The effect of averaging cardiac Doppler spectrograms on the reduction of their amplitude variability

ANALYSIS OF THE DOPPLER ULTRASOUND SIGNAL BY WAVELET PACKET TRANSFORM

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the arteries in the spectro-temporal domain using the wavelet packet transform. The spectro-temporal representation is obtained by the decomposition of the Doppler signal in frequency sub-band, using filter banks associated with a well chosen wavelet. It is shown that the decomposition level depends on the stationarity of the Doppler signal, and the best profile of blood flow velocity in arteries is obtained according to an appropriate choice of wavelet type.

Three types of wavelets have been tested on two Doppler signals previously recorded from the carotid and femoral arteries. The best representation is obtained when the frequency sub-bands of the filter bank associated with chosen wavelet are regularly distributed in the frequency domain and the level of decomposition is 7.

A comparison of the wavelet and short-time fourier transforms for Doppler spectral analysis

Doppler spectrum analysis provides a non-invasive means to measure blood flow velocity and to diagnose arterial occlusive disease. The time-frequency representation of the Doppler blood flow signal is normally computed by using the short-time Fourier transform (STFT). This transform requires stationarity of the signal during a finite time interval, and thus imposes some constraints on the representation estimate. In addition, the STFT has a fixed time-frequency window, making it inaccurate to analyze signals having relatively wide bandwidths that change rapidly with time. In the present study, wavelet transform (WT), having a flexible time-frequency window, was used to investigate its advantages and limitations for the analysis of the Doppler blood flow signal. Representations computed using the WT with a modified Morlet wavelet were investigated and compared with the theoretical representation and those computed using the STFT with a Gaussian window. The time and frequency resolutions of these two approaches were compared. Three indices, the normalized root-mean-squared errors of the minimum, the maximum and the mean frequency waveforms, were used to evaluate the performance of the WT. Results showed that the WT can not only be used as an alternative signal processing tool to the STFT for Doppler blood flow signals, but can also generate a time-frequency representation with better resolution than the STFT. In addition, the WT method can provide both satisfactory mean frequencies and maximum frequencies. This technique is expected to be useful for the analysis of Doppler blood flow signals to quantify arterial stenoses.

Statistics of the integrated backscatter estimate from a blood-mimicking fluid

This work evaluates the variance of the integrated backscatter (IBS) from moving blood [or blood-mimicking fluid (bmf)] as a way of determining the quality of the mean IBS estimate. The main motivation for this work comes from the fact that absolute IBS values from tissues adjacent to arterial blood can be found by normalizing the measured backscatter energy with the IBS of moving, deaggregated blood. The paper describes the parameters that control the statistics of the IBS estimate, which is calculated for the stochastic ultrasound backscatter signals from flowing blood. It further formulates how the measurement parameters should be specified so that an appropriately low blood IBS variance is ensured or, alternatively, a specified accuracy of the tissue IBS estimate is obtained. First, the paper provides an analytic formulation of the statistics of the IBS, based on a sequence of sampled echoes from a nonstationary Gaussian scattering medium. The analysis incorporates the correlation between the sample values as well as the correlation between the IBS of the individual echoes. The estimate of the mean IBS has been shown to be chi-squared distributed with a determinable order. With the degree of correlation between the samples and between the IBS of individual echoes specified, the number of measurements required to obtain an IBS estimate with a specified variance is readily calculated. Next, a sequence of synthetic echoes is produced and arranged as columns in a data matrix. The echoes are generated such that the second-order statistics along the rows and columns of the matrix match that of actually observed echoes. The actual variance of the mean IBS estimate for the synthetic echoes is calculated and compared with the variance determined from the analytic model, and a good agreement has been found. Finally, sequences of actual backscattered echoes from circulating blood-mimicking fluid are acquired and analyzed to determine the variance of their mean IBS estimate. Based on the measured second-order statistics of the rows and columns of the data matrix for the actual echoes, the observed variance of the mean IBS estimate was compared with the analytically determined variance and with good agreement. Thus, the paper has shown through modeling, simulations, and experiments how the variance of the IBS estimate of the blood backscatter signal can be quantified and reduced to a specified tolerable level.

Construction of a protocol for measuring blood flow by two-dimensional phase-contrast MRA

Our aim is to describe and demonstrate the steps we have found to be useful in the construction and evaluation of protocols for triggered and nontriggered measurement of blood flow by two-dimensional phase-contrast magnetic resonance angiography (MRA). To achieve this goal, we start with a survey of factors governing the accuracy (validity) and precision (repeatability) of MR flow measurements. This knowledge, combined with prior information regarding the diameter of the target vessel and the prevailing flow conditions, is then employed to define a protocol for measuring flow with negligible systematic error. In the absence of a gold standard for in vivo flow measurements, the protocol is subsequently validated for a range of flow conditions by representative phantom experiments. Precision is then calculated from the signal-to-noise ratio (SNR) of blood in the accompanying magnitude images or, less conveniently, estimated from the standard deviation of repeated measurements. The desired precision is finally achieved by adjusting the appropriate SNR parameters. All steps involved in protocol development are demonstrated for both flow-independent and flow-dependent acquisitions.

Relation of the flow field distal to a moderate stenosis to the Doppler power

An experimental investigation was undertaken to establish how different flow regimes affect the Doppler signal. A rigid tube model consisting of a 70% asymmetric area stenosis was used with steady and pulsatile flow conditions. The characteristics of the flow field at various sites was determined using a photochromic flow visualization method. Continuous-wave Doppler measurements were made using a 41% suspension of human red blood cells (RBCs) in saline as well as a dilute suspension of 4% fixed RBCs. For steady flow, the photochromic results indicated that for Reynolds numbers (Re) of 545 and 1410, turbulence was generated and the length of the turbulent region was found to increase with increasing Re. Under pulsatile flow conditions, turbulence was triggered around peak systole and began to dissipate in late deceleration, and by the end of diastole the flow field almost relaminarized. During the turbulent phase of the flow cycle, the poststenotic flow field was seen to consist of four distinct flow regimes similar to those observed for steady flow. For higher Womersley parameters and Reynolds numbers the turbulent zone was found to be larger and to occupy a greater fraction of the flow cycle. These flow visualization results were compared with the Doppler power measurements made at the same locations and under similar flow conditions. At physiological hematocrits (41%) the onset of turbulence for both steady and pulsatile flow increased the backscattered Doppler power. The location of the peak Doppler power coincided with the region of maximum turbulence observed using the photochromic technique.

Defining the limitations of measurements from Doppler spectral recordings

PURPOSE

The purpose of this study was to determine whether Doppler measurements of peak velocity and four other quantitative measures of spectral shape are affected significantly by the site of the Doppler recording in relation to the location of the maximum stenosis.

METHOD

Continuous-wave and pulsed Doppler recordings were made distal to a 70% (area reduction or 45% diameter reduction) asymmetric stenosis in an in vitro flow model under steady and pulsatile flow conditions. Recordings were taken at six different locations proximal and distal to the stenosis. A photochromic dye technique was used to visualize the actual flow field in the model.

RESULTS

Distal to the stenosis, the flow visualization results demonstrated a strong radial and axial variation of the velocity field and thus explained why the Doppler measurements of peak frequency and spectral broadening were strongly dependent on the recording site. The peak frequency was maximum within the throat of the stenosis and returned to the prestenotic value five tube diameters distal to the stenosis. Other measurements of spectral broadening and spectral shape varied greatly depending on the location of the recording site in the poststenotic region. Higher order spectral moments such as the coefficient of kurtosis were found to exhibit large temporal variability, which makes them inappropriate as diagnostic indicators.

CONCLUSIONS

Because of the complex nature of the poststenotic flow field, these results clearly demonstrate that no single Doppler measurement can accurately quantify the severity of a stenosis. Of the Doppler measurements only peak velocity is related to the severity of stenosis. Reproducible peak velocity measurements are obtained only if the Doppler sample volume is positioned at or very near the throat of the stenosis and at an appropriate radial site that may not necessarily be at the center of the vessel.

MR imaging of regional cardiac function: low-pass filtering of wall thickness curves

Wall thickness curves (WTCs) derived from MR images are subject to considerable measurement error. This study determines the effects of low-pass Fourier filtering of WTCs on functional parameters derived from the curve: peak rate of wall thinning (PRWT) and time to PRWT (TPRWT). The inter-subject standard deviation (SD) of PRWT changed from 0.35 to 0.18, and the SD of TPRWT from 34.3 to 29.5. Differences between neighboring segments decreased from 0.31 to 0.15% mean thickness/ms for PRWT (P = 0.012), and from 35.0 to 19.0 ms for TPRWT (P = 0.005). It is concluded that filtering of MR imaging-derived WTCs contributes to a better representation of myocardial wall motion.

Computer analysis of the early diastolic notch in Doppler sonograms of the uterine arteries

This article describes a set of processing and analysis techniques for automated identification and quantification of the early diastolic notch (EDN), a feature of Doppler sonograms from the uterine arteries which has been associated with adverse pregnancy outcomes such as preeclampsia and intrauterine growth retardation. Examples covering different sonogram types are provided to illustrate the effectiveness and reproducibility of the processing/analysis tools. Also, a receiver-operating characteristic-based evaluation of the EDN quantification and pulsatility indexes is presented, which examines the ability to predict hypertension and/or intrauterine growth retardation, using a set of uterine Doppler sonograms from 92 patients acquired at 18 weeks of gestation. In summary, the ROC results confirm the link between the EDN and abnormal pregnancy outcomes, and suggest that EDN quantification has a higher diagnostic accuracy than the pulsatility index, which characterises the flow waveform in a global manner and therefore does not take explicitly into account the localised nature of the EDN. Quantification of the EDN at 18 weeks of gestation appears to best predict the most severely abnormal pregnancy outcomes.

Comparison of time-frequency distribution techniques for analysis of simulated Doppler ultrasound signals of the femoral artery

The time-frequency distribution of the Doppler ultrasound blood flow signal is normally computed by using the short-time Fourier transform or autoregressive modeling. These two techniques require stationarity of the signal during a finite interval. This requirement imposes some limitations on the distribution estimate. In the present study, three new techniques for nonstationary signal analysis (the Choi-Williams distribution, a reduced interference distribution, and the Bessel distribution) were tested to determine their advantages and limitations for analysis of the Doppler blood flow signal of the femoral artery. For the purpose of comparison, a model stimulating the quadrature Doppler signal was developed, and the parameters of each technique were optimized based on the theoretical distribution. Distributions computed using these new techniques were assessed and compared with those computed using the short-time Fourier transform and autoregressive modeling. Three indexes, the correlation coefficient, the integrated squared error, and the normalized root-mean-squared error of the mean frequency waveform, were used to evaluate the performance of each technique. The results showed that the Bessel distribution performed the best, but the Choi-Williams distribution and autoregressive modeling are also techniques which can generate good time-frequency distributions of Doppler signals.

Cyclic variation of the power of ultrasonic Doppler signals backscattered by polystyrene microspheres and porcine erythrocyte suspensions

Factors affecting the power of the ultrasonic Doppler signal within the flow cycle have been evaluated experimentally using a pulsatile flow loop model. Polystyrene microspheres and porcine red cells suspended in saline solution for hematocrits between 2 and 40% were used as scattering fluid in the flow model. Experiments were performed at mean flow velocities of 11, 64, and 76 cm/s. In laminar flow experiments performed at a mean velocity of 11 cm/s, no variation of the Doppler power was found for both polystyrene microspheres and red cell suspensions (40% hematocrit). When turbulence was induced in the flow model, the power increased during systole, a maximum was observed early after peak systole, and a decrease was obtained in diastole during deceleration of flow. At higher mean flow velocities (64 and 76 cm/s), a significant cyclic variation of the Doppler power was also measured for all values of hematocrits (between 2 and 40%). The power of the signal scattered by microspheres and red cell suspensions at 4% hematocrit dropped in systole, reached a minimum at peak systole, and then increased during early diastole. For red cells suspended in saline at 40% hematocrit, a slightly different pattern of variation was obtained. The cyclic variations observed at high flow velocities and in the presence of turbulence are believed to be associated with cyclic changes in the correlation among particles. In the present study, the effect of red cell aggregation on the cyclic variation has not been addressed.

Cardiac Doppler blood-flow signal analysis. Part 2. Time/frequency representation based on autoregressive modelling

Doppler spectrograms obtained by using autoregressive (AR) modelling based on the Yule-Walker equations were investigated. A complex AR model using the in-phase and the quadrature components of the Doppler signal was used to provide blood-flow directions. The effect of model orders on the spectrogram estimation was studied using cardiac Doppler blood flow signals taken from 20 patients. The 'final prediction error' (FPE) and the 'Akaike's information criterion' (AIC) provided almost identical results in model-order selection. An index, the spectral envelope area (SEA), was used to evaluate the effect of window duration and sampling frequency on AR Doppler spectrogram estimation. The statistical analysis revealed that the SEA obtained from AR modelling was not sensitive to window duration and sampling frequency. This result verified the consistency of the AR Doppler spectrogram. The white-noise characteristics of the AR modelling error signal indicated that the Doppler blood-flow signal can be adequately modelled as a complex AR process. With appropriate model orders, AR modelling provided better Doppler spectrogram estimates than the periodogram.

Effect of ensemble averaging on amplitude and feature variabilities of Doppler spectrograms recorded in the lower limb arteries

The objective of the present study was to analyse the effect of averaging Doppler blood flow signals in lower limb arteries on amplitude and feature variabilities. Doppler signals recorded in 41 iliac and 35 superficial femoral arteries having different categories of stenosis were averaged over 1-15 cardiac cycles. Based on the relative decreasing rate of an index of variability, results indicated that amplitude variability of the spectrograms was exponentially reduced to 30, 6 and 1 per cent when averaging five, ten and 15 cardiac cycles, respectively. Nine diagnostic features were extracted from Doppler spectrograms and their variations from one cardiac cycle to the next quantified. Based on the relative decreasing rate of these variations, results indicated that feature variability was exponentially reduced to 30, 4 and 1 per cent when averaging five, ten and 15 cardiac cycles, respectively. The effect of averaging on the discriminant power of the features to separate the different categories of stenosis was also investigated by performing t-test analyses. Results showed that averaging between five and ten cardiac cycles provided the better discriminant power for most cases, whereas averaging over more than ten cardiac cycles was of little benefit. Based on the spectral analysis technique used in the present study, we conclude that averaging over ten cardiac cycles is sufficient for the analysis of Doppler spectrograms recorded in the lower limbs.