a small flow velocity gradient can exceed the other error sources. A detailed computer simulation evaluated the interdependencies of window length, beam width, vessel diameter, and viewing angle on the estimation of flow velocity.     

Estimation of the correlation amplitude of RF signals in small cutaneous vessels

Time domain correlation technique is a widely used method for blood flow velocity measurement. The time shift between a pair of windowed ultrasonic echoes is estimated by searching the temporal position of the maximum of the interpolated normalized correlation function. Between two consecutive echoes, the acoustical footprint of a group of scatterers, which are transported with the flow, moves and is deformed. This implies a decreasing of the amplitude of the normalized correlation coefficient. In the case of microcirculation (low flow rate, low SNR), the amplitude of the correlation peak can be used to detect the presence of blood flow and to discriminate false and true detections (reliability index). We have numerically evaluated the statistical performances of the cross-correlation algorithm used as a correlation peak amplitude estimator in severe conditions (short correlation window length, low SNR). These theoretical results have been compared with in vitro experimentation on a 100-/spl mu/m-diameter microcirculatory phantom and with in vivo experimentation on a 180-/spl mu/m-diameter vessel of a human leg carrying erysipelas.     

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.     

Contrast medium assisted fluid flow measurements

In this paper the development and evaluation of two new approaches for ultrasound time-domain fluid flow measurements by tracking echoes scattered by a contrast agent following injection of a bolus of the contrast agent are described. Their feasibility was investigated by measuring velocity or velocity profile of blood flowing in a mock circulatory loop in vitro. Measurements were made with a one transducer intravessel approach and a two transducer extravessel approach. A hybrid cluster or vector cross-correlation method was used to track the motion of the scatterers in the two transducer time-domain method. This cluster or vector cross correlation method was developed to reduce the ambiguity resulted from misregistration which is a common problem in target tracking by correlating signal patterns. The experimental results show a good agreement between the measured data and those estimated from timing the volume. Although the discussions given in this paper pertain only to blood flow measurements, there is no reason to indicate that these approaches can not be used for fluid flow measurements in an industrial environment if suitable contrast agents can be developed     

3-D velocity field measurement using multiple ultrasonic plane detections and high-order correlation analysis

A method of measuring the three-dimensional velocity field of laminarlike flow noninvasively by combining multiple ultrasonic plane detectors and a corresponding level of high-order cross-correlation analysis is presented. It is assumed that the velocity field consists of a set of straight line streams and that each stream contains random fluctuations that serve to tag the location of each stream as it passes through the detectors. The time delays of each stream between the various pairs of plane detectors are estimated by using high-order cross-correlation analysis of the detected signals. From the estimated time delays the stream velocities and their positions are measured and the three-dimensional velocity field pattern is reconstructed. To confirm the usefulness of this method, an actual measurement system has been constructed in a water tank, and experiments using controlled flow through thin tubes have been carried out. The details of the system and the results are shown.     

Estimation of the angle between ultrasound beam and blood velocitythrough correlation functions

Correlation functions, calculated on the ultrasonic echoes scattered by blood, provide a rich harvest of information concerning the local speed, which has often been underestimated; in particular, blood flow measurement usually yields only the longitudinal component of the velocity, even if significant information about the speed direction can be extracted. In this paper it is shown how correlation functions, calculated on the dependency of both time and space displacements, allow us to evaluate the angle Θ between ultrasound beam and blood flow; when straight vessels are considered, this single parameter, combined with the longitudinal velocity profile, permits the complete hemodynamic characterization. The underlying theory is developed and preliminary experimental results are presented     

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     

Angle-insensitive flow measurement using Doppler bandwidth

The ability to measure the velocity of blood flow independent of the orientation of the blood vessel could aid in evaluation of many disease processes, such as coronary lesions. Conventional ultrasonic Doppler techniques require knowledge of the beam-to-flow angle, and the Doppler effect vanishes when this angle is 90 degrees . By employing a spherically symmetrical range cell and the Doppler bandwidth instead of the Doppler shift, preliminary results show that flow measurement of ideal uniform flow that has a blunt velocity profile can be made without knowledge of tile orientation of the vessel, even when the angle of orientation is around 90 degrees . But when the technique is applied to a real how that has a parabolic velocity profile, the Doppler bandwidth decreases as the beam-to-flow angle increases. Although the Doppler bandwidth is sensitive to the transducer angle in this situation, the error in determining flow velocity might be acceptable if the transducer angle can be estimated to be within a small range. For this method to be regarded as practical for clinical use, however, a consistent relationship between bandwidth and flow velocity must be demonstrated over some set of clinically relevant conditions. The experimental techniques and results for how measurements of both the ideal uniform flow and the real flow are presented in this paper.     

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.     

Adaptive pattern correlation for two-dimensional blood flowmeasurements

One of the major drawbacks of ultrasonic Doppler instruments in measuring blood flow is their inability to measure the velocity perpendicular to the beam. Time domain RF echo or speckle tracking has been studied as an alternative to overcome this problem. By acquiring two-dimensional (2-D) echo signals, both lateral (perpendicular to the beam) and axial (parallel to the beam) velocities can be calculated with 2-D pattern correlation algorithms. One of the disadvantages of the current 2-D pattern correlation algorithms is the extensive computation time involved in computing the 2-D cross-correlation function. In this paper, we present several time-efficient bit-pattern correlation algorithms to execute 2-D speckle tracking. The proposed algorithms first estimate the noise level from the acquired signals and use it as a priori knowledge to minimize computation time. The reduction of computation time may make it more feasible for real-time measurements of flow velocities in two dimensions. Radio frequency and video data collected from two commercial scanners are used to validate the feasibility of these proposed algorithms with porcine blood as the flowing medium in in vitro experiments. The results obtained by the proposed algorithms are in good agreement with those computed from the cross-correlation function     

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.     

A theoretical and experimental analysis of the received signal fromdisturbed blood flow

A theoretical and experimental study of the received ultrasonic signal from calibrated stenotic flow phantoms is presented. A finite element analysis of the velocity profile for 30, 50, and 80% stenoses provides a basis for the study of the experimental results. High-resolution images of the returned signal obtained from a unique experimental system and a high volume concentration of scatterers are then presented. The authors show that in the presence of 30 and 50% stenoses, particularly for the low velocities which would be associated with diastole, the duration of the signal correlation increases in a region which is distal to the stenosis and near the vessel walls, rather than the expected decrease. This results from the decrease in the mean velocity and velocity spread within this region. In the presence of high velocities associated with systolic flow, the magnitude of the reverse flow component increases as does the peak velocity in the center of the vessel. These changes produce an increase in the radial velocity gradient, a shift in the gradient peak, and a decrease in the correlated signal interval in comparison with laminar flow. Thus, the spatial variation in the mean velocity and velocity gradient, and spatial variation in the signal correlation can be used to detect the change in the flow profile     

Speckle decorrelation due to two-dimensional flow gradients

The performance of ultrasonic velocity estimation methods is degraded by speckle decorrelation, the change in received echoes over time. Because ultrasonic speckle is formed by the complex sum of echoes from subresolution scatterers, it is sensitive to the relative motion of those scatterers. Velocity gradients in flowing blood result in relative scatterer motion and can be a significant source of speckle decorrelation. Computer simulations were performed to evaluate speckle decorrelation due to two-dimensional flow gradients. Results indicate that decorrelation due to flow gradients is sensitive to the angle of flow and has a maximum at a beam-vessel angle of 0 degrees , i.e., purely axial flow. A quantitative summary of the major factors causing speckle decorrelation indicates that flow gradients are the most significant contributors under the conditions modeled.     

A 3-D PW ultrasonic Doppler flowmeter: theory and experimental characterization

A complete 3-D ultrasonic pulsed Doppler system has been developed to measure quantitatively the velocity vector field of a fluid flow independently of the probe position. The probe consists of four 2.5 MHz piezocomposite ultrasonic transducers (one central transmitter and three receivers separated by 120°) to measure the velocity projections along three different directions. The Doppler shift of the three channels is calculated by analog phase and quadrature demodulation, then digitally processed to extract the mean velocity from the complex spectrum. The accuracy of the 3-D Doppler technique has been tested on a moving string phantom providing an error of about 4% for both amplitude and direction with an acquisition window of 100 ms     

Three-dimensional vector flow estimation using two transducers andspectral width

Current ultrasonic blood flow measurement systems estimate only that component of flow which is parallel to the incident ultrasound beam. This is done by relating the mean backscattered frequency shift to the axial velocity component through the classical Doppler equation. A number of ultrasonic techniques for estimating the two-dimensional (2D) blood velocity vector have been published, both Doppler and non-Doppler. Several three-dimensional (3D) blood velocity vector techniques have also been proposed, all of which require a multiplicity of transducers or lines of sight. Here a technique is described for estimating the total velocity vector, using only two transducers. This is achieved by measuring not only the frequency shifts but also the bandwidths of the backscattered spectra, making use of the fact that the bandwidth of a Doppler spectrum has been shown to be proportional to the velocity component normal to the sound beam. Partial experimental verification of the proposed vector flow estimation scheme is demonstrated by using a constant velocity thread phantom     

Quantitative real-time blood flow estimation with intravascular ultrasound in the presence of in-plane flow

Previously, we showed a source of error in blood flow estimation introduced by in-plane flow using a slow-time finite-impulse response (FIR) filter-bank method measuring blood flow through the image plane of an intravascular ultrasound (IVUS) catheter array. There is a monotonic relationship between flow velocity and the normalized second moment of the slow-time spectrum when flow is orthogonal to the image plane of a side-looking catheter array. However, this relationship changes in the presence of in-plane flow, as slow-time spectra shift and spread with varying in-plane and out-of-plane components. These two effects increase the normalized spectral second moment, resulting in flow overestimates. However, by resampling the received signal with variable time delay from pulse to pulse (i.e., tilting the slow-time signals), the slow-time spectrum shifts back to direct current (DC), and the orthogonal estimation method can be used. We present a method to correct this overestimation and accurately estimate blood flow through the image plane in real time. Initially, the tilt delay needed to shift the slow-time spectrum back to DC at each point within the flow field is calculated. Knowing this tilt delay, a tilted slow-time signal is obtained for the velocity component normal to the image plane, and its spectrum is estimated using a filter-bank. That spectrum then is used to estimate the flow speed using a mapping function closely related to the monotonic relationship between the slow-time spectrum and flow speed observed for orthogonal flow. To accurately estimate flow angles, we modified the filter-bank algorithm, applying slow-time filter coefficients in a tilted arrangement and studying the slow-time spectral energy as a function of tilt. The slow-time spectral estimate is constructed with the tilted output of eight narrow, band-pass filters from a filter-bank. Independent simulations show that, for blood slowing at angles between +/-6 degrees and +/-15 degrees at a speed of 300 mm/s, flow velocity would be overestimated by as much as 38.79% and 249%, respectively, using the direct filter-bank approach. However, this error can be corrected using the modified method presented here, reducing the maximum overestimation error by a factor of 2.69 and 10.88 for those angles, respectively. Although the remaining error is not negligible, the volume flow rate, calculated by integrating the flow velocity over the entire vessel lumen, differs by only 3% or less from the true value over the angular range considered here. This represents an improvement of a factor of 40 over uncompensated estimates at maximum flow angles. Consequently, the modified real-time method can quantitatively measure flow in most IVUS applications in which the catheter's image plane is not precisely orthogonal to the flow direction.     

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.     

Finite element analysis of internal flows with heat transfer

This paper presents a finite element-based model for the prediction of 2-D and 3-D internal flow problems. The Eulerian velocity correction method is used which can render a fast finite element code comparable with the finite difference methods. Nine different models for turbulent flows are incorporated in the code. A modified wall function approach for solving the energy equation with high Reynolds number models is presented for the first time. This is an extension of the wall function approach of Benim and Zinser and the method is insensitive to initial approximation. The performance of the nine turbulent models is evaluated by solving flow through pipes. The code is used to predict various internal flows such as flow in the diffuser and flow in a ribbed channel. The same Eulerian velocity correction method is extended to predict the 3-D laminar flows in various ducts. The steady state results have been compared with benchmark solutions and the agreement appears to be good.     

Improving accuracy in estimation of artery-wall displacement by referring to center frequency of RF echo

Noninvasive measurement of mechanical properties, such as elasticity, of the arterial wall, is useful for diagnosis of atherosclerosis. The elasticity of the arterial wall can be estimated by combining measurement of displacement of the arterial wall with that of blood pressure. In general, the displacement of the arterial wall is estimated from the phase shift of radio frequency (RF) echoes between two consecutive frames using a correlation estimator with quadrature demodulated complex signals. Recently, digitized data of broadband RF echoes are available in modern diagnostic equipment. The Fourier transform can be used to estimate the phase of the RF echo at each frequency within the RF frequency bandwidth. Therefore, the phase shifts between RF echoes of two consecutive frames can be estimated at multiple frequencies. In this estimation, due to object displacement, the RF echo is time shifted in comparison with that of the previous frame. However, the position of the time window for the Fourier transform is not changed between two consecutive frames. This change in relative position between the RF echo and the time window has a strong influence on the estimation of the artery-wall displacement, resulting in error. To suppress this error, the phase shift should be estimated at the actual RF center frequency. In this paper, this error suppression was investigated through simulation experiments and in vivo experiments on the human carotid artery.     

Stable and unbiased flow turbulence estimation from pulse echo ultrasound

A new method for stable and unbiased flow turbulence estimation has been developed for medical ultrasonic color flow imaging. Conventional turbulence estimates from a finite number of transmitted pulses could be biased, unreliable, and erroneous. We found that a conventional method cannot provide quantitative estimates of variance of flow velocity. We propose a new approach for flow turbulence estimation that is based on analysis of the flow velocity vectors. The new method estimates the variance of the flow velocity and provides reliable estimates for flow turbulence. Numerical examples, computer simulations, and experiments using a flow phantom demonstrate that the new method can estimate variance of flow velocity accurately and without bias. This work also reports a complete derivation in the time domain for both unbiased velocity and turbulence estimations. The results include two velocity estimation equations agreeing with the 1-D and 2-D autocorrelation methods derived from the frequency domain. The results indicate that the new method for flow turbulence is particularly useful when the 2-D autocorrelation method is used for color flow imaging. The new method also appears to be able to detect low turbulence; therefore, it may be useful for diagnosing abnormalities such as minor stenoses and valvular jets.