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

Stress amplification and relaxation imaging around cracks in nanocomposite gels using ultrasound elastography

The quantification and modeling of gel fracture under large strain and dissipative conditions is still an open issue. In this study, a novel method for investigating the mechanical behavior of gels under highly deformed states, specifically in the vicinity of the crack tip, was developed to gain insights into fracture processes. Shear wave elastography, originally developed for the biomedical community, is employed as a powerful tool to quantitatively map the local elasticity of model gels. Here, the local stress is experimentally measured from the shear wave velocity according to nonlinear acoustoelasticity theory. The stress concentration observed at the crack tip in elastic gels is validated using classical finite element methods. Subsequently, the mechanisms of network rearrangements in viscoelastic gels (with silica nanoparticles) are analyzed both spatially and temporally. These gels consist of 90 wt% water and are synthesized with sticky nanoparticles to introduce exchangeable sacrificial bonds that facilitate stress relaxation. The nanoparticles efficiently provide stress relaxation around the crack tip, mitigating a stress singularity. The amplitude of stress relaxation was measured quantitatively and appears to be higher closer to the crack. This paper showcases the feasibility and potential of a new experimental approach that enables non-invasive and dynamic mapping of gel fracture mechanics.

Integrating Learning-Based Priors With Physics-Based Models in Ultrasound Elasticity Reconstruction

Ultrasound elastography images, which enable quantitative visualization of tissue stiffness, can be reconstructed by solving an inverse problem. Classical model-based methods are usually formulated in terms of constrained optimization problems. To stabilize the elasticity reconstructions, regularization techniques, such as Tikhonov method, are used with the cost of promoting smoothness and blurriness in the reconstructed images. Thus, incorporating a suitable regularizer is essential for reducing the elasticity reconstruction artifacts, while finding the most suitable one is challenging. In this work, we present a new statistical representation of the physical imaging model, which incorporates effective signal-dependent colored noise modeling. Moreover, we develop a learning-based integrated statistical framework, which combines a physical model with learning-based priors. We use a dataset of simulated phantoms with various elasticity distributions and geometric patterns to train a denoising regularizer as the learning-based prior. We use fixed-point approaches and variants of gradient descent for solving the integrated optimization task following learning-based plug-and-play (PnP) prior and regularization by denoising (RED) paradigms. Finally, we evaluate the performance of the proposed approaches in terms of relative mean square error (RMSE) with nearly 20% improvement for both piecewise smooth simulated phantoms and experimental phantoms compared with the classical model-based methods and 12% improvement for both spatially varying breast-mimicking simulated phantoms and an experimental breast phantom, demonstrating the potential clinical relevance of our work. Moreover, the qualitative comparisons of reconstructed images demonstrate the robust performance of the proposed methods even for complex elasticity structures that might be encountered in clinical settings.

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 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.

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.

Shear Wave Elasticity Imaging Using Nondiffractive Bessel Apodized Acoustic Radiation Force

The acoustic radiation force impulse (ARFI) has been widely used in transient shear wave elasticity imaging (SWEI). For SWEI based on focused ARFI, the highest image quality exists inside the focal zone due to the limitation of the depth of focus and diffraction. Consequently, the areas outside the focal zone and in the near field present poor image quality. To address the limitations of the focused beam, we introduce Bessel apodized ARFI that enhances image quality and improves the depth of focus. The objective of this study is to evaluate the feasibility of SWEI based on Bessel ARF in simulation and experiment. We report measurements of elastogram image quality and depth of field in tissue-mimicking phantoms and ex vivo liver tissue. Our results demonstrate improved depth of field, image quality, and shear wave speed (SWS) estimation accuracy using Bessel push beams. As a result, Bessel ARF enlarges the field of view of elastograms. The signal-to-noise ratio (SNR) of Bessel SWEI is improved 26% compared with focused SWEI in homogeneous phantom. The estimated SWS by Bessel SWEI is closer to the measured SWS from a clinical scanner with an error of 0.3% compared to 2.4% with a focused beam. In heterogeneous phantoms, the contrast-to-noise ratios (CNRs) of shallow and deep inclusions are improved by 8.79 and 3.33 dB, respectively, under Bessel ARF. We also compare the results between Bessel SWEI and supersonic shear imaging (SSI), and the SNR of Bessel SWEI is improved by 8.1%. Compared with SSI, Bessel SWEI shows more accurate SWS estimates in high stiffness inclusions. Finally, Bessel SWEI can generate higher quality elastograms with less energy than conventional SSI.

Second-Generation Dual Scan Mammoscope With Photoacoustic, Ultrasound, and Elastographic Imaging Capabilities

We recently developed the photoacoustic dual-scan mammoscope (DSM), a system that images the patient in standing pose analog to X-ray mammography. The system simultaneously acquires three-dimensional photoacoustic and ultrasound (US) images of the mildly compressed breast. Here, we describe a second-generation DSM (DSM-2) system that offers a larger field of view, better system stability, higher ultrasound imaging quality, and the ability to quantify tissue mechanical properties. In the new system, we doubled the field of view through laterally shifted round-trip scanning. This new design allows coverage of the entire breast tissue. We also adapted precisely machined holders for the transducer-fiber bundle sets. The new holder increased the mechanical stability and facilitated image registration from the top and bottom scanners. The quality of the US image is improved by increasing the firing voltage and the number of firing angles. Finally, we incorporated quasi-static ultrasound elastography to allow comprehensive characterization of breast tissue. The performance of the new system was demonstrated through in vivo human imaging experiments. The experimental results confirmed the capability of the DSM-2 system as a powerful tool for breast imaging.

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.