Abstract: 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.

Abstract: 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.

Abstract: 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 ${\tilde {B}}$ and mean standard deviation ${\tilde {\sigma }}$ . 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.

Abstract: We report a miniature fiber-optic water vector flow sensor based on an array of silicon Fabry-Perot interferometers (FPIs). The flow sensor is composed of four silicon FPIs, one in the center with the other three equally distributed around it. The center FPI is heated by a cw laser at 980 nm, which is guided through the lead-in single mode fiber. The temperature structure established within the sensor head due to laser heating is a function of the flow vector (speed and direction), which can be deduced from the wavelength shifts of the four FPIs. Theoretical analysis has been conducted to illustrate the operating principle and experimental demonstration has been provided.

Abstract: A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non-linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.

Abstract: Vector Flow Imaging (VFI) has received an increasing attention in the scientific field of ultrasound, as it enables angle independent visualization of blood flow. VFI can be used in volume flow estimation, but a vessel segmentation is needed to make it fully automatic. A novel vessel segmentation procedure is crucial for wall-to-wall visualization, automation of adjustments, and quantification of flow in state-of-the-art ultrasound scanners. We propose and discuss a method for accurate vessel segmentation that fuses VFI data and B-mode for robustly detecting and delineating vessels. The proposed method implements automated VFI flow measures such as peak systolic velocity (PSV) and volume flow. An evaluation of the performance of the segmentation algorithm relative to expert manual segmentation of 60 frames randomly chosen from 6 ultrasound sequences (10 frame randomly chosen from each sequence) is also presented. Dice coefficient denoting the similarity between segmentations is used for the evaluation. The coefficient ranges between 0 and 1, where 1 indicates perfect agreement and 0 indicates no agreement. The Dice coefficient was 0.91 indicating to a very agreement between automated and manual expert segmentations. The flowrig results also demonstrated that the PSVs measured from VFI had a mean relative error of 14.5% in comparison with the actual PSVs. The error for the PSVs measured from spectral Doppler was 29.5%, indicating that VFI is 15% more precise than spectral Doppler in PSV measurement.

Abstract: This paper presents an in-house developed 2-D capacitive micromachined ultrasonic transducer (CMUT) applied for 3-D blood flow estimation. The probe breaks with conventional transducers in two ways; first, the ultrasonic pressure field is generated from thousands of small vibrating micromachined cells, and second, elements are accessed by row and/or column indices. The 62+62 2-D row-column addressed prototype CMUT probe was used for vector flow estimation by transmitting focused ultrasound into a flow-rig with a fully developed parabolic flow. The beam-to-flow angle was 90°. The received data was beamformed and processed offline. A transverse oscillation (TO) velocity estimator was used to estimate the 3-D vector flow along a line originating from the center of the transducer. The estimated velocities in the lateral and axial direction were close to zero as expected. In the transverse direction a characteristic parabolic velocity profile was estimated with a peak velocity of 0.48 m/s ± 0.02 m/s in reference to the expected 0.54 m/s. The results presented are the first 3-D vector flow estimates obtained with a row-column CMUT probe, which demonstrates that the CMUT technology is feasible for 3-D flow estimation.

Abstract: In this study, we propose 4D Ultrafast vector flow imaging, through the use of 4D plane-wave ultrafast and cross-beam vector Doppler imaging in order to map in-vivo blood flows in 3D, provide volumes of complex vector flow fields at high frame rate, and quantify the volumetric flow rate accurately. 4D Ultrafast vector flow imaging was performed in large volumetric field of views at high volume rates (>4000 volumes/s) using a 1024-channel 4D ultrafast scanner and a 2D matrix-array probe. The accuracy and precision of the technique was evaluated in-vitro in an artery phantom and compared with an industrial flow meter. Volumetric flow rate errors of less than 5% were found when volumetric flow rates were less than 360 ml/min. In-vivo feasibility was evaluated in 2 human carotid arteries. 4-D blood flow velocity was assessed during one heartbeat and in a full volume and volumetric flow rates of 375 ± 57 ml/min and 275 ± 43 ml/min were estimated. Finally, vortices were imaged in 3D at the carotid artery bifurcation.

Abstract: This work describes and demonstrates an approach for volumetric 3D vector flow imaging in the adult heart using a clinical matrix array transducer. Broad transmit beams are used to achieve a high frame rate acquisition, and a novel hybrid estimator combining Doppler and speckle tracking properties is used for flow velocity estimation.

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Abstract: This work presents the first in vivo results of 2-D high frame rate vector velocity imaging for transthoracic cardiac imaging. Measurements are made on a healthy volunteer using the SARUS experimental ultrasound scanner connected to an intercostal phased-array probe. Two parasternal long-axis view (PLAX) are obtained, one centred at the aortic valve and another centred at the left ventricle. The acquisition sequence was composed of 3 diverging waves for high frame rate synthetic aperture flow imaging. For verification a phantom measurement is performed on a transverse straight 5 mm diameter vessel at a depth of 100 mm in a tissue-mimicking phantom. A flow pump produced a 2 ml/s constant flow with a peak velocity of 0.2 m/s. The average estimated flow angle in the ROI was 86.22° ± 6.66° with a true flow angle of 90°. A relative velocity bias of −39% with a standard deviation of 13% was found. In-vivo acquisitions show complex flow patterns in the heart. In the aortic valve view, blood is seen exiting the left ventricle cavity through the aortic valve into the aorta during the systolic phase of the cardiac cycle. In the left ventricle view, blood flow is seen entering the left ventricle cavity through the mitral valve and splitting in two ways when approximating the left ventricle wall. The work presents 2-D velocity estimates on the heart from a non-invasive transthoracic scan. The ability of the method detecting flow regardless of the beam angle could potentially reveal a more complete view of the flow patterns presented on the heart.

Abstract: Directional beamforming (DB) estimates blood flow velocities accurately when the flow angle is known. However, for automatically finding the flow angle a computationally expensive approach is used. This work presents a method for estimating the flow angle using a combination of inexpensive transverse oscillation (TO) estimators and only 3 directional beamformed lines. The suggested DB vector flow estimator is employed with steered plane wave transmissions for high frame rate imaging. Two distinct plane wave sequences are used: a short sequence (3 angles) for fast flow and an interleaved long sequence (21 angles) for both slow flow and B-mode. Parabolic flow with a peak velocity of 0.5 m/s is measured at beam-to-flow angles of 60° and 90°. The DB method estimates the angle with a bias and standard deviation (STD) less than 2°, and the STD of the velocity magnitude is 2.5 %. This is 7 – 8.5 % when using TO. The long sequence has a higher sensitivity, and when used for estimation of slow flow with a peak velocity of 0.04 m/s, the SD is 2.5 % and bias is 0.1 %. This is a factor of 4 better than if the short sequence is used. The carotid bifurcation was scanned on a healthy volunteer, and the short sequence was used with TO and DB to estimate velocity vectors. The STD of the velocity profile over a cardiac cycle was 6.1 % for TO and 4.9 % for DB.

Abstract: 3-D blood flow quantification with high spatial and temporal resolution would strongly benefit clinical research on cardiovascular pathologies. Ultrasonic velocity techniques are known for their ability to measure blood flow with high precision at high spatial and temporal resolution. However, current volumetric ultrasonic flow methods are limited to one velocity component or restricted to a reduced field of view (FOV), e.g. fixed imaging planes, in exchange for higher temporal resolutions. To solve these problems, a previously proposed accurate 2-D high frame rate vector flow imaging (VFI) technique is extended to estimate the 3-D velocity components inside a volume at high temporal resolutions ( x , V y and V z respectively; each presented a mean relative standard deviation of 11.8%, 12.3% and 1.11%.

Abstract: In this paper, a vector flow imaging method is presented, which combines the directional transverse oscillation approach with synthetic aperture sequential beamforming to achieve an efficient estimation of the velocities. A double-oscillating field is synthesized using two sets of focused emissions separated by a distance in the lateral direction. A low-resolution line (LRL) is created for each emission in the first stage beamformer, and a second beamformer provides the high-resolution data used for the velocity estimation. The method makes it possible to have continuously available data in the whole image. Therefore, high and low velocities can be estimated with a high frame rate and a low standard deviation. The first stage is a fixed-focus beamformer that can be integrated in the transducer handle, enabling the wireless transmission of the LRLs. The approach does not require any angle compensation or prior knowledge on the beam-to-flow angle. The feasibility of the method is demonstrated through simulations and flow rig measurements of a parabolic flow in a vessel at 90-degree beam-to-flow angle. The mean bias obtained from 50 independent measurements is equal to −0.67% for the lateral profile and −0.43% for the axial profile. The relative standard deviation is 3.19% and 0.47% for the lateral and axial profiles. It is, therefore, demonstrated that vector velocity estimation can be efficiently integrated in a portable ultrasound scanner with state-of-the-art performance.

Abstract: The cardiac Magnetic Resonance Imaging (MRI) provides high resolution images of the heart without radiation exposure. It is an excellent noninvasive test used by radiologist for proper detection of heart diseases. The manual segmentation of left ventricle in cine short axis MRI sequences takes an ample amount of time as compared to semi-automated segmentation. In Gradient Vector Flow (GVF) model certain barriers hinder the performance such as weak edge detection, high computational time, limited capture range and its ambiguity with other parameters. In this paper segmentation of Endocardium is carried out on multistage MRI frames Using Adaptive Diffusion flow (ADF) model. This deformable model was tested on large scale number of Cardiac MRI images. We replace the smoothening energy term in GVF with active hyper-surface harmonic minimal function in order to avoid possible leakage at weak edges. The use of harmonic maps is adjusted in accordance with image characteristics. We also assimilate infinite Laplace function to move active contours into narrow concave sections. Experimental results and collation with GVF are presented in this paper which reveals several good results based on extraction of endocardium tissue from left and right ventricle, including less computational time, noise robustness and weak edge preserving on Cardiac MR Images.

Abstract: The invention discloses a method for extracting wave flow information based on coherent radar under a slow scanning mode. The method includes the steps of calculating radar echo doppler speed of each scattering unit in a selected inversion area, obtaining average of the radar echo doppler speed on each radial direction to obtain ocean current speed on each radial direction, acquiring sea level vector flow velocity and flow direction information through a least square method by using the ocean current speed on each radial direction, and establishing the mapping relation between ocean wave track speed spectrum and ocean wave number spectrum to obtain ocean wave number spectrum information. Since the extraction of wave flow information is mostly based on doppler speed information, the method compared with a conventional wave flow information extraction method based on echo intensity has the advantages of higher measuring precision and being capable of preventing tedious calibration work and errors caused by calibration.

Abstract: A new registration method between ultrasound (US) image and Magnetic resonance imaging (MRI) was presented, and a robust optical flow model for large deformation between US image (floating image) and MRI (reference image) was built, then the vector flow field was estimated. The proposed algorithm contends with larger deformation and performs well not only for local deformation but also for global deformation. Qualitative and quantitative analyses of multiple group comparison experiments showed that registration results using the proposed method led to the best registration results.

Abstract: 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 3.0 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 B̃ and mean standard deviation σ̃. 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. Three-dimensional 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 (vx, vy, vz). The estimated peak velocity is 48.5 cm/s ± 3.0 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 L/h ± 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 mL/stroke ± 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.

Abstract: Weld joints quality control with radiography technique is widely used. Unfortunately, the poor quality of these images and the presence of various kind of noise make processing of radiography film an intricate task. This paper presents a new anisotropic diffusion filtering method for radiography image noise reduction and sharpening. The proposed diffusion scheme is guided with the adaptive diffusion flow vector ADF. The use of the ADF vector flow permits to preserve perfectly weak image boundaries while removing noise. Experimental results on different synthetic and real welding radiography images confirm the efficiency and robustness of our model in comparison with other diffusion methods.

Abstract: Duplex Vector Flow Imaging (VFI) imaging is introduced as a replacement for spectral Doppler, as it automatically can yield fully quantitative flow estimates without angle correction. Continuous VFI data over 9 s for 10 pulse cycles were acquired by a 3 MHz convex probe connected to the SARUS scanner for pulsating flow mimicking the femoral artery from a CompuFlow 1000 pump (Shelley Medical). Data were used in four estimators based on directional transverse oscillation for velocity, flow angle, volume flow, and turbulence estimation and their respective precisions. An adaptive lag scheme gave the ability to estimate a large velocity range, or alternatively measure at two sites to find e.g. stenosis degree in a vessel. The mean angle at the vessel center was estimated to 90.9°±8.2° indicating a laminar flow from a turbulence index being close to zero (0.1 ±0.1). Volume flow was 1.29 ±0.26 mL/stroke (true: 1.15 mL/stroke, bias: 12.2%). Measurements down to 160 mm were obtained with a relative standard deviation and bias of less than 10% for the lateral component for stationary, parabolic flow. The method can, thus, find quantitative velocities, angles, and volume flows at sites currently inaccessible to spectral systems, and at much larger velocities and ranges than conventional systems without any angle correction making measurements less time-consuming and more correct.

Abstract: Due to the heavy computational cost and being vulnerable to noise pollution, traditional Gradient Vector Flow(GVF), which is a most popular method in image segmentation, often presents poor performance. A novel generating method of GVF field is presented in this letter. Only a part of image pixels will still use the standard GVF vector diffusion method. More pixels will use the proposed interpolation method. Experimental results show that the proposed method can reduce the computational cost significantly and improve robustness to noise pollution.

Abstract: This paper presents a method for measuring pressure changes in deep-tissue vessels using vector velocity ultrasound data. The large penetration depth is ensured by acquiring data using a low frequency phased array transducer. Vascular pressure changes are then calculated from 2-D angle-independent vector velocity fields using a model based on the Navier-Stokes equations. Experimental scans are performed on a fabricated flow phantom having a constriction of 36% at a depth of 100 mm. Scans are carried out using a phased array transducer connected to the experimental scanner, SARUS. 2-D fields of angle-independent vector velocities are acquired using directional synthetic aperture vector flow imaging. The obtained results are evaluated by comparison to a 3-D numerical simulation model with equivalent geometry as the designed phantom. The study showed pressure drops across the constricted phantom varying from -40 Pa to 15 Pa with a standard deviation of 32%, and a bias of 25% found relative to the peak simulated pressure drop. This preliminary study shows that pressure can be estimated non-invasively to a depth that enables cardiac scans, and thereby, the possibility of detecting the pressure drops across the mitral valve.

Abstract: Automatic and accurate detection of vertebral pose of low resolution x-ray images with different bone structure is essential to diagnose patient condition. Low resolution and incomplete x-ray image is created from low level of irradiating that can avoid radiation over doze. In this research, we propose a novel approach to estimate vertebral pose. There are three main steps including Vertical Projection, Gradient Vector Flow and Feature of Vector Field. Firstly, we segment vertebral zone from full image using Vertical Projection Average with Normal Distribution. Secondly, we introduce Gradient Vector Flow to identify background and foreground of image. Energy calculation helps to divide different objects on image. Then vector field algorithm will help to promote the exact border of the object. Finally, the horizontal field is chosen as the best information to identify the vertebral pose. From the experimental results, we can extract six main bone layouts. There are two normal layouts and four abnormal layouts. For each layout, we deploy different criteria to identify vertebral pose. For the layouts that located between 0–67 index, the separation hyperplane needs to be shifted up, otherwise shifted down. We use 80 low resolution and incomplete x-ray images from a local hospital. The accuracy rate is 79.25% compared with the ground-truth.

Abstract: Experimental 3-D vector flow estimates obtained with a 62+62 2-D row-column (RC) array with integrated apodization are presented. A transverse oscillation (TO) velocity estimator is implemented on a 3.0 MHz RC array, to yield real-time 3-D vector flow in a cross-sectional scan plane at 750 frames per second. The method is validated in a straight-vessel phantom (O = 8 mm) connected to a flow pump capable of generating time-varying carotid waveforms. The out-of-plane velocity component perpendicular to the cross section of the vessel and the cross-sectional area is used to estimate volumetric flow rates. The flow rate measured from five cycles is 2.3 mL/stroke ± 0.1 mL/stroke giving a negative 9.7% bias compared to the pump settings. It is concluded that 124 elements are sufficient to estimate 3-D vector flow, if they are positioned in a row-column wise manner.

Abstract: In order to solve the problem regarding steel wire defect detection, a gradient vector flow calculation method based on extended neighborhood is proposed in this article and applied to the steel wire defect detection. The new method is used to analyze the gradient vector flow model from the angle of mask film, wherein the original fourneighborhood mask film is replaced by the mask film with a larger neighborhood, thus to obtain the gradient vector flow calculation method based on the extended neighborhood. Actually, the new calculation method only needs less iterations to obtain better effect. Experimentally, the algorithm proposed in this article is feasible and has high algorithm execution efficiency and high complexity.

Abstract: A method of ultrasound imaging includes transmitting an ultrasound signal with an ultrasound transducer array The method further includes receiving from the ultrasound transducer array electrical signals indicative of ultrasound echoes received by the ultrasound transducer array The method further includes beamforming the electrical signals, which results in beamformed data The method further includes processing the beamformed data, which generates an image The image represents at least an anatomical vessel of interest The method further includes processing the beamformed data, which generates flow direction data and flow magnitude data for blood cells flowing in a predetermined region of the anatomical vessel The method further includes processing the flow direction data and the flow magnitude data, which creates a visualization of the flow direction data and the flow magnitude data for the entire predetermined region of the vessel The method further includes visually presenting the image with the visualization superimposed thereover