Directional velocity estimation using focusing along the flow direction. I: Theory and simulation

Advanced Fourier migration for Plane-Wave vector flow imaging

Ultrafast ultrasound imaging modalities have been studied extensively in the ultrasound community. It breaks the compromise between the frame rate and the region of interest by imaging the whole medium with wide unfocused waves. Continuously available data allow monitoring fast transient dynamics at hundreds to thousands of frames per second. This feature enables a more accurate and robust velocity estimation in vector flow imaging (VFI). On the other hand, the huge amount of data and real-time processing demands are still challenging in VFI. A solution is to provide a more efficient beamforming approach with smaller computation complexity than the conventional time-domain beamformer like delay-and-sum (DAS). Fourier-domain beamformers are shown to be more computationally efficient and can provide equally good image quality as DAS. However, previous studies generally focus on B-mode imaging. In this study, we propose a new framework for VFI which is based on two advanced Fourier migration methods, namely, slant stack migration (SSM) and ultrasound Fourier slice beamform (UFSB). By carefully modifying the beamforming parameters, we successfully apply the cross-beam technique within the Fourier beamformers. The proposed Fourier-based VFI is validated in simulation studies, in vitro, and in vivo experiments. The velocity estimation is evaluated via bias and standard deviation and the results are compared with conventional time-domain VFI using the DAS beamformer. In the simulation, the bias is 6.4%, -6.2%, and 5.7%, and the standard deviation is 4.3%, 2.4%, and 3.9% for DAS, UFSB, and SSM, respectively. In vitro studies reveal a bias of 4.5%, -5.3%, and 4.3% and a standard deviation of 3.5%, 1.3%, and 1.6% from DAS, UFSB, and SSM, respectively. The in vivo imaging of the basilic vein and femoral bifurcation also generate similar results using all three methods. With the proposed Fourier beamformers, the computation time can be shortened by up to 9 times and 14 times using UFSB and SSM.

An Angle Independent Depth Aware Fusion Beamforming Approach for Ultrafast Ultrasound Flow Imaging. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:3399-3402. [PMID: 34891969 DOI: 10.1109/embc46164.2021.9630742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In the case of vector flow imaging systems, the most employed flow estimation techniques are the directional beamforming based cross correlation and the triangulation-based autocorrelation. However, the directional beamforming-based techniques require an additional angle estimator and are not reliable if the flow angle is not constant throughout the region of interest. On the other hand, estimates with triangulation-based techniques are prone to large bias and variance at low imaging depths due to limited angle for left and right apertures. In view of this, a novel angle independent depth aware fusion beamforming approach is proposed and evaluated in this paper. The hypothesis behind the proposed approach is that the peripheral flows are transverse in nature, where directional beamforming can be employed without the need of an angle estimator and the deeper flows being non-transverse and directional, triangulation-based vector flow imaging can be employed. In the simulation study, an overall 67.62% and 74.71% reduction in magnitude bias along with a slight reduction in the standard deviation are observed with the proposed fusion beamforming approach when compared to triangulation-based beamforming and directional beamforming, respectively, when implemented individually. The efficacy of the proposed approach is demonstrated with in-vivo experiments.

Dealiasing High-Frame-Rate Color Doppler Using Dual-Wavelength Processing

Doppler ultrasound is the premier modality to analyze blood flow dynamics in clinical practice. With conventional systems, Doppler can either provide a time-resolved quantification of the flow dynamics in sample volumes (spectral Doppler) or an average Doppler velocity/power [color flow imaging (CFI)] in a wide field of view (FOV) but with a limited frame rate. The recent development of ultrafast parallel systems made it possible to evaluate simultaneously color, power, and spectral Doppler in a wide FOV and at high-frame rates but at the expense of signal-to-noise ratio (SNR). However, like conventional Doppler, ultrafast Doppler is subject to aliasing for large velocities and/or large depths. In a recent study, staggered multi-pulse repetition frequency (PRF) sequences were investigated to dealias color-Doppler images. In this work, we exploit the broadband nature of pulse-echo ultrasound and propose a dual-wavelength approach for CFI dealiasing with a constant PRF. We tested the dual-wavelength bandpass processing, in silico, in laminar flow phantom and validated it in vivo in human carotid arteries ( n = 25 ). The in silico results showed that the Nyquist velocity could be extended up to four times the theoretical limit. In vivo, dealiased CFI were highly consistent with unfolded Spectral Doppler ( r²=0.83 , y=1.1x+0.1 , N=25 ) and provided consistent vector flow images. Our results demonstrate that dual-wavelength processing is an efficient method for high-velocity CFI.

From Anatomy to Functional and Molecular Biomarker Imaging and Therapy: Ultrasound Is Safe, Ultrafast, Portable, and Inexpensive

Ultrasound is the most widely used medical imaging modality worldwide. It is abundant, extremely safe, portable, and inexpensive. In this review, we consider some of the current development trends for ultrasound imaging, which build upon its current strength and the popularity it experiences among medical imaging professional users.Ultrasound has rapidly expanded beyond traditional radiology departments and cardiology practices. Computing power and data processing capabilities of commonly available electronics put ultrasound systems in a lab coat pocket or on a user's mobile phone. Taking advantage of new contributions and discoveries in ultrasound physics, signal processing algorithms, and electronics, the performance of ultrasound systems and transducers have progressed in terms of them becoming smaller, with higher imaging performance, and having lower cost. Ultrasound operates in real time, now at ultrafast speeds; kilohertz frame rates are already achieved by many systems.Ultrasound has progressed beyond anatomical imaging and monitoring blood flow in large vessels. With clinical approval of ultrasound contrast agents (gas-filled microbubbles) that are administered in the bloodstream, tissue perfusion studies are now routine. Through the use of modern ultrasound pulse sequences, individual microbubbles, with subpicogram mass, can be detected and observed in real time, many centimeters deep in the body. Ultrasound imaging has broken the wavelength barrier; by tracking positions of microbubbles within the vasculature, superresolution imaging has been made possible. Ultrasound can now trace the smallest vessels and capillaries, and obtain blood velocity data in those vessels.Molecular ultrasound imaging has now moved closer to clinic; the use of microbubbles with a specific affinity to endothelial biomarkers allows selective accumulation and retention of ultrasound contrast in the areas of ischemic injury, inflammation, or neoangiogenesis. This will aid in noninvasive molecular imaging and may provide additional help with real-time guidance of biopsy, surgery, and ablation procedures.The ultrasound field can be tightly focused inside the body, many centimeters deep, with millimeter precision, and ablate lesions by energy deposition, with thermal or mechanical bioeffects. Some of such treatments are already in clinical use, with more indications progressing through the clinical trial stage. In conjunction with intravascular microbubbles, focused ultrasound can be used for tissue-specific drug delivery; localized triggered release of sequestered drugs from particles in the bloodstream may take time to get to clinic. A combination of intravascular microbubbles with circulating drug and low-power ultrasound allows transient opening of vascular endothelial barriers, including blood-brain barrier; this approach has reached clinical trial stage. Therefore, the drugs that normally would not be getting to the target tissue in the brain will now have an opportunity to produce therapeutic efficacy.Overall, medical ultrasound is developing at a brisk rate, even in an environment where other imaging modalities are also advancing rapidly and may be considered more lucrative. With all the current advances that we discuss, and many more to come, ultrasound may help solve many problems that modern medicine is facing.

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.

Estimation of High Velocities in Synthetic Aperture Imaging: I: Theory

The paper describes a new pulse sequence design and estimation approach, which can increase the maximum detectable velocity in synthetic aperture (SA) velocity imaging. In SA N spherical or plane waves are emitted, and the sequence is repeated continuously. The N emissions are combined to form a High Resolution Image (HRI). Correlation of HRIs is employed to estimate velocity, and the combination of N emissions lowers the effective pulse repetition frequency by N. Inter-leaving emission sequences can increase the effective pulse repetition frequency to the actual pulse repetition frequency, thereby increasing the maximum detectable velocity by a factor of N. This makes it possible to use longer sequences with better focusing properties. It can also increase the possible interrogation depth for vessels with large velocities. A new cross-correlation vector flow estimator is also presented, which can further increase the maximum detectable velocity by a factor of three. It is based on Transverse Oscillation (TO), a pre-processing stage, and cross-correlation of signals beamformed orthogonal to the ultrasound propagation direction. The estimator is self-calibrating without estimating the lateral TO wavelength. This paper develops the theory behind the two methods. The performance is demonstrated in the accompanying paper for convex and phased array probes connected to the SARUS scanner for parabolic flow for both conventional and SA imaging.

Estimation of High Velocities in Synthetic Aperture Imaging: II: Experimental Investigation

The paper describes the performance of a new pulse sequence design and estimation approach for increasing the maximum detectable velocity in synthetic aperture (SA) velocity imaging. Measurements are conducted for conventional imaging for comparing the velocity range detectable by a directional Transverse Oscillation (TO) autocorrelation estimator to a new cross-correlation estimator. For conventional focused emissions a 192-elements, 3 MHz convex array transducer is used together with the SARUS experimental scanner on a flow rig at beam-to-flow angles of 60°, 70° and 90°. Here the new estimator always yields a higher precision, and the aliasing limit is increased by a factor 3. The new SA inter-spaced scheme was investigated using Field II simulations and SARUS measurements. A 3 MHz, 128-elements phased array was employed with a 5 virtual source emissions scheme for flow estimation and 15 emissions for B-mode imaging. The scheme was interleaved three times for a positive, negative, and positive transmission, so that non-linear pulse inversion also could be made. The experiments were conducted at three angles and for 4 different pulse repetition frequencies. A peak transverse velocity of 0.51 m/s could be estimated at fprf=450 Hz, translating to 5.6 m/s at fprf=5 kHz showing the theoretical increase of a factor 10 predicted in the accompanying theory paper.

High-Frame Rate Vector Flow Imaging of the Carotid Bifurcation in Healthy Adults: Comparison With Color Doppler Imaging

OBJECTIVES

To evaluate the carotid bifurcation in healthy adults using a commercial system equipped with high-frame rate vector flow imaging (VFI) based on the plane wave and to compare VFI with color Doppler imaging.

METHODS

Carotid bifurcation diameters and flow characteristics of 60 vessels in 60 healthy volunteers were evaluated quantitatively and qualitatively to assess complex flow patterns and their extension and duration.

RESULTS

Complex flow in the internal carotid artery (ICA) was associated with a statistically significant difference in the ΔICA sinus-to-common carotid artery (CCA) diameter ratio (the relative change in diameter between the CCA and ICA sinus.) Vector flow imaging and color Doppler imaging were in accordance when detecting complex flow in 96.7% of cases; in 3.3% of cases, only VFI identified small recirculation areas of short duration. Vector flow imaging highlighted a larger extension of the complex flow (mean ± SD, 47.7 ± 28.5 mm² ; median, 45.5 mm² ) compared with color Doppler imaging (mean, 29.2 ± 19.9 mm² ; median, 29.5 mm² ) and better depicted different complex flow patterns; a strong correlation (r = 0.84) was found between the ΔICA sinus-to-CCA diameter ratio and the complex flow extension. Vector flow imaging showed a longer duration of the flow disturbances (mean, 380 ± 218 milliseconds; median, 352.5 milliseconds) compared with color Doppler imaging (mean, 325 ± 206 milliseconds; median, 333 milliseconds), and there was a strong correlation (r = 0.92).

CONCLUSIONS

Vector flow imaging is as effective as color Doppler imaging in the detection of flow disturbances, but it is more powerful in the assessment of complex flow patterns.

Accuracy and Precision of a Plane Wave Vector Flow Imaging Method in the Healthy Carotid Artery

The objective of the study described here was to investigate the accuracy and precision of a plane wave 2-D vector flow imaging (VFI) method in laminar and complex blood flow conditions in the healthy carotid artery. The approach was to study (i) the accuracy for complex flow by comparing the velocity field from a computational fluid dynamics (CFD) simulation to VFI estimates obtained from the scan of an anthropomorphic flow phantom and from an in vivo scan; (ii) the accuracy for laminar unidirectional flow in vivo by comparing peak systolic velocities from VFI with magnetic resonance angiography (MRA); (iii) the precision of VFI estimation in vivo at several evaluation points in the vessels. The carotid artery at the bifurcation was scanned using both fast plane wave ultrasound and MRA in 10 healthy volunteers. The MRA geometry acquired from one of the volunteers was used to fabricate an anthropomorphic flow phantom, which was also scanned using the fast plane wave sequence. The same geometry was used in a CFD simulation to calculate the velocity field. Results indicated that similar flow patterns and vortices were estimated with CFD and VFI in the phantom for the carotid bifurcation. The root-mean-square difference between CFD and VFI was within 0.12 m/s for velocity estimates in the common carotid artery and the internal branch. The root-mean-square difference was 0.17 m/s in the external branch. For the 10 volunteers, the mean difference between VFI and MRA was -0.17 m/s for peak systolic velocities of laminar flow in vivo. The precision in vivo was calculated as the mean standard deviation (SD) of estimates aligned to the heart cycle and was highest in the center of the common carotid artery (SD = 3.6% for velocity magnitudes and 4.5° for angles) and lowest in the external branch and for vortices (SD = 10.2% for velocity magnitudes and 39° for angles). The results indicate that plane wave VFI measures flow precisely and that estimates are in good agreement with a CFD simulation and MRA.

Real-Time 2-D Phased Array Vector Flow Imaging

Echocardiography examination of the blood flow is currently either restricted to 1-D techniques in real-time or experimental offline 2-D methods. This paper presents an implementation of transverse oscillation for real-time 2-D vector flow imaging (VFI) on a commercial BK Ultrasound scanner. A large field-of-view (FOV) sequence for studying flow dynamics at 11 frames per second (fps) and a sequence for studying peak systolic velocities (PSVs) with a narrow FOV at 36 fps were validated. The VFI sequences were validated in a flow rig with continuous laminar parabolic flow and in a pulsating flow pump system before being tested in vivo, where measurements were obtained on two healthy volunteers. Mean PSV from 11 cycles was 155 cms^-1 with a precision of ±9.0% for the pulsating flow pump. In vivo, PSV estimated in the ascending aorta was 135 cms^-1 ± 16.9% for eight cardiac cycles. Furthermore, in vivo flow dynamics of the left ventricle and in the ascending aorta were visualized. In conclusion, angle independent 2-D VFI on a phased array has been implemented in real time, and it is capable of providing quantitative and qualitative flow evaluations of both the complex and fully transverse flow.

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.

Directional Transverse Oscillation Vector Flow Estimation

A method for estimating vector velocities using transverse oscillation (TO) combined with directional beamforming is presented. In directional TO (DTO), a normal focused field is emitted and the received signals are beamformed in the lateral direction transverse to the ultrasound beam to increase the amount of data for vector velocity estimation. The approach is self-calibrating as the lateral oscillation period is estimated from the directional signal through a Fourier transform to yield quantitative velocity results over a large range of depths. The approach was extensively simulated using Field IIpro and implemented on the experimental Synthetic Aperture Real-time Ultrasound System (SARUS) scanner in connection with a BK Medical 8820e convex array transducer. Velocity estimates for DTO are found for beam-to-flow angles of 60°, 75°, and 90°, and vessel depths from 24 to 156 mm. Using 16 emissions, the standard deviation (SD) for angle estimation at depths ranging from 24 to 104 mm is between 6.01° and 0.93° with a mean SD of 2.8°. The mean relative SD for the lateral velocity component is 9.2% and the mean relative bias -3.4% or four times lower than for traditional TO. The approach also works for deeper lying vessels with a slight increase in SD to 15.7%, but a maintained bias of -3.5% from 126 to 156 mm. Data for a pulsating flow have also been acquired for 15 cardiac cycles using a CompuFlow 1000 pump. The relative SD was here 7.4% for a femoral artery waveform.

Fast Plane Wave 2-D Vector Flow Imaging Using Transverse Oscillation and Directional Beamforming

Several techniques can estimate the 2-D velocity vector in ultrasound. Directional beamforming (DB) estimates blood flow velocities with a higher precision and accuracy than transverse oscillation (TO), but at the cost of a high beamforming load when estimating the flow angle. In this paper, it is proposed to use TO to estimate an initial flow angle, which is then refined in a DB step. Velocity magnitude is estimated along the flow direction using cross correlation. It is shown that the suggested TO-DB method can improve the performance of velocity estimates compared with TO, and with a beamforming load, which is 4.6 times larger than for TO and seven times smaller than for conventional DB. Steered plane wave transmissions are employed for high frame rate imaging, and parabolic flow with a peak velocity of 0.5 m/s is simulated in straight vessels at beam-to-flow angles from 45° to 90°. The TO-DB method estimates the angle with a bias and standard deviation (SD) less than 2°, and the SD of the velocity magnitude is less than 2%. When using only TO, the SD of the angle ranges from 2° to 17° and for the velocity magnitude up to 7%. Bias of the velocity magnitude is within 2% for TO and slightly larger but within 4% for TO-DB. The same trends are observed in measurements although with a slightly larger bias. Simulations of realistic flow in a carotid bifurcation model provide visualization of complex flow, and the spread of velocity magnitude estimates is 7.1 cm/s for TO-DB, while it is 11.8 cm/s using only TO. However, velocities for TO-DB are underestimated at peak systole as indicated by a regression value of 0.97 for TO and 0.85 for TO-DB. An in vivo scanning of the carotid bifurcation is used for vector velocity estimations using TO and TO-DB. The SD of the velocity profile over a cardiac cycle is 4.2% for TO and 3.2% for TO-DB.

High-frame rate vector flow imaging of the carotid bifurcation

Abstract

Carotid artery atherosclerotic disease is still a significant cause of cerebrovascular morbidity and mortality. A new angle-independent technique, measuring and visualizing blood flow velocities in all directions, called vector flow imaging (VFI) is becoming available from several vendors. VFI can provide more intuitive and quantitative imaging of vortex formation, which is not clearly distinguishable in the color Doppler image. VFI, as quantitative method assessing disturbed flow patterns of the carotid bifurcation, has the potential to allow better understanding of the diagnostic value of complex flow and to enhance risk stratification. This pictorial review article will show which new information VFI adds for the knowledge of hemodynamics in comparison to the conventional ultrasound techniques.

Teaching points

• VFI is an angle-independent technique measuring flow velocities in all directions.

• This kind of VFI is based on a plane wave multidirectional excitation technique.

• VFI allows quantitative assessment of carotid streamlines progression and visualizes vorticity.

• VFI does not allow a precise comprehension of streamlines’ 3D shape.

• VFI allows a better understanding of carotid artery complex flows.

Electronic supplementary material

The online version of this article (doi:10.1007/s13244-017-0554-5) contains supplementary material, which is available to authorized users.

Low-Cost 3-D Flow Estimation of Blood With Clutter

Volumetric flow rate estimation is an important ultrasound medical imaging modality that is used for diagnosing cardiovascular diseases. Flow rates are obtained by integrating velocity estimates over a cross-sectional plane. Speckle tracking is a promising approach that overcomes the angle dependency of traditional Doppler methods, but suffers from poor lateral resolution. Recent work improves lateral velocity estimation accuracy by reconstructing a synthetic lateral phase (SLP) signal. However, the estimation accuracy of such approaches is compromised by the presence of clutter. Eigen-based clutter filtering has been shown to be effective in removing the clutter signal; but it is computationally expensive, precluding its use at high volume rates. In this paper, we propose low-complexity schemes for both velocity estimation and clutter filtering. We use a two-tiered motion estimation scheme to combine the low complexity sum-of-absolute-difference and SLP methods to achieve subpixel lateral accuracy. We reduce the complexity of eigen-based clutter filtering by processing in subgroups and replacing singular value decomposition with less compute-intensive power iteration and subspace iteration methods. Finally, to improve flow rate estimation accuracy, we use kernel power weighting when integrating the velocity estimates. We evaluate our method for fast- and slow-moving clutter for beam-to-flow angles of 90° and 60° using Field II simulations, demonstrating high estimation accuracy across scenarios. For instance, for a beam-to-flow angle of 90° and fast-moving clutter, our estimation method provides a bias of -8.8% and standard deviation of 3.1% relative to the actual flow rate.

Ultrasound Vector Flow Imaging-Part I: Sequential Systems

This paper gives a review of the most important methods for blood velocity vector flow imaging (VFI) for conventional sequential data acquisition. This includes multibeam methods, speckle tracking, transverse oscillation, color flow mapping derived VFI, directional beamforming, and variants of these. The review covers both 2-D and 3-D velocity estimation and gives a historical perspective on the development along with a summary of various vector flow visualization algorithms. The current state of the art is explained along with an overview of clinical studies conducted and methods for presenting and using VFI. A number of examples of VFI images are presented, and the current limitations and potential solutions are discussed.

Least-Squares Multi-Angle Doppler Estimators for Plane-Wave Vector Flow Imaging

Designing robust Doppler vector estimation strategies for use in plane-wave imaging schemes based on unfocused transmissions is a topic that has yet to be studied in depth. One potential solution is to use a multi-angle Doppler estimation approach that computes flow vectors via least-squares fitting, but its performance has not been established. Here, we investigated the efficacy of multi-angle Doppler vector estimators by: 1) comparing its performance with respect to the classical dual-angle (cross-beam) Doppler vector estimator and 2) examining the working effects of multi-angle Doppler vector estimators on flow visualization quality in the context of dynamic flow path rendering. Implementing Doppler vector estimators that use different combinations of transmit (Tx) and receive (Rx) steering angles, our analysis has compared the classical dual-angle Doppler method, a 5-Tx version of dual-angle Doppler, and various multi-angle Doppler configurations based on 3 Tx and 5 Tx. Two angle spans (10°, 20°) were examined in forming the steering angles. In imaging scenarios with known flow profiles (rotating disk and straight-tube parabolic flow), the 3-Tx, 3-Rx and 5-Tx, 5-Rx multi-angle configurations produced vector estimates with smaller variability compared with the dual-angle method, and the estimation results were more consistent with the use of a 20° angle span. Flow vectors derived from multi-angle Doppler estimators were also found to be effective in rendering the expected flow paths in both rotating disk and straight-tube imaging scenarios, while the ones derived from the dual-angle estimator yielded flow paths that deviated from the expected course. These results serve to attest that using multi-angle least-squares Doppler vector estimators, flow visualization can be consistently achieved.

3-D Vector Flow Estimation With Row-Column-Addressed Arrays

Simulation and experimental results from 3-D vector flow estimations for a 62 + 62 2-D row-column (RC) array with integrated apodization are presented. A method for implementing a 3-D transverse oscillation (TO) velocity estimator on a 3-MHz RC array is developed and validated. First, a parametric simulation study is conducted, where flow direction, ensemble length, number of pulse cycles, steering angles, transmit/receive apodization, and TO apodization profiles and spacing are varied, to find the optimal parameter configuration. The performance of the estimator is evaluated with respect to relative mean bias ~B and mean standard deviation ~σ . Second, the optimal parameter configuration is implemented on the prototype RC probe connected to the experimental ultrasound scanner SARUS. Results from measurements conducted in a flow-rig system containing a constant laminar flow and a straight-vessel phantom with a pulsating flow are presented. Both an M-mode and a steered transmit sequence are applied. The 3-D vector flow is estimated in the flow rig for four representative flow directions. In the setup with 90° beam-to-flow angle, the relative mean bias across the entire velocity profile is (-4.7, -0.9, 0.4)% with a relative standard deviation of (8.7, 5.1, 0.8)% for ( v_x, v_y, v_z ). The estimated peak velocity is 48.5 ± 3 cm/s giving a -3% bias. The out-of-plane velocity component perpendicular to the cross section is used to estimate volumetric flow rates in the flow rig at a 90° beam-to-flow angle. The estimated mean flow rate in this setup is 91.2 ± 3.1 L/h corresponding to a bias of -11.1%. In a pulsating flow setup, flow rate measured during five cycles is 2.3 ± 0.1 mL/stroke giving a negative 9.7% bias. It is concluded that accurate 3-D vector flow estimation can be obtained using a 2-D RC-addressed array.

Accurate Angle Estimator for High-Frame-Rate 2-D Vector Flow Imaging

This paper presents a novel approach for estimating 2-D flow angles using a high-frame-rate ultrasound method. The angle estimator features high accuracy and low standard deviation (SD) over the full 360° range. The method is validated on Field II simulations and phantom measurements using the experimental ultrasound scanner SARUS and a flow rig before being tested in vivo. An 8-MHz linear array transducer is used with defocused beam emissions. In the simulations of a spinning disk phantom, a 360° uniform behavior on the angle estimation is observed with a median angle bias of 1.01° and a median angle SD of 1.8°. Similar results are obtained on a straight vessel for both simulations and measurements, where the obtained angle biases are below 1.5° with SDs around 1°. Estimated velocity magnitudes are also kept under 10% bias and 5% relative SD in both simulations and measurements. An in vivo measurement is performed on a carotid bifurcation of a healthy individual. A 3-s acquisition during three heart cycles is captured. A consistent and repetitive vortex is observed in the carotid bulb during systoles.

Evaluation of the transverse oscillation method using the Cramer-Rao lower bound

The transverse oscillation method enables lateral displacement tracking by generating an oscillation orthogonal to the conventional RF signal. The widely varying methods used in the field to create such oscillations and perform displacement estimation make it difficult to compare the expected performance of alternative techniques. We derive closed-form expressions for the oscillating pressure fields produced by two common apodization functions-the rectangular and bi-lobed Gaussian apodizations-after heterodyning demodulation is applied to separate the orthogonally-oscillating signals. With these fields and spectra we present a form of the Cramer-Rao lower bound for ultrasonic signals that contains a spectrum shape term, allowing theoretical prediction of relative performance across different techniques and parameter choices. Simulations show good agreement with the trends predicted by the theoretical results for the chosen class of aperture functions. The simulations demonstrate the importance of frequency-space analysis in devising a transverse oscillation scheme and suggest that the study of other classes of aperture functions and field formation techniques should be continued to further improve the accuracy of lateral displacement tracking.

A transverse oscillation approach for estimation of three-dimensional velocity vectors, part I: concept and simulation study

A method for 3-D velocity vector estimation using transverse oscillations is presented. The method employs a 2-D transducer and decouples the velocity estimation into three orthogonal components, which are estimated simultaneously and from the same data. The validity of the method is investigated by conducting simulations emulating a 32 × 32 matrix transducer. The results are evaluated using two performance metrics related to precision and accuracy. The study includes several parameters including 49 flow directions, the SNR, steering angle, and apodization types. The 49 flow directions cover the positive octant of the unit sphere. In terms of accuracy, the median bias is -2%. The precision of v(x) and v(y) depends on the flow angle ß and ranges from 5% to 31% relative to the peak velocity magnitude of 1 m/s. For comparison, the range is 0.4 to 2% for v(z). The parameter study also reveals, that the velocity estimation breaks down with an SNR between -6 and -3 dB. In terms of computational load, the estimation of the three velocity components requires 0.75 billion floating point operations per second (0.75 Gflops) for a realistic setup. This is well within the capability of modern scanners.

High-frame-rate 2-D vector blood flow imaging in the frequency domain

Conventional ultrasound Doppler techniques estimate the blood velocity exclusively in the axial direction to produce the sonograms and color flow maps needed for diagnosis of cardiovascular diseases. In this paper, a novel method to produce bi-dimensional maps of 2-D velocity vectors is proposed. The region of interest (ROI) is illuminated by plane waves transmitted at the pulse repetition frequency (PRF) in a fixed direction. For each transmitted plane wave, the backscattered echoes are recombined offline to produce the radio-frequency image of the ROI. The local 2-D phase shifts between consecutive speckle images are efficiently estimated in the frequency domain, to produce vector maps up to 15 kHz PRF. Simulations and in vitro steady-flow experiments with different setup conditions have been conducted to thoroughly evaluate the method's performance. Bias is proved to be lower than 10% in most simulations and lower than 20% in experiments. Further simulations and in vivo experiments have been made to test the approach's feasibility in pulsatile flow conditions. It has been estimated that the computation of the frequency domain algorithm is more than 50 times faster than the computation of the reference 2-D cross-correlation algorithm.

Vector projectile imaging: time-resolved dynamic visualization of complex flow patterns

Achieving non-invasive, accurate and time-resolved imaging of vascular flow with spatiotemporal fluctuations is well acknowledged to be an ongoing challenge. In this article, we present a new ultrasound-based framework called vector projectile imaging (VPI) that can dynamically render complex flow patterns over an imaging view at millisecond time resolution. VPI is founded on three principles: (i) high-frame-rate broad-view data acquisition (based on steered plane wave firings); (ii) flow vector estimation derived from multi-angle Doppler analysis (coupled with data regularization and least-squares fitting); (iii) dynamic visualization of color-encoded vector projectiles (with flow speckles displayed as adjunct). Calibration results indicated that by using three transmit angles and three receive angles (-10°, 0°, +10° for both), VPI can consistently compute flow vectors in a multi-vessel phantom with three tubes positioned at different depths (1.5, 4, 6 cm), oriented at different angles (-10°, 0°, +10°) and of different sizes (dilated diameter: 2.2, 4.4 and 6.3 mm; steady flow rate: 2.5 mL/s). The practical merit of VPI was further illustrated through an anthropomorphic flow phantom investigation that considered both healthy and stenosed carotid bifurcation geometries. For the healthy bifurcation with 1.2-Hz carotid flow pulses, VPI was able to render multi-directional and spatiotemporally varying flow patterns (using a nominal frame rate of 416 fps or 2.4-ms time resolution). In the case of stenosed bifurcations (50% eccentric narrowing), VPI enabled dynamic visualization of flow jet and recirculation zones. These findings suggest that VPI holds promise as a new tool for complex flow analysis.

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.

Phased-array vector velocity estimation using transverse oscillations

A method for estimating the 2-D vector velocity of blood using a phased-array transducer is presented. The approach is based on the transverse oscillation (TO) method. The purposes of this work are to expand the TO method to a phased-array geometry and to broaden the potential clinical applicability of the method. A phased-array transducer has a smaller footprint and a larger field of view than a linear array, and is therefore more suited for, e.g., cardiac imaging. The method relies on suitable TO fields, and a beamforming strategy employing diverging TO beams is proposed. The implementation of the TO method using a phased-array transducer for vector velocity estimation is evaluated through simulation and flow-rig measurements are acquired using an experimental scanner. The vast number of calculations needed to perform flow simulations makes the optimization of the TO fields a cumbersome process. Therefore, three performance metrics are proposed. They are calculated based on the complex TO spectrum of the combined TO fields. It is hypothesized that the performance metrics are related to the performance of the velocity estimates. The simulations show that the squared correlation values range from 0.79 to 0.92, indicating a correlation between the performance metrics of the TO spectrum and the velocity estimates. Because these performance metrics are much more readily computed, the TO fields can be optimized faster for improved velocity estimation of both simulations and measurements. For simulations of a parabolic flow at a depth of 10 cm, a relative (to the peak velocity) bias and standard deviation of 4% and 8%, respectively, are obtained. Overall, the simulations show that the TO method implemented on a phased-array transducer is robust with relative standard deviations around 10% in most cases. The flow-rig measurements show similar results. At a depth of 9.5 cm using 32 emissions per estimate, the relative standard deviation is 9% and the relative bias is -9%. At the center of the vessel, the velocity magnitude is estimated to be 0.25 ± 0.023 m/s, compared with an expected peak velocity magnitude of 0.25 m/s, and the beam-to-flow angle is calculated to be 89.3° ± 0.77°, compared with an expected angle value between 89° and 90°. For steering angles up to ±20° degrees, the relative standard deviation is less than 20%. The results also show that a 64-element transducer implementation is feasible, but with a poorer performance compared with a 128-element transducer. The simulation and experimental results demonstrate that the TO method is suitable for use in conjunction with a phased-array transducer, and that 2-D vector velocity estimation is possible down to a depth of 15 cm.

Implementation of a versatile research data acquisition system using a commercially available medical ultrasound scanner

This paper describes the design and implementation of a versatile, open-architecture research data acquisition system using a commercially available medical ultrasound scanner. The open architecture will allow researchers and clinicians to rapidly develop applications and move them relatively easy to the clinic. The system consists of a standard PC equipped with a camera link and an ultrasound scanner equipped with a research interface. The ultrasound scanner is an easy-to-use imaging device that is capable of generating high-quality images. In addition to supporting the acquisition of multiple data types, such as B-mode, M-mode, pulsed Doppler, and color flow imaging, the machine provides users with full control over imaging parameters such as transmit level, excitation waveform, beam angle, and focal depth. Beamformed RF data can be acquired from regions of interest throughout the image plane and stored to a file with a simple button press. For clinical trials and investigational purposes, when an identical image plane is desired for both an experimental and a reference data set, interleaved data can be captured. This form of data acquisition allows switching between multiple setups while maintaining identical transducer, scanner, region of interest, and recording time. Data acquisition is controlled through a graphical user interface running on the PC. This program implements an interface for third-party software to interact with the application. A software development toolkit is developed to give researchers and clinicians the ability to utilize third-party software for data analysis and flexible manipulation of control parameters. Because of the advantages of speed of acquisition and clinical benefit, research projects have successfully used the system to test and implement their customized solutions for different applications. Three examples of system use are presented in this paper: evaluation of synthetic aperture sequential beamformation, transverse oscillation for blood velocity estimation, and acquisition of spectral velocity data for evaluating aortic aneurysms.

Ultrasonic colour Doppler imaging

Ultrasonic colour Doppler is an imaging technique that combines anatomical information derived using ultrasonic pulse-echo techniques with velocity information derived using ultrasonic Doppler techniques to generate colour-coded maps of tissue velocity superimposed on grey-scale images of tissue anatomy. The most common use of the technique is to image the movement of blood through the heart, arteries and veins, but it may also be used to image the motion of solid tissues such as the heart walls. Colour Doppler imaging is now provided on almost all commercial ultrasound machines, and has been found to be of great value in assessing blood flow in many clinical conditions. Although the method for obtaining the velocity information is in many ways similar to the method for obtaining the anatomical information, it is technically more demanding for a number of reasons. It also has a number of weaknesses, perhaps the greatest being that in conventional systems, the velocities measured and thus displayed are the components of the flow velocity directly towards or away from the transducer, while ideally the method would give information about the magnitude and direction of the three-dimensional flow vectors. This review briefly introduces the principles behind colour Doppler imaging and describes some clinical applications. It then describes the basic components of conventional colour Doppler systems and the methods used to derive velocity information from the ultrasound signal. Next, a number of new techniques that seek to overcome the vector problem mentioned above are described. Finally, some examples of vector velocity images are presented.

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.

In vivo validation of a blood vector velocity estimator with MR angiography

Conventional Doppler methods for blood velocity estimation only estimate the velocity component along the ultrasound beam direction. This implies that a Doppler angle under examination close to 90 degrees results in unreliable information about the true blood direction and blood velocity. The novel method transverse oscillation (TO), which combines estimates of the axial and the transverse velocity components in the scan plane, makes it possible to estimate the vector velocity of the blood regardless of the Doppler angle. The present study evaluates the TO method with magnetic resonance phase contrast angiography (MRA) by comparing in vivo measurements of stroke volume. Eleven healthy volunteers were included in this prospective study. From the obtained data sets recorded with the 2 modalities, vector velocity sequences were constructed and stroke volume calculated. Angle of insonation was approximately 90 degrees for TO measurements. The correlation between the stroke volume estimated by TO and MRA was 0.91 (p < 0.01) with the equation for the line of regression: MRA = 1.1.TO-0.4. A Bland-Altman plot was additionally constructed where the mean difference was 0.2 ml with limits of agreement at -1.4 ml and 1.9 ml. The results indicate that reliable vector velocity estimates can be obtained in vivo using the presented angle-independent 2-D vector velocity method. The TO method can be a useful alternative to conventional Doppler systems by avoiding the angle artifact, thus giving quantitative velocity information.

High frame-rate blood vector velocity imaging using plane waves: simulations and preliminary experiments

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.

Simulation and validation of arterial ultrasound imaging and blood flow

We reviewed the simulation and validation of arterial ultrasound imaging and blood flow assessment. The physical process of ultrasound imaging and measurement is complex, especially in disease. Simulation of physiological flow in a phantom with tissue equivalence of soft tissue, vessel wall and blood is now achievable. Outstanding issues are concerned with production of anatomical models, simulation of arterial disease, refinement of blood mimics to account for non-Newtonian behavior and validation of velocity measurements against an independent technique such as particle image velocimetry. String and belt phantoms offer simplicity of design, especially for evaluation of velocity estimators, and have a role as portable test objects. Electronic injection and vibrating test objects produce nonphysiologic Doppler signals, and their role is limited. Computational models of the ultrasound imaging and measurement process offer considerable flexibility in their ability to alter multiple parameters of both the propagation medium and ultrasound instrument. For these models, outstanding issues are concerned with the inclusion of different tissue types, multilayer arteries, inhomogeneous tissues and diseased tissues.

Examples of in vivo blood vector velocity estimation

In this paper, a case study of in-vivo blood vector velocity images of the carotid artery are presented. The transverse oscillation (TO) method for blood vector velocity estimation has been used to estimate the vector velocities. The carotid arteries of three healthy volunteers are scanned in-vivo at three different positions by experienced sonographers. The scanning regions are: 1) the common carotid artery at 88 degrees beam to flow angle, 2) the common carotid artery and the jugular vein at approximately 90 degrees beam to flow angle and 3) the bifurcation of the carotid artery. The resulting velocity estimates are displayed as vector velocity images, where the velocity vector is superimposed on a B-mode image showing the tissue structures. The volume flow is found for case 1) and when compared with MRI from the literature, a bias of approximately approximately 20% is found. The maximum flow velocity within the carotid artery is found to be 0.8 m/s, which is normal for a healthy person. In case 3), the estimated vector velocities are compared with numerical simulations. Qualitatively similar flow pattern can be seen in both simulations and in the vector velocity images. Furthermore, a vortex is identified in the carotid sinus at the deceleration phase after the peak systole. This vortex is seen in all of the three acquired cardiac cycles.

Improved transverse flow estimation using differential maximum Doppler frequency

Conventional Doppler technique can only provide the axial component of the blood flow vector, which is actually a three dimensional (3-D) quantity. To acquire the complete flow vector, estimations of the other two velocity components are essential. For the two dimensional (2-D) Doppler-bandwidth-based transverse estimation, however, accuracy is generally limited because of the complex dependence of the Doppler spectral shape on the flow variation within the sample volume. Two factors that may lead to the Doppler spectral change were considered in this study. One is the position offset of the sample volume and the other is the length of the sample volume. Simulations were performed and experimental data were also collected. Results indicate that the position offset may result in severe underestimation of Doppler shift frequency. Consequently, Doppler bandwidth is overestimated when it is determined by the difference between Doppler shift frequency and maximum Doppler frequency. Compared with the position offset, influence of the length of sample volume on the Doppler bandwidth is minor. To overcome this problem, a novel method, which is based on the differential maximum Doppler frequency, is proposed. Specifically, two beams with different beam widths are simultaneously generated to observe the blood flow and the difference between the corresponding maximum Doppler frequencies is used to estimate the transverse velocity. It is demonstrated that the accuracy and stability of transverse estimation are significantly improved by the proposed method even when the position offset is present.

Estimation of velocity vector angles using the directional cross-correlation method

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.

Directional velocity estimation using a spatio-temporal encoding technique based on frequency division for synthetic transmit aperture ultrasound

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.

Spectral velocity estimation in ultrasound using sparse data sets

Velocity distributions in blood vessels can be displayed using ultrasound scanners by making a Fourier transform of the received signal and then showing spectra in an M-mode display. It is desired to show a B-mode image for orientation, and data for this have to be acquired interleaved with the flow data. This either halves the effective pulse repetition frequency f(prf) or gaps appear in the spectrum from B-mode emissions. This paper presents a technique to maintain the highest possible f(prf) and at the same time show a B-mode image. The power spectrum can be calculated from the Fourier transform of the autocorrelation function, and it is shown that the autocorrelation function can be calculated for a sparse set of data where flow and B-mode emissions are interspaced. Both short deterministic sequences of emissions and full random sequences can be used. The dynamic range of the sparse sequence is reduced compared to a full sequence. Typically, a reduction of 20 dB is found when using 66% of the data compared to using all data. The theory of the method and examples from simulations of flow in arteries are presented. The audio signal can also be generated from the spectrogram.

Investigation of transverse oscillation method

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.

Directional synthetic aperture flow imaging

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.

Directional velocity estimation using focusing along the flow direction. II: Experimental investigation

A new method for directional velocity estimation is investigated through a number of flow rig measurements. The method uses beamformation along the flow direction to generate data, where the correct velocity magnitude can directly be estimated from the shift in position of the received consecutive signals. The shift is found by cross-correlating the beamformed lines. The approach can find the velocity in any direction, including transverse to the traditionally emitted ultrasound beam. The method is investigated using a flow rig with a peak velocity of 0.15 m/s. A 7-MHz linear array transducer is used together with a dedicated sampling system to acquire signals from 64 transducer elements simultaneously. A technique for obtaining 128-element data using multiplexing is also presented. The data is beamformed off-line on a PC. A relative standard deviation of 1.4% can be obtained for a beam-to-flow angle of 45 degrees and 4.3% at 90 degrees. Color flow images are displayed showing that the correct velocity magnitude can be obtained with the method for beam-to-flow angles of 60 and 90 degrees with an accuracy of 3 to 4%.