Comparison of the performance of the RF cross correlation and doppler autocorrelation technique to estimate the mean velocity of simulated ultrasound signals

In pulsed Doppler systems the received RF (radio frequency) signal is multiplied by a quadrature reference signal and subsequently averaged over a short depth range to obtain a sample of the complex Doppler signal. The mean frequency of the sampled Doppler signal, obtained with the autocorrelation function, reflects the mean velocity of the scatterers moving through the sample volume. An alternative is to evaluate the two-dimensional cross correlation function of a short segment of the RF signals over subsequent lines, giving the mean velocity of the scatterers. Both methods of velocity estimation were applied to computer-generated RF signals with varying RF bandwidth, signal-to-noise ratio, and mean and width of the imposed velocity distribution. The length of the RF signal segment and the number of lines for velocity estimation (package length) affects the accuracy of the velocity estimate. It can be concluded that the cross correlation technique behaves superiorly especially for a low velocity dispersion. Furthermore, the standard deviation of the velocity estimate decreases for an increasing sample volume length and package length, while the performance of the conventional Doppler technique is rather independent of the length of the sample volume. The difference between both techniques decreases for a greater package length or for signals simulating a wide velocity distribution.     

Estimation of Doppler shift frequency using selected phase information for high frame rate color flow mapping

Purpose We describe a new approach to processing signals used to estimate the Doppler shift frequency in high frame-rate color flow mapping with fewer pulse transmissions. When an ultrasound pulse is transmitted to a large number of scatterers, the echoes from the scatterers overlap and interfere with one another. This interference causes the phase of the received echo signal to fluctuate, thus disturbing the estimated shift in Doppler frequency. The technique proposed here eliminates this disturbed phase information, leaving the remaining information for use in estimating the shift in Doppler frequency. The instantaneous frequency of the echo signal can serve as an index of the influence of interference.Methods To test this technique in vivo we used radio-frequency echo signals from the carotid artery for simulation and evaluated the error of the estimated Doppler shift frequency in several cases.Conclusion Performance was enhanced when the number of pulses transmitted was limited and this technique was used.This article is a translation of the original that was published in Jpn J Med Ultrasonics 2001;28:J15–23     

Nonstationarity broadening in pulsed Doppler spectrum measurements

Conventional measurement of the spectrum of arterial signals from the pulsed ultrasonic Doppler instrument uses windowed, sequential data segments. The Doppler signal is assumed stationary for the duration of each segment. It is shown here that this assumption is often unreasonable and the effect of mean frequency variation during the data segment has been investigated for different windows and rates of change of mean frequency. A data segment length giving maximum spectral resolution is shown to exist for each window type and rate of frequency change.     

An efficient algorithm to remove low frequency Doppler signals in digital Doppler systems.

In color flow imaging, a high flow map rate in combination with a reasonable width of the map and good velocity resolution is essential to properly appreciate the time-dependent phenomena. The velocity resolution depends on the length of the signal segment considered in combination with the settling time of the high pass filter used to eliminate transients and low frequency artifacts. The latter can be reduced by appropriate processing. This paper presents an algorithm to suppress low frequency Doppler signals effectively and efficiently, while all the data points within the segment considered contribute equally to the average Doppler frequency computed. The algorithm is applied to computer generated Doppler signals to evaluate their time and frequency behavior. It is concluded that the proposed scheme functions adequately under various signal conditions.     

Optimization of processing parameters for the analysis and detection of embolic signals.

The fast Fourier transform (FFT), which is employed by all commercially available ultrasonic systems, provides a time-frequency representation of Doppler ultrasonic signals obtained from blood flow. The FFT assumes that the signal is stationary within the analysis window. However, the presence of short duration embolic signals invalidates this assumption. For optimal detection of embolic signals if FFT is used for signal processing, it is important that the FFT parameters such as window size, window type, and required overlap ratio should be optimized. The effect of varying window type, window size and window overlap ratio were investigated for both simulated embolic signals, and recorded from patients with carotid artery stenosis. An optimal compromise is the use of a Hamming or Hanning window with a FFT size of 64 (8.9 ms) or 128 (17.9 ms). A high overlap ratio should also be employed in order not to miss embolic events occurring at the edges of analysis windows. The degree of overlap required will depend on the FFT size. The minimum overlap should be 65% for a 64-point window and 80% for a 128-point window.     

A simulation of transit time effects in Doppler ultrasound signals

A signal model is proposed which can be used to study frequency extraction techniques for Doppler ultrasound. The signal is based on the physics of the Doppler process and depends on a sliding window used to average a set of independent Gaussian random numbers. This window is related to the shape of the sample volume for the Doppler pulse and depends on the Doppler angle. Simulation results compare favorably with results from flow experiments in terms of the variance of the estimated Doppler shift, the shape of the power spectra and the behavior of the signals with respect to Burg autoregressive power spectra. A potential use of the signal in the study of spectral analysis techniques is presented.     

Improved assessment of intravascular Doppler coronary flow velocity profile

Easy and safe in- vivo flow velocity studies in small coronary arteries have become feasible using a 0.014 ‘ or 0.018 ’ guidewire with an integrated Doppler probe in its tip (FloWire, Cardiometrics). Assessment of the flow velocity profile by the ratio of diastolic to systolic flow velocity (DSVR) is used as a diagnostic parameter. However, DSVR is a coarse quantifier of the flow velocity profile, and is subject to large physiologic variance and depends crucially on the quality of the Doppler signal. The aim of our study was to test parameters derived from statistical time series analysis for monitoring the quality of the instantaneous peak velocity (IPV) signal. Improvement of quantification of changes in quality and shape of flow velocity profiles by these parameters as compared to DSVR was a second goal. We investigated analog-digital converted IPV- signals and video registrations of corresponding greyscale spectra of intracoronary Doppler flow velocity signals. The signals were analyzed by using the autocorrelation function (ACF) in the time domain and a fast Fourier transform (FFT) in the frequency domain (standard time series statistics). The first minimum of autocorrelation function turned out to be very sensitive to signal quality, and Fisher's g of the periodogram was the parameter of choice for shape analysis. In 11 patients with coronary artery disease, pre and post PTCA, the sensitivity of DSVR and signal to noise ratio to changes in shape and quality of the flow velocity signals was compared to that of the new parameters. Nineteen Doppler flow velocity samples of good quality from measurements in nonstenotic vessels and 7 flow velocity tracings with visible artefacts were used to assess the value of these parameters in monitoring signal quality. By comparison with corresponding parameters in use (SNR and DSVR) a significantly improved performance of the new statistical parameters was observed with respect to sensitivity to changes in signal quality and flow profile. In view of these results and because of the short calculation time of these variables they should be used for on-line quality control and analysis of flow velocity profiles.     

Modeling of Doppler signal considering sample volume and field distribution

The ultrasound Doppler amplitude spectrum for a single scatterer and the power spectrum for multiple scatterers were calculated in terms of the echo signal from scatterers crossing the sample volume, defined by the transmitted pulse and the diffracted field distribution for cw. The observation time for the Doppler signal is also considered. Statistical parameters such as mean and variance of the Doppler power spectrum are studied as continuous functions of the intersection angle between the beam axis and the flow direction, the pulse length and the viewing position. The derived equations are valid whether the transit time is governed by the pulse length, or beam geometry, or both. It is shown that the Doppler power spectra calculated by the proposed model and by the Doppler signal obtained from field theory are in good agreement. It is also shown that, when the Doppler signal broadening due to the transmitted pulse and beam geometry is constant without regard to the intersection angle, the degree of spread of the velocity distribution can be estimated from the variance of the Doppler power spectrum measured by the Doppler system once the intersection angle is known.     

A comparison method for mean frequency estimators for Doppler ultrasound.

Mean frequency estimators as used in pulsed Doppler ultrasound equipment should provide an accurate (quality) and consistent (robustness) estimate over a wide range of signal conditions. In a simplified signal model, the main parameters to consider are the noise level, mean frequency, bandwidth and power of both the Doppler signal and the stationary component over a given time window. It may be expected that one estimator for a given parameter combination exhibits a good performance while another estimator for the same parameter combination behaves poorly. To allow direct comparison between different types of frequency estimators, a method is introduced to evaluate the quality and robustness of estimators for a common signal space covering a wide range of realistic parameter combinations. The method is illustrated using three different mean frequency estimators: (1) a first order autoregressive estimator in combination with a stationary echo filter; (2) a second order autoregressive estimator; and (3) a complex linear regression estimator in combination with a stationary echo filter. It is concluded that, for the parameter combination considered, the complex linear regression estimator exhibits the best quality (low variance and bias of the estimate) and robustness (consistent quality for all parameter combinations).     

Microembolic signal description: a reappraisal based on a customized digital postprocessing system

The high variability in presence and signature of microembolic signals (MES), detected with transcranial Doppler sonography (TCD) in the middle cerebral artery (MCA), cannot be explained with the currently available published data. We applied customized postprocessing on the radiofrequency (RF) signal of a standard TCD system. The spatial resolution was on the order of 2 mm, depending only on the length of the ultrasound (US) burst emitted. The amplitude of clutter-filtered RF signals was color-coded and plotted as a function of time and depth (range 30 mm). Additionally, 128 point fast Fourier transforms (FFTs) (50% temporal overlap) were calculated, visualizing both the background Doppler spectrum and the MES. We evaluated 122 gaseous MES from two patients during cardiac surgery and 52 particulate MES from four patients after carotid endarterectomy. Both MES categories showed comparable properties: they appeared in the RF amplitude plot as rather straight lines of increased intensity, indicating that the velocity remained approximately the same while they passed the US beam. The velocity calculated from the amplitude plot never exceeded that of the background Doppler spectrum. Various "MES patterns" could be identified with respect to the depth range at which the MES were visible. A quarter of the gaseous MES changed their direction at a specific depth, suggesting that the MES entered a branch (e.g., an M2 artery or the anterior cerebral artery). In the FFT analysis, these MES contained both positive and negative frequencies. It is concluded that MES show consistent signature patterns in the amplitude-time plots and that the previously reported variability of MES appearance in conventional Doppler systems is an artefact caused by relatively large signal amplitudes and sample volumes.     

Spectral composition of Doppler signals.

The spectral content of the Doppler signal (as revealed by spectral analysis) provides useful diagnostic information about local hemodynamic conditions. Changes in these conditions are used to diagnose atherosclerotic lesions in arteries accessible to ultrasound. Extremely high frequencies, as found in and distal to a tight stenosis, indicate the presence of a jet, while Doppler signals with a wide bandwidth are related to regions with wide velocity ranges and/or disturbed flow patterns. However, the random interactions of the scatterers, the dimensions of the sample volume, the velocity of the scatterers and the method of signal processing used affect the displayed spectral composition of the Doppler signal. This article reviews the basic mechanisms and cautions the investigator against a quick and superficial interpretation of the results obtained without a proper appreciation of the random fluctuations due to the methods used to record and process the signals.     

Time domain formulation of pulse-Doppler ultrasound and blood velocity estimation by cross correlation

The Doppler effect is usually described as a frequency shift of the backscattered signals from moving targets with respect to the frequency transmitted. Recently, real-time blood flow imaging has become possible thanks to the development of a new velocity estimator based on phase-shift measurements of successive echoes. However, this method suffers from the well-known limitations of pulse-Doppler instruments. A new formulation is presented which describes the pulse-Doppler effect on the successive echoes from a cloud of moving targets as a progressive translation in time due to the displacement of the scatterers between two excitations. This approach allows us to generate efficiently computer-simulated data in order to evaluate accurately the various processing techniques. Furthermore, it leads to a novel class of velocity estimators in the time domain which measure the time shifts which are proportional to the local blood velocity. Among them, the cross correlation of the received rf signals turns out to be well suited. A local cross-correlation function is first calculated from a consecutive pair of range-gated echoes and the time shift is then determined by searching for the time position with the maximum correlation. The time-correlation technique is shown to provide accurate velocity profiles with broadband transducers. Moreover, the classical velocity limitation of pulse-Doppler is overcome because there is no ambiguity in measuring a time shift instead of a phase shift. These major advantages should make quantitative flow mapping possible and more reliable.     

原发性甲亢的高频及多普勒超声表现

目的　探讨高频及多普勒超声对原发性甲状腺机能亢进 (Graves病 )的诊断价值。方法　对 171例Graves病患者及 5 0例正常人行高频及多普勒超声检查 ,并结合T3、T4结果进行分析。结果　甲亢患者甲状腺三维径值及容积显著增大 ,与对照组比差异显著 (P <0 .0 5 ) ,腺体回声增粗增强 ,血流信号增多 ,甲状腺上动脉收缩期峰值流速及阻力指数增高 ,与血T3、T4升高呈正相关 (r =0 .91,γ值经假设检验P <0 .0 1)。结论　高频与多普勒超声结合在原发性甲亢诊断中有较高价值     

The Leicester Doppler Phantom—A Digital Electronic Phantom for Ultrasound Pulsed Doppler System Testing

Doppler flow and string phantoms have been used to assess the performance of ultrasound Doppler systems in terms of parameters such as sensitivity, velocity accuracy and sample volume registration. However, because of the nature of their construction, they cannot challenge the accuracy and repeatability of modern digital ultrasound systems or give objective measures of system performance. Electronic Doppler phantoms are able to make use of electronically generated test signals, which may be controlled precisely in terms of frequency, amplitude and timing. The Leicester Electronic Doppler Phantom uses modern digital signal processing methods and field programmable gate array technology to overcome some of the limitations of previously described electronic phantoms. In its present form, it is able to give quantitative graphical assessments of frequency response and range gate characteristics, as well as measures of dynamic range and velocity measurement accuracy. The use of direct acoustic coupling eliminates uncertainties caused by Doppler beam effects, such as intrinsic spectral broadening, but prevents their evaluation. (E-mail: john.gittins@uhl-tr.nhs.uk)     

Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity

In Doppler analysis, the power spectral density (PSD), which accounts for the axial velocity distribution of the blood scatterers, is estimated. The conventional spectral estimator is Welch's method, which suffers from frequency leakage at small observation window length. The performance of adaptive techniques such as blood power Capon (BPC) has been promising at the cost of higher computation complexity. Reducing the computational complexity while retaining the benefits of BPC would be necessary for real-time implementation. The purpose of the work described here was to investigate whether it is possible to decrease the computation load in BPC and still obtain acceptable results. The computation complexity in BPC is owing primarily to the matrix inversion required for computing the PSD estimate. We here propose the subspace blood power Capon technique, which employs a data covariance matrix with reduced number of rows in estimation of the weight vector. In maximum velocity estimation in the spectra, the signal noise slope intersection envelop estimator that makes use of the integrated power spectrum is employed. The evaluations are made based on both simulated and in vivo data. The results indicate that it is possible to reduce the order of complexity to almost 12.25% at the cost of 2.31% and 2.24% increases in the relative standard deviation and relative bias of the estimates. Moreover, the Wiener post-filter as a post-weighting factor, which will be multiplied by the final weight vector of the spectral estimator, estimates the power of the desired signal and the power of the interference plus noise to improve the contrast. The proposed estimator has exhibited a promising performance at beam-to-flow angles of 45°, 60° and 75°. Furthermore, the robust performance of the proposed estimator against variation in the flow rate is also documented.     

Tissue pulsatility imaging of cerebral vasoreactivity during hyperventilation

Tissue pulsatility imaging (TPI) is an ultrasonic technique that is being developed at the University of Washington to measure tissue displacement or strain as a result of blood flow over the cardiac and respiratory cycles. This technique is based in principle on plethysmography, an older nonultrasound technology for measuring expansion of a whole limb or body part due to perfusion. TPI adapts tissue Doppler signal processing methods to measure the "plethysmographic" signal from hundreds or thousands of sample volumes in an ultrasound image plane. This paper presents a feasibility study to determine if TPI can be used to assess cerebral vasoreactivity. Ultrasound data were collected transcranially through the temporal acoustic window from four subjects before, during and after voluntary hyperventilation. In each subject, decreases in tissue pulsatility during hyperventilation were observed that were statistically correlated with the subject's end-tidal CO2 measurements. (     

Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The current processing performed by commercial instruments to obtain the time-frequency representation (TFR) of pulsed-wave Doppler signals may not be adequate to characterize turbulent flow motions. The assessment of the intensity of turbulence is of high clinical importance and measuring high-frequency (small-scale) flow motions, using Doppler ultrasound (US), is a difficult problem that has been studied very little. The objective was to optimize the performance of the spectrogram (SPEC), autoregressive modeling (AR), Choi-Williams distribution (CWD), Choi-Williams reduced interference distribution (CW-RID), Bessel distribution (BD), and matching pursuit method (MP) for mean velocity waveform estimation and turbulence detection. The intensity of turbulence was measured from the fluctuations of the Doppler mean velocity obtained from a simulation model under pulsatile flow. The Kolmogorov spectrum, which is used to determine the frequency of the fluctuations and, thus, the scale of the turbulent motions, was also computed for each method. The best set of parameters for each TFR method was determined by minimizing the error of the absolute frequency fluctuations and Kolmogorov spectral bandwidth measured from the simulated and computed Doppler spectra. The results showed that different parameters must be used for each method to minimize the velocity variance of the estimator, to optimize the detection of the turbulent frequency fluctuations, and to estimate the Kolmogorov spectrum. To minimize the variance and to measure the absolute turbulent frequency fluctuations, four methods provided similar results: SPEC (10-ms sine-cosine windows), AR (10-ms rectangular windows, model order = 8), CWD (w(N) and w(M) = 10-ms rectangular windows, sigma = 0.01), and BD (w(N) = 10-ms rectangular windows, alpha = 16). The velocity variance in the absence of turbulence was on the order of 0.04 m/s (coefficient of variation ranging from 8.0% to 14.5%, depending on the method). With these spectral techniques, the peak of the turbulence intensity was adequately estimated (velocity bias < 0.01 m/s). To track the frequency of turbulence, the best method was BD (w(N) = 2-ms rectangular windows, alpha = 2). The bias in the estimate of the -10 dB bandwidth of the Kolmogorov spectrum was 354 +/- 51 Hz in the absence of turbulence (the true bandwidth should be 0 Hz), and -193 +/- 371 Hz with turbulence (the simulated -10-dB bandwidth was estimated at 1256 Hz instead of 1449 Hz). In conclusion, several TFR methods can be used to measure the magnitude of the turbulent fluctuations. To track eddies ranging from large vortex to small turbulent fluctuations (wide Kolmogorov spectrum), the Bessel distribution with appropriate set of parameters is recommended.     

Listening to the Cochlea With High-Frequency Ultrasound

We have developed a high-frequency pulsed-wave Doppler ultrasound probe as a promising minimally-invasive technique for measuring intracochlear mechanics without damaging the cochlea. Using a custom high-frequency ultrasound system, we have measured dynamic motion of intracochlear structures by recording the pulsed-wave Doppler signal resulting from the vibration of the basilar and round window membranes. A 45 MHz needle-mounted Doppler probe was fabricated and placed against the round window membranes of eight different fresh human temporal bones. Pulsed-wave ultrasonic Doppler measurements were performed on the basilar membrane and round window membrane during the application of pure tones to the external ear canal. Doppler vibrational information for acoustic input frequencies ranging from 100–2000 Hz was collected and normalized to the sound pressure in the ear canal. The middle ear resonance, located at approximately 1000 Hz, could be characterized from the membrane velocities, which agreed well with literature values. The maximum normalized mean velocity of the round window and the basilar membrane were 180 μm/s/Pa and 27 μm/s/Pa at 800 Hz. The mean phase difference between the membrane displacements and the applied ear canal sound pressure showed a flat response almost up to 500 Hz where it began to accumulate. This is the first study that reports the application of high frequency pulsed wave Doppler ultrasound for measuring the vibration of basilar membrane through the round window. Since it is not required to open or damage the cochlea, this technique might be applicable for investigating cochlear dynamics, in vivo.     

血流切变率的多普勒估计方法

目的：研究血液动力学的一个重要参数—血流剪切率。方法：本文提出了一种利用超声多普勒技术估计血流剪切率的方法，这种方法先估计多普勒信号的平均频率曲线和最大频率曲线，然后计算血流的速度剖面，最后得到时变的血流剪切率。结果：文中还给出这方面研究的实验及结果。结论：本文提出的方法是无损估计血流剪切率的有效方法。     

Improved transverse flow estimation using differential maximum Doppler frequency

Conventional Doppler technique can only provide the axial component of the blood flow vector, which is actually a three dimensional (3-D) quantity. To acquire the complete flow vector, estimations of the other two velocity components are essential. For the two dimensional (2-D) Doppler-bandwidth-based transverse estimation, however, accuracy is generally limited because of the complex dependence of the Doppler spectral shape on the flow variation within the sample volume. Two factors that may lead to the Doppler spectral change were considered in this study. One is the position offset of the sample volume and the other is the length of the sample volume. Simulations were performed and experimental data were also collected. Results indicate that the position offset may result in severe underestimation of Doppler shift frequency. Consequently, Doppler bandwidth is overestimated when it is determined by the difference between Doppler shift frequency and maximum Doppler frequency. Compared with the position offset, influence of the length of sample volume on the Doppler bandwidth is minor. To overcome this problem, a novel method, which is based on the differential maximum Doppler frequency, is proposed. Specifically, two beams with different beam widths are simultaneously generated to observe the blood flow and the difference between the corresponding maximum Doppler frequencies is used to estimate the transverse velocity. It is demonstrated that the accuracy and stability of transverse estimation are significantly improved by the proposed method even when the position offset is present.