Ensemble tracking for 2D vector velocity measurement: Experimental and initial clinical results

We describe a new method, called ensemble tracking, for estimating two-dimensional velocities with ultrasound. Compared to previous speckle tracking techniques, ensemble tracking measures motion over smaller times and distances, increasing maximum velocities and reducing errors due to echo decorrelation. Ensemble tracking uses parallel receive processing, 2D pattern matching, and interpolation of the resulting tracking grid to estimate sub-pixel speckle translations between successive ultrasonic acquisitions. In this study, small translations of a tissue mimicking phantom were quantified at transducer angles of 0 degrees , 45 degrees , and 90 degrees . Measurements over three parallel beam spacings and all transducer angles had mean errors from -4% to +11%, when parallel beam amplitudes were normalized. Such amplitude normalization substantially improved results at 45 degrees and 90 degrees . The amplitude, spacing, and correlation between the parallel beams were quantified, and their effects on the accuracy and precision of estimates are discussed. Finally, initial clinical results demonstrate the ability to track and display blood flow in the carotid artery.     

Triple-beam lens transducers for three-dimensional ultrasonic fluidflow estimation

This paper reports on estimating the 3-D flow velocity vector of blood with ultrasound triple-beam lens transducers. The design, construction, and characterization of experimental lens transducers is described along with the theory of 3-D flow velocity estimation. A triple beam lens transducer consists of three piezoelectric elements mounted on the top surface of a lens. The lens acts to direct and focus the ultrasound from the elements such that three parallel, closely spaced ultrasound beams are generated. Blood cell scatterers are tracked as they move along the beams and from beam to beam using RF correlation techniques. Lenses from fused quartz and aluminum have been designed and fabricated, and the characteristics of the lenses along with lens design considerations and tradeoffs are discussed. The three-dimensional flow velocity vector of fluid in a blood flow phantom has been experimentally measured with an aluminum lens, indicating that the accurate estimation of the 3-D blood flow velocity vector is possible     

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: preliminary results

This paper describes a new ultrasound-based system for high-frame-rate measurement of periodic motion in 2-D for tissue elasticity imaging. Similarly to conventional 2-D flow vector imaging, the system acquires the RF signals from the region of interest at multiple steering angles. A custom sector subdivision technique is used to increase the temporal resolution while keeping the total acquisition time within the range suitable for real-time applications. Within each sector, 1-D motion is estimated along the beam direction. The intra- and inter-sector delays are compensated using our recently introduced delay compensation algorithm. In-plane 2-D motion vectors are then reconstructed from these delay-compensated 1-D motions. We show that Young's modulus images can be reconstructed from these 2-D motion vectors using local inversion algorithms. The performance of the system is validated quantitatively using a commercial flow phantom and a commercial elasticity phantom. At the frame rate of 1667 Hz, the estimated flow velocities with the system are in agreement with the velocity measured with a pulsed-wave Doppler imaging mode of a commercial ultrasound machine with manual angle correction. At the frame rate of 1250 Hz, phantom Young's moduli of 29, 6, and 54 kPa for the background, the soft inclusion, and the hard inclusion, are estimated to be 30, 11, and 53 kPa, respectively.     

Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load

This paper studies the dynamic responses of an elastically connected double-functionally graded beam system (DFGBS) carrying a moving harmonic load at a constant speed by using Euler–Bernoulli beam theory. The two functionally graded (FG) beams are parallel and connected with each other continuously by elastic springs. Six elastically connected double-functionally graded beam systems (DFGBSs) having different boundary conditions are considered. The point constraints in the form of supports are assumed to be linear springs of large stiffness. It is assumed that the material properties follow a power-law variation through the thickness direction of the beams. The equations of motion are derived with the aid of Lagrange’s equations. The unknown functions denoting the transverse deflections of DFGBS are expressed in polynomial form. Newmark method is employed to find the dynamic responses of DFGBS subjected to a concentrated moving harmonic load. The influences of the different material distribution, velocity of the moving harmonic load, forcing frequency, the rigidity of the elastic layer between the FG beams and the boundary conditions on the dynamic responses are discussed.     

Two-dimensional directional wavelets in image processing

The two-dimensional (2-D) continuous wavelet transform (CWT) is characterized by a rotation parameter, in addition to the usual translations and dilations. This enables is to detect edges and directions in images, provided a directional wavelet is used. First we review the general properties of the 2-D CWT and describe several useful representations. We describe various classes of wavelets, including the directional ones. Then we turn to the problem of wavelet calibration, in particular, the evaluation of the scale and angle resolving power of a wavelet. Finally we discuss several applications of directional wavelets. © 1996 John Wiley & Sons, Inc.     

A finite element formulation for sliding beams,Part I

We use the updated Lagrangian and the co-rotational finite element methods to obtain solutions for geometrically non-linear flexible sliding beams. Finite element formulations are normally carried out for fixed domains. Since the sliding beam is a system of changing mass, first we discretize the system by introducing a variable-domain beam element and model the sliding beam by a fixed number of elements with changing length. Second, we transform the system governing equations of motion to a fixed domain and use conventional finite elements (fixed size and number) to discretize the system. Then our investigation is followed by a comparison between two formulations. Finally, we use the co-rotational method in conjunction with a variable domain beam element to obtain the discretized system equations. To do so, we consider the beam to slide with respect to a fixed channel and later we consider a formulation in which the beam remains at rest and the channel slides with a prescribed velocity. We show that both formulations end up with identical discretized equations of motion. © 1998 John Wiley & Sons, Ltd.     

Ultrafast compound imaging for 2-D motion vector estimation: application to transient elastography

This paper describes a new technique for two-dimensional (2-D) imaging of the motion vector at a very high frame rate with ultrasound. Its potential is experimentally demonstrated for transient elastography. But, beyond this application, it also could be promising for color flow and reflectivity imaging. To date, only axial displacements induced in human tissues by low-frequency vibrators were measured during transient elastography. The proposed technique allows us to follow both axial and lateral displacements during the shear wave propagation and thus should improve Young's modulus image reconstruction. The process is a combination of several ideas well-known in ultrasonic imaging: ultra-fast imaging, multisynthetic aperture beamforming, 1-D speckle tracking, and compound imaging. Classical beamforming in the transmit mode is replaced here by a single plane wave insonification increasing the frame rate by at least a factor of 128. The beamforming is achieved only in the receive mode on two independent subapertures. Comparison of successive frames by a classical 1-D speckle tracking algorithm allows estimation of displacements along two different directions linked to the subapertures beams. The variance of the estimates is finally improved by tilting the emitting plane wave at each insonification, thus allowing reception of successive decorrelated speckle patterns.     

Parallel beamforming using synthetic transmit beams

Parallel beamforming is frequently used to increase the acquisition rate of medical ultrasound imaging. However, such imaging systems will not be spatially shift invariant due to significant variation across adjacent beams. This paper investigates a few methods of parallel beam-forming that aims at eliminating this flaw and restoring the shift invariance property. The beam-to-beam variations occur because the transmit and receive beams are not aligned. The underlying idea of the main method presented here is to generate additional synthetic transmit beams (STB) through interpolation of the received, unfocused signal at each array element prior to beamforming. Now each of the parallel receive beams can be aligned perfectly with a transmit beam--synthetic or real--thus eliminating the distortion caused by misalignment. The proposed method was compared to the other compensation methods through a simulation study based on the ultrasound simulation software Field II. The results have been verified with in vitro experiments. The simulations were done with parameters similar to a standard cardiac examination with two parallel receive beams and a transmit-line spacing corresponding to the Rayleigh criterion, wavelength times f-number (lambda x f#). From the results presented, it is clear that straightforward parallel beamforming reduces the spatial shift invariance property of an ultrasound imaging system. The proposed method of using synthetic transmit beams seems to restore this important property, enabling higher acquisition rates without loss of image quality.     

Three-dimensional motion measurements using feature tracking

Feature tracking was developed to efficiently compute motion measurements from volumetric ultrasound images. Prior studies have demonstrated the motion magnitude accuracy and computation speed of feature tracking. However, the previous feature tracking implementations were limited by performance of their calculations in rectilinear coordinates. Also, the previous feature tracking approaches did not fully explore the three dimensional (3- D) nature of volumetric image analysis or utilize the 3-D directional information from the tracking calculations. This study presents an improved feature tracking method which achieves further computation speed gains by performing all calculations in the native spherical coordinates of the 3-D ultrasound image. The novel method utilizes a statistical analysis of tracked directions of motion to achieve better rejection of false tracking matches. Results from in vitro tracking of a speckle target show that the new feature tracking method is significantly faster than correlation search and can accurately determine target motion magnitude and 3-D direction.     

Dual-beam CO2 laser cutting of thick metallic materials

A dual-beam technique involving two CO₂ gas lasers with a power capacity of 1.5 kW each, was used to cut steel and superalloy. A comparison with single-beam CO₂ laser cutting showed that dual beams were capable of enhancing the cutting thickness and speed without deteriorating the quality of cut. Heat-conduction models, assuming the laser beams as line sources, were used to estimate the cutting thickness and speed as a function of distance between the two laser beams. Experimental data, coupled with theoretical modelling, have provided a new concept, namely stretching the width of the laser beam in the direction of cutting to cut thicker section solids at moderate speeds.     

Free vibration analysis of pre-twisted rotating FGM beams

The natural frequencies of vibration of a rotating pre-twisted functionally graded cantilever beam are investigated. Rotating cantilever beam with pre-twist made of a functionally gradient material (FGM) consisting of metal and ceramic is considered for the study. The material properties of the FGM beam symmetrically vary continuously in thickness direction from core at mid section to the outer surfaces according to a power-law form. Equations of motion for free vibration are derived using Lagrange’s equation and the natural frequencies are determined using Rayleigh–Ritz method. The effect of parameters such as the pre-twist angle, power law index, hub radius and rotational speed on the natural frequencies of rotating functionally graded pre-twisted cantilever beams are examined through numerical studies and comparison is made with the numerical results obtained using other methods reported in literature. The effect of coupling between chordwise and flapwise bending modes on the natural frequencies has also been investigated.     

Ultrafast beam self-switching by using coupled vertical-cavity surface-emitting lasers

Dynamic beam switching of vertical-cavity surface-emitting lasers (VCSELs) has important applications for switching and routeing in optical interconnect networks. VCSEL arrays of various kinds have been quite extensively researched for tailoring and engineering near- and far-field patterns. In this paper, a new method of directional beam switching is proposed that uses two coupled VCSELs. When two VCSELs are coupled by a small separation and biased at the same steady current near threshold, then the resulting light output is dynamic at an extremely high frequency. The model equations are based on an approximation to the semiconductor Maxwell-Bloch equations. The simulations are for coupled VCSELs operating at 980 nm with circular current apertures of 5.6 μm diameter. Figures of the results will show far-field beam intensity patterns during a cycle of oscillation. The simulation results show directional switching at a speed of about 40 μm GHz and between directions about 8° apart. Results of addition simulations are also presented. Simulations that use two square VCSELs show that the frequency of oscillation increases to 50 GHz and that the far-field pattern remains similar. Finally, for four round VCSELs in a square pattern, two far-field circularly shaped beams moved left and right at a frequency of 50 GHz.     

Single beam two-views holographic particle image velocimetry

Holographic particle image velocimetry (HPIV) is presently the only method that can measure at high resolution all three components of the velocity in a finite volume. In systems that are based on recording one hologram, velocity components parallel to the hologram can be measured throughout the sample volume, but elongation of the particle traces in the depth direction severely limits the accuracy of the velocity component that is perpendicular to the hologram. Previous studies overcame this limitation by simultaneously recording two orthogonal holograms, which inherently required four windows and two recording systems. This paper introduces a technique that maintains the advantages of recording two orthogonal views, but requires only one window and one recording system. Furthermore, it enables a quadruple increase in the spatial resolution. This method is based on placing a mirror in the test section that reflects the object beam at an angle of 45 degrees. Particles located in the volume in which the incident and reflected beams from the mirror overlap are illuminated twice in perpendicular directions. Both views are recorded on the same hologram. Off-axis holography with conjugate reconstruction and high-pass filtering is used for recording and analyzing the holograms. Calibration tests show that two views reduce the uncertainty in the three-dimensional (3-D) coordinates of the particle centroids to within a few microns. The velocity is still determined plane-by-plane by use of two-dimensional particle image velocimetry procedures, but the images are filtered to trim the elongated traces based on the 3-D location of the particle. Consequently, the spatial resolution is quadrupled. Sample data containing more than 200 particles/mm3 are used for calculating the 3-D velocity distributions with interrogation volumes of 220 x 154 x 250 microm, and vector spacing of 110 x 77 x 250 microm. Uncertainty in velocity is addressed by examining how well the data satisfies the continuity equation. The results show significant improvements compared with previous procedures. Limitations of the technique are also discussed.     

Quantification of valvular regurgitation area and geometry using HPRF 3-D doppler

It is important to determine the severity of valvular regurgitation accurately because surgery is indicated only in severe regurgitations. The evaluation of, for example, mitral regurgitation is complex, and the current methods have limitations. We have developed a 3-D Doppler method to estimate the cross-sectional area and the geometry of a regurgitant jet at the vena contracta just downstream from the actual orifice. The back-scattered Doppler signal from multiple beams distributed over the area of interest was measured. The received power from these beams was then calibrated using both a priori knowledge of the lateral extent of the beams and a reference beam that was completely enclosed by the vena contracta. To isolate the Doppler signal received from the core of a regurgitant jet, a high pulse repetition frequency and a steep clutter filter are required. The method has been implemented and verified by computer simulations and by in vitro experiments using a pulsatile flow phantom and prosthetic valves with a range of holes. We were able to distinguish between mild, moderate, and severe valvular regurgitation. We were also able to quantify the regurgitational area as well as show the geometry of the regurgitation.     

一种用于物流快递分拣的2-RPU/2-SPU并联机构设计

目的 针对目前大量的快递件需要进行分拣和搬运,为解决人力成本问题并提高物流线上的自动化程度,提出一种2-RPU/2-SPU并联机构。方法 用螺旋理论对此机构进行自由度分析,求出此机构的运动约束。通过闭环矢量法求出该机构的位置逆解和各个支链间的相互约束条件。通过逆解和约束对该机构的运动进行仿真,求出此机构的可达工作范围。结果 2-RPU/2-SPU并联机构具有两转两移（2R2T）4个自由度,分别是沿y_a轴移动,沿z_a轴移动,绕x_a轴转动,绕y_a轴转动,动作较灵活,工作空间范围较大,并且在机构运动过程中没有出现奇异位形的情况。结论 2-RPU/2-SPU并联机构具有较大的工作范围,可以在物流线上进行分拣工作,并且在分拣过程中可以实现快速、精准控制,工作过程较灵活,运动性能良好,其中2R2T的运动性能能更好地适应分拣机构斜置时的分拣。     

Adaptive pattern correlation for two-dimensional blood flowmeasurements

One of the major drawbacks of ultrasonic Doppler instruments in measuring blood flow is their inability to measure the velocity perpendicular to the beam. Time domain RF echo or speckle tracking has been studied as an alternative to overcome this problem. By acquiring two-dimensional (2-D) echo signals, both lateral (perpendicular to the beam) and axial (parallel to the beam) velocities can be calculated with 2-D pattern correlation algorithms. One of the disadvantages of the current 2-D pattern correlation algorithms is the extensive computation time involved in computing the 2-D cross-correlation function. In this paper, we present several time-efficient bit-pattern correlation algorithms to execute 2-D speckle tracking. The proposed algorithms first estimate the noise level from the acquired signals and use it as a priori knowledge to minimize computation time. The reduction of computation time may make it more feasible for real-time measurements of flow velocities in two dimensions. Radio frequency and video data collected from two commercial scanners are used to validate the feasibility of these proposed algorithms with porcine blood as the flowing medium in in vitro experiments. The results obtained by the proposed algorithms are in good agreement with those computed from the cross-correlation function     

Comparison between 2-D cross correlation with 2-D sub-sampling and 2-D tracking using beam steering

We have previously presented multi-dimensional sub-sample motion estimation techniques that use multi-dimensional polynomial fitting to the discrete cross-correlation function to jointly estimate the sub-sample motion in all three spatial directions. Previous simulation and experimental results showed that these estimators significantly improve the performance of the motion estimation in 2-D and 3-D. In this short communication, we present additional simulation results and compare these techniques to 2-D tracking using beam steering. The results show that beam steering technique performs better in estimating the motion vector especially the lateral component.     

Generation of sinc wave by a one-dimensional array for applicationsin ultrasonic imaging

A new solution to the 2-D scalar wave equation is presented which describes an ultrasonic beam maintaining the lateral field response expressed by the sinc function over a finite depth of field. This new beam is realizable with a linear array transducer, and less subject to diffraction spreading than conventional focused beams, physically, it is a superposition of plane waves having the same wavelength, but traveling at different angles. It is shown by numerical simulation that the beam can provide more uniform lateral beamwidth and smoother on-axis field magnitude over a greater depth of field than the rectangular transducers and Gaussian apodized transmitters which have been used to increase the limited depth of field of conventional focused beams. Compared with currently developed limited diffraction beams which must be generated by 2-D array transducers, the beam has a wider lateral beamwidth but with lower sidelobe levels. In ultrasonic medical imaging, the beam enables one to obtain a line focus using a 1-D array transducer and to eliminate the diffraction correction required in some applications such as tissue characterization     

Quasi-achromatic laser Doppler anemometry systems based on a diffractive beam splitter

We propose a new beam-splitter system that makes it possible to use nonstabilized laser diodes for laser Doppler anemometry (LDA) systems by making the system wavelength independent. The beam splitter consists of two linear diffraction gratings that produce two parallel beams with a beam spacing that is wavelength dependent. This ensures passive wavelength compensation for the fringe spacing in the measurement volume. One can choose the distance between the two parallel beams by changing the distance between the two gratings, whereas the distance to the measurement volume can be designed by choice of a condensing lens with the proper focal length. This means that the system can be designed to have a desired fringe spacing in the measurement volume. The gratings are implemented as surface-relief holograms in photoresist, which makes it possible to mass produce the beam-splitter system at low cost through replication of the structure. The method for passive wavelength compensation for the fringe spacing is demonstrated both theoretically and experimentally.