Simulated Doppler Signals Research Articles

Adaptive Spectral Envelope Estimation for Doppler Ultrasound.

Estimation of accurate maximum velocities and spectral envelope in ultrasound Doppler blood flow spectrograms are both essential for clinical diagnostic purposes. However, obtaining accurate maximum velocity is not straightforward due to intrinsic spectral broadening and variance in the power spectrum estimate. The method proposed in this paper for maximum velocity point detection has been developed by modifying an existing method-signal noise slope intersection, incorporating in it steps from an altered version of another method called geometric method. Adaptive noise estimation from the spectrogram ensures that a smooth spectral envelope is obtained postdetection of these maximum velocity points. The method has been tested on simulated Doppler signal with scatterers possessing a parabolic flow velocity profile constant in time, steady and pulsatile string phantom recordings, as well as in vivo recordings from uterine, umbilical, carotid, and subclavian arteries. The results from simulation experiments indicate a bias of less than 2.5% in maximum velocities when estimated for a range of peak velocities, Doppler angles, and SNR levels. Standard deviation in the envelope is low-less than 2% in the case of experiments done by varying the peak velocity and Doppler angle for steady phantom and simulated flow, and also less than 2% in the case of experiments done by varying SNR but keeping constant flow conditions for in vivo and simulated flow. Low variability in the envelope makes the prospect of using the envelope for automated blood flow measurements possible and is illustrated for the case of pulsatility index estimation in uterine and umbilical arteries.

Empirical Mode Decomposition of simulated and real ultrasonic Doppler signals of periodic fetal activity

Simulated signals comprising components (trains of Gaussian packets) resulting from cardiac movements and from pseudorespiratory movements with added white noise were submitted to Empirical Mode Decomposition. The increase of sampling frequency fs (from 0.5kHz to 5kHz) for given signal to noise ratio SNR moves signal components toward higher order intrinsic mode functions (IMFs) and increases their number. The increase of the SNR (from −5dB to 10dB, fixed fs) moves the signal components to lower order IMFs. The separation of components is most efficient for SNR≥5dB and fs not exceeding 1kHz, for lower SNRs fs should be at least 2kHz. SNR=∞ results in erroneous decomposition and therefore limited noise level is beneficial. Recommended number of sifting iterations is 10. Fetal data obtained using 2MHz emission frequency and sampled at 2kHz were decomposed. The cardiac signal always appears in IMF3, frequently also in IMF1 and IMF2. The pseudobreathing signal, appearing mainly in IMF4-6, is easy to separate. Signals resulting from fetal displacements due to maternal respiration appear in IMF7 or IMF8. The EMD performs better than the classic linear filtering as a tool for separation of the pseudorespiration signals and provides inferior results in terms of separation of the cardiac signals.

Laser Doppler Velocimetry Signal Processing Based on Spectral Refinement and Correction

In order to improve the accuracy of signal processing in Laser Doppler Velocimetry, a method based on the association of spectral refinement and correction is presented. Zoom-FFT and ratio correction are adopted to realize this method. Basic principles of zoom-FFT and ratio correction are expounded. FFT and the method are adopted to process sinusoidal signals and simulated laser Doppler signals with different frequencies separately in circumstance of MATLAB 7.0. Comparisons between the results of FFT and the method are carried out. The comparisons show that this method has the capability to improve the accuracy of laser Doppler signal processing significantly and the operation time is acceptable for LDV system.

Analysis of Index Modulation in Microembolic Doppler Signals Part I: Radiation Force as a New Hypothesis—Simulations

The purpose of this study was to reveal the cause of frequency modulation (FM) present in microembolic Doppler ultrasound signals. This novel explanation should help the development of sensitive microembolus discrimination techniques. We suggest that the frequency modulation detected is caused by the ultrasonic radiation force (URF) acting directly on microemboli. The frequency modulation and the imposed displacement were calculated using a numerical dynamic model. By setting simulation parameters with practical values, it was possible to reproduce most microembolic frequency modulation signatures. The most interesting findings in this study were that: (1) the ultrasound radiation force acting on a gaseous microembolus and its corresponding cumulative displacement were far higher than those obtained for a solid microembolus, and that is encouraging for discrimination purposes; and 2) the calculated frequency modulation indices (FMIs) (≈20 kHz) were in good agreement with literature results. By taking into account the URF, the flow pulsatility, the beam-to-flow angle and both the velocity and the ultrasound beam profiles, it was possible to explain all erratic FM signatures of a microbubble. Finally, by measuring FMI from simulated Doppler signals and by using a constant threshold of 1 KHz, it was possible to discriminate gaseous from solid microemboli with ease. (E-mail: jean-marc.girault@univ-tours.fr)

Assessment of arterial distension based on continuous wave Doppler ultrasound with an improved Hilbert-Huang processing

A novel approach based on continuous wave (CW) Doppler ultrasound and the Hilbert-Huang transform with end-effect restraint by mirror extending is proposed to assess arterial distension. In the approach, bidirectional Doppler signals were first separated using the phasing-filter technique from the mixed quadrature Doppler signals, which were produced by bidirectional blood and vessel wall movements. Each separated unidirectional signal was decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition with end effect restraint by mirror extending algorithm, and then the relevant IMFs that contribute to the vessel wall components were identified. Finally, the displacement waveforms of the vessel wall were calculated by integrating its moving velocity waveforms, which were extracted from the bidirectional Hilbert spectrum estimated from the identified wall IMFs. This approach was applied to simulated and clinical Doppler signals from normal common carotid arteries (CCAs). In the simulation study, the estimated wall moving velocity and displacement waveforms were compared with the theoretical ones, respectively. The mean and standard deviation of the root-mean-square errors between the estimated and theoretical wall distension of the 30 realizations was 4.2 +/- 0.4 microm. In the clinical study, peak-to-peak distension was extracted in a subject and then averaged over 15 cardiac cycles, resulting in 603 +/- 22 microm. The mean and standard deviation of the CCA distension averaged over the experimental measurements of 12 healthy subjects gave the result of 620 +/- 154 microm. The clinical results were in agreement with those measured by using the multigate Doppler ultrasound and echo tracking systems. The results show that based on the CW Doppler ultrasound, the proposed approach is practical for extracting arterial wall peak-to-peak distension correctly and could be an alternative method for the vessel wall distension estimation.

Preservation of quadrature Doppler signals from bidirectional slow blood flow close to the vessel wall using an adaptive decomposition algorithm

A novel approach based on the phasing-filter (PF) technique and the empirical mode decomposition (EMD) algorithm is proposed to preserve quadrature Doppler signal components from bidirectional slow blood flow close to the vessel wall. Bidirectional mixed Doppler ultrasound signals, which were echoed from the forward and reverse moving blood and vessel wall, were initially separated to avoid the phase distortion of quadrature Doppler signals (which is induced from direct decomposition by the nonlinear EMD processing). Separated unidirectional mixed Doppler signals were decomposed into intrinsic mode functions (IMFs) using the EMD algorithm and the relevant IMFs that contribute to blood flow components were identified and summed to give the blood flow signals, whereby only the components from the bidirectional slow blood flow close to the vessel wall were retained independently. The complex quadrature Doppler blood flow signal was reconstructed from a combination of the extracted unidirectional Doppler blood flow signals. The proposed approach was applied to simulated and clinical Doppler signals. It is concluded from the experimental results that this approach is practical for the preservation of quadrature Doppler signal components from the bidirectional slow blood flow close to the vessel wall, and may provide more diagnostic information for the diagnosis and treatment of vascular diseases.

Numerical simulations of a Mars geodesy network experiment: Effect of orbiter angular momentum desaturation on Mars' rotation estimation

The scientific objectives of a geodetic experiment based on a network of landers, such as NEIGE (NEtlander Ionosphere and Geodesy Experiment) are to improve the current knowledge of Mars' interior and atmosphere dynamics. Such a network science experiment allows monitoring the motions of the Martian rotation axis with a precision of a few centimeters (or milli-arc-seconds (mas)) over annual and sub-annual periods. Thereto, besides radio tracking of a Mars orbiter from the Earth, radio Doppler shifts between this orbiter and several landers at the planet's surface will be performed. From the analysis of these radio Doppler data, it is possible to reconstruct the orbiter motion and Mars' orientation in space. The errors on the orbit determination (position and velocity of the orbiter) have an impact on the geodetic parameters determination from the Doppler shifts and must be removed from the signal in order to achieve a high enough accuracy. In this paper, we perform numerical simulations of the two Doppler signals involved in such an experiment to estimate the impact of the spacecraft angular momentum desaturations on the determination of Mars' orientation variations. The attitude control of the orbiter needs such desaturation maneuvers regularly repeated. They produce velocity variations that must be taken into account when determining the orbit. For our simulations, we use a priori models of the Martian rotation and introduce the spacecraft velocity variations induced by each desaturation event. By a least-squares adjustment of the simulated Doppler signals, we then estimate the orbiter velocity variations and the parameters of the Mars' rotation model. We show that these velocity variations are ill resolved when the spacecraft is not tracked, therefore requiring a near-continuous tracking from the Earth to accurately determine the orbit. In such conditions we show that only 15– 20 min of lander–orbiter tracking per week allows recovering Mars' orientation parameters with a precision of a few mas over a period of 1 Martian year.

Denoising quadrature Doppler signals from bi-directional flow using the wavelet frame

A novel approach was proposed to denoise quadrature Doppler signals from bi-directional blood flow using the wavelet frame and a soft-thresholding algorithm. A direction separation step was carried out first to avoid the phase distortion of quadrature Doppler signals, which is induced from the nonlinear, soft-thresholding processing. Then real parts of separated complex signals from the unidirectional flow were denoised independently. The quadrature Doppler signals from the bi-directional flow were reconstructed from the denoised separated signals. The approach has been applied to the simulated Doppler signals from a femoral artery. It is concluded from the experimental results that this method is practical for denoising quadrature Doppler signals.

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.

Performance of short-time spectral parametric methods for reducing the variance of the Doppler ultrasound mean instantaneous frequency estimation.

To achieve an accurate estimation of the instantaneous turbulent velocity fluctuations downstream of prosthetic heart valves in vivo, the variability of the spectral method used to measure the mean frequency shift of the Doppler signal (i.e. the Doppler velocity) should be minimised. This paper investigates the performance of various short-time spectral parametric methods such as the short-time Fourier transform, autoregressive modelling based on two different approaches, autoregressive moving average modelling based on the Steiglitz-McBride method, and Prony's spectral method. A simulated Doppler signal was used to evaluate the performance of the above mentioned spectral methods and Gaussian noise was added to obtain a set of signals with various signal-to-noise ratios. Two different parameters were used to evaluate the performance of each method in terms of variability and accurate matching of the theoretical Doppler mean instantaneous frequency variation within the cardiac cycle. Results show that autoregressive modelling outperforms the other investigated spectral techniques for window lengths varying between 1 and 10 ms. Among the autoregressive algorithms implemented, it is shown that the maximum entropy method based on a block data processing technique gives the best results for a signal-to-noise ratio of 20 dB. However, at 10 and 0 dB, the Levinson-Durbin algorithm surpasses the performance of the maximum entropy method. It is expected that the intrinsic variance of the spectral methods can be an important source of error for the estimation of the turbulence intensity. The range of this error varies from 0.38% to 24% depending on the parameters of the spectral method and the signal-to-noise ratio.

A study of the spectral broadening of simulated Doppler signals using FFT and AR modelling

Doppler ultrasound is used clinically to detect stenosis in the carotid artery. The presence of stenosis may be identified by disturbed flow patterns distal to the stenosis that cause spectral broadening in the spectrum of the Doppler signal around peak systole. This paper investigates the behaviour of the spectral broadening index (SBI) derived from wide-band spectra obtained using autoregressive modelling (AR), compared with the SBI based on the fast-Fourier transform (FFT) spectra. Simulated Doppler signals were created using white noise and shaped filters to analyse spectra typically found around the systolic peak and to assess the magnitude and variance of AR and FFT-SBI for a range of signal-to-noise ratios. The results of the analysis show a strong correlation between the indices calculated using the FFT and AR algorithms. Despite the qualitative improvement of the AR spectra over the FFT, the estimation of SBI for short data frames is not significantly improved using AR.

Correction for nonstationarity and window broadening in Doppler spectrum estimation

The width of the time-varying spectrum of signals from the pulsed Doppler ultrasonic blood flow detector is overestimated as a result of window and nonstationarity broadening when analyzed using the conventional short-term Fourier transform (STFT). By deriving the broadening function width from a consideration of signal phase variation arising from the deterministic spectral center-frequency variation during each window, the increase In the root-mean-squared (RMS) spectral width can be calculated and the spectral width estimation corrected. Using this procedure on simulated Doppler signals of known characteristics, a significant reduction in spectral width estimation error can be demonstrated.

Doppler Ultrasound Simulation Model for Pulsatile Flow with Nonaxial Components

A numerical model that can produce pulsed Doppler signals for nonaxial, pulsatile flow is presented. The model takes into account both hemodynamic and acoustic factors that affect the Doppler signal, such that a wide range of flow patterns and arbitrary transducer types can be simulated. The physics of blood flow is modeled by solving the Navier-Stokes equations utilizing a finite element technique, and the acoustic field is modeled using the acoustic impulse response method. The model was validated by comparison to the Womersley theory. The median deviation was 3.45%. Doppler signals from flow through a 50% stenosis were also simulated. The calculated spectra demonstrated the changing flow patterns from jets and vortices. This new computer model can be used to test spectral analysis tools on simulated Doppler signals, whose underlying flow patterns are of clinical importance.

Doppler Ultrasound Simulation Model for Pulsatile Flow with Nonaxial Components

A numerical model that can produce pulsed Doppler signals for nonaxial, pulsatile flow is presented. The model takes into account both hemodynamic and acoustic factors that affect the Doppler signal, such that a wide range of flow patterns and arbitrary transducer types can be simulated. The physics of blood flow is modeled by solving the Navier-Stokes equations utilizing a finite element technique, and the acoustic field is modeled using the acoustic impulse response method. The model was validated by comparison to the Womersley theory. The median deviation was 3.45%. Doppler signals from flow through a 50% stenosis were also simulated. The calculated spectra demonstrated the changing flow patterns from jets and vortices. This new computer model can be used to test spectral analysis tools on simulated Doppler signals, whose underlying flow patterns are of clinical importance.

Comparison of Doppler signal analysis techniques for velocity waveform, turbulence and vortex measurement: A simulation study

Simulated time-varying Doppler signals incorporating bandwidth, power variation and vortex simulation have been used to compare a number of signal analysis techniques with a view to optimising the accuracy of convective velocity waveform, spectral broadening and vortex signal estimation. The shorttime Fourier transform (STFT), the autoregressive (AR) modified covariance estimator, the time-frequency pseudo-Wigner-Ville and Choi-Williams distributions and a partial stationarising algorithm were investigated for a range of some analysis parameters (such as window duration, AR model order). It was found that all methods could estimate the convective velocity waveform well and all the nonclassical methods were an improvement over the STFT for bandwidth estimation with the stationarising method giving the lowest error. For vortex measurement, using parameters that were optimum for mean frequency and bandwidth estimation, the stationarising, modified covariance, pseudo-Wigner-Ville with a 10-ms window and Choi-Williams methods gave improved performances compared with the STFT.

Nonstationarity broadening reduction in pulsed Doppler spectrum measurements using time-frequency estimators.

The spectral width of Doppler signals is used as measure of lesion-induced flow disturbance. Its estimation accuracy is compromised using the conventional short-term Fourier transform (STFT) since this method implicitly assumes signal stationarity during the signal window while the Doppler signals from arteries are markedly nonstationary. The Wigner-Ville (WVD), Choi-Williams (CWD) and Bessel distributions (BD), specifically designed for nonstationary signals, have been optimized for spectral width estimation accuracy and compared to the STFT under different signal to noise ratios using simulated Doppler signals of known time-frequency characteristics. The optimum parameter values for each method were determined as a Hanning window duration of 10 ms for the STFT, 40 ms for the WVD and CWD and 20 ms for the BD and dimensionless time-frequency smoothing constant values of five in the CWD and two in the BD. Thresholding was used to reduce the effect of cross terms and side lobes in the WVD and BD. With no added noise the WVD gave the lowest estimation error followed by the CWD. At signal-to-noise ratios (SNR's) of 10 dB and 20 dB the CWD and BD had similar errors and were markedly better than the other estimators. Overall the CWD gave the best performance.

Compensation of the bias caused by the wall filter on the mean Doppler frequency

In the presence of noise, any wall filter induces a bias on the mean Doppler frequency estimated by the algorithm based on the calculation of the phase of the autocorrelation function at lag 1. In this paper, it is shown that the bias results from the nonzero value of the autocorrelation function of the filtered noise at lag 1. A general method for compensating the bias was then deduced. It consists of a preliminary estimation of the filtered noise contribution and its subtraction from the autocorrelation function of the Doppler signal. The method is independent of the nature of the noise and wall filter. An evaluation of this method on simulated Doppler signals and on measurements from a moving-string phantom showed that effective compensation of the bias was obtained, but at the expense of a higher variance. Taking into account both the bias and the variance, however, it was shown that this method offers an improvement over the noncompensated method. Finally, the performance of this method was demonstrated using in vivo measurements taken from a human aorta.

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.

Fractal concept and its analysis method for doppler ultrasound signals

A method to obtain the fractal dimension of Doppler ultrasound signals is described, and its application to the analysis of simulated and real Doppler signals is demonstrated.

A Doppler signal simulator (medical ultrasound)

A simulated Doppler signal generator has been developed using computer controlled band-pass filtering of a broad-band noise source. The instrument may be used to generate simulated Doppler signals of known spectral characteristics in order to test Doppler signal analysers.