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.     

Doppler angle and flow velocity estimations using the classic and transverse Doppler effects

Current clinical Doppler ultrasound systems could only measure the flow vector parallel to the ultrasound beam axis, and the knowledge of the Doppler angle (beam-to-flow angle) is needed to calculate the real flow velocity. Currently, the Doppler angle is determined visually by manually aligning a vessel axis marker along the blood vessel on the duplex scan image of the ultrasound. The application of this procedure is often limited by practical constraints; therefore, measurements are not reliable. In order to overcome this problem, the authors developed a simple Doppler angle and flow velocity estimation method using a combination of the classic and transverse Doppler effects. This method uses only a single focused annular array transducer to estimate the Doppler angle and the flow velocity. The authors have verified experimentally that this method is successful for measuring constant flow in a flow phantom between 45 degrees and 80 degrees Doppler angle. The standard deviation of the estimated Doppler angles is less than 4.5 degrees . This method could be implemented easily in medical Doppler ultrasound systems to automatically estimate the Doppler angle and the flow velocity.     

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     

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.     

A swept-scanning mode for estimation of blood velocity in the microvasculature

In contrast to previous systems in which an ultrasonic pulse was repeatedly directed to a discrete line of sight, a new method has been developed to continuously scan over a region in order to rapidly assess blood velocities in superficial small blood vessels. Using this technique, which we call swept-scan, a high frequency transducer can rapidly translate across a region of interest, and sensitive maps of blood velocity in small blood vessels can be constructed. This system has been applied to flow mapping in the anterior segment of the eye, which is clinically significant in cases of trauma and glaucoma. No previous imaging technique has been capable of estimating blood velocities within this region in a clinically useful manner. With this new technique, each 2-D scan of the eye can be obtained in an interval on the order of 1 second, and blood flow through the iris and ciliary body can be detected in vessels as small as 40 microns. A major implication of this new technique is that a wall filter can be applied continuously to the return from all regions, thus eliminating the transient response that occurs along each line of sight in traditional Doppler systems.     

Doppler angle estimation using AR modeling

The transit time spectrum broadening effect has long been explored for Doppler angle estimation. Given acoustic beam geometry, the Doppler angle can be derived based on the mean Doppler frequency and the Doppler bandwidth. Spectral estimators based on the fast Fourier transform (FFT) are typically used. One problem with this approach is that a long data acquisition time is required to achieve adequate spectral resolution, with typically 32-128 flow samples being needed. This makes the method unsuitable for real-time two-dimensional Doppler imaging. This paper proposes using an autoregressive (AR) model to obtain the Doppler spectrum using a small number (e.g., eight) of flow samples. The flow samples are properly selected, then extrapolated to ensure adequate spectral resolution. Because only a small number of samples are used, the data acquisition time is significantly reduced and real-time, two-dimensional Doppler angle estimation becomes feasible. The approach was evaluated using both simulated and experimental data. Flows with various degrees of velocity gradient were simulated, with the Doppler angle ranging from 20° to 75°. The results indicate that the AR method generally provided accurate Doppler bandwidth estimates. In addition, the AR method outperformed the FFT method at smaller Doppler angles. The experimental data for Doppler angles, ranging from 33° to 72°, showed that the AR method using only eight flow samples had an average estimation error of 3.6°, which compares favorably to the average error of 4.7° for the FFT method using 64 flow samples. Because accurate estimates can be obtained using a small number of flow samples, it is concluded that real-time, two-dimensional estimation of the Doppler angle over a wide range of angles is possible using the AR method     

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.     

单边狭窄血管中超声多普勒信号的仿真研究

超声多普勒技术作为一种无损检测手段被广泛应用于血管狭窄的检测。以往的血管狭窄仿真信号的研究仅限于双边狭窄的对称情况,文章提出了一种单边狭窄血管中超声多普勒信号的仿真方法。首先用有限元分析方法(FEM)计算出狭窄血管中血流流速场分布情况,然后用总体分布非参数估计法计算出超声多普勒信号的功率谱密度(PSD),再用余弦叠加法获取仿真的超声多普勒时域信号。用快速傅里叶变换(FFT)计算仿真超声多普勒信号的频谱,从中计算最大频率、平均频率和频谱宽度等参数,分析它们在不同流速和狭窄程度下的特征,为血管疾病的诊断提供敏感的参数。     

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 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     

A new adaptive mean frequency estimator: application to constant variance color flow mapping

A class of adapted mean frequency estimators is proposed for color flow mapping. These estimators can be fitted to the specific characteristics of a given Doppler signal to optimize the compromise between the range of analysable frequencies and the variance of mean frequency estimation. A sub-optimal estimator is derived for real-time applications, and an adaptive criterion based on the Doppler signal variance is developed for color flow mapping applications. Its performance is compared to that of the usual correlation phase estimator on simulated Doppler signals and on synthetic Doppler images. An improvement in image quality is achieved, mainly for low signal-to-noise ratio Doppler signals.     

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.     

A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection

We present a new signal processing strategy for high frequency color flow mapping in moving tissue environments. A new application of an eigendecomposition-based clutter rejection filter is presented with modifications to deal with high blood-to-clutter ratios (BCR). Additionally, a new method for correcting blood velocity estimates with an estimated tissue motion profile is detailed. The performance of the clutter filter and velocity estimation strategies is quantified using a new swept-scan signal model. In vivo color flow images are presented to illustrate the potential of the system for mapping blood flow in the microcirculation with external tissue motion.     

A new high resolution color flow system using an eigendecomposition-based adaptive filter for clutter rejection

We present a new signal processing strategy for high frequency color flow mapping in moving tissue environments. A new application of an eigendecomposition-based clutter rejection filter is presented with modifications to deal with high blood-to-clutter ratios (BCR). Additionally, a new method for correcting blood velocity estimates with an estimated tissue motion profile is detailed. The performance of the clutter filter and velocity estimation strategies is quantified using a new swept-scan signal model. In vivo color flow images are presented to illustrate the potential of the system for mapping blood flow in the microcirculation with external tissue motion.     

Estimation of a dense velocity field based on the statistics of dynamic speckle

This article presents a new technique for flow velocity estimation from ultrasound image sequences. The method is based on the analysis of the temporal statistics of the speckle pattern in motion. We demonstrate that the biased local temporal variance (LTV) of a single pixel within an image of dynamic speckle is related to velocity. This allows us to estimate the total velocity magnitude without the requirement of neither block matching nor autocovariance estimation. A new estimator, asymptotically without bias, called LTV is presented. Results conducted on experimental B mode sequences (40 MHz) of blood mimicking fluid with calibrated velocities are presented. Performances of the estimator are studied and results show good agreement with the statistical model. Magnitude of the 3D velocity vector in the range of 0.1–2 mm/s have been estimated with a standard deviation error of less than 12%. The validity of the method and its limitations are then discussed. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 268‐276, 2010     

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.     

Decision-directed channel estimation based on iterative linear minimum mean square error for orthogonal frequency division multiplexing systems

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.     

Doppler angle estimation using correlation

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