Spectral Doppler estimation utilizing 2-D spatial information and adaptive signal processing

The trade-off between temporal and spectral resolution in conventional pulsed wave (PW) Doppler may limit duplex/triplex quality and the depiction of rapid flow events. It is therefore desirable to reduce the required observation window (OW) of the Doppler signal while preserving the frequency resolution. This work investigates how the required observation time can be reduced by adaptive spectral estimation utilizing 2-D spatial information obtained by parallel receive beamforming. Four adaptive estimation techniques were investigated, the power spectral Capon (PSC) method, the amplitude and phase estimation (APES) technique, multiple signal classification (MUSIC), and a projection-based version of the Capon technique. By averaging radially and laterally, the required covariance matrix could successfully be estimated without temporal averaging. Useful PW spectra of high resolution and contrast could be generated from ensembles corresponding to those used in color flow imaging (CFI; OW = 10). For a given OW, the frequency resolution could be increased compared with the Welch approach, in cases in which the transit time was higher or comparable to the observation time. In such cases, using short or long pulses with unfocused or focused transmit, an increase in temporal resolution of up to 4 to 6 times could be obtained in in vivo examples. It was further shown that by using adaptive signal processing, velocity spectra may be generated without high-pass filtering the Doppler signal. With the proposed approach, spectra retrospectively calculated from CFI may become useful for unfocused as well as focused imaging. This application may provide new clinical information by inspection of velocity spectra simultaneously from several spatial locations.     

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.     

Ultrafast compound Doppler imaging: providing full blood flow characterization

Doppler-based flow analysis methods require acquisition of ultrasound data at high spatio-temporal sampling rates. These rates represent a major technical challenge for ultrasound systems because a compromise between spatial and temporal resolution must be made in conventional approaches. Consequently, ultrasound scanners can either provide full quantitative Doppler information on a limited sample volume (spectral Doppler), or averaged Doppler velocity and/or power estimation on a large region of interest (Doppler flow imaging). In this work, we investigate a different strategy for acquiring Doppler information that can overcome the limitations of the existing Doppler modes by significantly reducing the required acquisition time. This technique is called ultrafast compound Doppler imaging and is based on the following concept: instead of successively insonifying the medium with focused beams, several tilted plane waves are sent into the medium and the backscattered signals are coherently summed to produce high-resolution ultrasound images. We demonstrate that this strategy allows reduction of the acquisition time by a factor of up to of 16 while keeping the same Doppler performance. Depending on the application, different directions to increase performance of Doppler analysis are proposed and the improvement is quantified: the ultrafast compound Doppler method allows faster acquisition frame rates for high-velocity flow imaging, or very high sensitivity for low-flow applications. Full quantitative Doppler flow analysis can be performed on a large region of interest, leading to much more information and improved functionality for the physician. By leveraging the recent emergence of ultrafast parallel beamforming systems, this paper demonstrates that breakthrough performances in flow analysis can be reached using this concept of ultrafast compound Doppler.     

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     

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     

Spectrum of Doppler ultrasound signals from nonstationary blood flow

A new formulation for the Doppler signal generation process in pulsatile flow has been developed enabling easier identification and quantification of the mechanisms involved in spectral broadening and the development of a simple estimation formula for the measured rms spectral width. The accuracy of the estimation formula was tested by comparing it with the spectral widths found by using conventional spectral estimation on simulated Doppler signals from pulsatile flow. The influence of acceleration, sample volume size, and time window duration on the Doppler spectral width was investigated for flow with blunt and parabolic velocity profiles passing through Gaussian-shaped sample volumes. Our results show that, for short duration windows, the spectral width is dominated by window broadening and that acceleration has a small effect on the spectral width. For long duration windows, the effect of acceleration must be taken into account. The size of the sample volume affects the spectral width of the Doppler signal in two ways: by intrinsic broadening and by the range of velocities passing through it. These effects act in opposite directions. The simple spectral width estimation formula was shown to have excellent agreement with widths calculated using the model and indicates the potential for correcting not only for window and nonstationarity broadening but also for intrinsic broadening.     

Position dependent velocity profiles in granular avalanches

We present velocity profile measurements in granular avalanches flowing down a flat chute with wide rectangular cross section. The flow is recorded through a transparent side-wall by a high-speed camera, which is able to capture 1,825 pictures in a second. Due to the high frame rate of the camera, several flow features can be observed. Quantitative statements can be made by analysing the images with a pattern matching algorithm. This provides us with flow-normal velocity profiles with a very high temporal and spatial resolution. We find that even on flat surfaces, velocity profiles are strongly changing through the flow and for the range of investigated chute angles (from 26° to 36°) clear trends can be recognised. In the head of the avalanche the velocity is highest, decreasing continuously over the length of the avalanche. Thus, the investigated granular avalanches stretch through the flow. The experimental method allows us to study the evolution of characteristic flow properties such as depth averaged velocity, slip velocity, surface velocity, shear rates or flow depth. Side-wall friction effects are estimated.     

Ultrasound methods for investigating the non-Newtoniancharacteristics of whole blood

The development and evaluation of new techniques for investigating the non-Newtonian characteristics of blood are described. Ultrasound B-mode imaging (7 MHz) was used to measure simultaneously the echogenicity and velocity profiles of 28% hematocrit porcine whole blood. Measurements were made at various locations in a large diameter (D=2.54 cm) long (>60 D) tube, under steady flow conditions. A block matching (correlation) technique between successive digitized images was used to determine the velocity profiles, and from these, shear rate profiles were calculated. The optimal block dimensions were found to be dependent on the magnitude and direction of the flow shear rate. Echogenicity profiles were determined from ensemble averaged images. It is shown how such profiles in combination with the corresponding shear rate profiles enables information to be obtained concerning the dependence of aggregation on shear rate. Pulsed Doppler ultrasound (20 MHz) was also used to measure the velocity and backscattered power profiles at 60 D from the tube entrance. Velocity profiles measured using B-mode were in good agreement with those obtained using both pulsed Doppler and magnetic resonance imaging and mean velocity errors of less that 5% were achieved     

Experimental evaluation of intrinsic and nonstationary ultrasonic Doppler spectral broadening in steady and pulsatile flow loop models

Intrinsic and nonstationary Doppler spectral broadening, and the skewness of the spectral representation, were evaluated experimentally using porcine red cell suspensions as ultrasonic scatterers. Theoretically, the relative Doppler bandwidth, defined as the intrinsic bandwidth divided by the mean Doppler frequency shift, should be velocity independent. The relative Doppler bandwidth invariance theorem was experimentally verified with an in vitro steady laminar blood flow model. It is shown that the relative bandwidth is both independent of the flow velocity and blood hematocrit. Using a pulsatile laminar flow model, the authors demonstrated that the relative Doppler bandwidth invariance theorem did not hold during flow acceleration and deceleration. In addition, a positive skewness of the Doppler spectra was observed during acceleration while a negative skewness was measured during the deceleration of blood. The effect of the window duration used in the Fourier spectral computation, on nonstationary broadening, is characterized.     

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。     

Experimental proof of Doppler bandwidth invariance

A line flow of scatterers crossing the sound field produced by a focused circular transducer at uniform velocity originates a quasi-triangular Doppler spectrum. It is known that the spectrum shape and width depend on the line flow to beam axis angle, as well as on the transducer geometry. It has recently been theoretically predicted that this spectrum width is independent of the flow line location in the sound field. Experimental verification of the new theorem, based on the use of a thread phantom operated at various orientations, ranges, and offsets, with respect to the ultrasound transducer, is presented. The tests were made with a computerized pulsed Doppler system designed to perform optimal real-time spectral analysis of data obtained in this application. The prototype system and the experimental procedure adopted for demonstrating in vitro the invariance of the Doppler spectral bandwidth are described.     

Electro-optically modulated polarizing Fourier-transform spectrometer for plasma spectroscopy applications

A new electro-optically modulated optical solid-state (MOSS) interferometer has been constructed for measurement of quantities related to the low-order spectral moments of line emission from optically thin radiant media such as plasmas. When Doppler broadening is dominant, the spectral moments give the Radon transform of corresponding moments of the velocity distribution function of the radiating species. The instrument, which is based on the principle of the Fourier-transform spectrometer, has high etendue and is rugged and compact. When electro-optical path-length modulation techniques are employed, the spectral information is encoded in the temporal frequency domain at harmonics of the modulation frequency and can be obtained by use of a single photodetector. Specifically, for a plasma in drifting local thermodynamic equilibrium the zeroth moment (brightness) is given by the average signal level, the first moment (shift) by the interferometric phase, and the second moment (linewidth) by the fringe visibility. To illustrate the MOSS performance, I present spectroscopic measurements of the time evolution of the plasma ion temperature and flow velocity for rf-heated discharges in the H-1 heliac, a toroidal plasma magnetic confinement at the Australian National University.     

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     

Target velocity estimation with FM and PW echo ranging Doppler systems. II. Systems analysis

For part I see ibid., vol.40, no.4, pp.366-372 (1993). In Part I, the encoding of the velocity and range information into the received and demodulated signals based on transmission of coherent repetitive linear sweep signals, was discussed. In the present work, two different implementations of FM Doppler systems that can be used to obtain velocity profiles are presented. The first implementation is similar to the implementation of a conventional pulsed wave (PW) Doppler system, based on measurement of phase shift (correlation based system): the second implementation is a frequency-domain analog to the PW Doppler system, based on time shift measurements (cross correlation-based system).     

Adaptive spectral doppler estimation

In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to provide good spectral resolution and contrast even when the observation window is very short. The 2 adaptive techniques are tested and compared with the averaged periodogram (Welch's method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set of matched filters (one for each velocity component of interest) and filtering the blood process over slow-time and averaging over depth to find the PSD. The methods are tested using various experiments and simulations. First, controlled flow-rig experiments with steady laminar flow are carried out. Simulations in Field II for pulsating flow resembling the femoral artery are also analyzed. The simulations are followed by in vivo measurement on the common carotid artery. In all simulations and experiments it was concluded that the adaptive methods display superior performance for short observation windows compared with the averaged periodogram. Computational costs and implementation details are also discussed.     

Real-time measurements of spatial velocity distribution with a laser Doppler imaging system

A new laser Doppler imaging system with a TV camera has been constructed, which brightly displays 1-D velocity distribution on a monitor. Some characteristics of this system have been experimentally investigated from measurements of simple velocity distribution on a constantly rotating ground glass disk. From an adaptation to fluid flow, it has been shown that the measurements of spatial velocity distribution can be achieved in real time.     

Determination of the axial velocity component by a laser-Doppler velocity profile sensor

We report about the determination of the axial velocity component by a laser Doppler velocity profile sensor that is based on two superposed fanlike interference fringe systems. Evaluation of the ratio of the Doppler frequencies obtained from each fringe system yields the lateral velocity component and the axial position inside the fringe system. Inclined particle trajectories result in chirped burst signals, where the change of the Doppler frequency in one burst signal is directly related to the axial velocity component. For one single tracer particle it is possible to determine (i) the lateral velocity component, (ii) the axial velocity component including the direction, and (iii) the axial position of the tracer trajectory. In this paper we present the measurement principle and report about results from simulation and experiments. An uncertainty of the axial velocity component of about 3% and a spatial resolution in the micrometer range were achieved. Possible applications of the sensor lie in three-component velocity measurements of flow fields where only one optical access is available.     

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.     

High-speed video recording of basal shear layers in snow chute flows

Run-out distances and flow velocities of snow avalanches are mainly determined by frictional processes originating from the interaction with the ground. At the SLF snow chute at the Weissfluhjoch near Davos, a setup was developed which allowed us to record high-speed movies of the basal shear layer of small-scale avalanches with a frame rate of 1000 frames per second. Shear processes could be observed in high-resolution slow motion. Downstream velocity profiles were extracted by a pattern matching algorithm. The comparison of computed profiles with velocity profiles obtained from optical sensors showed good agreement. However, the temporal and spatial resolutions are much higher for the high-speed video data. Because the optical velocity sensors are one-dimensional, we found that they overestimate the velocities when a flow-normal velocity component exists as well. All measured velocity profiles exhibited very high shear rates near the ground. The maximum shear rates were up to 600/s for dry snow and 200/s for wet snow avalanches. The observations of the video images suggested a turbulent motion of the snow in the basal shear layer.     

Setup and Test of a Laser Doppler Velocimeter for Investigations of Flow Behaviour of Polymer Melts

The flow behaviour of a low-density polyethylene melt is investigated in a specifically developed flow channel by means of Laser Doppler Velocimetry (LDV). The used flow channel is a slit die with a planar contraction of 14:1. The investigation of the velocity fields was performed in the steady state of flow. The optics of the LDV system as well as the used frequency analyser proved to be reliable for measurements of velocities down to 250μm/s. By adding TiO₂ tracer particles to the pellets the signal quality as well as the signal frequency were improved. It is demonstrated that the Laser Doppler Velocimeter is suited to detect velocities of polymer melts with an error of a few per cent by comparing the measured volume flow rate to the directly determined mass flow rate. Using simple fluid mechanics the viscosity function is obtained by measuring only one velocity profile within the fully developed flow in the slit die. Over a wide range of shear rates the viscosity function obtained via LDV measurement corresponds with the viscosity function which was determined by the classical mass-flow-rate method. Both resulting viscosity functions were additionally checked by performing measurements with a capillary rheometer. The LDV setup described in this paper is a powerful experimental tool to investigate the flow behaviour of polymer melts. Its accuracy and the high spatial and temporal resolution opens a way to get more quantitative insight into the flow of polymer melts and to check the validity of model calculations. This revised version was published online in August 2006 with corrections to the Cover Date.