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Pressure gradient estimations are used as a biomarker for cardiovascular diseases. Here non-invasive pressure gradients are desired over invasive catheterization. This study estimates non-invasive pressure gradients from synthetic aperture ultrasound using the work-energy method. The method is translated to 2D synthetic aperture ultrasound by assuming rotational symmetric blood vessels and is hypothesised to yield more precise estimation compared to the unsteady Bernoulli method along a streamline. The method uses flow rates, blood velocities and acceleration for estimating the pressure gradient. Data are acquired using a 256 elements, 6.5 MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner with a pulse repetition frequency equal to 5 kHz. A interleaved sequence using 12 virtual sources is used for both flow estimations and B-mode imaging. The interleaved sequence allows correlation frames to be separated by only the pulse repetition time, making it possible to estimate high velocities. The work energy method is compared to a previously validated unsteady Bernoulli method (streamline method) using experimental data from a blood vessel phantom with a 60% stenosis. The result shows that the work-energy method detects a maximum pressure difference of 3.42 Pa and a minimum pressure difference of -53.3 Pa with a precision of 3.04% across eleven pulse cycles. The unsteady Bernoulli method detected pressure differences changing from 5.44 Pa to -68.2 Pa with a precision of 3.23%.

Purpose This paper investigates the accuracy of blood flow velocities simulated from a geometry prescribed computational fluid dynamics (CFD) pipeline by applying it to a dynamic heart phantom. The CFD flow patterns are compared to a direct flow measurement by ultrasound vector flow imaging (VFI). The hypothesis is that the simulated velocity magnitudes are within one standard deviation of the measured velocities. Methods The CFD pipeline uses computed tomography angiography (CTA) images with 20 volumes per cardiac cycle as geometry input. Fluid domain movement is prescribed from volumetric image registration using the CTA image data. Inlet and outlet conditions are defned by the experimental setup. VFI is systematically measured in parallel planes, and compared to the corresponding planes in the simulated time dependent three dimensional fluid velocity field. Results The measured VFI and simulated CFD have similar flow patterns when compared qualitatively. A quantitative comparison of the velocity magnitude is also performed at specific regions of interest. These are evaluated at 11 non-overlapping time bins and compared by linear regression giving R2 = 0.809, SD = 0.060 m/s, intercept = − 0.039 m/s, and slope = 1.09. Excluding an outlier at the inlet, the correspondence between CFD and VFI improves to: R2 = 0.823, SD = 0.048 m/s, intercept = -0.030 m/s, and slope = 1.01. Conclusion The direct comparison of flow patterns shows that the proposed CFD pipeline provide realistic flow patterns in a well-controlled experimental setup. The demanded accuracy is obtained close to the inlet and outlet, but not in locations far from these.

This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier–Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) interleaved sequence with 2 × 12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields an R-square of 0.985 and an RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from −59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flo

Local pressure differences estimated using vector flow imaging (VFI) and direct catheterization in seven carotid bifurcation phantoms were compared with simulated pressure fields. VFI correlated strongly with simulated peak pressure differences (r = 0.99, p < 0.00001), with an average overestimation of 12.3 Pa (28.6%). The range between the lowest and highest pressure difference of VFI underestimated simulations by 4.6 Pa (8.06%; r = 0.99, p < 0.0001). The catheter method exhibited no correlation (r = –0.09, p = 0.85). Ten repeated measurements on one phantom revealed a small standard deviation (SD) for VFI (SD = 8.4%, mean estimated SD = 11.5%), but not for the catheter method (SD = 785.6%). An in vivo peak systolic pressure difference of 97.9 Pa (estimated SD = 30%) was measured using VFI in one healthy individual. This study indicates that VFI pressure difference estimation is feasible in phantoms and in vivo and realistic estimates of the SD can be attained from the data.

In this work the accuracy of row-column tensor velocity imaging, i.e., 3-D vector flow imaging in 3-D space over time, is quantified on complex, clinically relevant flow. The quantification is achieved by transferring flow simulated using computational fluid dynamics to a Field II simulation environment and this allows for a direct comparison between the actual and estimated velocities. Carotid bifurcation flow simulations were performed with a peak inlet velocity of 80 cm/s, non-rigid vessel walls, and a flow cycle duration of 1.2 s. The flow was simulated from two observation angles and it was acquired using a 3 MHz 62+62 row-column addressed array at a pulse repetition frequency (fprf) of 10 and 20 kHz. The tensor velocities were obtained at a frame rate of 208.3 Hz, at fprf = 10 kHz, and the results from two velocity estimators were compared. The two estimators were the directional transverse oscillation cross-correlation estimator, and a proposed auto-correlation estimator. Linear regression between the actual and estimated velocity components yielded for the cross-correlation estimator an R2 value in the range of 0.89-0.91, 0.46-0.77, and 0.91-0.97 for the x-, y- and z-components, and 0.87-0.89, 0.40-0.83, and 0.91-0.96, when using the auto-correlation estimator. The results demonstrates that a row-column addressed array can with just 62 receive channels measure complex 3-D flow fields at a high volume rate.

Local pressure differences estimated using vector flow imaging (VFI) and direct catheterization in seven carotid bifurcation phantoms were compared with simulated pressure fields. VFI correlated strongly with simulated peak pressure differences (r = 0.99, p < 0.00001), with an average overestimation of 12.3 Pa (28.6%). The range between the lowest and highest pressure difference of VFI underestimated simulations by 4.6 Pa (8.06%; r = 0.99, p < 0.0001). The catheter method exhibited no correlation (r = –0.09, p = 0.85). Ten repeated measurements on one phantom revealed a small standard deviation (SD) for VFI (SD = 8.4%, mean estimated SD = 11.5%), but not for the catheter method (SD = 785.6%). An in vivo peak systolic pressure difference of 97.9 Pa (estimated SD = 30%) was measured using VFI in one healthy individual. This study indicates that VFI pressure difference estimation is feasible in phantoms and in vivo and realistic estimates of the SD can be attained from the data.

A method for volumetric Tensor Velocity Imaging employing row-column (RC) addressed array with low computational complexity is investigated in simulations. An interleaved and non-interleaved sliding aperture sequence with 11 rows and 11 columns emissions by a 62 + 62 RC addressed array was used. The 3D velocities were estimated by a transverse oscillation (TO) cross-correlation estimator. Parabolic profiles at six different orientations corresponding to combinations of 0, 45 degrees azimuth angles and 90, 75, 60 beam-to-flow angles were investigated with 5 kHz pulse repetition frequencies. The Field II simulations were performed at a depth of 30 mm with peak velocity of 0.3 m/s. Across all vessel orientations, the relative mean bias varied from 2.3% to -14.26%, and the relative standard deviation varied from 0.43% to 5.5%. The best and worst performance was found at beam to flow angles of 90 degrees with 0 degrees rotation angle and 60 degrees beam-to-flow angle with 45 degrees rotation angle respectively. Due to the low channel count of the RC array and the low computational complexity, real-time implementation is feasible on conventional ultrasound systems.

This study presents a new method for noninvasive pressure gradient estimations. It combines a new method for estimating the spatio-temporal acceleration of the flowing blood with the Navier-Stokes equation. The method is based on a double cross-correlation approach, which is hypothesized to generate more precise pressure gradients than previous methods. The acceleration is determined by cross-correlating the correlation functions attained from the velocity estimation. Data are acquired using a 5.2 MHz linear transducer in combination with a Verasonics research scanner. A permuted, pulse inverted, interleaved sequence with four virtual sources evenly distributed on the aperture is used. The performance of the method is tested on experimental data, measured on a bifurcation phantom of the common carotid artery. The pressure drop across nine flow cycles varied from -20 Pa to 40 Pa, with a standard deviation of 15.7%.

This paper presents an imaging scheme capable of estimating the full 3-D velocity vector field in a volume using rowcolumn addressed (RCA) arrays at a high volume rate. A 62+62 RCA array is employed with an interleaved synthetic aperture sequence. It contains repeated emissions with rows and columns interleaved with B-mode emissions. The sequence contains 80 emissions in total and can provide continuous volumetric data at a volume rate above 125 Hz. A transverse oscillation crosscorrelation estimator determines all three velocity components. The approach is investigated using Field II simulations and measurements using a specially built 3 MHz 62+62 RCA array connected to the SARUS experimental scanner. Both the B-mode and flow sequences have a penetration depth of 14 cm when measured on a tissue mimicking phantom (0.5 dB/[MHz·cm] attenuation). Simulations of a parabolic flow in a 12 mm diameter vessel at a depth of 30 mm, beam-to-flow angle of 90°, and xyrotation of 45° gave a standard deviation (SD) of (3.3, 3.4, 0.4)% and bias of (-3.3, -3.9, -0.1)%, for (vx, vy, vz). Decreasing the beam-to-flow angle to 60° gave a SD of (8.9, 9.1, 0.8)% and bias of (-7.6, -9.5, -7.2)%, showing a slight increase. Measurements were carried out using a similar setup, and pulsing at 2 kHz yielded comparable results at 90° with a SD of (5.8, 5.5, 1.1)% and bias of (1.4, -6.4, 2.4)%. At 60° the SD was (5.2, 4.7 1.2)% and bias (-4.6, 6.9, -7.4)%. Results from measurements across all tested settings showed a maximum SD of 6.8% and a maximum bias of 15.8%, for a peak velocity of 10 cm/s. A tissue mimicking phantom with a straight vessel was used to introduce clutter, tissue motion, and a pulsating flow. The pulsating velocity magnitude was estimated across 10 pulse periods and yielded an SD of 10.9%. The method was capable of estimating transverse flow components precisely, but underestimated the flow with small beam-to-flow angles. The sequence provided continuous data in both time and s

Non-invasive assessment is preferred for monitoring arteriovenous dialysis fistulas (AVFs). Vector concentration assesses flow complexity, which may correlate with stenosis severity. We determined whether vector concentration could assess stenosis severity in dysfunctional AVFs. Vector concentration was estimated in four stenotic phantoms at different pulse repetition frequencies. Spectral Doppler peak velocity and vector concentration were measured in 12 patients with dysfunctional AVFs. Additionally, 5 patients underwent digital subtraction angiography (DSA). In phantoms, vector concentration exhibited an inverse relationship with stenosis severity and was less affected by aliasing in severe stenoses. In nine stenoses of 5 patients undergoing DSA, vector concentration correlated strongly with stenosis severity (first stenosis: r = –0.73, p = 0.04; other stenoses; r = –0.69, p = 0.02) and mid-stenotic diameter (first stenosis: r = 0.87, p = 0.006; other stenoses: r = 0.70, p = 0.02) as opposed to peak velocities (p > 0.05). Vector concentration is less affected by aliasing in severe stenoses and correlates with DSA in patients with dysfunctional AVF.

Row Column (RC) Arrays can produce highresolution 3-D volumetric images with only 2N interconnections compared to N2 for matrix probes. A 62+62 RC probe has four times larger surface area and one-eighth of the channel count when compared to the same-pitch fully populated 32x32 matrix probe. This research investigates the performance of such a prototype array for volumetric Synthetic Aperture (SA) B-mode and vector flow imaging using defocused waves. An interleaved SA sequence was implemented on the SARUS scanner using a 3 MHz, λ/2-pitch 62+62 RC piezoelectric probe. The sequence contains repeated emissions with rows and columns interleaved with B-mode emissions. The sequence contains 80 emissions in total and can provide a volume rate above 125 Hz yielding continuous data. Velocities were estimated using the Directional Transverse Oscillation Cross-Correlation method. Measurements were made on a circulating flow rig with a parabolic profile with a peak velocity of 0.25 m/s and beam-to-flow angle of 90º, and two different rotation angles (0º, 45º). Results showed a maximum bias of -17.5% and a standard deviation of 3.9%. A second setup used a tissue mimicking phantom with pulsating flow showing full volumetric flow estimated using the method. The flow was visualized in the entire rectilinear volume at once, with B-mode planes selectable in the entire region. This was attained using only 62 channels in receive making full volumetric imaging and velocity estimation implementable on current scanner hardware.

Hypertension is a common health problem and may be caused by dysfunction of the stretch sensitive baroreceptors in the carotid bulb. Velocity changes and vortices are present in the carotid bulb, and a better evaluation of the local flow and pressures may be important to further understand hypertension. The intravascular pressure catheter is a common tool in the clinic and is currently considered to be the reference standard for intravascular pressure measurement, but the method is invasive, ionizing, and has been reported to be inaccurate. Vector flow imaging (VFI) is an angle independent, noninvasive, and nonionizing ultrasound method that can estimate pressure differences. In this study, pressure differences between the common carotid artery and the carotid bulb obtained with VFI were compared with catheter measurements in three carotid bifurcation phantoms. A fluid-structure interaction (FSI) simulation model was used as reference. Additionally, 10 repeated VFI and catheter measurements were performed in one phantom for a precision assessment. The mean absolute pressure difference between the catheter and FSI method in the three phantoms was 140.5 Pa, and 10 repeated catheter tests measured a mean pressure decrease with a large variation (mean: -133.3 Pa, SD: 786%). VFI estimated pressure increases in all phantoms with a mean standard deviation of 11.6%, and the mean absolute pressure difference compared with FSI was 16.7 Pa. Ten repeated VFI estimations found a mean pressure increase with low variation (mean: 40.1 Pa, SD: 10.9%). VFI precisely estimated small pressure differences in a carotid bifurcation phantom setup, whereas the fluid-filled pressure catheter measurements were imprecise.

This study is an initial evaluation of a validation platform for computational fluid dynamics (CFD) pipelines made for human intra-cardiac flow estimation. The pipelines use imagebased prescribed geometry CFD from computed tomography angiography (CTA). In this study the CTA provides approximately 20 volumetric images within one cardiac cycle. The validation platform consists of a dynamic heart phantom which mimics the human heart in CTA and ultrasound (US) measurements. The flow inside the phantom right ventricle (RV) was measured using two methods: 1) a novel CFD pipeline applied using the CTA data (3D+time). 2) US vector flow imaging (VFI) measured directly on the phantom (2D+time). The CFD and VFI are compared quantitatively by comparing point evaluations (line averages) of the in-plane fluid velocity magnitude. The similarity of the line averages, assessed from plots, is found to be depending on the spatial position of the lines. Some positions are very similar in CFD and VFI and some are not. Furthermore a qualitatively comparison is made by plotting the corresponding 2D slices of the vector fields which confirms the quantitative assessment: the overall flow patterns are similar but not everywhere.

Ultrasound imaging of flow has seen a tremendous development over the last sixty years from 1-D spectral displays to color flow mapping and the latest Vector Flow Imaging (VFI). The paper gives an overview of the development from current commercial vector flow systems to the latest advances in fast 4-D volumetric visualizations. It includes a description of the radical break with the current sequential data acquisition by the introduction of synthetic aperture imaging, where the whole region of interest is insonified using either spherical or plane waves also known as ultrafast imaging. This makes it possible to track flow continuously in all directions at frame rates of thousands of images per second. The latest research translates this to full volumetric imaging by employing matrix arrays and row-column arrays for full 3-D vector velocity estimation at all spatial points visualized at very high volume rates (4-D).

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 w

A noninvasive method for estimating intravascular pressure changes using 2-D vector velocity is presented. The method was first validated on computational fluid dynamic (CFD) data and with catheter measurements on phantoms. Hereafter, the method was tested in vivo at the carotid bifurcation and at the aortic valve of two healthy volunteers. Ultrasound measurements were performed using the experimental scanner SARUS, in combination with an 8 MHz linear array transducer for experimental scans and a carotid scan, whereas a 3.5-MHz phased array probe was employed for a scan of an aortic valve. Measured 2-D fields of angle-independent vector velocities were obtained using synthetic aperture imaging. Pressure drops from simulated steady flow through six vessel geometries spanning different degrees of diameter narrowing, running from 20%-70%, showed relative biases from 0.35% to 12.06%, depending on the degree of constriction. Phantom measurements were performed on a vessel with the same geometry as the 70% constricted CFD model. The derived pressure drops were compared to pressure drops measured by a clinically used 4F catheter and to a finite-element model. The proposed method showed peak systolic pressure drops of -3 kPa ± 57 Pa, while the catheter and the simulation model showed -5.4 kPa ± 52 Pa and -2.9 kPa, respectively. An in vivo acquisition of 10 s was made at the carotid bifurcation. This produced eight cardiac cycles from where pressure gradients of -227 ± 15 Pa were found. Finally, the aortic valve measurement showed a peak pressure drop of -2.1 kPa over one cardiac cycle. In conclusion, pressure gradients from convective flow changes are detectable using 2-D vector velocity ultrasound.

In this study, a comparison between velocity fields for a plane wave 2-D vector flow imaging (VFI) method and a computational fluid dynamics (CFD) simulation is made. VFI estimates are obtained from the scan of a flow phantom, which mimics the complex flow conditions in the carotid artery. Furthermore, the precision of the VFI method is investigated under laminar and complex flow conditions in vivo. The carotid bifurcation of a healthy volunteer was scanned using both fast plane wave ultrasound and magnetic resonance imaging (MRI). The acquired MRI geometry of the bifurcation was used for fabricating an anthropomorphic flow phantom, which was also ultrasound scanned. The same geometry was used in a CFD simulation to calculate the velocity field. Results showed that similar flow patterns and vortices were estimated using CFD and VFI in the phantom. Velocity magnitudes were estimated with a mean difference within 15 %, however, it was 23 % in the external branch. For the in vivo scan, the precision in terms of mean standard deviation (SD) of estimates aligned to the cardiac cycle was highest in the center of the common carotid artery (SD 4.7◦ for angles) and lowest in the external branch and close to the vessel wall (SD 15.0◦ for angles).

The purpose of this study was to investigate the accuracy and precision of fast plane wave 2-D vector flow imaging (VFI) under laminar and complex flow conditions in a human subject. The method has previously been validated in simulations and straight-vessel phantoms, however, complex flow patterns remain challenging to study, since there are no other imaging techniques accurately enough to compare with. Here, the approach was to study (1) the accuracy by comparing VFI obtained from a patient-specific phantom measurement to computational fluid dynamics (CFD) simulated velocities derived from the same geometry; and (2) the precision in vivo by calculating the standard deviation (SD) of VFI estimates at several evaluation points.

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.

A non-invasive method for estimating pressure changes along a streamline using ultrasound is presented. The suggested method estimates pressure gradients from 2-D vector velocity fields. Changes in pressure are derived using a model based on the Navier-Stokes equations. Scans of a carotid bifurcation phantom with a 70% constriction are performed using a linear array transducer connected to the experimental scanner, SARUS. 2-D fields of angle-independent vector velocities are acquired to a depth of 3 cm using directional synthetic aperture vector flow imaging. The performance of the suggested estimator is evaluated by comparing its results to a 3-D numerical simulation model. The study showed pressure drops across the constricted phantom varying from -5 Pa to 7 Pa with a standard deviation of 4%. The proposed method had a normalised rootmean-square error of 10% in reference to the simulation model. Further, an in-vivo scan of the carotid bifurcation is made to show the feasibility of the technique in a less experimental environment

Ultrasound measurements are used for evaluating biomechanics of the abdominal aorta (AA) predicted by a fluid- structure interaction (FSI) simulation model. FSI simulation models describe the complete arterial physiology by quantify- ing the mechanical response in the vessel wall caused by the percolating pulsating blood. But the predictability of FSI models needs validation for these to be usable for diagnostic purposes. Ultrasound measurements are suitable for such an evaluation as the wall displacement can be measured in vivo and compared to the wall displacement simulated in the FSI model. Spectral Doppler velocity data from 3 healthy male volunteers were used to construct inlet profiles for the FSI model. Simultaneously, wall movement was tracked and used for comparison to FSI model results. Ultrasound data were acquired using a scanner equipped with a research interface. The wall displacement was estimated by time shift estimation obtained from cross-correlation of signals to a fixed reference. The FSI model was constructed as a 2D axis- symmetric pipe with lumen diameter predicted by B-mode images from each volunteer. Visual comparison of wall displacement over 1 cardiac cycle show agreement except for 1 volunteer (Male, 23 yrs.). The magnitude of the displacement in simulation, u fsi , and in vivo , u iv , is within the same order of magnitude for the young ( u iv = 1 : 48 mm, u fsi = 1 : 12 mm) and middle-aged volunteer ( u iv = 0 : 783 mm, u fsi = 1 : 31 mm). For the elderly volunteer the simulated displacement ( u fsi = 0 : 975 10

This paper investigates how pressure gradients in a pulsatile flow environment can be measured non-invasively using ultrasound. The presented set-up is based on vector velocity fields measured on a blood mimicking fluid moving at a peak flow rate of 1 ml/s through a constricted vessel. Fields of pressure gradients are calculated using the Navier-Stokes equations. Flow data are acquired to a depth of 3 cm using directional synthetic aperture flow imaging on a linear array transducer producing 1500 image frames of velocity estimates per second. Scans of a carotid bifurcation phantom with a 70% constriction are performed using an experimental scanner. The performance of the presented estimator is evaluated by comparing its results to a numerical simulation model, which geometry is reconstructed from MRI data. The study showed pressure gradients varying from 0 kPa/m to 4.5 kPa/m with a maximum bias and standard deviation of 10% and 13%, respectively, relative to peak estimated gradient. The paper concludes that maps of pressure gradients can be measured non-invasively using ultrasound with a precision of more than 85%