An improved spectral width Doppler method for estimating Doppler angles in flows with existence of velocity gradients

Doppler angle (i.e., beam-to-flow angle) is an important parameter for quantitative flow measurements. With known Doppler angles, volumetric flows can be obtained by the mean flow velocity times the cross-section area of the vessel. The differences or changes between prestenotic and poststenotic volumetric flows have been quantified as an indicator for assessing the clinical severity of the stenosis. Therefore, several research groups have dedicated themselves to developing user-independent methods to determine automatically the Doppler angle. Nevertheless, most of these methods were developed for narrow ultrasound beam measurements. For small vessels, where the beam width is a significant fraction of the diameter of the vessel, the effect of velocity gradients plays an important role and should not be ignored in the Doppler angle estimations. Accordingly, this paper is concerned with a method for improving the estimation of Doppler angles from spectral width Doppler (SWD) method, but correcting for velocity-gradient broadening that may arise when the beam has a nonzero width. In our method, Doppler angles were firstly calculated by SWD and then were corrected by an artificial neural network (ANN) method to neutralize the contribution of velocity gradient broadening (VGB). This SWD and ANN conjoint method has been successfully applied to estimate Doppler angles from 50 degrees to 80 degrees for constant flows in 10 mm, 4 mm and 1 mm diameter tubes, whose mean flow velocities were 15.3, 19.9 and 25.5 cm/s, respectively, and the achieved mean absolute errors of the estimated Doppler angles were 1.46 degrees , 1.01 degrees and 1.3 degrees.     

Doppler angle estimation of pulsatile flows using AR modeling

In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 3o degrees to 78 degrees) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50 degrees compared to an average error of 7.08 degrees for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.     

Doppler spectral characterization of flow disturbances in the carotid with the Doppler probe at right angles to the vessel axis

This paper reports on a new method intended to detect early flow disturbances generated by small lesions, using conventional clinical instrumentation. In vitro experiments on models of stenotic vessels are presented which prove that ultrasound Doppler, with the beam directed at right angles to the vessel axis can detect vortices and other flow disturbances caused by wall irregularities. These disturbances characterized by small velocity components first toward and then away from the transducer correlate with the spectrum of vortices caused by small artificial lesions. We found these disturbances in flow to be too small to cause detectable broadening in the Doppler spectrum acquired in the traditional way (i.e. with the beam at an angle less than 90 degrees). The detected flow disturbances were found to depend on the surface roughness, the profile of the obstructive lesion and the narrowing of the vessel. Similar flow disturbances to those detected in vitro were demonstrated in vivo for this new beam orientation in regions of the carotid, such as the bulb and the beginning of the common carotid, where vortex-like flows are expected.     

Effects of beam steering in pulsed-wave ultrasound velocity estimation

Experimental and computer simulation methods have been used to investigate the significance of beam steering as a potential source of error in pulsed-wave flow velocity estimation. By simulating a typical linear-array transducer system as used for spectral flow estimation, it is shown that beam steering can cause an angle offset resulting in a change in the effective beam-flow angle. This offset primarily depends on the F-number and the nominal steering angle. For example, at an F-number of 3 and a beam-flow angle of 70 degrees , the velocity error changed from -5% to + 5% when the steering angle changed from -20 degrees to + 20 degrees . Much higher errors can occur at higher beam-flow angles, with smaller F-numbers and greater steering. Our experimental study used a clinical ultrasound system, a tissue-mimicking phantom and a pulsatile waveform to determine peak flow velocity errors for various steering and beam-flow angles. These errors were found to be consistent with our simulation results.     

Measurement of volume flow with time domain and M-mode imaging: in vitro and in vivo validation studies.

Color velocity imaging quantification is a commercially available technique that estimates volume flow within vessels by combining velocity data, acquired by time domain correlation, with vessel diameter measurements obtained by M-mode imaging. By integrating the velocity profile over time, quantitative volume flow calculations may be made. To investigate the accuracy of this system, we used two flow phantoms over a range of steady and pulsatile flows for in vitro evaluation, and the common carotid artery of 10 women on five consecutive occasions was insonated for in vivo assessment. In flow phantom studies, accuracy was within 8% for flows above 200 ml/min, but decreased at lower flows depending on the depth, beam-vessel angle used, and steering of the beam. At angles greater than 70 degrees, velocity errors made quantitative measurement of flow unreliable, whereas at angles less than 30 degrees, the increased error in calculating vessel diameter led to large errors of area estimation, and hence made flow measurements unreliable. For the in vivo studies on the carotid artery the intraoperator repeatability values for the three operators were 9.92% (A), 13.74% (B), and 13.24% (C). The interoperator repeatability for the group was 15.30%. This study suggests that the color velocity imaging quantification technique is an accurate and reproducible method of assessing volume flow in vessels. However, in our experience, obtaining volume flow data is more time consuming and operator dependent than traditional Doppler techniques. The color velocity imaging quantification system may be of use in monitoring conditions in which changes in volume flow in a vessel or to an organ is an important part of the disease process.     

Accuracy and Reproducibility of a Novel Dual-Beam Vector Doppler Method

Conventional Doppler ultrasound (US) investigations are limited to detect only the axial component of the blood velocity vector. A novel dual-beam method has been recently proposed in which the Doppler angle is estimated through a reference US beam, and the velocity magnitude through a measuring US beam, respectively. In this study, the performance of such a method has been assessed quantitatively through in vitro and in vivo measurements made in different experimental conditions. In vitro, more than 300 acquisitions were completed using seven transducers to insonify a straight tube phantom at different Doppler angles. In steady laminar flow conditions, the velocity magnitude was measured with mean error of –1.9% (95% confidence interval: –2.33% to –1.47%) and standard deviation of 3.4%, with respect to a reference velocity. In pulsatile flow conditions, reproducibility tests of the entire velocity waveforms provided an average coefficient of variation (CV) of 6.9%. For peak velocity measurements made at five Doppler angles and three flow rates, the intrasession and intersession CVs were in the range 0.8–3.7% and 2.9–10.6%, respectively. The peak systolic velocities (PSVs) in the common carotid arteries of 21 volunteers were estimated with 95% limits of agreement of ± 9.6 cm/s (intersession). This analysis shows that the proposed dual-beam method is capable of overcoming the Doppler angle ambiguity by producing reliable velocity measurements over a large set of experimental conditions. (E-mail: piero.tortoli@unifi.it)     

Angle-dependence and reproducibility of dual-beam vector doppler ultrasound in the common carotid arteries of normal volunteers

Dual-beam vector Doppler has the potential to improve peak systolic blood velocity measurement accuracy by automatically correcting for the beam-flow Doppler angle. Using a modified linear-array system with a split receive aperture, we have assessed the angle-dependence over Doppler angles of 40 degrees -70 degrees and the reproducibility of the dual-beam blood maximum velocity estimate measured in the common carotid arteries (CCA) 1 to 2 cm prior to the bifurcation of 9 presumed-healthy volunteers. The velocity magnitude estimate was reduced by approximately 7.9% as the angle between the transmit beam and the vessel axis was increased from 40 degrees to 70 degrees. With repeat measurements made, on average, approximately 6 weeks apart, the 95% velocity magnitude limits of agreement were as follows: Intraobserver -41.3 to +45.2 cm/s; interobserver -29.6 to +46.8 cm/s. There was an 8.6 cm/s interobserver bias in velocity magnitude. We conclude that the dual-beam vector Doppler system can measure blood velocity within its scan plane with low dependence on angle and with similar reproducibility to that of single-beam systems.     

Comparison of conventional and transverse Doppler sonograms

When measuring flow velocity using the conventional ultrasonic Doppler effect, beam axis-to-flow angles approaching 90 degrees are avoided as the Doppler spectrum frequency shift is known to go to zero at this angle. In this paper, the conventional Doppler technique is compared with the transverse Doppler method, in which the Doppler spectrum bandwidth is used to estimate flow, allowing flow to be probed at 90 degrees. The comparison is made using a moving thread flow phantom capable of executing various velocity profiles. This technique may allow the probing of vessels that are inaccessible to conventional oblique probing, thus complementing the conventional Doppler technique.     

An Automatic Angle Tracking Procedure for Feasible Vector Doppler Blood Velocity Measurements

Two-dimensional angle-independent blood velocity estimates typically combine the Doppler frequencies independently measured by two ultrasound beams with known interbeam angle. A different dual-beam approach was recently introduced in which one (reference) beam is used to identify the flow direction, and the second (measuring) beam directly estimates the true flow velocity at known beam-flow angle. In this paper, we present a procedure to automatically steer the two beams along optimal orientations so that the velocity magnitude can be measured. The operator only takes care of locating the Doppler sample volume in the region of interest and, through the extraction of appropriate parameters from the Doppler spectrum, the reference beam is automatically steered toward right orientation to the flow. The velocity magnitude is thus estimated by the measuring beam, which is automatically oriented with respect to the (known) flow direction at a suitable Doppler angle. The implementation of the new angle tracking method in the ULtrasound Advanced Open Platform (ULA-OP), connected to a linear array transducer, is reported. A series of experiments shows that the proposed method rapidly locks the flow direction and measures the velocity magnitude with low variability for a large range of initial probe orientations. In vitro tests conducted in both steady and pulsatile flow conditions produced coefficients of variability (CV) below 2.3% and 8.3%, respectively. The peak systolic velocities have also been measured in the common carotid arteries of 13 volunteers, with mean CV of 7%. (E-mail: piero.tortoli@unifi.it).     

Modeling of Doppler signal considering sample volume and field distribution

The ultrasound Doppler amplitude spectrum for a single scatterer and the power spectrum for multiple scatterers were calculated in terms of the echo signal from scatterers crossing the sample volume, defined by the transmitted pulse and the diffracted field distribution for cw. The observation time for the Doppler signal is also considered. Statistical parameters such as mean and variance of the Doppler power spectrum are studied as continuous functions of the intersection angle between the beam axis and the flow direction, the pulse length and the viewing position. The derived equations are valid whether the transit time is governed by the pulse length, or beam geometry, or both. It is shown that the Doppler power spectra calculated by the proposed model and by the Doppler signal obtained from field theory are in good agreement. It is also shown that, when the Doppler signal broadening due to the transmitted pulse and beam geometry is constant without regard to the intersection angle, the degree of spread of the velocity distribution can be estimated from the variance of the Doppler power spectrum measured by the Doppler system once the intersection angle is known.     

Measurement of pulsatile total blood flow in the human and rat retina with ultrahigh speed spectral/Fourier domain OCT

We present an approach to measure pulsatile total retinal arterial blood flow in humans and rats using ultrahigh speed Doppler OCT. The axial blood velocity is measured in an en face plane by raster scanning and the flow is calculated by integrating over the vessel area, without the need to measure the Doppler angle. By measuring flow at the central retinal artery, the scan area can be very small. Combined with ultrahigh speed, this approach enables high volume acquisition rates necessary for pulsatile total flow measurement without modification in the OCT system optics. A spectral domain OCT system at 840nm with an axial scan rate of 244kHz was used for this study. At 244kHz the nominal axial velocity range that could be measured without phase wrapping was ±37.7mm/s. By repeatedly scanning a small area centered at the central retinal artery with high volume acquisition rates, pulsatile flow characteristics, such as systolic, diastolic, and mean total flow values, were measured. Real-time Doppler C-scan preview is proposed as a guidance tool to enable quick and easy alignment necessary for large scale studies. Data processing for flow calculation can be entirely automatic using this approach because of the simple and robust algorithm. Due to the rapid volume acquisition rate and the fact that the measurement is independent of Doppler angle, this approach is inherently less sensitive to involuntary eye motion. This method should be useful for investigation of small animal models of ocular diseases as well as total blood flow measurements in human patients in the clinic.     

Turbulence measurements with pulsed doppler ultrasound employing a frequency tracking method

A phase lock loop method of tracking Doppler ultrasound frequencies is applied to the measurement of turbulent velocities. A pulsed Doppler ultrasound system capable of detecting two velocity components was employed to resolve axial and radial velocity components at the centerline of turbulent pipe flows and distal to stenoses in pulsatile flow. Measurements with the ultrasound system are compared with laser Doppler and hot film anemometer data. The results demonstrate that the phase lock loop method of tracking accurately follows turbulent velocity fluctuations for turbulence intensities up to approx. 20%, after which signal dropout becomes a significant factor. An important application of the method is that of detecting flow disturbances created by mild to moderate degrees of stenosis in arterial disease.     

体外模拟实验研究心脏运动对频谱多普勒血流速度测定的影响

目的：通过体外模拟实验，研究心脏运动对频谱多普勒血流速度测定的影响。方法：设计一套仪器，使它模拟心脏运动的速度和频率并使在其内流动的模拟血液的流速和频率及这两种运动的开启和停止时间都分别可控，观察模拟血流的频谱多普勒在模拟心脏运动影响下的变化及它们之间量的关系。结果：在模拟心脏运动作用下，原来的模拟血流波形已不存在，代之以模拟心脏运动和模拟血流控速度矢量相加规律所组成的复合波，而模拟心脏运动所产生的多普勒频移信号的振幅和频率都未改变且与上述血流信号并存于频谱中，结论：通常所谓的血流速度频谱实际上是血细胞在心脏内流动速度和心脏运动速度的矢量和。即两项运动的复合频谱。所以，为减少误差，在用多普勒血流速度频谱测定血流参数时，应考虑校正问题。     

An investigation of simulated umbilical artery Doppler waveforms. I. The effect of three physical parameters on the maximum frequency envelope and on pulsatility index

The effect of three physical parameters on the accuracy of estimation of the maximum frequency envelope and pulsatility index (PI) of simulated umbilical artery Doppler waveforms was investigated. The physical parameters were beam-vessel angle, the offset between the beam axis and vessel axis, and the thickness of overlying attenuating material. Waveforms were acquired using a physiological flow phantom. The maximum frequency envelope was calculated using a threshold maximum frequency follower which was adaptive to the level of background noise. A gold standard maximum frequency envelope was obtained from the ensemble averaged waveform when there was alignment of beam and vessel axis, a 50 degrees beam-vessel angle and 2 cm of attenuating material. Indices of bias, variability and accuracy of estimation of the maximum frequency envelope and PI were calculated by comparing subsequent maximum frequency envelopes with the gold standard maximum frequency envelope. Both the maximum frequency envelope and PI were estimated to a similar degree of accuracy over a wide range of physical conditions. In this study, the error in PI was less than 0.15 for beam-vessel angles less than 80 degrees, for beam-vessel axis offset distances less than 7.5 mm, at a transducer-vessel distance of 5 cm, and for attenuator thicknesses less than 4.5 cm. The percentage root-mean square error for estimation of the maximum frequency envelope was approximately 10% or less for beam-vessel angles less than 75 degrees, for beam-vessel axis offset distances less than 7.5 mm, and for attenuator thicknesses less than 4 cm.     

A triangulation method for the quantitative measurement of arterial blood velocity magnitude and direction in humans

A triangulation method has been applied to a duplex ultrasound scanner to quantify blood flow velocities in two dimensions. A position locating system (PLS) connected to the scanhead locates the sample volume (SV) in 3-D space to a precision of 1 mm. The PLS is used to obtain flow velocity data from two independent lines of sight in the human femoral artery. Data are gathered from anatomic sites of interest along one line of sight. Later the computer directs the SV to interrogate the same points in space from a second line of sight. Water tank studies using both constant velocity and pulsatile string targets were used to validate the method. Velocity magnitudes could be calculated to within 5% error for Doppler angles below 75 degrees for various string depths and speeds; the error in Doppler angle calculation was usually less than 3 degrees. Results from the superficial femoral artery show flow velocity vectors are nearly parallel to the vessel walls. Peak systolic velocity magnitudes range from 63-66 cm/s in three presumed normal individuals. Following the validation studies addressed in this paper, this triangulation approach is intended in future work to document the complex nonaxial character of blood flow that occurs normally at branch points and in regions of intraluminal disease.     

心脏运动影响多普勒血流速度频谱测定的机制实验研究

目的 探讨模拟心脏与模拟血流同步及非同步运动时,心脏运动对多普勒血流速度频谱测定的影响机制。方法 用自行设计的仪器,使模拟心脏运动和模拟血液的脉动频率按一定的相位同步,非同步,观察当这两种运动同时发生时,模拟心脏运动对模拟血流速度频谱的影响及它们之间的定量关系。结果 当模拟心脏和模拟血流做同步或非同步运动时,所记录到的模拟血流频谱为模拟心脏运动和模拟血流按速度矢量相加规律所组成的复合波,而模拟心脏运动所产生的多普勒频移信号的振幅和频率都未改变且与血流信号并存于频谱中,结论 我们通常所谓的血流速度频谱实际上是血细胞在心脏内流动速度和心脏运动速度的矢量和,即两项运动的复合频谱,即便当模拟心脏和模拟血流做同步或非同步运动时也是如此。     

Development of a Flexible Implantable Sensor for Postoperative Monitoring of Blood Flow

We have developed a blood flow measurement system using Doppler ultrasound flow sensors fabricated of thin and flexible piezoelectric‐polymer films. These flow sensors can be wrapped around a blood vessel and accurately measure flow. The innovation that makes this flow sensor possible is the diffraction‐grating transducer. A conventional transducer produces a sound beam perpendicular to its face; therefore, when placed on the wall of a blood vessel, the Doppler shift in the backscattered ultrasound from blood theoretically would be 0. The diffraction‐grating transducer produces a beam at a known angle to its face; therefore, backscattered ultrasound from the vessel will contain a Doppler signal. Flow sensors were fabricated by spin coating a poly(vinylidene fluoride–trifluoroethylene) copolymer film onto a flexible substrate with patterned gold electrodes. Custom‐designed battery‐operated continuous wave Doppler electronics along with a laptop computer completed the system. A prototype flow sensor was evaluated experimentally by measuring blood flow in a flow phantom and the infrarenal aorta of an adult New Zealand White rabbit. The flow phantom experiment demonstrated that the error in average velocity and volume blood flow was less than 6% for 30 measurements taken over a 2.5‐hour period. The peak blood velocity through the rabbit infrarenal aorta measured by the flow sensor was 118 cm/s, within 1.7% of the measurement obtained using a duplex ultrasound system. The flow sensor and electronics operated continuously during the course of the 5‐hour experiment after the incision on the animal was closed.     

Should results of ultrasound Doppler studies be reported in units of frequency or velocity?

There is a current tendency to report the results of ultrasound Doppler studies in units of velocity instead of Doppler frequency. This is probably motivated by the intuitive feeling that blood flow studies should naturally be reported in cm/s and the notion that "velocity" is a normalizing factor for Doppler ultrasound studies. In order to determine velocity, the Doppler angle theta or angle formed by the ultrasound beam and flow velocity vector, must be known. It is not possible, using currently available systems, to obtain an accurate estimate of this angle. The physics related to the Doppler equation are reviewed in this paper along with examples to illustrate the origin and magnitude of errors that could arise when reporting in units of velocity. Guidelines are provided for thinking about and reporting results of Doppler studies in units of velocity. An understanding of the Doppler equation and its use in clinical studies are promoted in this paper to enhance the diagnostic usefulness of Doppler ultrasound studies and to reduce serious errors which could lead to faulty information dictating patient management.     

Doppler flow measurement using surface integration of velocity vectors (SIVV): in vitro validation

Blood flow measurement using an improved surface integration of velocity vectors (SIVV) technique was tested in in vitro phantoms. SIVV was compared with true flow (12-116 mL/s) in a steady-state model using two angles of insonation (45 degrees and 60 degrees ) and two vessel sizes (internal diameter = 11 and 19 mm). Repeatability of the method was tested at various flow rates for each angle of insonation and vessel. In a univentricular pulsatile model, SIVV flow measured at the mitral inlet was compared to true flow (29-61 mL/s). Correlation was excellent for the 19-mm vessel (r(2)= 0.99). There was a systematic bias but close limits of agreement (mean +/- 2 SD = -24.1% +/- 7.6% at 45 degrees; +16.4% +/- 11.0% at 60 degrees ). Using the 11-mm vessel, a quadratic relationship was demonstrated between between SIVV and true flow (r(2) = 0.98-0.99), regardless of the angle of insonation. In the pulsatile system, good agreement and correlation were shown (r(2) = 0.94, mean +/- 2 SD = -4.7 +/- 10.1%). The coefficients of variation for repeated SIVV measurements ranged from 0.9% to 10.3%. This method demonstrates precision and repeatability, and is potentially useful for clinical measurements.