Adaptive spectral estimators for fast flow-profile detection

Adaptive Spectral Doppler Estimation Based on the Modified Amplitude Spectrum Capon

In conventional ultrasound systems, the compromise between frequency and temporal resolution limits the quality of the spectrograms and the ability to track fast blood flows. The main objective of this study was to identify a method that could reduce spectral broadening over time by reducing the observations and improving the spectral resolution and contrast. This problem is more pronounced in the process of imaging at higher blood velocities when using a short Doppler signal observation window (OW) in adaptive methods. The proposed adaptive technique, which is based on the covariance matrix Eigen space and the amplitude spectrum Capon (ASC) algorithm, managed to improve the spectral resolution and contrast compared with other adaptive algorithms within a shorter observation time, and it offered a narrower power spectrum and a more accurate spectrogram over time in combination with a coherence-based post filter. All methods were tested through various simulations. First, an analysis was carried out by simulating the femoral artery flow and the time-independent parabolic flow using the Field II simulator. Then, the performance of the proposed method was evaluated under more realistic conditions using a computational fluid dynamics simulation of complex flow fields in a carotid bifurcation model. Afterward, in vivo clinical data on the hepatic vein were used to validate the proposed method. Finally, the accuracy of the velocity estimated by different methods was evaluated through a mean-square-error assessment. Not only could the proposed method show significant improvements using extreme small OWs, N=[2, 4] , in the simulated data in terms of frequency resolution and contrast, but it also managed to offer an improvement of 74%, 73.3%, 22.2%, and 50% in frequency resolution, and an increase of 96.5, 90.2, 49, and 31.5 dB in contrast using in vivo clinical data compared with the Capon, amplitude and phase estimation (APES), projection-based Capon, and projection-based APES, respectively, for the OW of N=4 .

Adaptive transverse blood velocity estimation in medical ultrasound: A simulation study

Undoubtedly, highly valuable information about vascular anomalies is attained by the examination of the blood flow profile. The chief drawback of the conventional medical ultrasound in preparation of the blood periodogram is the measurement system shortcoming at the beam to flow angles near 90°. Recently, a method based on transverse oscillation (TO) approach, known as "Fourth-order estimation", has been developed to directly estimate the transverse power spectral density (PSD) of the fully transverse blood flow. One of the basic requirements to accomplish acceptable PSDs by this technique is the sufficiently large observation window. In this paper, two adaptive approaches for efficient estimation of the velocity spectrum of a fully transverse flow by a limited observation window length are described. The first proposed adaptive approach is based on the minimum variance adaptive spectral estimation in combination with the well-known TO technique (TO-MV). Then, by exploiting the eigenspace separation of the observed data to eliminate the contribution of the undesired components, the second technique (TO-EIBMV) is developed. The approaches are validated using Field II simulations for pulsating flow. The proposed methods are tested and compared to the conventional TO transverse spectral estimator by metrics of relative standard deviation (RSD) and relative bias (RB). One of the main achievements is the decrement of the required data samples for spectrogram estimation, which leads to a better temporal resolution. Moreover, for the analyzed adaptive techniques, the robustness of the estimation results for the beam to flow angles of 60-90° and vessel depths ranging from 20 mm to 60 mm are investigated.

Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity

In Doppler analysis, the power spectral density (PSD), which accounts for the axial velocity distribution of the blood scatterers, is estimated. The conventional spectral estimator is Welch's method, which suffers from frequency leakage at small observation window length. The performance of adaptive techniques such as blood power Capon (BPC) has been promising at the cost of higher computation complexity. Reducing the computational complexity while retaining the benefits of BPC would be necessary for real-time implementation. The purpose of the work described here was to investigate whether it is possible to decrease the computation load in BPC and still obtain acceptable results. The computation complexity in BPC is owing primarily to the matrix inversion required for computing the PSD estimate. We here propose the subspace blood power Capon technique, which employs a data covariance matrix with reduced number of rows in estimation of the weight vector. In maximum velocity estimation in the spectra, the signal noise slope intersection envelop estimator that makes use of the integrated power spectrum is employed. The evaluations are made based on both simulated and in vivo data. The results indicate that it is possible to reduce the order of complexity to almost 12.25% at the cost of 2.31% and 2.24% increases in the relative standard deviation and relative bias of the estimates. Moreover, the Wiener post-filter as a post-weighting factor, which will be multiplied by the final weight vector of the spectral estimator, estimates the power of the desired signal and the power of the interference plus noise to improve the contrast. The proposed estimator has exhibited a promising performance at beam-to-flow angles of 45°, 60° and 75°. Furthermore, the robust performance of the proposed estimator against variation in the flow rate is also documented.

Data-Adaptive Coherent Demodulator for High Dynamics Pulse-Wave Ultrasound Applications

Pulse-Wave Doppler (PWD) ultrasound has been applied to the detection of blood flow for a long time; recently the same method was also proven effective in the monitoring of industrial fluids and suspensions flowing in pipes. In a PWD investigation, bursts of ultrasounds at 0.5–10 MHz are periodically transmitted in the medium under test. The received signal is amplified, sampled at tens of MHz, and digitally processed in a Field Programmable Gate Array (FPGA). First processing step is a coherent demodulation. Unfortunately, the weak echoes reflected from the fluid particles are received together with the echoes from the high-reflective pipe walls, whose amplitude can be 30–40 dB higher. This represents a challenge for the input dynamics of the system and the demodulator, which should clearly detect the weak fluid signal while not saturating at the pipe wall components. In this paper, a numerical demodulator architecture is presented capable of auto-tuning its internal dynamics to adapt to the feature of the actual input signal. The proposed demodulator is integrated into a system for the detection of the velocity profile of fluids flowing in pipes. Simulations and experiments with the system connected to a flow-rig show that the data-adaptive demodulator produces a noise reduction of at least of 20 dB with respect to different approaches, and recovers a correct velocity profile even when the input data are sampled at 8 bits only instead of the typical 12–16 bits.

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.

Real-Time Blood Velocity Vector Measurement Over a 2-D Region

Quantitative blood velocity measurements, as currently implemented in commercial ultrasound scanners, are based on pulsed-wave (PW) spectral Doppler and are limited to detect the axial component of the velocity in a single sample volume. On the other hand, vector Doppler methods produce angle-independent estimates by, e.g., combining the frequency shifts measured from different directions. Moreover, thanks to the transmission of plane waves, the investigation of a 2-D region is possible with high temporal resolution, but, unfortunately, the clinical use of these methods is hampered by the massive calculation power required for their real-time execution. In this paper, we present a novel approach based on the transmission of plane waves and the simultaneous reception of echoes from 16 distinct subapertures of a linear array probe, which produces eight lines distributed over a 2-D region. The method was implemented on the ULAO-OP 256 research scanner and tested both in phantom and in vivo. A continuous real-time refresh rate of 36 Hz was achieved in duplex combination with a standard B-mode at pulse repetition frequency of 8 kHz. Accuracies of -11% on velocity and of 2°on angle measurements have been obtained in phantom experiments. Accompanying movies show how the method improves the quantitative measurements of blood velocities and details the flow configurations in the carotid artery of a volunteer.

Combined 2-D Vector Velocity Imaging and Tracking Doppler for Improved Vascular Blood Velocity Quantification

Measurement of the maximum blood flow velocity is the primary means for determining the degree of carotid stenosis using ultrasound. The current standard for estimating the maximum velocity is pulsed-wave Doppler with manual angle correction, which is prone to error and interobserver variability. In addition, spectral broadening in the velocity spectra leads to overestimation of maximal velocities. In this paper, we propose to combine two velocity estimation methods to reduce the bias and variability in maximum velocity measurements. First, the direction of the blood flow is estimated using an aliasing-resistant least squares vector Doppler technique. Then, tracking Doppler is performed on the same data, using the direction of the vector Doppler estimate as the tracking direction. Simulations show that the method can estimate a maximum velocity of 2 m/s with accuracy 5% for beam-to-flow angles between 20° and 75°, and that the primary source of error is inaccuracy in the flow direction estimate from vector Doppler. Simulations of complex flow in a carotid bifurcation demonstrated that the combined technique provided spectral velocity profiles corresponding well with the true maximum velocity trace, and that the bias originating from the directional estimate was within 5% for all spatial points. A healthy volunteer and a volunteer with carotid artery stenosis were imaged, showing in vivo feasibility of the method, for high velocities and with beam-to-flow angles varying throughout the cardiac cycle.

Adaptive Spectral Estimation Methods in Color Flow Imaging

Clutter rejection for color flow imaging (CFI) remains a challenge due to either a limited amount of temporal samples available or nonstationary tissue clutter. This is particularly the case for interleaved CFI and B-mode acquisitions. Low velocity blood signal is attenuated along with the clutter due to the long transition band of the available clutter filters, causing regions of biased mean velocity estimates or signal dropouts. This paper investigates how adaptive spectral estimation methods, Capon and blood iterative adaptive approach (BIAA), can be used to estimate the mean velocity in CFI without prior clutter filtering. The approach is based on confining the clutter signal in a narrow spectral region around the zero Doppler frequency while keeping the spectral side lobes below the blood signal level, allowing for the clutter signal to be removed by thresholding in the frequency domain. The proposed methods are evaluated using computer simulations, flow phantom experiments, and in vivo recordings from the common carotid and jugular vein of healthy volunteers. Capon and BIAA methods could estimate low blood velocities, which are normally attenuated by polynomial regression filters, and may potentially give better estimation of mean velocities for CFI at a higher computational cost. The Capon method decreased the bias by 81% in the transition band of the used polynomial regression filter for small packet size ( N=8 ) and low SNR (5 dB). Flow phantom and in vivo results demonstrate that the Capon method can provide color flow images and flow profiles with lower variance and bias especially in the regions close to the artery walls.

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.

Real-time vector velocity assessment through multigate Doppler and plane waves

Several ultrasound (US) methods have been recently proposed to produce 2-D velocity vector fields with high temporal and spatial resolution. However, the real-time implementation in US scanners is heavily hampered by the high calculation power required. In this work, we report a real-time vector Doppler imaging method which has been integrated in an open research system. The proposed approach exploits the plane waves transmitted from two sub-arrays of a linear probe to estimate the velocity vectors in 512 sample volumes aligned along the probe axis. The method has been tested for accuracy and reproducibility through simulations and in vitro experiments. Simulations over a 0° to 90° angle range of a 0.5 m/s peak parabolic flow have yielded 0.75° bias and 1.1° standard deviation for direction measurement, and 0.6 cm/s bias with 3.1% coefficient of variation for velocity assessment. In vitro tests have supported the simulation results. Preliminary measurements on the carotid artery of a volunteer have highlighted the real-time system capability of imaging complex flow configurations in an intuitive, easy, and quick way, as shown in a sample supplementary movie. These features have allowed reproducible peak velocity measurements to be obtained, as needed for quantitative investigations on patients.

Accuracy and reproducibility of a novel dynamic volume flow measurement method

In clinical practice, blood volume flow (BVF) is typically calculated assuming a perfect parabolic and axisymmetric velocity distribution. This simple approach cannot account for the complex flow configurations that are produced by vessel curvatures, pulsatility and diameter changes and, therefore, results in a poor estimation. Application of the Womersley model allows compensation for the flow distortion caused by pulsatility and, with some adjustment, the effects of slight curvatures, but several problems remain unanswered. Two- and three-dimensional approaches can acquire the actual velocity field over the whole vessel section, but are typically affected by a limited temporal resolution. The multigate technique allows acquisition of the actual velocity profile over a line intersecting the vessel lumen and, when coupled with a suitable wall-tracking method, can offer the ideal trade-off among attainable accuracy, temporal resolution and required calculation power. In this article, we describe a BVF measurement method based on the multigate spectral Doppler and a B-mode edge detector algorithm for wall-position tracking. The method has been extensively tested on the research platform ULA-OP, with more than 1700 phantom measurements at flow rates between 60 and 750 mL/min, steering angles between 10 ° and 22 ° and constant, sinusoidal or pulsed flow trends. In the averaged BVF measurement, we found an underestimation of about -5% and a coefficient of variability (CV) less than 6%. In instantaneous measurements (e.g., systolic peak) the CV was in the range 2%-8.5%. These results were confirmed by a preliminary test on the common carotid artery of 10 volunteers (CV = 2%-11%).