Towards an acoustic model-based poroelastic imaging method: II. experimental investigation

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.

Further characterization of changes in axial strain elastograms due to the presence of slippery tumor boundaries

Elastography measures tissue strain, which can be interpreted under certain simplifying assumptions to be representative of the underlying stiffness distribution. This is useful in cancer diagnosis where tumors tend to have a different stiffness to healthy tissue and has also shown potential to provide indication of the degree of bonding at tumor-tissue boundaries, which is clinically useful because of its dependence on tumor pathology. We consider the changes in axial strain for the case of a symmetrical model undergoing uniaxial compression, studied by characterizing changes in tumor contrast transfer efficiency (CTE), inclusion to background strain contrast and strain contrast generated by slip motion, as a function of Young's modulus contrast and applied strain. We present results from a finite element simulation and an evaluation of these results using tissue-mimicking phantoms. The simulation results show that a discontinuity in displacement data at the tumor boundary, caused by the surrounding tissue slipping past the tumor, creates a halo of "pseudostrain" across the tumor boundary. Mobile tumors also appear stiffer on elastograms than adhered tumors, to the extent that tumors that have the same Young's modulus as the background may in fact be visible as low-strain regions, or those that are softer than the background may appear to be stiffer than the background. Tumor mobility also causes characteristic strain heterogeneity within the tumor, which exhibits low strain close to the slippery boundary and increasing strain toward the center of the tumor. These results were reproduced in phantom experiments. In addition, phantom experiments demonstrated that when fluid lubrication is present at the boundary, these effects become applied strain-dependent as well as modulus-dependent, in a systematic and characteristic manner. The knowledge generated by this study is expected to aid interpretation of clinical strain elastograms by helping to avoid misinterpretation as well as provide additional diagnostic criteria stated in the paper and stimulate further research into the application of elastography to tumor mobility assessment.

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.

A New Class of Phantom Materials for Poroelastography Imaging Techniques

Poroelastography is an elastographic technique used to image the temporal mechanical behavior of tissues. One of the major challenges in determining experimental potentials and limitations of this technique has been the lack of complex and realistic controlled phantoms that could be used to corroborate the limited number of theoretical and simulation studies available in the literature as well as to predict its performance in complex experimental situations and in a variety of conditions. In the study described here, we propose and analyze a new class of phantom materials for temporal elastography imaging. The results indicate that, by using polyacrylamide, we can generate inhomogeneous elastographic phantoms with controlled fluid content and fluid flow properties, while maintaining mechanical and ultrasonic properties similar to those of soft tissues.

A dynamic mechanical analysis technique for porous media

Dynamic mechanical analysis (DMA) is a common way to measure the mechanical properties of materials as functions of frequency. Traditionally, a viscoelastic mechanical model is applied and current DMA techniques fit an analytical approximation to measured dynamic motion data by neglecting inertial forces and adding empirical correction factors to account for transverse boundary displacements. Here, a finite-element (FE) approach to processing DMA data was developed to estimate poroelastic material properties. Frequency-dependent inertial forces, which are significant in soft media and often neglected in DMA, were included in the FE model. The technique applies a constitutive relation to the DMA measurements and exploits a nonlinear inversion to estimate the material properties in the model that best fit the model response to the DMA data. A viscoelastic version of this approach was developed to validate the approach by comparing complex modulus estimates to the direct DMA results. Both analytical and FE poroelastic models were also developed to explore their behavior in the DMA testing environment. All of the models were applied to tofu as a representative soft poroelastic material that is a common phantom in elastography imaging studies. Five samples of three different stiffnesses were tested from 1-14 Hz with rough platens placed on the top and bottom surfaces of the material specimen under test to restrict transverse displacements and promote fluid-solid interaction. The viscoelastic models were identical in the static case, and nearly the same at frequency with inertial forces accounting for some of the discrepancy. The poroelastic analytical method was not sufficient when the relevant physical boundary constraints were applied, whereas the poroelastic FE approach produced high quality estimates of shear modulus and hydraulic conductivity. These results illustrated appropriate shear modulus contrast between tofu samples and yielded a consistent contrast in hydraulic conductivity as well.

Acoustic waves in medical imaging and diagnostics

Up until about two decades ago acoustic imaging and ultrasound imaging were synonymous. The term ultrasonography, or its abbreviated version sonography, meant an imaging modality based on the use of ultrasonic compressional bulk waves. Beginning in the 1990s, there started to emerge numerous acoustic imaging modalities based on the use of a different mode of acoustic wave: shear waves. Imaging with these waves was shown to provide very useful and very different information about the biological tissue being examined. We discuss the physical basis for the differences between these two basic modes of acoustic waves used in medical imaging and analyze the advantages associated with shear acoustic imaging. A comprehensive analysis of the range of acoustic wavelengths, velocities and frequencies that have been used in different imaging applications is presented. We discuss the potential for future shear wave imaging applications.

Effect of permeability on the performance of elastographic imaging techniques

Elastography is a well-established imaging modality. While a number of studies aimed at evaluating the performance of elastographic techniques are retrievable in the literature, very little information is available on the effects that the presence of an underlying permeability contrast in the tissue may have on the resulting elastograms. Permeability is a fundamental tissue parameter, which characterizes the ease with which fluid can move within a tissue. This parameter plays a central role both biomechanically in the description of the temporal behavior of fluid-filled tissues and clinically in the development of a number of diagnostic and therapeutic modalities. In this paper, we present a simulation study that investigates selected elastographic image quality factors in nonhomogeneous materials, modeled as poroelastic media with different geometries and permeability contrasts. The results of this study indicate that the presence of an underlying permeability contrast may create a new contrast mechanism in the spatial and temporal distributions of the axial strains and the effective Poisson's ratios experienced by the tissue and as imaged by the corresponding elastograms. The effect of permeability on the elastographic image quality factors analyzed in this study was found to be a nonsymmetric function of the underlying mechanical contrast between background and target, the geometry of the material and the boundary conditions.

MR elastography of liver tumours: value of viscoelastic properties for tumour characterisation

OBJECTIVES

To assess the value of the viscoelastic parameters in the characterisation of liver tumours at MR elastography.

PATIENTS AND METHODS

Ninety-four patients with liver tumours >1 cm prospectively underwent MR elastography using 50-Hz mechanical waves and a full three-directional motion-sensitive sequence. The model-free viscoelastic parameters (the complex shear modulus and its real and imaginary parts, i.e. the storage and loss moduli) were calculated in 72 lesions after exclusion of cystic, treated or histopathologically undetermined tumours.

RESULTS

We observed higher absolute shear modulus and loss modulus in malignant versus benign tumours (3.38 ± 0.26 versus 2.41 ± 0.15 kPa, P < 0.01 and 2.25 ± 0.26 versus 1.05 ± 0.13 kPa, P < 0.001, respectively). Moreover, the loss modulus of hepatocellular carcinomas was significantly higher than in benign hepatocellular tumours. The storage modulus did not differ significantly between malignant and benign tumours. The area under the receiver-operating characteristic curve of loss modulus was significantly larger than that of the absolute shear modulus and storage modulus when comparing malignant and benign lesions.

CONCLUSIONS

The increased loss modulus is a better discriminator between benign and malignant tumours than the increased storage modulus or absolute value of the shear modulus.

KEY POINTS

• Magnetic Resonance elastography is a new method of assessing the liver. • Increased loss modulus is an indicator of malignancy in hepatic tumours. • Loss modulus is a better discriminator than absolute shear modulus values. • The viscoelastic properties of lesions offer promise for characterising liver tumours.

A new nonlinear parameter in the developed strain-to-applied strain of the soft tissues and its application in ultrasound elasticity imaging

Strain developed under quasi-static deformation has been mostly used in ultrasound elasticity imaging (UEI) to determine the stiffness change of tissues. However, the strain measure in UEI is often less sensitive to a subtle change of stiffness. This is particularly true for Crohn's disease where we have applied strain imaging to the differentiation of acutely inflamed bowel from chronically fibrotic bowel. In this study, a new nonlinear elastic parameter of the soft tissues is proposed to overcome this limit. The purpose of this study is to evaluate the newly proposed method and demonstrate its feasibility in the UEI. A nonlinear characteristic of soft tissues over a relatively large dynamic range of strain was investigated. A simplified tissue model based on a finite element (FE) analysis was integrated with a laboratory developed ultrasound radio-frequency (RF) signal synthesis program. Two-dimensional speckle tracking was applied to this model to simulate the nonlinear behavior of the strain developed in a target inclusion over the applied average strain to the surrounding tissues. A nonlinear empirical equation was formulated and optimized to best match the developed strain-to-applied strain relation obtained from the FE simulation. The proposed nonlinear equation was applied to in vivo measurements and nonlinear parameters were further empirically optimized. For an animal model, acute and chronic inflammatory bowel disease was induced in Lewis rats with trinitrobenzene sulfonic acid (TNBS)-ethanol treatments. After UEI, histopathology and direct mechanical measurements were performed on the excised tissues. The extracted nonlinear parameter from the developed strain-to-applied strain relation differentiated the three different tissue types with 1.96 ± 0.12 for normal, 1.50 ± 0.09 for the acutely inflamed and 1.03 ± 0.08 for the chronically fibrotic tissue. T-tests determined that the nonlinear parameters between normal, acutely inflamed and fibrotic tissue types were statistically significantly different (normal/ fibrotic [p = 0.0000185], normal/acutely inflamed [p = 0.0013] and fibrotic/acutely inflamed [p = 0.0029]). This technique may provide a sensitive and robust tool to assess subtle stiffness changes in tissues such as in acutely inflamed bowel wall.

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.

Medical ultrasound: imaging of soft tissue strain and elasticity

After X-radiography, ultrasound is now the most common of all the medical imaging technologies. For millennia, manual palpation has been used to assist in diagnosis, but it is subjective and restricted to larger and more superficial structures. Following an introduction to the subject of elasticity, the elasticity of biological soft tissues is discussed and published data are presented. The basic physical principles of pulse-echo and Doppler ultrasonic techniques are explained. The history of ultrasonic imaging of soft tissue strain and elasticity is summarized, together with a brief critique of previously published reviews. The relevant techniques-low-frequency vibration, step, freehand and physiological displacement, and radiation force (displacement, impulse, shear wave and acoustic emission)-are described. Tissue-mimicking materials are indispensible for the assessment of these techniques and their characteristics are reported. Emerging clinical applications in breast disease, cardiology, dermatology, gastroenterology, gynaecology, minimally invasive surgery, musculoskeletal studies, radiotherapy, tissue engineering, urology and vascular disease are critically discussed. It is concluded that ultrasonic imaging of soft tissue strain and elasticity is now sufficiently well developed to have clinical utility. The potential for further research is examined and it is anticipated that the technology will become a powerful mainstream investigative tool.

AN OVERVIEW OF ELASTOGRAPHY - AN EMERGING BRANCH OF MEDICAL IMAGING

From times immemorial manual palpation served as a source of information on the state of soft tissues and allowed detection of various diseases accompanied by changes in tissue elasticity. During the last two decades, the ancient art of palpation gained new life due to numerous emerging elasticity imaging (EI) methods. Areas of applications of EI in medical diagnostics and treatment monitoring are steadily expanding. Elasticity imaging methods are emerging as commercial applications, a true testament to the progress and importance of the field.In this paper we present a brief history and theoretical basis of EI, describe various techniques of EI and, analyze their advantages and limitations, and overview main clinical applications. We present a classification of elasticity measurement and imaging techniques based on the methods used for generating a stress in the tissue (external mechanical force, internal ultrasound radiation force, or an internal endogenous force), and measurement of the tissue response. The measurement method can be performed using differing physical principles including magnetic resonance imaging (MRI), ultrasound imaging, X-ray imaging, optical and acoustic signals.Until recently, EI was largely a research method used by a few select institutions having the special equipment needed to perform the studies. Since 2005 however, increasing numbers of mainstream manufacturers have added EI to their ultrasound systems so that today the majority of manufacturers offer some sort of Elastography or tissue stiffness imaging on their clinical systems. Now it is safe to say that some sort of elasticity imaging may be performed on virtually all types of focal and diffuse disease. Most of the new applications are still in the early stages of research, but a few are becoming common applications in clinical practice.

Real-time quasi-static ultrasound elastography

Ultrasound elastography is a technique used for clinical imaging of tissue stiffness with a conventional ultrasound machine. It was first proposed two decades ago, but active research continues in this area to the present day. Numerous clinical applications have been investigated, mostly related to cancer imaging, and though these have yet to prove conclusive, the technique has seen increasing commercial and clinical interest. This paper presents a review of the most widely adopted, non-quantitative, techniques focusing on technical innovations rather than clinical applications. The review is not intended to be exhaustive, concentrating instead on placing the various techniques in context according to the authors' perspective of the field.

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.

Magnetic resonance poroelastography: an algorithm for estimating the mechanical properties of fluid-saturated soft tissues

Magnetic resonance poroelastography (MRPE) is introduced as an alternative to single-phase model-based elastographic reconstruction methods. A 3-D finite element poroelastic inversion algorithm was developed to recover the mechanical properties of fluid-saturated tissues. The performance of this algorithm was assessed through a variety of numerical experiments, using synthetic data to probe its stability and sensitivity to the relevant model parameters. Preliminary results suggest the algorithm is robust in the presence of noise and capable of producing accurate assessments of the underlying mechanical properties in simulated phantoms. Furthermore, a 3-D time-harmonic motion field was recorded for a poroelastic phantom containing a single cylindrical inclusion and used to assess the feasibility of MRPE image reconstruction from experimental data. The elastograms obtained from the proposed poroelastic algorithm demonstrate significant improvement over linearly elastic MRE images generated using the same data. In addition, MRPE offers the opportunity to estimate the time-harmonic pressure field resulting from tissue excitation, highlighting the potential for its application in the diagnosis and monitoring of disease processes associated with changes in interstitial pressure.

Poro-Viscoelastic Behavior of Gelatin Hydrogels Under Compression-Implications for Bioelasticity Imaging

Ultrasonic elasticity imaging enables visualization of soft tissue deformation for medical diagnosis. Our aim is to understand the role of flow-dependent and flow-independent viscoelastic mechanisms in the response of biphasic polymeric media, including biological tissues and hydrogels, to low-frequency forces. Combining the results of confined and unconfined compression experiments on gelatin hydrogels with finite element analysis (FEA) simulations of the experiments, we explore the role of polymer structure, loading, and boundary conditions in generating contrast for viscoelastic features. Feature estimation is based on comparisons between the biphasic poro-elastic and biphasic poro-viscoelastic (BPVE) material models, where the latter adds the viscoelastic response of the solid polymer matrix. The approach is to develop a consistent FEA material model (BPVE) from confined compression-stress relaxation measurements to extract the strain dependent hydraulic permeability variation and cone-plate rheometer measurements to obtain the flow-independent viscoelastic constants for the solid-matrix phase. The model is then applied to simulate the unconfined compression experiment to explore the mechanics of hydropolymers under conditions of quasi-static elasticity imaging. The spatiotemporal distributions of fluid and solid-matrix behavior within the hydrogel are studied to propose explanations for strain patterns that arise during the elasticity imaging of heterogeneous media.

Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression

In this paper, we report new progress in developing the instrument and software platform of a combined X-ray mammography/diffuse optical breast imaging system. Particularly, we focus on system validation using a series of balloon phantom experiments and the optical image analysis of 49 healthy patients. Using the finite-element method for forward modeling and a regularized Gauss-Newton method for parameter reconstruction, we recovered the inclusions inside the phantom and the hemoglobin images of the human breasts. An enhanced coupling coefficient estimation scheme was also incorporated to improve the accuracy and robustness of the reconstructions. The recovered average total hemoglobin concentration (HbT) and oxygen saturation (SO2) from 68 breast measurements are 16.2 microm and 71%, respectively, where the HbT presents a linear trend with breast density. The low HbT value compared to literature is likely due to the associated mammographic compression. From the spatially co-registered optical/X-ray images, we can identify the chest-wall muscle, fatty tissue, and fibroglandular regions with an average HbT of 20.1+/-6.1 microm for fibroglandular tissue, 15.4+/-5.0 microm for adipose, and 22.2+/-7.3 microm for muscle tissue. The differences between fibroglandular tissue and the corresponding adipose tissue are significant (p < 0.0001). At the same time, we recognize that the optical images are influenced, to a certain extent, by mammographical compression. The optical images from a subset of patients show composite features from both tissue structure and pressure distribution. We present mechanical simulations which further confirm this hypothesis.

Stable, intelligible ultrasonic strain imaging

BACKGROUND: Freehand quasistatic strain imaging can reveal qualitative information about tissue stiffness with good spatial accuracy. Clinical trials, however, repeatedly cite instability and variable signal-to-noise ratio as significant drawbacks. METHODS: This study investigates three post-processing strategies for quasistatic strain imaging. Normalisation divides the strain by an estimate of the stress field, the intention being to reduce sensitivity to variable applied stress. Persistence aims to improve the signal-to-noise ratio by time-averaging multiple frames. The persistence scheme presented in this article operates at the pixel level, weighting each frame's contribution by an estimate of the strain precision. Precision-based display presents the clinician with an image in which regions of indeterminate strain are obscured behind a colour wash. This is achieved using estimates of strain precision that are faithfully propagated through the various stages of signal processing. RESULTS AND DISCUSSION: The post-processing strategy is evaluated qualitatively on scans of a breast biopsy phantom and in vivo head and neck examinations. Strain images processed in this manner are observed to benefit from improved stability and signal-to-noise ratio. There are, however, limitations. In unusual though conceivable circumstances, the normalisation procedure might suppress genuine stiffness variations evident in the unprocessed strain images. In different circumstances, the raw strain images might fail to capture significant stiffness variations, a situation that no amount of post-processing can improve. CONCLUSION: The clinical utility of freehand quasistatic strain imaging can be improved by normalisation, precision-weighted pixel-level persistence and precision-based display. The resulting images are stable and generally exhibit a better signal-to-noise ratio than any of the original, unprocessed strain images.

The spatio-temporal strain response of oedematous and nonoedematous tissue to sustained compression in vivo

Poroelastic theory predicts that compression-induced fluid flow through a medium reveals itself via the spatio-temporal behaviour of the strain field. Such strain behaviour has already been observed in simple poroelastic phantoms using generalised elastographic techniques (Berry et al. 2006a, 2006b). The aim of this current study was to investigate the extent to which these techniques could be applied in vivo to image and interpret the compression-induced time-dependent local strain response in soft tissue. Tissue on both arms of six patients presenting with unilateral lymphoedema was subjected to a sustained compression for up to 500 s, and the induced strain was imaged as a function of time. The strain was found to exhibit time-dependent spatially varying behaviour, which we interpret to be consistent with that of a heterogeneous poroelastic material. This occurred in both arms of all patients, although it was more easily seen in the ipsilateral (affected) arm than in the contralateral (apparently unaffected) arm in five out of the six patients. Further work would appear to be worthwhile to determine if poroelasticity imaging could be used in future both to diagnose lymphoedema and to explore the patho-physiology of the condition.