Doppler angle estimation of pulsatile flows using AR modeling

In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 3o degrees to 78 degrees) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50 degrees compared to an average error of 7.08 degrees for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.     

A real-time autoregressive spectrum analyzer for Doppler ultrasound signals

A system based on a digital signal processor and a microcomputer has been programmed to estimate the maximum entropy autoregressive (AR) power spectrum of ultrasonic Doppler shift signals and display the results in the form of a sonogram in real-time on a computer screen. The system, which is based on a TMS 320C25 digital signal processor chip, calculates spectra with 128 frequency components from 64 samples of the Doppler signal. The samples are collected at a programmable rate of up to 40.96 kHz, and the computation of each spectrum takes typically 3.2 ms. The feasibility of on-line AR spectral estimation makes this type of analysis an attractive alternative to the more conventional fast Fourier transform approach to the analysis of Doppler ultrasound signals.     

Multigate doppler signal analysis using 3-D regularized long AR modelling.

Autoregressive (AR) modelling has already been proposed as an alternative to fast Fourier transform to process ultrasound (US) Doppler signals. Previous works introduced long AR models, set up under a regularization framework. The latter may be in 1-D (frequency) or 2-D (frequency and space or time). This study generalizes the spectrum regularization in the three dimensions frequency, space and time. The problem of the penalization function is addressed, and a new convex solution is proposed, taking into account possible nonstationarity of the Doppler signal. The parameter tuning is based on simulations using a standard Doppler signal model. The first results show that this processing improves the spectral estimation, and is well suited to flow interpretation.     

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.     

A new method of encoding and displaying audio Doppler-shift signals: the chromagram

A technique based on chromaticity is described for processing and displaying audio Doppler-shift signals. A chromaticity vector is derived for a fixed time interval (e.g. 5 ms) of the input Doppler signal, which is directly related to the Fourier power spectrum distribution of that signal over that interval. An approximated approach is then described for implementing the above "chromagraphic analysis" in order to meet Doppler ultrasound real-time requirements. A static and dynamic chromagram display format is defined which enables the chromaticity information to be displayed in colour on a digital television monitor.     

Sizing gaseous emboli using Doppler embolic signal intensity

Extension of transcranial Doppler embolus detection to estimation of bubble size has historically been hindered by difficulties in applying scattering theory to the interpretation of clinical data. This article presents a simplified approach to the sizing of air emboli based on analysis of Doppler embolic signal intensity, by using an approximation to the full scattering theory that can be solved to estimate embolus size. Tests using simulated emboli show that our algorithm is theoretically capable of sizing 90% of "emboli" to within 10% of their true radius. In vitro tests show that 69% of emboli can be sized to within 20% of their true value under ideal conditions, which reduces to 30% of emboli if the beam and vessel are severely misaligned. Our results demonstrate that estimation of bubble size during clinical monitoring could be used to distinguish benign microbubbles from potentially harmful macrobubbles during intraoperative clinical monitoring.     

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.     

Estimation of the Doppler ultrasound maximal umbilical waveform envelope: I. Estimation method

We developed a parametric method of estimating the Doppler ultrasound (US) umbilical maximal flow waveform envelope that is robust to varying levels of signal-to-noise ratio (SNR). The method differs from previously proposed estimation algorithms in that it does not incorporate preliminary removal or reduction of noise; thus, avoiding potential resulting biases. Instead, we relied on a multiple time series interpretation that facilitates a regression approach. The maximal waveform shape was assumed to take the form of a periodic series of gamma functions with a hidden baseline that is typically not reached on the downward diastolic phase before the flow increases to the systolic peak. The waveform shape is fitted via optimisation of the cross correlation of the Doppler signal and a periodic reference function locating the cardiac cycles within the blood flow image. Starting values for the iterative optimisation process were obtained using nonstandard least squares regression. Assessments of the fit of the model to waveform data were carried out through visual inspection. In 7 of 327 images analysed (2.1%), there appeared to be some discrepancy between the waveform shape and the gamma waveform envelope, such as variations in systolic or diastolic flows. Modification of the estimation procedure to incorporate blood flow cycles of slightly different lengths and use of other functional forms may improve the fit for waveforms for which the gamma fit is poor. The method has been developed with special reference to umbilical blood flow images, but it can be used directly to model blood flow in other low-resistance vessels or adapted for other vessels with different shape characteristics.     

Measurement accuracy of the flow velocity in pulsed ultrasound Doppler velocimeter

This paper presents a numerical simulation method for evaluating the measurement accuracy of the high-frequency pulsed ultrasound Doppler velocimeter (PUDV). The frequency distribution of the Doppler signal from a sample volume is calculated by dividing the sample volume into small cells and using the statistics of the velocities of the cells. The distribution is used to analyze the accuracy of the poststenotic velocity measurements of a 20-MHz 80-channel PUDV. The target flow field is obtained by solving Navier-Stokes equations numerically. It was shown that the velocities evaluated by the zero-cross and Fourier transform methods agreed well with the given velocities, and that flow separation was successfully detected. It was also shown that the tube diameter should be at least twice as large as the diameter of the sample volume to obtain accurate measurements.     

A feasability study of color flow doppler vectorization for automated blood flow monitoring

An ongoing issue in vascular medicine is the measure of the blood flow. Catheterization remains the gold standard measurement method, although non-invasive techniques are an area of intense research. We hereby present a computational method for real-time measurement of the blood flow from color flow Doppler data, with a focus on simplicity and monitoring instead of diagnostics. We then analyze the performance of a proof-of-principle software implementation. We imagined a geometrical model geared towards blood flow computation from a color flow Doppler signal, and we developed a software implementation requiring only a standard diagnostic ultrasound device. Detection performance was evaluated by computing flow and its determinants (flow speed, vessel area, and ultrasound beam angle of incidence) on purposely designed synthetic and phantom-based arterial flow simulations. Flow was appropriately detected in all cases. Errors on synthetic images ranged from nonexistent to substantial depending on experimental conditions. Mean errors on measurements from our phantom flow simulation ranged from 1.2 to 40.2% for angle estimation, and from 3.2 to 25.3% for real-time flow estimation. This study is a proof of concept showing that accurate measurement can be done from automated color flow Doppler signal extraction, providing the industry the opportunity for further optimization using raw ultrasound data.     

Spectrogram enhancement algorithm: a soft thresholding-based approach.

Enhancing the spectrogram by denoising the Doppler ultrasound signal is a preliminary step, and important for further processing. Because the spectrogram may be based on the short-time fast Fourier transform (FFT) of the Doppler ultrasound signal, whose power spectrum density is time-varying, traditional denoising algorithms that simply optimize the mean-squared error are not appropriate, and they may exhibit considerable undesirable, noise-induced frequency components. A soft thresholding-based denoising algorithm is put forward in this paper, that achieves almost the minimax mean square error (MSE) over a wide range of function classes having norms measuring smoothness (i.e., it meets both the requirement of smoothness and MSE). Due to the importance of noise level estimation while applying this method, several robust L-estimators are compared and the median absolute deviation (MAD) method is chosen to estimate the noise level. The simulation study shows better performance of the later algorithm under various quantification measures, compared to the FFT thresholding and the hard thresholding wavelet method, and the results of clinical data also confirm it.     

Parametric spectral analysis of umbilical artery doppler signals for fetal heart rate variability evaluation

Objective: To improve the measurement resolution of the fetal heart rate (FHR) beat-to-beat variation, which is an important prognostic indicator of fetal well-being. Method: The goal was reached using an autoregressive (AR) approach, instead of conventional algorithms based on the Fast Fourier Transform (FFT), for the analysis of the umbilical artery Doppler signals. Results: The resolution improvement obtainable with the proposed technique in the FHR beat-to-beat variation was proved both with simulation and with experimental results. The method was implemented in a personal computer (PC) based equipment which works in a quasi-real time mode. Conclusions: The proposed technique can be usefully applied to the FHR beat-to-beat variation measurements; the developed prototype is at present used for clinical practice at the ^cClinica Ostetrica e Ginecologica' of the University of Firenze.     

Comparison of four digital maximum frequency estimators for Doppler ultrasound

The performance of four methods for digitally estimating the maximum frequency waveform from the Doppler ultrasound spectrum, are described. The methods investigated are: a percentile method, D'Alessio's threshold crossing method [D'Alessio T. (1985) "Objective" algorithm for maximum frequency estimation in Doppler spectral analysers. Med. Biol. Engng and Comput. 23, 63-68.], a modified threshold crossing method, and a new hybrid algorithm. Evaluations of the variance and bias were performed using stationary simulated continuous wave (CW) Doppler signals of different bandwidths and signal/noise ratios (SNR) of 9 and 17 dB. Furthermore, a simulated nonstationary Doppler signal, similar to that from a normal internal carotid artery, was also used to compare the various methods. Overall, it was found that the modified threshold method and the new hybrid method have the best performance over a wide range of signal and noise hybrid method have the best performance over a wide range of signal and noise conditions; however, D'Alessio's method also performs well for low SNR's.     

Spatially variant noise estimation in MRI: A homomorphic approach

The reliable estimation of noise characteristics in MRI is a task of great importance due to the influence of noise features in extensively used post-processing algorithms. Many methods have been proposed in the literature to retrieve noise features from the magnitude signal. However, most of them assume a stationary noise model, i.e., the features of noise do not vary with the position inside the image. This assumption does not hold when modern scanning techniques are considered, e.g., in the case of parallel reconstruction and intensity correction. Therefore, new noise estimators must be found to cope with non-stationary noise. Some methods have been recently proposed in the literature. However, they require multiple acquisitions or extra information which is usually not available (biophysical models, sensitivity of coils). In this work we overcome this drawback by proposing a new method that can accurately estimate the non-stationary parameters of noise from just a single magnitude image. In the derivation, we considered the noise to follow a non-stationary Rician distribution, since it is the most common model in real acquisitions (e.g., SENSE reconstruction), though it can be easily generalized to other models. The proposed approach makes use of a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is then estimated by a low pass filtering with a Rician bias correction. Results in real and synthetic experiments evidence the better performance and the lowest error variance of the proposed methodology when compared to the state-of-the-art methods.     

Doppler developments in the last quinquennium

The major advances which have taken place during the last five years in the development of ultrasonic Doppler devices and methods of Doppler signal analysis are reviewed. The following aspects of instrumentation are considered: crossed beam Doppler systems, range measuring Doppler systems, duplex systems, flow mapping systems, transducers and measurements of system performance. Analytical methods are discussed in the following categories: waveform analysis, including the extraction of single-value waveforms and their applications to the diagnosis of vascular disease; spectral analysis, including the derivation of frequency spectra and their application in the study of blood flow; and volume flow estimation. It is concluded that it is likely to be in the study of the information in Doppler frequency spectra, two-dimensional real-time Doppler images and in the measurement of blood flow volume that most progress will be made.     

Use of a time-staggered FMCW signal for portable high-frequency surface wave radar

Herein is proposed a low-power-density signal based on time-staggered frequency modulated continuous waveform (TS-FMCW) for portable high-frequency (HF) radar. According to the principle of pulse compression that the signal-to-noise ratio (SNR) is related to the total energy, the proposed signals can carry more energy to get higher SNR within same level power density in time–frequency plane. The range grating lobes and Doppler grating lobes shown in the ambiguity function of our proposed waveform can be avoided in the practical HF radar application. A signal processing architecture containing low-pass filtering and fast Fourier transform is proposed. Experimental results demonstrate that higher SNRs are achievable with the same range and Doppler resolution when the same power density is used as the conventional FMCW.     

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).     

Measurements of tissue T1 spin-lattice relaxation time and discrimination of large draining veins using transient EPI data sets in BOLD-weighted fMRI acquisitions

The signal intensity during the dynamic approach to the equilibrium state of longitudinal magnetization is a function of sequence parameters, such as repetition time and flip angle, and depends on tissue characteristics, including longitudinal relaxation time of stationary tissue and the rate of blood inflow. A method is presented to extract information from data acquired during the transient state prior to T1 equilibrium using echo-planar acquisitions in T2*-weighted functional magnetic resonance imaging (fMRI) experiments. A voxel in a single slice acquisition is assumed to contain either stationary tissue or large vessels with flowing blood. Models are presented to characterize longitudinal magnetization relaxation of heterogeneous stationary tissue and blood inflow. The data were fitted to theoretical models for longitudinal relaxation of stationary tissue and inflowing blood assuming no residual signal prior to each RF excitation. Parameters were estimated at 3 T for each model using least squares estimation. A goodness-of-fit criterion was applied to exclude voxels that have transient data that does not fit the selected (best fit) model. Voxels that best fit the inflow model, measured at various TR and flip angles, were assumed to contain large draining veins and were excluded from functional maps. Histogram analysis of T1 distributions for activated voxels in a visual paradigm demonstrated the distributions are centered at T1 values of gray matter with tails at both sides of the center due to partial voluming of gray matter with white matter and CSF respectively. The mean gray matter volume fraction in activated voxels was about 0.9. The results indicate that transient data sets can provide additional information that is useful for both localization and characterization of the functionally relevant BOLD response.     

Adaptive estimation of the mean frequency of a doppler signal from short data windows

The color Doppler estimator (CE₁), which is calculated from the phase of the first correlation lag of the Doppler signal, is compared to the general mean frequency estimator (CE_n), which is based on a weighted summation of all the available correlation lags, for long and short Doppler data sets (typically 48 and 8 Doppler samples). A new estimator of the Doppler signal mean frequency is derived from the results of this study. It optimizes the compromise between the range of analyzable frequencies and the estimation variance for the characteristics of the Doppler signal. Demonstration is provided that the behavior of this estimator shifts from that of CE₁ to that of CE_n, according to the setting of a single parameter. An adaptive version of this estimator is implemented and applied to Doppler recordings. Applications can be contemplated for color Doppler imaging.     

The wall signal removal in Doppler ultrasound systems based on recursive PCA

In Doppler ultrasound (US) systems, a high-pass filter is usually employed to remove the wall component from the blood flow signal. However, this will lead to the loss of information from the low velocity flow. In this paper, an algorithm based on the principal components analysis (PCA) is proposed, in which singular value decomposition (SVD) is used to extract the main component from the mixed signals. Furthermore, the recursive process is incorporated into the PCA method to improve the performance of wall signal removal. This approach and the traditional high-pass filtering one are, respectively, applied to analyze the computer-simulated in vitro and in vivo Doppler US signals. With the proposed method, the wall signal can be removed while a large portion of low-velocity blood signal remains. Comparison experiments show that this novel approach can satisfy the requirements of Doppler US system and is practicable under a broad range of measurement conditions. Because this algorithm is based on real data, it is currently applied to unidirectional signals.