Angle-insensitive flow measurement using Doppler bandwidth

The ability to measure the velocity of blood flow independent of the orientation of the blood vessel could aid in evaluation of many disease processes, such as coronary lesions. Conventional ultrasonic Doppler techniques require knowledge of the beam-to-flow angle, and the Doppler effect vanishes when this angle is 90 degrees . By employing a spherically symmetrical range cell and the Doppler bandwidth instead of the Doppler shift, preliminary results show that flow measurement of ideal uniform flow that has a blunt velocity profile can be made without knowledge of tile orientation of the vessel, even when the angle of orientation is around 90 degrees . But when the technique is applied to a real how that has a parabolic velocity profile, the Doppler bandwidth decreases as the beam-to-flow angle increases. Although the Doppler bandwidth is sensitive to the transducer angle in this situation, the error in determining flow velocity might be acceptable if the transducer angle can be estimated to be within a small range. For this method to be regarded as practical for clinical use, however, a consistent relationship between bandwidth and flow velocity must be demonstrated over some set of clinically relevant conditions. The experimental techniques and results for how measurements of both the ideal uniform flow and the real flow are presented in this paper.     

Flow velocity profile via time-domain correlation: error analysis and computer simulation

An ultrasonic human-blood-flow velocity profile measurement method using time-domain correlation of consecutive echo pairs has been developed. The time shift between a pair of range gated echoes is estimated by searching for the shift that results in the maximum correlation. The time shift indicates the distance a group of scatterers has moved, from which flow velocity is estimated. The basis for the computer simulations and error analyses of the scheme includes a band-passed white Gaussian noise signal model for an echo from a scattering medium, the estimate of flow velocity from both a single scatterer and multiple scatterers, and a derived precision estimation. The error analysis via computer simulation includes an evaluation of errors associated with the correlation method. For a uniform flow velocity profile, beamwidth modulation represents the greatest error source. However, for a nonuniform flow velocity profile, the jitter caused by a small flow velocity gradient can exceed the other error sources. A detailed computer simulation evaluated the interdependencies of window length, beam width, vessel diameter, and viewing angle on the estimation of flow velocity.     

A simplified approach for real-time detection of arterial wall velocity and distension

Arterial stiffness is known to increase with age and with many vascular diseases, but its noninvasive assessment in patients still represents a difficult task. The measurement of diameter change during the cardiac cycle (distension) has been proposed as a means to estimate arterial compliance and stiffness. Therefore, we have developed a simple PC-based device and algorithm for noninvasive quantification of vessel wall motion and diameter change in humans. This goal is achieved in real-time by processing the base-band signals from a commercial ultrasound Doppler system. Real-time operation is of crucial importance, because it allows a rapid achievement of optimal measurement conditions. The system was evaluated in a laboratory using a string phantom and was tested on the carotid arteries of 10 volunteers. Wall velocities from 0.05 to 600 mm/s and displacements lower than 2 μm were detected with phantoms. The measured carotid diameter change in the volunteers ranged from 7.5 to 11.8% (mean=9.8%) and agrees closely with values reported in the literature. The difference between values taken one hour apart ranged from 0.2 to 0.5%. We conclude that the new system provides rapid, accurate, and repeatable measurements of vessel distension in humans     

New low-cost technique for accurate surface velocity measurement of a rotating drum

The accurate determination of the velocity profile of an almost uniformly rotating drum is considered. The quality of estimation of the surface velocity obtained through usage of a measuring wheel placed in direct contact with the drum, and rigidly coupled to an encoder of high line count, is usually poor, due to wheel eccentricities and misalignment of the wheel and drum. A new algorithm is described which achieves the nonlinear filtering of the encoder output in such a manner as to yield a very close approximation to the actual drum velocity in most circumstances. A very good estimate of the effective variable gearing ratio between the drum and measuring wheel is achieved, yielding excellent discrimination between drum-based and wheel-based variations. The compensation method is justified theoretically. Computer simulation and experimental results obtained from a web processing plant illustrate the utility of the method. The latter results are shown to compare well with data obtained from a costly laser Doppler-based measurement system.     

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.     

Doppler angle and flow velocity estimations using the classic and transverse Doppler effects

Current clinical Doppler ultrasound systems could only measure the flow vector parallel to the ultrasound beam axis, and the knowledge of the Doppler angle (beam-to-flow angle) is needed to calculate the real flow velocity. Currently, the Doppler angle is determined visually by manually aligning a vessel axis marker along the blood vessel on the duplex scan image of the ultrasound. The application of this procedure is often limited by practical constraints; therefore, measurements are not reliable. In order to overcome this problem, the authors developed a simple Doppler angle and flow velocity estimation method using a combination of the classic and transverse Doppler effects. This method uses only a single focused annular array transducer to estimate the Doppler angle and the flow velocity. The authors have verified experimentally that this method is successful for measuring constant flow in a flow phantom between 45 degrees and 80 degrees Doppler angle. The standard deviation of the estimated Doppler angles is less than 4.5 degrees . This method could be implemented easily in medical Doppler ultrasound systems to automatically estimate the Doppler angle and the flow velocity.     

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.     

Estimation of turbulence velocities induced by magnetic stirring during continuous casting

Abstract

In this paper the turbulent flow generated in a cylindrical container by a low-frequency rotating magnetic field is considered. The rotational part of the electromagnetic body force is steady and axisymmetric, driving an azimuthal swirl flow. It is shown that curvature effects are negligible near the wall of the containing vessel and consequently the velocity profile in that region has the standard logarithmic form. Extrapolating this profile to the core allows an estimate of the core angular velocity to be made. This estimate is consistent with published experimental data and with the results of a more complex two-parameter closure model.

MST/207     

Invariance of the Doppler bandwidth with range cell size above a critical beam-to-flow angle

For a sound beam impinging on a blood vessel, with a range cell much smaller than the vessel diameter, it is known that the breadth of the echo Doppler spectrum is proportional to the velocity of the flow through the range cell. As the range cell is lengthened to include a greater range of velocities, the spectrum is expected to widen proportionately. It is shown theoretically, and confirmed experimentally, that if the beam-to-flow angle is greater than a critical value, the Doppler spectrum bandwidth is independent of the length of the range cell, and depends only on the maximum velocity encompassed by it. This happens because for angles greater than the critical, the narrow spectra produced by lower velocity flows near the vessel walls are contained within the broader spectrum produced by the higher speed flow near the vessel axis. The critical angle is the angle at which the flow axis is normal to one of the beam edges.     

Optical alignment-induced errors in holographic particle image velocimetry

A ray-tracing analysis of point-source imaging in the presence of optical misalignment is used to analyze relative image shift as a source of measurement error in holographic particle image velocimetry (HPIV). Although single-reference-beam HPIV is relatively insensitive to optical misalignment, dual-reference-beam systems may suffer substantial errors because of misalignments of the order of microradians. These systems are particularly sensitive to rotations of the hologram about an axis perpendicular to the film and to reconstruction beam misalignment. In a swirling flow experiment, a proposed error-compensation scheme was able to reduce uncertainty from 130% to 10% of the mean measured velocity.     

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.     

细管道中流速的超声相关法测量

针对应用常规超声波方法测量极小管径(5 mm及以下)中流体速度的精度较低问题,文章应用相关函数法精确测量时延,降低噪声对测量结果的影响,提高了极小管径中流体速度的测量精度.首先,利用COMSOLMultiphysics有限元仿真软件建立管道传输模型,然后将被顺、逆水流影响后的超声波波形数据分别导入Matlab软件,用插...     

Modelling the chilling of the leg, loin and shoulder of beef carcasses using an evolutionary method

An evolutionary algorithm was used to adjust unknown parameters during the beef cooling process. These parameters are the equivalent diameter and the initial temperature profile, which are difficult to estimate given the irregular geometry, the elapsed time after slaughter and variations in both the air temperature and velocity. The adjusted parameters produced accurate predictions of the center and surface temperature profiles of the leg, loin and shoulder. The adjusted dimensions agreed very well with the measured carcass dimensions. Empirical equations were obtained to correlate this diameter with the weight and fat grade of beef carcasses.     

Quantitative real-time blood flow estimation with intravascular ultrasound in the presence of in-plane flow

Previously, we showed a source of error in blood flow estimation introduced by in-plane flow using a slow-time finite-impulse response (FIR) filter-bank method measuring blood flow through the image plane of an intravascular ultrasound (IVUS) catheter array. There is a monotonic relationship between flow velocity and the normalized second moment of the slow-time spectrum when flow is orthogonal to the image plane of a side-looking catheter array. However, this relationship changes in the presence of in-plane flow, as slow-time spectra shift and spread with varying in-plane and out-of-plane components. These two effects increase the normalized spectral second moment, resulting in flow overestimates. However, by resampling the received signal with variable time delay from pulse to pulse (i.e., tilting the slow-time signals), the slow-time spectrum shifts back to direct current (DC), and the orthogonal estimation method can be used. We present a method to correct this overestimation and accurately estimate blood flow through the image plane in real time. Initially, the tilt delay needed to shift the slow-time spectrum back to DC at each point within the flow field is calculated. Knowing this tilt delay, a tilted slow-time signal is obtained for the velocity component normal to the image plane, and its spectrum is estimated using a filter-bank. That spectrum then is used to estimate the flow speed using a mapping function closely related to the monotonic relationship between the slow-time spectrum and flow speed observed for orthogonal flow. To accurately estimate flow angles, we modified the filter-bank algorithm, applying slow-time filter coefficients in a tilted arrangement and studying the slow-time spectral energy as a function of tilt. The slow-time spectral estimate is constructed with the tilted output of eight narrow, band-pass filters from a filter-bank. Independent simulations show that, for blood slowing at angles between +/-6 degrees and +/-15 degrees at a speed of 300 mm/s, flow velocity would be overestimated by as much as 38.79% and 249%, respectively, using the direct filter-bank approach. However, this error can be corrected using the modified method presented here, reducing the maximum overestimation error by a factor of 2.69 and 10.88 for those angles, respectively. Although the remaining error is not negligible, the volume flow rate, calculated by integrating the flow velocity over the entire vessel lumen, differs by only 3% or less from the true value over the angular range considered here. This represents an improvement of a factor of 40 over uncompensated estimates at maximum flow angles. Consequently, the modified real-time method can quantitatively measure flow in most IVUS applications in which the catheter's image plane is not precisely orthogonal to the flow direction.     

Impact of surrounding tissue on conductance measurement of coronary and peripheral lumen area

Parallel conductance (electric current flow through surrounding tissue) is an important determinant of accurate measurements of arterial lumen diameter, using the conductance method. The present study is focused on the role of non-uniform geometrical/electrical configurations of surrounding tissue, which are a primary source of electric current leakage. Computational models were constructed to simulate the conductance catheter measurement with two different excitation electrodes spacings (i.e. 12 and 20 mm for coronary and peripheral sizing, respectively) for different vessel–tissue configurations: (i) blood vessel fully embedded in muscle tissue, (ii) blood vessel superficially embedded in muscle tissue, and (iii) blood vessel superficially embedded in muscle tissue with fat covering half of the arterial vessel (anterior portion). The simulations suggest that the parallel conductance and accuracy of measurement is dependent on the inhomogeneous/anisotropic configuration of surrounding tissue, including the asymmetric dimension and anisotropy in electrical conductivity of surrounding tissue. Specifically, the measurement was shown to be accurate as long as the vessel was superficial, regardless of the considerable total surrounding tissue dimension for coronary or peripheral arteries. Moreover, it was shown that the unfavourable impact of parallel conductance on the accuracy of conductance catheter measurement is decreased by the combination of a lower transverse electrical conductivity of surrounding muscle tissue, a smaller electrode spacing and a larger lumen diameter. The present findings confirm that the conductance catheter technique provides an accurate platform for sizing of clinically relevant (i.e. superficial and diseased) arteries.     

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° 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° 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.     

Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis

There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In this paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.     

Hot Wire Anemometer Measurements in Flows Where Direction of Mean Velocity Changes during a Traverse

This paper describes a simple method that allows X-array hot wire measurements to be made in a flow where the direction of the mean velocity changes during a traverse. Such situations are encountered in measurements behind turbulence promoters, flow across curved surfaces, in diffusers, nozzles, and many others. Variations in mean flow direction of up to 55° are allowable without requiring extensive angle calibration at each new measurement point.     

Analysis of debris clouds produced by impact of aluminum spheres with aluminum sheets

Results of two-stage light gas gun testing of two diameters of aluminum spheres impacting 0.5 mm and 1.0 mm thickness aluminum plates were described in this paper. Impact velocities for these tests were between 3.16 km/s and 5.17 km/s. The components of debris cloud and damage patterns in the witness plate were described. The morphologic features of debris clouds such as shape, axial velocity, and diametral velocity were discussed. The size and number of fragments in the internal structure of debris cloud were not evaluated quantitatively, but described qualitatively. As a result, the shape of the leading face of the internal structure of debris cloud appeared to be sensitive to impact velocity, but not t/D ratio (bumper-thickness-to-projectile diameter ratio). The point at which the maximum diameter of the external bubble of debris cloud occurred had a same half spray angle of 30 degree and the last fragments ejected from bumper had a same half spray angle of 42 degree for each test. Fragments after the point mentioned above in the external bubble of debris cloud were ejected as several chains, the number of which is sensitive to impact velocity, but not t/D ratio. The changes in normalized velocity of the measurement points at debris cloud appeared the same trend as conclusions presented by Piekutowski except for the normalized internal structure expanding velocity. A certain value of t/D ratio, at two sides of which, the normalized internal structure expanding velocity appeared different variety trend existed.     

Modeling and phantom studies of ultrasonic wall shear rate measurements using coded pulse excitation

Wall shear rate (WSR) is the derivative of blood velocity with respect to vessel radius at the endothelial cell (EC) surface. The product of WSR and blood viscosity is the wall shear stress (WSS) that has been identified as an important factor for atherosclerosis development. High echo signal-to-noise ratio (eSNR) and high spatial resolution are crucial for minimizing the errors in WSR estimates. By transmitting coded pulses with time-bandwidth product greater than one, high eSNR from weak blood scatter can be achieved without increasing instantaneous power or sacrificing spatial resolution. This paper summarizes a series of measurements in a straight tube (5-mm diameter), constant velocity flow phantom using a 10 MHz transducer (60% bandwidth, f/1.5) imaged with a 72 degrees Doppler angle, 125 MHz sampling frequency and 1 kHz pulse repetition frequency. Measurements were made using a frequency-modulated (FM) code, phase-modulated (PM) codes, and uncoded broadband and narrow band pulse transmissions. Both simulation and experimental results show that coded-pulse excitation increases accuracy and precision in WSR estimation for laminar flow over a broad range of peak velocity values when compared to standard pulsing techniques in noise-limited conditions (eSNR < 30 dB). The code sequence and its length are selected to balance range lobe suppression with eSNR and echo coherence enhancements to minimize WSR errors. In our study, the combination of an eight bit Optimal coded pulse with a Wiener compression filter yielded the highest WSR estimation performance.