Jorgen Avdal

An Extended Least Squares Method for Aliasing-Resistant Vector Velocity Estimation

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit-receive setups. Furthermore, it is demonstrated that careful design of the transmit-receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At -5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers.

Effects of reverberations and clutter filtering in pulsed Doppler using sparse sequences

Duplex ultrasound is a modality in which an ultrasound system is used for simultaneous acquisition of both B-mode images and velocity (Doppler) data. Conventional duplex sequences interleave packets of B-mode and Doppler transmissions, producing undesirable gaps during B-mode interruptions. In recent years, several techniques have been proposed for avoiding such gaps by using sparse sequences, in which velocity spectra are generated from nonuniformly sampled Doppler data containing frequent B-mode interruptions. In this work, two negative effects are discussed that may influence velocity estimation when using nonuniformly sampled sequences. First, it is shown that long reverberation times lead to discontinuities in the signal from stationary clutter after each B-mode interruption. Second, using frequency analysis, it is shown that clutter filtering of nonuniformly sampled data may introduce artifacts in the velocity spectrum, and also lead to significant bias in mean velocity estimates. Methods are presented for quantification of these effects, and utilized to analyze three types of sparse duplex sequences for blood velocity estimation. In particular, it is argued that the use of such sequences in cardiac applications is not recommended because of long reverberation time. Additionally, it is found that the use of regression filters to filter nonuniformly sampled data may produce significant artifacts in pulsed wave Doppler spectra, but is less significant for color Doppler imaging applications. In vitro and in vivo examples are included showing the presence and magnitude of these problems in clinically relevant applications.

Investigations of spectral resolution and angle dependency in a 2-D tracking doppler method

An important source of error in velocity measurements from conventional pulsed wave (PW) Doppler is the angle used for velocity calibration. Because there are great uncertainties and interobserver variability in the methods used for Doppler angle correction in the clinic today, it is desirable to develop new and more robust methods. In this work, we have investigated how a previously presented method, 2-D tracking Doppler, depends on the tracking angle. A signal model was further developed to include tracking along any angle, providing velocity spectra which showed good agreement with both experimental data and simulations. The full-width at half-maximum (FWHM) bandwidth and the peak value of predicted power spectra were calculated for varying tracking angles. It was shown that the spectra have lowest bandwidth and maximum power when the tracking angle is equal to the beam-to-flow angle. This may facilitate new techniques for velocity calibration, e.g., by manually adjusting the tracking angle, while observing the effect on the spectral display. An in vitro study was performed in which the Doppler angles were predicted by the minimum FWHM and the maximum power of the 2-D tracking Doppler spectra for 3 different flow angles. The estimated Doppler angles had an overall error of 0.24° ± 0.75° when using the minimum FWHM. With an in vivo example, it was demonstrated that the 2-D tracking Doppler method is suited for measurements in a patient with carotid stenosis.

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.

Combined 2-D vector and tracking Doppler imaging for improved blood velocity quantification

The maximum velocity of blood flow is the primary means for determining the degree of stenosis in the carotid artery. The current standard for estimating the maximum velocity is Pulsed Wave (PW) Doppler with manual angle correction, assuming that the flow is parallel to the vessel wall. This assumption is not always correct, leading to errors in the velocity estimates and potentially in the assessment of the degree of stenosis. In addition, spectral broadening in the velocity spectra lead to overestimation of maximal velocities. In this work, 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 a least squares vector Doppler technique. Then, tracking Doppler is performed on the same data, using the direction of the vector Doppler estimate as tracking direction. Simulation results show that the method can estimate the maximum velocity with a bias smaller than 5% for beam-to-flow angles between 30° and 85°, and that the primary source of error is inaccuracy in the flow direction estimate from vector Doppler. In vivo results show the feasibility of the method in the common carotid artery of a healthy volunteer, and also indicate that the beam-to-flow angle changes during 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.

3D tracking Doppler for quantitative blood flow assessment of coronary arteries

Several challenges limit the use of Pulsed Wave (PW) Doppler to assess coronary blood flow: 1) Transit time effect causes spectral broadening in regions with high blood flow such as stenoses, leading to overestimation of maximum velocities. 2) High beam to flow angles (>60°) and out of plane components often occur, making manual positioning of the sample volume and angle correction difficult. 2D tracking Doppler (2D TD) is a previously presented method that can reduce transit time effect by tracking blood scatterers along the flow direction and improve spectral resolution [Fredriksen, 2013]. In this work, we perform 3D high frame rate imaging of the coronaries to enable easier retrospective Doppler estimation. We also extend the previously proposed algorithm to track along any 3D direction, enabling us to measure out of plane components which could not be otherwise estimated.

3D tracking Doppler for improved quantitative blood flow assessment of coronary arteries

Several challenges limit the use of Pulsed Wave (PW) Doppler to assess blood flow in the coronary arteries. The transit time effect causes spectral broadening in regions with high blood velocities such as coronary stenoses, leading to overestimation of maximum velocities. In this work we use a modified commercial 3D ultrasound imaging system to perform trans-thoracic, 3D high frame-rate imaging of the coronary arteries and enable retrospective Doppler estimation. We also introduce 3D tracking Doppler, a spectral estimator that increases transit time by tracking the blood scatterers along a manually defined direction in the imaging volume. In vitro results from a thread phantom at 1 m/s and 70° beam-to-flow angle show a three times reduction in spectral broadening and a 5 dB increase in spectral SNR. In vivo feasibility of the method is also shown in a healthy volunteer.

Adaptive clutter filtering based on tissue vector velocities

Color Doppler and Vector Flow imaging are ultrasound imaging modalities that are primarily used for qualitative measurements or navigation. One main challenge before these modalities can be used quantitatively in clinical applications, is that clutter suppression filters or residual clutter signal lead to bias and variance in the blood velocity estimates which varies throughout the cardiac cycle. In this work, a Finite Impulse Response filter with adaptive filter order is evaluated for quantification of blood flow velocities, and compared to an eigenvector based filter with adaptive clutterspace dimension. The techniques were applied to data from a healthy volunteer, and data from a volunteer with a carotid stenosis. Results showed good correspondence between the two adaptive methods, and both methods produced more robust results than obtained using a Finite Impulse Response with fixed filter order.

Fast ultrasound simulation method for evaluation of velocity estimators

Both mean velocity and spectral Doppler techniques are prone to estimation errors and variance, and new velocity estimation techniques need to be validated extensively before they can be considered for clinical use. Quantitative validation is commonly performed using simulations, with the advantage that the underlying velocity field is known. However, simulations typically produce only realizations of the signal, so that multiple simulations or long temporal windows are necessary to estimate the statistical properties of the estimators.