A Model-Based Approach to Investigate the Effect of a Long Bone Fracture on Ultrasound Strain Elastography

A Novel Poroelastography Method for High-Quality Estimation of Lateral Strain, Solid Stress, and Fluid Pressure In Vivo

Assessment of mechanical and transport properties of tissues using ultrasound elasticity imaging requires accurate estimations of the spatiotemporal distribution of volumetric strain. Due to physical constraints such as pitch limitation and the lack of phase information in the lateral direction, the quality of lateral strain estimation is typically significantly lower than the quality of axial strain estimation. In this paper, a novel lateral strain estimation technique based on the physics of compressible porous media is developed, tested and validated. This technique is referred to as "Poroelastography-based Ultrasound Lateral Strain Estimation" (PULSE). PULSE differs from previously proposed lateral strain estimators as it uses the underlying physics of internal fluid flow within a local region of the tissue as theoretical foundation. PULSE establishes a relation between spatiotemporal changes in the axial strains and corresponding spatiotemporal changes in the lateral strains, effectively allowing assessment of lateral strains with comparable quality of axial strain estimators. We demonstrate that PULSE can also be used to accurately track compression-induced solid stresses and fluid pressure in cancers using ultrasound poroelastography (USPE). In this study, we report the theoretical formulation for PULSE and validation using finite element (FE) and ultrasound simulations. PULSE-generated results exhibit less than 5% percentage relative error (PRE) and greater than 90% structural similarity index (SSIM) compared to ground truth simulations. Experimental results are included to qualitatively assess the performance of PULSE in vivo. The proposed method can be used to overcome the inherent limitations of non-axial strain imaging and improve clinical translatability of USPE.

MixTURE: L1-Norm-Based Mixed Second-Order Continuity in Strain Tensor Ultrasound Elastography

Energy-based displacement tracking of ultrasound images can be implemented by optimizing a cost function consisting of a data term, a mechanical congruency term, and first- and second-order continuity terms. This approach recently provided a promising solution to 2-D axial and lateral displacement tracking in ultrasound strain elastography. However, the associated second-order regularizer only considers the unmixed second derivatives and disregards the mixed derivatives, thereby providing suboptimal noise suppression and limiting possibilities for total strain tensor imaging. We propose to improve axial, lateral, axial shear, and lateral shear strain estimation quality by formulating and optimizing a novel -norm-based second-order regularizer that penalizes both mixed and unmixed displacement derivatives. We name the proposed technique -MixTURE, which stands for -norm Mixed derivative for Total UltRasound Elastography. When compared with simulated ground-truth results, the mean structural similarity (MSSIM) obtained with -MixTURE ranged 0.53-0.86 and the mean absolute error (MAE) ranged 0.00053-0.005. In addition, the mean elastographic signal-to-noise ratio (SNR) achieved with simulated, experimental phantom, and in vivo breast datasets ranged 1.87-52.98, and the mean elastographic contrast-to-noise ratio (CNR) ranged 7.40-24.53. When compared with a closely related existing technique that does not consider the mixed derivatives, -MixTURE generally outperformed the MSSIM, MAE, SNR, and CNR by up to 37.96%, 67.82%, and 25.53% in the simulated, experimental phantom, and in vivo datasets, respectively. These results collectively highlight the ability of -MixTURE to deliver highly accurate axial, lateral, axial shear, and lateral shear strain estimates and advance the state-of-the-art in elastography-guided diagnostic and interventional decisions.

Multimodal mechano-microscopy reveals mechanical phenotypes of breast cancer spheroids in three dimensions

Cancer cell invasion relies on an equilibrium between cell deformability and the biophysical constraints imposed by the extracellular matrix (ECM). However, there is little consensus on the nature of the local biomechanical alterations in cancer cell dissemination in the context of three-dimensional (3D) tumor microenvironments (TMEs). While the shortcomings of two-dimensional (2D) models in replicating in situ cell behavior are well known, 3D TME models remain underutilized because contemporary mechanical quantification tools are limited to surface measurements. Here, we overcome this major challenge by quantifying local mechanics of cancer cell spheroids in 3D TMEs. We achieve this using multimodal mechano-microscopy, integrating optical coherence microscopy-based elasticity imaging with confocal fluorescence microscopy. We observe that non-metastatic cancer spheroids show no invasion while showing increased peripheral cell elasticity in both stiff and soft environments. Metastatic cancer spheroids, however, show ECM-mediated softening in a stiff microenvironment and, in a soft environment, initiate cell invasion with peripheral softening associated with early metastatic dissemination. This exemplar of live-cell 3D mechanotyping supports that invasion increases cell deformability in a 3D context, illustrating the power of multimodal mechano-microscopy for quantitative mechanobiology in situ.

Non-Invasive Imaging of Mechanical Properties of Cancers In Vivo Based on Transformations of the Eshelby's Tensor Using Compression Elastography

Knowledge of the mechanical properties is of great clinical significance for diagnosis, prognosis and treatment of cancers. Recently, a new method based on Eshelby's theory to simultaneously assess Young's modulus (YM) and Poisson's ratio (PR) in tissues has been proposed. A significant limitation of this method is that accuracy of the reconstructed YM and PR is affected by the orientation/alignment of the tumor with the applied stress. In this paper, we propose a new method to reconstruct YM and PR in cancers that is invariant to the 3D orientation of the tumor with respect to the axis of applied stress. The novelty of the proposed method resides on the use of a tensor transformation to improve the robustness of Eshelby's theory and reconstruct YM and PR of tumors with high accuracy and in realistic experimental conditions. The method is validated using finite element simulations and controlled experiments using phantoms with known mechanical properties. The in vivo feasibility of the developed method is demonstrated in an orthotopic mouse model of breast cancer. Our results show that the proposed technique can estimate the YM and PR with overall accuracy of (97.06 ± 2.42) % under all tested tumor orientations. Animal experimental data demonstrate the potential of the proposed methodology in vivo. The proposed method can significantly expand the range of applicability of the Eshelby's theory to tumors and provide new means to accurately image and quantify mechanical parameters of cancers in clinical conditions.

Alternating direction method of multipliers for displacement estimation in ultrasound strain elastography

BACKGROUND

Ultrasound strain imaging, which delineates mechanical properties to detect tissue abnormalities, involves estimating the time delay between two radio-frequency (RF) frames collected before and after tissue deformation. The existing regularized optimization-based time-delay estimation (TDE) techniques suffer from at least one of the following drawbacks: (1) The regularizer is not aligned with the tissue deformation physics due to taking only the first-order displacement derivative into account; (2) TheL 2 $L2$ -norm of the displacement derivatives, which oversmooths the estimated time-delay, is utilized as the regularizer; (3) The modulus function defined mathematically should be approximated by a smooth function to facilitate the optimization ofL 1 $L1$ -norm.

PURPOSE

Our purpose is to develop a novel TDE technique that resolves the aforementioned shortcomings of the existing algorithms.

METHODS

Herein, we propose employing the alternating direction method of multipliers (ADMM) for optimizing a novel cost function consisting ofL 2 $L2$ -norm data fidelity term andL 1 $L1$ -norm first- and second-order spatial continuity terms. ADMM empowers the proposed algorithm to use different techniques for optimizing different parts of the cost function and obtain high-contrast strain images with smooth backgrounds and sharp boundaries. We name our technique ADMM for totaL variaTion RegUlarIzation in ultrasound STrain imaging (ALTRUIST). ALTRUIST's efficacy is quantified using absolute error (AE), Structural SIMilarity (SSIM), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain ratio (SR) with respect to GLUE, OVERWIND, andL 1 $L1$ -SOUL, three recently published energy-based techniques, and UMEN-Net, a state-of-the-art deep learning-based algorithm. Analysis of variance (ANOVA)-led multiple comparison tests and paired t $t$ -tests at5 % $5\%$ overall significance level were conducted to assess the statistical significance of our findings. The Bonferroni correction was taken into account in all statistical tests. Two simulated layer phantoms, three simulated resolution phantoms, one hard-inclusion simulated phantom, one multi-inclusion simulated phantom, one experimental breast phantom, and three in vivo liver cancer datasets have been used for validation experiments. We have published the ALTRUIST code at http://code.sonography.ai.

RESULTS

ALTRUIST substantially outperforms the four state-of-the-art benchmarks in all validation experiments, both qualitatively and quantitatively. ALTRUIST yields up to573 % ∗ ${573\%}^{*}$ ,41 % ∗ ${41\%}^{*}$ , and51 % ∗ ${51\%}^{*}$ SNR improvements and443 % ∗ ${443\%}^{*}$ ,53 % ∗ ${53\%}^{*}$ , and15 % ∗ ${15\%}^{*}$ CNR improvements overL 1 $L1$ -SOUL, its closest competitor, for simulated, phantom, and in vivo liver cancer datasets, respectively, where the asterisk (*) indicates statistical significance. In addition, ANOVA-led multiple comparison tests and paired t $t$ -tests indicate that ALTRUIST generally achieves statistically significant improvements over GLUE, UMEN-Net, OVERWIND, andL 1 $L1$ -SOUL in terms of AE, SSIM map, SNR, and CNR.

CONCLUSIONS

A novel ultrasonic displacement tracking algorithm named ALTRUIST has been developed. The principal novelty of ALTRUIST is incorporating ADMM for optimizing anL 1 $L1$ -norm regularization-based cost function. ALTRUIST exhibits promising performance in simulation, phantom, and in vivo experiments.

Exploiting Mechanics-Based Priors for Lateral Displacement Estimation in Ultrasound Elastography

Tracking the displacement between the pre- and post-deformed radio-frequency (RF) frames is a pivotal step of ultrasound elastography, which depicts tissue mechanical properties to identify pathologies. Due to ultrasound's poor ability to capture information pertaining to the lateral direction, the existing displacement estimation techniques fail to generate an accurate lateral displacement or strain map. The attempts made in the literature to mitigate this well-known issue suffer from one of the following limitations: 1) Sampling size is substantially increased, rendering the method computationally and memory expensive. 2) The lateral displacement estimation entirely depends on the axial one, ignoring data fidelity and creating large errors. This paper proposes exploiting the effective Poisson's ratio (EPR)-based mechanical correspondence between the axial and lateral strains along with the RF data fidelity and displacement continuity to improve the lateral displacement and strain estimation accuracies. We call our techniques MechSOUL (Mechanically-constrained Second-Order Ultrasound eLastography) and L1 -MechSOUL ( L1 -norm-based MechSOUL), which optimize L2 - and L1 -norm-based penalty functions, respectively. Extensive validation experiments with simulated, phantom, and in vivo datasets demonstrate that MechSOUL and L1 -MechSOUL's lateral strain and EPR estimation abilities are substantially superior to those of the recently-published elastography techniques. We have published the MATLAB codes of MechSOUL and L1 -MechSOUL at https://code.sonography.ai.

Assessment of spinal cord injury using ultrasound elastography in a rabbit model in vivo

The effect of the mechanical micro-environment on spinal cord injury (SCI) and treatment effectiveness remains unclear. Currently, there are limited imaging methods that can directly assess the localized mechanical behavior of spinal cords in vivo. In this study, we apply new ultrasound elastography (USE) techniques to assess SCI in vivo at the site of the injury and at the time of one week post injury, in a rabbit animal model. Eleven rabbits underwent laminectomy procedures. Among them, spinal cords of five rabbits were injured during the procedure. The other six rabbits were used as control. Two neurological statuses were achieved: non-paralysis and paralysis. Ultrasound data were collected one week post-surgery and processed to compute strain ratios. Histologic analysis, mechanical testing, magnetic resonance imaging (MRI), computerized tomography and MRI diffusion tensor imaging (DTI) were performed to validate USE results. Strain ratios computed via USE were found to be significantly different in paralyzed versus non-paralyzed rabbits. The myelomalacia histologic score and spinal cord Young's modulus evaluated in selected animals were in good qualitative agreement with USE assessment. It is feasible to use USE to assess changes in the spinal cord of the presented animal model. In the future, with more experimental data available, USE may provide new quantitative tools for improving SCI diagnosis and prognosis.

Non-invasive imaging of interstitial fluid transport parameters in solid tumors in vivo

In this paper, new and non-invasive imaging methods to assess interstitial fluid transport parameters in tumors in vivo are developed, analyzed and experimentally validated. These parameters include extracellular volume fraction (EVF), interstitial fluid volume fraction (IFVF) and interstitial hydraulic conductivity (IHC), and they are known to have a critical role in cancer progression and drug delivery effectiveness. EVF is defined as the volume of extracellular matrix per unit volume of the tumor, while IFVF refers to the volume of interstitial fluid per unit bulk volume of the tumor. There are currently no established imaging methods to assess interstitial fluid transport parameters in cancers in vivo. We develop and test new theoretical models and imaging techniques to assess fluid transport parameters in cancers using non-invasive ultrasound methods. EVF is estimated via the composite/mixture theory with the tumor being modeled as a biphasic (cellular phase and extracellular phase) composite material. IFVF is estimated by modeling the tumor as a biphasic poroelastic material with fully saturated solid phase. Finally, IHC is estimated from IFVF using the well-known Kozeny-Carman method inspired by soil mechanics theory. The proposed methods are tested using both controlled experiments and in vivo experiments on cancers. The controlled experiments were performed on tissue mimic polyacrylamide samples and validated using scanning electron microscopy (SEM). In vivo applicability of the proposed methods was demonstrated using a breast cancer model implanted in mice. Based on the controlled experimental validation, the proposed methods can estimate interstitial fluid transport parameters with an error below 10% with respect to benchmark SEM data. In vivo results demonstrate that EVF, IFVF and IHC increase in untreated tumors whereas these parameters are observed to decrease over time in treated tumors. The proposed non-invasive imaging methods may provide new and cost-effective diagnostic and prognostic tools to assess clinically relevant fluid transport parameters in cancers in vivo.

Lateral Strain Imaging Using Self-Supervised and Physically Inspired Constraints in Unsupervised Regularized Elastography

Convolutional Neural Networks (CNN) have shown promising results for displacement estimation in UltraSound Elastography (USE). Many modifications have been proposed to improve the displacement estimation of CNNs for USE in the axial direction. However, the lateral strain, which is essential in several downstream tasks such as the inverse problem of elasticity imaging, remains a challenge. The lateral strain estimation is complicated since the motion and the sampling frequency in this direction are substantially lower than the axial one, and a lack of carrier signal in this direction. In computer vision applications, the axial and the lateral motions are independent. In contrast, the tissue motion pattern in USE is governed by laws of physics which link the axial and lateral displacements. In this paper, inspired by Hooke's law, we, first propose Physically Inspired ConsTraint for Unsupervised Regularized Elastography (PICTURE), where we impose a constraint on the Effective Poisson's ratio (EPR) to improve the lateral strain estimation. In the next step, we propose self-supervised PICTURE (sPICTURE) to further enhance the strain image estimation. Extensive experiments on simulation, experimental phantom and in vivo data demonstrate that the proposed methods estimate accurate axial and lateral strain maps.

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.

Incorporating Gradient Similarity for Robust Time Delay Estimation in Ultrasound Elastography

Energy-based ultrasound elastography techniques minimize a regularized cost function consisting of data and continuity terms to obtain local displacement estimates based on the local time-delay estimation (TDE) between radio frequency (RF) frames. The data term associated with the existing techniques takes only the amplitude similarity into account and hence is not sufficiently robust to the outlier samples present in the RF frames under consideration. This drawback creates noticeable artifacts in the strain image. To resolve this issue, we propose to formulate the data function as a linear combination of the amplitude and gradient similarity constraints. We estimate the adaptive weight concerning each similarity term following an iterative scheme. Finally, we optimize the nonlinear cost function in an efficient manner to convert the problem to a sparse system of linear equations which are solved for millions of variables. We call our technique rGLUE: robust data term in GLobal Ultrasound Elastography. rGLUE has been validated using simulation, phantom, in vivo liver, and breast datasets. In all our experiments, rGLUE substantially outperforms the recent elastography methods both visually and quantitatively. For simulated, phantom, and in vivo datasets, respectively, rGLUE achieves 107%, 18%, and 23% improvements of signal-to-noise ratio (SNR) and 61%, 19%, and 25% improvements of contrast-to-noise ratio (CNR) over global ultrasound elastography (GLUE), a recently published elastography algorithm.

Second-Order Ultrasound Elastography With L1-Norm Spatial Regularization

Time delay estimation (TDE) between two radio-frequency (RF) frames is one of the major steps of quasi-static ultrasound elastography, which detects tissue pathology by estimating its mechanical properties. Regularized optimization-based techniques, a prominent class of TDE algorithms, optimize a nonlinear energy functional consisting of data constancy and spatial continuity constraints to obtain the displacement and strain maps between the time-series frames under consideration. The existing optimization-based TDE methods often consider the L2 -norm of displacement derivatives to construct the regularizer. However, such a formulation over-penalizes the displacement irregularity and poses two major issues to the estimated strain field. First, the boundaries between different tissues are blurred. Second, the visual contrast between the target and the background is suboptimal. To resolve these issues, herein, we propose a novel TDE algorithm where instead of L2 -, L1 -norms of both first- and second-order displacement derivatives are taken into account to devise the continuity functional. We handle the non-differentiability of L1 -norm by smoothing the absolute value function's sharp corner and optimize the resulting cost function in an iterative manner. We call our technique Second-Order Ultrasound eLastography (SOUL) with the L1 -norm spatial regularization ( L1 -SOUL). In terms of both sharpness and visual contrast, L1 -SOUL substantially outperforms GLobal Ultrasound Elastography (GLUE), tOtal Variation rEgulaRization and WINDow-based time delay estimation (OVERWIND), and SOUL, three recently published TDE algorithms in all validation experiments performed in this study. In cases of simulated, phantom, and in vivo datasets, respectively, L1 -SOUL achieves 67.8%, 46.81%, and 117.35% improvements of contrast-to-noise ratio (CNR) over SOUL. The L1 -SOUL code can be downloaded from http://code.sonography.ai.

Estimation of Mechanical and Transport Parameters in Cancers Using Short Time Poroelastography

Mechanical and transport properties of cancers such as Young's modulus (YM), Poisson's ratio (PR), and vascular permeability (VP) have great clinical importance in cancer diagnosis, prognosis, and treatment. However, non-invasive estimation of these parameters in vivo is challenged by many practical factors. Elasticity imaging methods, such as "poroelastography", require prolonged data acquisition, which can limit their clinical applicability. In this paper, we investigate a new method to perform poroelastography experiments, which results in shorter temporal acquisition windows. This method is referred to as "short-time poroelastography" (STPE). Finite element (FE) and ultrasound simulations demonstrate that, using STPE, it is possible to accurately estimate YM, PR (within 10% error) using windows of observation (WoOs) of length as short as 1 underlying strain Time Constant (TC). The error was found to be almost negligible (< 3%) when using WoOs longer than 2 strain TCs. In the case of VP estimation, WoOs of at least 2 strain TCs are required to obtain an error < 8% (in simulations). The stricter requirement for the estimation of VP with respect to YM and PR is due its reliance on the transient strain behavior while YM and PR depend on the steady state strain values only. In vivo experimental data are used as a proof-of-principle of the potential applicability of the proposed methodology in vivo. The use of STPE may provide a means to efficiently perform poroelastography experiments without compromising the accuracy of the estimated tissue properties.

Deep GRU-CNN Model for COVID-19 Detection From Chest X-Rays Data

In the current era, data is growing exponentially due to advancements in smart devices. Data scientists apply a variety of learning-based techniques to identify underlying patterns in the medical data to address various health-related issues. In this context, automated disease detection has now become a central concern in medical science. Such approaches can reduce the mortality rate through accurate and timely diagnosis. COVID-19 is a modern virus that has spread all over the world and is affecting millions of people. Many countries are facing a shortage of testing kits, vaccines, and other resources due to significant and rapid growth in cases. In order to accelerate the testing process, scientists around the world have sought to create novel methods for the detection of the virus. In this paper, we propose a hybrid deep learning model based on a convolutional neural network (CNN) and gated recurrent unit (GRU) to detect the viral disease from chest X-rays (CXRs). In the proposed model, a CNN is used to extract features, and a GRU is used as a classifier. The model has been trained on 424 CXR images with 3 classes (COVID-19, Pneumonia, and Normal). The proposed model achieves encouraging results of 0.96, 0.96, and 0.95 in terms of precision, recall, and f1-score, respectively. These findings indicate how deep learning can significantly contribute to the early detection of COVID-19 in patients through the analysis of X-ray scans. Such indications can pave the way to mitigate the impact of the disease. We believe that this model can be an effective tool for medical practitioners for early diagnosis.

An unsupervised learning approach to ultrasound strain elastography with spatio-temporal consistency

Quasi-static ultrasound elastography (USE) is an imaging modality that measures deformation (i.e. strain) of tissue in response to an applied mechanical force. In USE, the strain modulus is traditionally obtained by deriving the displacement field estimated between a pair of radio-frequency data. In this work we propose a recurrent network architecture with convolutional long-short-term memory decoder blocks to improve displacement estimation and spatio-temporal continuity between time series ultrasound frames. The network is trained in an unsupervised way, by optimising a similarity metric between the reference and compressed image. Our training loss is also composed of a regularisation term that preserves displacement continuity by directly optimising the strain smoothness, and a temporal continuity term that enforces consistency between successive strain predictions. In addition, we propose an open-access in vivo database for quasi-static USE, which consists of radio-frequency data sequences captured on the arm of a human volunteer. Our results from numerical simulation and in vivo data suggest that our recurrent neural network can account for larger deformations, as compared with two other feed-forward neural networks. In all experiments, our recurrent network outperformed the state-of-the-art for both learning-based and optimisation-based methods, in terms of elastographic signal-to-noise ratio, strain consistency, and image similarity. Finally, our open-source code provides a 3D-slicer visualisation module that can be used to process ultrasound RF frames in real-time, at a rate of up to 20 frames per second, using a standard GPU.

Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

Changes in biomechanical properties of biological soft tissues are often associated with physiological dysfunctions. Since biological soft tissues are hydrated, viscoelasticity is likely suitable to represent its solid-like behavior using elasticity and fluid-like behavior using viscosity. Shear wave elastography is a non-invasive imaging technology invented for clinical applications that has shown promise to characterize various tissue viscoelasticity. It is based on measuring and analyzing velocities and attenuations of propagated shear waves. In this review, principles and technical developments of shear wave elastography for viscoelasticity characterization from organ to cellular levels are presented, and different imaging modalities used to track shear wave propagation are described. At a macroscopic scale, techniques for inducing shear waves using an external mechanical vibration, an acoustic radiation pressure or a Lorentz force are reviewed along with imaging approaches proposed to track shear wave propagation, namely ultrasound, magnetic resonance, optical, and photoacoustic means. Then, approaches for theoretical modeling and tracking of shear waves are detailed. Following it, some examples of applications to characterize the viscoelasticity of various organs are given. At a microscopic scale, a novel cellular shear wave elastography method using an external vibration and optical microscopy is illustrated. Finally, current limitations and future directions in shear wave elastography are presented.

Manufacturing and Characterization of Hybrid Bulk Voxelated Biomaterials Printed by Digital Anatomy 3D Printing

The advent of 3D digital printers has led to the evolution of realistic anatomical organ shaped structures that are being currently used as experimental models for rehearsing and preparing complex surgical procedures by clinicians. However, the actual material properties are still far from being ideal, which necessitates the need to develop new materials and processing techniques for the next generation of 3D printers optimized for clinical applications. Recently, the voxelated soft matter technique has been introduced to provide a much broader range of materials and a profile much more like the actual organ that can be designed and fabricated voxel by voxel with high precision. For the practical applications of 3D voxelated materials, it is crucial to develop the novel high precision material manufacturing and characterization technique to control the mechanical properties that can be difficult using the conventional methods due to the complexity and the size of the combination of materials. Here we propose the non-destructive ultrasound effective density and bulk modulus imaging to evaluate 3D voxelated materials printed by J750 Digital Anatomy 3D Printer of Stratasys. Our method provides the design map of voxelated materials and substantially broadens the applications of 3D digital printing in the clinical research area.

Displacement Estimation in Ultrasound Elastography Using Pyramidal Convolutional Neural Network

In this article, two novel deep learning methods are proposed for displacement estimation in ultrasound elastography (USE). Although convolutional neural networks (CNNs) have been very successful for displacement estimation in computer vision, they have been rarely used for USE. One of the main limitations is that the radio frequency (RF) ultrasound data, which is crucial for precise displacement estimation, has vastly different frequency characteristics compared with images in computer vision. Top-rank CNN methods used in computer vision applications are mostly based on a multilevel strategy, which estimates finer resolution based on coarser ones. This strategy does not work well for RF data due to its large high-frequency content. To mitigate the problem, we propose modified pyramid warping and cost volume network (MPWC-Net) and RFMPWC-Net, both based on PWC-Net, to exploit information in RF data by employing two different strategies. We obtained promising results using networks trained only on computer vision images. In the next step, we constructed a large ultrasound simulation database and proposed a new loss function to fine-tune the network to improve its performance. The proposed networks and well-known optical flow networks as well as state-of-the-art elastography methods are evaluated using simulation, phantom, and in vivo data. Our two proposed networks substantially outperform current deep learning methods in terms of contrast-to-noise ratio (CNR) and strain ratio (SR). Also, the proposed methods perform similar to the state-of-the-art elastography methods in terms of CNR and have better SR by substantially reducing the underestimation bias.

Incorporating Multiple Observations in global Ultrasound Elastography

In this paper, we propose a novel framework for time delay estimation in ultrasound elastography. In the presence of high acquisition noise, the state-of-the-art motion tracking techniques suffer from inaccurate estimation of displacement field. To resolve this issue, instead of one, we collect several ultrasound Radio-Frequency (RF) frames from both pre- and post-deformed scan planes to better investigate the data statistics. We formulate a non-linear cost function incorporating all observation frames from both levels of deformations. Beside data similarity, we impose axial and lateral continuity to exploit the prior information of spatial coherence. Most importantly, we consider the continuity among the displacement estimates obtained from different observation RF frames. This novel continuity constraint mainly contributes to the robustness of the proposed technique to high noise power. We efficiently optimize the aforementioned cost function to derive a sparse system of linear equations where we solve for millions of variables to estimate the displacement of all samples of all of the incorporated RF frames simultaneously. We call the proposed algorithm GLobal Ultrasound Elastography using multiple observations (mGLUE). Our primary validation of mGLUE against soft and hard inclusion simulation phantoms proves that mGLUE is capable of obtaining high quality strain map while dealing with noisy ultrasound data. In case of the soft inclusion phantom, Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) have improved by 75.37% and 57.08%, respectively. In addition, SNR and CNR improvements of 32.19% and 38.57% have been observed for the hard inclusion case.

Novel 2D Dynamic Elasticity Maps for Inspection of Anisotropic Properties in Fused Deposition Modeling Objects

In this study, a novel ultrasonic non-destructive and non-invasive elastography method was introduced and demonstrated to evaluate the mechanical properties of fused deposition modeling 3D printed objects using two-dimensional dynamical elasticity mapping. Based on the recently investigated dynamic bulk modulus and effective density imaging technique, an angle-dependent dynamic shear modulus measurement was performed to extract the dynamic Young’s modulus distribution of the FDM structures. The elastographic image analysis demonstrated the presence of anisotropic dynamic shear modulus and dynamic Young’s modulus existing in the fused deposition modeling 3D printed objects. The non-destructive method also differentiated samples with high contrast property zones from that of low contrast property regions. The angle-dependent elasticity contrast behavior from the ultrasonic method was compared with conventional and static tensile tests characterization. A good correlation between the nondestructive technique and the tensile test measurements was observed.

Non-invasive imaging of Young's modulus and Poisson's ratio in cancers in vivo

Alterations of Young's modulus (YM) and Poisson's ratio (PR) in biological tissues are often early indicators of the onset of pathological conditions. Knowledge of these parameters has been proven to be of great clinical significance for the diagnosis, prognosis and treatment of cancers. Currently, however, there are no non-invasive modalities that can be used to image and quantify these parameters in vivo without assuming incompressibility of the tissue, an assumption that is rarely justified in human tissues. In this paper, we developed a new method to simultaneously reconstruct YM and PR of a tumor and of its surrounding tissues based on the assumptions of axisymmetry and ellipsoidal-shape inclusion. This new, non-invasive method allows the generation of high spatial resolution YM and PR maps from axial and lateral strain data obtained via ultrasound elastography. The method was validated using finite element (FE) simulations and controlled experiments performed on phantoms with known mechanical properties. The clinical feasibility of the developed method was demonstrated in an orthotopic mouse model of breast cancer. Our results demonstrate that the proposed technique can estimate the YM and PR of spherical inclusions with accuracy higher than 99% and with accuracy higher than 90% in inclusions of different geometries and under various clinically relevant boundary conditions.

Enhanced Instantaneous Elastography in Tissues and Hard Materials Using Bulk Modulus and Density Determined Without Externally Applied Material Deformation

Ultrasound is a continually developing technology that is broadly used for fast, non-destructive mechanical property detection of hard and soft materials in applications ranging from manufacturing to biomedical. In this study, a novel monostatic longitudinal ultrasonic pulsing elastography imaging method is introduced. The existing elastography methods require an acoustic radiational or dynamic compressive externally applied force to determine the effective bulk modulus or density. This new, passive M-mode imaging technique does not require an external stress and can be effectively used for both soft and hard materials. Strain map imaging and shear wave elastography are two current categories of M-mode imaging that show both relative and absolute elasticity information. The new technique is applied to hard materials and soft material tissue phantoms for demonstrating effective bulk modulus and effective density mapping. When compared with standard techniques, the effective parameters fall within 10% of standard characterization methods for both hard and soft materials. As neither the standard A-mode imaging technique nor the presented technique require an external applied force, the techniques are applied to composite heterostructures and the findings presented for comparison. The presented passive M-mode technique is found to have enhanced resolution over standard A-mode modalities.

A Spline Interpolation-based Data Reconstruction Technique for Estimation of Strain Time Constant in Ultrasound Poroelastography

Ultrasound poroelastography is a cost-effective and noninvasive imaging technique, which can be used to reconstruct mechanical parameters of tissues such as Young's modulus, Poisson's ratio, interstitial permeability, and vascular permeability. To estimate interstitial permeability and vascular permeability using poroelastography, accurate estimation of the strain time constant (TC) is required. This can be a challenging task due to the nonlinearity of the exponential strain curve and noise affecting the experimental data. Due to motion artifacts caused by the sonographer, animal/patient, and/or the environment, noise affecting some strain frames can be significantly higher than the strain signal. If these frames are used for the computation of the strain TC, the resulting TC estimate can be highly inaccurate, which, in turn, can cause high errors in the reconstructed mechanical parameters. In this paper, we introduce a cubic spline-based interpolation method, which allows to use only good quality strain frames (i.e., frames with sufficiently high signal-to-noise ratio [SNR]) to estimate the strain TC. Using finite element simulations, we demonstrate that the proposed interpolation method can improve the estimation accuracy of the strain TC by 46% with respect to the case where no interpolation and filtering are used and by 37% with respect to the case where the strain frames are Kalman filtered before TC estimation (at an SNR of 30 dB). We also prove the technical feasibility of the proposed technique using in vivo experimental data. While detecting the bad frames in both simulations and experiments, we assumed the lower limit SNR to be below 10 dB. Based on our results, the proposed technique may be of great help in applications relying on the accurate assessment of the temporal behavior of strain data.

Non-Invasive Imaging of Normalized Solid Stress in Cancers in Vivo

The solid stress (SSg) that develops inside a cancer is an important marker of cancer’s growth, invasion and metastasis. Currently, there are no non-invasive methods to image SSg inside tumors. In this paper, we develop a new, non-invasive and cost-effective imaging method to assess SSg inside tumors that uses ultrasound poroelastography. Center to the proposed method is a novel analytical model, which demonstrates that SSg and the compression-induced stress (SSc) that generates inside the cancer in a poroelastography experiment have the same spatial distribution. To show the clinical feasibility of the proposed technique, we imaged and analyzed the normalized SSg inside treated and untreated human breast cancers in a small animal model. Given the clinical significance of assessing SSg in cancers and the advantages of the proposed ultrasonic methods, our technique could have a great impact on cancer diagnosis, prognosis and treatment methods.

Estimation of Vascular Permeability in Irregularly Shaped Cancers Using Ultrasound Poroelastography

OBJECTIVE

Vascular permeability (VP) is a mechanical parameter which plays an important role in cancer initiation, metastasis, and progression. To date, there are only a few non-invasive methods that can be used to image VP in solid tumors. Most of these methods require the use of contrast agents and are expensive, limiting widespread use.

METHODS

In this paper, we propose a new method to image VP in tumors, which is based on the use of ultrasound poroelastography. Estimation of VP by poroelastography requires knowledge of the Young's modulus (YM), Poisson's ratio (PR), and strain time constant (TC) in the tumors. In our method, we find the ellipse which best fits the tumor (regardless of its shape) using an eigen-system-based fitting technique and estimate the YM and PR using Eshelby's elliptic inclusion formulation. A Fourier method is used to estimate the axial strain TC, which does not require any initial guess and is highly robust to noise.

RESULTS

It is demonstrated that the proposed method can estimate VP in irregularly shaped tumors with an accuracy of above [Formula: see text] using ultrasound simulation data with signal-to-noise ratio of 20 dB or higher. In vivo feasibility of the proposed technique is demonstrated in an orthotopic mouse model of breast cancer.

CONCLUSION

The proposed imaging method can provide accurate and localized estimation of VP in cancers non-invasively and cost-effectively.

SIGNIFICANCE

Accurate and non-invasive assessment of VP can have a significant impact on diagnosis, prognosis, and treatment of cancers.

A Robust Method to Estimate the Time Constant of Elastographic Parameters

Novel viscoelastic and poroelastic elastography techniques rely on the accurate estimation of the temporal behavior of the axial or lateral strains and related parameters. From the temporal curve of the elastographic parameter of interest, the time constant (TC) is estimated using analytical models and curve-fitting techniques such as Levenberg-Marquardt (LM), Nelder-Mead (NM), and trust-region reflective (TR). In this paper, we propose a new technique named variable projection (VP) to estimate accurately and robustly the TC and steady-state value of the elastographic parameter of interest from its temporal curve. As a testing platform, the method is used with a novel analytical model, which can be used for both poroelastic and viscoelastic tissues and in most practical experimental conditions of clinical interest. Finite element and ultrasound simulations and experimental results demonstrate that VP is robust to noise and capable of estimating the TC of the elastographic parameter with accuracy higher than that of typically employed curve-fitting techniques. The results also demonstrate that the performance of VP is not affected by an incorrect initial TC guess. For example, in simulations, VP can estimate the TC of axial strain and effective Poisson's ratio accurately for initial guesses ranging from 0.001 to infinite times of the true TC value even in fairly noisy conditions (30-dB signal to noise ratio). In experiments, VP always estimates the axial strain TC reliably, whereas the LM, NM, and TR methods fail to converge or converge to wrong solutions in most of the cases.

Assessment of the long bone inter-fragmentary gap size in ultrasound strain elastograms

The inter-fragmentary gap size (IFGS) is a critical factor affecting the propensity of bone healing. In this paper, we present a study to analyze ultrasound strain elastographic numerical features in samples with distinct IFGS using both simulations and experiments. Six fractured rabbit hind leg samples in total were used in this study with controlled IFGS of 1 mm, 5 mm and 1 cm. For the simulation, computed tomography (CT) scans of all six samples were used to create solid models. Finite element analysis (FEA) and subsequent elastography simulations were performed on the 3D models to produce tensorial strain field data. Features of bony fragment separation were defined on different strain components and computed for strains segmented at varying thresholds to evaluate their performance in estimating the IFGS. A threshold for each strain component was then determined, based on which extra 3D features of interest were defined and extracted from the segmented strain data. Then, all 3D features were compared statistically among the three nominal groups. Additional simulations and experiments of axial shear strain elastography (ASSE) on the median coronal plane of the same samples were also performed. Our results indicate that coronal plane axial shear (CPAS) strain elastography produces a separation feature which is statistically correlated with the IFGS, and that our elastography simulation module is effective in predicting the CPAS elastographic strain behavior for different IFGS.

A Model-Based Approach to Investigate the Effect of a Long Bone Fracture on Ultrasound Strain Elastography

The mechanical behavior of long bones and fractures has been under investigation for many decades due to its complexity and clinical relevance. In this paper, we report a new subject-specific methodology to predict and analyze the mechanical behavior of the soft tissue at a bone interface with the intent of identifying the presence and location of bone abnormalities with high accuracy, spatial resolution, and contrast. The proposed methodology was tested on both intact and fractured rabbit femur samples with finite element-based 3-D simulations, created from actual femur computed tomography data, and ultrasound elastography experiments. The results included in this study demonstrate that elastographic strains at the bone/soft tissue interface can be used to differentiate fractured femurs from the intact ones on a distribution level. These results also demonstrate that coronal plane axial shear strain creates a unique contrast mechanism that can be used to reliably detect fractures (both complete and incomplete) in long bones. Kruskal-Wallis test further demonstrates that the contrast measure for the fracture group (simulation: 2.1286±0.2206; experiment: 2.7034 ± 1.0672) is significantly different from that for the intact group (simulation: 0 ± 0; experiment: 1.1540±0.6909) when using coronal plane axial shear strain elastography ( < 0.01). We conclude that: 1) elastography techniques can be used to accurately identify the presence and location of fractures in a long bone and 2) the proposed model-based approach can be used to predict and analyze strains at a bone fracture site and to better interpret experimental elastographic data.

A model-based approach to investigate the effect of elevated interstitial fluid pressure on strain elastography

Finite element (FE) modeling provides a useful tool to understand the mechanical behavior of complex tissues, such as cancers, in a variety of testing conditions. Although a number of numerical and analytical models for cancerous tumors are retrievable in the literature, none of these models is capable of completely describing the behavior of a cancer embedded in a normal tissue in the conditions typical for an ultrasound elastography experiment. In this paper, we first design and implement a realistic FE model of the mechanical behavior of a cancer embedded in a normal tissue under ultrasound elastography testing conditions. In addition to the commonly used tissue mechanical properties, for the cancer, elevated interstitial fluid pressure (IFP) is incorporated in the model. IFP is a parameter of great clinical significance, but it is not typically considered in elastographic models of tumors. The developed model is then used to thoroughly study the effect of IFP on the axial, lateral and volumetric strains inside the tumor. The results of this study demonstrate that the presence of the IFP affects both the temporal and spatial distributions of the axial, lateral, volumetric strains and related elastographic parameters. Thus, these results lead to two important considerations: (1) that a correct interpretation of experimental elastographic data need a clear understanding of the effect of the IFP on the obtained elastograms and (2) that this IFP-dependent alteration of the elastographic parameters may provide an opportunity to non-invasively gain localized information about this clinically relevant parameter.

A novel filter for accurate estimation of fluid pressure and fluid velocity using poroelastography

Fluid pressure and fluid velocity carry important information for cancer diagnosis, prognosis and treatment. Recent work has demonstrated that estimation of these parameters is theoretically possible using ultrasound poroelastography. However, accurate estimation of these parameters requires high quality axial and lateral strain estimates from noisy ultrasound radio frequency (RF) data. In this paper, we propose a filtering technique combining two efficient filters for removal of noise from strain images, i.e., Kalman and nonlinear complex diffusion filters (NCDF). Our proposed filter is based on a novel noise model, which takes into consideration both additive and amplitude modulation noise in the estimated strains. Using finite element and ultrasound simulations, we demonstrate that the proposed filtering technique can significantly improve image quality of lateral strain elastograms along with fluid pressure and velocity elastograms. Technical feasibility of the proposed method on an in vivo set of data is also demonstrated. Our results show that the CNRe of the lateral strain, fluid pressure and fluid velocity as estimated using the proposed technique is higher by at least 10.9%, 51.3% and 334.4% when compared to the results obtained using a Kalman filter only, by at least 8.9%, 27.6% and 219.5% when compared to the results obtained using a NCDF only and by at least 152.3%, 1278% and 742% when compared to the results obtained using a median filter only for all SNRs considered in this study.