Comparison of the performance of three maximum Doppler frequency estimators coupled with different spectral estimation methods

Automatic Max-Likelihood Envelope Detection Algorithm for Quantitative High-Frame-Rate Ultrasound for Neonatal Brain Monitoring

OBJECTIVE

Post-operative brain injury in neonates may result from disturbed cerebral perfusion, but accurate peri-operative monitoring is lacking. High-frame-rate (HFR) cerebral ultrasound could visualize and quantify flow in all detectable vessels using spectral Doppler; however, automated quantification in small vessels is challenging because of low signal amplitude. We have developed an automatic envelope detection algorithm for HFR pulsed wave spectral Doppler signals, enabling neonatal brain quantitative parameter maps during and after surgery.

METHODS

HFR ultrasound data from high-risk neonatal surgeries were recorded with a custom HFR mode (frame rate = 1000 Hz) on a Zonare ZS3 system. A pulsed wave Doppler spectrogram was calculated for each pixel containing blood flow in the image, and spectral peak velocity was tracked using a max-likelihood estimation algorithm of signal and noise regions in the spectrogram, where the most likely cross-over point marks the blood flow velocity. The resulting peak systolic velocity (PSV), end-diastolic velocity (EDV) and resistivity index (RI) were compared with other detection schemes, manual tracking and RIs from regular pulsed wave Doppler measurements in 10 neonates.

RESULTS

Envelope detection was successful in both high- and low-quality arterial and venous flow spectrograms. Our technique had the lowest root mean square error for EDV, PSV and RI (0.46 cm/s, 0.53 cm/s and 0.15, respectively) when compared with manual tracking. There was good agreement between the clinical pulsed wave Doppler RI and HFR measurement with a mean difference of 0.07.

CONCLUSION

The max-likelihood algorithm is a promising approach to accurate, automated cerebral blood flow monitoring with HFR imaging in neonates.

Resistivity index mapping in Kidney based on ultrasensitive Pulsed-Wave Doppler and automatic spectrogram envelope detection

In recent years, ultrasensitive Pulsed-Wave Doppler (uPWD) ultrasound (US) has emerged as an alternative imaging approach for microcirculation imaging and as a complementary tool to other imaging modalities, such as positron emission tomography (PET). uPWD is based on the acquisition of a large set of highly spatiotemporally coherent frames, which allows high-quality images of a wide field of view to be obtained. In addition, these acquired frames allow calculation of the resistivity index (RI) of the pulsatile flow detected over the entire field of view, which is of great interest to clinicians, for example, in monitoring the transplanted kidney course. This work aims to develop and evaluate a method to automatically obtain an RI map of the kidney based on the uPWD approach. The effect of time gain compensation (TGC) on the visualization of vascularization and aliasing on the blood flow frequency response, was also assessed. A pilot study conducted in patients referred for renal transplant Doppler examination showed that the proposed method provided relative errors of about 15% for RI measurements with respect to conventional pulsed-wave (PW) Doppler.

Stable Automatic Envelope Estimation for Noisy Doppler Ultrasound

Doppler ultrasound technology is widespread in clinical applications and is principally used for blood flow measurements in the heart, arteries, and veins. A commonly extracted parameter is the maximum velocity envelope. However, current methods of extracting it cannot produce stable envelopes in high noise conditions. This can limit clinical and research applications using the technology. In this article, a new method of automatic envelope estimation is presented. The method can handle challenging signals with high levels of noise and variable envelope shapes. Envelopes are extracted from a Doppler spectrogram image generated directly from the Doppler audio signal, making it less device-dependent than existing image-processing methods. The method's performance is assessed using simulated pulsatile flow, a flow phantom, and in vivo ascending aortic flow measurements and is compared with three state-of-the-art methods. The proposed method is the most accurate in noisy conditions, achieving, on average, for phantom data with signal-to-noise ratios (SNRs) below 10 dB, bias and standard deviation of 0.7% and 3.3% lower than the next-best performing method. In addition, a new method for beat segmentation is proposed. When combined, the two proposed methods exhibited the best performance using in vivo data, producing the least number of incorrectly segmented beats and 8.2% more correctly segmented beats than the next best performing method. The ability of the proposed methods to reliably extract timing indices for cardiac cycles across a range of signal quality is of particular significance for research and monitoring applications.

Adaptive Maximal Blood Flow Velocity Estimation From Transcranial Doppler Echos

OBJECTIVE

Novel applications of transcranial Doppler (TCD) ultrasonography, such as the assessment of cerebral vessel narrowing/occlusion or the non-invasive estimation of intracranial pressure (ICP), require high-quality maximal flow velocity waveforms. However, due to the low signal-to-noise ratio of TCD spectrograms, measuring the maximal flow velocity is challenging. In this work, we propose a calibration-free algorithm for estimating maximal flow velocities from TCD spectrograms and present a pertaining beat-by-beat signal quality index.

METHODS

Our algorithm performs multiple binary segmentations of the TCD spectrogram and then extracts the pertaining envelopes (maximal flow velocity waveforms) via an edge-following step that incorporates physiological constraints. The candidate maximal flow velocity waveform with the highest signal quality index is finally selected.

RESULTS

We evaluated the algorithm on 32 TCD recordings from the middle cerebral and internal carotid arteries in 6 healthy and 12 neurocritical care patients. Compared to manual spectrogram tracings, we obtained a relative error of -1.5%, when considering the whole waveform, and a relative error of -3.3% for the peak systolic velocity.

CONCLUSION

The feedback loop between the signal quality assessment and the binary segmentation yields a robust algorithm for maximal flow velocity estimation. Clinical Impact: The algorithm has already been used in our ICP estimation pipeline. By making the code and the data publicly available, we hope that the algorithm will be a useful building block for the development of novel TCD applications that require high-quality flow velocity waveforms.

A Robust Automatic Ultrasound Spectral Envelope Estimation

Accurate estimation of ultrasound Doppler spectrogram envelope is essential for clinical pathological diagnosis of various cardiovascular diseases. However, due to intrinsic spectral broadening in the power spectrum and speckle noise existing in ultrasound images, it is difficult to obtain the accurate maximum velocity. Each of the standard existing methods has their own limitations and does not work well in complicated recordings. This paper proposes a robust automatic spectral envelope estimation method that is more accurate in phantom recordings and various in-vivo recordings than the currently used methods. Comparisons were performed on phantom recordings of the carotid artery with varying noise and additional in-vivo recordings. The accuracy of the proposed method was on average 8% greater than the existing methods. The experimental results demonstrate the wide applicability under different blood conditions and the robustness of the proposed algorithm.

Quantitative Doppler Analysis Using Conventional Color Flow Imaging Acquisitions

Interleaved acquisitions used in conventional triplex mode result in a tradeoff between the frame rate and the quality of velocity estimates. On the other hand, workflow becomes inefficient when the user has to switch between different modes, and measurement variability is increased. This paper investigates the use of power spectral Capon estimator in quantitative Doppler analysis using data acquired with conventional color flow imaging (CFI) schemes. To preserve the number of samples used for velocity estimation, only spatial averaging was utilized, and clutter rejection was performed after spectral estimation. The resulting velocity spectra were evaluated in terms of spectral width using a recently proposed spectral envelope estimator. The spectral envelopes were also used for Doppler index calculations using in vivo and string phantom acquisitions. In vivo results demonstrated that the Capon estimator can provide spectral estimates with sufficient quality for quantitative analysis using packet-based CFI acquisitions. The calculated Doppler indices were similar to the values calculated using spectrograms estimated on a commercial ultrasound scanner.

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.

Pitfalls of Doppler Measurements for Arterial Blood Flow Quantification in Small Animal Research: A Study Based on Virtual Ultrasound Imaging

High-resolution Doppler is a popular tool for evaluating cardiovascular physiology in mutant mice, though its 1-D nature and spectral broadening processes complicate interpretation of the measurement. Hence, it is crucial for pre-clinical researchers to know how error sources in Doppler assessments reveal themselves in the murine arterial system. Therefore, we performed virtual Doppler experiments in a computer model of an aneurysmatic murine aorta with full control of the imaging and insonified fluid dynamics. We observed significant variability in Doppler performance and derived vascular indices depending on the interrogated flow, operator settings and signal processing. In particular, we found that (i) Doppler spectra in the upper aortic branches and celiac artery exhibited more broadening because of complex out-of-beam flow paths; (ii) mean frequency tracking outperforms tracking of the outer envelope, but is sensitive to errors in angle correction; and (iii) imaging depths deviating much from the elevation focus suffer from decreased spectral quality.

Accurate blood peak velocity estimation using spectral models and vector doppler

Ultrasound blood peak velocity estimates are routinely used for diagnostics, such as the grading of a stenosis. The peak velocity is typically assessed from the Doppler spectrum by locating the highest frequency detectable from noise. The selected frequency is then converted to velocity by the Doppler equation. This procedure contains several potential sources of error: the frequency selection is noise dependent and sensitive to the spectral broadening, which, in turn, is affected by the Doppler angle uncertainty. The result is, often, an inaccurate estimate. In this work we propose a new method that removes the aforementioned errors. The frequency is selected by exploiting a mathematical model of the Doppler spectrum that has recently been introduced. When a very large sample volume is used, which includes all the vessel section, the model is capable of predicting the exact threshold to be used without the need of broadening compensation. The angle ambiguity is solved by applying the threshold to the Doppler spectra measured from two different directions, according to the vector Doppler technique. The proposed approach has here been validated through Field II simulations, phantom experiments, and tests on volunteers by using defocused waves to insonify a large region from a linear array probe. A mean error lower than 1% and a mean coefficient of variability lower than 5% were measured in a variety of experimental conditions.

An improved Doppler model for obtaining accurate maximum blood velocities

Maximum blood velocity estimates are frequently required in diagnostic applications, including carotid stenosis evaluation, arteriovenous fistula inspection, and maternal-fetal examinations. However, the currently used methods for ultrasound measurements are inaccurate and often rely on applying heuristic thresholds to a Doppler power spectrum. A new method that uses a mathematical model to predict the correct threshold that should be used for maximum velocity measurements has recently been introduced. Although it is a valuable and deterministic tool, this method is limited to parabolic flows insonated by uniform pressure fields. In this work, a more generalized technique that overcomes such limitations is presented. The new approach, which uses an extended Doppler spectrum model, has been implemented in an experimental set-up based on a linear array probe that transmits defocused steered waves. The improved model has been validated by Field II simulations and phantom experiments on tubes with diameters between 2mm and 8mm. Using the spectral threshold suggested by the new model significantly higher accuracy estimates of the peak velocity can be achieved than are now clinically attained, including for narrow beams and non-parabolic velocity profiles. In particular, an accuracy of +1.2±2.5 cm/s has been obtained in phantom measurements for velocities ranging from 20 to 80 cm/s. This result represents an improvement that can significantly affect the way maximum blood velocity is investigated today.

Finding the peak velocity in a flow from its Doppler spectrum

The signal backscattered by blood cells crossing a sample volume produces a Doppler power spectrum determined by the scatterers¿ velocity distribution. Because of intrinsic spectral broadening, the peak Doppler frequency observed does not correspond to the peak velocity in the flow. Several methods have been proposed for estimating the maximum velocity component--an important clinical parameter--but these methods are approximate, based on heuristic thresholds that can be inaccurate and strongly affected by noise. Reported here is a method of modeling the Doppler power spectrum of a flow, and from that model, determining what Doppler frequency on the descending slope of the power spectrum corresponds to the peak velocity in the insonated flow. It is shown that, for a fully insonated flow with a parabolic velocity distribution, the peak velocity corresponds to the Doppler frequency at the half-power point on that slope. The method is demonstrated to be robust with regard to the effects of noise and valid for a wide range of acquisition parameters. Experimental maximum velocity measurements on steady flows with rates between 100 and 300 mL/min (peak velocity range 6.6 cm/s to 19.9 cm/s) show a mean bias error that is smaller than 1%.

Statistical distributions of potential interest in ultrasound speckle analysis

Compound statistical modelling of the uncompressed envelope of the backscattered signal has received much interest recently. In this note, a comprehensive collection of models is derived for the uncompressed envelope of the backscattered signal by compounding the Nakagami distribution with 13 flexible families. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. The sensitivity of the models to their various parameters is examined. It is expected that this work could serve as a useful reference and lead to improved modelling of the uncompressed envelope of the backscattered signal.

Effect of vessel curvature on Doppler derived velocity profiles and fluid flow

Side-branches and curvatures in the arterial tree yield deviations from the axial oriented velocity. Velocity or volume flow estimates based on the assumption that flow is axially oriented are of limited value at these sites. This article evaluates information obtainable by using a multigate Doppler ultrasound (US) instrument used with curved phantoms, which resemble the human coronary arteries. The comparison of experimental velocity data with data provided by an accurate computational fluid dynamics (CFD) method shows differences in the range of 4 to 11% for four curvatures with different radii. Multigate data are also used to estimate the volume flow in the curved segments at different experimental conditions. An error lower than 15% is obtained, to be compared with a 24% error obtained by assuming a parabolic velocity profile. In particular, it is shown that the residual error is not related to the small deviation of the velocity vectors from the axial direction due to the presence of secondary velocity components, which are found to be of magnitude less than 10% with respect to the axial velocity component.

Improved Maximum Frequency Estimation With Application to Instantaneous Mean Frequency Estimation of Surface Electromyography

The purpose of this study was to improve the maximum-frequency estimation. Three methods to estimate the maximum frequency of a bandlimited signal with additive white noise were compared. Two existing methods, the threshold-crossing method (TCM) and the hybrid method, were modified for time-frequency representations. A novel approach, the running-block threshold method (RBTM), was introduced. Based on calculation of detection probability (sensitivity) the RBTM improved the maximum-frequency estimate as compared with the TCM. The maximum-frequency estimation methods were also used to determine the integration interval for instantaneous mean-frequency (IMNF) estimation from synthesized surface electromyography containing white noise. Results showed that the IMNF estimate was improved by using any of the three methods and that the RBTM gave the best IMNF estimate.

An in vitro system for Doppler ultrasound flow studies in the stenosed carotid artery bifurcation

To investigate the correlation between disease severity and Doppler spectral measurements in the carotid artery bifurcation, a unique in vitro system has been developed that mimics the human vasculature with respect to both anatomy and flow perfusion. Agar-based carotid phantoms are perfused with a blood-mimicking fluid using a computer-controlled pump and realistic pulsatile flow waveform. A three-axis translational stage allows the lumen to be interrogated with a 0.6-microL Doppler sample volume at the desired spatial intervals using a semiautomated acquisition system, to collect 10 cardiac cycles of gated quadrature data at each site. Off-line analysis, including a 1024-point FFT, produces a 4-D (i.e., time-varying 3-D) Doppler velocity data set with 1.3-cm/s velocity resolution and 12-ms temporal resolution. Using this system, in vitro flow in bifurcations with both normal and stenosed lumen geometry (from 30% to 80% stenosis by NASCET criteria) can be studied, along with the effect of factors, such as stenosis geometry (concentric vs. eccentric) and flow rate, on the observed Doppler ultrasound (US) spectra and haemodynamic patterns.

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.

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.

Detection of vascular haemodynamics through a high-speed velocity profiler

OBJECTIVE

This paper aims at demonstrating that ultrasound Doppler multigate spectral analysis performed with advanced equipment may provide detailed and significant haemodynamic information.

METHODS

A novel multigate system was recently introduced and shown capable of performing real-time spectral analysis of Doppler data from 64 resolution cells located at different depths from the transducer. The system extends the typical capabilities of conventional Pulsed Wave (PW) equipment by displaying the full spectral content of Doppler signals over an ultrasound scan line rather than in a single resolution cell. In cases where it is appropriate to display the available information in a simpler form, parameters such as the maximum frequency can be extracted from each spectrum, by using conventional or advanced image processing methods.

RESULTS

In-vitro experiments show that the multigate system can perform velocity measurements with good accuracy and precision. Examples of in vivo profiles detected from carotid, femoral and radial arteries are presented. In particular, the first results obtained from the aorta are shown.

CONCLUSIONS

Blood flow behavior can be accurately investigated using a real-time multigate system which extends Doppler spectral analysis to a whole scan line.

Spectrogram analysis of arterial Doppler signals for off-line automated hits detection

Recently, a time processing of arterial Doppler signals was proposed to detect automatically high-intensity transient signals (HITS). This technique provided satisfactory detection results, but was not always constantly accurate, particularly with high-resistance blood velocity profiles. A time-frequency processing, based on the spectrogram, is presented to detect the presence of emboli in the arterial Doppler signals. The method uses the narrow-band hypothesis and extracts the detection criterion from the time-frequency representation (TFR). A first database of 560 peripheral arterial Doppler HITS was created to study microemboli and to define the normal limits to be used in our method. A threshold was experimentally defined using this database, and then applied to 38 recordings from 12 patients. Using another database, 6 human expert Doppler users reported 140, 176, 155, 161, 161 and 146 HITS, corresponding to a total of 197 different observed HITS. When an event was detected by at least 6, 5, 4, 3, 2 and 1 of the observers, sensitivity of the automatic detection was 93.9, 91.7, 89.6, 88.7, 84.7 and 73.1%, respectively. The sensitivity of our automatic detection is, thus, highly associated with the number of observers in agreement. A preliminary experiment has been performed to test the method in the case of long recording duration. In 15 patients, 6 h 24 min of recordings have been analyzed. The proposed automated processing provided an overall sensibility of 91.5%. The present work shows that this detection scheme preserves good sensibility and improves the positive predictive value compared with the time-processing recently proposed.