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A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part II: Methods and results.

Various alternative spectral estimation methods are examined and compared in order to assess their possible application for real-time analysis of Doppler ultrasound arterial signals. Specifically, five general frequency domain models are examined, including the periodogram, the general autoregressive moving average (ARMA) model which has the autoregressive (AR) and moving average (MA) models as special cases, and Capon's maximum likelihood spectral model. A stimulated stationary Doppler signal with a known theoretical spectrum was used as the reference test sequence, and white noise was added to enable various signal/noise conditions to be created. The performance of each method representative of each spectral model was assessed using both qualitative and quantitative schemes that convey information related to the bias and variance of the spectral estimates. Three integrated performance indices were implemented for quantitative analysis. The relative computational complexity for each algorithm was also investigated. Our results indicate that both the AR(Yule-Walker) and ARMA(singular value decomposition) models of orders (8) and (4,4), respectively, show good agreement with the theoretical spectrum, and yield estimates with variances considerably less than the Fast Fourier Transform (FFT). Preliminary results obtained with these methods using a clinical, non-stationary Doppler signal supports these observations.

Algorithms

On AR modelling for MEG spectral estimation, data compression and classification.

The use of the autoregressive (AR) model for magnetoencephalogram (MEG) processing is examined and compared to other methods. Spectral estimation, classification and data compression of MEG signals are studied. In application to spectral estimation the AR model is compared to the classical modified periodogram method. Also, AR modelling appears to perform very successfully when used for the classification of normal and epileptic MEG signals. Finally, the 17:1 to 23:1 data compression achieved by AR modelling, along with the above-mentioned advantages, render it suitable for storage applications. For comparison, the method of feature selection via orthogonal expansion is used as a tool to achieve data reduction. It is seen that while effective, this is less drastic than the compression of data volume achieved by AR modelling.

Brain Mapping

AR identification and spectral estimate applied to the R-R interval measurements.

The methods of identification and spectral estimate are applied to the tachogram, i.e. the time series constituted by the cycle-by-cycle R-R interval durations measured on the ECG signal from cardiological patients in ambulatory rehabilitation training after episodes of myocardial infarction or ischemic disease. The Batch Least Squares Method is applied to identify the series as an AR process of 5th order. The whiteness test and Rissanen's optimization criterion are also fulfilled. The clinical information is in this way highly compressed in the pole diagram and in the Maximum Entropy Spectrum (MES) estimated on the basis of the AR coefficients. The experimental results in a restricted set of patients confirm the feasibility of new instrumentation design criteria for non-conventional R-R intervals parametrisation, successive diagnostic classification and beat prediction. Finally, some preliminary considerations about the capabilities of the introduced methods put into evidence the role of computerized techniques in recognizing the fundamental patterns of physiopathological heart rate variability, which the usual conventional methods of ECG analysis are not able to detect in a reliable way.

Arrhythmias, Cardiac

The application of parametric multichannel spectral estimates in the study of electrical brain activity.

A parametric autoregressive model was applied to the multichannel EEG time series. Small statistical fluctuations of the spectral estimates obtained from the short data strings made possible to follow the time changes of the signals. The multiple and partial coherences were calculated for the four channel process and compared with the coherences computed between the pairs of channels. From the study it followed that the partial coherences are the proper measure of the synchronization of brain structures and their intrinsic relationships. The partial phase spectra give the information about the phase delays. The advantages of the parametric description of signals in the frequency domain in respect to the modelling of dynamic systems was pointed out.

Brain

Respiratory impedance spectral estimation for digitally created random noise.

Measurement of respiratory input mechanical impedance (Zrs) is noninvasive, requires minimal subject cooperation, and contains information related to mechanical lung function. A common approach to measure Zrs is to apply random noise pressure signals at the airway opening, measure the resulting flow variations, and then estimate Zrs using Fast-Fourier Transform (FFT) techniques. The goal of this study was to quantify how several signal processing issues affect the quality of a Zrs spectral estimate when the input pressure sequence is created digitally. Random noise driven pressure and flow time domain data were simulated for three models, which permitted predictions of Zrs characteristics previously reported from 0-4, 4-32, and 4-200 Hz. Then, the quality of the Zrs estimate was evaluated as a function of the number of runs ensemble averaged, windowing, flow signal-to-noise ratio (SNR), and pressure spectral magnitude shape magnitude of P(j omega). For a magnitude of P(j omega) with uniform power distribution and a SNR less than 100, the 0-4 Hz and 4-200 Hz Zrs estimates for 10 runs were poor (minimum coherence gamma 2 less than 0.75) particularly where Zrs is high. When the SNR greater than 200 and 10 runs were averaged, the minimum gamma 2 greater than 0.95. However, when magnitude of P(j omega) was matched to magnitude of Zrs, gamma 2 greater than 0.91 even for 5 runs and a SNR of 20. For data created digitally with equally spaced spectral content, the rectangular window was superior to the Hanning. Finally, coherence alone may not be a reliable measure of Zrs quality because coherence is only an estimate itself. We conclude that an accurate estimate of Zrs is best obtained by matching magnitude of P(j omega) to magnitude of Zin (subject and speaker) and using rectangular windowing.

Airway Resistance

Frequency domain analysis of highly amplified ECG on the basis of maximum entropy spectral estimation.

Recognition of patients with high risk for ventricular tachycardia (VT) or sudden cardiac death is of high clinical importance. We have investigated the efficiency of maximum entropy spectral estimation (MES) to detect such risk patients on the basis of highly amplified surface ECG. In comparison with the traditionally applied periodogram (fast Fourier transform), the MES produces sharper and more pronounced peaks in the power density spectrum (PS). The main problem is the influence of residual noise (after averaging), which often leads to additional components in the PS. To completely avoid this negative noise influence we developed a new algorithm, called the variance subtraction method. In a first clinical investigation 86 per cent of patients with myocardial infarction and ventricular tachycardia have shown frequency components above 80 Hz in the PS compared with healthy persons where no frequency components above this 80 Hz level could be detected.

Algorithms

Autoregressive spectral estimation of fetal breathing movement.

Fetal breathing movement (FBM) in utero may be an indicator of fetal health. This paper provides a second-by-second estimate of FBM rate. In the absence of a statistical model for the fetal breathing movement, block data structured autoregressive spectral estimation is used. The optimum tapered Burg algorithm provides a minimum variance breathing rate estimate from a short block of data. The data were recorded using a PVDF (PolyVinyliDeneFluoride) transducer which picks up maternal abdominal wall movements. A peak tracking algorithm is used to extract the fetal breathing rate. Results from these signals are presented in graphical form. Further analysis of the fetal breathing rate has revealed periodicities, similar to that observed in the fetal heart rate.

Algorithms

Advanced spectral estimators for detailed blood flow studies.

Recent publications have emphasized the relationship between the spectrum of the backscattered acoustic signal, beam geometry, and flow patterns in the measurement of blood flow by Doppler ultrasound. On this basis, we believe that in the future more importance will be placed on analyzing various characteristics of the spectral shape rather than absolute parameters of measurement, such as the mean frequency. The potential of this approach for extracting more information from the raw Doppler signal is introduced by considering the Spectral Broadening Index (SBI). We explain the use of the SBI parameter for measuring flow angle under restricted flow conditions. This is done by using an analytic/computational model for prediction of the spectral broadening effect. By simulation study, the performance of various spectral estimators for determining the SBI from finite Doppler signal segments is evaluated.

Blood Flow Velocity

Autoregressive modeling and power spectral estimate of R-R interval time series in arrhythmic patients.

The signal constituted by the successive R-R intervals in the ECG tracing carries important information about the control mechanisms of heart rate. The present paper describes advanced methods of parameter extraction from the R-R duration time series which use autoregressive (AR) modeling and power spectral estimates applied to patients in the MIT-BIH arrhythmia data base. The described methodologies enhance information which characterize the most common rhythm disturbances (A-V block, bigeminy/trigeminy, atrial and ventricular flutter, atrial fibrillation, etc.). Important applications of such methods are in the area of the pathophysiological comprehension of cardiac rhythm control mechanisms in the research side and the classification of abnormal rhythms as well in the clinical side. A few examples from the data base are illustrated which show interesting properties of signal processing and classification in respect to the more traditional methods.

Arrhythmias, Cardiac

Spectral estimation of temporal series at unequal intervals.

Many biological variables present rhythmic oscillations at different frequencies. Most common techniques, which statistically characterize temporal series and permit the study of these rhythms, require equidistant sampling. However, it is not always possible to register at regular intervals many of the variables under study, either because of the nature of the phenomenon which generates them or because of the difficulty in obtaining the samples. This paper proposes a method for spectral estimation by means of fitting to the cosine functions of sampled variables using a nonuniform point process.

Animals

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part I: Estimation methods.

When compared to the classical Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) approach, modern estimation methods offer the potential for achieving significant improvements in estimating the power density spectrum of Doppler ultrasound signals. Such improvements, for example, might enable minor flow disturbances to be detected, thereby improving the sensitivity in arterial disease assessment. Specifically, reduction in the variance and bias can be achieved, and this may enable disturbed flow to be detected in a more sensitive manner. The approach taken here, is to consider spectral estimation methods as a problem of fitting an assumed model to the Doppler signal. The models described assume that the signal is stationary. Since the Doppler signal is generally nonstationary, it is assumed that a short enough time window interval can be chosen over which the signal can be considered stationary. We shall review the various methods and when appropriate, relate them to the nature of the Doppler signal.

Arterial Occlusive Diseases

Real-time system for robust spectral parameter estimation in Doppler signal analysis.

In assessing the level of stenosis in extracranial Doppler analysis, spectral analysis has until now been used qualitatively, for the most part. Owing to the many variables affecting the measurements (mainly noise level and instrument setting made subjectively by the operator), the reliability of the inferences on the degree of stenosis is not clearly definable. Under such conditions the need arises for algorithms and systems that can estimate spectral parameters with a higher degree of accuracy, to verify whether reliable inferences can indeed by made or if this technique is only a qualitative one. In the paper a real-time spectral analysis system is described. The system relies on a new spectral estimation algorithm which gives estimates with good robustness with respect to noise. Moreover, a clear measurement procedure which eliminates the many subjective factors affecting the estimates has also been proposed and used. The system has been evaluated with simulated signals and in clinical trials and has shown better performance than the commonly used commercial analysers.

Adult