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Ultrasound (US) examination of the common carotid artery was compared with a through-plane magnetic resonance imaging (MRI) sequence to validate a recently proposed technique for 3-D US vector flow imaging. Data from the first volunteer examined were used as the training set, before volume flow and peak velocities were calculated for the remaining eight volunteers. Peak systolic velocities (PSVs) and volume flow obtained with 3-D US were, on average, 34% higher and 24% lower than those obtained with MRI, respectively. A high correlation was observed for PSV (r = 0.79), whereas a lower correlation was observed for volume flow (r = 0.43). The overall standard deviations were ±5.7% and ±5.7% for volume flow and PSV with 3-D US, compared with ±2.7% and ±3.2% for MRI. Finally, the data were re-processed with a change in the parameter settings for the echo-canceling filter to investigate its influence on overall performance. PSV was less affected by the re-processing, whereas the difference in volume flow between 3-D vector flow imaging and MRI was reduced to -9%, and with an improved overall standard deviation of ±4.7%. The results illustrate the feasibility of using 3-D US for precise and angle-independent volume flow and PSV estimation in vivo., (Copyright © 2017 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.)

A method for vector velocity volume flow estimation is presented, along with an investigation of its sources of error and correction of actual volume flow measurements. Volume flow errors are quantified theoretically by numerical modeling, through flow phantom measurements, and studied in vivo. This paper investigates errors from estimating volumetric flow using a commercial ultrasound scanner and the common assumptions made in the literature. The theoretical model shows, e.g. that volume flow is underestimated by 15%, when the scan plane is off-axis with the vessel center by 28% of the vessel radius. The error sources were also studied in vivo under realistic clinical conditions, and the theoretical results were applied for correcting the volume flow errors. Twenty dialysis patients with arteriovenous fistulas were scanned to obtain vector flow maps of fistulas. When fitting an ellipsis to cross-sectional scans of the fistulas, the major axis was on average 10.2mm, which is 8.6% larger than the minor axis. The ultrasound beam was on average 1.5mm from the vessel center, corresponding to 28% of the semi-major axis in an average fistula. Estimating volume flow with an elliptical, rather than circular, vessel area and correcting the ultrasound beam for being off-axis, gave a significant (p=0.008) reduction in error from 31.2% to 24.3%. The error is relative to the Ultrasound Dilution Technique, which is considered the gold standard for volume flow estimation for dialysis patients. The study shows the importance of correcting for volume flow errors, which are often made in clinical practice., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Secondary rotational flow and systolic backflow are seen in the ascending aorta and, in this study, were analyzed with the vector velocity method transverse oscillation. Twenty-five patients were scanned intra-operatively, and the vector velocities were related to estimates of transesophageal echocardiography and pulmonary artery catheter thermodilution, and associated with gender, age, aortic diameter, atherosclerotic plaques, left ventricular ejection fraction and previous myocardial infarctions. Secondary flow was present for all patients. The duration and rotational frequency (p < 0.001) and the duration and flow direction of the secondary flow (p < 0.002) were associated. Systolic backflow was present in 40% of the patients and associated with systolic velocities (p < 0.002) and the presence of atherosclerotic plaques (p < 0.001). No other significant associations were observed. The study indicates that backflow is injurious and that secondary flow is a normal flow phenomenon. The study also shows that transverse oscillation can provide new information on blood flow in the ascending aorta., (Copyright © 2016 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.)

In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to provide good spectral resolution and contrast even when the observation window is very short. The 2 adaptive techniques are tested and compared with the averaged periodogram (Welch's method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set of matched filters (one for each velocity component of interest) and filtering the blood process over slow-time and averaging over depth to find the PSD. The methods are tested using various experiments and simulations. First, controlled flow-rig experiments with steady laminar flow are carried out. Simulations in Field II for pulsating flow resembling the femoral artery are also analyzed. The simulations are followed by in vivo measurement on the common carotid artery. In all simulations and experiments it was concluded that the adaptive methods display superior performance for short observation windows compared with the averaged periodogram. Computational costs and implementation details are also discussed.

This paper investigates the use of coded excitation for blood flow estimation in medical ultrasound. Traditional autocorrelation estimators use narrow-band excitation signals to provide sufficient signal-to-noise-ratio (SNR) and velocity estimation performance. In this paper, broadband coded signals are used to increase SNR, followed by subband processing. The received broadband signal is filtered using a set of narrow-band filters. Estimating the velocity in each of the bands and averaging the results yields better performance compared with what would be possible when transmitting a narrow-band pulse directly. Also, the spatial resolution of the narrow-band pulse would be too poor for brightness-mode (B-mode) imaging, and additional transmissions would be required to update the B-mode image. For the described approach in the paper, there is no need for additional transmissions, because the excitation signal is broadband and has good spatial resolution after pulse compression. This means that time can be saved by using the same data for B-mode imaging and blood flow estimation. Two different coding schemes are used in this paper, Barker codes and Golay codes. The performance of the codes for velocity estimation is compared with a conventional approach transmitting a narrow-band pulse. The study was carried out using an experimental ultrasound scanner and a commercial linear array 7 MHz transducer. A circulating flow rig was scanned with a beam-to-flow angle of 60 degrees. The flow in the rig was laminar and had a parabolic flow-profile with a peak velocity of 0.09 m/s. The mean relative standard deviation of the velocity estimate using the reference method with an 8-cycle excitation pulse at 7 MHz was 0.544% compared with the peak velocity in the rig. Two Barker codes were tested with a length of 5 and 13 bits, respectively. The corresponding mean relative standard deviations were 0.367% and 0.310%, respectively. For the Golay coded experiment, two 8-bit codes were used, and the mean relative standard deviation was 0.335%.

Conventional ultrasound methods for acquiring color images of blood velocity are limited by a relatively low frame-rate and are restricted to give velocity estimates along the ultrasound beam direction only. To circumvent these limitations, the method presented in this paper uses 3 techniques: 1) The ultrasound is not focused during the transmissions of the ultrasound signals; 2) A 13-bit Barker code is transmitted simultaneously from each transducer element; and 3) The 2-D vector velocity of the blood is estimated using 2-D cross-correlation. A parameter study was performed using the Field II program, and performance of the method was investigated when a virtual blood vessel was scanned by a linear array transducer. An improved parameter set for the method was identified from the parameter study, and a flow rig measurement was performed using the same improved setup as in the simulations. Finally, the common carotid artery of a healthy male was scanned with a scan sequence that satisfies the limits set by the Food and Drug Administration. Vector velocity images were obtained with a frame-rate of 100 Hz where 40 speckle images are used for each vector velocity image. It was found that the blood flow approximately followed the vessel wall, and that maximum velocity was approximately 1 m/s, which is a normal value for a healthy person. To further evaluate the method, the test person was scanned with magnetic resonance (MR) angiography. The volume flow derived from the MR scanning was compared with that from the ultrasound scanning. A deviation of 9% between the 2 volume flow estimates was found.

Wilson (1991) presented an ultrasonic wideband estimator for axial blood flow velocity estimation through the use of the 2-D Fourier transform. It was shown how a single velocity component was concentrated along a line in the 2-D Fourier space, where the slope was given by the axial velocity. Later, it was shown that this approach could also be used for finding the lateral velocity component by also including a lateral sampling. A single velocity component would then be concentrated along a plane in the 3-D Fourier space, tilted according to the 2 velocity components. This paper presents 2 new velocity estimators for finding both the axial and lateral velocity components. The estimators essentially search for the plane in the 3- D Fourier space, where the integrated power spectrum is largest. The first uses the 3-D Fourier transform to find the power spectrum, while the second uses a minimum variance approach. Based on this plane, the axial and lateral velocity components are estimated. Several phantom measurements, for flow-to-depth angles of 60, 75, and 90 degrees, were performed. Multiple parallel lines were beamformed simultaneously, and 2 different receive apodization schemes were tried. The 2 estimators were then applied to the data. The axial velocity component was estimated with an average standard deviation below 2.8% of the peak velocity, while the average standard deviation of the lateral velocity estimates was between 2.0% and 16.4%. The 2 estimators were also tested on in vivo data from a transverse scan of the common carotid artery, showing the potential of the vector velocity estimation method under in vivo conditions.

Ultrasonic color flow maps are made by estimating the velocities line by line over the region of interest. For each velocity estimate, multiple repetitions are needed. This sets a limit on the frame rate, which becomes increasingly severe when imaging deeper lying structures or when simultaneously acquiring spectrogram data for triplex imaging. This paper proposes a method for decreasing the data acquisition time by simultaneously sampling multiple lines for color flow maps, using narrow band signals with approximately disjoint spectral support. The signals are separated in the receiver by filters matched to the emitted waveforms, producing a number of data sets with different center frequencies. The autocorrelation estimator is then applied to each of the data sets. The method is presented, various side effects are considered, and the method is tested on data from a recirculating flow phantom. A mean standard deviation across the flow profile of 3.1, 2.5, and 2.1% of the peak velocity was found for bands at 5 MHz, 7 MHz, and 9 MHz, respectively. Alternatively, the method can be used for simultaneously sampling data for a color flow map and for multiple spectrograms using different spectral bands. Using three spectral bands, data for a color flow map and two independent spectrograms can be acquired at the time normally spent on acquiring data for a color flow map only. This yields an expansion of triplex imaging called multifrequency quadroplex imaging, which enables study of the flow over an arterial stenosis by simultaneously acquiring spectrograms on both sides of the stenosis, while maintaining the color flow map. The method was tested in vivo on data from the common carotid artery of a healthy male volunteer, both for fast color flow mapping and for multifrequency quadroplex imaging.

Previously, a synthetic aperture vector velocity estimation method was proposed. Data are beamformed at different directions through a point, where the velocity is estimated. The flow direction is estimated by a search for the direction where the normalized cross-correlation peaks and the velocity magnitude along this direction are found. In this paper, different effects that influence the focusing in this method are investigated. These include the effect of phase errors in the emitted spherical waves, motion effects, and the effect of various interpolation methods in beam-forming. A model based on amplitude drop and phase error for spherical waves created using the virtual source concept is derived. This model can be used to determine the opening angle of a virtual source. Simulations for different virtual source placements are made, and it is recommended that the virtual sources be placed behind the aperture when shallow structures are imaged, and when deeper-lying structures are imaged the virtual sources be placed in front of the aperture. Synthetic aperture methods involve summation of data from numerous emissions. Motion between these emissions results in incoherence and affects resolution, contrast, and the signal-to-noise ratio. The effects of motion on the synthetic aperture vector velocity estimation method are investigated, and it is shown that for both axial and lateral motion, the contrast and signal-to-noise ratio can be seriously affected. A compensation method using the previous vector velocity estimate, when new data are beamformed, is implemented and tested. It is shown from a number of flow phantom experiments that a significant improvement with respect to bias and standard deviation of the velocity estimates can be obtained by using this compensation. Increased performance is gained at the expense of computation time. Different interpolation methods can be used for beam-forming the data. In this paper, the velocity estimation performance using various more complex interpolation schemes are compared to that using linear interpolation. No significant difference in the performance of the method is seen when other interpolation methods are used.

The paper describes the use of synthetic aperture (SA) imaging in medical ultrasound. SA imaging is a radical break with today's commercial systems, where the image is acquired sequentially one image line at a time. This puts a strict limit on the frame rate and the possibility of acquiring a sufficient amount of data for high precision flow estimation. These constrictions can be lifted by employing SA imaging. Here data is acquired simultaneously from all directions over a number of emissions, and the full image can be reconstructed from this data. The paper demonstrates the many benefits of SA imaging. Due to the complete data set, it is possible to have both dynamic transmit and receive focusing to improve contrast and resolution. It is also possible to improve penetration depth by employing codes during ultrasound transmission. Data sets for vector flow imaging can be acquired using short imaging sequences, whereby both the correct velocity magnitude and angle can be estimated. A number of examples of both phantom and in vivo SA images will be presented measured by the experimental ultrasound scanner RASMUS to demonstrate the many benefits of SA imaging.

A method for determining both velocity magnitude and angle in a synthetic aperture ultrasound system is described. The approach uses directional beamforming along the flow direction and cross correlation to determine velocity magnitude. The angle of the flow is determined from the maximum normalized correlation calculated as a function of angle. This assumes the flow direction is within the imaging plane. Simulations of the angle estimation method show both biases and standard deviations of the flow angle estimates below 3 degrees for flow angles from 20 degrees to 90 degrees (transverse flow). The method is also investigated using data measured by an experimental ultrasound scanner from a flow rig. A commercial 128 element 7-MHz linear array transducer is used, and data are measured for flow angles of 60 degrees and 90 degrees . Data are acquired using the RASMUS experimental ultrasound scanner, which samples 64 channels simultaneously. A 20-micros chirp was used during emission and eight virtual transmit sources were created behind the transducer using 11 transmitting elements. Data from the eight transmissions are beamformed and coherently summed to create high-resolution lines at different angles for a set of points within the region of flow. The velocity magnitude is determined with a precision of 0.36% (60 degrees) and 1.2% (90 degrees), respectively. The 60 degrees angle is estimated with a bias of 0.54 degrees and a standard deviation of 2.1 degrees. For 90 degrees the bias is 0.0003 degrees and standard deviation 1.32 degrees. A parameter study with regard to correlation length and number of emissions is performed to reveal the accuracy of the method. Real time data covering 2.2 s of the carotid artery of a healthy 30-year-old male volunteer is acquired and then processed offline using a computer cluster. The direction of flow is estimated using the above mentioned method. It is compared to the flow angle of 106 degrees with respect to the axial direction, determined visually from the B-mode image. For a point in the center of the common carotid artery, 76% of the flow angle estimates over the 2.2 s were within 10 degrees of the visually determined flow angle. The standard deviation of these estimates was below 2.7 degrees. Full color flow maps from different parts of the cardiac cycle are presented, including vector arrows indicating both estimated flow direction and velocity magnitude.

A method for determining both velocity magnitude and angle in any direction is suggested. The method uses focusing along the velocity direction and cross-correlation for finding the correct velocity magnitude. The angle is found from beamforming directional signals in a number of directions and then selecting the angle with the highest normalized correlation between directional signals. The approach is investigated using Field II simulations and data from the experimental ultrasound scanner RASMUS and a circulating flow rig with a parabolic flow having a peak velocity of 0.3 m/s. A 7-MHz linear array transducer is used with a normal transmission of a focused ultrasound field. In the simulations the relative standard deviation of the velocity magnitude is between 0.7% and 7.7% for flow angles between 45 degrees and 90 degrees. The study showed that angle estimation by directional beamforming can be estimated with a high precision. The angle estimation performance is highly dependent on the choice of the time ktprf x Tprf (correlation time) between signals to correlate. One performance example is given with a fixed value of ktprf for all flow angles. The angle estimation on measured data for flow at 60 degrees to 90 degrees yields a probability of valid estimates between 68% and 98%. The optimal value of ktprf for each flow angle is found from a parameter study; with these values, the performance on simulated data yields angle estimates with no outlier estimates and with standard deviations below 2 degrees.

This paper investigates the possibility of flow estimation using spatio-temporal encoding of the transmissions in synthetic transmit aperture imaging (STA). The spatial encoding is based on a frequency division approach. In STA, a major disadvantage is that only a single transmitter (denoting single transducer element or a virtual source) is used in every transmission. The transmitted acoustic energy will be low compared to a conventional focused transmission in which a large part of the aperture is used. By using several transmitters simultaneously, the total transmitted energy can be increased. However, to focus the data properly, the signals originating from the different transmitters must be separated. To do so, the pass band of the transducer is divided into a number of subbands with disjoint spectral support. At every transmission, each transmitter is assigned one of the subbands. In receive, the signals are separated using a simple filtering operation. To attain high axial resolution, broadband spectra must be synthesized for each of the transmitters. By multiplexing the different waveforms on different transmitters over a number of transmissions, this can be accomplished. To further increase the transmitted energy, the waveforms are designed as linear frequency modulated signals. Therefore, the full excitation amplitude can be used during most of the transmission. The method has been evaluated for blood velocity estimation for several different velocities and incident angles. The program Field II was used. A 128-element transducer with a center frequency of 7 MHz was simulated. The 64 transmitting elements were used as the transmitting aperture and 128 elements were used as the receiving aperture. Four virtual sources were created in every transmission. By beamforming lines in the flow direction, directional data were extracted and correlated. Hereby, the velocity of the blood was estimated. The pulse repetition frequency was 16 kHz. Three different setups were investigated with flow angles of 45, 60, and 75 degrees with respect to the acoustic axis. Four different velocities were simulated for each angle at 0.10, 0.25, 0.50, and 1.00 m/s. The mean relative bias with respect to the peak flow for the three angles was less than 2%, 2%, and 4%, respectively.

Conventional ultrasound scanners can display only the axial component of the blood velocity vector, which is a significant limitation when vessels nearly parallel to the skin surface are scanned. The transverse oscillation (TO) method overcomes this limitation by introducing a TO and an axial oscillation in the pulse echo field. The theory behind the creation of the double oscillation pulse echo field is explained as well as the theory behind the estimation of the vector velocity. A parameter study of the method is performed, using the ultrasound simulation program Field II. A virtual linear-array transducer with center frequency 7 MHz and 128 active elements is created, and a virtual blood vessel of radius 6.4 mm is simulated. The performance of the TO method is found around an initial point in the parameter space. The parameters varied are: flow angle, transmit focus depth, receive apodization, pulse length, transverse wave length, number of emissions, signal-to-noise ratio (SNR), and type of echo-canceling filter used. Using an experimental scanner, the performance of the TO method is evaluated. An experimental flowrig is used to create laminar parabolic flow in a blood mimicking fluid, and the fluid is scanned under different flow-to-beam angles. The relative standard deviation on the transverse velocity estimate is found to be less than 10% for all angles between 50 degrees and 90 degrees. Furthermore, the TO method is evaluated in the flowrig using pulsatile flow, which resembles the flow in the femoral artery. The estimated volume flow as a function of time is compared to the volume flow derived from a conventional axial method at a flow-to-beam angle of 60 degrees. It is found that the method is highly sensitive to the angle between the flow and the beam direction. Also, the choice of echo canceling filter affects the performance significantly.

A method for flow estimation using synthetic aperture imaging and focusing along the flow direction is presented. The method can find the correct velocity magnitude for any flow angle, and full color flow images can be measured using only 32 to 128 pulse emissions. The approach uses spherical wave emissions with a number of defocused elements and a linear frequency-modulated pulse (chirp) to improve the signal-to-noise ratio. The received signals are dynamically focused along the flow direction and these signals are used in a cross-correlation estimator for finding the velocity magnitude. The flow angle is manually determined from the B-mode image. The approach can be used for both tissue and blood velocity determination. The approach was investigated using both simulations and a flow system with a laminar flow. The flow profile was measured with a commercial 7.5 MHz linear array transducer. A plastic tube with an internal diameter of 17 mm was used with an EcoWatt 1 pump generating a laminar, stationary flow. The velocity profile was measured for flow angles of 90 and 60 degrees. The RASMUS research scanner was used for acquiring radio frequency (RF) data from 128 elements of the array, using 8 emissions with 11 elements in each emission. A 20-micros chirp was used during emission. The RF data were subsequently beamformed off-line and stationary echo canceling was performed. The 60-degree flow with a peak velocity of 0.15 m/s was determined using 16 groups of 8 emissions, and the relative standard deviation was 0.36% (0.65 mm/s). Using the same setup for purely transverse flow gave a standard deviation of 1.2% (2.1 mm/s). Variation of the different parameters revealed the sensitivity to number of lines, angle deviations, length of correlation interval, and sampling interval. An in vivo image of the carotid artery and jugular vein of a healthy 29-year-old volunteer was acquired. A full color flow image using only 128 emissions could be made with a high-velocity precision.

The aspect of correlation among the blood velocities in time and space has not received much attention in previous blood velocity estimators. The theory of fluid mechanics predicts this property of the blood flow. Additionally, most estimators based on a cross-correlation analysis are limited on the maximum velocity detectable. This is due to the occurrence of multiple peaks in the cross-correlation function. In this study a new estimator (CMLE), which is based on correlation (C) properties inherited from fluid flow and maximum likelihood estimation (MLE), is derived and evaluated on a set of simulated and in vivo data from the carotid artery. The estimator is meant for two-dimensional (2-D) color flow imaging. The resulting mathematical relation for the estimator consists of two terms. The first term performs a cross-correlation analysis on the signal segment in the radio frequency (RF)-data under investigation. The flow physic properties are exploited in the second term, as the range of velocity values investigated in the cross-correlation analysis are compared to the velocity estimates in the temporal and spatial neighborhood of the signal segment under investigation. The new estimator has been compared to the cross-correlation (CC) estimator and the previously developed maximum likelihood estimator (MLE). The results show that the CMLE can handle a larger velocity search range and is capable of estimating even low velocity levels from tissue motion. The CC and the MLE produce incorrect velocity estimates due to the multiple peaks, when the velocity search range is increased above the maximum detectable velocity. The root-mean square error (RMS) on the velocity estimates for the simulated data is on the order of 7 cm/s (14%) for the CMLE, and it is comparable to the RMS for the CC and the MLE. When the velocity search range is set to twice the limit of the CC and the MLE, the number of incorrect velocity estimates are 0, 19.1, and 7.2% for the CMLE, CC, and MLE, respectively. The ability to handle a larger search range and estimating low velocity levels was confirmed on in vivo data.