Directional velocity estimation using focusing along the flow direction. II: Experimental investigation

For pt. I see ibid., vol. 50, no. 7, p. 857 (2003). A new method for directional velocity estimation is investigated through a number of flow rig measurements. The method uses beam-formation along the flow direction to generate data, where the correct velocity magnitude can directly be estimated from the shift in position of the received consecutive signals. The shift is found by cross-correlating the beamformed lines. The approach can find the velocity in any direction, including transverse to the traditionally emitted ultrasound beam. The method is investigated using a flow rig with a peak velocity of 0.15 m/s. A 7-MHz linear array transducer is used together with a dedicated sampling system to acquire signals from 64 transducer elements simultaneously. A technique for obtaining 128-element data using multiplexing is also presented. The data is beamformed off-line on a PC. A relative standard deviation of 1.4% can be obtained for a beam-to-flow angle of 45/spl deg/ and 4.3% at 90/spl deg/. Color flow images are displayed showing that the correct velocity magnitude can be obtained with the method for beam-to-flow angles of 60 and 90/spl deg/ with an accuracy of 3 to 4%.     

Estimation of velocity vector angles using the directional cross-correlation method

A method for determining both velocity magnitude and angle in any direction is suggested. The method uses focusing along the velocity direction and cross-correlation for finding the correct velocity magnitude. The angle is found from beamforming directional signals in a number of directions and then selecting the angle with the highest normalized correlation between directional signals. The approach is investigated using Field II simulations and data from the experimental ultrasound scanner RASMUS and a circulating flow rig with a parabolic flow having a peak velocity of 0.3 m/s. A 7-MHz linear array transducer is used with a normal transmission of a focused ultrasound field. In the simulations the relative standard deviation of the velocity magnitude is between 0.7% and 7.7% for flow angles between 45 degrees and 90 degrees. The study showed that angle estimation by directional beamforming can be estimated with a high precision. The angle estimation performance is highly dependent on the choice of the time ktprf x Tprf (correlation time) between signals to correlate. One performance example is given with a fixed value of ktprf for all flow angles. The angle estimation on measured data for flow at 60 degrees to 90 degrees yields a probability of valid estimates between 68% and 98%. The optimal value of ktprf for each flow angle is found from a parameter study; with these values, the performance on simulated data yields angle estimates with no outlier estimates and with standard deviations below 2 degrees.     

声学多普勒测速仪标校技术研究

为了提高声学多普勒测速仪输出速度的准确度,安装过程中测速基阵与载体之间的偏差角不可忽略,安装偏差角包括航向偏角,横摇角及纵摇角三类。介绍了一种三维空间上的多普勒标定技术,通过高精度的GPS导航仪以及多普勒测速仪对海底测速,利用速度比值差校准航偏角。通过纵向剖面的几何关系,从航偏角出发进而获得纵摇角和横摇角的大小,完成了三维方向上多普勒测速仪的校准,使多普勒测速仪坐标系与载体坐标系能够进行精确转换,从而提高了声学多普勒测速仪输出速度的准确度。外场试验较好地证明了该方法的有效性,分析结论看出在二维平面上,造成误差的原因主要在于安装偏角的航向偏角,而在三维空间上,尤其垂向速度,误差主要由纵摇角和横摇角产生。该方法可以快速地对三维安装偏角进行校准,运算量小,并且在对海水测速后续研究中可以形成一套体系。     

基于遗传算法的单矢量水听器多目标方位估计

矢量水听器能同时获得声场中某一点的声压标量和质点振速矢量,获得了比常规声压水听器更多的信息。矢量水听器自身是一个空间共点阵,具有一定的空间指向性,这些特点使矢量信号处理技术与声压信号处理技术具有重大差异。根据单个矢量水听器多目标分辨的数学模型,即声压和振速的偶次阶矩组成的非线性联立方程组,研究了该方程的解算方法,给出了可以使用遗传算法求解该非线性方程组的结论和计算精度。     

A new method for estimation of velocity vectors

The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.     

Estimating the blood velocity vector using aperture domain data

Most conventional blood flow estimation methods measure only the axial component of the blood velocity vector. In this study, we developed a new method for two-dimensional (2-D) velocity vector estimation in which time shifts resulting from blood motion are calculated for the individual channels using aperture domain data. This allows the construction of a time-shift profile along the array direction as a function of channel index, which is approximated by a first-order polynomial whose zeroth-order and first-order terms can be used to determine the axial and lateral velocity components, respectively. The efficacy of the proposed method was verified by simulations and experiments in which the transducer array had 64 elements, an aperture size of 1.96 cm, and a center frequency of 5 MHz. The flow velocity ranged from 5 to 35 cm/s and the Doppler angle ranged from 0 degrees to 90 degrees. The experimental results show that the accuracy of axial velocity estimation is higher for the new method than for the autocorrelation-based conventional method when the signal-to-noise ratio is larger than 0 dB. The mean estimation error for the axial velocity component is 2.18% for the new method, compared to 4.51% for the conventional method. The mean estimation error for the lateral velocity component is 15%, which is comparable to existing methods.     

Error propagation bounds in dual and triple beam vector Doppler ultrasound

Measurement of the velocity components along two (three) directions enables the two (three)dimensional velocity vector to be estimated exactly. However, in practical systems employing such multiple beam techniques, there will usually be errors in the measured velocity components along each beam, which will lead to errors in the estimated velocity magnitude and direction. This error propagation problem is analyzed in both two and three dimensions by decomposition of the velocity estimation matrix, and exact upper and lower bounds are derived for both the magnitude and angle bias as a function of the angle between the beams. The bias in triple beam systems is shown to have identical bounds to that in dual beam systems with an equivalent interbeam angle. It is found that small errors in the individual beam velocity components can be magnified in the final determination of velocity magnitude and angle. Plots are presented to assist system designers to specify the interbeam angle(s) to avoid gross velocity estimation errors.     

Directional velocity estimation using focusing along the flow direction. I: Theory and simulation

A new method for directional velocity estimation is presented. The method uses beam formation along the flow direction to generate data in which the correct velocity magnitude can be directly estimated from the shift in position of the received consecutive signals. The shift is found by cross-correlating the beamformed lines. The approach can find the velocity in any direction, including transverse to the traditionally emitted ultrasound beam. The velocity estimation is studied through extensive simulations using Field II. A 128-element, 7-MHz linear array is used. A parabolic velocity profile with a peak velocity of 0.5 m/s is simulated for different beam-to-flow angles and for different emit foci. At 45/spl deg/ the relative standard deviation over the profile is 1.6% for a transmit focus at 40 mm. At 90/spl deg/ the approach gave a relative standard deviation of 6.6% with a transmit focus of 80 mm, when using 8 pulse-echo lines and stationary echo canceling. Pulsatile flow in the femoral artery was also simulated using Womersley's flow model. A purely transverse flow profile could be obtained with a relative standard deviation of less than 10% over the whole cardiac cycle using 8 pulse emissions for each imaging direction, which is sufficient to show clinically relevant transverse color flow images.     

Directional velocity estimation using a spatio-temporal encoding technique based on frequency division for synthetic transmit aperture ultrasound

This paper investigates the possibility of flow estimation using spatio-temporal encoding of the transmissions in synthetic transmit aperture imaging (STA). The spatial encoding is based on a frequency division approach. In STA, a major disadvantage is that only a single transmitter (denoting single transducer element or a virtual source) is used in every transmission. The transmitted acoustic energy will be low compared to a conventional focused transmission in which a large part of the aperture is used. By using several transmitters simultaneously, the total transmitted energy can be increased. However, to focus the data properly, the signals originating from the different transmitters must be separated. To do so, the pass band of the transducer is divided into a number of subbands with disjoint spectral support. At every transmission, each transmitter is assigned one of the subbands. In receive, the signals are separated using a simple filtering operation. To attain high axial resolution, broadband spectra must be synthesized for each of the transmitters. By multiplexing the different waveforms on different transmitters over a number of transmissions, this can be accomplished. To further increase the transmitted energy, the waveforms are designed as linear frequency modulated signals. Therefore, the full excitation amplitude can be used during most of the transmission. The method has been evaluated for blood velocity estimation for several different velocities and incident angles. The program Field II was used. A 128-element transducer with a center frequency of 7 MHz was simulated. The 64 transmitting elements were used as the transmitting aperture and 128 elements were used as the receiving aperture. Four virtual sources were created in every transmission. By beamforming lines in the flow direction, directional data were extracted and correlated. Hereby, the velocity of the blood was estimated. The pulse repetition frequency was 16 kHz. Three different setups were investigated with flow angles of 45, 60, and 75 degrees with respect to the acoustic axis. Four different velocities were simulated for each angle at 0.10, 0.25, 0.50, and 1.00 m/s. The mean relative bias with respect to the peak flow for the three angles was less than 2%, 2%, and 4%, respectively.     

Estimation of the surface normal velocity of high frequency ultrasound transducers

This paper is concerned with the characterization of the true locally resolved surface normal velocity of an assumed piston-type ultrasonic transducer. Instead of involving a very complicated direct pointwise measurement of the velocity distribution, an inverse problem is solved which yields a spatially discretized weighting vector for the surface normal velocity of the transducer. The study deals with a spherically focused high frequency transducer, which is driven in pulse-echo mode. As a means of posing the inverse problem, the active transducer surface is divided into annuli of equal surface so that for each annulus the spatial impulse response can be calculated. An acrylic glass plate acts as a simple structured target. The resulting ill-posed nonlinear inverse problem is solved with an iterative regularized Gauss-Newton algorithm. The solution of the inverse problem yields an estimated weight for the surface normal velocity for each annulus. Experimental results for a thin copper wire target are compared to simulation results for both uniform and estimated surface normal velocities.     

基于支持向量机的地震预警震级快速估算研究

以更准确的估算地震预警(earthquake early warning,EEW)震级为目标,利用P波触发后3 s内的日本K-net强震数据,选取幅值参数、周期参数、能量参数、衍生参数这4大类共12个P波特征参数作为输入,构建基于支持向量机震级预测模型(support vector machine for earthquake magnitude estimation,SVM-M)。结果表明,比较传统的震级估算“τc方法”与“P d方法”,建立的SVM-M模型震级预测误差明显减小且不受震中距变化的影响,小震高估问题得到明显改善。2016年日本熊本地震主震(M j7.3)与2008年中国汶川地震主震(M s8.0)的震例分析结果表明,3 s时间窗不能匹配震源破裂全过程而出现了一定程度的震级低估,但仍可在P波触发后短时间窗内明确是大地震事件。建立的SVM-M模型可应用于地震预警震级快速估算。     

Effects influencing focusing in synthetic aperture vector flow imaging

Previously, a synthetic aperture vector velocity estimation method was proposed. Data are beamformed at different directions through a point, where the velocity is estimated. The flow direction is estimated by a search for the direction where the normalized cross-correlation peaks and the velocity magnitude along this direction are found. In this paper, different effects that influence the focusing in this method are investigated. These include the effect of phase errors in the emitted spherical waves, motion effects, and the effect of various interpolation methods in beam-forming. A model based on amplitude drop and phase error for spherical waves created using the virtual source concept is derived. This model can be used to determine the opening angle of a virtual source. Simulations for different virtual source placements are made, and it is recommended that the virtual sources be placed behind the aperture when shallow structures are imaged, and when deeper-lying structures are imaged the virtual sources be placed in front of the aperture. Synthetic aperture methods involve summation of data from numerous emissions. Motion between these emissions results in incoherence and affects resolution, contrast, and the signal-to-noise ratio. The effects of motion on the synthetic aperture vector velocity estimation method are investigated, and it is shown that for both axial and lateral motion, the contrast and signal-to-noise ratio can be seriously affected. A compensation method using the previous vector velocity estimate, when new data are beamformed, is implemented and tested. It is shown from a number of flow phantom experiments that a significant improvement with respect to bias and standard deviation of the velocity estimates can be obtained by using this compensation. Increased performance is gained at the expense of computation time. Different interpolation methods can be used for beam-forming the data. In this paper, the velocity estimation performance using various more complex interpolation schemes are compared to that using linear interpolation. No significant difference in the performance of the method is seen when other interpolation methods are used.     

基于单矢量水听器的水面目标运动分析

介绍了一种基于单个三维矢量水听器对水面目标进行跟踪定位和运动速度估计的简单方法。首先利用平均声能流法得到目标波达方向的极大似然估计;当矢量水听器深度已知,由目标波达方向的估计序列可得到目标空间位置和运动速度的估计序列。但随着信噪比的降低,目标定向性能随之下降,导致目标位置和速度的估计误差急剧增大。针对直线运动目标,提出利用线性最小二乘法进行目标轨迹拟合的改进算法。仿真结果表明,拟合算法大大提高了目标定位精度和运动速度估计精度,增强了基于单矢量水听器的水面目标运动分析的结果的可靠性。     

Vector-velocity estimation in swept-scan using a K-space approach

The swept-scan technique (i.e., continuously moving a single-crystal transducer during pulse-echo data acquisition) is used in high-frequency, ultrasonic flow imaging. Relative to the conventional step-scan technique, swept scanning improves the rate of data acquisition and enables near-real-time, high-frequency color flow mapping. However, the continuous transducer movement may have non-negligible effects on accuracy of velocity estimation. This paper introduces a spatial frequency domain (i.e., k-space) approach that quantifies the effects of both lateral and axial motions in a swept scan. It is shown that the k-space representation is equivalent to a Doppler-radio frequency (RF) frequency domain representation, and that transducer movement in the swept-scan technique results in a change in Doppler bandwidth. In addition, a vector velocity estimator is developed based on the proposed k-space approach. Both simulations and flow-phantom experiments were performed to evaluate the performance of the proposed vector velocity estimator. A 45-MHz transducer was scanned at 20 mm/s. The Doppler angle ranged from 29 degrees to 90 degrees, and the flow velocities ranged from 15 to 30 mm/s. The results show that the proposed k-space vector velocity estimator exhibited a mean error of 2.6 degrees for flow-direction estimation, with the standard deviation ranging from 2.2 degrees to 8.2 degrees. In comparison, for the conventional spectral-broadening-based vector velocity estimator ignoring the swept-scan effect, the mean error became 15 degrees and the standard deviations were from 2.7 degrees to 6.6 degrees.     

Estimation of blood velocity with high frequency ultrasound

In order to map blood velocity in small regions near the transducer, we evaluate the performance of the wideband maximum likelihood (WMLE) strategy and infinite impulse response (IIR) filters for blood velocity estimation with a transducer center frequency of 38 MHz. Using a short transmitted pulse and the narrow lateral beam width obtained using this frequency, we show that velocities smaller than 1 mm/s can be estimated reliably. In addition, using both changes in the location and magnitude of the peak of the RF correlation, vessels as small as 40 μm can be visualized in the RF signal and distinguished from stationary tissue. The experimental system also provides the opportunity to examine changes in flow and in the vessel wall over a cardiac cycle     

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.     

Contrast medium assisted fluid flow measurements

In this paper the development and evaluation of two new approaches for ultrasound time-domain fluid flow measurements by tracking echoes scattered by a contrast agent following injection of a bolus of the contrast agent are described. Their feasibility was investigated by measuring velocity or velocity profile of blood flowing in a mock circulatory loop in vitro. Measurements were made with a one transducer intravessel approach and a two transducer extravessel approach. A hybrid cluster or vector cross-correlation method was used to track the motion of the scatterers in the two transducer time-domain method. This cluster or vector cross correlation method was developed to reduce the ambiguity resulted from misregistration which is a common problem in target tracking by correlating signal patterns. The experimental results show a good agreement between the measured data and those estimated from timing the volume. Although the discussions given in this paper pertain only to blood flow measurements, there is no reason to indicate that these approaches can not be used for fluid flow measurements in an industrial environment if suitable contrast agents can be developed     

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.     

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.     

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.