Viscoelasticity imaging using ultrasound: parameters and error analysis

Deep learning in ultrasound elastography imaging: A review

It is known that changes in the mechanical properties of tissues are associated with the onset and progression of certain diseases. Ultrasound elastography is a technique to characterize tissue stiffness using ultrasound imaging either by measuring tissue strain using quasi-static elastography or natural organ pulsation elastography, or by tracing a propagated shear wave induced by a source or a natural vibration using dynamic elastography. In recent years, deep learning has begun to emerge in ultrasound elastography research. In this review, several common deep learning frameworks in the computer vision community, such as multilayer perceptron, convolutional neural network, and recurrent neural network are described. Then, recent advances in ultrasound elastography using such deep learning techniques are revisited in terms of algorithm development and clinical diagnosis. Finally, the current challenges and future developments of deep learning in ultrasound elastography are prospected. This article is protected by copyright. All rights reserved.

Prostate Cancer Detection Using 3-D Shear Wave Elasticity Imaging

Transrectal ultrasound (TRUS) B-mode imaging provides insufficient sensitivity and specificity for prostate cancer (PCa) targeting when used for biopsy guidance. Shear wave elasticity imaging (SWEI) is an elasticity imaging technique that has been commercially implemented and is sensitive and specific for PCa. We have developed a SWEI system capable of 3-D data acquisition using a dense acoustic radiation force (ARF) push approach that leads to enhanced shear wave signal-to-noise ratio compared with that of the commercially available SWEI systems and facilitates screening of the entire gland before biopsy. Additionally, we imaged and assessed 36 patients undergoing radical prostatectomy using 3-D SWEI and determined a shear wave speed threshold separating PCa from healthy prostate tissue with sensitivities and specificities akin to those for multiparametric magnetic resonance imaging fusion biopsy. The approach measured the mean shear wave speed in each prostate region to be 4.8 m/s (Young's modulus E = 69.1 kPa) in the peripheral zone, 5.3 m/s (E = 84.3 kPa) in the central gland and 6.0 m/s (E = 108.0 kPa) for PCa with statistically significant (p < 0.0001) differences among all regions. Three-dimensional SWEI receiver operating characteristic analyses identified a threshold of 5.6 m/s (E = 94.1 kPa) to separate PCa from healthy tissue with a sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and area under the curve (AUC) of 81%, 82%, 69%, 89% and 0.84, respectively. Additionally, a shear wave speed ratio was assessed to normalize for tissue compression and patient variability, which yielded a threshold of 1.11 to separate PCa from healthy prostate tissue and was accompanied by a substantial increase in specificity, PPV and AUC, where the sensitivity, specificity, PPV, NPV and AUC were 75%, 90%, 79%, 88% and 0.90, respectively. This work illustrates the feasibility of using 3-D SWEI data to detect and localize PCa and demonstrates the benefits of normalizing for applied compression during data acquisition for use in biopsy targeting studies.

Multi-parameter Sub-Hertz Analysis of Viscoelasticity With a Quality Metric for Differentiation of Breast Masses

We applied sub-Hertz analysis of viscoelasticity (SAVE) to differentiate breast masses in pre-biopsy patients. Tissue response during external ramp-and-hold stress was ultrasonically detected. Displacements were used to acquire tissue viscoelastic parameters. The fast instantaneous response and slow creep-like deformations were modeled as the response of a linear standard solid from which viscoelastic parameters were estimated. These parameters were used in a multi-variable classification framework to differentiate malignant from benign masses identified by pathology. When employing all viscoelasticity parameters, SAVE resulted in 71.43% accuracy in differentiating lesions. When combined with ultrasound features and lesion size, accuracy was 82.24%. Adding a quality metric based on uniaxial motion increased the accuracy to 81.25%. When all three were combined with SAVE, accuracy was 91.3%. These results confirm the utility of SAVE as a robust ultrasound-based diagnostic tool for non-invasive differentiation of breast masses when used as stand-alone biomarkers or in conjunction with ultrasonic features.

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

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

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.

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

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

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.

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.

Viscoelastic biomarker for differentiation of benign and malignant breast lesion in ultra- low frequency range

Benign and malignant tumors differ in the viscoelastic properties of their cellular microenvironments and in their spatiotemporal response to very low frequency stimuli. These differences can introduce a unique viscoelastic biomarker in differentiation of benign and malignant tumors. This biomarker may reduce the number of unnecessary biopsies in breast patients. Although different methods have been developed so far for this purpose, none of them have focused on in vivo and in situ assessment of local viscoelastic properties in the ultra-low (sub-Hertz) frequency range. Here we introduce a new, noninvasive model-free method called Loss Angle Mapping (LAM). We assessed the performance results on 156 breast patients. The method was further improved by detection of out-of-plane motion using motion compensation cross correlation method (MCCC). 45 patients met this MCCC criterion and were considered for data analysis. Among this population, we found 77.8% sensitivity and 96.3% specificity (p < 0.0001) in discriminating between benign and malignant tumors using logistic regression method regarding the pre known information about the BIRADS number and size. The accuracy and area under the ROC curve, AUC, was 88.9% and 0.94, respectively. This method opens new avenues to investigate the mechanobiology behavior of different tissues in a frequency range that has not yet been explored in any in vivo patient studies.

Impact of Acoustic Radiation Force Excitation Geometry on Shear Wave Dispersion and Attenuation Estimates

Shear wave elasticity imaging (SWEI) characterizes the mechanical properties of human tissues to differentiate healthy from diseased tissue. Commercial scanners tend to reconstruct shear wave speeds for a region of interest using time-of-flight methods reporting a single shear wave speed (or elastic modulus) to the end user under the assumptions that tissue is elastic and shear wave speeds are not dependent on the frequency content of the shear waves. Human tissues, however, are known to be viscoelastic, resulting in dispersion and attenuation. Shear wave spectroscopy and spectral methods have been previously reported in the literature to quantify shear wave dispersion and attenuation, commonly making an assumption that the acoustic radiation force excitation acts as a cylindrical source with a known geometric shear wave amplitude decay. This work quantifies the bias in shear dispersion and attenuation estimates associated with making this cylindrical wave assumption when applied to shear wave sources with finite depth extents, as commonly occurs with realistic focal geometries, in elastic and viscoelastic media. Bias is quantified using analytically derived shear wave data and shear wave data generated using finite-element method models. Shear wave dispersion and attenuation bias (up to 15% for dispersion and 41% for attenuation) is greater for more tightly focused acoustic radiation force sources with smaller depths of field relative to their lateral extent (height-to-width ratios <16). Dispersion and attenuation errors associated with assuming a cylindrical geometric shear wave decay in SWEI can be appreciable and should be considered when analyzing the viscoelastic properties of tissues with acoustic radiation force source distributions with limited depths of field.

Modeling Ramp-hold Indentation Measurements based on Kelvin-Voigt Fractional Derivative Model

Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt Fractional Derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an Atomic Force Microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3 - 1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.

Automated In Vivo Sub-Hertz Analysis of Viscoelasticity (SAVE) for Evaluation of Breast Lesions

We present an automated method for acquiring images and contrast parameters based on mechanical properties of breast lesions and surrounding tissue at load frequencies less than 1 Hz. The method called sub-Hertz analysis of viscoelasticity (SAVE) uses a compression device integrated with ultrasound imaging to perform in vivo ramp-and-hold uniaxial creep-like test on human breast in vivo. It models the internal deformations of tissues under constant surface stress as a linear viscoelastic response. We first discuss different aspects of our unique measurement approach and the expected variability of the viscoelastic parameters estimated based on a simplified one-dimensional reconstruction model. Finite-element numerical analysis is used to justify the advantages of using imaging contrast over viscoelasticity values. We then present the results of SAVE applied to a group of patients with breast masses undergoing biopsy.

Automated Compression Device for Viscoelasticity Imaging

Noninvasive measurement of tissue viscoelastic properties is gaining more attention for screening and diagnostic purposes. Recently, measuring dynamic response of tissue under a constant force has been studied for estimation of tissue viscoelastic properties in terms of retardation times. The essential part of such a test is an instrument that is capable of creating a controlled axial force and is suitable for clinical applications. Such a device should be lightweight, portable, and easy to use for patient studies to capture tissue dynamics under external stress. In this paper, we present the design of an automated compression device for studying the creep response of materials with tissue-like behaviors. The device can be used to apply a ramp-and-hold force excitation for a predetermined duration of time and it houses an ultrasound probe for monitoring the creep response of the underlying tissue. To validate the performance of the device, several creep tests were performed on tissue-mimicking phantoms, and the results were compared against those from a commercial mechanical testing instrument. Using a second-order Kelvin-Voigt model and surface measurement of the forces and displacements, retardation times T1 and T2 were estimated from each test. These tests showed strong agreement between our automated compression device and the commercial mechanical testing system, with an average relative error of 2.9% and 12.4%, for T1 and T2, respectively. Also, we present the application of compression device to measure local retardation times for four different phantoms with different size and stiffness.

Virtual Breast Quasi-static Elastography (VBQE)

Viscoelasticity Imaging (VEI) has been proposed to measure relaxation time constants for characterization of in vivo breast lesions. In this technique, an external compression force on the tissue being imaged is maintained for a fixed period of time to induce strain creep. A sequence of ultrasound echo signals is then utilized to generate time-resolved strain measurements. Relaxation time constants can be obtained by fitting local time-resolved strain measurements to a viscoelastic tissue model (e.g., a modified Kevin-Voigt model). In this study, our primary objective is to quantitatively evaluate the contrast transfer efficiency (CTE) of VEI, which contains useful information regarding image interpretations. Using an open-source simulator for virtual breast quasi-static elastography (VBQE), we conducted a case study of contrast transfer efficiency of VEI. In multiple three-dimensional (3D) numerical breast phantoms containing various degrees of heterogeneity, finite element (FE) simulations in conjunction with quasi-linear viscoelastic constitutive tissue models were performed to mimic data acquisition of VEI under freehand scanning. Our results suggested that there were losses in CTE, and the losses could be as high as -18 dB. FE results also qualitatively corroborated clinical observations, for example, artifacts around tissue interfaces.

Optimization of a Pixel-to-Pixel Curve-Fitting Method for Poroelastography Imaging

Ultrasound poroelastography is an imaging modality used to characterize the temporal behavior of soft tissue that can be modeled as a solid permeated by interconnected pores filled with liquid (poroelastic medium). It could be useful in the stage classification of lymphedema. Generally, time-constant models are applied to strain images, and precision of the fitting process, computational cost and versatility in response to changes in tissues properties are crucial aspects of clinical applications. In the work described here, we performed creep experiments on poroelastic phantoms and used rheologic models to visualize the changes in viscoelastic response associated with fluid mobility. We used the Levenberg-Marquardt algorithm as a fitting tool and performed parametric studies to improve its performance. On the basis of these studies, we proposed an optimization schema for the pixel-to-pixel curve-fitting process. We determined that the bimodal Kelvin-Voigt model describes efficiently the temporal evolution of the strain images in heterogeneous phantoms.

Design and Testing of a Single-Element Ultrasound Viscoelastography System for Point-of-Care Edema Quantification

Management of fluid overload in patients with end-stage renal disease represents a unique challenge to clinical practice because of the lack of accurate and objective measurement methods. Currently, peripheral edema is subjectively assessed by palpation of the patient's extremities, ostensibly a qualitative indication of tissue viscoelastic properties. New robust quantitative estimates of tissue fluid content would allow clinicians to better guide treatment, minimizing reactive treatment decision making. Ultrasound viscoelastography (UVE) can be used to estimate strain in viscoelastic tissue, deriving material properties that can help guide treatment. We are developing and testing a simple, low-cost UVE system using a single-element imaging transducer that is simpler and less computationally demanding than array-based systems. This benchtop validation study tested the feasibility of using the UVE system by measuring the mechanical properties of a tissue-mimicking material under large strains. We generated depth-dependent creep curves and viscoelastic parameter maps of time constants and elastic moduli for the Kelvin model of viscoelasticity. During testing, the UVE system performed well, with mean UVE-measured strain matching standard mechanical testing with maximum absolute errors ≤4%. Motion tracking revealed high correlation and signal-to-noise ratios, indicating that the system is reliable.

Magnetomotive Optical Coherence Elastography for Magnetic Hyperthermia Dosimetry Based on Dynamic Tissue Biomechanics

Magnetic nanoparticles (MNPs) have been used in many diagnostic and therapeutic biomedical applications over the past few decades to enhance imaging contrast, steer drugs to targets, and treat tumors via hyperthermia. Optical coherence tomography (OCT) is an optical biomedical imaging modality that relies on the detection of backscattered light to generate high-resolution cross-sectional images of biological tissue. MNPs have been utilized as imaging contrast and perturbative mechanical agents in OCT in techniques called magnetomotive OCT (MM-OCT) and magnetomotive elastography (MM-OCE), respectively. MNPs have also been independently used for magnetic hyperthermia treatments, enabling therapeutic functions such as killing tumor cells. It is well known that the localized tissue heating during hyperthermia treatments result in a change in the biomechanical properties of the tissue. Therefore, we propose a novel dosimetric technique for hyperthermia treatment based on the viscoelasticity change detected by MM-OCE, further enabling the theranostic function of MNPs. In this paper, we first review the basic principles and applications of MM-OCT, MM-OCE, and magnetic hyperthermia, and present new preliminary results supporting the concept of MM-OCE-based hyperthermia dosimetry.

Characterization of material properties of soft solid thin layers with acoustic radiation force and wave propagation

Evaluation of tissue engineering constructs is performed by a series of different tests. In many cases it is important to match the mechanical properties of these constructs to those of native tissues. However, many mechanical testing methods are destructive in nature which increases cost for evaluation because of the need for additional samples reserved for these assessments. A wave propagation method is proposed for characterizing the shear elasticity of thin layers bounded by a rigid substrate and fluid-loading, similar to the configuration for many tissue engineering applications. An analytic wave propagation model was derived for this configuration and compared against finite element model simulations and numerical solutions from the software package Disperse. The results from the different models found very good agreement. Experiments were performed in tissue-mimicking gelatin phantoms with thicknesses of 1 and 4 mm and found that the wave propagation method could resolve the shear modulus with very good accuracy, no more than 4.10% error. This method could be used in tissue engineering applications to monitor tissue engineering construct maturation with a nondestructive wave propagation method to evaluate the shear modulus of a material.

Effect of temporal acquisition parameters on image quality of strain time constant elastography

Ultrasound methods to image the time constant (TC) of elastographic tissue parameters have been recently developed. Elastographic TC images from creep or stress relaxation tests have been shown to provide information on the viscoelastic and poroelastic behavior of tissues. However, the effect of temporal ultrasonic acquisition parameters and input noise on the image quality of the resultant strain TC elastograms has not been fully investigated yet. Understanding such effects could have important implications for clinical applications of these novel techniques. This work reports a simulation study aimed at investigating the effects of varying windows of observation, acquisition frame rate, and strain signal-to-noise ratio (SNR) on the image quality of elastographic TC estimates. A pilot experimental study was used to corroborate the simulation results in specific testing conditions. The results of this work suggest that the total acquisition time necessary for accurate strain TC estimates has a linear dependence to the underlying strain TC (as estimated from the theoretical strain-vs.-time curve). The results also indicate that it might be possible to make accurate estimates of the elastographic TC (within 10% error) using windows of observation as small as 20% of the underlying TC, provided sufficiently fast acquisition rates (>100 Hz for typical acquisition depths). The limited experimental data reported in this study statistically confirm the simulation trends, proving that the proposed model can be used as upper bound guidance for the correct execution of the experiments.

Algorithms for quantitative quasi-static elasticity imaging using force data

Quasi-static elasticity imaging can improve diagnosis and detection of diseases that affect the mechanical behavior of tissue. In this methodology, images of the shear modulus of the tissue are reconstructed from the measured displacement field. This is accomplished by seeking the spatial distribution of mechanical properties that minimizes the difference between the predicted and the measured displacement fields, where the former is required to satisfy a finite element approximation to the equations of equilibrium. In the absence of force data, the shear modulus is determined only up to a multiplicative constant. In this manuscript, we address the problem of calibrating quantitative elastic modulus reconstructions created from measurements of quasi-static deformations. We present two methods that utilize the knowledge of the applied force on a portion of the boundary. The first involves rescaling the shear modulus of the original minimization problem to best match the measured force data. This approach is easily implemented but neglects the spatial distribution of tractions. The second involves adding a force-matching term to the original minimization problem and a change of variables wherein we seek the log of the shear modulus. We present numerical results that demonstrate the usefulness of both methods.

Viscoelastic properties of rodent mammary tumors using ultrasonic shear-wave imaging

Images of tumor mechanical properties provide important insights into malignant-cell processes manifest by extracellular matrix (ECM) stiffening and remodeling. This article presents a pilot study measuring in vivo mechanical-property characteristics of rodent mammary tumors using an ultrasonic shear-wave imaging technique. Shear waves are generated by a needle inserted into the tumor of anesthetized rodents that is vibrated harmonically between 50 and 450 Hz. Particle motion in the tumor associated with the radiation of cylindrical shear waves is imaged using pulsed-Doppler ultrasound techniques. Estimating the spatial gradient of shear-wave phase along the direction of propagation at frequencies in the measurement range yields shear-speed dispersion curves. Measured dispersion curves were fit to those predicted by three different rheological models to estimate the elastic and viscous coefficients of the complex shear modulus. The investigation was performed in vivo on four rat-mammary fibroadenoma tumors and five xenograft mouse-mammary carcinoma tumors. Each tumor was subsequently excised for histological imaging and composition analysis. Collagen composition was measured using hydroxyproline assays that were then correlated with mechanical measurements. The goal was to relate soft-tissue mechanical behavior to biological characteristics of tumor structures, specifically the collagenous ECM protein content. The choice of rheological model and the effects of artifacts induced by shear-wave reflections at internal tissue boundaries are carefully examined in this article. Addressing these issues is of great importance when selecting force-excitation methods and modulus estimation method to assess intrinsic tissue properties responsible for disease-specific elastographic contrast.

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

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.

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

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This paper reviews current approaches to elastography in three areas--quasi-static, harmonic and transient--and describes inversion schemes for each elastographic imaging approach. Approaches include first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper's objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the complex mechanical behavior of soft tissues and (3) developing better test procedures to evaluate the performance of modulus elastograms.

Integration of crawling waves in an ultrasound imaging system. Part 2: signal processing and applications

This paper introduces methods to generate crawling wave interference patterns from the displacement fields generated from radiation force pushes on a GE Logiq 9 scanner. The same transducer and system provides both the pushing pulses to generate the shear waves and the tracking pulses to measure the displacements. Acoustic power and system limitations result in largely impulsive displacement fields. Measured displacements from pushes on either side of a region-of-interest (ROI) are used to calculate continuously varying interference patterns. This technique is explained along with a brief discussion of the conventional mechanical source-driven crawling waves for comparison. We demonstrate the method on three example cases: a gelatin-based phantom with a cylindrical inclusion, an oil-gelatin phantom and mouse livers. The oil-gelatin phantom and the mouse livers demonstrate not only shear speed estimation, but the frequency dependence of the shear wave speeds.

Principles of ultrasound elastography

Many manufacturers of ultrasound systems offer elastography capabilities. Though the research literature describes techniques involving external actuators, commercial systems have preferred to adopt techniques that may be used with a single transducer. Techniques may be divided into those which measure strain and those which measure shear wave velocity. Strain elastography involves deformation of the tissue followed by imaging of the degree of compression or extension of the tissue. Strain elastography does not estimate tissue stiffness; however, the strain ratio may be used as a surrogate index of stiffness. Shear wave elastography provides true quantitative information on elastic modulus. This involves induction of shear waves, estimation of shear wave velocity c s and conversion to elastic modulus E using the equation E = 3 ρ cs2 where ρ is the density. The description of tissues as being purely elastic is simplistic. In practice they may also exhibit time-dependent viscous behaviour. Recent literature describe methods that have been developed for estimation of the viscoelastic behaviour from the change in strain with time or by estimation of the shear wave dispersion, a technique known as ‘shear wave spectroscopy’. These methods may become commercially available in the medium term, offering a new quantity (tissue viscosity) for diagnostic use.

Performance analysis of a new real-time elastographic time constant estimator

New elastographic techniques such as poroelastography and viscoelasticity imaging aim at imaging the temporal mechanical behavior of tissues. These techniques usually involve the use of curve fitting methods being applied to noisy data to estimate new elastographic parameters. As of today, however, current elastographic implementations of poroelastography and viscoelasticity imaging methods are in general too slow and not optimized for clinical applications. Furthermore, image quality performance of these new elastographic techniques is still largely unknown due to a paucity of data and the lack of systematic studies that analyze their performance limitations. In this paper, we propose a new elastographic time constant (TC) estimator, which is based on the use of the least square error (LSE) curve-fitting method and the Levenberg-Marquardt (LM) optimization rule as applied to noisy elastographic data obtained from a material in a creep-type experiment. The algorithm is executed on a massively parallel general purpose graphics processing unit (GPGPU) to achieve real-time performance. The estimator's performance is analyzed using simulations. Experimental results obtained from poroelastic phantoms are presented as a proof of principle of the new estimator's technical applicability on real experimental data. The results of this study demonstrate that the newly proposed elastographic estimator can produce highly accurate and sensitive elastographic TC estimates in real-time and at high signal-to-noise ratios.

Ultrasonic viscoelasticity imaging of nonpalpable breast lesions

The prognosis of breast cancer patients improves with early and accurate diagnosis. A small clinical study was conducted with 21 women having a single nonpalpable breast lesion, each detected mammographically with later pathology confirmation. Elasticity images were acquired on each patient to test for the ability to differentiating malignant and benign lesions. The mechanical relaxation time T(1) images showed a tissue-specific T(1) contrast that is negative for all 11 malignant lesions and positive for all 10 benign lesions. Strain images were estimated using a regularized multi-scale optical flow (ROF) algorithm. Adjustments to the input parameters to the ROF and their subsequent effects on T(1) estimation and computation time are shown to have a strong effect of diagnostic performance.

Investigation of temperature-dependent viscoelastic properties of thermal lesions in ex vivo animal liver tissue

The viscoelastic characteristics of thermal lesions in ex vivo animal liver are investigated in this paper. Characterization of the moduli of thermal lesions prepared at several temperatures will provide additional information for the elastographic monitoring of radio frequency ablation of hepatic tumors. In this study, the frequency-dependent complex modulus of thermal lesions prepared at temperatures ranging from 60 to 90 degrees C over a frequency range from 0.1 to 50Hz are presented. Lesions were prepared using either radio frequency ablation or double immersion boiling. It was found that both the magnitude and phase of the modulus increase with frequency, a behavior that has been noted in the literature. A new result reported shows that the modulus dependence on temperature reveals a local maximum around 70-75 degrees C corresponding to the temperature at which tissue has released most of its water content. The modulus values at temperatures higher than 70 degrees C continued to increase, but the extent of increase depend on animal species and other factors.

Fractional derivative models for ultrasonic characterization of polymer and breast tissue viscoelasticity

The viscoelastic response of hydropolymers, which include glandular breast tissues, may be accurately characterized for some applications with as few as 3 rheological parameters by applying the Kelvin-Voigt fractional derivative (KVFD) modeling approach. We describe a technique for ultrasonic imaging of KVFD parameters in media undergoing unconfined, quasi-static, uniaxial compression. We analyze the KVFD parameter values in simulated and experimental echo data acquired from phantoms and show that the KVFD parameters may concisely characterize the viscoelastic properties of hydropolymers. We then interpret the KVFD parameter values for normal and cancerous breast tissues and hypothesize that this modeling approach may ultimately be applied to tumor differentiation.

pH-induced contrast in viscoelasticity imaging of biopolymers

Understanding contrast mechanisms and identifying discriminating features is at the heart of diagnostic imaging development. This paper focuses on how pH influences the viscoelastic properties of biopolymers to better understand the effects of extracellular pH on breast tumour elasticity imaging. Extracellular pH is known to decrease as much as 1 pH unit in breast tumours, thus creating a dangerous environment that increases cellular mutation rates and therapeutic resistance. We used a gelatin hydrogel phantom to isolate the effects of pH on a polymer network with similarities to the extracellular matrix in breast stroma. Using compressive unconfined creep and stress relaxation measurements, we systematically measured the viscoelastic features sensitive to pH by way of time-domain models and complex modulus analysis. These results are used to determine the sensitivity of quasi-static ultrasonic elasticity imaging to pH. We found a strong elastic response of the polymer network to pH, such that the matrix stiffness decreases as pH was reduced; however, the viscous response of the medium to pH was negligible. While physiological features of breast stroma such as proteoglycans and vascular networks are not included in our hydrogel model, observations in this study provide insight into viscoelastic features specific to pH changes in the collagenous stromal network. These observations suggest that the large contrast common in breast tumours with desmoplasia may be reduced under acidic conditions, and that viscoelastic features are unlikely to improve discriminability.

Ultrasonic viscoelasticity imaging of nonpalpable breast tumors: preliminary results

RATIONALE AND OBJECTIVES

Improvements in the diagnosis of early breast cancers depend on a physician's ability to obtain the information necessary to distinguish nonpalpable malignant and benign tumors. Viscoelastic features that describe mechanical properties of tissues may help to distinguish these types of lesions.

MATERIALS AND METHODS

Twenty-one patients with nonpalpable, pathology-confirmed Breast Imaging Reporting and Data System (BIRADS) 4 or 5 breast lesions (10 benign, 11 malignant) detected by mammography were studied. Viscoelastic parameters were extracted from a time sequence of ultrasonic strain images, and differences in the parameters between malignant and benign tumors were compared. Parametric data were color coded and superimposed on sonograms.

RESULTS

The strain retardance time parameter, T(1), provided the best discrimination between malignant and benign tumors (P < .01). T(1) measures the time required for tissues to fully deform (strain) once compressed; therefore, it describes the time-varying viscous response of tissue to a small deforming force. Compared to the surrounding background tissues, malignant lesions have smaller average T(1) values, whereas benign lesions have higher T(1) values. This tissue-specific contrast correlates with known changes in the extracellular matrix of breast stroma.

CONCLUSION

Characterization of nonpalpable breast lesions is improved by the addition of viscoelastic strain imaging parameters. The differentiation of malignant and benign BI-RADS 4 or 5 tumors is especially evident with the use of the retardation time estimates, T(1).

Viscoelastic characterization of soft tissue from dynamic finite element models

An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A new dynamic finite element model that is consistent with known rheological models has been derived to account for the viscoelastic changes in soft tissue. The model assumes known lumped masses at the nodes, and comprises two vectors of elasticity and viscosity parameters that depend on the material elasticity and viscosity distribution, respectively. Using this deformation model and the observed dynamic data for harmonic excitation, the inverse problem is solved to reconstruct the viscosity and elasticity in the medium by using a Gauss-Newton-based approach. As in other inverse problems, previous knowledge of the parameters on the boundaries of the medium is necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The sensitivity of the solutions to noise, model and boundary conditions has been studied through numerical simulations. Experimental results are also presented. The viscosity and elasticity of a gelatin-based phantom with inclusion of known properties have been reconstructed and have been shown to be close to the values obtained using standard rheometry.

Ultrasonic measurements of breast viscoelasticity

In vivo measurements of the viscoelastic properties of breast tissue are described. Ultrasonic echo frames were recorded from volunteers at 5 fps while applying a uniaxial compressive force (1-20 N) within a 1 s ramp time and holding the force constant for up to 200 s. A time series of strain images was formed from the echo data, spatially averaged viscous creep curves were computed, and viscoelastic strain parameters were estimated by fitting creep curves to a second-order Voigt model. The useful strain bandwidth from this quasi-static ramp stimulus was 10(-2) < or = omega < or = 10(0) rad/s (0.0016-0.16 Hz). The stress-strain curves for normal glandular tissues are linear when the surface force applied is between 2 and 5 N. In this range, the creep response was characteristic of biphasic viscoelastic polymers, settling to a constant strain (arrheodictic) after 100 s. The average model-based retardance time constants for the viscoelastic response were 3.2 +/- 0.8 and 42.0 +/- 28 s. Also, the viscoelastic strain amplitude was approximately equal to that of the elastic strain. Above 5 N of applied force, however, the response of glandular tissue became increasingly nonlinear and rheodictic, i.e., tissue creep never reached a plateau. Contrasting in vivo breast measurements with those in gelatin hydrogels, preliminary ideas regarding the mechanisms for viscoelastic contrast are emerging.

Viscoelastic parameter estimation based on spectral analysis

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

Monitored steady-state excitation and recovery (MSSER) radiation force imaging using viscoelastic models

Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.

Radiological interpretation 2020: toward quantitative image assessment

The interpretation of medical images by radiologists is primarily and fundamentally a subjective activity, but there are a number of clinical applications such as tumor imaging where quantitative imaging (QI) metrics (such as tumor growth rate) would be valuable to the patient's care. It is predicted that the subjective interpretive environment of the past will, over the next decade, evolve toward the increased use of quantitative metrics for evaluating patient health from images. The increasing sophistication and resolution of modern tomographic scanners promote the development of meaningful quantitative end points, determined from images which are in turn produced using well-controlled imaging protocols. For the QI environment to expand, medical physicists, physicians, other researchers and equipment vendors need to work collaboratively to develop the quantitative protocols for imaging, scanner calibrations, and robust analytical software that will lead to the routine inclusion of quantitative parameters in the diagnosis and therapeutic assessment of human health. Most importantly, quantitative metrics need to be developed which have genuine impact on patient diagnosis and welfare, and only then will QI techniques become integrated into the clinical environment.

Characterization of the viscosity and elasticity in soft tissue using dynamic finite elements

An iterative solution to the inverse problem of elasticity and viscosity is proposed in this paper. A finite elements model has been derived to account for the viscoelastic changes in soft tissue that is consistent with known rheological models. Using this deformation model and the observed dynamic data, the viscosity and elasticity have been reconstructed in the medium by using a Gauss-Newton based approach. Previous knowledge of the parameters on the boundaries of the medium are necessary to assure uniqueness and convergence and to obtain an accurate map of the viscoelastic properties. The methods have been studied in FEM simulations and also tested through experiments, where the viscosity and elasticity of a gelatin based phantom with an inclusion of known properties have been reconstructed successfully.