Acoustoelasticity in soft solids: assessment of the nonlinear shear modulus with the acoustic radiation force

SWENet: A Physics-Informed Deep Neural Network (PINN) for Shear Wave Elastography

Shear wave elastography (SWE) enables the measurement of elastic properties of soft materials in a non-invasive manner and finds broad applications in various disciplines. The state-of-the-art SWE methods rely on the measurement of local shear wave speeds to infer material parameters and suffer from wave diffraction when applied to soft materials with strong heterogeneity. In the present study, we overcome this challenge by proposing a physics-informed neural network (PINN)-based SWE (SWENet) method. The spatial variation of elastic properties of inhomogeneous materials has been introduced in the governing equations, which are encoded in SWENet as loss functions. Snapshots of wave motions have been used to train neural networks, and during this course, the elastic properties within a region of interest illuminated by shear waves are inferred simultaneously. We performed finite element simulations, tissue-mimicking phantom experiments, and ex vivo experiments to validate the method. Our results show that the shear moduli of soft composites consisting of matrix and inclusions of several millimeters in cross-section dimensions with either regular or irregular geometries can be identified with excellent accuracy. The advantages of the SWENet over conventional SWE methods consist of using more features of the wave motions and enabling seamless integration of multi-source data in the inverse analysis. Given the advantages of SWENet, it may find broad applications where full wave fields get involved to infer heterogeneous mechanical properties, such as identifying small solid tumors with ultrasound SWE, and differentiating gray and white matters of the brain with magnetic resonance elastography.

In Vivo Ultrasound Shear Wave Elastography Assessment of Acute Compartment Syndrome in a Turkey Model

OBJECTIVE

The aim of the work described here was to evaluate the objectivity and reproducibility of non-invasive intra-compartment pressure (ICP) measurement using ultrasound shear wave elastography (SWE) in a turkey model in vivo and to determine the biological and histologic changes in acute compartment syndrome (ACS).

METHODS

Twenty-four turkeys were randomly divided into four groups based on the duration and fasciotomy of ACS created by infusion of up to 50 mm Hg in the tibialis muscle: group 1, ACS 2 h; group 2, ACS 4 h; group 3, ACS 2 h + fasciotomy 2 h; group 4, ACS 4 h + fasciotomy 2 h. For each turkey, the contralateral limb was considered the control. Time-synchronized measures of SWE and ICP from each leg were collected. Then turkeys were euthanized for histology and quantitative reverse transcription polymerase chain reaction (qRT-PCR) examination.

RESULTS

All models created reproducible increases in ICP and SWE, which had a strong linear relationship (r = 0.802, p < 0.0001) during phase 1. SWE remained stable (50.86 ± 9.64 kPa) when ICP remained at 50.28 ± 2.17 mm Hg in phase 2. After fasciotomy, SWE declined stepwise and then normalized (r = 0.737, p < 0.0001). Histologically, the myofiber diameter of group 2 (82.31 ± 22.92 μm) and group 4 (90.90 ± 20.48 μm) decreased significantly (p < 0.01) compared with that of the control group (103.1 ± 20.39 μm); the interstitial space of all groups increased significantly (p < 0.01). Multifocal muscle damage revealed neutrophilic infiltration, degeneration, hemorrhage and necrosis, especially in group 4. Quantitative RT-PCR verified that interleukin-6 and heparin-binding EGF-like growth factor were significantly increased in group 4.

CONCLUSION

SWE provided sensitive measurements correlating to ICP in a clinically relevant ACS animal model. Once ACS time was exceeded, progression to irreversible necrosis continued spontaneously, even after fasciotomy. SWE may help surgeons in the early detection, monitoring, prognosis and decision making on fasciotomy for ACS.

Effect of interstitial fluid pressure on shear wave elastography: an experimental and computational study

Objective. An elevated interstitial fluid pressure (IFP) can lead to strain-induced stiffening of poroelastic biological tissues. As shear wave elastography (SWE) measures functional tissue stiffness based on the propagation speed of acoustically induced shear waves, the shear wave velocity (SWV) can be used as an indirect measurement of the IFP. The underlying biomechanical principle for this stiffening behavior with pressurization is however not well understood, and we therefore studied how IFP affects SWV through SWE experiments and numerical modeling.Approach. For model set-up and verification, SWE experiments were performed while dynamically modulating IFP in a chicken breast. To identify the confounding factors of the SWV-IFP relationship, we manipulated the material model (linear poroelastic versus porohyperelastic), deformation assumptions (geometric linearity versus nonlinearity), and boundary conditions (constrained versus unconstrained) in a finite element model mimicking the SWE experiments.Main results. The experiments demonstrated a statistically significant positive correlation between the SWV and IFP. The model was able to reproduce a similar SWV-IFP relationship by considering an unconstrained porohyperelastic tissue. Material nonlinearity was identified as the primary factor contributing to this relationship, whereas geometric nonlinearity played a smaller role. The experiments also highlighted the importance of the dynamic nature of the pressurization procedure, as indicated by a different observed SWV-IFP for pressure buildup and relaxation, but its clinical relevance needs to be further investigated.Significance. The developed model provides an adaptable framework for SWE of poroelastic tissues and paves the way towards non-invasive measurements of IFP.

Viscoelastic dynamics of a soft strip subject to a large deformation

To produce sounds, we adjust the tension of our vocal folds to shape their properties and control the pitch. This efficient mechanism offers inspiration for designing reconfigurable materials and adaptable soft robots. However, understanding how flexible structures respond to a significant static strain is not straightforward. This complexity also limits the precision of medical imaging when applied to tensioned organs like muscles, tendons, ligaments and blood vessels among others. In this article, we experimentally and theoretically explore the dynamics of a soft strip subject to a substantial static extension, up to 180%. Our observations reveal a few intriguing effects, such as the resilience of certain vibrational modes to a static deformation. These observations are supported by a model based on the incremental displacement theory. This has promising practical implications for characterizing soft materials but also for scenarios where external actions can be used to tune properties.

The evaluation of retrobulbar fat tissue in Graves' orbitopathy with shear-wave ultrasound elastography

PURPOSE

To evaluate retrobulbar adipose tissue of patients with active and inactive Graves' orbitopathy (GO) by shear-wave ultrasound elastography (SWE).

METHODS

Followed-up in our ophthalmology clinic due to GO, 72 eyes of 36 patients and 38 eyes of 19 healthy controls were included in this cross-sectional case-control study. Graves' patients were divided into two subgroups under clinical activity score (CAS): active Graves' orbitopathy (AGO) (CAS ≥ 3) and inactive Graves' orbitopathy (IGO) (CAS < 3). SWE measurement values of retrobulbar adipose tissue of all participants were recorded in meters/second, and the intergroup comparisons were performed.

RESULTS

Thirty-four eyes of 17 patients in AGO, 38 eyes of 19 patients in IGO, and 38 eyes of 19 participants in the control group were included in the study. Mean values measured from retrobulbar adipose tissue through SWE were 1.00 ± 0.01 m/sec in AGO, 1.16 ± 0.01 m/sec in IGO, and 0.94 ± 0.01 m/sec in the control groups. Even so, the mean SWE value was significantly higher in the IGO group than in the other groups (p < 0.001). Mean SWE values were significantly higher in the AGO group than in the controls (p = 0.008). In the correlation analysis performed, a significant positive correlation was found between SWE and Hertel exophthalmometer measurement values (p = 0.026, r = 0.212), and thyroid-stimulating hormone receptor antibody (TSHR-Ab) levels (p = 0.018, r = 0.224).

CONCLUSION

We detected SWE values of retrobulbar adipose tissue high in GO, especially in the IGO group. Such a situation, which we associated with the development of fibrosis, may be an indicator of unresponsiveness to immunomodulatory treatments.

Unravelling anisotropic nonlinear shear elasticity in muscles: Towards a non-invasive assessment of stress in living organisms

Acoustoelasticity theory describes propagation of shear waves in uniaxially stressed medium and allows the retrieval of nonlinear elastic coefficients of tissues. In transverse isotropic medium such as muscles the theory leads to 9 different configurations of propagating shear waves (stress axis vs. fibers axis vs. shear wave polarization axis vs. shear wave propagation axis). In this work we propose to use 4 configurations to quantify these nonlinear parameters ex vivo and in vivo. Ex vivo experiments combining ultrasound shear wave elastography and mechanical testing were conducted on iliopsoas pig muscles to quantify three third-order nonlinear coefficients A, H and K that are possibly linked to the architectural structure of muscles. In vivo experiments were performed with human volunteers on biceps brachii during a stretching exercise on an ergometer. A combination of the third order nonlinear elastic parameters was assessed. The knowledge of this nonlinear elastic parameters paves the way to quantify in vivo the local forces produced by muscle during exercise, contraction or movements.

Chinese Ultrasound Doctors Association Guideline on Operational Standards for 2-D Shear Wave Elastography Examination of Musculoskeletal Tissues

The Ultrasound Physician Branch of the Chinese Medical Doctor Association sought to develop evidence-based recommendations on the operational standards for 2-D shear wave elastography examination of musculoskeletal tissues. A consensus panel of 22 Chinese musculoskeletal ultrasound experts reviewed current scientific evidence and proposed a set of 12 recommendations for 13 key issues, including instruments, operating methods, influencing factors and image interpretation. A final consensus was reached through discussion and voting. On the basis of research evidence and expert opinions, the strength of recommendation for each proposition was assessed using a visual analog scale, while further emphasizing the best available evidence during the question-and-answer session. These expert consensus guidelines encourage facilitation of the standardization of clinical practices for collecting and reporting shear wave elastography data.

Nonlinear fourth-order elastic characterization of the cornea using torsional wave elastography

Measuring the mechanical nonlinear properties of the cornea remains challenging due to the lack of consensus in the methodology and in the models that effectively predict its behaviour. This study proposed developing a procedure to reconstruct nonlinear fourth-order elastic properties of the cornea based on a mathematical model derived from the theory of Hamilton et al. and using the torsional wave elastography (TWE) technique. In order to validate its diagnostic capability of simulated pathological conditions, two different groups were studied, non-treated cornea samples (n=7), and ammonium hydroxide ([Formula: see text]) treated samples (n=7). All the samples were measured in-plane by a torsional wave device by increasing IOP from 5 to 25 mmHg with 5 mmHg steps. The results show a nonlinear variation of the shear wave speed with the IOP, with higher values for higher IOPs. Moreover, the shear wave speed values of the control group were higher than those of the treated group. The study also revealed significant differences between the control and treated groups for the Lamé parameter [Formula: see text] (25.9-6.52 kPa), third-order elastic constant A (215.09-44.85 kPa), and fourth-order elastic constant D (523.5-129.63 kPa), with p-values of 0.010, 0.024, and 0.032, respectively. These findings demonstrate that the proposed procedure can distinguish between healthy and damaged corneas, making it a promising technique for detecting diseases associated with IOP alteration, such as corneal burns, glaucoma, or ocular hypertension.

Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

Load sharing between synergistic muscles characterized by a ligand-binding approach and elastography

The skeletal muscle contraction is determined by cross-bridge formation between the myosin heads and the actin active sites. When the muscle contracts, it shortens, increasing its longitudinal shear elastic modulus ([Formula: see text]). Structurally, skeletal muscle can be considered analogous to the molecular receptors that form receptor-ligand complexes and exhibit specific ligand-binding dynamics. In this context, this work aims to apply elastography and the ligand-binding framework to approach the possible intrinsic mechanisms behind muscle synergism. Based on the short-range stiffness principle and the acoustic-elasticity theory, we define the coefficient [Formula: see text], which is directly related to the fraction saturation of molecular receptors and links the relative longitudinal deformation of the muscle to its [Formula: see text]. We show that such a coefficient can be obtained directly from [Formula: see text] estimates, thus calculating it for the biceps brachii, brachioradialis, and brachialis muscles during isometric elbow flexion torque (τ) ramps. The resulting [Formula: see text] curves were analyzed by conventional characterization methods of receptor-ligand systems to study the dynamical behavior of each muscle. The results showed that, depending on muscle, [Formula: see text] exhibits typical ligand-binding dynamics during joint torque production. Therefore, the above indicates that these different behaviors describe the longitudinal shortening pattern of each muscle during load sharing. As a plausible interpretation, we suggested that this could be related to the binding kinetics of the cross-bridges during their synergistic action as torque increases. Likewise, it shows that elastography could be useful to assess contractile processes at different scales related to the change in the mechanical properties of skeletal muscle.

The fundamental mechanisms of the Korotkoff sounds generation

Blood pressure measurement is the most widely performed clinical exam to predict mortality risk. The gold standard for its noninvasive assessment is the auscultatory method, which relies on listening to the so-called "Korotkoff sounds" in a stethoscope placed at the outlet of a pneumatic arm cuff. However, more than a century after their discovery, the origin of these sounds is still debated, which implies a number of clinical limitations. We imaged the Korotkoff sound generation in vivo at thousands of images per second using ultrafast ultrasound. We showed with both experience and theory that Korotkoff sounds are paradoxically not sound waves emerging from the brachial artery but rather shear vibrations conveyed in surrounding tissues by the nonlinear pulse wave propagation. When these shear vibrations reached the stethoscope, they were synchronous, correlated, and comparable in intensity with the Korotkoff sounds. Understanding this mechanism could ultimately improve blood pressure measurement and provide additional understanding of arterial mechanical properties.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,μ0US= 12.3 ± 0.3 kPa andμ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

Imaging fibrosis in pediatric kidney transplantation: A pilot study

BACKGROUND

Noninvasive alternatives to biopsy for assessment of interstitial fibrosis and tubular atrophy (IFTA), the major determinant of kidney transplant failure, remain profoundly limited. Elastography is a noninvasive technique that propagates shear waves across tissues to measure their stiffness. We aimed to test utility of elastography for early detection of IFTA in pediatric kidney allografts.

METHODS

We compared ultrasound (USE) and MR elastography (MRE) stiffness measurements, performed on pediatric transplant recipients referred for clinically indicated biopsies, and healthy controls.

RESULTS

Ten transplant recipients (median age 16 years) and eight controls (median age 16.5 years) were enrolled. Three transplant recipients had "stable" allografts and seven had Banff Grade 1 IFTA. Median time from transplantation to biopsy was 12 months. Mean estimated glomerular filtration rate was 61.5 mL/min/1.73m2 by creatinine-cystatin-C CKiD equation at time of biopsy. Mean stiffness, calculated through one-way ANOVA, was higher for IFTA allografts (23.4 kPa USE/5.6 kPa MRE) than stable allografts (13.7 kPa USE/4.4 kPa MRE) and controls (9.1 kPa USE/3.6 kPa MRE). Pearson's coefficient between USE and MRE stiffness values was strong (r = .97). AUC for fibrosis prediction in transplanted kidneys was high for both modalities (0.91 USE and 0.89 MRE), although statistically nonsignificant (p > .05). Stiffness cut-off values for USE and MRE were 13.8 kPa and 4.6 kPa, respectively. Both values yielded a sensitivity of 100% but USE specificity (72%) was slightly higher than MRE (67%).

CONCLUSION

Elastography shows potential for detection of low-grade IFTA in allografts although a larger sample is imperative for clinical validation.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.

Noninvasive measurement of local stress inside soft materials with programmed shear waves

Mechanical stresses across different length scales play a fundamental role in understanding biological systems' functions and engineering soft machines and devices. However, it is challenging to noninvasively probe local mechanical stresses in situ, particularly when the mechanical properties are unknown. We propose an acoustoelastic imaging-based method to infer the local stresses in soft materials by measuring the speeds of shear waves induced by custom-programmed acoustic radiation force. Using an ultrasound transducer to excite and track the shear waves remotely, we demonstrate the application of the method by imaging uniaxial and bending stresses in an isotropic hydrogel and the passive uniaxial stress in a skeletal muscle. These measurements were all done without the knowledge of the constitutive parameters of the materials. The experiments indicate that our method will find broad applications, ranging from health monitoring of soft structures and machines to diagnosing diseases that alter stresses in soft tissues.

Biaxial Tensile Prestress and Waveguide Effects on Estimates of the Complex Shear Modulus Using Optical-Based Dynamic Elastography in Plate-Like Soft Tissue Phantoms

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a novel configuration, inspired by corneal elastography but generalizable to other applications, is studied. A polymer phantom layer is statically elongated via an in-plane biaxial normal stress while the phantom's response to transverse vibratory excitation is measured. We examine the interplay between biaxial prestress and waveguide effects in this plate-like tissue phantom. Finite static deformations caused by prestressing coupled with waveguide effects lead to results that are predicted by a novel coordinate transformation approach previously used to simplify reconstruction of anisotropic properties. Here, the approach estimates material viscoelastic properties independent of the nonzero prestress conditions without requiring advanced knowledge of those stress conditions.

Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness?

Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Phase and group velocities for shear wave propagation in an incompressible, hyperelastic material with uniaxial stretch

Objective. Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch. Approach. Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities. Main results. Sample results are presented for the Arruda–Boyce, Mooney–Rivlin, and Isihara material models using model parameters previously determined in a phantom. Significance. Results for the Mooney–Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda–Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.

Nonlinear Elasticity Assessment with Optical Coherence Elastography for High-Selectivity Differentiation of Breast Cancer Tissues

Soft biological tissues, breast cancer tissues in particular, often manifest pronounced nonlinear elasticity, i.e., strong dependence of their Young’s modulus on the applied stress. We showed that compression optical coherence elastography (C-OCE) is a promising tool enabling the evaluation of nonlinear properties in addition to the conventionally discussed Young’s modulus in order to improve diagnostic accuracy of elastographic examination of tumorous tissues. The aim of this study was to reveal and quantify variations in stiffness for various breast tissue components depending on the applied pressure. We discussed nonlinear elastic properties of different breast cancer samples excised from 50 patients during breast-conserving surgery. Significant differences were found among various subtypes of tumorous and nontumorous breast tissues in terms of the initial Young’s modulus (estimated for stress < 1 kPa) and the nonlinearity parameter determining the rate of stiffness increase with increasing stress. However, Young’s modulus alone or the nonlinearity parameter alone may be insufficient to differentiate some malignant breast tissue subtypes from benign. For instance, benign fibrous stroma and fibrous stroma with isolated individual cancer cells or small agglomerates of cancer cells do not yet exhibit significant difference in the Young’s modulus. Nevertheless, they can be clearly singled out by their nonlinearity parameter, which is the main novelty of the proposed OCE-based discrimination of various breast tissue subtypes. This ability of OCE is very important for finding a clean resection boundary. Overall, morphological segmentation of OCE images accounting for both linear and nonlinear elastic parameters strongly enhances the correspondence with the histological slices and radically improves the diagnostic possibilities of C-OCE for a reliable clinical outcome.

A Non-invasive Method to Estimate the Stress-Strain Curve of Soft Tissue Using Ultrasound Elastography

Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress- strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress-strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress-strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress-strain curve for tissue-mimicking materials.

An in vivo model for overloading-induced soft tissue injury

This proof-of-concept study demonstrates that repetitive loading to the pain threshold can safely recreate overloading-induced soft tissue damage and that localised tissue stiffening can be a potential marker for injury. This concept was demonstrated here for the soft tissue of the sole of the foot where it was found that repeated loading to the pain threshold led to long-lasting statistically significant stiffening in the overloaded areas. Loading at lower magnitudes did not have the same effect. This method can shed new light on the aetiology of overloading injury in the foot to improve the management of conditions such as diabetic foot ulceration and heel pain syndrome. Moreover, the link between overloading and tissue stiffening, which was demonstrated here for the first time for the plantar soft tissue, opens the way for an assessment of overloading thresholds that is not based on the subjective measurement of pain thresholds.

The combined importance of finite dimensions, anisotropy, and pre-stress in acoustoelastography

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties that are altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasistatic tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article, we review how prestress alters both bulk mechanical wave motion and wave motion in one- and two-dimensional waveguides. Key findings are linked to studies on skeletal muscle and the human cornea, as one- and two-dimensional waveguide examples. This study highlights the underappreciated combined acoustoelastic and waveguide challenge to elastography. Can elastography truly determine viscoelastic properties of a material when what it is measuring is affected by both these material properties and unknown prestress and other boundary conditions?

Imaging the Local Nonlinear Viscoelastic Properties of Soft Tissues: Initial Validation and Expected Benefits

Imaging tissue mechanical properties has shown promise in noninvasive assessment of numerous pathologies. Researchers have successfully measured many linear tissue mechanical properties in laboratory and clinical settings. Currently, multiple complex mechanical effects such as frequency-dependence, anisotropy, and nonlinearity are being investigated separately. However, a concurrent assessment of these complex effects may enable more complete characterization of tissue biomechanics and offer improved diagnostic sensitivity. In this work, we report for the first time a method to map the frequency-dependent nonlinear parameters of soft tissues on a local scale. We recently developed a nonlinear elastography model that combines strain measurements from arbitrary tissue compression with radiation-force-based broadband shear wave speed (WS) measurements. Here, we extended this model to incorporate local measurements of frequency-dependent shear modulus. This combined approach provides a local frequency-dependent nonlinear parameter that can be obtained with arbitrary, clinically realizable tissue compression. Initial assessments using simulations and phantoms validate the accuracy of this approach. We also observed improved contrast in nonlinearity parameter at higher frequencies. Results from ex-vivo liver experiments show 32, 25, 34, and 38 dB higher contrast in elastograms than traditional linear elasticity, elastic nonlinearity, viscosity, and strain imaging methods, respectively. A lesion, artificially created by injection of glutaraldehyde into a liver specimen, showed a 59% increase in the frequency-dependent nonlinear parameter and a 17% increase in contrast ratio.

A unifying model of weakly nonlinear elastic waves; large on large theory

This article reconsiders traditional topics in nonlinear elastic waves and nonlinear ultrasonics. Herein, higher-order coupling between finite initial deformation and finite amplitude waves are considered. To allow for coupling, a large-on-large deformation model is developed and used to generate the equations of motion relative to the deformed and undeformed material configurations. Thus, the equations of motion provide a single setting to describe topics in nonlinear elastic waves such as acoustoelasticity, second harmonic generation, and coupling relations between these topics. The model is evaluated to recover the traditional linearized acoustoelastic relations and predicted second harmonic amplitudes. Then, the so-called large acoustoelasticity theory is developed for anisotropic materials with specific results given for isotropic materials. Last, the stress influence on second harmonic generation is presented.

Optical coherence elastography for assessing the influence of intraocular pressure on elastic wave dispersion in the cornea

The cornea is a highly specialized organ that relies on its mechanical stiffness to maintain its aspheric geometry and refractive power, and corneal diseases such as keratoconus have been linked to abnormal tissue stiffness and biomechanics. Dynamic optical coherence elastography (OCE) is a clinically promising non-contact and non-destructive imaging technique that can provide measurements of corneal tissue stiffness directly in vivo. The method relies on the concepts of elastography where shear waves are generated and imaged within a tissue to obtain mechanical properties such as tissue stiffness. The accuracy of OCE-based measurements is ultimately dependent on the mathematical theories used to model wave behavior in the tissue of interest. In the cornea, elastic waves propagate as guided wave modes which are highly dispersive and can be mathematically complex to model. While recent groups have developed detailed theories for estimating corneal tissue properties from guided wave behavior, the effects of intraocular pressure (IOP)-induced prestress have not yet been considered. It is known that prestress alone can strongly influence wave behavior, in addition to the associated non-linear changes in tissue properties. This present study shows that failure to account for the effects of prestress may result in overestimations of the corneal shear moduli, particularly at high IOPs. We first examined the potential effects of IOP and IOP-induced prestress using a combination of approximate mathematical theories describing wave behavior in thin plates with observations made from data published in the OCE literature. Through wave dispersion analysis, we deduce that IOP introduces a tensile hoop stress and may also influence an elastic foundational effect that were observable in the low-frequency components of the dispersion curves. These effects were incorporated into recently developed models of wave behavior in nearly incompressible, transversely isotropic (NITI) materials. Fitting of the modified NITI model with ex vivo porcine corneal data demonstrated that incorporation of the effects of IOP resulted in reduced estimates of corneal shear moduli. We believe this demonstrates that overestimation of corneal stiffness occurs if IOP is not taken into consideration. Our work may be helpful in separating inherent corneal stiffness properties that are independent of IOP; changes in these properties and in IOP are distinct, clinically relevant issues that affect the cornea health.

Nonlinear Characterization of Tissue Viscoelasticity With Acoustoelastic Attenuation of Shear Waves

Shear-wave elastography (SWE) measures shear-wave speed (SWS), which is related to the underlying shear modulus of soft tissue. SWS in soft tissue changes depending on the amount of external strain that soft tissue is subjected to due to the acoustoelastic (AE) phenomenon. In the literature, variations of SWS as a function of applied uniaxial strain were used for nonlinear characterization, assuming soft tissues to be elastic, although soft tissues are indeed viscoelastic in nature. Hence, nonlinear characterization using SWS alone is insufficient. In this work, we use SWS together with shear-wave attenuation (SWA) during incremental quasi-static compressions in order to derive biomechanical characterization based on the AE theory in terms of well-defined storage and loss moduli. As part of this study, we also quantify the effect of applied strain on measurements of SWS and SWA since such confounding effects need to be taken into account when using SWS and/or SWA, e.g., for staging a disease state, while such effects can also serve as an additional imaging biomarker. Our results from tissue-mimicking phantoms with varying oil percentages and ex vivo porcine liver experiments demonstrate the feasibility of our proposed methods. In both experiments, SWA was observed to decrease with applied strain. For 10% compression in ex vivo livers, shear-wave attenuation decreased, on average, by 28% (93 Np/m), while SWS increased, on average, by 20% (0.26 m/s).

Acoustoelasticity in transversely isotropic soft tissues: Quantification of muscle nonlinear elasticity

Recent developments in the field of elastography aim at developing the quantification of new mechanical properties of tissues, that are complementary to the shear modulus, which is characteristic of the linear elastic properties of a quasi-incompressible medium. In this context, measurement of the elastic nonlinearity of tissues was recently proposed based on acoustoelasticity. Up to now, most of the experimental applications of acoustoelasticity theory using Landau formalism in human tissues have assumed isotropy. However, this strong hypothesis does not hold in all human tissues, such as muscles that are generally considered as transversely isotropic (TI). In this work, after reviewing the constraints imposed by TI symmetry on the linear and nonlinear elastic properties of TI media, the acoustoelasticity theory in TI incompressible media is developed and implemented experimentally on a TI polyvinyl alcohol phantom and on ex vivo muscular tissues. Based on this theory and on the evolutions of the shear wave speed, with respect to uniaxial static stress, the nonlinear elastic parameter A is experimentally quantified. The estimations of A in ex vivo bovine and porcine muscles are on the order of hundreds of kPa. This work paves the way for more thorough muscle mechanical properties characterization as well as for the development of a potential new biomarker.

Noninvasive Assessment of In Vivo Passive Skeletal Muscle Mechanics as a Composite Material Using Biomedical Ultrasound

OBJECTIVE

This study develops a biomedical ultrasound imaging method to infer microstructural information (i.e., tissue level) from imaging mechanical behavior of skeletal muscle (i.e., organ level).

METHODS

We first reviewed the constitutive model of skeletal muscle by regarding it as a transversely isotropic (TI) hyperelastic composite material, for which a theoretical formula was established among shear wave speed, deformation, and material parameters (MPs) using the acoustoelasticity theory. The formula was evaluated by finite element (FE) simulations and experimentally examined using ultrasound shear wave imaging (SWI) and strain imaging (SI) on in vivo passive biceps brachii muscles of two healthy volunteers. The imaging sequence included 1) generation of SW in multiple propagation directions while resting the muscle at an elbow angle of 90; 2) generation of SW propagating along the myofiber direction during continuous uniaxial muscle extension by passively changing the elbow angle from 90 to 120. Ultrasound-quantified SW speeds and muscle deformations were fitted by the theoretical formula to estimate MPs of in vivo passive muscle.

RESULTS

Estimated myofiber stiffness, stiffness ratio of myofiber to extracellular matrix (ECM), ECM volume ratio all agreed with literature findings.

CONCLUSION

The proposed mathematical formula together with our in-house ultrasound imaging method enabled assessing microstructural material properties of in vivo passive skeletal muscle from organ-level mechanical behavior in an entirely noninvasive way.

SIGNIFICANCE

Noninvasive assessment of both micro and macro properties of in vivo skeletal muscle will advance our understanding of complex muscle dynamics and facilitate treatment and rehabilitation planning.

Speed of sound and shear wave speed for calf soft tissue composition and nonlinearity assessment

Background

The purpose of this study was threefold: (I) to study the correlation of speed-of-sound (SoS) and shear-wave-speed (SWS) ultrasound (US) in the gastrocnemius muscle, (II) to use reproducible tissue compression to characterize tissue nonlinearity effects, and (III) to compare the potential of SoS and SWS for tissue composition assessment.

Methods

Twenty gastrocnemius muscles of 10 healthy young subjects (age range, 23-34 years, two females and eight males) were prospectively examined with both clinical SWS (GE Logiq E9, in m/s) and a prototype system that measures SoS (in m/s). A reflector was positioned opposite the US probe as a timing reference for SoS, with the muscle in between. Reproducible tissue compression was applied by reducing probe-reflector distance in 5 mm steps. The Ogden hyperelastic model and the acoustoelastic theory were used to characterize SoS and SWS variations with tissue compression and extract novel metrics related to tissue nonlinearity. The body fat percentage (BF%) of the subjects was estimated using bioelectrical impedance analysis.

Results

A weak negative correlation was observed between SWS and SoS (r=-0.28, P=0.002). SWS showed an increasing trend with increasing tissue compression (P=0.10) while SoS values decayed nonlinearly (P<0.001). The acoustoelastic modeling showed a weak correlation for SWS (r=-0.36, P<0.001) but a very strong correlation for SoS (r=0.86, P<0.001), which was used to extract the SoS acoustoelastic parameter. SWS showed higher variability between both calves [intraclass correlation coefficient (ICC) =0.62, P=0.08] than SoS (ICC =0.91, P<0.001). Correlations with BF% were strong and positive for SWS (r=0.60, P<0.001), moderate and negative for SoS (r=-0.43, P=0.05), and moderate positive for SoS acoustoelastic parameter (r=0.48, P=0.03).

Conclusions

SWS and SoS provide independent information about tissue elastic properties. SWS correlated stronger with BF% than SoS, but measurements were less reliable. SoS enabled the extraction of novel metrics related to tissue nonlinearity with potential complementary information.

Technical feasibility and correlations between shear-wave elastography and histology in kidney fibrosis in children

BACKGROUND

Ultrasound elastography has been suggested for assessing organ fibrosis.

OBJECTIVE

To study the feasibility of shear-wave elastography in children with kidney disease and the correlation between elasticity and kidney fibrosis in order to reduce the indications for kidney biopsy and its complications.

MATERIALS AND METHODS

Four operators measured kidney elasticity in children with kidney diseases or transplants, all of whom also had a renal biopsy. We assessed the feasibility and the intraobserver variability of the elasticity measurements for each probe used and each kidney explored. Then we tested the correlation between elasticity measurements and the presence of fibrosis.

RESULTS

Overall, we analyzed 95 children and adolescents, 31 of whom had renal transplant. Measurements with the convex probe were possible in 100% of cases. Linear probe analysis was only possible for 20% of native kidneys and 50% of transplants. Intraobserver variabilities ranged from moderate to high, depending on the probe and kidney studied. Elasticity was higher with the linear probe than with the convex probe (P<0.001 for left kidney and P=0.03 for right kidney). Measurements did not differ from one kidney to another in the same child. Elasticity and fibrosis were both higher in transplant patients (P=0.02 with convex probe; P=0.01 with linear probe; P=0.04 overall). There was no correlation between elasticity and fibrosis.

CONCLUSION

Of the devices used in this work, kidney elastography was more accurately analyzed with a convex probe. Our study did not identify any correlation between elasticity and kidney fibrosis.

Acousto-elasticity of transversely isotropic incompressible soft tissues: characterization of skeletal striated muscle

Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or antagonistic actions of adjacent muscles, we select theflexor digiti minimimuscle, whose sole function is to extend the little finger. To link the wave speed to the stiffness, we develop an acousto-elastic theory for shear waves in homogeneous, transversely isotropic, incompressible solids subject to an uniaxial stress. We then provide measurements of the apparent shear elastic modulus along, and transversely to, the fibre axis for six healthy human volunteers of different age and sex. The results display a great variety across the six subjects. We find that the slope of the apparent shear elastic modulus along the fibre direction changes inversely to the maximum voluntary contraction (MVC) produced by the volunteer. We propose an interpretation of our results by introducing the S (slow) or F (fast) nature of the fibres, which harden the muscle differently and accordingly, produce different MVCs. A natural follow-up on this study is to apply the method to patients with musculoskeletal disorders or neurodegenerative diseases.

Use of the AE Effect to Determine the Stresses State in AAC Masonry Walls under Compression

Safety and reliability of constructions operated are predicted using the known mechanical properties of materials and geometry of cross-sections, and also the known internal forces. The extensometry technique (electro-resistant tensometers, wire gauges, sensor systems) is a common method applied under laboratory conditions to determine the deformation state of a material. The construction sector rarely uses ultrasonic extensometry with the acoustoelastic (AE) method which is based on the relation between the direction of ultrasonic waves and the direction of normal stresses. It is generally used to identify stress states of machine or vehicles parts, mainly made of steel, characterized by high homogeneity and a lack of inherent internal defects. The AE effect was detected in autoclaved aerated concrete (AAC), which is usually used in masonry units. The acoustoelastic effect was used in the tests described to identify the complex stress state in masonry walls (masonry units) made of AAC. At first, the relationships were determined for mean hydrostatic stresses P and mean compressive stresses σ₃ with relation to velocities of the longitudinal ultrasonic wave c_p. These stresses were used to determine stresses σ₃. The discrete approach was used which consists in analyzing single masonry units. Changes in velocity of longitudinal waves were identified at a test stand to control the stress states of an element tested by the digital image correlation (DIC) technique. The analyses involved density and the impact of moisture content of AAC. Then, the method was verified on nine walls subjected to axial compression and the model was validated with the FEM micromodel. It was demonstrated that mean compressive stresses σ₃ and hydrostatic stresses, which were determined for the masonry using the method considered, could be determined even up to ca. 75% of failure stresses at the acceptable error level of 15%. Stresses σ₁ parallel to bed joints were calculated using the known mean hydrostatic stresses and mean compressive stresses σ₃.

The Immediate Effects of Foam Rolling and Stretching on Iliotibial Band Stiffness: A Randomized Controlled Trial

BACKGROUND

Iliotibial Band Syndrome (ITBS) is a common clinical condition likely caused by abnormal compressive forces to the iliotibial band (ITB). Stretching interventions are common in ITBS treatment and may predominantly affect tensor fascia latae (TFL). Another ITBS treatment is foam rolling, which may more directly affect the ITB. Shear wave ultrasound elastography (SWUE) measures real-time soft tissue stiffness, allowing tissue changes to be measured and compared.

PURPOSE

To examine effects of foam rolling and iliotibial complex stretching on ITB stiffness at 0˚ and 10˚ of hip adduction and hip adduction passive range of motion (PROM).

STUDY DESIGN

Randomized controlled trial.

METHODS

Data from 11 males (age = 30.5 ± 9.0 years, Body Mass Index (BMI) = 27.8 ± 4.0) and 19 females (age = 23.5 ± 4.9, BMI = 23.2 ± 2.1) were analyzed for this study. Subjects were randomly assigned to one of three groups: control, stretching, and foam rolling. Shear wave ultrasound elastography measurements included ITB Young's modulus at the mid-thigh, the distal femur and the TFL muscle belly. ITB-to-femur depth was measured at mid-thigh level. Hip adduction PROM was measured from digital images taken during the movement.

RESULTS

No significant interactions or main effects were found for group or time differences in ITB Young's modulus at the three measured locations. The ITB stiffness at the mid-thigh and distal femur increased with 10° adduction, but TFL stiffness did not increase. A main effect for adduction PROM was observed, where PROM increased 0.8˚ post-treatment (p = 0.02).

CONCLUSION

A single episode of stretching and foam rolling does not affect short-term ITB stiffness. The lack of ITB stiffness changes may be from an inadequate intervention stimulus or indicate that the interventions have no impact on ITB stiffness.

LEVELS OF EVIDENCE

1b.

Tumor Solid Stress: Assessment with MR Elastography under Compression of Patient-Derived Hepatocellular Carcinomas and Cholangiocarcinomas Xenografted in Mice

Malignant tumors have abnormal biomechanical characteristics, including high viscoelasticity, solid stress, and interstitial fluid pressure. Magnetic resonance (MR) elastography is increasingly used to non-invasively assess tissue viscoelasticity. However, solid stress and interstitial fluid pressure measurements are performed with invasive methods. We studied the feasibility and potential role of MR elastography at basal state and under controlled compression in assessing altered biomechanical features of malignant liver tumors. MR elastography was performed in mice with patient-derived, subcutaneously xenografted hepatocellular carcinomas or cholangiocarcinomas to measure the basal viscoelasticity and the compression stiffening rate, which corresponds to the slope of elasticity versus applied compression. MR elastography measurements were correlated with invasive pressure measurements and digital histological readings. Significant differences in MR elastography parameters, pressure, and histological measurements were observed between tumor models. In multivariate analysis, collagen content and interstitial fluid pressure were determinants of basal viscoelasticity, whereas solid stress, in addition to collagen content, cellularity, and tumor type, was an independent determinant of compression stiffening rate. Compression stiffening rate had high AUC (0.87 ± 0.08) for determining elevated solid stress, whereas basal elasticity had high AUC for tumor collagen content (AUC: 0.86 ± 0.08). Our results suggest that MR elastography compression stiffening rate, in contrast to basal viscoelasticity, is a potential marker of solid stress in malignant liver tumors.

A review of physical and engineering factors potentially affecting shear wave elastography

It has been recognized that tissue stiffness provides useful diagnostic information, as with palpation as a screening for diseases such as cancer. In recent years, shear wave elastography (SWE), a technique for evaluating and imaging tissue elasticity quantitatively and objectively in diagnostic imaging, has been put into practical use, and the amount of clinical knowledge about SWE has increased. In addition, some guidelines and review papers regarding technology and clinical applications have been published, and the status as a diagnostic technology is in the process of being established. However, there are still unclear points about the interpretation of shear wave speed (SWS) and converted elastic modulus in SWE. To clarify these, it is important to investigate the factors that affect the SWS and elastic modulus. Therefore, physical and engineering factors that potentially affect the SWS and elastic modulus are discussed in this review paper, based on the principles of SWE and a literature review. The physical factors include the propagation properties of shear waves, mechanical properties (viscoelasticity, nonlinearity, and anisotropy), and size and shape of target tissues. The engineering factors include the region of interest depth and signal processing. The aim of this review paper is not to provide an answer to the interpretation of SWS. It is to provide information for readers to formulate and verify the hypothesis for the interpretation. Therefore, methods to verify the hypothesis for the interpretation are also reviewed. Finally, studies on the safety of SWE are discussed.

Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations

The goal of non-linear ultrasound elastography is to characterize tissue mechanical properties under finite deformations. Existing methods produce high contrast non-linear elastograms under conditions of pure uni-axial compression, but exhibit bias errors of 10-50% when the applied deformation deviates from the uni-axial condition. Since freehand transducer motion generally does not produce pure uniaxial compression, a motion-agnostic non-linearity estimator is desirable for clinical translation. Here we derive an expression for measurement of the Non-Linear Shear Modulus (NLSM) of tissue subject to combined shear and axial deformations. This method gives consistent nonlinear elasticity estimates irrespective of the type of applied deformation, with a reduced bias in NLSM values to 6-13%. The method combines quasi-static strain imaging with Single-Track Location-Shear Wave Elastography (STL-SWEI) to generate local estimates of axial strain, shear strain, and Shear Wave Speed (SWS). These local values were registered and non-linear elastograms reconstructed with a novel nonlinear shear modulus estimation scheme for general deformations. Results on tissue mimicking phantoms were validated with mechanical measurements and multiphysics simulations for all deformation types with an error in NLSM of 6-13%. Quantitative performance metrics with the new compound-motion tracking strategy reveal a 10-15 dB improvement in Signal-to-Noise Ratio (SNR) for simple shear versus pure compressive deformation for NLSM elastograms of homogeneous phantoms. Similarly, the Contrast-to-Noise Ratio (CNR) of NLSM elastograms of inclusion phantoms improved by 25-30% for simple shear over pure uni-axial compression. Our results show that high fidelity NLSM estimates may be obtained at ~30% lower strain under conditions of shear deformation as opposed axial compression. The reduction in strain required could reduce sonographer effort and improve scan safety.

Hyperelastic Ex Vivo Cervical Tissue Mechanical Characterization

This paper presents the results of the comparison between a proposed Fourth Order Elastic Constants (FOECs) nonlinear model defined in the sense of Landau's theory, and the two most contrasted hyperelastic models in the literature, Mooney-Rivlin, and Ogden models. A mechanical testing protocol is developed to investigate the large-strain response of ex vivo cervical tissue samples in uniaxial tension in its two principal anatomical locations, the epithelial and connective layers. The final aim of this work is to compare the reconstructed shear modulus of the epithelial and connective layers of cervical tissue. According to the obtained results, the nonlinear parameter A from the proposed FOEC model could be an important biomarker in cervical tissue diagnosis. In addition, the calculated shear modulus depended on the anatomical location of the cervical tissue (μepithelial = 1.29 ± 0.15 MPa, and μconnective = 3.60 ± 0.63 MPa).

Imaging of Thermal Effects during High-Intensity Ultrasound Treatment in Liver by Passive Elastography: A Preliminary Feasibility in Vitro Study

High-intensity focused ultrasound is a non-invasive modality for thermal ablation of tissues through locally increased temperature. Thermal lesions can be monitored by elastography, following the changes in the elastic properties of the tissue as reflected by the shear-wave velocity. Most studies on ultrasound elastography use shear waves created by acoustic radiation force. However, in the human body, the natural noise resulting from cardiac activity or arterial pulsatility can be used to characterize elasticity through noise-correlation techniques, in the method known as passive elastography. The objective of this study was to investigate the feasibility of monitoring high-intensity ultrasound treatments of liver tissue using passive elastography. Bovine livers were heated to 80°C using a high-intensity planar transducer and imaged with a high-frame-rate ultrasound imaging device. The dynamics of lesion formation are captured through tissue stiffening and lesion expansion.

C-Elastography: In Vitro Feasibility Phantom Study

C-Elastography (CE) is a new ultrasound technique that locally maps the non-linear elasticity of soft tissue using low-frequency (150-250 Hz) shear waves generated by the acoustic radiation force (ARF). CE is based on a recent finding that the magnitude of the ARF in an isotropic tissue-like solid is related linearly to a third-order modulus of elasticity, C, which is responsible for the coupling between deviatoric and volumetric constitutive behaviors. The main objective of the work described here was to examine the feasibility of using and performance of C-elastography in differentiating and characterizing soft tissue via a pilot study on ex vivo tissue and tissue-mimicking inclusions cast in a gelatin block. In this vein, the CE technique deploys a combination of ultrasound motion sensing and 3-D visco-elastodynamic simulation to estimate the non-linear modulus C. As ultrasound focusing inherently confines the ARF to a small region, CE provides the means for measuring C within O(mm3) volumes. Equipped with such data analysis, we performed in vitro CE experiments on agar-based, xenograft and normal breast tissue samples embedded in a gelatin matrix. The compound C-elastograms indicate marked (and sharp) C-contrast, with average values of 1.9 and 5.6 at push points inside the featured soft and hard inclusions, respectively.

Analysis of multiple shear wave modes in a nonlinear soft solid: Experiments and finite element simulations with a tilted acoustic radiation force

Tissue nonlinearity is conventionally measured in shear wave elastography by studying the change in wave speed caused by the tissue deformation, generally known as the acoustoelastic effect. However, these measurements have mainly focused on the excitation and detection of one specific shear mode, while it is theoretically known that the analysis of multiple wave modes offers more information about tissue material properties that can potentially be used to refine disease diagnosis. This work demonstrated proof of concept using experiments and finite element simulations in a uniaxially stretched phantom by tilting the acoustic radiation force excitation axis with respect to the material's symmetry axis. Using this unique set-up, we were able to visualize two propagating shear wave modes across the stretch direction for stretches larger than 140%. Complementary simulations were performed using material parameters determined from mechanical testing, which enabled us to convert the observed shear wave behavior into a correct representative constitutive law for the phantom material, i.e. the Isihara model. This demonstrates the potential of measuring shear wave propagation in combination with shear wave modeling in complex materials as a non-invasive alternative for mechanical testing.

Mechanical Strength Evaluation of Elastic Materials by Multiphysical Nondestructive Methods: A Review

The main purpose of industrial nondestructive testing (NDT) is to diagnose the stability, reliability and failure probability of materials, components and structures. Industrial component mechanical strength is one of the most important properties NDT is used to characterize. Subtle but perceptible changes in stress-strain behavior can be reliable indicators of defect formation. A detailed review on the state-of-the-art NDT methods using optical-radiation, photoacoustic, and photothermal techniques for mechanical strength evaluation and defect pre-diagnosis is presented in this article. Mechanical strength is analyzed in terms of the deformation/strain field, the stress-strain relation, and the residual stress in an elastic material subjected to tensile or compressive loading, or impact. By introducing typical NDT experiments, the history and features of each methodology are revisited and typical applications are discussed. This review also aims to be used as a reference toward further research and development of NDT technologies characterizing mechanical strength of materials and components.

Tractable calculation of the Green's tensor for shear wave propagation in an incompressible, transversely isotropic material

Assessing material properties from observations of shear wave propagation following an acoustic radiation force impulse (ARFI) excitation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this paper, we describe a method to calculate shear wave signals using Green’s tensor methods in an incompressible, transversely isotropic (TI) material characterized by three material parameters. The Green’s tensor is written as the sum of an analytic expression for the SH propagation mode, and an integral expression for the SV propagation mode that can be evaluated by interpolation within precomputed integral functions with an efficiency comparable to the evaluation of a closed-form expression. By using parametrized integral functions, the number of requried numerical integrations is reduced by a factor of 10² − 10⁹ depending on the specific problem under consideration. Results are presented for the case of a point source positioned at the origin and a tall Gaussian source similar to an ARFI excitation. For an experimental configuration with a tilted material symmetry axis, results show that shear wave signals exhibit structures that are sufficiently complex to allow measurement of all three material parameters that characterize an incompressible, TI material.

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.

Spectral Quantification of Nonlinear Elasticity Using Acoustoelasticity and Shear-Wave Dispersion

Tissue biomechanical properties are known to be sensitive to pathological changes. Accordingly, various techniques have been developed to estimate tissue mechanical properties. Shear-wave elastography (SWE) measures shear-wave speed (SWS) in tissues, which can be related to shear modulus. Although viscosity or stress-strain nonlinearity may act as confounder of SWE, their explicit characterization may also provide additional information about tissue composition as a contrast modality. Viscosity can be related to frequency dispersion of SWS, which can be characterized using multi-frequency measurements, herein called spectral SWE (SSWE). Additionally, nonlinear shear modulus can be quantified and parameterized based on SWS changes with respect to applied stress, a phenomenon called acoustoelasticity (AE). In this work, we characterize the nonlinear parameters of tissue as a function of excitation frequency by utilizing both AE and SSWE together. For this, we apply incremental amounts of quasi-static stress on a medium, while imaging and quantifying SWS dispersion via SSWE. Results from phantom and ex vivo porcine liver experiments demonstrate the feasibility of measuring frequency-dependent nonlinear parameters using the proposed method. SWS propagation in porcine liver tissue was observed to change from 1.8 m/s at 100 Hz to 3.3 m/s at 700 Hz, while increasing by approximately 25% from a strain of 0% to 12% across these frequencies.

Nonlinear Shear Modulus Estimation With Bi-Axial Motion Registered Local Strain

Nonlinear elasticity imaging provides additional information about tissue behavior that is potentially diagnostic and avoids errors inherent in applying a linear elastic model to tissue under large strains. Nonlinear elasticity imaging is challenging to perform due to the large deformations required to obtain sufficient tissue strain to elicit nonlinear behavior. This work uses a method of axial and lateral displacement tracking to estimate local axial strain with simultaneous measurement of shear modulus at multiple compression levels. By following the change in apparent shear modulus and the stress deduced from the strain maps, we are able to accurately quantify nonlinear shear modulus (NLSM). We have validated our technique with a mechanical NLSM measurement system. Our results demonstrate that 2-D tracking provides more consistent NLSM estimates than those obtained by 1-D (axial) tracking alone, especially where lateral motion is significant. The elastographic contrast-to-noise ratio in heterogeneous phantoms was 12.5%-60% higher using our method than that of 1-D tracking. Our method is less susceptible to mechanical variations, with deviations in mean elastic values of 2%-4% versus 5%-37% for 1-D tracking.