Quantitative imaging of nonlinear shear modulus by combining static elastography and shear wave elastography

Quantification of Cervical Elasticity During Pregnancy Based on Transvaginal Ultrasound Imaging and Stress Measurement

Strain elastography and shear wave elastography are commonly used to quantify cervical elasticity. However, the absence of stress information in strain elastography causes difficulty in inter-session elasticity comparison, and the robustness of shear wave elastography is compromised by cervical tissue's high inhomogeneity.

OBJECTIVE

To overcome these limitations, we develop a quantitative cervical elastography system by adding a stress sensor to a clinically used transvaginal ultrasound imaging system.

METHODS

We record the cervical deformation in B-mode images and measure the probe-surface stress through the sensor. Then we quantify the strain using a customized algorithm and estimate the cervical Young's modulus through stress-strain linear regression.

RESULTS

In phantom experiments, we demonstrate the system's high accuracy (alignment with the quasi-static compression method, p-value = 0.369 > 0.05), robustness (alignment between 60°- and 90°-contact measurements, p-value = 0.638 > 0.05), repeatability (consistency of single sonographers' measurements, coefficient of variation < 0.06), and reproducibility (alignment between two sonographers' measurements, Pearson correlation coefficient = 0.981). Applying it to pregnant participants, we observe significant cervical softening (p-value < 0.001): Young's modulus decreases 3.95% weekly and its geometric mean value during the first (11 to 13 weeks), second, and third trimesters are 13.07 kPa, 7.59 kPa, and 4.40 kPa, respectively.

CONCLUSION

The proposed system is accurate, robust, and safe, and enables longitudinal and inter-examiner comparisons.

SIGNIFICANCE

The system applies to different ultrasound machines with minor software updates, which allows for studies of cervical softening patterns in pregnancy for larger populations, facilitating insights into conditions such as preterm birth.

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.

Reliability and Validity of Shore Hardness in Plantar Soft Tissue Biomechanics

Shore hardness (SH) is a cost-effective and easy-to-use method to assess soft tissue biomechanics. Its use for the plantar soft tissue could enhance the clinical management of conditions such as diabetic foot complications, but its validity and reliability remain unclear. Twenty healthy adults were recruited for this study. Validity and reliability were assessed across six different plantar sites. The validity was assessed against shear wave (SW) elastography (the gold standard). SH was measured by two examiners to assess inter-rater reliability. Testing was repeated following a test/retest study design to assess intra-rater reliability. SH was significantly correlated with SW speed measured in the skin or in the microchamber layer of the first metatarsal head (MetHead), third MetHead and rearfoot. Intraclass correlation coefficients and Bland-Altman plots of limits of agreement indicated satisfactory levels of reliability for these sites. No significant correlation between SH and SW elastography was found for the hallux, 5th MetHead or midfoot. Reliability for these sites was also compromised. SH is a valid and reliable measurement for plantar soft tissue biomechanics in the first MetHead, the third MetHead and the rearfoot. Our results do not support the use of SH for the hallux, 5th MetHead or midfoot.

A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization

OBJECTIVE

Ultrasound elasticity imaging is a class of ultrasound techniques with applications that include the detection of malignancy in breast lesions. Although elasticity imaging traditionally assumes linear elasticity, the large strain elastic response of soft tissue is known to be nonlinear. This study evaluates the nonlinear response of breast lesions for the characterization of malignancy using force measurement and force-controlled compression during ultrasound imaging.

METHODS

54 patients were recruited for this study. A custom force-instrumented compression device was used to apply a controlled force during ultrasound imaging. Motion tracking derived strain was averaged over lesion or background ROIs and matched with compression force. The resulting force-matched strain was used for subsequent analysis and curve fitting.

RESULTS

Greater median differences between malignant and benign lesions were observed at higher compressional forces (p-value < 0.05 for compressional forces of 2-6N). Of three candidate functions, a power law function produced the best fit to the force-matched strain. A statistically significant difference in the scaling parameter of the power function between malignant and benign lesions was observed (p-value = 0.025).

CONCLUSIONS

We observed a greater separation in average lesion strain between malignant and benign lesions at large compression forces and demonstrated the characterization of this nonlinear effect using a power law model. Using this model, we were able to differentiate between malignant and benign breast lesions.

SIGNIFICANCE

With further development, the proposed method to utilize the nonlinear elastic response of breast tissue has the potential for improving non-invasive lesion characterization for potential malignancy.

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.

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.

Possible depth-resolved reconstruction of shear moduli in the cornea following collagen crosslinking (CXL) with optical coherence tomography and elastography

Corneal collagen crosslinking (CXL) is commonly used to prevent or treat keratoconus. Although changes in corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic optical coherence elastography (OCE) by tracking mechanical wave propagation, depth dependent changes are still unclear if the cornea is not crosslinked through the whole depth. Here, phase-decorrelation measurements on optical coherence tomography (OCT) structural images are combined with acoustic micro-tapping (AµT) OCE to explore possible reconstruction of depth-dependent stiffness within crosslinked corneas in an ex vivo human cornea sample. Experimental OCT images are analyzed to define the penetration depth of CXL into the cornea. In a representative ex vivo human cornea sample, crosslinking depth varied from ∼100 µm in the periphery to ∼150 µm in the cornea center and exhibited a sharp in-depth transition between crosslinked and untreated areas. This information was used in an analytical two-layer guided wave propagation model to quantify the stiffness of the treated layer. We also discuss how the elastic moduli of partially CXL-treated cornea layers reflect the effective engineering stiffness of the entire cornea to properly quantify corneal deformation.

Identification of a cantilever beam's spatially uncertain stiffness

This study identifies non-homogeneous stiffnesses in a non-destructive manner from simulated noisy measurements of a structural response. The finite element method serves as a discretization for the respective cantilever beam example problems: static loading and modal analysis. Karhunen-Loève expansions represent the stiffness random fields. We solve the inverse problems using Bayesian inference on the Karhunen-Loève coefficients, hereby introducing a novel resonance frequency method. The flexible descriptions of both the structural stiffness uncertainty and the measurement noise characteristics allow for straightforward adoption to measurement setups and a range of non-homogeneous materials. Evaluating the inversion performance for varying stiffness covariance functions shows that the static analysis procedure outperforms the modal analysis procedure in a mean sense. However, the solution quality depends on the position within the beam for the static analysis approach, while the confidence interval height remains constant along the beam for the modal analysis. An investigation of the effect of the signal-to-noise ratio reveals that the static loading procedure yields lower errors than the dynamic procedure for the chosen configuration with ideal boundary 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'.

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.

Stiffness prediction on elastography images and neuro-fuzzy based segmentation for thyroid cancer detection

The elastography method detects metastatic changes by measuring the stiffness of tissues. Estimation of elasticities from elastography images facilitates more precise identification of the metastatic region and detection of the same. In this study, an automated segmentation algorithm is proposed that calculates pixel-wise elasticity values to detect thyroid cancer from elastography images. This intensity to elasticity conversion is achieved by constructing a fuzzy inference system using an adaptive neuro-fuzzy inference system supported by two meta-heuristic algorithms: genetic algorithm and particle swarm optimization. Pixels of the input color images (red, green, and blue) are replaced by equivalent elasticity values (in kilo Pascal) and are stored in a two-dimensional array to form an "elasticity matrix." The elasticity matrix is then segmented into three regions, namely, suspicious, near-suspicious, and non-suspicious, based on the elasticity measures, where the threshold limits are calculated using the fuzzy entropy maximization method optimized by the differential evolution algorithm. Segmentation performances are evaluated by Kappa and the dice similarity co-efficient, and average values achieved are 0.94±0.11 and 0.93±0.12, respectively. Sensitivity and specificity values achieved by the proposed method are 86.35±0.34% and 97.67±0.40%, respectively, showing an overall accuracy of 93.50±0.42%. Results justify the importance of pixel stiffness for segmentation of thyroid nodules in elastography images.

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).

Measured Hyperelastic Properties of Cervical Tissue with Shear-Wave Elastography

The nonlinear mechanical behaviour of cervical tissue causes unpredictable changes in measured elastograms when pressure is applied. These uncontrolled variables prevent the reliable measurement of tissue elasticity in a clinical setting. Measuring the nonlinear properties of tissue is difficult due to the need for both shear modulus and strain to be taken simultaneously. A simulation-based method is proposed in this paper to resolve this. This study describes the nonlinear behaviour of cervical tissue using the hyperelastic material models of Demiray–Fung and Veronda–Westmann. Elastograms from 33 low-risk patients between 18 and 22 weeks gestation were obtained. The average measured properties of the hyperelastic material models are: Demiray–Fung—A1α = 2.07 (1.65–2.58) kPa, α = 6.74 (4.07–19.55); Veronda–Westmann—C1C2 = 4.12 (3.24–5.04) kPa, C2 = 4.86 (2.86–14.28). The Demiray–Fung and Veronda–Westmann models performed similarly in fitting to the elastograms with an average root mean square deviation of 0.41 and 0.47 ms−1, respectively. The use of hyperelastic material models to calibrate shear-wave speed measurements improved the consistency of measurements. This method could be applied in a large-scale clinical setting but requires updated models and higher data resolution.

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.

Effects of compressive lesions on intraoperative human spinal cord elasticity

OBJECTIVE

Although evaluating tissue elasticity has various clinical applications, spinal cord elasticity (SCE) in humans has never been well documented. In this study, the authors aimed to evaluate the impact of compression on human SCE in vivo.

METHODS

The authors prospectively assessed SCE using intraoperative shear wave elastography (SWE). All consecutive patients undergoing spinal cord (SC) decompression (laminectomy or corpectomy) between June 2018 and June 2019 were included. After intraoperative exposure of the patient's dura mater, at least three SWE measurements of the SC and its coverings were performed. Intraoperative neurological monitoring in the form of motor and somatosensory evoked potentials was utilized. Cases were divided into two groups based on the state of SC compression following bone removal (laminectomy or corpectomy): patients with adequate decompression (the decompressed SC group [DCG]) following bone removal and patients with remining compression, e.g., compressing tumor or instability (the compressed SC group [COG]).

RESULTS

A total of 25 patients were included (8 females and 17 males) with a mean age of 48.28 ± 21.47 years. Most cases were degenerative diseases (10 cases) followed by tumors (6 cases), and the compression was observed at cervical (n = 14), thoracic (n = 9), and conus medullaris (n = 2) levels. The COG (6 cases) expressed significantly higher elasticity values, i.e., greater stiffness (median 93.84, IQR 75.27-121.75 kPa) than the decompressed SC in DCG (median 9.35, IQR 6.95-11.22 kPa, p < 0.001). Similarly, the compressed dura mater in the COG was significantly stiffer (mean ± SD 121.83 ± 70.63 kPa) than that in the DCG (29.78 ± 18.31 kPa, p = 0.042). Following SC decompression in COG, SCE values were significantly reduced (p = 0.006; adjusted for multiple comparisons). Intraoperative monitoring demonstrated no worsening from the baseline.

CONCLUSIONS

The current study is to the authors' knowledge the first to quantitatively demonstrate increased stiffness (i.e., elasticity value) of the human SC and dura mater in response to external compression in vivo. It appears that SCE is a dynamic phenomenon and is reduced following decompression. Moreover, the evaluation of human SCE using the SWE technique is feasible and safe. Information from future studies aiming to further define SCE could be valuable in the early and accurate diagnosis of the compressed SC.

Acoustic Radiation Force: A Review of Four Mechanisms for Biomedical Applications

Radiation force is a universal phenomenon in any wave motion where the wave energy produces a static or transient force on the propagation medium. The theory of acoustic radiation force (ARF) dates back to the early 19th century. In recent years, there has been an increasing interest in the biomedical applications of ARF. Following a brief history of ARF, this article describes a concise theory of ARF under four physical mechanisms of radiation force generation in tissue-like media. These mechanisms are primarily based on the dissipation of acoustic energy of propagating waves, the reflection of the incident wave, gradients of the compressional wave speeds, and the spatial variations of energy density in standing acoustic waves. Examples describing some of the practical applications of ARF under each mechanism are presented. This article concludes with a discussion on selected ideas for potential future applications of ARF in biomedicine.

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.

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.

Ultrasound elastography reveals the relation between body posture and soft-tissue stiffness which is relevant to the etiology of sitting-acquired pressure ulcers

OBJECTIVE

Sitting-acquired pressure ulcers (PUs) are common in wheelchair users. These PUs are often serious and may involve deep tissue injury (DTI). Investigating the mechanical properties of the tissues susceptible to DTI may help in guiding the prevention and early detection of PUs. In this study, shear wave elastography (SWE) was used to measure the normative mechanical properties of the soft tissues of the buttocks, i.e. skeletal muscle and subcutaneous fat, under the ischial tuberosities, in a convenient sample of healthy adults without weight bearing and with weight bearing of different times.

APPROACH

We compared the stiffness properties of these soft tissues between the lying prone and sitting postures, to determine whether there are detectable property changes that may be associated with the type of posture. We hypothesized that muscle contractions and 3D tissue configurations associated with the posture may influence the measured tissue stiffnesses.

MAIN RESULTS

Our results have shown that indeed, SWE values differed significantly across postures, but not over time in a specific posture or for the right versus left sides of the body.

SIGNIFICANCE

We have therefore demonstrated that soft-tissue stiffness increases when sitting with weight bearing and may contribute to increasing the potential PU risk in sitting compared to lying prone, given the stiffer behavior of tissues observed in sitting postures.

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.

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.

Why Are Viscosity and Nonlinearity Bound to Make an Impact in Clinical Elastographic Diagnosis?

The adoption of multiscale approaches by the biomechanical community has caused a major improvement in quality in the mechanical characterization of soft tissues. The recent developments in elastography techniques are enabling in vivo and non-invasive quantification of tissues' mechanical properties. Elastic changes in a tissue are associated with a broad spectrum of pathologies, which stems from the tissue microstructure, histology and biochemistry. This knowledge is combined with research evidence to provide a powerful diagnostic range of highly prevalent pathologies, from birth and labor disorders (prematurity, induction failures, etc.), to solid tumors (e.g., prostate, cervix, breast, melanoma) and liver fibrosis, just to name a few. This review aims to elucidate the potential of viscous and nonlinear elastic parameters as conceivable diagnostic mechanical biomarkers. First, by providing an insight into the classic role of soft tissue microstructure in linear elasticity; secondly, by understanding how viscosity and nonlinearity could enhance the current diagnosis in elastography; and finally, by compounding preliminary investigations of those elastography parameters within different technologies. In conclusion, evidence of the diagnostic capability of elastic parameters beyond linear stiffness is gaining momentum as a result of the technological and imaging developments in the field of biomechanics.

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.

Generalization of the Zabolotskaya equation to all incompressible isotropic elastic solids

We study elastic shear waves of small but finite amplitude, composed of an anti-plane shear motion and a general in-plane motion. We use a multiple scales expansion to derive an asymptotic system of coupled nonlinear equations describing their propagation in all isotropic incompressible nonlinear elastic solids, generalizing the scalar Zabolotskaya equation of compressible nonlinear elasticity. We show that for a general isotropic incompressible solid, the coupling between anti-plane and in-plane motions cannot be undone and thus conclude that linear polarization is impossible for general nonlinear two-dimensional shear waves. We then use the equations to study the evolution of a nonlinear Gaussian beam in a soft solid: we show that a pure (linearly polarized) shear beam source generates only odd harmonics, but that introducing a slight in-plane noise in the source signal leads to a second harmonic, of the same magnitude as the fifth harmonic, a phenomenon recently observed experimentally. Finally, we present examples of some special shear motions with linear polarization.

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.

Acoustoelasticity Analysis of Transient Waves for Non-Invasive In Vivo Assessment of Urinary Bladder

A non-invasive method for measurement of the bladder wall nonlinear elastic behavior is presented. The method is based on acoustoelasticity modeling of the elasticity changes in bladder tissue modulus at different volumetric strain levels. At each volume, tissue strain is obtained from the real-time ultrasound images. Using acoustic radiation force, a transient Lamb wave is excited on the bladder wall and instantaneous modulus of shear elasticity is obtained from the 2-D Fourier analysis of the spatial-temporal dispersion maps. Measured elasticity and strain data are then used in an acoustoelasticity formulation to obtain the third order elastic coefficient, referred to as nonlinearity parameter A, and initial resting elasticity μ₀. The method was tested in ex vivo porcine bladder samples (N = 9) before and after treatment with formalin. The estimated nonlinearity parameter, A, was significantly higher in the treated samples compared to intact (p < 0.00062). The proposed method was also applied on 16 patients with neurogenic bladders (10 compliant and 6 non-compliant subjects). The estimated nonlinearity parameter A was significantly higher in the non-compliant cases compared to the compliant (p < 0.0293). These preliminary results promise a new method for non-invasive evaluation of the bladder tissue nonlinearity which may serve as a new diagnostic and prognostic biomarker for management of the patients with neurogenic bladders.

Application of Acoustoelasticity to Evaluate Nonlinear Modulus in Ex Vivo Kidneys

Currently, dynamic elastography techniques estimate the linear elastic shear modulus of different body tissues. New methods that investigate other properties of soft tissues such as anisotropy, viscosity, and shear nonlinearity would provide more information about the structure and function of the tissue and might provide a better contrast than tissue stiffness and hence provide more effective diagnostic tools for some diseases. It has previously been shown that shear wave velocity in a medium changes due to an applied stress, a phenomenon called acoustoelasticity (AE). Applying a stress to compress a medium while measuring the shear wave velocity versus strain provides data with which the third-order nonlinear shear modulus can be estimated. To evaluate the feasibility of estimating , we evaluated ten ex vivo porcine kidneys embedded in 10% porcine gelatin to mimic the case of a transplanted kidney. Under assumptions of an elastic incompressible medium for AE measurements, the shear modulus was quantified at each compression level and the applied strain was assessed by measuring the change in the thickness of the kidney cortex. Finally, was calculated by applying the AE theory. Our results demonstrated that it is possible to estimate a nonlinear shear modulus by monitoring the changes in strain and due to kidney deformation. The magnitudes of are higher when the compression is performed progressively and when using a plate attached to the transducer. Nevertheless, the values obtained for are similar to those previously reported in the literature for breast tissue.

Shear Wave Speed Measurements Using Crawling Wave Sonoelastography and Single Tracking Location Shear Wave Elasticity Imaging for Tissue Characterization

Elastography provides tissue stiffness information that attempts to characterize the elastic properties of tissue. However, there is still limited literature comparing elastographic modalities for tissue characterization. This study focuses on two quantitative techniques using different vibration sources that have not been compared to date: crawling wave sonoelastography (CWS) and single tracking location shear wave elasticity imaging (STL-SWEI). To understand each technique's performance, shear wave speed (SWS) was measured in homogeneous phantoms and ex vivo beef liver tissue. Then, the contrast, contrast-to-noise ratio (CNR), and lateral resolution were measured in an inclusion and two-layer phantoms. The SWS values obtained with both modalities were validated with mechanical measurements (MM) which serve as ground truth. The SWS results for the three different homogeneous phantoms (10%, 13%, and 16% gelatin concentrations) and ex vivo beef liver tissue showed good agreement between CWS, STL-SWEI, and MM as a function of frequency. For all gelatin phantoms, the maximum accuracy errors were 2.52% and 2.35% using CWS and STL-SWEI, respectively. For the ex vivo beef liver, the maximum accuracy errors were 9.40% and 7.93% using CWS and STL-SWEI, respectively. For lateral resolution, contrast, and CNR, both techniques obtained comparable measurements for vibration frequencies less than 300 Hz (CWS) and distances between the push beams ( ∆x ) between 3 mm and 5.31 mm (STL-SWEI). The results obtained in this study agree over an SWS range of 1-6 m/s. They are expected to agree in perfectly linear, homogeneous, and isotropic materials, but the SWS overlap is not guaranteed in all materials because each of the three methods have unique features.

Probe Oscillation Shear Elastography (PROSE): A High Frame-Rate Method for Two-Dimensional Ultrasound Shear Wave Elastography

Ultrasound shear wave elastography (SWE) utilizes the propagation of induced shear waves to characterize the shear modulus of soft tissue. Many methods rely on an acoustic radiation force (ARF) "push beam" to generate shear waves. However, specialized hardware is required to generate the push beams, and the thermal stress that is placed upon the ultrasound system, transducer, and tissue by the push beams currently limits the frame-rate to about 1 Hz. These constraints have limited the implementation of ARF to high-end clinical systems. This paper presents Probe Oscillation Shear Elastography (PROSE) as an alternative method to measure tissue elasticity. PROSE generates shear waves using a harmonic mechanical vibration of an ultrasound transducer, while simultaneously detecting motion with the same transducer under pulse-echo mode. Motion of the transducer during detection produces a "strain-like" compression artifact that is coupled with the observed shear waves. A novel symmetric sampling scheme is proposed such that pulse-echo detection events are acquired when the ultrasound transducer returns to the same physical position, allowing the shear waves to be decoupled from the compression artifact. Full field-of-view (FOV) two-dimensional (2D) shear wave speed images were obtained by applying a local frequency estimation (LFE) technique, capable of generating a 2D map from a single frame of shear wave motion. The shear wave imaging frame rate of PROSE is comparable to the vibration frequency, which can be an order of magnitude higher than ARF based techniques. PROSE was able to produce smooth and accurate shear wave images from three homogeneous phantoms with different moduli, with an effective frame rate of 300 Hz. An inclusion phantom study showed that increased vibration frequencies improved the accuracy of inclusion imaging, and allowed targets as small as 6.5 mm to be resolved with good contrast (contrast-to-noise ratio ≥ 19 dB) between the target and background.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity

Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

In Vivo Quantification of the Nonlinear Shear Modulus in Breast Lesions: Feasibility Study

Breast cancer detection in the early stages is of great importance since the prognosis, and the treatment depends more on this. Multiple techniques relying on the mechanical properties of soft tissues have been developed to help in early detection. In this study, we implemented a technique that measures the nonlinear shear modulus (NLSM) (μ(NL)) in vivo and showed its utility to detect breast lesions from healthy tissue. The technique relies on the acoustoelasticity theory in quasi-incompressible media. In order to recover μ(NL), static elastography and supersonic shear imaging are combined to subsequently register strain maps and shear modulus maps while the medium is compressed. Then, μ(NL) can be recovered from the relationship between the stress, deduced from strain maps, and the shear modulus. For this study, a series of five nonlinear phantoms were built using biological tissue (pork liver) inclusions immersed in an agar-gelatin gel. Furthermore, 11 in vivo acquisitions were performed to characterize the NLSM of breast tissue. The phantom results showed a very good differentiation of the liver inclusions when measuring μ(NL) with a mean value of -114.1 kPa compared to -34.7 kPa for the gelatin. Meanwhile, values for the shear modulus for the liver and the gelatin were very similar, 3.7 and 3.4 kPa, respectively. In vivo NLSM mean value for the healthy breast tissue was of -95 kPa, while mean values of the benign and the malignant lesions were -619 and -806 kPa with a strong v ariability, respectively. This study shows the potential of the acoustoelasticity theory in quasi-incompressible medium to bring a new parameter for breast cancer diagnosis.

Assessment of the Cervix in Pregnant Women Using Shear Wave Elastography: A Feasibility Study

The quantitative assessment of the cervix is crucial for the estimation of pre-term delivery risk and the prediction of the success of labor induction. We conducted a cross-sectional study using shear wave elastography based on the supersonic shear imaging technique. The shear wave speed (SWS) of the lower anterior part of the cervix was quantified over an 8-mm region of interest in 157 pregnant women. Cervical SWS is slightly but significantly reduced in patients diagnosed with pre-term labor and in patients who actually delivered pre-term.

Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure

The tumour microenvironment may contribute to tumorigenesis owing to mechanical forces such as fibrotic stiffness or mechanical pressure caused by the expansion of hyper-proliferative cells. Here we explore the contribution of the mechanical pressure exerted by tumour growth onto non-tumorous adjacent epithelium. In the early stage of mouse colon tumour development in the Notch(+)Apc(+/1638N) mouse model, we observed mechanistic pressure stress in the non-tumorous epithelial cells caused by hyper-proliferative adjacent crypts overexpressing active Notch, which is associated with increased Ret and β-catenin signalling. We thus developed a method that allows the delivery of a defined mechanical pressure in vivo, by subcutaneously inserting a magnet close to the mouse colon. The implanted magnet generated a magnetic force on ultra-magnetic liposomes, stabilized in the mesenchymal cells of the connective tissue surrounding colonic crypts after intravenous injection. The magnetically induced pressure quantitatively mimicked the endogenous early tumour growth stress in the order of 1,200 Pa, without affecting tissue stiffness, as monitored by ultrasound strain imaging and shear wave elastography. The exertion of pressure mimicking that of tumour growth led to rapid Ret activation and downstream phosphorylation of β-catenin on Tyr654, imparing its interaction with the E-cadherin in adherens junctions, and which was followed by β-catenin nuclear translocation after 15 days. As a consequence, increased expression of β-catenin-target genes was observed at 1 month, together with crypt enlargement accompanying the formation of early tumorous aberrant crypt foci. Mechanical activation of the tumorigenic β-catenin pathway suggests unexplored modes of tumour propagation based on mechanical signalling pathways in healthy epithelial cells surrounding the tumour, which may contribute to tumour heterogeneity.

Characterization of transverse isotropy in compressed tissue-mimicking phantoms

Tissues such as skeletal muscle and kidneys have well-defined structure that affects the measurements of mechanical properties. As an approach to characterize the material properties of these tissues, different groups have assumed that they are transversely isotropic (TI) and measure the shear wave velocity as it varies with angle with respect to the structural architecture of the organ. To refine measurements in these organs, it is desirable to have tissue-mimicking phantoms that exhibit similar anisotropic characteristics. Some approaches involve embedding fibers into a material matrix. However, if a homogeneous solid is under compression due to a static stress, an acoustoelastic effect can manifest that makes the measured wave velocities change with the compression stress. We propose to exploit this characteristic to demonstrate that stressed tissue mimicking phantoms can be characterized as a TI material. We tested six phantoms made with different concentrations of gelatin and agar. Stress was applied by the weight of a water container centered on top of a plate on top of the phantom. A linear array transducer and a V-1 Verasonics system were used to induce and measure shear waves in the phantoms. The shear wave motion was measured using a compound plane wave imaging technique. Autocorrelation was applied to the received in-phase/quadrature data. The shear wave velocity, c, was estimated using a Radon transform method. The transducer was mounted on a rotating stage so measurements were made every 10° over a range of 0° to 360°, where the stress is applied along 0° to 180° direction. The shear moduli were estimated. A TI model was fit to the data and the fractional anisotropy was evaluated. This approach can be used to explore many configurations of transverse isotropy with the same phantom, simply by applying stress to the tissue-mimicking phantom.

Mechanical induction of the tumorigenic β-catenin pathway by tumour growth pressure

The tumour microenvironment may contribute to tumorigenesis owing to mechanical forces such as fibrotic stiffness or mechanical pressure caused by the expansion of hyper-proliferative cells. Here we explore the contribution of the mechanical pressure exerted by tumour growth onto non-tumorous adjacent epithelium. In the early stage of mouse colon tumour development in the Notch(+)Apc(+/1638N) mouse model, we observed mechanistic pressure stress in the non-tumorous epithelial cells caused by hyper-proliferative adjacent crypts overexpressing active Notch, which is associated with increased Ret and β-catenin signalling. We thus developed a method that allows the delivery of a defined mechanical pressure in vivo, by subcutaneously inserting a magnet close to the mouse colon. The implanted magnet generated a magnetic force on ultra-magnetic liposomes, stabilized in the mesenchymal cells of the connective tissue surrounding colonic crypts after intravenous injection. The magnetically induced pressure quantitatively mimicked the endogenous early tumour growth stress in the order of 1,200 Pa, without affecting tissue stiffness, as monitored by ultrasound strain imaging and shear wave elastography. The exertion of pressure mimicking that of tumour growth led to rapid Ret activation and downstream phosphorylation of β-catenin on Tyr654, imparing its interaction with the E-cadherin in adherens junctions, and which was followed by β-catenin nuclear translocation after 15 days. As a consequence, increased expression of β-catenin-target genes was observed at 1 month, together with crypt enlargement accompanying the formation of early tumorous aberrant crypt foci. Mechanical activation of the tumorigenic β-catenin pathway suggests unexplored modes of tumour propagation based on mechanical signalling pathways in healthy epithelial cells surrounding the tumour, which may contribute to tumour heterogeneity.

Comb-push ultrasound shear elastography of breast masses: initial results show promise

Purpose or Objective

To evaluate the performance of Comb-push Ultrasound Shear Elastography (CUSE) for classification of breast masses.

Materials and Methods

CUSE is an ultrasound-based quantitative two-dimensional shear wave elasticity imaging technique, which utilizes multiple laterally distributed acoustic radiation force (ARF) beams to simultaneously excite the tissue and induce shear waves. Female patients who were categorized as having suspicious breast masses underwent CUSE evaluations prior to biopsy. An elasticity estimate within the breast mass was obtained from the CUSE shear wave speed map. Elasticity estimates of various types of benign and malignant masses were compared with biopsy results.

Results

Fifty-four female patients with suspicious breast masses from our ongoing study are presented. Our cohort included 31 malignant and 23 benign breast masses. Our results indicate that the mean shear wave speed was significantly higher in malignant masses (6 ± 1.58 m/s) in comparison to benign masses (3.65 ± 1.36 m/s). Therefore, the stiffness of the mass quantified by the Young’s modulus is significantly higher in malignant masses. According to the receiver operating characteristic curve (ROC), the optimal cut-off value of 83 kPa yields 87.10% sensitivity, 82.61% specificity, and 0.88 for the area under the curve (AUC).

Conclusion

CUSE has the potential for clinical utility as a quantitative diagnostic imaging tool adjunct to B-mode ultrasound for differentiation of malignant and benign breast masses.

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis

We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

Characterization of the nonlinear elastic properties of soft tissues using the supersonic shear imaging (SSI) technique: inverse method, ex vivo and in vivo experiments

Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed.

Spatial characterization of corneal biomechanical properties with optical coherence elastography after UV cross-linking

Corneal collagen cross-linking (CXL) is a clinical treatment for keratoconus that structurally reinforces degenerating ocular tissue, thereby limiting disease progression. Clinical outcomes would benefit from noninvasive methods to assess tissue material properties in affected individuals. Regional variations in tissue properties were quantified before and after CXL in rabbit eyes using optical coherence elastography (OCE) imaging. Low-amplitude (<1µm) elastic waves were generated using micro air-pulse stimulation and the resulting wave amplitude and speed were measured using phase-stabilized swept-source OCE. OCE imaging following CXL treatment demonstrates increased corneal stiffness through faster elastic wave propagation speeds and lower wave amplitudes.

Acoustic waves in medical imaging and diagnostics

Up until about two decades ago acoustic imaging and ultrasound imaging were synonymous. The term ultrasonography, or its abbreviated version sonography, meant an imaging modality based on the use of ultrasonic compressional bulk waves. Beginning in the 1990s, there started to emerge numerous acoustic imaging modalities based on the use of a different mode of acoustic wave: shear waves. Imaging with these waves was shown to provide very useful and very different information about the biological tissue being examined. We discuss the physical basis for the differences between these two basic modes of acoustic waves used in medical imaging and analyze the advantages associated with shear acoustic imaging. A comprehensive analysis of the range of acoustic wavelengths, velocities and frequencies that have been used in different imaging applications is presented. We discuss the potential for future shear wave imaging applications.