Niels Oddershede

Estimation of Velocity Vectors in Synthetic Aperture Ultrasound 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 3deg for flow angles from 20deg to 90deg (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 60deg and 90deg. Data are acquired using the RASMUS experimental ultrasound scanner, which samples 64 channels simultaneously. A 20-mus 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% (60deg) and 1.2% (90deg), respectively. The 60deg angle is estimated with a bias of 0.54deg and a standard deviation of 2.1deg. For 90deg the bias is 0.0003deg and standard deviation 1.32deg. 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 106deg 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 10deg of the visually determined flow angle. The standard deviation of these estimates was below 2.7deg. Full color flow maps from different parts of the cardiac cycle are presented, including vector arrows indicating both estimated flow direction and velocity magnitude

Effects Influencing Focusing in Synthetic Aperture Vector Flow 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.

In vivo comparison of three ultrasound vector velocity techniques to MR phase contrast angiography.

The objective of this paper is to validate angle independent vector velocity methods for blood velocity estimation. Conventional Doppler ultrasound (US) only estimates the blood velocity along the US beam direction where the estimate is angle corrected assuming laminar flow parallel to vessel boundaries. This results in incorrect blood velocity estimates, when angle of insonation approaches 90 degrees or when blood flow is non-laminar. Three angle independent vector velocity methods are evaluated in this paper: directional beamforming (DB), synthetic aperture flow imaging (STA) and transverse oscillation (TO). The performances of the three methods were investigated by measuring the stroke volume in the right common carotid artery of 11 healthy volunteers with magnetic resonance phase contrast angiography (MRA) as reference. The correlation with confidence intervals (CI) between the three vector velocity methods and MRA were: DB vs. MRA: R=0.84 (p<0.01, 95% CI: 0.49-0.96); STA vs. MRA: R=0.71 (p<0.05, 95% CI: 0.19-0.92) and TO vs. MRA: R=0.91 (p<0.01, 95% CI: 0.69-0.98). No significant differences were observed for any of the three comparisons (DB vs. MRA: p=0.65; STA vs. MRA: p=0.24; TO vs. MRA: p=0.36). Bland-Altman plots were additionally constructed, and mean differences with limits of agreements (LoA) for the three comparisons were: DB vs. MRA=0.17 ml (95% CI: -0.61-0.95) with LoA=-2.11-2.44 ml; STA vs. MRA=-0.55 ml (95% CI: -1.54-0.43) with LoA=-3.42-2.32 ml; TO vs. MRA=0.24 ml (95% CI: -0.32-0.81) with LoA=-1.41-1.90 ml. According to the results, reliable volume flow estimates can be obtained with all three methods. The three US vector velocity techniques can yield quantitative insight into flow dynamics and visualize complex flow patterns, which potentially can give the clinician a novel tool for cardiovascular disease assessment.

Recent advances in blood flow vector velocity imaging

A number of methods for ultrasound vector velocity imaging are presented in the paper. The transverse oscillation (TO) method can estimate the velocity transverse to the ultrasound beam by introducing a lateral oscillation in the received ultrasound field. The approach has been thoroughly investigated using both simulations, flow rig measurements, and in-vivo validation against MR scans. The TO method obtains a relative accuracy of 10% for a fully transverse flow in both simulations and flow rig experiments. In-vivo studies performed on 11 healthy volunteers comparing the TO method with magnetic resonance phase contrast angiography (MRA) revealed a correlation between the stroke volume estimated by TO and MRA of 0.91 (p<;0.01) with an equation for the line of regression given as: MRA = 1.1 · TO-0.4 ml. Several clinical examples of complex flow in e.g. bifurcations and around valves have been acquired using a commercial implementation of the method (BK Medical ProFocus Ultraview scanner). A range of other methods are also presented. This includes synthetic aperture imaging using either spherical or plane waves with velocity estimation performed with directional beamforming or speckle tracking. The key advantages of these techniques are very fast imaging that can attain an order of magnitude higher precision than conventional methods. SA flow imaging was implemented on the experimental scanner RASMUS using an 8-emission spherical emission sequence and reception of 64 channels on a BK Medical 8804 transducer. This resulted in a relative standard deviation of 1.2% for a fully transverse flow. Plane wave imaging was also implemented on the RASMUS scanner and a 100 Hz frame rate was attained. Several vector velocity image sequences of complex flow were acquired, which demonstrates the benefits of fast vector flow imaging. A method for extending the 2D TO method to 3D vector velocity estimation is presented and the implications for future vector velocity imaging is indicated.

Estimating 2-D vector velocities using multidimensional spectrum analysis

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.

Multi-frequency encoding for fast color flow or quadroplex imaging

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 multi-frequency 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 multi-frequency quadroplex imaging.

P3C-4 Motion Compensated Beamforming in Synthetic Aperture Vector Flow Imaging

In synthetic aperture imaging the beamformed data from a number of emissions are summed to create dynamic focusing in transmit. This makes the method susceptible to motion, which is especially the case for the synthetic aperture flow estimation method, where large movements are expected. In this paper, these motion effects are considered. A number of Field II simulations of a single scatterer moving at different velocities are performed both for axial and lateral velocities from 0 to 1 m/s. Data are simulated at a pulse repetition frequency of 5 kHz. The signal-to-noise ratio (SNR) of the beamformed response from the scatterer at all velocities is compared to that of a stationary scatterer. For lateral movement, the SNR drops almost linearly with velocity to -4 dB at 1 m/s, while for axial movement the SNR drop is largest, when the scatterer moves a quarter of a wavelength between emissions. Here the SNR is -10 dB compared to the stationary scatterer. A 2D motion compensation method for synthetic aperture vector flow imaging is proposed, where the former vector velocity estimate is used for compensating the beamforming of new data. This method is tested on data from an experimental flow rig acquired using our RASMUS experimental ultrasound scanner and a 5.5 MHz linear array transducer. A 11.25 mus non-linear chirp is used as excitation and the data from 128 emissions is used for estimating the flow direction and magnitude at a profile across the tube. The measurement was conducted at a flow angle of 60deg with respect to the axial direction and a peak velocity of 0.1 m/s sampled at a pulse repetition frequency of 1 kHz. The mean bias across the profile was -8.4 % with respect to the peak velocity and the mean standard deviation was 12.2 % prior to compensation. When the proposed compensation was applied a mean bias of -3.6 % and a mean standard deviation of 2.8 % was seen

P6B-4 Multi-Dimensional Spectrum Analysis for 2-D Vector Velocity Estimation

Wilson (1991) presented a wide-band estimator for axial blood flow velocity estimation through the use of the two-dimensional (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. This paper presents an expansion of this study. If data are sampled within a region, instead of along a line, a three- dimensional (3-D) data matrix is created along lateral space, axial space, and pulse repetitions. It is shown, that a single velocity component will be concentrated along a plane in the 3-D Fourier space, which is found through the 3-D Fourier transform of the data matrix, and that the plane is tilted according to the axial and lateral velocity components. Two estimators are derived for finding 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. A number of phantom flow measurements, for flow-to-beam angles of 60, 75, and 90 degrees, were performed to test the estimator. The data were collected using our RASMUS experimental ultrasound scanner and a 128 element commercial linear array transducer. The receive apodization function was manipulated, creating an oscillation in the lateral direction, and multiple parallel lines were beamformed simultaneously. The two estimators were then applied to the data. Finally, an in-vivo scan of the common carotid artery was performed. The average standard deviation was found across the phantom tube, for both the axial and the lateral velocity estimate. Twenty independent estimates were made for each positions. The average standard deviation of the lateral velocity estimates ranged from 16.4%c to 2.1%, relative to the peak velocity, while the average standard deviation of the axial velocity ranged from 2.05% to 0.2%. Both estimators performed best for flow-to-beam angles of 90 degrees. The in-vivo scan showed the potential of the method, yielding an estimate of the velocity magnitude independent of vessel orientation.

In-vivo evaluation of three ultrasound vector velocity techniques with MR angiography

In conventional Doppler ultrasound (US) the blood velocity is only estimated along the US beam direction. The estimate is angle corrected assuming laminar flow parallel to the vessel boundaries. As the flow in the vascular system never is purely laminar, the velocities estimated with conventional Doppler US are always incorrect. Three angle independent vector velocity methods are evaluated in this paper: directional beamforming (DB), synthetic aperture flow imaging (STA) and transverse oscillation (TO). The performances of the three methods were investigated by measuring the stroke volume in the right common carotid artery of eleven healthy volunteers, with magnetic resonance phase contrast angiography (MRA) as reference. The correlation between the three vector velocity methods and MRA were: DB/MRA R=0.84 (pLt0.01); STA/MRA R=0.95 (pLt0.01); TO/MRA R=0.91 (pLt0.01). Bland-Altman plots were additionally constructed and mean differences for the three comparisons were: DB/MRA = 0.17 ml; STA/MRA = 0.07 ml; TO/MRA = 0.24 ml. The three US vector velocity techniques yield quantitative insight in to flow dynamics and can potentially give the clinician a powerful tool in cardiovascular disease assessment.

12B-6 Multi-Frequency Encoding for Rapid Color Flow and Quadroplex Imaging

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 at different spatial positions for the color flow map using narrow band signals with disjoint spectral support. The signals are separated in the receiver by filters matched to the emitted waveforms and the autocorrelation estimator is applied. Alternatively, one spectral band can be used for creating a color flow map, while data for a number of spectrograms are acquired simultaneously. Using three disjoint spectral bands, this will result in a multi-frequency quadroplex imaging mode featuring a color flow map and two spectrograms at the same frame rate as a normal color flow map. The method is presented, various side-effects are considered, and the method is tested on data from a re-circulating flow phantom where a constant parabolic flow with a peak of 0.1 m/s is generated with a flow angle of 60 degrees. A commercial linear array transducer is used and data are sampled using our RASMUS multi-channel sampling system. An in-vivo multi- frequency quadroplex movie of the common carotid artery of a healthy male volunteer was created. The flow phantom measurements gave a mean standard deviation across the flow profile of 3.1%, 2.5%, and 2.1% of the peak velocity for bands at 5 MHz, 7 MHz, and 9 MHz, respectively. The in-vivo multi-frequency quadroplex movie showed the color flow map, and the two independent spectrograms at different spatial positions. This enables studying the flow over an arterial stenosis by simultaneously acquiring spectrograms on both sides of the stenosis, while maintaining the color flow map. A frame rate of 21.4 frames per second was achieved in this in-vivo experiment.