Nonlinear viscoelastic properties of tissue assessed by ultrasound

Cross-Image Dependency Modeling for Breast Ultrasound Segmentation

We present a novel deep network (namely BUSSeg) equipped with both within- and cross-image long-range dependency modeling for automated lesions segmentation from breast ultrasound images, which is a quite daunting task due to (1) the large variation of breast lesions, (2) the ambiguous lesion boundaries, and (3) the existence of speckle noise and artifacts in ultrasound images. Our work is motivated by the fact that most existing methods only focus on modeling the within-image dependencies while neglecting the cross-image dependencies, which are essential for this task under limited training data and noise. We first propose a novel cross-image dependency module (CDM) with a cross-image contextual modeling scheme and a cross-image dependency loss (CDL) to capture more consistent feature expression and alleviate noise interference. Compared with existing cross-image methods, the proposed CDM has two merits. First, we utilize more complete spatial features instead of commonly used discrete pixel vectors to capture the semantic dependencies between images, mitigating the negative effects of speckle noise and making the acquired features more representative. Second, the proposed CDM includes both intra- and inter-class contextual modeling rather than just extracting homogeneous contextual dependencies. Furthermore, we develop a parallel bi-encoder architecture (PBA) to tame a Transformer and a convolutional neural network to enhance BUSSeg's capability in capturing within-image long-range dependencies and hence offer richer features for CDM. We conducted extensive experiments on two representative public breast ultrasound datasets, and the results demonstrate that the proposed BUSSeg consistently outperforms state-of-the-art approaches in most metrics.

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.

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.

Study on the Viscoelasticity Measurement of Materials Based on Surface Reflected Waves

The reflected waves received from ultrasonic waves propagating in materials contain information that constitutes the physical properties, material composition, defects, and degradation states. When measuring the dynamic viscoelasticity, the traditional bottom reflection method (BRM) cannot be used to measure the bottom irregular samples. In this paper, the storage modulus, loss modulus, and loss tangent are extracted by the surface reflection method (SRM) to evaluate the elastomer sample viscoelasticity. A theoretical study on the phase change caused by multiple reflections in the case of non-thin layer coupling is conducted. Based on this research, the experimental system is built. The results show that considering the thickness of the coupling layer can optimize the determination of viscoelasticity and reduce the error of the viscoelastic evaluation results of an elastomer with the traditional BRM. Finally, based on the principle of the SRM, the density of the elastomers is measured, and the feasibility and overall efficiency of this method are verified by experiments.

Curl-Based Finite Element Reconstruction of the Shear Modulus Without Assuming Local Homogeneity: Time Harmonic Case

In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.

A nonlinear elasticity phantom containing spherical inclusions

The strain image contrast of some in vivo breast lesions changes with increasing applied load. This change is attributed to differences in the nonlinear elastic properties of the constituent tissues suggesting some potential to help classify breast diseases by their nonlinear elastic properties. A phantom with inclusions and long-term stability is desired to serve as a test bed for nonlinear elasticity imaging method development, testing, etc. This study reports a phantom designed to investigate nonlinear elastic properties with ultrasound elastographic techniques. The phantom contains four spherical inclusions and was manufactured from a mixture of gelatin, agar and oil. The phantom background and each of the inclusions have distinct Young's modulus and nonlinear mechanical behavior. This phantom was subjected to large deformations (up to 20%) while scanning with ultrasound, and changes in strain image contrast and contrast-to-noise ratio between inclusion and background, as a function of applied deformation, were investigated. The changes in contrast over a large deformation range predicted by the finite element analysis (FEA) were consistent with those experimentally observed. Therefore, the paper reports a procedure for making phantoms with predictable nonlinear behavior, based on independent measurements of the constituent materials, and shows that the resulting strain images (e.g., strain contrast) agree with that predicted with nonlinear FEA.

Theoretical limitations of the elastic wave equation inversion for tissue elastography

This article examines the theoretical limitations of the local inversion techniques for the measurement of the tissue elasticity. Most of these techniques are based on the estimation of the phase speed or the algebraic inversion of a one-dimensional wave equation. To analyze these techniques, the wave equation in an elastic continuum is revisited. It is proven that in an infinite medium, harmonic shear waves can travel at any phase speed greater than the classically known shear wave speed, mu/rho, by demonstrating this for a special case with cylindrical symmetry. Hence in addition to the mechanical properties of the tissue, the phase speed depends on the geometry of the wave as well. The elastic waves in an infinite cylindrical rod are studied. It is proven that multiple phase speeds can coexist for a harmonic wave at a single frequency. This shows that the phase speed depends not only on the mechanical properties of the tissue but also on its shape. The final conclusion is that the only way to avoid theoretical artifacts in the elastograms obtained by the local inversion techniques is to use the shear wave equation as expressed in the curl of the displacements, i.e., the rotations, for the inversion.

Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility

We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with overall strain, the variation of the secant modulus with overall applied strain and finally the distribution of the nonlinear parameter in a fully nonlinear hyperelastic model of the breast tissue.

Freehand real-time elastography: impact of scanning parameters on image quality and in vitro intra- and interobserver validations

Real-time elastography is a method for visualization of the elastic properties of soft tissue and may potentially enable differentiation between malignant and benign pathologic lesions. Our aim was to validate the method on a tissue-mimicking (TM) phantom and to evaluate the influence of different scanning parameters and investigator variability. A TM-phantom containing eight spherical inclusions with known storage modulus was examined using two different transducers on an ultrasound (US) scanner equipped with software for real-time elasticity imaging. The ultrasound transducers were moved vertically in a repetitive manner to induce strain. Two investigators performed series of standardized elastography scans applying a 0-4 categorical quality scale to evaluate the influence of seven parameters: dynamic range of elasticity, region-of-interest, frequency of transducer movement, rejection of elastogram noise, frame rate, persistence and smoothing. Subsequently, repeated examinations of four selected inclusions were performed using a visual analog scale (VAS) where investigators marked a 100 mm horizontal line representing the span in image quality based on experience from the first examination. The hardest and softest inclusions were imaged more clearly than the inclusions with elasticity more similar to the background material. Intraobserver agreement on elastogram quality was good (kappa: 0.67 - 0.75) and interobserver agreement average (kappa: 0.55 - 0.56) when using the categorical scale. The subsequent VAS evaluation gave intraclass-correlation coefficients for the two observers of 0.98 and 0.93, respectively, and an interclass-correlation coefficient of 0.93. Real-time elastography adequately visualized isoechoic inclusions with different elastic properties in a TM-phantom with acceptable intra- and interobserver agreement. Dynamic range of elasticity was the parameter with most impact on the elastographic visualization of inclusions.

Viscoelastic parameter estimation based on spectral analysis

This paper introduces a new technique for the robust estimation of relaxation-time distribution in tissue. The main novelty is in the use of the phase of transfer functions calculated from a time series of strain measurements at multiple locations. Computer simulations with simulated measurement noise demonstrate the feasibility of the approach. An experimental apparatus and software were developed to confirm the simulations. The setup can be used both as a rheometer to characterize the overall mechanical properties of a material or as a vibro-elastography imaging device using an ultrasound system. The algorithms were tested on tissue mimicking phantoms specifically developed to exhibit contrast in elasticity and relaxation time. The phantoms were constructed using a combination of gelatin and a polyvinyl alcohol sponge to produce the desired viscoelastic properties. The tissue parameters were estimated and the elasticity and relaxation time of the materials have been used as complementary features to distinguish different materials. The estimation results are consistent with the rheometry, verifying that the relaxation time can be used as a complementary feature to elasticity to delineate the mechanical properties of the phantom.

Harmonic motion imaging for focused ultrasound (HMIFU): a fully integrated technique for sonication and monitoring of thermal ablation in tissues

FUS (focused ultrasound), or HIFU (high-intensity-focused ultrasound) therapy, a minimally or non-invasive procedure that uses ultrasound to generate thermal necrosis, has been proven successful in several clinical applications. This paper discusses a method for monitoring thermal treatment at different sonication durations (10 s, 20 s and 30 s) using the amplitude-modulated (AM) harmonic motion imaging for focused ultrasound (HMIFU) technique in bovine liver samples in vitro. The feasibility of HMI for characterizing mechanical tissue properties has previously been demonstrated. Here, a confocal transducer, combining a 4.68 MHz therapy (FUS) and a 7.5 MHz diagnostic (pulse-echo) transducer, was used. The therapy transducer was driven by a low-frequency AM continuous signal at 25 Hz, producing a stable harmonic radiation force oscillating at the modulation frequency. A pulser/receiver was used to drive the pulse-echo transducer at a pulse repetition frequency (PRF) of 5.4 kHz. Radio-frequency (RF) signals were acquired using a standard pulse-echo technique. The temperature near the ablation region was simultaneously monitored. Both RF signals and temperature measurements were obtained before, during and after sonication. The resulting axial tissue displacement was estimated using one-dimensional cross correlation. When temperature at the focal zone was above 48 degrees C during heating, the coagulation necrosis occurred and tissue damage was irreversible. The HMI displacement profiles in relation to the temperature and sonication durations were analyzed. At the beginning of heating, the temperature at the focus increased sharply, while the tissue stiffness decreased resulting in higher HMI displacements. This was confirmed by an increase of 0.8 microm degrees C(-1)(r=0.93, p<.005). After sustained heating, the tissue became irreversibly stiffer, followed by an associated decrease in the HMI displacement (-0.79 microm degrees C(-1), r=-0.92, p<0.001). Repeated experiments showed a reproducible pattern of the HMI displacement changes with a temperature at a slope equal to 0.8+/-0.11 and -0.79+/-0.14 microm degrees C(-1), prior to and after lesion formation in seven bovine liver samples, respectively. This technique was thus capable of following the protein-denatured lesion formation based on the variation of the HMI displacements. This method could, therefore, be applied for real-time monitoring of temperature-related stiffness changes of tissues during FUS, HIFU or other thermal therapies.