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

Collective almost synchronization-based model to extract and predict features of EEG signals

Understanding the brain is important in the fields of science, medicine, and engineering. A promising approach to better understand the brain is through computing models. These models were adjusted to reproduce data collected from the brain. One of the most commonly used types of data in neuroscience comes from electroencephalography (EEG), which records the tiny voltages generated when neurons in the brain are activated. In this study, we propose a model based on complex networks of weakly connected dynamical systems (Hindmarsh-Rose neurons or Kuramoto oscillators), set to operate in a dynamic regime recognized as Collective Almost Synchronization (CAS). Our model not only successfully reproduces EEG data from both healthy and epileptic EEG signals, but it also predicts EEG features, the Hurst exponent, and the power spectrum. The proposed model is able to forecast EEG signals 5.76 s in the future. The average forecasting error was 9.22%. The random Kuramoto model produced the outstanding result for forecasting seizure EEG with an error of 11.21%.

ANALYSIS OF CAROTID ARTERIAL DOPPLER SIGNALS USING STFT AND WIGNER–VILLE DISTRIBUTION (WVD)

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the carotid arteries in the time-frequency domain using the short time Fourier transform (STFT) and the Wigner–Ville distribution (WVD). This study is carried out in order to investigate the behavior of the spectral broadening index (SBI) derived from spectra obtained using these methods. The variations in the shape of the Doppler power spectra as a function of time are presented in the form of sonograms in order to determine the degree of primitive carotid artery stenosis. The obtained results show a qualitative improvement in the appearance of the sonograms generated using the WVD over the STFT. However, despite this qualitative improvement the WVD suffers from some drawbacks: the presence of the cross terms which are primarily due to its quadratic nature. The application of the Choi–Williams distribution (CWD) in this analysis shows a noticeable reduction of these cross terms, improving therefore the quality of the sonograms. From these generated sonograms, the ultrasound frequency envelopes are extracted. The maximum and the mean frequencies in these envelopes are used to determine the SBI. The magnitude of the CWD-SBI is significantly greater than that of the STFT-SBI. In addition, there is a correlation between the SBIs obtained using the STFT and the CWD and the degree of severity of stenosis measured by 2D Doppler imaging.

In vivo Doppler ultrasound quantification of turbulence intensity using a high-pass frequency filter method

The objective of this investigation was to implement a high-pass frequency filter method to analyze Doppler ultrasound velocity waveforms and quantify turbulence intensity (TI) in vivo. Doppler velocity data were analyzed using two techniques, based on either ensemble averaging or high-pass frequency domain filtering of the periodic waveforms. The accuracy and precision of TI measurements were determined with controlled in vitro experiments, using a pulsatile-flow model of a stenosed carotid bifurcation. The high-pass filter technique was also applied in vivo to determine whether this technique could successfully distinguish between pertinent hemodynamic sites within the carotid artery bifurcation. Twenty-five seconds of Doppler audio data were acquired at three sites (common carotid artery [CCA], internal carotid artery [ICA] stenosis and distal ICA) within 10 human carotid arteries, and repeated three times. Doppler velocity data were analyzed using a ninth-order high-pass Butterworth filter with a 12-Hz inflection point. TI measured within the CCA and distal ICA was found to be significantly different (p < 0.0001) for moderate to nearly occluded carotid artery classifications. Also, TI measured within the distal ICA increased with stenosis severity, with the ability to distinguish between each stenosis class (p < 0.05). This investigation demonstrated the ability to precisely quantify TI using a conventional Doppler ultrasound machine in human subjects, without interfering with normal clinical protocols.

In vitro Doppler ultrasound investigation of turbulence intensity in pulsatile flow with simulated cardiac variability

An in vitro investigation of turbulence intensity (TI) associated with a severe carotid stenosis in the presence of physiological cardiac variability is described. The objective of this investigation was to determine if fluctuations due to turbulence could be quantified with conventional Doppler ultrasound (DUS) in the presence of normal physiological cycle-to-cycle cardiac variability. An anthropomorphic model of a 70% stenosed carotid bifurcation was used in combination with a programmable flow pump to generate pulsatile flow with a mean flow rate of 6 mL/s. Utilizing the pump, we studied normal, nonrepetitive cycle-to-cycle cardiac variability (+/-3.9%) in flow, as well as waveform shapes with standard deviations equal to 0, 2 and 3 times the normal variation. Eighty cardiac cycles of Doppler data were acquired at two regions within the model, representing either laminar or turbulent flow; each measurement was repeated six times. Turbulence intensity values were found to be 11 times higher (p < 0.001), on average, in the turbulent region than in the laminar region, with a mean difference of 24 cm/s. Twenty cardiac cycles were required for confidence in TI values. In conclusion, these results indicate that it is possible to quantify TI in vitro, even in the presence of normal and exaggerated cycle-to-cycle cardiac variability.

Comparison of fast Fourier transformation and autoregressive modelling as a diagnostic tool in analysis of lower extremity venous signals

In this study, we have compared the efficacy of autoregressive modelling (ARM) and fast Fourier transformation (FFT) of Doppler signals from lower extremity veins of healthy volunteers in various physiologic situations. Compared to FFT, ARM produced smooth spectra and less spectral broadening both in sonograms and power spectra. However, faulty positioning of the peaks along the time axis in FFT-derived power spectral density curves show that FFT is not a suitable method if these graphs are to be used as a diagnostic tool. Analysis of ARM-based venous sonograms and power spectral density graphs revealed that FFT should not be used in signals with high power spectral density levels and low-frequency bandwidth within limited segments of time.

Spectral analysis of internal carotid arterial Doppler signals using FFT, AR, MA, and ARMA methods

In this study, Doppler signals recorded from internal carotid artery of 45 subjects were processed by PC-computer using classical (fast Fourier transform) and model-based (autoregressive, moving average, autoregressive moving average (ARMA) methods) methods. Power spectral density estimates of internal carotid arterial Doppler signals were obtained using these spectral analysis methods. The variations in the shape of the Doppler power spectra as a function of time were presented in the form of sonograms in order to determine the degree of internal carotid artery stenosis. These Doppler power spectra and sonograms were then used to compare the applied methods in terms of their frequency resolution and the impact on determining stenosis in internal carotid arteries. Based on the results, performance characteristics of the autoregressive and ARMA methods were found extremely valuable for spectral analysis of internal carotid arterial Doppler signals obtained from healthy subjects and unhealthy subjects having artery stenosis.

Spectral broadening of ophthalmic arterial Doppler signals using STFT and wavelet transform

In this study, short-time Fourier transform (STFT) and wavelet transform (WT) were used for spectral analysis of ophthalmic arterial Doppler signals. Using these spectral analysis methods, the variations in the shape of the Doppler spectra as a function of time were presented in the form of sonograms in order to obtain medical information. These sonograms were then used to compare the applied methods in terms of their frequency resolution and the effects in determination of spectral broadening in the presence of ophthalmic artery stenosis. A qualitative improvement in the appearance of the sonograms obtained using the WT over the STFT was noticeable. Despite the qualitative improvement in the individual sonograms, no quantitative advantage in using the WT over the STFT for the determination of spectral broadening index was obtained due to the poorer variance of the wavelet transform-based spectral broadening index and the additional computational requirements of the wavelet transform.

Comparison of eigenvector methods with classical and model-based methods in analysis of internal carotid arterial Doppler signals

Doppler ultrasound is known as a reliable technique, which demonstrates the flow characteristics and resistance of arteries in various vascular disease. In this study, internal carotid arterial Doppler signals recorded from 105 subjects were processed by PC-computer using classical, model-based, and eigenvector methods. The classical method (fast Fourier transform), two model-based methods (Burg autoregressive, least-squares modified Yule-Walker autoregressive moving average methods), and three eigenvector methods (Pisarenko, multiple signal classification, and Minimum-Norm methods) were selected for processing internal carotid arterial Doppler signals. Doppler power spectra of internal carotid arterial Doppler signals were obtained using these spectrum analysis techniques. The variations in the shape of the Doppler power spectra were examined in order to obtain medical information. These power spectra were then used to compare the applied methods in terms of their frequency resolution and the effects in determination of stenosis and occlusion in internal carotid arteries.

Application of classical and model-based spectral methods to ophthalmic arterial Doppler signals with uveitis disease

In this study, Doppler signals recorded from ophthalmic artery of 75 subjects were processed by PC-computer using classical and model-based methods. The classical method (fast Fourier transform) and three model-based methods (Burg autoregressive, moving average, least-squares modified Yule-Walker autoregressive moving average methods) were selected for processing ophthalmic arterial Doppler signals with uveitis disease. Doppler power spectra of ophthalmic arterial Doppler signals were obtained by using these spectrum analysis techniques. The variations in the shape of the Doppler spectra as a function of time were presented in the form of sonograms in order to obtain medical information. These Doppler spectra and sonograms were then used to compare the applied methods in terms of their frequency resolution and the effects in determination of uveitis disease.

Determination of stenosis and occlusion in arteries with the application of FFT, AR, and ARMA methods

Doppler ultrasound is a noninvasive technique that allows the examination of the direction, velocity, and volume of blood flow. Therefore, Doppler ultrasonography is known as reliable technique, which demonstrates the flow characteristics and resistance of arteries in various vascular disease. In this study, arterial Doppler signals recorded from 105 subjects were processed by PC-computer using fast Fourier transform, Burg autoregressive, and least squares modified Yule-Walker autoregressive moving average methods. Doppler power spectrums of arterial Doppler signals were obtained by using these spectrum analysis techniques. The variations in the shape of the Doppler power spectrums as a function of time were presented in the form of sonograms in order to obtain medical information. These sonograms were then used to compare the applied methods in terms of their frequency resolution and the effects in determination of stenosis and occlusion in arteries. Reliable information on hemodynamic alterations in arteries can be obtained by evaluation of these sonograms.

High resolution processing techniques for ultrasound doppler velocimetry in the presence of colored noise. Part II: Multiplephase pipe-flow velocity measurement

This paper presents an application of continuous wave ultrasound Doppler velocity measurements to two-phase flow in pipes. In many petroleum wells, the multiphase flow is separated into two phases: the first is a liquid phase and the second is a gas phase with small scatterers. The problem of multiphase velocity profile measurements has not been satisfactorily solved by classical approaches due to the multiphase nature of the fluid and the presence of colored noise, which introduces a significant bias in classical frequency estimators. We propose the use of high resolution frequency techniques to overcome the classical limitations. Direct estimation of Doppler frequency then obtained using either time frequency maximum frequency or arguments of poles of the parametric model that identifies the Doppler part of the signal is discussed. The tests made with synthetic Doppler signals and two-phase flow have demonstrated the excellent performance of the high resolution techniques based on reassignment and parametric techniques.

MP3 compression of Doppler ultrasound signals

The effect of lossy, MP3 compression on spectral parameters derived from Doppler ultrasound (US) signals was investigated. Compression was tested on signals acquired from two sources: 1. phase quadrature and 2. stereo audio directional output. A total of 11, 10-s acquisitions of Doppler US signal were collected from each source at three sites in a flow phantom. Doppler signals were digitized at 44.1 kHz and compressed using four grades of MP3 compression (in kilobits per second, kbps; compression ratios in brackets): 1400 kbps (uncompressed), 128 kbps (11:1), 64 kbps (22:1) and 32 kbps (44:1). Doppler spectra were characterized by peak velocity, mean velocity, spectral width, integrated power and ratio of spectral power between negative and positive velocities. The results suggest that MP3 compression on digital Doppler US signals is feasible at 128 kbps, with a resulting 11:1 compression ratio, without compromising clinically relevant information. Higher compression ratios led to significant differences for both signal sources when compared with the uncompressed signals.

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 degrees to 75 degrees. 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 degrees to 72 degrees, showed that the AR method using only eight flow samples had an average estimation error of 3.6 degrees, which compares favorably to the average error of 4.7 degrees 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.

Sources of error in maximum velocity estimation using linear phased-array Doppler systems with steady flow

Using linear-array Doppler ultrasound (US) transducers, the measured maximum velocity may be in error and lead to incorrect clinical diagnosis. This study investigates the existence and cause of maximum velocity estimation errors for steady flow of a blood-mimicking fluid in a tissue-mimicking phantom. A specially designed system was used that enabled fine control of flow rate, transducer positioning and transducer angle relative to the flow phantom. Doppler machine settings (transducer aperture size, focal depth, beam-steering, gain) were varied to investigate a wide range of clinical applications. To estimate the maximum velocity, a new signal-to-noise ratio (SNR) independent method was developed to calculate the maximum frequency from an ensemble averaged Doppler power spectrum. This enabled the impact of each factor on the total Doppler error to be determined. When using the new maximum frequency estimator, it was found that the effect of transducer focal depth, intratransducer, intramachine, intermachine (that was tested) and beam-steering did not significantly contribute to maximum velocity estimation errors. Instead, it was the dependence of the maximum velocity on the Doppler angle that made, by far, the greatest contribution to the estimation error. Because our maximum frequency estimator took into account the effect of intrinsic spectral broadening, the degree of overestimation error was not as great as that previously published. Thus, the effects of Doppler angle and intrinsic spectral broadening are the chief sources of Doppler US error and should be the focus of future efforts to improve the accuracy.

Application of autoregressive methods to multigate spectral analysis

Multigate analysis is known to be capable of detecting accurate blood velocity profiles from human vessels. Experimental systems so far presented in the literature use time-domain frequency estimations and, more recently, the fast Fourier transform (FFT) for real-time analysis of Doppler signals from multiple range cells. This experimental study is aimed at evaluating the application of an autoregressive (AR) method (Burg algorithm) to multigate Doppler analysis. Both in vitro and in vivo results were collected with a commercial Duplex scanner coupled with a prototype multigate unit developed in our laboratory. The same multigate signals are, thus, processed according to both the FFT and the Burg algorithms. The related spectral and maximum frequency profiles are reported and statistically compared. AR, implemented with the Burg algorithm, is demonstrated to be a way to perform multigate spectral analysis with reduced spectral variance, suitable for maximum velocity profile extraction through a simple threshold.

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.

Spectral broadening of clinical Doppler signals using FFT and autoregressive modelling

OBJECTIVE

This paper investigates the behaviour of the spectral broadening index (SBI) derived from spectra obtained using autoregressive (AR) modelling compared to that of SBI based on fast Fourier transform (FFT) analysis of clinical Doppler ultrasound scans.

METHODS

Doppler signals from internal carotid arteries of patients with normal and diseased vessels with up to 80% stenosis were analysed. A threshold at -6 dB of the maximum magnitude component of each individual spectrum was implemented to reject low-level noise. The SBI was obtained using the maximum and the mean frequency envelopes extracted from the sonogram.

RESULTS

A qualitative improvement in both the appearance of the AR sonograms and the shape of the individual AR spectra was noticeable. The AR approach consistently produced narrower spectra than the FFT and the shapes of the frequency envelopes derived from the AR sonogram and the FFT sonogram were also rather different. Despite these differences a strong correlation was observed between the value of the FFT-based SBI and the AR-based SBI. The mean value of the FFT-SBI is larger than that of the AR-SBI and the variance of the FFT-SBI is smaller than that of the AR-SBI based on a set of at least 20 sequentially recorded heartbeats.

CONCLUSIONS

It was established that, for all cases where significant stenosis was present, a statistically significant value for SBI could be obtained using four or more heartbeats if five spectra around the peak systole were used to estimate the SBI of each individual heartbeat. No quantitative advantage in using the AR approach over the FFT for the determination of SBI was obtained due to the poorer variance of the AR-SBI and the additional computational complexity of the AR approach.