Haemodynamics and blood flow measured using ultrasound imaging

Evaluation of Turbulence Index and Flow Pattern for Atherosclerotic Carotid Stenosis: A High-Frame-Rate Vector Flow Imaging Study

OBJECTIVE

The emerging high-frame-rate vector flow imaging provides a new way of hemodynamic evaluation for complex blood flow. This study was aimed at exploring quantitatively the characteristics of complex flow with turbulence (Tur) index and analyzing flow patterns in atherosclerotic internal carotid artery stenosis (ICAS) using high-frame-rate vector flow imaging.

METHODS

This study prospectively included 60 patients with ICAS. Tur values in different segments of stenosis and cardiac phases were compared. Spearman correlation analysis was performed between clinical plaque characteristics with turbulence grading by ln(Tur). Three complex flow patterns were qualitatively drawn on vector flow mode, and the rates of detection of flow patterns in different stenosis groups and ulceration groups were compared.

RESULTS

Highly disordered blood flow was observed in the stenotic (Tur [M, QR] = 12.5%, 21.5%) and distal segment (15.4%, 27.2%), particularly during systole (21.0%, 30.7%, 33.3%, 38.7%, p < 0.05). Spearman correlation analysis revealed that stenosis rate was correlated with turbulence grading in the stenotic (ρ = 0.65, p < 0.05) and distal segment (ρ = 0.79, p < 0.05), and ulcer formation was correlated with turbulence grading in the stenotic segment (ρ = 0.58, p < 0.05). The overall rate of detection of three flow patterns was higher in the severe stenosis group (22/22) versus the mild to moderate stenosis group (21/38) (p < 0.001) and in the ulcer group (21/23) versus the non-ulcer group (23/37) (p < 0.001).

CONCLUSION

High-frame-rate vector flow imaging was helpful in assessing the severity and characteristics of flow turbulence. Lumen geometric factors could affect flow turbulence and blood flow patterns around the plaque. This would provide important hemodynamic information for the detection of high-risk plaque.

Coded Excitation for Ultrasonic Testing: A Review

Originating in the early 20th century, ultrasonic testing has found increasingly extensive applications in medicine, industry, and materials science. Achieving both a high signal-to-noise ratio and high efficiency is crucial in ultrasonic testing. The former means an increase in imaging clarity as well as the detection depth, while the latter facilitates a faster refresh of the image. It is difficult to balance these two indicators with a conventional short pulse to excite the probe, so in general handling methods, these two factors have a trade-off. To solve the above problems, coded excitation (CE) can increase the pulse duration and offers great potential to improve the signal-to-noise ratio with equivalent or even higher efficiency. In this paper, we first review the fundamentals of CE, including signal modulation, signal transmission, signal reception, pulse compression, and optimization methods. Then, we introduce the application of CE in different areas of ultrasonic testing, with a focus on industrial bulk wave single-probe detection, industrial guided wave detection, industrial bulk wave phased array detection, and medical phased array imaging. Finally, we point out the advantages as well as a few future directions of CE.

Time-Resolved Wall Shear Rate Mapping Using High-Frame-Rate Ultrasound Imaging

In atherosclerosis, low wall shear stress (WSS) is known to favor plaque development, while high WSS increases plaque rupture risk. To improve plaque diagnostics, WSS monitoring is crucial. Here, we propose wall shear imaging (WASHI), a noninvasive contrast-free framework that leverages high-frame-rate ultrasound (HiFRUS) to map the wall shear rate (WSR) that relates to WSS by the blood viscosity coefficient. Our method measures WSR as the tangential flow velocity gradient along the arterial wall from the flow vector field derived using a multi-angle vector Doppler technique. To improve the WSR estimation performance, WASHI semiautomatically tracks the wall position throughout the cardiac cycle. WASHI was first evaluated with an in vitro linear WSR gradient model; the estimated WSR was consistent with theoretical values (an average error of 4.6% ± 12.4 %). The framework was then tested on healthy and diseased carotid bifurcation models. In both scenarios, key spatiotemporal dynamics of WSR were noted: 1) oscillating shear patterns were present in the carotid bulb and downstream to the internal carotid artery (ICA) where retrograde flow occurs; and 2) high WSR was observed particularly in the diseased model where the measured WSR peaked at 810 [Formula: see text] due to flow jetting. We also showed that WASHI could consistently track arterial wall motion to map its WSR. Overall, WASHI enables high temporal resolution mapping of WSR that could facilitate investigations on causal effects between WSS and atherosclerosis.

Unfocused Field Analysis of a Density-Tapered Spiral Array for High-Volume-Rate 3-D Ultrasound Imaging

Spiral array transducers with a sparse 2-D aperture have demonstrated their potential in realizing 3-D ultrasound imaging with reduced data rates. Nevertheless, their feasibility in high-volume-rate imaging based on unfocused transmissions has yet to be established. From a metrology standpoint, it is essential to characterize the acoustic field of unfocused transmissions from spiral arrays not only to assess their safety but also to identify the root cause of imaging irregularities due to the array's sparse aperture. Here, we present a field profile analysis of unfocused transmissions from a density-tapered spiral array transducer (256 hexagonal elements, 220- [Formula: see text] element diameter, and 1-cm aperture diameter) through both simulations and hydrophone measurements. We investigated plane- and diverging-wave transmissions (five-cycle, 7.5-MHz pulses) from 0° to 10° steering for their beam intensity characteristics and wavefront arrival time profiles. Unfocused firings were also tested for B-mode imaging performance (ten compounded angles, -5° to 5° span). The array was found to produce unfocused transmissions with a peak negative pressure of 93.9 kPa at 2 cm depth. All transmissions steered up to 5° were free of secondary lobes within 12 dB of the main beam peak intensity. All wavefront arrival time profiles were found to closely match the expected profiles with maximum root-mean-squared errors of [Formula: see text] for plane wave (PW) and [Formula: see text] for diverging wave. The B-mode images showed good spatial resolution with a penetration depth of 22 mm in PW imaging. Overall, these results demonstrate that the density-tapered spiral array can facilitate unfocused transmissions below regulatory limits (mechanical index: 0.034; spatial-peak, pulse-average intensity: 0.298 W/cm2) and with suppressed secondary lobes while maintaining smooth wavefronts.

Measurement of Flow Volume in the Presence of Reverse Flow with Ultrasound Speckle Decorrelation

Direct measurement of volumetric flow rate in the cardiovascular system with ultrasound is valuable but has been a challenge because most current 2-D flow imaging techniques are only able to estimate the flow velocity in the scanning plane (in-plane). Our recent study demonstrated that high frame rate contrast ultrasound and speckle decorrelation (SDC) can be used to accurately measure the speed of flow going through the scanning plane (through-plane). The volumetric flow could then be calculated by integrating over the luminal area, when the blood vessel was scanned from the transverse view. However, a key disadvantage of this SDC method is that it cannot distinguish the direction of the through-plane flow, which limited its applications to blood vessels with unidirectional flow. Physiologic flow in the cardiovascular system could be bidirectional due to its pulsatility, geometric features, or under pathologic situations. In this study, we proposed a method to distinguish the through-plane flow direction by inspecting the flow within the scanning plane from a tilted transverse view. This method was tested on computer simulations and experimental flow phantoms. It was found that the proposed method could detect flow direction and improved the estimation of the flow volume, reducing the overestimation from over 100% to less than 15% when there was flow reversal. This method showed significant improvement over the current SDC method in volume flow estimation and can be applied to a wider range of clinical applications where bidirectional flow exists.

Live Ultrasound Color-Encoded Speckle Imaging Platform for Real-Time Complex Flow Visualization In Vivo

Complex flow patterns are prevalent in the vasculature, but they are difficult to image noninvasively in real time. This paper presents the first real-time scanning platform for a high-frame-rate ultrasound technique called color-encoded speckle imaging (CESI) and its use in visualizing arterial flow dynamics in vivo. CESI works by simultaneously rendering flow speckles and color-coded flow velocity estimates on a time-resolved basis. Its live implementation was achieved by integrating a 192-channel programmable ultrasound front-end module, a 4.8-GB/s capacity data streaming link, and a series of computing kernels implemented on the graphical processing unit (GPU) for beamforming and Doppler processing. A slow-motion replay mode was also included to offer coherent visualization of CESI frames acquired at high frame rate [3000 frames per second (fps) in our experiments]. The live CESI scanning platform was found to be effective in facilitating real-time image guidance (at least 20 fps for live video display with 55-fps GPU processing throughout). In vivo pilot trials also showed that live CESI, when running in replay mode, can temporally resolve triphasic flow at the brachial bifurcation and can reveal flow dynamics in the brachial vein during a fist-clenching maneuver. Overall, live CESI has potential for use in routine investigations in vivo that seek to identify complex flow dynamics in real time and relate these dynamics to vascular physiology.

High frame rate doppler ultrasound bandwidth imaging for flow instability mapping

Purpose

Flow instability has been shown to contribute to the risk of future cardiovascular and cerebrovascular events. Nonetheless, it is challenging to noninvasively detect and identify flow instability in blood vessels. Here, we present a new framework called Doppler ultrasound bandwidth imaging (DUBI) that uses high‐frame‐rate ultrasound and Doppler bandwidth analysis principles to assess flow instability within an image view.

Methods

Doppler ultrasound bandwidth imaging seeks to estimate the instantaneous Doppler bandwidth based on autoregressive modeling at every pixel position of data frames acquired from high‐frame‐rate plane wave pulsing. This new framework is founded upon the principle that flow instability naturally gives rise to a wide range of flow velocities over a sample volume, and such velocity range in turn yields a larger Doppler bandwidth estimate. The ability for DUBI to map unstable flow was first tested over a range of fluid flow conditions (ranging from laminar to turbulent) with a nozzle‐flow phantom. As a further demonstration, DUBI was applied to assess flow instability in healthy and stenosed carotid bifurcation phantoms.

Results

Nozzle‐flow phantom results showed that DUBI can effectively detect and visualize the difference in Doppler bandwidth magnitude (increased from 2.1 to 5.2 kHz) at stable and unstable flow regions in an image view. Receiver operating characteristic analysis also showed that DUBI can achieve optimal sensitivity and specificity of 0.72 and 0.83, respectively. In the carotid phantom experiments, differences were observed in the spatiotemporal dynamics of Doppler bandwidth over a cardiac cycle. Specifically, as the degree of stenosis increased (from 50% to 75%), DUBI showed an increase in Doppler bandwidth magnitude from 1.4 kHz in the healthy bifurcation to 7.7 kHz at the jet tail located downstream from a 75% stenosis site, thereby indicating flow perturbation in the stenosed bifurcations.

Conclusion

DUBI can detect unstable flow. This new technique can provide useful hemodynamic information that may aid clinical diagnosis of atherosclerosis.

Walled Carotid Bifurcation Phantoms for Imaging Investigations of Vessel Wall Motion and Blood Flow Dynamics

As a major application domain of vascular ultrasound, the carotid artery has long been the subject of anthropomorphic phantom design. It is nevertheless not trivial to develop walled carotid phantoms that are compatible for use in integrative imaging of carotid wall motion and flow dynamics. In this paper, we present a novel phantom design protocol that can enable efficient fabrication of walled carotid bifurcation phantoms with: (i) high acoustic compatibility, (ii) artery-like vessel elasticity, and (iii) stenotic narrowing feature. Our protocol first involved direct fabrication of the vessel core and an outer mold using computer-aided design tools and 3-D printing technology; these built parts were then used to construct an elastic vessel tube through investment casting of a polyvinyl alcohol containing mixture, and an agar-gelatin tissue mimicking slab was formed around the vessel tube. For demonstration, we applied our protocol to develop a set of healthy and stenosed (25%, 50%, 75%) carotid bifurcation phantoms. Plane wave imaging experiments were performed on these phantoms using an ultrasound scanner with channel-level configurability. Results show that the wall motion dynamics of our phantoms agreed with pulse wave propagation in an elastic vessel (pulse wave velocity of 4.67±0.71 m/s measured at the common carotid artery), and their flow dynamics matched the expected ones in healthy and stenosed bifurcation (recirculation and flow jet formation observed). Integrative imaging of vessel wall motion and blood flow dynamics in our phantoms was also demonstrated, from which we observed fluid-structure interaction differences between healthy and diseased bifurcation phantoms. These findings show that the walled bifurcation phantoms developed with our new protocol are useful in vascular imaging studies that individually or jointly assess wall motion and flow dynamics.

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.

Microbubble Void Imaging: A Non-invasive Technique for Flow Visualisation and Quantification of Mixing in Large Vessels Using Plane Wave Ultrasound and Controlled Microbubble Contrast Agent Destruction

There is increasing recognition of the influence of the flow field on the physiology of blood vessels and their development of pathology. Preliminary work is reported on a novel non-invasive technique, microbubble void imaging, which is based on ultrasound and controlled destruction of microbubble contrast agents, permitting flow visualisation and quantification of flow-induced mixing in large vessels. The generation of microbubble voids can be controlled both spatially and temporally using ultrasound parameters within the safety limits. Three different model vessel geometries-straight, planar-curved and helical-with known effects on the flow field and mixing were chosen to evaluate the technique. A high-frame-rate ultrasound system with plane wave transmission was used to acquire the contrast-enhanced ultrasound images, and an entropy measure was calculated to quantify mixing. The experimental results were cross-compared between the different geometries and with computational fluid dynamics. The results indicated that the technique is able to quantify the degree of mixing within the different configurations, with a helical geometry generating the greatest mixing, and a straight geometry, the lowest. There is a high level of concordance between the computational fluid dynamics and experimental results. The technique could also serve as a flow visualisation tool.

Comparison of vortical structures induced by arteriovenous grafts using vector Doppler ultrasound

Arteriovenous prosthetic grafts are used in hemodialysis. Stenosis in the venous anastomosis is the main cause of occlusion and the role of local hemodynamics in this is considered significant. A new spiral graft design has been proposed to stabilize the flow phenomena in the host vein. Cross-flow vortical structures in the outflow of this graft were compared with those from a control device. Both grafts were integrated in identical in-house ultrasound-compatible flow phantoms with realistic surgical configurations. Constant flow rates were applied. In-plane 2-D velocity and vorticity mapping was developed using a vector Doppler technique. One or two vortices were detected for the spiral graft and two to four for the control, along with reduced stagnation points for the former. The in-plane peak velocity and circulation were calculated and found to be greater for the spiral device, implying increased in-plane mixing, which is believed to inhibit thrombosis and neo-intimal hyperplasia.

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.

Secondary flow in peripheral vascular prosthetic grafts using vector Doppler imaging

Prosthetic grafts are used for the treatment of peripheral arterial disease. Re-stenosis in the distal anastomosis of these grafts is a common reason for graft occlusion. The role of local hemodynamics in development of neo-intimal hyperplasia is well known. A new graft design has been proposed for the induction of optimized spiral flow in the host vessel. The secondary flow motions induced by this graft were compared with those of a control device. Both types of grafts were connected with vessel mimic and positioned in ultrasound flow phantoms with identical geometry. Constant flow rates were applied. Data collected in the cross-sectional view distal from the graft outflow and dual-beam vector Doppler was applied to create 2-D velocity maps. A single-spiral flow pattern was found for the flow-modified graft, and double or triple spirals for the control graft. In-plane maximum velocity was greater for the flow-modified graft than for the control device.

High-frame-rate ultrasound color-encoded speckle imaging of complex flow dynamics

Realization of flow imaging at high frame rates is essential to the visualization of complex flow patterns with fast-changing spatiotemporal dynamics. In this study, we present an experimental demonstration of a novel ultrasound-based high-frame-rate flow visualization technique called color-encoded speckle imaging (CESI), which depicts flow information in a hybrid form comprising flow speckle pattern and color-encoded velocity mapping. This technique works by integrating two key principles: (i) using broad-view data acquisition schemes like plane wave compounding to obtain image data at frame rates well beyond the video display range and (ii) deriving and displaying both flow speckles and velocity estimates from the acquired broad-view image data. CESI was realized on a channel-domain ultrasound imaging research platform, and its performance was evaluated in the context of monitoring complex flow dynamics inside a carotid bifurcation flow phantom with 25% eccentric stenosis at the inlet of the internal carotid artery. Results show that, using an imaging frame rate of 2000 frames per second (based on plane wave compounding with five steering angles), CESI can effectively render flow acceleration and deceleration with visual continuity. It is also effective in depicting how stenosis-related flow disturbance events, such as flow jet formation and post-stenotic flow recirculation, evolve spatiotemporally over a pulse cycle. We anticipate that CESI can represent a rational approach to rendering flow information in ultrasound-based vascular diagnoses.

Mapping mean and fluctuating velocities by Bayesian multipoint MR velocity encoding-validation against 3D particle tracking velocimetry

PURPOSE

To validate Bayesian multipoint MR velocity encoding against particle tracking velocimetry for measuring velocity vector fields and fluctuating velocities in a realistic aortic model.

METHODS

An elastic cast of a human aortic arch equipped with an 80 or 64% stenotic section was driven by a pulsatile pump. Peak velocities and peak turbulent kinetic energies of more than 3 m/s and 1000 J/m(3) could be generated. Velocity vector fields and fluctuating velocities were assessed using Bayesian multipoint MR velocity encoding with varying numbers of velocity encoding points and particle tracking velocimetry in the ascending aorta.

RESULTS

Velocities and turbulent kinetic energies measured with 5-fold k-t undersampled 10-point MR velocity encoding and particle tracking velocimetry were found to reveal good correlation with mean differences of -4.8 ± 13.3 cm/s and r(2) = 0.98 for velocities and -21.8 ± 53.9 J/m(3) and r(2) = 0.98 for turbulent kinetic energies, respectively. Three-dimensional velocity patterns of fast flow downstream of the stenoses and regions of elevated velocity fluctuations were found to agree well.

CONCLUSION

Accelerated Bayesian multipoint MR velocity encoding has been demonstrated to be accurate for assessing mean and fluctuating velocities against the reference standard particle tracking velocimetry. The MR method holds considerable potential to map velocity vector fields and turbulent kinetic energies in clinically feasible exam times of <15 min.

Vascular Strategies for Enhancing Tumour Response to Radiation Therapy

Radiation therapy is prescribed to more than 50% of patients diagnosed with cancer. Although mechanisms of interaction between radiation and tumour cells are well understood on a molecular level, much remains uncertain concerning the interaction of radiation with the tumour as a whole. Recent studies have demonstrated that single large doses of radiation (8–20 Gy) may primarily target tumour endothelial cells, leading to secondary tumour clonogenic cell death. These studies suggest that blood vessels play an important role in radiation response. As a result, various strategies have been proposed to effectively combine radiation with vascular targeting agents. While most proposed schemes focus on methods to disrupt tumour blood vessels, recent evidence supporting that some anti-angiogenic agents may “normalize” tumour blood vessels, in turn enhancing tumour oxygenation and radiosensitivity, indicates that there may be more efficient strategies. Furthermore, vascular targeting agents have recently been demonstrated to enhance radiation therapy by targeting endothelial cells. When combined with radiation, these agents are believed to cause even more localized vascular destruction followed by tumour clonogenic cell death. Taken together, it is now crucial to elucidate the role of tumour blood vessels in radiation therapy response, in order to make use of this knowledge in developing therapeutic strategies that target tumour vasculature above and beyond classic clonogenic tumour cell death. In this report, we review some major developments in understanding the importance of tumour blood vessels during radiation therapy. A discussion of current imaging modalities used for studying vascular response to treatments will also be presented.

In vitro and preliminary in vivo validation of echo particle image velocimetry in carotid vascular imaging

Noninvasive, easy-to-use and accurate measurements of wall shear stress (WSS) in human blood vessels have always been challenging in clinical applications. Echo particle image velocimetry (Echo PIV) has shown promise for clinical measurements of local hemodynamics and wall shear rate. Thus far, however, the method has only been validated under simple flow conditions. In this study, we validated Echo PIV under in vitro and in vivo conditions. For in vitro validation, we used an anatomically correct, compliant carotid bifurcation flow phantom with pulsatile flow conditions, using optical particle image velocimetry (optical PIV) as the reference standard. For in vivo validation, we compared Echo PIV-derived 2-D velocity fields obtained at the carotid bifurcation in five normal subjects against phase-contrast magnetic resonance imaging (PC-MRI)-derived velocity measurements obtained at the same locations. For both studies, time-dependent, 2-D, two-component velocity vectors; peak/centerline velocity, flow rate and wall shear rate (WSR) waveforms at the common carotid artery (CCA), carotid bifurcation and distal internal carotid artery (ICA) were examined. Linear regression, correlation analysis and Bland-Altman analysis were used to quantify the agreement of different waveforms measured by the two techniques. In vitro results showed that Echo PIV produced good images of time-dependent velocity vector maps over the cardiac cycle with excellent temporal (up to 0.7 ms) and spatial (∼0.5 mm) resolutions and quality, comparable with optical PIV results. Further, good agreement was found between Echo PIV and optical PIV results for velocity and WSR measurements. In vivo results also showed good agreement between Echo PIV velocities and phase contrast MRI velocities. We conclude that Echo PIV provides accurate velocity vector and WSR measurements in the carotid bifurcation and has significant potential as a clinical tool for cardiovascular hemodynamics evaluation.

Validation of endoscopic ultrasound measured flow rate in the azygos vein using a flow phantom

Increase in flow rate within the azygos vein may be used as an indicator of the degree of liver cirrhosis. The aim of this study was to evaluate the error in measurement of flow rate using a commercial endoscopic ultrasound system, using a flow phantom that mimicked azygos vein depth, diameter and flow rate. Diameter was underestimated in all cases, with an average underestimation of 0.09 cm. Maximum velocity was overestimated, by 4 ± 4% at 50°, 11 ± 3% at 60° and 23 ± 7% at 70°. The increase in error with beam-vessel angle is consistent with the error as arising from geometric spectral broadening. Flow was underestimated by amounts up to 33%, and it is noted that the overestimation caused by geometric spectral broadening is in part compensated by underestimation of diameter. It was concluded that measurement of flow rate using a commercially available endoscopic ultrasound system is dependent on the beam-vessel angle, with errors up to 33% for typical vessel depths, diameter and beam-vessel angle.