Quo vadis elasticity imaging?

In the past decade, an important field that has emerged as complementary to ultrasonic imaging is that of elasticity imaging. The term encompasses a variety of techniques that can depict a mechanical response or property of tissues. In ultrasound, its premise is built on two important facts: (a) that significant differences between mechanical properties of several tissue components exist and (b) that the information contained in the coherent scattering, or speckle, is sufficient to depict these differences following an external or internal mechanical stimulus. Parameters, such as velocity of vibration, displacement, strain, strain rate, velocity of wave propagation and elastic modulus, have all been demonstrated feasible in their estimation and have resulted in the accurate depiction of stiffer tissue masses, such as tumors, high-intensity focused ultrasound (HIFU) lesions and atherosclerotic plaques. More recently, through the development of ultrafast algorithms tailored to suitable hardware as well as the familiarity of the physician with the sensitivity of the methods used, one elasticity imaging technique in particular, elastography, has been shown applicable in a typical clinical ultrasound setting. In other words, elastograms can currently be obtained at quasi real-time (approximately at a frame rate of 8 frames/s) and with the use of a hand-held transducer (as opposed to the previously used frame-suspended setup) during and simultaneously with an ultrasound exam of, e.g., the breast or the prostate. The higher frame rate available with certain clinical ultrasound scanners has also resulted in the successful application of elasticity imaging techniques on the myocardium and monitoring its deformation over several cardiac cycles for the detection of ischemic regions. As a result, elasticity imaging with its ever increasing number of applications and demonstrated applicability in a typical, clinical ultrasound setting promises to make an important contribution to the ultrasound practice as we know it.     

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal(MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.     

Elasticity reconstruction for ultrasound elastography using a radial compression: an inverse approach

To reduce the inherent mechanical artifacts in the strain images, many groups have investigated solutions to the inverse problem in elastography. However, in prostate elastography or intravascular elastography where the compression direction is radial, the inverse problem has not been studied thoroughly. In this paper, an iterative approach is proposed to reconstruct tissue elasticity for ultrasound elastography using a radial compression. The method is based upon the stress-strain relations in the polar coordinates. Computer simulations in an intravascular model are performed to illustrate the feasibility of this method in reducing the mechanical artifacts of the strain images. The reconstructed elasticity error and the contrast-transfer efficiency (CTE) as a function of the iteration number show that the inverse approach converges with a few iterations.     

A unified view of imaging the elastic properties of tissue

A number of different approaches have been developed to estimate and image the elastic properties of tissue. The biomechanical properties of tissues are vitally linked to function and pathology, but cannot be directly assessed by conventional ultrasound, MRI, CT, or nuclear imaging. Research developments have introduced new approaches, using either MRI or ultrasound to image the tissue response to some stimulus. A wide range of stimuli has been evaluated, including heat, water jets, vibration shear waves, compression, and quasistatic compression, using single or multiple steps or low-frequency (<10 Hz) cyclic excitation. These may seem to be greatly dissimilar, and appear to produce distinctly different types of information and images. However, our purpose in this tutorial is to review the major classes of excitation stimuli, and then to demonstrate that they produce responses that fall within a common spectrum of elastic behavior. Within this spectrum, the major classes of excitation include step compression, cyclic quasistatic compression, harmonic shear wave excitation, and transient shear wave excitation. The information they reveal about the unknown elastic distribution within an imaging region of interest are shown to be fundamentally related because the tissue responses are governed by the same equation. Examples use simple geometry to emphasize the common nature of the approaches.     

Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers

Magnetic resonance elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MRE applications. A cone-like hemispherical distribution of shear waves being generated by these drivers and the wave propagation being governed by diffraction in the near field are shown. Using MRE visualization of the vector displacement field, we studied the properties of the shear wave field created by longitudinal MRE drivers of various sizes to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition.     

Doppler ultrasound detection of shear waves remotely induced in tissue phantoms and tissue in vitro

In shear wave elasticity imaging (SWEI), mechanical excitation within the tissue is remotely generated using radiation force of focused ultrasound. The induced shear strain is subsequently detected to estimate visco-elastic properties of tissue and thus aid diagnostics. In this paper, the mechanical response of tissue to radiation force was detected using a modified ultrasound Doppler technique. The experiments were performed on tissue mimicking and tissue containing phantoms using a commercial diagnostic scanner. This scanner was modified to control both the pushing and probing beams. The pushing beam was fired repetitively along a single direction while interlaced probing beams swept the surrounding region of interest to detect the induced motion. The detectability of inhomogeneous inclusions using ultrasonic Doppler SWEI method has been demonstrated in this study. The displacement fields measured in elastic phantoms clearly reveal the oscillatory nature of the mechanical relaxation processes in response to impulsive load due to the boundary effects. This relaxation dynamics was also present in cooked muscle tissue, but was not detected in more viscous and less elastic phantom and raw muscles. Presence of a local heterogeneity in the vicinity of the focal region of the pushing beam results in generation of a standing wave field pattern which is manifested in the oscillatory response of the excited region of the tissue. There has been made an assumption that dynamic characteristics of the relaxation process may be used for visualization of inhomogeneities.     

利用先验估计自适应加窗的准静态超声弹性成像位移估计算法

准静态弹性成像技术是基于组织压缩前和压缩后超声回波射频信号进行组织运动重构的弹性成像技术。提出了一种基于先验估计的自适应窗函数算法,在位移估计过程中,使用已估计的临近窗的时延值作为先验信息,自动调整截取压缩后射频信号段的截取窗函数,提高了互相关运算所需的压缩前和压缩后信号段之间的相关性。仿真实验结果表明,该算法不仅大大提高了成像速度,而且提高了信噪比较低时的成像质量,同时该算法具有更宽的应变通带。      

Lattice with vacancies: elastic fields and effective properties in frameworks of discrete and continuum models

Linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies is considered. Closed-form analytical expressions for displacement field in the lattice with doubly periodic system of vacancies are derived. Effective elastic moduli are calculated. The results are compared with the ones obtained by molecular dynamics simulations of a lattice with random distribution of vacancies. At low vacancy concentrations, less than 4%, random and periodic distributions of vacancies produce the same effect on elastic moduli. One of the main goals is to examine the possibilities and limitations of modelling of the lattice with vacancies by an elastic continuum with holes. It is found that the effective elastic properties are modelled adequately, provided the shape of the holes is chosen appropriately. On the contrary, the strain field, in particular, strain concentration differs significantly.     

Cancer cell recognition--mechanical phenotype

The major characteristics of cancer metastasis is the ability of the primary tumor cells to migrate by way of the blood or lymph vessels and to form tumors at multiple, distant sites. There are evidences that cancer progression is characterized by disruption and/or reorganization of cytoskeleton (i.e. cellular scaffold). This is accompanied by various molecular alterations influencing the overall mechanical resistance of cells. Current approach in diagnosis focuses mainly on microbiological, immunological, and pathological aspects rather than on the biomechanics of diseases. The determination of mechanical properties of an individual living cell has became possible with the development of local measurement techniques, such as atomic force microscopy, magnetic or optical tweezers. The advantage of them lies in the capability to measure living cells at a single cell level and in liquid conditions, close to natural environment. Here, we present the studies on mechanical properties of single cells originating from various cancers. The results show that, independently of the cancer type (bladder, melanoma, prostate, breast and colon), single cells are characterized by the lower Young's modulus, denoting higher deformability of cancerous cells. However, the obtained Young's modulus values were dependent on various factors, like the properties of substrates used for cell growth, force loading rate, or indentation depth. Their influence on elastic properties of cells was considered. Based on these findings, the identification of cancerous cells based on their elastic properties was performed. These results proved the AFM capability in recognition of a single, mechanically altered cell, also in cases when morphological changes are not visible. The quantitative analysis of cell deformability carried out using normal (reference) and cancerous cells and, more precisely, their characterization (qualitative and quantitative) can have a significant impact on the development of methodological approaches toward precise identification of pathological cells and would allow for more effective detection of cancer-related changes.     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

Evaluation of elastic modulus of cantilever beam by TA-ESPI

The paper proposes an evaluation technique for the elastic modulus of a cantilever beam by vibration analysis based on time average electronic speckle pattern interferometry (TA-ESPI) and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of a thin film are the Nano indentation test, Buldge test, Micro-tensile test, and so on. They each have strength and weakness in the preparation of the test specimen and the analysis of experimental results. ESPI is a type of laser speckle interferometry technique offering non-contact, high-resolution and whole-field measurement. The technique is a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI can be used to find the resonance frequency for each vibration mode shape. And the elastic modules of a test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique can be used to find the elastic modulus of a material requiring simple preparation process and analysis.     

A phase-field model for elastically anisotropic polycrystalline binary solid solutions

A phase-field model for modeling the diffusional processes in an elastically anisotropic polycrystalline binary solid solution is described. The elastic interactions due to coherency elastic strain are incorporated by solving the mechanical equilibrium equation using an iterative-perturbation scheme taking into account elastic modulus inhomogeneity stemming from different grain orientations. We studied the precipitate interactions among precipitates across a grain boundary and grain boundary segregation–precipitate interactions. It was shown that the local pressure field from one coherent precipitate influences the shape of precipitates in other grains. The local pressure distribution due to primary coherent precipitates near the grain boundary leads to inhomogeneous solute distribution along the grain boundary, resulting in non-uniform distribution of secondary nuclei at the grain boundary.     

Ultrasonic elastography using sector scan imaging and a radial compression

Elastography is an imaging technique based on strain estimation in soft tissues under quasi-static compression. The stress is usually created by a compression plate, and the target is imaged by an ultrasonic linear array. This configuration is used for breast elastography, and has been investigated both theoretically and experimentally. Phenomena such as strain decay with tissue depth and strain concentrations have been reported. However in some in vivo situations, like prostate or blood vessels imaging, this set-up cannot be used. We propose a device to acquire in vivo elastograms of the prostate. The compression is applied by inflating a balloon that covers a transrectal sector probe. The 1D algorithm used to calculate the radial strain fails if the center of the imaging probe does not correspond to the center of the compressor. Therefore, experimental elastograms are calculated with a 2D algorithm that accounts for tangential displacements of the tissue. In this article, in order to gain a better understanding of the image formation process, the use of ultrasonic sector scans to image the radial compression of a target is investigated. Elastograms of homogeneous phantoms are presented, and compared with simulated images. Both show a strain decay with tissue depth. Then experimental and simulated elastograms of a phantom that contains a hard inclusion are presented, showing that strain concentrations occur as well. A method to compensate for strain decay and therefore to increase the contrast of the strain elastograms is proposed. It is expected that such information will help to interpret and possibly improve the elastograms obtained via radial compression.     

Research on enhancement sensitivity of embedded fiber Bragg grating sensor

With its unique advantages, embedded fiber Bragg grating (FBG) sensor is more and more used in the field of engineering structural health monitoring. According to the actual needs of engineering monitoring, we combined with the internal structure to make sensitivity design of the sensor. It mainly through setting the elastic modulus and the radius of sensor's inner sheath intermediate section, to make the strain of middle section larger than average strain, In order to achieve the increasing sensitivity. Through the analysis, the enhancement degree is relevant to the length, radius and elastic modulus of the middle section, so it could achieved different requirement of sensitizing by adjusting these parameters. Through the analysis of the core strain in the sensitizing structure, it can obtain the strain transfer distribution in the scope of sensor. All these could provide the theory basis for the realization of embedded FBG sensor's sensitivity enhancement.     

Acoustic radiation force optical coherence elastography for elasticity assessment of soft tissues

Biomechanical properties of soft tissues are important indicators of tissue functions which can be used for clinical diagnosis and disease monitoring. Elastography, incorporating the principles of elasticity measurements into imaging modalities, provides quantitative assessment of elastic properties of biological tissues. Benefiting from high-resolution, noninvasive, and three-dimensional optical coherence tomography, optical coherence elastography (OCE) is an emerging optical imaging modality to characterize and map biomechanical properties of soft tissues. Recently, acoustic radiation force (ARF)–OCE has been developed for elasticity measurements of ocular tissues, detection of vascular lesions, and monitoring of blood coagulation based on remote and noninvasive ARF excitation to both internal and superficial tissues. Here, we describe the advantages of the ARF–OCE technique, the measurement methods in ARF–OCE, the applications in biomedical detection, current challenges, and advances. ARF–OCE technology has the potential to become a powerful tool for in vivo elasticity assessment of biological samples in a noncontact, noninvasive, and high-resolution nature.     

Investigation of the radial compression of carbon nanotubes with a scanning probe microscope

Efforts have been made to characterize the mechanical properties of carbon nanotubes. Previous work has concentrated on the tubes' longitudinal properties, and studies of their radial properties have lagged behind. We have used a scanning probe microscope with an indentation/scratch function to investigate the radial compression of multiwalled carbon nanotubes under an asymmetric stress. In particular, we have determined the radial compressive elastic modulus at different compression levels and have estimated the compressive strength to be well beyond 5.3 GPa.     

High-pressure elastic properties of solid argon to 70 GPa

The acoustic velocities, adiabatic elastic constants, bulk modulus, elastic anisotropy, Cauchy violation, and density in an ideal solid argon (Ar) have been determined at high pressures up to 70 GPa in a diamond anvil cell by making new approaches of Brillouin spectroscopy. These results place the first complete study for elastic properties of dense Ar and provide an improved basis for making the theoretical calculations of rare-gas solids over a wide range of compression.     

Transient displacement induced in shear wave elastography: comparison between analytical results and ultrasound measurements

It is now accepted that an effective way to investigate the elastic properties of soft tissues is to generate a localized transient acoustic radiation force and to follow the associated displacements in the time/space domain. Shear waves induced by this stress field are particularly interesting in this kind of medium because they are governed by the shear elastic modulus mu, which is directly linked to the Young modulus, and spatial distribution and temporal evolution of the transient motion induced must therefore be obtained in detail. We report here a model based on the elastodynamic Green's function formalism to describe these displacements. 3D simulation of radiation force in homogenous elastic media was performed and the displacement curves computed at different radial distances for different temporal force profiles. Amplitude and duration of displacement were found to be reliable parameters to characterize the elastic properties of the medium. Experimental measurements were performed in a homogeneous agar-gelatin tissue-mimicking phantom, and two transducers were used to generate the radiation force and follow the induced displacements. Displacements obtained from different lateral locations around the applied force axis were then used to reconstruct the shear-wave propagation in a scan plane as a function of time. The experimental displacements/curves agreed with the theoretical profiles obtained by the elastodynamic Green's function formalism.     

Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.