Elastic Contrast Research Articles

Spherical lesion phantoms for testing the performance of elastography systems

A set of three cubic one-litre phantoms containing spherical simulated lesions was produced for use in comparing lesion detection performance of different elastography systems. The materials employed are known to be stable in heterogeneous configurations regarding geometry and elastic contrast ≡ (storage modulus of lesion material) ÷ (storage modulus of background material), and regarding ultrasound and NMR properties. The materials mimic soft tissues in terms of elastic, ultrasound and NMR properties. Each phantom has only one value of elastic contrast (3.3, 4.6 or 5.5) and contains arrays of 1.6 mm, 2 mm, 3 mm and 4 mm diameter spherical simulated lesions. All the spheres of a given diameter are arranged in a regular array with coplanar centres. Elastograms of an array made with ultrasound allow determination of the depth range over which lesions of that diameter and elastic contrast can be detected. Two phantoms are made from agar-plus-gelatin-based materials, and one is made from oil-in-gelatin dispersions. The methods for producing the phantoms are described in detail. Lesion detection performances for two ultrasound systems, both operating at about 7.5 MHz and focused at about 5 cm, were quantified with distinctions between the two systems demonstrated. Neither system was capable of detecting any of the 1.6 mm lesions. Phantoms such as these should be useful in research labs that are refining hardware and/or software for elastography.

Tissue-mimicking agar/gelatin materials for use in heterogeneous elastography phantoms

Five 9 cm × 9 cm × 9 cm phantoms, each with a 2-cm-diameter cylindrical inclusion, were produced with various dry-weight concentrations of agar and gelatin. Elastic contrasts ranged from 1.5 to 4.6, and values of the storage modulus (real part of the complex Young's modulus) were all in the soft tissue range. Additives assured immunity from bacterial invasion and can produce tissue-mimicking ultrasound and NMR properties. Monitoring of strain ratios over a 7 to 10 month period indicated that the mechanical properties of the phantoms were stable, allowing about 1 month for the phantom to reach chemical equilibrium. The only dependable method for determining the storage moduli of the inclusions is to make measurements on samples excised from the phantoms. If it is desired to produce and accurately characterize a phantom with small inclusions with other shapes, such as an array of small spheres, an auxiliary phantom with the geometry of the cylindrical inclusion phantoms or the equivalent should be made at the same time using the same materials. The elastic contrast can then be determined using samples excised from the auxiliary phantom. A small increase of about 10% in volume of the cylindrical inclusions occurred—a tolerable increase. Interestingly, the smallest increase (about 5%) occurred in the phantom with the largest elastic contrast.

The role of elastic contrast on the strain energy and the stress state of a spheroidal inclusion with a general eigenstrain state

Based on a recent contribution by two of the authors [Fischer FD, Böhm HJ. Acta Mater 2005;53:367–74] exact analytical relations are presented for the strain energy density and selected values of the stress components for a class of inhomogeneous spheroidal inclusions that are subjected to general normal and shear eigenstrain states. Among the inclusion shapes covered are discs, spheres and cylinders (“needles”). The reported relations can be used for the understanding of the eigenstrain state on the development of a wide field of inclusions (precipitates).

Characteristics of Surface Waves in Media with Significant Vertical Variations in Elasto-Dynamic Properties

In media with strong vertical variations in elasto-dynamic properties, the characteristics of surface waves may deviate significantly from their typical appearance in media with small contrasts. Different numerical examples suggest that ignoring this behavior may lead to poor results in surface wave analysis. The cases analysed are: (1) Neighboring surface wave modes which exchange their major characteristics at osculation points of their dispersion curves; (2) Quasi-channel waves propagating inside a buried low velocity channel; (3) Surface waves in the presence of a low-velocity layer at the very surface; and (4) Rayleigh surface waves in the presence of a very high velocity contrast allowing normal quasi-compressional pseudo-modes. Amplitude-depth functions are used to analyze the physical cause of the unusual characteristics. One important result is a vanishing vertical displacement of the fundamental mode and dominance of the first higher Rayleigh mode at low frequency for cases with a large elastic contrast at shallow depth (increase in Vs approaching 300% at [Formula: see text]). If the displacement is treated as the fundamental mode, a systematic overestimate of deeper shear wave velocity will arise in the inversion, since higher modes have higher phase velocity. A second result is from a profile with a very thin, surficial low-velocity layer, where higher modes dominating the response might prevent fundamental mode detection and inversion. Finally, if shear wave velocity of the half-space exceeds the compressional wave velocity of an overlying layer, quasi-compressional waves (or guided P-waves) come into the velocity range of normal modes. This may lead to surface wave mode-misidentification.

The Multiscale Analysis of Multiple Interacting Inclusions Problem: Finite Number of Interacting Inclusions

A hybrid method based on the combination of the volume integral equation (VIE) method and the boundary integral equation (BIE) method is proposed for the micro-macro solution of elastostatic 2D and 3D multiscale problems in bounded or unbounded solids containing interacting multiple inclusions of essentially different scale. The hybrid micro-macro formulation allows decomposition of the complete problem into two associated subproblems, one residing entirely at the micro-level and the other at the macro-level at each iteration. The efficiency of the standard iterative scheme of the BIE and VIE methods for the singular integral equations involved is enhanced by the use of a modification in the spirit of a subtraction technique as well as by the advantageous choice of the initial analytical approximation for interacting inclusions (micro-level) in an unbounded medium subjected to inhomogeneous loading. The latter is evaluated by the macro-scale BIE technique capable of handling complex finite geometries and mixed boundary conditions. The iteration method proposed converges rapidly in a wide class of problems considered with high matrix-inclusion elastic contrast, with continuously varying anisotropic and nonlinear elastic properties of inclusions, as well as with sizes of interacting inclusions differing by a factor varying in the interval from 1 to 107. The accuracy and efficiency of the method are examined through comparison with results obtained from finite-element analysis and boundary element analysis as well as from analytical solution.

Isolated modes and percolation in the lattice dynamics of (Be, Zn)Se

The mixed II–VI semiconductor Zn1 − x Be x Se possesses non-trivial vibration properties, because its two constituent compounds, ZnSe and BeSe, show very different degrees of covalency and hence high elastic contrast. An anomalous Be–Se vibration line has been observed, mostly at intermediate Be content, in the Raman spectra of thin (Zn,Be)Se films. In order to explain the microscopic origin and detailed composition of these lines, a first-principles calculation of the vibration frequencies in a mixed crystal has been performed, with the frozen-phonon technique and supercell setup within the density functional theory, using the SIESTA method, which uses norm-conserving pseudopotentials and strictly localized numerical basis functions. The calculations confirmed an earlier assumption that the anomalous Be–Se line appears due to the formation of continuous chains of a more rigid Be-rich pseudo-continuous phase formed within the more soft Zn-rich host region on crossing the Be–Se bond percolation threshold (x ∼ 0.19). Different local deformations in percolated and non-percolated regions affect the interatomic elastic interactions and split the corresponding vibration lines. Besides confirming the percolation model qualitatively, the calculation provides details concerning the vibration patterns in different phonon modes.

Nonlinear elasticity imaging:theory and phantom study

In tissue the Young's modulus cannot be assumed constant over a wide deformation range. For example, direct mechanical measurements on human prostate show up to a threefold increase in Young's modulus over a 10% deformation. In conventional elasticity imaging, these effects produce strain-dependent elastic contrast. Ignoring these effects generally leads to suboptimal contrast (stiffer tissues at lower strain are contrasted against softer tissues at higher strain), but measuring the nonlinear behavior results in enhanced tissue differentiation. To demonstrate the methods extracting nonlinear elastic properties, both simulations and measurements were performed on an agar-gelatin phantom. Multiple frames of phase-sensitive ultrasound data are acquired as the phantom is deformed by 12%. All interframe displacement data are brought back to the geometry of the first frame to form a three-dimensional (3-D) data set (depth, lateral, and preload dimensions). Data are fit to a 3-D second order polynomial model for each pixel that adjusts for deformation irregularities. For the phantom geometry and elastic properties considered in this paper, reconstructed frame-to-frame strain images using this model result in improved contrast to noise ratios (CNR) at all preload levels, without any sacrifice in spatial resolution. From the same model, strain hardening at all preload levels can be extracted. This is an independent contrast mechanism. Its maximum CNR occurs at 5.13% preload, and it is a 54% improvement over the best case (preload 10.6%) CNR for frame-to-frame strain reconstruction. Actual phantom measurements confirm the essential features of the simulation. Results show that modeling of the nonlinear elastic behavior has the potential to both increase detectability in elasticity imaging and provide a new independent mechanism for tissue differentiation.

Nonlinear Elasticity Imaging: Theory and Phantom Study

In tissue the Young's modulus cannot be assumed constant over a wide deformation range. For example, direct mechanical measurements on human prostate show up to a threefold increase in Young's modulus over a 10% deformation. In conventional elasticity imaging, these effects produce strain-dependent elastic contrast. Ignoring these effects generally leads to suboptimal contrast (stiffer tissues at lower strain are contrasted against softer tissues at higher strain), but measuring the nonlinear behavior results in enhanced tissue differentiation. To demonstrate the methods extracting nonlinear elastic properties, both simulations and measurements were performed on an agar-gelatin phantom. Multiple frames of phase-sensitive ultrasound data are acquired as the phantom is deformed by 12%. All interframe displacement data are brought back to the geometry of the first frame to form a three-dimensional (3-D) data set (depth, lateral, and preload dimensions). Data are fit to a 3-D second order polynomial model for each pixel that adjusts for deformation irregularities. For the phantom geometry and elastic properties considered in this paper, reconstructed frame-to-frame strain images using this model result in improved contrast to noise ratios (CNR) at all preload levels, without any sacrifice in spatial resolution. From the same model, strain hardening at all preload levels can be extracted. This is an independent contrast mechanism. Its maximum CNR occurs at 5.13% preload, and it is a 54% improvement over the best case (preload 10.6%) CNR for frame-to-frame strain reconstruction. Actual phantom measurements confirm the essential features of the simulation. Results show that modeling of the nonlinear elastic behavior has the potential to both increase detectability in elasticity imaging and provide a new independent mechanism for tissue differentiation.

Nonlinear elasticity imaging: Theory and phantom study

In tissue the Young's modulus cannot be assumed constant over a wide deformation range. For example, direct mechanical measurements on human prostate show up to a threefold increase in Young's modulus over a 10% deformation. In conventional elasticity imaging, these effects produce strain-dependent elastic contrast. Ignoring these effects generally leads to suboptimal contrast (stiffer tissues at lower strain are contrasted against softer tissues at higher strain), but measuring the nonlinear behavior results in enhanced tissue differentiation. To demonstrate the methods extracting nonlinear elastic properties, both simulations and measurements were performed on an agar-gelatin phantom. Multiple frames of phase-sensitive ultrasound data are acquired as the phantom is deformed by 12%. All interframe displacement data are brought back to the geometry of the first frame to form a three-dimensional (3-D) data set (depth, lateral, and preload dimensions). Data are fit to a 3-D second order polynomial model for each pixel that adjusts for deformation irregularities. For the phantom geometry and elastic properties considered in this paper, reconstructed frame-to-frame strain images using this model result in improved contrast to noise ratios (CNR) at all preload levels, without any sacrifice in spatial resolution. From the same model, strain hardening at all preload levels can be extracted. This is an independent contrast mechanism. Its maximum CNR occurs at 5.13% preload, and it is a 54% improvement over the best case (preload 10.6%) CNR for frame-to-frame strain reconstruction. Actual phantom measurements confirm the essential features of the simulation. Results show that modeling of the nonlinear elastic behavior has the potential to both increase detectability in elasticity imaging and provide a new independent mechanism for tissue differentiation.

Digital Image-Based Elasto-Tomography: Proof of Concept Studies for Surface Based Mechanical Property Reconstruction

Digital Image-based Elasto-Tomography (DIET) is a novel method of determining the distribution of elastic properties within the breast. Using an array of calibrated digital cameras and an inverse reconstruction algorithm, DIET allows reconstruction of the internal elastic stiffness distribution of the breast using only motions at the breast surface. This reconstructed stiffness should clearly show carcinoma based on their high elastic property contrast with healthy tissue. Proof of concept studies are presented for both the calibration of the digital imaging system and the inverse reconstruction algorithm. The reconstruction algorithm identified high stiffness tumors in the majority of test cases, even with the addition of random noise based on expected calibration accuracy.

Rock physics of a gas hydrate reservoir

Gas hydrates are solids composed of a hydrogen-bonded water lattice with entrapped guest molecules of gas. There are convincing arguments that vast amounts of methane gas hydrate are present in sediments under the world's oceans as well as in onshore sediments in the Arctic. This hydrate is possibly the largest carbon and methane pool on earth. As such, methane hydrate may be the principal factor in global climate balancing. One may also treat this methane pool as a potential energy source. These considerations ignite the scientific and business community's interest in quantifying the amount of methane hydrate in the subsurface. Gas hydrate reservoir characterization is, in principle, no different from the traditional hydrocarbon reservoir characterization. Similar and well-developed remote sensing techniques can be used, seismic reflection profiling being the dominant among them. Seismic response of the subsurface is determined by the spatial distribution of the elastic properties. By mapping the elastic contrast, the geophysicist can illuminate tectonic features and geobodies, hydrocarbon reservoirs included. To accurately translate elastic-property images into images of lithology, porosity, and the pore-filling phase, quantitative knowledge is needed that relates the rock's elastic properties to its bulk properties and conditions. Specifically, to quantitatively characterize a natural gas hydrate reservoir, we must be able to relate the elastic properties of the sediment to the volume of gas hydrate present and, if at all possible, the permeability. One way of achieving this goal is through rock physics effective-medium modeling. Several attempts to construct a relation between hydrate concentration and the compressional velocity in sediments have followed the path of modifying the popular Wyllie's time average equation which states that total traveltime through rock is the volume-weighted sum of traveltimes through the solid phase and the fluid phase considered independently of each other; i.e., V P −1 = (1-ϕ) V …

Three Springs Talc Mine: A new view on an old deposit

A successful application of the high resolution seismic reflection method for talc exploration, is demonstrated using an experimental seismic line, recorded over the Three Springs talc deposit. Since 1973, a variety of ground and airborne geophysical techniques had been applied to talc exploration at Three Springs, with limited success. However, wireline logging and laboratory petrophysical measurements have provided new insights into the physical properties of talc and contrasts between talc and adjacent dolomite and dolerite rocks. In particular, P-wave velocity measurements demonstrated that the elastic contrast between the talc mineralisation and surrounding rocks may be sufficient for the application of seismic reflection methods to talc exploration. Between 1989 and 1993, seismic reflection and refraction surveys were acquired on a single profile across the Three Springs talc deposit. The results of this work were disappointing, apparently contradicting physical property measurements. Greatly improved results from re-processing of the `old? seismic data, in 2000, suggested seismic reflection may indeed assist in mapping of the talc mineralisation, as well as providing important detailed structural information. Additional experimental data acquisition, undertaken in 2000, confirmed the potential application of the seismic reflection method to deposit ? scale talc exploration. However, whether the seismic technique can be routinely applied, in a cost ? effective manner, providing the required geological detail, remains to be seen.

Anomalous acoustic reflection on a sliding interface or a shear band

We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity-strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from that of the static interface. In particular, the system being open, the energy of an in-plane polarized wave is no longer conserved, the work of the external pulling force being partitioned between frictional dissipation and gain (of either sign) of coherent acoustic energy. Large values of the friction coefficient favor energy gain, while velocity strengthening tends to suppress it. An interface with infinite elastic contrast (one rigid medium) and v-independent (Coulomb) friction exhibits spontaneous acoustic emission, as already shown by Nosonovsky and Adams [Int. J. Eng. Sci. 39, 1257 (2001)]. But this pathology is cured by a moderately large V strengthening of friction, or, for systems with not too large friction coefficients, by any finite elastic contrast. We show that (i) positive gain should be observable for rough-on-flat multicontact interfaces and (ii) a sliding shear band in a granular medium should give rise to sizable reflection, which opens a promising possibility for the detection of shear localization.

Lateral resolution in elastography

The factors that control the lateral resolution in elastography were investigated using a simulation study. The lateral resolution was estimated from the simulated axial strain elastograms as the smallest measurable distance between two equally stiff lesions embedded in a homogeneously softer background. The lesions were symmetrically positioned lateral to the center of the target, at the focus of the transducer. Ultrasound (US) systems with different transducer frequencies, bandwidths and f-numbers were simulated. The effects of the ultrasonic parameters, the lateral spacing between adjacent echo signals, the cross-correlation window length, the lesion/background elastic contrast and the lateral motion of scatterers on the estimated lateral resolution were investigated. The results show that the lateral resolution in elastography is proportional to the beamwidth of the US system used to acquire the data, and is on the same order as the sonographic lateral resolution. (E-mail: Jonathan.Ophir@uth.tmc.edu)

Phonons in colloidal systems

Rich phonon spectra were observed experimentally by Brillouin spectroscopy in liquid, glassy, and crystalline state of colloidal systems of low and high elastic constant contrast. The nature of these phonons was elucidated by theoretical calculations of the single sphere scattering cross section, the energy density distribution, the light scattering intensity, and determination of the band structure by the multiple scattering method. Besides the ordinary acoustic phonon, localized optic-like modes, mixed modes, and Bragg induced modes were identified. Their relation to the physical state of a colloidal suspension sensitively depends on the micromechanical mismatch between particle and surrounding medium and the coherence of the crystalline structure. Polycrystalline colloidal suspensions show distinct acoustic excitations in the high wave vector–low frequency region.

Tissue-mimicking oil-in-gelatin dispersions for use in heterogeneous elastography phantoms.

A ten-month study is presented of materials for use in heterogeneous elastography phantoms. The materials consist of gelatin with or without a suspension of microscopic safflower oil droplets. The highest volume percent of oil in the materials is 50%. Thimerosal acts as a preservative. The greater the safflower oil concentration, the lower the Young's modulus. Elastographic data for heterogeneous phantoms, in which the only variable is safflower oil concentration, demonstrate stability of inclusion geometry and elastic strain contrast. Young's modulus ratios (elastic contrasts) producible in a heterogeneous phantom are as high as 2.7. The phantoms are particularly useful for ultrasound elastography. They can also be employed in MR elastography, although the highest achievable ratio of longitudinal to transverse relaxation times is considerably less than is the case for soft tissues.

Thermal enhancement of AFM phase contrast for imaging diblock copolymer thin film morphology

A simple and effective means of increasing the morphological detail in AFM phase micrographs of microphase separated block copolymer films is presented. Effective AFM phase imaging of microphase separated systems hinges upon the existence of appropriate contrast mechanisms such as differences in elasticity between the microphase separated domains. For some systems, AFM phase imaging at room temperature results in low contrast images due to a paucity of differential mechanical behavior between the microphase domains, e.g. at room temperature both species are glassy. Through the use of a heating apparatus custom-designed for AFM, an elastic contrast mechanism can be created in some systems by raising the specimen to a temperature between the glass transitions of the constituent polymer species. This serves to preferentially soften one species with respect to the other, thus enhancing the phase contrast mechanism, which results in micrographs with superior detail. This simple technique is demonstrated using films of a series of polystyrene-b-poly( n-alkyl methacrylate) diblock copolymers and both commercial and custom-built heating stages. By choosing appropriate measurement temperatures, AFM phase contrast could be greatly enhanced, or indeed created, when compared to room temperature images of these specimens. For these materials, contrast enhancement required that the sample be heated roughly 20°C above the glass transition of the lower- T g species.

Misfit dislocations in epitaxial heterostructures with different elastic constants of the substrate and epitaxial layer

Abstract We calculate the elastic energy of a heterostructure consisting of materials with different elastic moduli. In the framework of the continuous theory of elasticity we obtain an analytical solution for the elastic field of a periodic arrangement of screw misfit dislocations. This solution allows to calculate the critical thickness of the epitaxial layer (epilayer) and to analyse its dependence on the elastic contrast between the substrate and the epilayer. Analysis of the total elastic energy of the heterostructure shows that a transition from a pseudomorphic state to a state with misfit dislocations occurs similarly to either a first-order or a second-order phase transition. The type of transition that the system follows depends on the relation between the elastic moduli of the substrate and the epilayer.

Computation of contrasts in atomic resolution electron spectroscopic images of planar defects in crystalline specimens

The image obtained in a conventional transmission electron microscope contains contributions from elastically and from inelastically scattered electrons. The electron spectroscopic imaging mode of an energy-filtering transmission electron microscope allows us to separate these two different contributions by inserting an energy-selecting slit in the energy-dispersive plane of an imaging energy filter. Selecting a specific energy loss corresponding to the ionization of the inner shell of a particular element one can obtain information on the distribution of the element within the specimen. The contrast is then caused by inelastically scattered electrons. For crystalline specimens, however, the contrast will be influenced additionally by the elastic contrast. This elastic contrast arises from electron diffraction and increases with increasing crystal thickness. Therefore the intensity distribution in the image cannot directly be interpreted as an elemental map. For a reliable interpretation of contrast formation in elemental maps it is therefore necessary to compute theoretical energy-loss images for various crystal thicknesses and compare these images with the experimental images. As an example we discuss the influence of electron diffraction effects on energy-loss images of two crystals with planar defects. Linescans are computed for various thicknesses of these crystals. Our calculations are performed using first-order perturbation theory to describe the transitions between the Bloch-wave states of the incident electron. The computed linescans for various crystal thicknesses show clearly that the influence of the elastic contrast on an image increases when we investigate thicker specimens. Furthermore, the comparison between elastic and energy-loss images demonstrates the partial preservation of the elastic contrast as a function of thickness. We find that for specimens thicker than about one third of the extinction length (here ∼80–100 Å) it is impossible to interpret an energy-loss image directly as elemental map.

Zero-loss image formation and modified contrast transfer theory in EFTEM

For a weak phase/weak amplitude object the information transfer in the imaging process of TEM is described by the common formalism of the contrast transfer function (CTF). So far the effects of inelastic scattering were not accounted for in this formalism. In conventional imaging they were simply neglected. In energy filtering TEM (EFTEM), where removal of inelastic electrons leads to higher specimen contrast, they were modelled by a global increase of the elastic amplitude contrast. Thus, the description of inelastic and elastic scattering was mixed. Here a new ansatz is proposed which treats elastic and inelastic contrast transfer separately by adding an inelastic contribution to the scattering potentials. In EFTEM this has the effect of adding a filter contrast which depends on the characteristics of the inelastic scattering. For samples with dominant plasmon loss the additional filter contrast is restricted to low resolution. Because of its strong dependence on the nature of the inelastic scattering process, the filter contrast cannot in general be unified with the conventional elastic amplitude contrast. The modified CTF theory for EFTEM was tested experimentally on a variety of samples. Images of amorphous layers of copper, aluminium, and carbon films, as well as zero-loss images of proteins embedded in amorphous ice were evaluated. The values of the parameters of the additional filter contrast were determined for carbon film and proteins embedded in vitrified ice. Comparison of different CTF models used to reconstruct 3D volumes from zero-loss images confirmed that best agreement with the atomic model is attained with the new, modified CTF theory.