Speckle motion artifact under tissue rotation

Speckle patterns in ultrasound images may move in a way which bears no simple relationship to the motion of the corresponding tissues. In some instances the speckle motion replicates the underlying tissue motion, in others it does not. The authors name “speckle motion artifact” the difference between the speckle and the underlying tissue motion. An echographic image formation model is used to study the motion artifact produced by a rotating phantom and observed by a linear scan imaging system with a Gaussian beam. The authors propose that when the tissue is modeled as a random array of small and numerous scatterers, such motion aberration be accounted for by the 2D phase characteristics of the imaging system. An analytic prediction of this motion artifact in relation to the imaging system characteristics (beam width, transducer frequency, pulse duration) is presented. It is shown that the artifact results from the curvature of the system point spread function, which in turn determines the curvature of the 2D phase characteristics. To the authors' knowledge, it is the first time a comprehensive model of ultrasonic speckle motion artifact is presented. The model has been developed to study rotation-induced artifact; the method is however quite general and can be extended to study the effects of other tissue motion, in particular deformation and shear     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Lateral RF image synthesis using a synthetic aperture imaging technique

The oscillating profile naturally present in ultrasound images has been shown to be extremely valuable in different applications, particularly in motion estimation. Recent studies have shown that it is possible to produce images with transverse oscillations (TOs) based on a specific type of beamforming. However, there is still a great difference between the nature of the lateral oscillations produced with current methods and the axial profile of ultrasound images. In this study, we propose to combine synthetic aperture imaging (synthetic transmit aperture, STA) using a specific beamformer in both transmit mode and receive mode combined with a heterodyning demodulation method to produce lateral radiofrequency signals (LRFs). The aim was to produce lateral signals as close as possible to conventional axial signals, which would make it possible to estimate lateral displacements with the same accuracy as in the axial direction. The feasibility of this approach was validated in simulation and experimentally on an ultrasound research platform, the Ultrasonix RP system. We show that the combination of STA and the heterodyning demodulation can divide the wavelength of the LRF signals by 4 and divide the width of the lateral envelope of the point spread function (PSF) by 2 compared with the previous approaches using beamforming in receive mode only. Finally, we also illustrate the potential of our beamforming for motion estimation compared with previous TO methods.     

Strain compounding: a new approach for speckle reduction

A new compounding technique for reducing speckle brightness variations is proposed. This method exploits the decorrelation between signals under different strain states. The different strain states can be created using externally applied forces such as the ones used in sonoelastography. Such forces produce three-dimensional tissue motion. By correcting only the in-plane (i.e., axial and lateral) motion, the images under different strain states have similar characteristics except for speckle appearance caused by the uncorrected out-of-plane (i.e., elevational) motion. Additional speckle decorrelation is also introduced through tissue motion correction caused by the change of effective in-plane sample volume geometry. Therefore, these images can be combined for speckle reduction with less degradation in in-plane spatial resolution than conventional approaches. In this paper, three-dimensional tissue motion under various strain conditions were simulated. It was found that significant speckle decorrelation existed at strains achievable in some clinical situations. Experiments were also conducted to test efficacy of this approach. Pulse-echo data from a gelatin-based phantom were acquired using a 5-MHz, single crystal transducer, and both conventional and compound B-mode images were formed. Results indicated that speckle brightness variations were reduced, and detectability of low contrast objects was enhanced. Performance limitations and fundamental differences between the proposed technique and existing techniques are discussed     

Filter-based compounded delay estimation with application to strain imaging

Ultrasonic wave interference produces local fluctuations in both the envelope, known as speckle, and phase of echoes. Furthermore, such fluctuations are correlated in space, and subsequent motion estimation from the envelope and/or phase signal produces patterned, correlated errors. Compounding, or combining information from multiple decorrelated looks, reduces such effects. We propose using a filter bank to create multiple looks to produce a compounded motion estimate. In particular, filtering in the lateral direction is shown to preserve delay estimation accuracy in the filtered sub-bands while creating decorrelation between sub-bands at the expense of some lateral resolution. For Gaussian apodization, we explicitly compute the induced signal decorrelation produced by Gabor filters. Furthermore, it is shown that lateral filtering is approximately equivalent to steering, in which filtered sub-bands correspond to signals extracted from shifted sub-apertures. Field II simulation of a point spread function verifies this claim. We use phase zero and its variants as displacement estimators for our compounded result. A simplified deformation model is used to provide computer simulations of deforming an elastic phantom. Simulations demonstrate root mean square error (RMSE) reduction in both displacement and strain of the compounded result over conventional and its laterally blurred versions. Then we apply the methods to experimental data using a commercial elastic phantom, demonstrating an improvement in strain SNR.     

Optical in-plane strain field sensor

A whole-field speckle strain sensor is presented. The speckle strain sensor allows the measurement of all three in-plane components of the strain field simultaneously without touching the surface of the sample. The strain fields are extracted from the in-plane motion of defocused laser speckles in a telecentric imaging system. To distinguish the contribution to the speckle motion from surface translation, rotation, and strain, the speckle motion from three lasers with different illumination directions and wavelengths has to be analyzed separately. Simultaneous acquisition of the three individual speckle patterns is achieved by means of splitting the light from the lasers onto separate but synchronized detectors with the aid of dichroic mirrors. The motion of the speckles is calculated with digital speckle photography (speckle correlation), which enables the strain sensor to measure strain fields with noise levels as low as 10 microstrain.     

Improving thermal ablation delineation with electrode vibration elastography using a bidirectional wave propagation assumption

Thermal ablation procedures are commonly used to treat hepatic cancers and accurate ablation representation on shear wave velocity images is crucial to ensure complete treatment of the malignant target. Electrode vibration elastography is a shear wave imaging technique recently developed to monitor thermal ablation extent during treatment procedures. Previous work has shown good lateral boundary delineation of ablated volumes, but axial delineation was more ambiguous, which may have resulted from the assumption of lateral shear wave propagation. In this work, we assume both lateral and axial wave propagation and compare wave velocity images to those assuming only lateral shear wave propagation in finite element simulations, tissue-mimicking phantoms, and bovine liver tissue. Our results show that assuming bidirectional wave propagation minimizes artifacts above and below ablated volumes, yielding a more accurate representation of the ablated region on shear wave velocity images. Area overestimation was reduced from 13.4% to 3.6% in a stiff-inclusion tissue-mimicking phantom and from 9.1% to 0.8% in a radio-frequency ablation in bovine liver tissue. More accurate ablation representation during ablation procedures increases the likelihood of complete treatment of the malignant target, decreasing tumor recurrence.     

Hyperbolic and pseudo-hyperbolic equations in the theory of vibration

Longitudinal vibration of bars is usually considered in mathematical physics in terms of a classicalmodel described by the wave equation under the assumption that the bar is thin and relatively long. Moregeneral theories have been formulated taking into consideration the effect of the lateral motion of a relativelythick bar (beam). The mathematical formulation of these models includes higher-order derivatives in theequation of motion. Rayleigh derived the simplest generalization of the classical model in 1894, by includingthe effects of lateral motion and neglecting the shear stress. Bishop obtained the next generalization of thetheory in 1952. The Rayleigh–Bishop model is described by a fourth-order partial differential equation notcontaining the fourth-order time derivative. He took into account the effects of shear stress. Both Rayleigh’sand Bishop’s theories consider lateral displacement being proportional to the longitudinal strain. The Bishopmodel was generalized by Mindlin and Herrmann. They considered the lateral displacement proportional toan independent function of time and longitudinal coordinate. This result is formulated as a system of twodifferential equations of second order, which could be replaced by a single equation of fourth order resolvedwith respect to the highest order time derivative. To obtain a more general class of equations, the longitudinaland lateral displacements are expressed in the form of a power series expansion in the lateral coordinate. In thispaper, all of the above-mentioned equations are considered in the framework of a general theory of hyperbolicequations, with the aim of classifying the equations into general groups. The solvability of the correspondingproblems is also discussed.     

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.     

Lateral blood flow velocity estimation based on ultrasound speckle size change with scan velocity

Conventional (Doppler-based) blood flow velocity measurement methods using ultrasound are capable of resolving the axial component (i.e., that aligned with the ultrasound propagation direction) of the blood flow velocity vector. However, these methods are incapable of detecting blood flow in the direction normal to the ultrasound beam. In addition, these methods require repeated pulse-echo interrogation at the same spatial location. A new method has been introduced which estimates the lateral component of blood flow within a single image frame using the observation that the speckle pattern corresponding to blood reflectors (typically red blood cells) stretches (i.e., is smeared) if the blood is moving in the same direction as the electronically-controlled transducer line selection in a 2-D image. The situation is analogous to the observed distortion of a subject photographed with a moving camera. The results of previous research showed a linear relationship between the stretch factor (increase in lateral speckle size) and blood flow velocity. However, errors exist in the estimation when used to measure blood flow velocity. In this paper, the relationship between speckle size and blood flow velocity is investigated further with both simulated flow data and measurements from a blood flow phantom. It can be seen that: 1) when the blood flow velocity is much greater than the scan velocity (spatial rate of A-line acquisition), the velocity will be significantly underestimated because of speckle decorrelation caused by quick blood movement out of the ultrasound beam; 2) modeled flow gradients increase the average estimation error from a range between 1.4% and 4.4%, to a range between 4.4% and 6.8%; and 3) estimation performance in a blood flow phantom with both flow gradients and random motion of scatterers increases the average estimation error to between 6.1% and 7.8%. Initial attempts at a multiple-scan strategy for estimating flow by a least-squares model suggest the possibility of increased accuracy using multiple scan velocities.     

Speckle Method for the Measurement of Helical Motion of a Rigid Body

The helical motion of an object having the rotation axis parallel to the axis of the optical system is measured by the double exposure speckle technique. The object is illuminated with a multimode dye laser light, and the amounts of the rotation angle as well as the translation are obtained from the interference fringes modulating the optical Fourier transforms of specific points on the exposed photographic plate.     

一种改进的MRI图像刚性平移运动伪影的校正

在磁共振成像过程中由于患者的运动会在图像中造成运动伪影,从而造成图像的退化,严重影响临床诊断．本文对MRI图像刚性平移运动伪影提出了一个改进的后处理方法：首先用谱平移理论消除频率编码方向平移运动;然后建立模糊模型表示图像的背景并对其进行抑制,用数学形态学的方法确定图像的支撑域;最后以能量熵为收敛准则,用相位恢复算法对频率编码方向残余的子像素移动造成的伪影和相位编码方向的伪影进行消除．实验表明,应用本研究提出的方法能够明显地消除图像空间运动造成的伪影．     

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.     

Two-dimensional axisymmetric winding model for finite deformation

A two-dimensional axisymmetric winding model for wound rolls of thin web is developed. The model accounts for radial and axial displacements and radial, circumferential, axial and shear stresses. The roll build-up is modeled as an incremental accretion process. The material behaviour of the roll is considered as hyperelastic, orthotropic and radially nonlinear. The numerical solution is developed using the finite element method and the total Lagrangian formulation. The model is applied to the winding of paper rolls. It is shown that centrifugal forces may considerably affect the resulting stress distributions. For nonzero Poisson’s ratios significant edge effects in the roll stresses are found. In particular, high shear stresses and shear stress gradients are discovered in the vicinity of the core near the roll ends. A remarkable stress leveling phenomenon is found where the effect of a non-constant incoming web tension is evened out in the roll axial direction.     

Motion of a spherical particle inside a liquid film

The motion of a spherical particle inside a liquid film coated on a plane wall is considered under conditions of Stokes flow in the limit of vanishing capillary number where the interfacial deformation is infinitesimal. The problem is formulated in terms of a system of one-dimensional integral equations for the velocity and traction Fourier coefficients along the trace of the interface, wall, and particle contour in a meridional plane, and the solution is found using a boundary-element method. Comprehensive results for the force and torque resistance coefficients are presented in the case of particle rotation and translation in quiescent fluids. The velocity of translation and angular velocity or rotation of a freely suspended particle in simple shear flow are computed and discussed over a broad range of conditions.     

Rigid rotations of a plate and the related speckle displacements in the image plane

We describe an optical setup created for the verification of theoretical results concerning the displacement of speckles in the plane imaging a surface, which performs rotational motion. On the whole, the experimental results are consistent with the theory: there is a linear relationship between the surface rotation and the speckle displacement. The sensitivity of this method is proportional to the distance from a lens to the observation plane.     

Total Lagrangian formulation for the large displacement analysis of rectangular plates

In this paper, a method for the non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co-ordinate system using the assumptions of the classical theories of plates. Non-linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time-invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two-parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non-linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non-linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.     

Variation of natural frequencies of beams using the active stiffening effect

The present study investigates the stiffening effects of a simply supported and clamped–free symmetric piezolaminated composite type beams. The structure consists of PZT layers or two sets of patches bonded to the surface of the beam. The analysis considers the linear piezoelectric constitutive relations and a first order shear deformation theory (FSDT). The influence of the actuators is evaluated by means of the pin-force model and their size and location along the beam are taken into account. Two coupled equations of motion for the lateral displacement and bending rotation and one uncoupled equation for the axial displacement of symmetric piezolaminated composite beam are solved numerically to obtain the natural frequencies and mode shapes. Numerical experiments demonstrate that the natural frequencies and mode shapes of the beam can be actively altered using the piezoelectric bonded actuators. The results of the present degenerated model are compared to results presented in the literature. The comparisons yielded excellent matches.