Non-invasive quantitative reconstruction of tissue elasticity using an iterative forward approach

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Relative identifiability of anisotropic properties from magnetic resonance elastography

Although magnetic resonance elastography (MRE) has been used to estimate isotropic stiffness in the heart, myocardium is known to have anisotropic properties. This study investigated the determinability of global transversely isotropic material parameters using MRE and finite-element modeling (FEM). A FEM-based material parameter identification method, using a displacement-matching objective function, was evaluated in a gel phantom and simulations of a left ventricular (LV) geometry with a histology-derived fiber field. Material parameter estimation was performed in the presence of Gaussian noise. Parameter sweeps were analyzed and characteristics of the Hessian matrix at the optimal solution were used to evaluate the determinability of each constitutive parameter. Four out of five material stiffness parameters (Young's modulii E1 and E3 , shear modulus G13 and damping coefficient s), which describe a transversely isotropic linear elastic material, were well determined from the MRE displacement field using an iterative FEM inversion method. However, the remaining parameter, Poisson's ratio, was less identifiable. In conclusion, Young's modulii, shear modulii and damping can theoretically be well determined from MRE data, but Poisson's ratio is not as well determined and could be set to a reasonable value for biological tissue (close to 0.5).

Advances and Future Direction of Magnetic Resonance Elastography

The mechanical properties of soft tissues are closely associated with a variety of diseases. This motivates the development of elastography techniques in which tissue mechanical properties are quantitatively estimated through imaging. Magnetic resonance elastography (MRE) is a noninvasive phase-contrast MR technique wherein shear modulus of soft tissue can be spatially and temporally estimated. MRE has recently received significant attention due to its capability in noninvasively estimating tissue mechanical properties, which can offer considerable diagnostic potential. In this work, recent technology advances of MRE, its future clinical applications, and the related limitations will be discussed.

Stiffness reconstruction methods for MR elastography

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave-motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

Shear Wave Speed Estimation Using Reverberant Shear Wave Fields: Implementation and Feasibility Studies

Elastography is a modality that estimates tissue stiffness and, thus, provides useful information for clinical diagnosis. Attention has focused on the measurement of shear wave propagation; however, many methods assume shear wave propagation is unidirectional and aligned with the lateral imaging direction. Any deviations from the assumed propagation result in biased estimates of shear wave speed. To address these challenges, directional filters have been applied to isolate shear waves with different propagation directions. Recently, a new method was proposed for tissue stiffness estimation involving creation of a reverberant shear wave field propagating in all directions within the medium. These reverberant conditions lead to simple solutions, facile implementation and rapid viscoelasticity estimation of local tissue. In this work, this new approach based on reverberant shear waves was evaluated and compared with another well-known elastography technique using two calibrated elastic and viscoelastic phantoms. Additionally, the clinical feasibility of this technique was analyzed by assessing shear wave speed in human liver and breast tissues, in vivo. The results indicate that it is possible to estimate the viscoelastic properties in each scanned medium. Moreover, a better approach to estimation of shear wave speed was obtained when only the phase information was taken from the reverberant waves, which is equivalent to setting all magnitudes within the bandpass equal to unity: an idealization of a perfectly isotropic reverberant shear wave field.

A Comparison of Finite Element-Based Inversion Algorithms, Local Frequency Estimation, and Direct Inversion Approach Used in MRE

In quantitative elastography, maps of the mechanical properties of soft tissue, or elastograms, are calculated from the measured displacement data by solving an inverse problem. The model assumptions have a significant effect on elastograms. Motivated by the high sensitivity of imaging results to the model assumptions for in vivo magnetic resonance elastography of the prostate, we compared elastograms obtained with four different methods. Two finite-element method (FEM)-based methods developed by our group were compared with two other commonly used methods, local frequency estimator (LFE) and curl-based direct inversion (c-DI). All the methods assume a linear isotropic elastic model, but the methods vary in their assumptions, such as local homogeneity or incompressibility, and in the specific approach used. We report results using simulations, phantom, and ex vivo and in vivo data. The simulation and phantom studies show, for regions with an inclusion, that the contrast to noise ratio (CNR) for the FEM methods is about three to five times higher than the CNR for the LFE and c-DI and the rms error is about half. The LFE method produces very smooth results (i.e., low CNR) and is fast. c-DI is faster than the FEM methods but it is only accurate in areas where elasticity variations are small. The artifacts resulting from the homogeneity assumption in c-DI is detrimental in regions with large variations. The ex vivo and in vivo results also show similar trends as the simulation and phantom studies. The c-FEM method is more sensitive to noise compared with the mixed-FEM due to higher orders derivatives. This is especially evident at lower frequencies, where the wave curvature is smaller and it is more prone to such error, causing a discrepancy in the absolute values between the mixed-FEM and c-FEM in our in vivo results. In general, the proposed FEMs use fewer simplifying assumptions and outperform the other methods but they are computationally more expensive.

Systematic feasibility analysis of a quantitative elasticity estimation for breast anatomy using supine/prone patient postures

PURPOSE

Breast elastography is a critical tool for improving the targeted radiotherapy treatment of breast tumors. Current breast radiotherapy imaging protocols only involve prone and supine CT scans. There is a lack of knowledge on the quantitative accuracy with which breast elasticity can be systematically measured using only prone and supine CT datasets. The purpose of this paper is to describe a quantitative elasticity estimation technique for breast anatomy using only these supine/prone patient postures. Using biomechanical, high-resolution breast geometry obtained from CT scans, a systematic assessment was performed in order to determine the feasibility of this methodology for clinically relevant elasticity distributions.

METHODS

A model-guided inverse analysis approach is presented in this paper. A graphics processing unit (GPU)-based linear elastic biomechanical model was employed as a forward model for the inverse analysis with the breast geometry in a prone position. The elasticity estimation was performed using a gradient-based iterative optimization scheme and a fast-simulated annealing (FSA) algorithm. Numerical studies were conducted to systematically analyze the feasibility of elasticity estimation. For simulating gravity-induced breast deformation, the breast geometry was anchored at its base, resembling the chest-wall/breast tissue interface. Ground-truth elasticity distributions were assigned to the model, representing tumor presence within breast tissue. Model geometry resolution was varied to estimate its influence on convergence of the system. A priori information was approximated and utilized to record the effect on time and accuracy of convergence. The role of the FSA process was also recorded. A novel error metric that combined elasticity and displacement error was used to quantify the systematic feasibility study. For the authors' purposes, convergence was set to be obtained when each voxel of tissue was within 1 mm of ground-truth deformation.

RESULTS

The authors' analyses showed that a ∼97% model convergence was systematically observed with no-a priori information. Varying the model geometry resolution showed no significant accuracy improvements. The GPU-based forward model enabled the inverse analysis to be completed within 10-70 min. Using a priori information about the underlying anatomy, the computation time decreased by as much as 50%, while accuracy improved from 96.81% to 98.26%. The use of FSA was observed to allow the iterative estimation methodology to converge more precisely.

CONCLUSIONS

By utilizing a forward iterative approach to solve the inverse elasticity problem, this work indicates the feasibility and potential of the fast reconstruction of breast tissue elasticity using supine/prone patient postures.

MaterialCloning: Acquiring Elasticity Parameters from Images for Medical Applications

We present a practical approach for automatically estimating the material properties of soft bodies from two sets of images, taken before and after deformation. We reconstruct 3D geometry from the given sets of multiple-view images; we use a coupled simulation-optimization-identification framework to deform one soft body at its original, non-deformed state to match the deformed geometry of the same object in its deformed state. For shape correspondence, we use a distance-based error metric to compare the estimated deformation fields against the actual deformation field from the reconstructed geometry. The optimal set of material parameters is thereby determined by minimizing the error metric function. This method can simultaneously recover the elasticity parameters of multiple types of soft bodies using Finite Element Method-based simulation (of either linear or nonlinear materials undergoing large deformation) and particle-swarm optimization methods. We demonstrate this approach on real-time interaction with virtual organs in patient-specific surgical simulation, using parameters acquired from low-resolution medical images. We also highlight the results on physics-based animation of virtual objects using sketches from an artist's conception.

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.

Theoretical limitations of the elastic wave equation inversion for tissue elastography

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

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.

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.

Mechanical property assessment of tissue-mimicking phantoms using remote palpation and optical read-out for amplitude of vibration and refractive index modulation

A coherent light beam is used to interrogate the focal region within a tissue-mimicking phantom insonified by an ultrasound transducer. The ultrasound-tagged photons exiting from the object carry with them information on local optical path length fluctuations caused by refractive index variations and medium vibration. Through estimation of the force distribution in the focal region of the ultrasound transducer, and solving the forward elastography problem for amplitude of vibration of tissue particles, we observe that the amplitude is directed along the axis of the transducer. It is shown that the focal region interrogated by photons launched along the transducer axis carries phase fluctuations owing to both refractive index variations and particle vibration, whereas the photons launched perpendicular to the transducer axis carry phase fluctuations arising mainly from the refractive index variations, with only smaller contribution from vibration of particles. Monte-Carlo simulations and experiments done on tissue-mimicking phantoms prove that as the storage modulus of the phantom is increased, the detected modulation depth in autocorrelation is reduced, significantly for axial photons and only marginally for the transverse-directed photons. It is observed that the depth of modulation is reduced to a significantly lower and constant value as the storage modulus of the medium is increased. This constant value is found to be the same for both axial and transverse optical interrogation. This proves that the residual modulation depth is owing to refractive index fluctuations alone, which can be subtracted from the overall measured modulation depth, paving the way for a possible quantitative reconstruction of storage modulus. Moreover, since the transverse-directed photons are not significantly affected by storage modulus variations, for a quantitatively accurate read-out of absorption coefficient variation, the interrogating light should be perpendicular to the focusing ultrasound transducer axis.

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.

Ultrasonic tracking of acoustic radiation force-induced displacements in homogeneous media

The use of ultrasonic methods to track the tissue deformation generated by acoustic radiation force is subject to jitter and displacement underestimation errors, with displacement underestimation being primarily caused by lateral and elevation shearing within the point spread function (PSF) of the ultrasonic beam. Models have been developed using finite element methods and Field II, a linear acoustic field simulation package, to study the impact of focal configuration, tracking frequency, and material properties on the accuracy of ultrasonically tracking the tissue deformation generated by acoustic radiation force excitations. These models demonstrate that lateral and elevation shearing underneath the PSF of the tracking beam leads to displacement underestimation in the focal zone. Displacement underestimation can be reduced by using tracking beams that are narrower than the spatial extent of the displacement fields. Displacement underestimation and jitter decrease with time after excitation as shear wave propagation away from the region of excitation reduces shearing in the lateral and elevation dimensions. The use of higher tracking frequencies in broadband transducers, along with 2D focusing in the elevation dimension, will reduce jitter and improve displacement tracking accuracy. Relative displacement underestimation remains constant as a function of applied force, whereas jitter increases with applied force. Underdeveloped speckle (SNR < 1.91) leads to greater levels of jitter and peak displacement underestimation. Axial shearing is minimal over the tracking kernel lengths used in acoustic radiation force impulse imaging and thus does not impact displacement tracking.

Application of ultrasound-tagged photons for measurement of amplitude of vibration of tissue caused by ultrasound: theory, simulation, and experiments

We investigate the modulation of an optical field caused by its interaction with an ultrasound beam in a tissue mimicking phantom. This modulation appears as a modulation in the intensity autocorrelation, which is measured by a photon counting correlator. The factors contributing to the modulation are: 1. amplitude of vibration of the particles of the tissue, 2. refractive index modulation, and 3. absorption coefficient in the region of the tissue intercepted by the ultrasound beam and light. We show in this work that a significant part of the contribution to this modulation comes from displacement of the tissue particles, which in turn is governed by the elastic properties of the tissue. We establish, both through simulations and experiments using an optical elastography phantom, the effects of the elasticity and absorption coefficient variations on the modulation of intensity autocorrelation. In the case where there is no absorption coefficient variation, we suggest that the depth of modulation can be calibrated to measure the displacement of tissue particles that, in turn, can be used to measure the tissue elasticity.

Analysis of contrast in images generated with transient acoustic radiation force

Several mechanical imaging methods are under investigation that use focused ultrasound (US) as a source of mechanical excitation. Images are then generated of the tissue response to this localized excitation. One such method, acoustic radiation force impulse (ARFI) imaging, utilizes a single US transducer on a commercial US system to transmit brief, high-energy, focused acoustic pulses to generate radiation force in tissue and correlation-based US methods to detect the resulting tissue displacements. Local displacements reflect relative mechanical properties of tissue. The resolution of these images is comparable with that of conventional B-mode imaging. The response of tissue to focused radiation force excitation is complex and depends upon tissue geometry, forcing function geometry (i.e., region of excitation, or ROE) and tissue mechanical and acoustic properties. Finite element method (FEM) simulations using an experimentally validated model and phantom experiments have been performed using varying systems, system configurations and tissue-mimicking phantoms to determine their impact on image quality. Image quality is assessed by lesion contrast. Due to the dynamic nature of ARFI excitation, lesion contrast is temporally-dependent. Contrast of spherical inclusions is highest immediately after force cessation, decreases with time postforce and then reverses, due to shear wave interaction with internal boundaries, differences in shear modulus between lesions and background and inertial effects. In images generated immediately after force cessation, contrast does not vary with applied force, increases with lesion stiffness and increases as the ROE size decreases relative to the size of the structure being imaged. These studies indicate that improved contrast in radiation force-generated images will be achieved as ROE size decreases; however, frame rate and thermal considerations present trade-offs with small ROE size.

Design, fabrication, and characterization of a tissue-equivalent phantom for optical elastography

We suitably adapt the design of a tissue-equivalent phantom used for photoacoustic imaging to construct phantoms for optical elastography. The elastography phantom we consider should have optical properties such as scattering coefficient, scattering anisotropy factor, and refractive index; mechanical properties such as storage and loss modulus; and acoustic properties such as ultrasound velocity, attenuation coefficient, and acoustic impedance to match healthy and diseased tissues. The phantom is made of poly (vinyl alcohol) (PVA) and its mechanical, optical, and acoustic properties are tailored by physical cross-linking effected through subjecting a suitable mix of PVA stock and water to a number of freeze-thaw cycles and by varying the degree of hydrolysis in the PVA stock. The optical, mechanical, and acoustic properties of the samples prepared are measured by employing different techniques. The measured variations in the values of optical scattering coefficient, scattering anisotropy factor, and refractive index and storage modulus are found to be comparable to those in normal and diseased breast tissues. The acoustic properties such as sound speed, acoustic attenuation coefficient, and density are found to be close to the average values reported in the literature for normal breast tissue.

Assessment of vulnerable plaque composition by matching the deformation of a parametric plaque model to measured plaque deformation

Intravascular ultrasound (IVUS) elastography visualizes local radial strain of arteries in so-called elastograms to detect rupture-prone plaques. However, due to the unknown arterial stress distribution these elastograms cannot be directly interpreted as a morphology and material composition image. To overcome this limitation we have developed a method that reconstructs a Young's modulus image from an elastogram. This method is especially suited for thin-cap fibroatheromas (TCFAs), i.e., plaques with a media region containing a lipid pool covered by a cap. Reconstruction is done by a minimization algorithm that matches the strain image output, calculated with a parametric finite element model (PFEM) representation of a TCFA, to an elastogram by iteratively updating the PFEM geometry and material parameters. These geometry parameters delineate the TCFA media, lipid pool and cap regions by circles. The material parameter for each region is a Young's modulus, EM, EL, and EC, respectively. The method was successfully tested on computer-simulated TCFAs (n = 2), one defined by circles, the other by tracing TCFA histology, and additionally on a physical phantom (n = 1) having a stiff wall (measured EM = 16.8 kPa) with an eccentric soft region (measured EL = 4.2 kPa). Finally, it was applied on human coronary plaques in vitro (n = 1) and in vivo (n = 1). The corresponding simulated and measured elastograms of these plaques showed radial strain values from 0% up to 2% at a pressure differential of 20, 20, 1, 20, and 1 mmHg respectively. The used/reconstructed Young's moduli [kPa] were for the circular plaque EL = 50/66, EM = 1500/1484, EC = 2000/2047, for the traced plaque EL = 25/1, EM = 1000/1148, EC = 1500/1491, for the phantom EL = 4.2/4 kPa, EM = 16.8/16, for the in vitro plaque EL = n.a./29, EM = n.a./647, EC = n.a./1784 kPa and for the in vivo plaque EL = n.a./2, EM = n.a./188, Ec = n.a./188 kPa.

Modality independent elastography (MIE): a new approach to elasticity imaging

The correlation between tissue stiffness and health is an accepted form of organ disease assessment. As a result, there has been a significant amount of interest in developing methods to image elasticity parameters (i.e., elastography). The modality independent elastography (MIE) method combines a nonlinear optimization framework, computer models of soft-tissue deformation, and standard measures of image similarity to reconstruct elastic property distributions within soft tissue. In this paper, simulation results demonstrate successful elasticity image reconstructions in breast cross-sectional images acquired from magnetic resonance (MR) imaging. Results from phantom experiments illustrate its modality independence by reconstructing elasticity images of the same phantom in both MR and computed tomographic imaging units. Additional results regarding the performance of a new multigrid strategy to MIE and the implementation of a parallel architecture are also presented.

Determining the mechanical properties of rat skin with digital image speckle correlation

BACKGROUND

Accurate measurement of the mechanical properties of skin has numerous implications in surgical repair, dermal disorders and the diagnosis and treatment of trauma to the skin. Investigation of facial wrinkle formation, as well as research in the areas of skin aging and cosmetic product assessment can also benefit from alternative methodologies for the measurement of mechanical properties.

OBJECTIVE

A noncontact, noninvasive technique, digital image speckle correlation (DISC), has been successfully introduced to measure the deformation field of a skin sample loaded by a material test machine. With the force information obtained from the loading device, the mechanical properties of the skin, such as Young's modulus, linear limitation and material strength, can be calculated using elastic or viscoelastic theory.

METHODS

The DISC method was used to measure the deformation of neonatal rat skin, with and without a glycerin-fruit-oil-based cream under uniaxial tension.

RESULTS

Deformation to failure procedure of newborn rat skin was recorded and analyzed. Single skin layer failures were observed and located by finding the strain concentration. Young's moduli of freshly excised rat skin, cream-processed rat skin and unprocessed rat skin, 24 h after excision, were found with tensile tests to be 1.6, 1.4 and 0.7 MPa, respectively.

CONCLUSION

Our results have shown that DISC provides a novel technique for numerous applications in dermatology and reconstructive surgeries.

Shear-wave generation using acoustic radiation force: in vivo and ex vivo results

Acoustic radiation force impulse (ARFI) imaging involves the mechanical excitation of tissue using localized, impulsive radiation force. This results in shear-wave propagation away from the region of excitation. Using a single diagnostic transducer on a modified commercial ultrasound (US) scanner with conventional beam-forming architecture, repeated excitations with multiple look directions facilitate imaging shear-wave propagation. Direct inversion methods are then applied to estimate the associated Young's modulus. Shear-wave images are generated in tissue-mimicking phantoms, ex vivo human breast tissue and in vivo in the human abdomen. Mean Young's modulus values of between 3.8 and 5.6 kPa, 11.7 kPa and 14.0 kPa were estimated for fat, fibroadenoma and skin, respectively. Reasonable agreement is demonstrated between structures in matched B-mode and reconstructed modulus images. Although the relatively small magnitude of the displacement data presents some challenges, the reconstructions suggest the clinical feasibility of radiation force induced shear-wave imaging.

Tissue-mimicking oil-in-gelatin dispersions for use in heterogeneous elastography phantoms

A ten-month study is presented of materials for use in heterogeneous elastography phantoms. The materials consist of gelatin with or without a suspension of microscopic safflower oil droplets. The highest volume percent of oil in the materials is 50%. Thimerosal acts as a preservative. The greater the safflower oil concentration, the lower the Young's modulus. Elastographic data for heterogeneous phantoms, in which the only variable is safflower oil concentration, demonstrate stability of inclusion geometry and elastic strain contrast. Young's modulus ratios (elastic contrasts) producible in a heterogeneous phantom are as high as 2.7. The phantoms are particularly useful for ultrasound elastography. They can also be employed in MR elastography, although the highest achievable ratio of longitudinal to transverse relaxation times is considerably less than is the case for soft tissues.

Quantitative elasticity imaging: what can and cannot be inferred from strain images

We examine the inverse problem associated with quantitative elastic modulus imaging: given the equilibrium strain field in a 2D incompressible elastic material, determine the elastic stiffness (shear modulus). We show analytically that a direct formulation of the inverse problem has no unique solution unless stiffness information is known a priori on a sufficient portion of the boundary. This implies that relative stiffness images constructed on the assumption of constant boundary stiffness are in error, unless the stiffness is truly constant on the boundary. We show further that using displacement boundary conditions in the forward incompressible elasticity problem leads to a nonunique inverse problem. Indeed, we give examples in which exactly the same strain field results from different elastic modulus distributions under displacement boundary conditions. We also show that knowing the stress on the boundary can, in certain configurations, lead to a well-posed inverse problem for the elastic stiffness. These results indicate what data must be taken if the elastic modulus is to be reconstructed reliably and quantitatively from a strain image.

Vibro-acoustic tissue mammography

A novel method for detection and imaging of microcalcifications in breast tissue is presented. The method, called vibro-acoustography, uses the radiation force of ultrasound to vibrate tissue at low (kHz) frequency and utilizes the resulting response to produce images that are related to the hardness of the tissue. The method is tested on human breast tissues. The resulting vibro-acoustographic images are in agreement with corresponding X-ray mammography images of the specimens. The existence of microcalcifications in locations indicated by vibro-acoustography is confirmed by histology. Microcalcifications as small as 110 microm in diameter are detected by this method. Resulting vibro-acoustographic images show microcalcifications with high contrast with respect to the background soft tissue. Structures such as dense sclerotic tissue do not seem to interfere with detection of microcalcifications.

Shear wave focusing for three-dimensional sonoelastography

A new vibration scheme is shown to provide localized vibration fields for three-dimensional sonoelastography imaging. The theoretical vibration distributions of double strip loads vibrating normally to the surface of a semi-infinite elastic space are calculated. A localization or focusing of shear waves inbetween the double-strip loads is predicted. Experimentally, two parallel rigid rectangular cross-section bars are mounted on an electromagnetic shaker. Driven by the signal source, the bars vibrate against the surface of a tissue-mimicking phantom. The double-bar source is also used to propagate shear wave into an ex vivo prostate phantom with a 6 mm "tumor" in it. A combination of high frequencies (400-600 Hz) is used to drive the double-bar applicator. In the phantom experiments, a shear wave focal zone with higher vibration amplitude and uniformity predicted by the theory was confirmed. The position of the focal zone is controllable when adjusting the separation of the bars as the theory shows. When this vibration scheme was used in a prostate phantom experiment, high-resolution tumor images with clear boundaries are obtained. The parallel bar is an ideal applicator to create more uniform vibration within a controllable localized volume. The field has uniformity especially in the direction along the bars.