Model-based elastography: a survey of approaches to the inverse elasticity problem

Continuous Shear Wave Elastography for Liver Using Frame-to-Frame Equalization of Complex Amplitude

This study addresses a crucial necessity in the field of noninvasive liver fibrosis diagnosis by introducing the concept of continuous shear wave elastography (C-SWE), utilizing an external vibration source and color Doppler imaging. However, an application of C-SWE to assess liver elasticity, a deep region within the human body, arises an issue of signal instability in the obtained data. To tackle this challenge, this work proposes a method involving the acquisition of multiple frames of datasets, which are subsequently compressed. Furthermore, the proposed frame-to-frame equalization method compensates discrepancies in the initial phase that might exist among multiple-frame datasets, thereby significantly enhancing signal stability. The experimental validation of this approach encompasses both phantom tests and in vivo experiments. In the phantom tests, the proposed technique is validated through a comparison with the established shear wave elastography (SWE) technique. The results demonstrate a remarkable agreement, with an error in shear wave velocity of less than 4.2%. Additionally, the efficacy of the proposed method is confirmed through in vivo tests. As a result, the stabilization of observed shear waves using the frame-to-frame equalization technique exhibits promising potential for accurately assessing human liver elasticity. These findings collectively underscore the viability of C-SWE as a potential diagnostic instrument for liver fibrosis.

[Reconstruction of elasticity modulus distribution base on semi-supervised neural network]

Accurate reconstruction of tissue elasticity modulus distribution has always been an important challenge in ultrasound elastography. Considering that existing deep learning-based supervised reconstruction methods only use simulated displacement data with random noise in training, which cannot fully provide the complexity and diversity brought by in-vivo ultrasound data, this study introduces the use of displacement data obtained by tracking in-vivo ultrasound radio frequency signals (i.e., real displacement data) during training, employing a semi-supervised approach to enhance the prediction accuracy of the model. Experimental results indicate that in phantom experiments, the semi-supervised model augmented with real displacement data provides more accurate predictions, with mean absolute errors and mean relative errors both around 3%, while the corresponding data for the fully supervised model are around 5%. When processing real displacement data, the area of prediction error of semi-supervised model was less than that of fully supervised model. The findings of this study confirm the effectiveness and practicality of the proposed approach, providing new insights for the application of deep learning methods in the reconstruction of elastic distribution from in-vivo ultrasound data.

On the soft tissue ultrasound elastography using FEM based inversion approach

Elastography is a medical imaging modality that enables visualization of tissue stiffness. It involves quasi-static or harmonic mechanical stimulation of the tissue to generate a displacement field which is used as input in an inversion algorithm to reconstruct tissue elastic modulus. This paper considers quasi-static stimulation and presents a novel inversion technique for elastic modulus reconstruction. The technique follows an inverse finite element framework. Reconstructed elastic modulus maps produced in this technique do not depend on the initial guess, while it is computationally less involved than iterative reconstruction approaches. The method was first evaluated using simulated data (in-silico) where modulus reconstruction's sensitivity to displacement noise and elastic modulus was assessed. To demonstrate the method's performance, displacement fields of two tissue mimicking phantoms determined using three different motion tracking techniques were used as input to the developed elastography method to reconstruct the distribution of relative elastic modulus of the inclusion to background tissue. In the next stage, the relative elastic modulus of three clinical cases pertaining to liver cancer patient were determined. The obtained results demonstrate reasonably high elastic modulus reconstruction accuracy in comparison with similar direct methods. Also it is associated with reduced computational cost in comparison with iterative techniques, which suffer from convergence and uniqueness issues, following the same formulation concept. Moreover, in comparison with other methods which need initial guess, the presented method does not require initial guess while it is easy to understand and implement.

Physics-informed UNets for discovering hidden elasticity in heterogeneous materials

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance - both in terms of accuracy and computational cost - by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods.

Unveiling the future of breast cancer assessment: a critical review on generative adversarial networks in elastography ultrasound

Elastography Ultrasound provides elasticity information of the tissues, which is crucial for understanding the density and texture, allowing for the diagnosis of different medical conditions such as fibrosis and cancer. In the current medical imaging scenario, elastograms for B-mode Ultrasound are restricted to well-equipped hospitals, making the modality unavailable for pocket ultrasound. To highlight the recent progress in elastogram synthesis, this article performs a critical review of generative adversarial network (GAN) methodology for elastogram generation from B-mode Ultrasound images. Along with a brief overview of cutting-edge medical image synthesis, the article highlights the contribution of the GAN framework in light of its impact and thoroughly analyzes the results to validate whether the existing challenges have been effectively addressed. Specifically, This article highlights that GANs can successfully generate accurate elastograms for deep-seated breast tumors (without having artifacts) and improve diagnostic effectiveness for pocket US. Furthermore, the results of the GAN framework are thoroughly analyzed by considering the quantitative metrics, visual evaluations, and cancer diagnostic accuracy. Finally, essential unaddressed challenges that lie at the intersection of elastography and GANs are presented, and a few future directions are shared for the elastogram synthesis research.

Myofascial and discogenic origins of lumbar pain: A critical review

The purpose of this three-part narrative review is to examine the anatomy of, and the research which supports, either the lumbar myofascia or intervertebral disc (IVD) as principal sources of our patient's low back pain. A comprehensive understanding of anatomical lumbar pain generators in combination with the current treatment-based classification system will further improve and enhance clinical decision-making skills. Section I reviews the anatomy of the spinal myofascia, myofascial sources of lumbar pain, and imaging of myofascial tissues. Part II reviews the anatomy of the IVD, examines the IVD as a potential lumbar pain generator, and includes detailed discussion on Nerve Growth Factor, Inflammatory Cytokines, Vertebral End Plates and Modic change, Annular tears, and Discogenic instability. Part III looks at the history of myofascial pain, lab-based research and myofascial pain, and various levels of discogenic pain provocation research including animal, laboratory and human subjects. Our review concludes with author recommendations on developing a comprehensive understanding of altered stress concentrations affecting the posterior annulus fibrosis, neo-innervation of the IVD, inflammatory cytokines, discogenic instability, and how this knowledge can complement use of the Treatment-Based Classification System.

Physics-Informed Deep-Learning For Elasticity: Forward, Inverse, and Mixed Problems

Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics-informed deep-learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the "eggshell" effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond.

A wavelet neural operator based elastography for localization and quantification of tumors

BACKGROUND AND OBJECTIVES

The application of intelligent imaging techniques and deep learning in the field of computer-aided diagnosis and medical imaging have improved and accelerated the early diagnosis of many diseases. Elastography is an imaging modality where an inverse problem is solved to extract the elastic properties of tissues and subsequently mapped to anatomical images for diagnostic purposes. In the present work, we propose a wavelet neural operator-based approach for correctly learning the non-linear mapping of elastic properties directly from measured displacement field data.

METHODS

The proposed framework learns the underlying operator behind the elastic mapping and thus can map any displacement data from a family to the elastic properties. The displacement fields are first uplifted to a high-dimensional space using a fully connected neural network. On the lifted data, certain iterations are performed using wavelet neural blocks. In each wavelet neural block, the lifted data are decomposed into low, and high-frequency components using wavelet decomposition. To learn the most relevant patterns and structural information from the input, the neural network kernels are directly convoluted with the outputs of the wavelet decomposition. Thereafter the elasticity field is reconstructed from the outputs from convolution. The mapping between the displacement and the elasticity using wavelets is unique and remains stable during training.

RESULTS

The proposed framework is tested on several artificially fabricated numerical examples, including a benign-cum-malignant tumor prediction problem. The trained model was also tested on real Ultrasound-based elastography data to demonstrate the applicability of the proposed scheme in clinical usage. The proposed framework reproduces the highly accurate elasticity field directly from the displacement inputs.

CONCLUSIONS

The proposed framework circumvents different data pre-processing and intermediate steps utilized in traditional methods, hence providing an accurate elasticity map. The computationally efficient framework requires fewer epochs for training, which bodes well for its clinical usability for real-time predictions. The weights and biases from pre-trained models can also be employed for transfer learning, which reduces the effective training time with random initialization.

Reconstructing the Spatial Distribution of the Relative Shear Modulus in Quasi-static Ultrasound Elastography: Plane Stress Analysis

Quasi-static ultrasound elastography (QSUE) is an imaging technique that mainly provides axial strain maps of tissues when the latter are subjected to compression. In this article, a method for reconstructing the relative shear modulus distribution within a linear elastic and isotropic medium, in QSUE, is introduced. More specifically, the plane stress inverse problem is considered. The proposed method is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces, and only requires displacement fields in the analyzed media to be determined. Results from plane stress and 3-D numerical simulations, as well as from phantom experiments, showed that the method is able to reconstruct the different regions within a medium, with shear modulus contrasts that unambiguously reveal whether inclusions are stiffer or softer than the surrounding material. More specifically, for the plane stress simulations, inclusion-to-background modulus ratios were found to be very accurately estimated, with an error lower than 3%. For the 3-D simulations, for which the plane stress conditions are no longer satisfied, these ratios were, as expected, less accurate, with an error that remained lower than 10% for two of the three cases analyzed but was around 34% for the last case. Concerning the phantom experiments, a comparison with a shear wave elastography technique from a clinical ultrasound scanner was also made. Overall, the inclusion-to-background shear modulus ratios obtained with our approach were found to be closer to those given by the phantom manufacturer than the ratios provided by the clinical system.

Reverberant magnetic resonance elastographic imaging using a single mechanical driver

Reverberant elastography provides fast and robust estimates of shear modulus; however, its reliance on multiple mechanical drivers hampers clinical utility. In this work, we hypothesize that for constrained organs such as the brain, reverberant elastography can produce accurate magnetic resonance elastograms with a single mechanical driver. To corroborate this hypothesis, we performed studies on healthy volunteers (n= 3); and a constrained calibrated brain phantom containing spherical inclusions with diameters ranging from 4-18 mm. In both studies (i.e. phantom and clinical), imaging was performed at frequencies of 50 and 70 Hz. We used the accuracy and contrast-to-noise ratio performance metrics to evaluate reverberant elastograms relative to those computed using the established subzone inversion method. Errors incurred in reverberant elastograms varied from 1.3% to 16.6% when imaging at 50 Hz and 3.1% and 16.8% when imaging at 70 Hz. In contrast, errors incurred in subzone elastograms ranged from 1.9% to 13% at 50 Hz and 3.6% to 14.9% at 70 Hz. The contrast-to-noise ratio of reverberant elastograms ranged from 63.1 to 73 dB compared to 65 to 66.2 dB for subzone elastograms. The average global brain shear modulus estimated from reverberant and subzone elastograms was 2.36 ± 0.07 kPa and 2.38 ± 0.11 kPa, respectively, when imaging at 50 Hz and 2.70 ± 0.20 kPa and 2.89 ± 0.60 kPa respectively, when imaging at 70 Hz. The results of this investigation demonstrate that reverberant elastography can produce accurate, high-quality elastograms of the brain with a single mechanical driver.

Quasi-static ultrasound elastography of ex-vivo porcine vocal folds during passive elongation and adduction

OBJECTIVES

The elastic properties of the vocal folds have great influence on the primary sound and thus on the entire subsequent phonation process. Muscle contractions in the larynx can alter the elastic properties of the vocal fold tissue. Quasi-static ultrasound elastography is a non-destructive examination method that can be applied to ex-vivo vocal folds. In this work, porcine vocal folds were passively elongated and adducted and the changes of the elastic properties due to that manipulations were measured.

METHODS

Manipulations were performed by applying force to sewn-in sutures. Elongation was achieved by a suture attached to the thyroid cartilage, which was pulled forward by defined weights. Adduction was effected by two sutures exerting torque on the arytenoid cartilage. A series of ten specimens was examined and evaluated using a quasi-static elastography algorithm. In addition, the surface stretch was measured optically using tattooed reference points.

RESULTS

This study showed that the expected stiffening of the tissue during the manipulations can be measured using quasi-static ultrasound elastography. The measured effect of elongation and adduction, both of which result in stretching of the tissue, is stiffening. However, the relative change of specific manipulations is not the same for the same load on different larynges, but is rather related to stretch caused and other uninvestigated factors.

CONCLUSION

The passive elongation and adduction of vocal folds stiffen the tissue of the vocal folds and can be measured using ultrasound elastography.

Ensemble Kalman inversion for magnetic resonance elastography

Magnetic resonance elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this paper a new and powerful method (ensemble Kalman inversion with level sets (EKI)) of MRE inversion is proposed and tested. The method has critical advantages: material property variation at disease boundaries can be accurately identified, and uncertainty of the reconstructed material properties can be evaluated by consequence of the probabilistic nature of the method. EKI is tested in 2D and 3D experiments with synthetic MRE data of the human kidney. It is demonstrated that the proposed inversion method is accurate and fast.

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'.

Intravascular optical coherence elastography

Optical coherence elastography (OCE), a functional extension of optical coherence tomography (OCT), visualizes tissue strain to deduce the tissue's biomechanical properties. In this study, we demonstrate intravascular OCE using a 1.1 mm motorized catheter and a 1.6 MHz Fourier domain mode-locked OCT system. We induced an intraluminal pressure change by varying the infusion rate from the proximal end of the catheter. We analysed the pixel-matched phase change between two different frames to yield the radial strain. Imaging experiments were carried out in a phantom and in human coronary arteries in vitro. At an imaging speed of 3019 frames/s, we were able to capture the dynamic strain. Stiff inclusions in the phantom and calcification in atherosclerotic plaques are associated with low strain values and can be distinguished from the surrounding soft material, which exhibits elevated strain. For the first time, circumferential intravascular OCE images are provided side by side with conventional OCT images, simultaneously mapping both the tissue structure and stiffness.

Reproducibility assessment of a biomechanical model-based elasticity imaging method for identifying changes in left ventricular mechanical stiffness

Purpose

Cardiotoxicity of antineoplastic therapies is increasingly a risk to cancer patients treated with curative intent with years of life to protect. Studies highlight the importance of identifying early cardiac decline in cancer patients undergoing cardiotoxic therapies. Accurate tools to study this are a critical clinical need. Current and emerging methods for assessing cardiotoxicity are too coarse for identifying preclinical cardiac degradation or too cumbersome for clinical implementation.

Approach

In the previous work, we developed a noninvasive biomechanical model-based elasticity imaging methodology (BEIM) to assess mechanical stiffness changes of the left ventricle (LV) based on routine cine cardiac magnetic resonance (CMR) images. We examine this methodology to assess methodological reproducibility. We assessed a cohort of 10 participants that underwent test/retest short-axis CMR imaging at baseline and follow-up sessions as part of a previous publicly available study. We compare test images to retest images acquired within the same session to assess within-session reproducibility. We also compare test and retest images acquired at the baseline imaging session to test and retest images acquired at the follow-up imaging session to assess between-session reproducibility.

Results

We establish the within-session and between-session reproducibility of our method, with global elasticity demonstrating repeatability within a range previously demonstrated in cardiac strain imaging studies. We demonstrate increased repeatability of global elasticity compared to segmental elasticity for both within-session and between-session. Within-subject coefficients of variation for within-session test/retest images globally for all modulus directions and a mechanical fractional mechanical stiffness anisotropy metric ranged from 11% to 28%.

Conclusions

Results suggest that our methodology can reproducibly generate estimates of relative mechanical elasticity of the LV and provides a threshold for distinguishing true changes in myocardial mechanical stiffness from experimental variation. BEIM has applications in identifying preclinical cardiotoxicity in breast cancer patients undergoing antineoplastic therapies.

Ultrasound estimation of strain time constant and vascular permeability in tumors using a CEEMDAN and linear regression-based method

Ultrasound poroelastography focuses on the estimation of the spatio-temporal mechanical behavior of tissues using data often corrupted with non-stationary noise. The cumulative strain calculated from prolonged temporal acquisition of RF data can face the problem of aggregate noise. This noise can significantly affect the accuracy of curve fitting techniques necessary to estimate the clinically significant strain Time Constant (TC) and related parameters. We present a new technique, which decomposes the non-linear temporal behavior of the differential strain to extract the monotonic decaying trend by using the time-domain and data-driven Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm. A linear regression scheme is then used to obtain the slope of the transformed non-linear trend, which carries information about the strain TC. Assessment of Vascular Permeability (VP), a transport parameter indicative of tumor growth, requires accurate strain TC estimations. Finite Element (FE), ultrasound simulations and in vivo experiments are used to investigate the performance of the proposed technique. Based on the simulation analysis, the average Percentage Relative Error (PRE) values of our method are 4.15% (for TC estimation) and 5.00% (for VP estimation) at 20 dB SNR level for different Percentage of Good Frames (PGF) (i.e., 20%, 50%, 75%, and 100%). These PRE values are substantially lower than those obtained using other conventional elastographic techniques. Our proposed method could become a new data-adaptive tool for analyzing the non-linear time-dependent response of complex tissues such as cancers.

Analyses of internal structures and defects in materials using physics-informed neural networks

Characterizing internal structures and defects in materials is a challenging task, often requiring solutions to inverse problems with unknown topology, geometry, material properties, and nonlinear deformation. Here, we present a general framework based on physics-informed neural networks for identifying unknown geometric and material parameters. By using a mesh-free method, we parameterize the geometry of the material using a differentiable and trainable method that can identify multiple structural features. We validate this approach for materials with internal voids/inclusions using constitutive models that encompass the spectrum of linear elasticity, hyperelasticity, and plasticity. We predict the size, shape, and location of the internal void/inclusion as well as the elastic modulus of the inclusion. Our general framework can be applied to other inverse problems in different applications that involve unknown material properties and highly deformable geometries, targeting material characterization, quality assurance, and structural design.

Evaluation of breast stiffness pathology based on breast compression during mammography: Proposal for novel breast stiffness scale classification

Breast cancer is diagnosed through a patient's Breast Self-Examination (BSE), Clinical Breast Examination (CBE), or para-clinical methods. False negativity of PCM in breast cancer diagnostics leads to a persisting problem associated with breast tumors diagnosed only in advanced stages. As the tumor volume/size at which it becomes invasive is not clear, BSE and CBE play an exceedingly important role in the early diagnosis of breast cancer. The quality and effectiveness of BSE and CBE depend on several factors, among which breast stiffness is the most important one. In this study, the authors present four methods for evaluating breast stiffness pathology during mammography examination based on the outputs obtained during the breast compression process, id est, without exposing the patient to X-Ray radiation. Based on the subjective assessment of breast stiffness by experienced medical examiners, a novel breast stiffness classification was designed, and the best method of its objective measurement was calibrated to fit the scale. Hence, this study provides an objective tool for the identification of patients who, being unable to perform valid BSE, could benefit from an increased frequency of mammography screening. Dum vivimus servimus.

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.

Reconstruction of shear wave speed in tissue-mimicking phantoms from aliased pulse-echo imaging of high-frequency wavefields

Quantitative elasticity estimation in medical and industrial applications may benefit from advancements in reconstruction of shear wave speed with enhanced resolution. Here, shear wave speed is reconstructed from pulse-echo ultrasound imaging of elastic waves induced by high-frequency (>400 Hz), time-harmonic mechanical excitation. Particle displacement in shear wavefields is mapped from measured interframe phase differences with compensation for timing of multiple scan lines, then processed by spatial Fourier analysis to estimate the predominant wave speed and analyzed by algebraic wavefield inversion to reconstruct wave speed maps. Reconstructions of shear wave speed from simulated wavefields illustrate the accuracy and spatial resolution available with both methods, as functions of signal-to-noise ratio and sizes of windows used for Fourier analysis or wavefield smoothing. The methods are applied to shear wavefields with frequencies up to six times the Nyquist rate, thus extending the frequency range measurable by a given imaging system. Wave speed measurements in tissue-mimicking phantoms are compared with supersonic shear imaging and mechanical tensile testing, demonstrating feasibility of the wavefield measurement and wave speed reconstruction methods employed.

In silicoevaluation and optimisation of magnetic resonance elastography of the liver

Objective.Magnetic resonance elastography (MRE) is widely adopted as a biomarker of liver fibrosis. However,in vivoMRE accuracy is difficult to assess.Approach.Finite element model (FEM) simulation was employed to evaluate liver MRE accuracy and inform methodological optimisation. MRE data was simulated in a 3D FEM of the human torso including the liver, and compared with spin-echo echo-planar imaging MRE acquisitions. The simulated MRE results were compared with the ground truth magnitude of the complex shear modulus (∣G*∣) for varying: (1) ground truth liver ∣G*∣; (2) simulated imaging resolution; (3) added noise; (4) data smoothing. Motion and strain-based signal-to-noise (SNR) metrics were evaluated on the simulated data as a means to select higher-quality voxels for preparation of acquired MRE summary statistics of ∣G*∣.Main results.The simulated MRE accuracy for a given ground truth ∣G*∣ was found to be a function of imaging resolution, motion-SNR and smoothing. At typical imaging resolutions, it was found that due to under-sampling of the MRE wave-field, combined with motion-related noise, the reconstructed simulated ∣G*∣ could contain errors on the scale of the difference between liver fibrosis stages, e.g. 54% error for ground truth ∣G*∣ = 1 kPa. Optimum imaging resolutions were identified for given ground truth ∣G*∣ and motion-SNR levels.Significance.This study provides important knowledge on the accuracy and optimisation of liver MRE. For example, for motion-SNR ≤ 5, to distinguish between liver ∣G*∣ of 2 and 3 kPa (i.e. early-stage liver fibrosis) it was predicted that the optimum isotropic voxel size is 4-6 mm.

Reconstructing the shear modulus contrast of linear elastic and isotropic media in quasi-static ultrasound elastography

This study focuses on the reconstruction of the shear modulus contrast in linear elastic and isotropic media, in quasi-static ultrasound elastography. The method proposed is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces to estimate the parameters of interest. Experimental results obtained with CIRS phantoms are presented, for which regions with different mechanical properties can be clearly identified in the stiffness contrast maps. Elastic modulus images collected with a shear-wave elastography technique from a clinical ultrasound scanner (Aixplorer) are also provided for comparison. Results show very similar values for the modulus ratios determined by the two elastography approaches.

2D tissue strain tensor imaging in quasi-static ultrasound elastography. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021;2021:2847-2851. [PMID: 34891841 DOI: 10.1109/embc46164.2021.9630570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Accurately estimating all strain components in quasi-static ultrasound elastography is crucial for the full analysis of biological media. In this paper, 2D strain tensor imaging is investigated, using a partial differential equation (PDE)-based regularization method. More specifically, this method employs the tissue property of incompressibility to smooth the displacement fields and reduce the noise in the strain components. The performance of the method is assessed with phantoms and in vivo breast tissues. For all the media examined, the results showed a significant improvement in both lateral displacement and strain but also, to a lesser extent, in the shear strain. Moreover, axial displacement and strain were only slightly modified by the regularization, as expected. Finally, the easier detectability of the inclusion/lesion in the final lateral strain images is associated with higher elastographic contrast-to-noise ratios (CNRs), with values in the range [0.68 - 9.40] vs [0.09 - 0.38] before regularization.

Validations of the microchannel flow model for characterizing vascularized tissues

The microchannel flow model postulates that stress-strain behavior in soft tissues is influenced by the time constants of fluid-filled vessels related to Poiseuille’s law. A consequence of this framework is that changes in fluid viscosity and changes in vessel diameter (through vasoconstriction) have a measurable effect on tissue stiffness. These influences are examined through the theory of the microchannel flow model. Then, the effects of viscosity and vasoconstriction are demonstrated in gelatin phantoms and in perfused tissues, respectively. We find good agreement between theory and experiments using both a simple model made from gelatin and from living, perfused, placental tissue ex vivo.

Technological perspectives on laser speckle micro-rheology for cancer mechanobiology research

SIGNIFICANCE

The ability to measure the micro-mechanical properties of biological tissues and biomaterials is crucial for numerous fields of cancer research, including tumor mechanobiology, tumor-targeting drug delivery, and therapeutic development.

AIM

Our goal is to provide a renewed perspective on the mainstream techniques used for micro-mechanical evaluation of biological tissues and biomimetic scaffoldings. We specifically focus on portraying the outlook of laser speckle micro-rheology (LSM), a technology that quantifies the mechanical properties of biomaterials and tissues in a rapid, non-contact manner.

APPROACH

First, we briefly explain the motivation and significance of evaluating the tissue micro-mechanics in various fields of basic and translational cancer research and introduce the key concepts and quantitative metrics used to explain the mechanical properties of tissue. This is followed by reviewing the general active and passive themes of measuring micro-mechanics. Next, we focus on LSM and elaborate on the theoretical grounds and working principles of this technique. Then, the perspective for measuring the micro-mechanical properties via LSM is outlined. Finally, we draw an overview picture of LSM in cancer mechanobiology research.

RESULTS

With the continued emergence of new approaches for measuring the mechanical attributes of biological tissues, the field of micro-mechanical imaging is at its boom. As one of these competent innovations, LSM presents a tremendous potential for both technical maturation and prospective applications in cancer biomechanics and mechanobiology research.

CONCLUSION

By elaborating the current viewpoint of LSM, we expect to accelerate the expansion of this approach to new territories in both technological domains and applied fields. This renewed perspective on LSM may also serve as a road map for other micro-mechanical measurement concepts to be applied for answering mechanobiological questions.

Reverberant shear wave phase gradients for elastography

Reverberant shear wave fields are produced when multiple sources and multiple reflections establish a complex three-dimensional wave field within an organ. The expected values are assumed to be isotropic across all directions and the autocorrelation functions for velocity are expressed in terms of spherical Bessel functions. These results provide the basis for adroit implementations of elastography from imaging systems that can map out the internal velocity or displacement of tissues during reverberant field excitations. By examining the phase distribution of the reverberant field, additional estimators can be derived. In particular, we demonstrate that the reverberantphase gradientis shown to be proportional to the local value of wavenumber. This phase estimator is less sensitive to imperfections in the reverberant field distribution and requires a smaller support window, relative to earlier estimators based on autocorrelation. Applications are shown in simulations, phantoms, andin vivoliver.

Learning hidden elasticity with deep neural networks

Elastography is an imaging technique to reconstruct elasticity distributions of heterogeneous objects. Since cancerous tissues are stiffer than healthy ones, for decades, elastography has been applied to medical imaging for noninvasive cancer diagnosis. Although the conventional strain-based elastography has been deployed on ultrasound diagnostic-imaging devices, the results are prone to inaccuracies. Model-based elastography, which reconstructs elasticity distributions by solving an inverse problem in elasticity, may provide more accurate results but is often unreliable in practice due to the ill-posed nature of the inverse problem. We introduce ElastNet, a de novo elastography method combining the theory of elasticity with a deep-learning approach. With prior knowledge from the laws of physics, ElastNet can escape the performance ceiling imposed by labeled data. ElastNet uses backpropagation to learn the hidden elasticity of objects, resulting in rapid and accurate predictions. We show that ElastNet is robust when dealing with noisy or missing measurements. Moreover, it can learn probable elasticity distributions for areas even without measurements and generate elasticity images of arbitrary resolution. When both strain and elasticity distributions are given, the hidden physics in elasticity-the conditions for equilibrium-can be learned by ElastNet.

Quantitative Determination of Local Density of Iron Oxide Nanoparticles Used for Drug Targeting Employing Inverse Magnetomotive Ultrasound

Numerous medical applications make use of magnetic nanoparticles, which increase the demand for imaging procedures that are capable of visualizing this kind of particle. Magnetomotive ultrasound (MMUS) is an ultrasound-based imaging modality that can detect tissue, which is permeated by magnetic nanoparticles. However, currently, MMUS can only provide a qualitative mapping of the particle density in the particle-loaded tissue. In this contribution, we present an enhanced MMUS procedure, which enables an estimation of the quantitative level of the local nanoparticle concentration in tissue. The introduced modality involves an adjustment of simulated data to measurement data. To generate these simulated data, the physical processes that arise during the MMUS imaging procedure have to be emulated which can be a computing-intensive proceeding. Since this considerable calculation effort may handicap clinical applications, we further present an efficient approach to calculate the decisive physical quantities and a suitable way to adjust these simulated quantities to the measurement data with only moderate computational effort. For this purpose, we use the result data of a conventional MMUS measurement and the knowledge on the magnetic field quantities and on the mechanical parameters describing the biological tissue, namely, the density, the longitudinal wave velocity, and the shear wave velocity. Experiments on tissue-mimicking phantoms demonstrate that the presented technique can indeed be utilized to determine the local nanoparticle concentration in tissue quantitatively in the correct order of magnitude. By investigating test phantoms of simple geometry, the mean particle concentration of the particle-laden area could be determined with less than 22% deviation to the nominal value.

Inversion-recovery MR elastography of the human brain for improved stiffness quantification near fluid-solid boundaries

PURPOSE

In vivo MR elastography (MRE) holds promise as a neuroimaging marker. In cerebral MRE, shear waves are introduced into the brain, which also stimulate vibrations in adjacent CSF, resulting in blurring and biased stiffness values near brain surfaces. We here propose inversion-recovery MRE (IR-MRE) to suppress CSF signal and improve stiffness quantification in brain surface areas.

METHODS

Inversion-recovery MRE was demonstrated in agar-based phantoms with solid-fluid interfaces and 11 healthy volunteers using 31.25-Hz harmonic vibrations. It was performed by standard single-shot, spin-echo EPI MRE following 2800-ms IR preparation. Wave fields were acquired in 10 axial slices and analyzed for shear wave speed (SWS) as a surrogate marker of tissue stiffness by wavenumber-based multicomponent inversion.

RESULTS

Phantom SWS values near fluid interfaces were 7.5 ± 3.0% higher in IR-MRE than MRE (P = .01). In the brain, IR-MRE SNR was 17% lower than in MRE, without influencing parenchymal SWS (MRE: 1.38 ± 0.02 m/s; IR-MRE: 1.39 ± 0.03 m/s; P = .18). The IR-MRE tissue-CSF interfaces appeared sharper, showing 10% higher SWS near brain surfaces (MRE: 1.01 ± 0.03 m/s; IR-MRE: 1.11 ± 0.01 m/s; P < .001) and 39% smaller ventricle sizes than MRE (P < .001).

CONCLUSIONS

Our results show that brain MRE is affected by fluid oscillations that can be suppressed by IR-MRE, which improves the depiction of anatomy in stiffness maps and the quantification of stiffness values in brain surface areas. Moreover, we measured similar stiffness values in brain parenchyma with and without fluid suppression, which indicates that shear wavelengths in solid and fluid compartments are identical, consistent with the theory of biphasic poroelastic media.

A Quasi-Static Quantitative Ultrasound Elastography Algorithm Using Optical Flow

Ultrasound elastography is a constantly developing imaging technique which is capable of displaying the elastic properties of tissue. The measured characteristics could help to refine physiological tissue models, but also indicate pathological changes. Therefore, elastography data give valuable insights into tissue properties. This paper presents an algorithm that measures the spatially resolved Young’s modulus of inhomogeneous gelatin phantoms using a CINE sequence of a quasi-static compression and a load cell measuring the compressing force. An optical flow algorithm evaluates the resulting images, the stresses and strains are computed, and, conclusively, the Young’s modulus and the Poisson’s ratio are calculated. The whole algorithm and its results are evaluated by a performance descriptor, which determines the subsequent calculation and gives the user a trustability index of the modulus estimation. The algorithm shows a good match between the mechanically measured modulus and the elastography result—more precisely, the relative error of the Young’s modulus estimation with a maximum error 35%. Therefore, this study presents a new algorithm that is capable of measuring the elastic properties of gelatin specimens in a quantitative way using only the image data. Further, the computation is monitored and evaluated by a performance descriptor, which measures the trustability of the results.

MR Elastography of the Abdomen: Experimental Protocols

Application of MRE for noninvasive evaluation of renal fibrosis has great potential for noninvasive assessment in patients with chronic kidney disease (CKD). CKD leads to severe complications, which require dialysis or kidney transplant and could even result in death. CKD in native kidneys and interstitial fibrosis in allograft kidneys are the two major kidney fibrotic pathologies where MRE may be clinically useful. Both these conditions can lead to extensive morbidity, mortality, and high health care costs. Currently, biopsy is the standard method for renal fibrosis staging. This method of diagnosis is painful, invasive, limited by sampling bias, exhibits inter- and intraobserver variability, requires prolonged hospitalization, poses risk of complications and significant bleeding, and could even lead to death. MRE based methods can potentially be useful to noninvasively detect, stage, and monitor renal fibrosis, reducing the need for renal biopsy. In this chapter, we describe experimental procedure and step by step instructions to run MRE along with some illustrative applications. We also includes sections on how to perform data quality check and analysis methods.This publication is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers.

An adversarial machine learning framework and biomechanical model-guided approach for computing 3D lung tissue elasticity from end-expiration 3DCT

PURPOSE

Lung elastography aims at measuring the lung parenchymal tissue elasticity for applications ranging from diagnostic purposes to biomechanically guided deformations. Characterizing the lung tissue elasticity requires four-dimensional (4D) lung motion as an input, which is currently estimated by deformably registering 4D computed tomography (4DCT) datasets. Since 4DCT imaging is widely used only in a radiotherapy treatment setup, there is a need to predict the elasticity distribution in the absence of 4D imaging for applications within and outside of radiotherapy domain.

METHODS

In this paper, we present a machine learning-based method that predicts the three-dimensional (3D) lung tissue elasticity distribution for a given end-expiration 3DCT. The method to predict the lung tissue elasticity from an end-expiration 3DCT employed a deep neural network that predicts the tissue elasticity for the given CT dataset. For training and validation purposes, we employed five-dimensional CT (5DCT) datasets and a finite element biomechanical lung model. The 5DCT model was first used to generate end-expiration lung geometry, which was taken as the source lung geometry for biomechanical modeling. The deformation vector field pointing from end expiration to end inhalation was computed from the 5DCT model and taken as input in order to solve for the lung tissue elasticity. An inverse elasticity estimation process was employed, where we iteratively solved for the lung elasticity distribution until the model reproduced the ground-truth deformation vector field. The machine learning process uses a specific type of learning process, namely a constrained generalized adversarial neural network (cGAN) that learned the lung tissue elasticity in a supervised manner. The biomechanically estimated tissue elasticity together with the end-exhalation CT was the input for the supervised learning. The trained cGAN generated the elasticity from a given breath-hold CT image. The elasticity estimated was validated in two approaches. In the first approach, a L2-norm-based direct comparison was employed between the estimated elasticity and the ground-truth elasticity. In the second approach, we generated a synthetic four-dimensional CT (4DCT0 using a lung biomechanical model and the estimated elasticity and compared the deformations with the ground-truth 4D deformations using three image similarity metrics: mutual Information (MI), structured similarity index (SSIM), and normalized cross correlation (NCC).

RESULTS

The results show that a cGAN-based machine learning approach was effective in computing the lung tissue elasticity given the end-expiration CT datasets. For the training data set, we obtained a learning accuracy of 0.44 ± 0.2 KPa. For the validation dataset, consisting of 13 4D datasets, we were able to obtain an accuracy of 0.87 ± 0.4 KPa. These results show that the cGAN-generated elasticity correlates well with that of the underlying ground-truth elasticity. We then integrated the estimated elasticity with the biomechanical model and applied the same boundary conditions in order to generate the end inhalation CT. The cGAN-generated images were very similar to that of the original end inhalation CT. The average value of the MI is 1.77 indicating the high local symmetricity between the ground truth and the cGAN elasticity-generated end inhalation CT data. The average value of the structural similarity for the 13 patients was observed to be 0.89 indicating the high structural integrity of the cGAN elasticity-generated end inhalation CT. Finally, the average NCC value of 0.97 indicates that potential variations in the contrast and brightness of the cGAN elasticity-generated end inhalation CT and the ground-truth end inhalation CT.

CONCLUSION

The cGAN-generated lung tissue elasticity given an end-expiration CT image can be computed in near real time. Using the lung tissue elasticity along with a biomechanical model, 4D lung deformations can be generated from a given end-expiration CT image within clinically acceptable numerical accuracy.

MR elastography of liver: current status and future perspectives

Non-invasive evaluation of liver fibrosis has evolved over the last couple of decades. Currently, elastography techniques are the most widely used non-invasive methods for clinical evaluation of chronic liver disease (CLD). MR elastography (MRE) of the liver has been used in the clinical practice for nearly a decade and continues to be widely accepted for detection and staging of liver fibrosis. With MRE, one can directly visualize propagating shear waves through the liver and an inversion algorithm in the scanner automatically converts the shear wave properties into an elastogram (stiffness map) on which liver stiffness can be calculated. The commonly used MRE method, two-dimensional gradient recalled echo (2D-GRE) sequence has produced excellent results in the evaluation of liver fibrosis in CLD from various etiologies and newer clinical indications continue to emerge. Advances in MRE technique, including 3D MRE, automated liver elasticity calculation, improvements in shear wave delivery and patient experience, are promising to provide a faster and more reliable MRE of liver. Innovations, including evaluation of mechanical parameters, such as loss modulus, displacement, and volumetric strain, are promising for comprehensive evaluation of CLD as well as understanding pathophysiology, and in differentiating various etiologies of CLD. In this review, the current status of the MRE of liver in CLD are outlined and followed by a brief description of advanced techniques and innovations in MRE of liver.

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.

Toward Quantitative and Operator-independent Quasi-static Ultrasound Elastography: An Ex Vivo Feasibility Study

It is known that the elasticity of liver reduces progressively in the case of diffuse liver disease. Currently, the diagnosis of diffuse liver disease requires a biopsy, which is an invasive procedure. In this paper, we evaluate and report a noninvasive method that can be used to quantify liver stiffness using quasi-static ultrasound elastography approach. Quasi-static elastography is popular in clinical applications where the qualitative assessment of relative tissue stiffness is enough, whereas its potential is relatively underutilized in liver imaging due to lack of local stiffness contrast in the case of diffuse liver disease. Recently, we demonstrated an approach of using a calibrated reference layer to produce quantitative modulus elastograms of the target tissue in simulations and phantom experiments. In a separate work, we reported the development of a compact handheld device to reduce inter- and intraoperator variability in freehand elastography. In this work, we have integrated the reference layer with a handheld controlled compression device and evaluate it for quantitative liver stiffness imaging application. The performance of this technique was assessed on ex vivo goat liver samples. The Young's modulus values obtained from indentation measurements of liver samples acted as the ground truth for comparison. The results from this work demonstrate that by combining the handheld device along with reference layer, the estimated Young's modulus value approaches the ground truth with less error compared with that obtained using freehand compression (8% vs. 15%). The results suggest that the intra- and interoperator reproducibility of the liver elasticity also improved when using the handheld device. Elastography with a handheld compression device and reference layer is a reliable and simple technique to provide a quantitative measure of elasticity.

Advances in Magnetic Resonance Elastography of Liver

Magnetic resonance elastography (MRE) is the most accurate noninvasive technique in diagnosing fibrosis and cirrhosis in patients with chronic liver disease (CLD). The accuracy of hepatic MRE in distinguishing the severity of disease has been validated in studies of patients with various CLDs. Advanced hepatic MRE is a reliable, comfortable, and inexpensive alternative to liver biopsy for disease diagnosing, progression monitoring, and clinical decision making in patients with CLDs. This article summarizes current knowledge of the technical advances and innovations in hepatic MRE, and the clinical applications in various hepatic diseases.

Linearized Bayesian inference for Young's modulus parameter field in an elastic model of slender structures

The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young's modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions.

Physics-guided machine learning for 3-D quantitative quasi-static elasticity imaging

We present a 3D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2D QUSE and demonstrate the feasibility of recovering the 3D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3D material property distribution, but may significantly improve the accuracy of the Young's modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young's modulus from force-displacement measurements.

Actuator-assisted Subpitch Translation-capable Transducer for Elastography: Preliminary Performance Assessment

In conventional linear array (CLA)-based elastography tissue compression in one direction (e.g., axial) leads to an expansion in all other directions (lateral, elevation). Therefore, the estimation of the lateral displacements and strains may provide additional information on the tissue mechanical properties. However, these are not exploited fully due to the inherent limitation in lateral sampling. Recently, a method named actuator-assisted beam translation (ABT) was demonstrated to address this issue, wherein the focused beam was translated at subpitch locations using an external bench-top setup. However, because such bench-top setup may be impractical for routine clinical use, an ultrasound transducer was customized to have an internal actuator. The performance of the customized transducer was studied through experiments on phantoms for rotation elastography application, which requires precise lateral displacement estimation. Furthermore, the results obtained from ABT was compared against the currently practiced spatial displacement compounding (SDC) method, which is known to yield better quality lateral displacement estimates than conventional approaches. The results show that the ABT method yields a full-width half-maximum (FWHM) value, taken from the lateral profile across a point scatterer, which is 65% and 24% smaller than that obtained using CLA and SDC methods, respectively. Furthermore, the contrast-to-noise ratio (CNR) estimated from rotation elastogram obtained using ABT method is better by 300% and 35% compared with that obtained by using CLA and SDC methods, respectively. Furthermore, the results demonstrate an additional advantage of having larger field of view (FoV) for the ABT method compared with spatial compounding approach.

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.

Inversion of displacement fields to quantify the magnetic particle distribution in homogeneous elastic media from magnetomotive ultrasound

Magnetomotive ultrasound (MMUS) contrasts superparamagnetic iron-oxide nanoparticles (SPIOs) that undergo submicrometer-scale displacements in response to a magnetic gradient force applied to an imaging sample. Typically, MMUS signals are defined in a way that is proportional to the medium displacement, rendering an indirect measure of the density distribution of SPIOs embedded within. Displacement-based MMUS, however, suffers from 'halo effects' that extend into regions without SPIOs due to their inherent mechanical coupling with the medium. To reduce such effects and to provide a more accurate representation of the SPIO density distribution, we propose a model-based inversion of MMUS displacement fields by reconstructing the body force distribution. Displacement fields are modelled using the static Navier-Cauchy equation for linear, homogeneous, and isotropic media, and the body force fields are, in turn, reconstructed by minimizing a regularized least-squares error functional between the modelled and the measured displacement fields. This reconstruction, when performed on displacement fields of two tissue-mimicking phantoms with cuboidal SPIO-laden inclusions, improved the range of errors in measured heights and widths of the inclusions from 54%-282% pre-inversion to-15%-20%. Likewise, the post-inversion contrast to noise ratios (CNRs) of the images were significantly larger than displacement-derived CNRs alone (p   =  0.0078, Wilcoxon signed rank test). Qualitatively, it was found that inversion ameliorates halo effects and increases overall detectability of the inclusion. These findings highlight the utility of model-based inversion as a tool for both signal processing and accurate characterization of the number density distribution of SPIOs in magnetomotive imaging.

Data-Driven Elasticity Imaging Using Cartesian Neural Network Constitutive Models and the Autoprogressive Method

Quasi-static elasticity imaging techniques rely on model-based mathematical inverse methods to estimate mechanical parameters from force-displacement measurements. These techniques introduce simplifying assumptions that preclude exploration of unknown mechanical properties with potential diagnostic value. We previously reported a data-driven approach to elasticity imaging using artificial neural networks (NNs) that circumvents limitations associated with model-based inverse methods. NN constitutive models can learn stress-strain behavior from force-displacement measurements using the autoprogressive (AutoP) method without prior assumptions of the underlying constitutive model. However, information about internal structure was required. We invented Cartesian NN constitutive models (CaNNCMs) that learn the spatial variations of material properties. We are presenting the first implementation of CaNNCMs trained with AutoP to develop data-driven models of 2-D linear-elastic materials. Both simulated and experimental force-displacement data were used as input to AutoP to show that CaNNCMs are able to model both continuous and discrete material property distributions with no prior information of internal object structure. Furthermore, we demonstrate that CaNNCMs are robust to measurement noise and can reconstruct reasonably accurate Young's modulus images from a sparse sampling of measurement data. CaNNCMs are an important step toward clinical use of data-driven elasticity imaging using AutoP.

Reconstruction of Viscosity Maps in Ultrasound Shear Wave Elastography

Change in viscoelastic properties of biological tissues may often be symptomatic of a dysfunction that can be correlated to tissue pathology. Shear wave elastography is an imaging method mainly used to assess stiffness but with the potential to measure viscoelasticity of biological tissues. This can enable tissue characterization; and thus, can be used as a marker to improve diagnosis of pathological lesions. In this study, a frequency-shift method based framework is presented for the reconstruction of viscosity by analyzing the spectral properties of acoustic radiation force-induced shear waves. The aim of the study was to investigate the feasibility of viscosity reconstruction maps in homogeneous as well as heterogeneous samples. Experiments were performed in four in vitro phantoms, two ex vivo porcine liver samples, two ex vivo fatty duck liver samples, and one in vivo fatty goose liver. Successful viscosity maps were reconstructed in homogeneous and heterogeneous phantoms with embedded mechanical inclusions having different geometries. Quantitative values of viscosity obtained for two porcine liver tissues, two fatty duck liver samples, and one goose fatty liver were (mean ± SD) 0.61 ± 0.21, 0.52 ± 0.35; 1.28 ± 0.54, 1.36 ± 0.73, and 1.67 ± 0.70 Pa.s, respectively.

Towards quantitative quasi-static ultrasound elastography using a reference layer for liver imaging application: A preliminary assessment

Changes in tissue elasticity are generally correlated with pathological phenomena. For example, diffuse liver disease progressively reduces the elasticity of the liver. Quasi-static elastography is popular in clinical applications to visualize regions with different relative stiffness. However, the limitation of this technique is that it provides only qualitative information. To overcome this, we investigate the use of a calibrated reference layer, sandwiched between the transducer and the tissue surface, to quantitatively image the unknown modulus of the examined tissue. The performance of the method was studied through simulations and experiments on agar-gelatin phantoms having Young's modulus within a range appropriate for the liver application. Furthermore, we explored the translational capability of the proposed method to work with existing commercially-available ultrasound scanners having elastography option. The Young's modulus value of the phantom estimated from quantitative elastography in simulation and experiment was compared against the corresponding ground-truth modulus value obtained from COMSOL and Universal Testing Machine (UTM) results, respectively. The results obtained for the compressive elastic modulus of the underlying phantom using quasi-static ultrasound elastography was found to be within 6% and 11% in simulation and experiments, respectively, to the corresponding ground-truth values.

Volumetric quantitative optical coherence elastography with an iterative inversion method

It is widely accepted that accurate mechanical properties of three-dimensional soft tissues and cellular samples are not available on the microscale. Current methods based on optical coherence elastography can measure displacements at the necessary resolution, and over the volumes required for this task. However, in converting this data to maps of elastic properties, they often impose assumptions regarding homogeneity in stress or elastic properties that are violated in most realistic scenarios. Here, we introduce novel, rigorous, and computationally efficient inverse problem techniques that do not make these assumptions, to realize quantitative volumetric elasticity imaging on the microscale. Specifically, we iteratively solve the three-dimensional elasticity inverse problem using displacement maps obtained from compression optical coherence elastography. This is made computationally feasible with adaptive mesh refinement and domain decomposition methods. By employing a transparent, compliant surface layer with known shear modulus as a reference for the measurement, absolute shear modulus values are produced within a millimeter-scale sample volume. We demonstrate the method on phantoms, on a breast cancer sample ex vivo, and on human skin in vivo. Quantitative elastography on this length scale will find wide application in cell biology, tissue engineering and medicine.

Dispersion in Tissue-Mimicking Gels Measured with Shear Wave Elastography and Torsional Vibration Rheometry

Dispersion, or the frequency dependence of mechanical parameters, is a primary confounding factor in elastography comparisons. We present a study of dispersion in tissue-mimicking gels over a wide frequency band using a combination of ultrasound shear wave elastography (SWE), and a novel torsional vibration rheometry which allows independent mechanical measurement of SWE samples. Frequency-dependent complex shear modulus was measured in homogeneous gelatin hydrogels of two different bloom strengths while controlling for confounding factors such as temperature, water content and material aging. Furthermore, both techniques measured the same physical samples, thereby eliminating possible variation caused by batch-to-batch gel variation, sample geometry differences and boundary artifacts. The wide-band measurement, from 1 to 1800 Hz, captured a 30%-50% increase in the storage modulus and a nearly linear increase with frequency of the loss modulus. The magnitude of the variation suggests that accounting for dispersion is essential for meaningful comparisons between SWE implementations.