Elasticity reconstruction from displacement and confidence measures of a multi-compressed ultrasound RF sequence

Ultrasound elasticity imaging shows promise as a new way for early detection of cancers by assessing the elastic characteristics of soft tissue. So far the commonly used approach involves solving the so-called inverse elasticity problem of recovering elastic parameters from displacement measurements. We propose a finite-elementbased nonlinear scheme to estimate the elasticity distribution of soft tissue from multi-compressed ultrasound radio frequency (RF) data. An experimental ultrasound workstation has been developed to acquire multi-compressed data. A composite probe was employed as the compression plate. The contact forces and torques were acquired at the same time as imaging. Axial displacements under different static loads are estimated from the RF data before and after deformation using a cross-correlation technique. The confidence of displacement estimates is employed as a weighting factor in solving the objective function describing the inverse elasticity reconstruction problem. A novel splitand- merge strategy is employed over the image sequence in which strain images are used to provide a priori knowledge of the relative stiffness distribution of the tissue to constrain the inverse problem solution. The experimental study has allowed us to investigate the performance of our approach in the controlled environment of simulated and phantom data. For a simulated single inclusion model with 5% axial displacement estimation error, the L2-error between the target and the reconstructed Young's modulus was found to be about 1%. In vivo validation of the proposed method has been carried out and some preliminary results are presented.     

Measuring the nonlinear elastic properties of tissue-like phantoms

A direct mechanical system simultaneously measuring external force and deformation of samples over a wide dynamic range is used to obtain force-displacement curves of tissue-like phantoms under plain strain deformation. These measurements, covering a wide deformation range, then are used to characterize the nonlinear elastic properties of the phantom materials. The model assumes incompressible media, in which several strain energy potentials are considered. Finite-element analysis is used to evaluate the performance of this material characterization procedure. The procedures developed allow calibration of nonlinear elastic phantoms for elasticity imaging experiments and finite-element simulations.     

Target detectability in acoustic elastography

The clinically relevant task of visually detecting low contrast targets in noisy strain images estimated from ultrasonic signals is studied. Detectability is measured quantitatively using contrast-to-noise ratio (CNR) analysis. Contrast in strain images is generated by a complex interaction among the soft tissue elasticity shear modulus distribution, target shape and location in the stress field, and external boundary conditions. Although a large strain variation is preferred for enhancing the contrast, this also increases the signal-dependent noise in strain estimates in a nonlinear fashion. Therefore, understanding the tradeoffs between contrast and noise is necessary for improving the diagnostic performance of strain imaging. In this paper, targets with slab, cylindrical, and spherical geometries are studied. Strains in the target and background and the precision of their estimates are described in terms of the corresponding shear modulus values for each geometry. These results are then incorporated into the CNR expression to investigate the changes in target detectability with the variation of shear modulus in the target and the ultrasonic signal parameters (echo signal-to-noise ratio and inverse fractional bandwidth) as well as the signal processing variables (time-bandwidth product and fractional window overlap).     

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.     

Nonlinear elastic equation of state of solids subjected to uniaxial homogeneous loading

Applying the finite deformation theory to a solid, which possesses either cubic or isotropic symmetry at stress-free natural state and is subsequently loaded homogeneously in uniaxial direction, one obtains a stress (or strain) dependence of the Young's modulus, Poisson's ratio, and a volume (or density) change, together with a nonlinear elastic relation between stress and strain. These are all expressed in terms of the second and third order elastic constants of the solid material. These expressions are illustrated with examples of cubic silicon crystal, isotropic carbon steel, Pyrex glass, and polystyrene at the relaxed state.     

Model-based reconstructive elasticity imaging of deep venous thrombosis

Deep venous thrombosis (DVT) and its sequela, pulmonary embolism, is a significant clinical problem. Once detected, DVT treatment is based on the age of the clot. There are no good noninvasive methods, however, to determine clot age. Previously, we demonstrated that imaging internal mechanical strains can identify and possibly age thrombus in a deep vein. In this study the deformation geometry for DVT elasticity imaging and its effect on Young's modulus estimates is addressed. A model-based reconstruction method is presented to estimate elasticity in which the clot-containing vessel is modeled as a layered cylinder. Compared to an unconstrained approach in reconstructive elasticity imaging, the proposed model-based approach has several advantages: only one component of the strain tensor is used; the minimization procedure is very fast; the method is highly efficient because an analytic solution of the forward elastic problem is used; and the method is not very sensitive to the details of the external load pattern--a characteristic that is important for free-hand, external, surface-applied deformation. The approach was tested theoretically using a numerical model, and experimentally on both tissue-like phantoms and an animal model of DVT. Results suggest that elasticity reconstruction may prove to be a practical adjunct to triplex scanning to detect, diagnose, and stage DVT.     

Silver Nanoflower Decorated Graphene Oxide Sponges for Highly Sensitive Variable Stiffness Stress Sensors

Soft conductive materials should enable large deformation while keeping high electrical conductivity and elasticity. The graphene oxide (GO)‐based sponge is a potential candidate to endow large deformation. However, it typically exhibits low conductivity and elasticity. Here, the highly conductive and elastic sponge composed of GO, flower‐shaped silver nanoparticles (AgNFs), and polyimide (GO‐AgNF‐PI sponge) are demonstrated. The average pore size and porosity are 114 µm and 94.7%, respectively. Ag NFs have thin petals (8–20 nm) protruding out of the surface of a spherical bud (300–350 nm) significantly enhancing the specific surface area (2.83 m² g^?1). The electrical conductivity (0.306 S m^?1 at 0% strain) of the GO‐AgNF‐PI sponge is increased by more than an order of magnitude with the addition of Ag NFs. A nearly perfect elasticity is obtained over a wide compressive strain range (0–90%). The strain‐dependent, nonlinear variation of Young's modulus of the sponge provides a unique opportunity as a variable stiffness stress sensor that operates over a wide stress range (0–10 kPa) with a high maximum sensitivity (0.572 kPa^?1). It allows grasping of a soft rose and a hard bottle, with the minimal object deformation, when attached on the finger of a robot gripper.     

Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up

Collagen constitutes one-third of the human proteome, providing mechanical stability, elasticity, and strength to organisms and is the prime construction material in biology. Collagen is also the dominating material in the extracellular matrix and its stiffness controls cell differentiation, growth, and pathology. However, the origin of the unique mechanical properties of collagenous tissues, and in particular its stiffness, extensibility, and nonlinear mechanical response at large deformation, remains unknown. By using X-ray diffraction data of a collagen fibril (Orgel, J. P. R. O. et al. Proc. Natl. Acad. Sci. 2006, 103, 9001) here we present an experimentally validated model of the nanomechanics of a collagen microfibril that incorporates the full biochemical details of the amino acid sequence of constituting molecules and the nanoscale molecular arrangement. We demonstrate by direct mechanical testing that hydrated (wet) collagen microfibrils feature a Young's modulus of ≈300 MPa at small, and ≈1.2 GPa at larger deformation in excess of 10% strain, which is in excellent agreement with experimental data. We find that dehydrated (dry) collagen microfibrils show a significantly increased Young's modulus of ≈1.8-2.25 GPa, which is in agreement with experimental measurements and owing to tighter molecular packing. Our results show that the unique mechanical properties of collagen microfibrils arise due to their hierarchical structure at the nanoscale, where key deformation mechanisms are straightening of twisted triple-helical molecules at small strains, followed by axial stretching and eventual molecular uncoiling. The establishment of a model of hierarchical deformation mechanisms explains the striking difference of the elastic modulus of collagen fibrils compared with single molecules, which is found in the range of 4.8 ± 2 GPa, or ≈10-20 times greater. We find that collagen molecules alone are not capable of providing the broad range of mechanical functionality required for physiological function of collagenous tissues. Rather, the existence of an array of deformation mechanisms, derived from the hierarchical makeup of the material, is critical to the material's ability to confer key mechanical properties, specifically large extensibility, strain hardening, and toughness, despite the limitation that collagenous materials are constructed from only few distinct amino acids. The atomistic model of collagen microfibril mechanics now enables the bottom-up elucidation of structure-property relationships in a broader class of collagen materials (e.g., tendon, bone, cornea), including studies of genetic disease where the incorporation of biochemical details is essential. The availability of a molecular-based model of collagen tissues may eventually result in novel nanomedicine approaches to develop treatments for a broad class of collagen diseases and the design of de novo biomaterials for regenerative medicine.     

Frequency dependency of Young's modulus of dental cocomposites

The Young's modulus of 15 commercial dental particulate filled composites was measured with three different methods. The materials were tested with static, low-frequency, and high-frequency elastic deformations. The analysis of the results shows that the frequency dependence of the Young's modulus of elasticity follows the same empirical law for all frequencies. Furthermore, knowledge of the Young's modulus for the resin component at all frequencies suffices to predict the Young's modulus of any particulate-filled composite.     

Reconstructive elasticity imaging for large deformations

A method is presented to reconstruct the elastic modulus of soft tissue based on ultrasonic displacement and strain images for comparatively large deformations. If the average deformation is too large to be described with a linear elastic model, nonlinear displacement-strain relations must be used and the mechanical equilibrium equations must include high order spatial derivatives of the displacement. Numerical methods were developed to reduce error propagation in reconstruction algorithms, including these higher order derivatives. Problems arising with the methods, as well as results using ultrasound measurements on gel-based, tissue equivalent phantoms, are given. Comparison to reconstructions using a linear elastic model shows that equivalent image quality can be produced with algorithms appropriate for finite amplitude deformations.     

Use of longitudinal ultrasonic velocity as a predictor of elastic moduli and density of sintered uranium dioxide

Nondestructive characterization of sintered uranium dioxide using ultrasonics is addressed. The values of elastic moduli and ultrasonic velocity of uranium dioxide as a function of pore volume fraction are compared with the predicted values of elasticity and self-consistent scattering theories. Analysis of data shows that the longitudinal ultrasonic velocity may be used as a predictor of density and elastic moduli and that the relationship between the elastic moduli and longitudinal velocity is linear over a change of Young's modulus by 50%     

Instrumented indentation and ultrasonic velocity techniques for the evaluation of creep cavitation in silicon nitride

Instrumented indentation and ultrasonic wave velocity techniques combined with precise density change measurements and transmission electron microscopy (TEM) were used to investigate the changes of elastic moduli in silicon nitride after tensile deformation up to 3%. Linear dependencies on strain were also found for the degradation of the indentation modulus, longitudinal and transverse ultrasonic wave velocities, Young's, shear and bulk moduli and Poisson's ratio. The results obtained by indentation technique and ultrasonic method were essentially identical. TEM observation confirmed that multigrain junction cavities were responsible for the density changes and the elastic moduli degradation. The density changes were linearly proportional to tensile strain with the slope of 0.75. Thus, cavitation is the dominant creep mechanism in silicon nitride studied. Instrumented indentation and ultrasound velocity techniques are suitable for non-destructive monitoring of creep damage accumulation in ceramic components.     

Contribution of damage by multiple crack growth to the strain-rate sensitivity of a polycrystalline alumina at elevated temperatures

The strength of a polycrystalline aluminium oxide measured in four-point bending at elevated temperatures over a range of displacement-controlled loading rates was observed to exhibit an unusually high strain-rate dependence. Scanning electron microscopy revealed that at the lower values of strain-rate, failure was accompanied by the formation of a number of additional macrocracks adjacent to the plane of fracture. Separate measurements of specimens deformed to approximately 75% of the fracture strain indicated that, at these lower values of strain rate, the effective Young's modulus was decreased by as much as a factor of two. It is suggested that the high strain-rate sensitivity was the direct result of a strain-rate dependent decrease in Young's modulus and associated effect of strain-softening for conditions of displacement-rate controlled mechanical loading. The validity of this hypothesis was verified by a fracture-mechanics analysis of a mechanical model subjected to displacement-controlled tensile loading, with elastic behaviour expressed in terms of the effect of cracks on continuum elastic properties.     

Estimation of polyvinyl alcohol cryogel mechanical properties with four ultrasound elastography methods and comparison with gold standard testings

Tissue-mimicking phantoms are very useful in the field of tissue characterization and essential in elastography for the purpose of validating motion estimators. This study is dedicated to the characterization of polyvinyl alcohol cryogel (PVA-C) for these types of applications. A strict fabrication procedure was defined to optimize the reproducibility of phantoms having a similar elasticity. Following mechanical stretching tests, the phantoms were used to compare the accuracy of four different elastography methods. The four methods were based on a one-dimensional (1-D) scaling factor estimation, on two different implementations of a 2-D Lagrangian speckle model estimator (quasistatic elastography methods), and on a 1-D shear wave transient elastography technique (dynamic method). Young's modulus was investigated as a function of the number of freeze-thaw cycles of PVA-C, and of the concentration of acoustic scatterers. Other mechanical and acoustic parameters-such as the speed of sound, shear wave velocity, mass density, and Poisson's ratio-also were assessed. The Poisson's ratio was estimated with good precision at 0.499 for all samples, and the Young's moduli varied in a range of 20 kPa for one freeze-thaw cycle to 600 kPa for 10 cycles. Nevertheless, above six freeze-thaw cycles, the results were less reliable because of sample geometry artifacts. However, for the samples that underwent less than seven freeze-thaw cycles, the Young's moduli estimated with the four elastography methods showed good matching with the mechanical tensile tests with a regression coefficient varying from 0.97 to 1.07, and correlations R2 varying from 0.93 to 0.99, depending on the method.     

Characterizing the viscoelastic properties of thin hydrogel-based constructs for tissue engineering applications.

We present a novel indentation method for characterizing the viscoelastic properties of alginate and agarose hydrogel based constructs, which are often used as a model system of soft biological tissues. A sensitive long working distance microscope was used for measuring the time-dependent deformation of the thin circular hydrogel membranes under a constant load. The deformation of the constructs was measured laterally. The elastic modulus as a function of time can be determined by a large deformation theory based on Mooney-Rivlin elasticity. A viscoelastic theory, Zener model, was applied to correlate the time-dependent deformation of the constructs with various gel concentrations, and the creep parameters can therefore be quantitatively estimated. The value of Young's modulus was shown to increase in proportion with gel concentration. This finding is consistent with other publications. Our results also showed the great capability of using the technique to measure gels with incorporated corneal stromal cells. This study demonstrates a novel and convenient technique to measure mechanical properties of hydrogel in a non-destructive, online and real-time fashion. Thus this novel technique can become a valuable tool for soft tissue engineering.     

An elasticity microscope. Part II: Experimental results

For pt.I see ibid., vol.44, no.6, pp.1304-19 (1997). Initial experimental results from a 50 MHz elasticity microscope are shown. Using methods discussed previously, we present measured displacement and normal axial strain fields from a tissue mimicking phantom. Results from this homogenous gel are compared to a finite element simulation of the deformation experiment. The spatial resolution is estimated to be approximately 52 μm for axial displacements, and 71 μm for normal axial strains. These estimates were further tested by imaging a phantom containing a hard cylindrical inclusion with cross-sectional diameter of 265 μm. By examining the strain transition between regions in this image, the spatial resolution of the normal axial strain was verified to be at most 88 μm. A typical experiment produces peak normal axial strain around 3%. These experiments demonstrate the potential of high frequency ultrasound as a means for elasticity microscopy. Preliminary deformation experiments are presented on porcine epidermis     

Elastic property measurement using Rayleigh-Lamb waves

A nondestructive technique is described for the measurement of elastic constants of isotropic plates using ultrasonic Rayleigh-Lamb waves. The experimental method employs continuous harmonic waves and a pair of variable-angle contact transducers in pitch-catch mode. The phase velocity of the R-L waves at a particular frequency is determined from the phase shift over a measured path length. This simple experimental technique can measure phase velocity over the range 1–10 mm/µs with an error of less than 0.5% over a frequency range of 50 kHz-2 MHz. Individual symmetric and antisymmetric modes can be generated through the selection of transducer angle and frequency. Young's modulus and Poisson's ratio for the material are calculated from measurements of frequency and phase velocity by a nonlinear least squares solution to the dispersion equations. The sensitivity of the nonlinear least squares function to the measurement region of the dispersion curve is investigated. It was found that estimations of material properties are more accurate and less sensitive to small experimental errors when only selected frequencies and R-L modes are used in the least squares calculation. This technique is demonstrated with several isotropic materials and with both thick (6 mm) and thin (0.8 mm) plates. Values for elastic constants determined by the contact transducer Lamb wave technique compare favorably with values measured using the pulse-echo-overlap method. The uncertainty in measurements of Young's modulus and Poisson's ratio was less than 1% and 2%, respectively. The technique has advantages over more traditional methods for measuring elastic properties when it is desirable to use wavelengths greater than the plate thickness, when properties may vary with frequency, or when it is necessary to measure in-plane elastic properties of thin plate structures.     

Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.     

Description of depth-dependent nonlinear viscoelastic behavior for articular cartilage in unconfined compression

An optimized digital image correlation (DIC) technique was applied to investigate the depth-dependent nonlinear viscoelastic properties of articular cartilage and simultaneously the biphasic nonlinear viscoelastic relaxation model of cartilage was proposed and validated. The stress relaxation tests were performed with different strain levels and it is found that the initial stress and relaxed stress at any time increase with increasing strain levels. The depth-dependent strain of cartilage was obtained by analyzing the images acquired using the optimized DIC technique and moreover the inhomogeneous relaxation modulus distributions within the tissues were determined at different relaxation time points under strain of 11.35, 19.35 and 30% respectively. The strain rate dependent nonlinear stress and strain curves were obtained for articular cartilage through uniaxial compression tests. It is noted that the Young's modulus exhibits a slight increase near the cartilage surface, and then increases fast with depth and both the magnitude and the variation of the Young's modulus are affected by increasing strain rates. A biphasic nonlinear viscoelastic relaxation model was proposed to predict the depth-dependent relaxation behavior of cartilage under unconfined compression and the results show that there are good agreements between the experimental data and predictions.     

Mechanical characterization of Co/Cu multilayered nanowires

The mechanical deformation properties of (110) Co/Cu multilayered nanowires were studied by Molecular Dynamics under uniaxial tensile and compressive stresses. The potential of the immiscible CoCu system was modeled by a second-moment tight-binding approximation. Stress-strain curves at different conditions were obtained and the elastic modulus and yield stress were analyzed. Both magnitudes are approximately independent of the strain rate, except at high values. They decrease linearly with increasing temperature. Below a volume-to-surface-area ratio, their values drastically increase and diverge from the bulk values. If the thickness of the Cu sublayers increases, the Young's modulus and yield stress decrease, although in a different way. The elastic modulus decreases linearly and the yield stress falls steeply whenever Cu is present in the nanowire, since the lattice distortion takes place firstly and fundamentally in Cu sublayers. The change in the axial stress at the interface is little significant on average and rather localized. Unlike, the transverse stress has a non-uniform distribution along the Cu sublayer, especially at the yield point. The Young's modulus and yield stress are larger in tension than in compression. Under tensile stress, nanowires slip via partial dislocation nucleation and propagation. Unlike, compressive deformation of nanowires takes place via both partial and full dislocations.