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

Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography

Probing the mechanical properties of tissue on the microscale could aid in the identification of diseased tissues that are inadequately detected using palpation or current clinical imaging modalities, with potential to guide medical procedures such as the excision of breast tumours. Compression optical coherence elastography (OCE) maps tissue strain with microscale spatial resolution and can delineate microstructural features within breast tissues. However, without a measure of the locally applied stress, strain provides only a qualitative indication of mechanical properties. To overcome this limitation, we present quantitative micro-elastography, which combines compression OCE with a compliant stress sensor to image tissue elasticity. The sensor consists of a layer of translucent silicone with well-characterized stress-strain behaviour. The measured strain in the sensor is used to estimate the two-dimensional stress distribution applied to the sample surface. Elasticity is determined by dividing the stress by the strain in the sample. We show that quantification of elasticity can improve the ability of compression OCE to distinguish between tissues, thereby extending the potential for inter-sample comparison and longitudinal studies of tissue elasticity. We validate the technique using tissue-mimicking phantoms and demonstrate the ability to map elasticity of freshly excised malignant and benign human breast tissues.

Oestreicher and elastography

A sphere moving back and forth in tissue generates the kinds of complex displacement fields that are used in elastography. The analytical solution of Hans Oestreicher for this phenomenon [(1951). J. Acoust. Soc. Am. 23, 704-714] gives an understanding of the transverse and longitudinal, fast and slow waves that are generated. The results suggest several ways to determine the absorption coefficients of tissues, which together with phase velocity permit the computation of both the real shear modulus and the shear viscosity as functions of frequency.

Magnetic resonance elastography of the brain: An in silico study to determine the influence of cranial anatomy

PURPOSE

Magnetic resonance elastography (MRE) of the brain has demonstrated potential as a biomarker of neurodegenerative disease such as dementia but requires further evaluation. Cranial anatomical features such as the falx cerebri and tentorium cerebelli membranes may influence MRE measurements through wave reflection and interference and tissue heterogeneity at their boundaries. We sought to determine the influence of these effects via simulation.

METHODS

MRE-associated mechanical stimulation of the brain was simulated using steady state harmonic finite element analysis. Simulations of geometrical models and anthropomorphic brain models derived from anatomical MRI data of healthy individuals were compared. Constitutive parameters were taken from MRE measurements for healthy brain. Viscoelastic moduli were reconstructed from the simulated displacement fields and compared with ground truth.

RESULTS

Interference patterns from reflections and heterogeneity resulted in artifacts in the reconstructions of viscoelastic moduli. Artifacts typically occurred in the vicinity of boundaries between different tissues within the cranium, with a magnitude of 10%-20%.

CONCLUSION

Given that MRE studies for neurodegenerative disease have reported only marginal variations in brain elasticity between controls and patients (e.g., 7% for Alzheimer's disease), the predicted errors are a potential confound to the development of MRE as a biomarker of dementia and other neurodegenerative diseases. Magn Reson Med 76:645-662, 2016. © 2015 Wiley Periodicals, Inc.

Mechanical contrast in spectroscopic magnetomotive optical coherence elastography

The viscoelastic properties of tissues are altered during pathogenesis of numerous diseases and can therefore be a useful indicator of disease status and progression. Several elastography studies have utilized the mechanical frequency response and the resonance frequencies of tissue samples to characterize their mechanical properties. However, using the resonance frequency as a source of mechanical contrast in heterogeneous samples is complicated because it not only depends on the viscoelastic properties but also on the geometry and boundary conditions. In an elastography technique called magnetomotive optical coherence elastography (MM-OCE), the controlled movement of magnetic nanoparticles (MNPs) within the sample is used to obtain the mechanical properties. Previous demonstrations of MM-OCE have typically used point measurements in elastically homogeneous samples assuming a uniform concentration of MNPs. In this study, we evaluate the feasibility of generating MM-OCE elastograms in heterogeneous samples based on a spectroscopic approach which involves measuring the magnetomotive response at different excitation frequencies. Biological tissues and tissue-mimicking phantoms with two elastically distinct regions placed in side-by-side and bilayer configurations were used for the experiments, and finite element method simulations were used to validate the experimental results.

Guidewire path determination for intravascular applications

Vascular diseases are among the major causes of death in developed countries and the treatment of those pathologies may require endovascular interventions, in which the physician utilizes guidewires and catheters through the vascular system to reach the injured vessel region. Several computational studies related to endovascular procedures are in constant development. Thus, predicting the guidewire path may be of great value for both physicians and researchers. However, attaining good accuracy and precision is still an important issue. We propose a method to simulate and predict the guidewire and catheter path inside a blood vessel based on equilibrium of a new set of forces, which leads, iteratively, to the minimum energy configuration. This technique was validated with phantoms using a ∅0.33 mm stainless steel guidewire and compared to other relevant methods in the literature. This method presented RMS error 0.30 mm and 0.97 mm, which represents less than 2% and 20% of the lumen diameter of the phantom, in 2D and 3D cases, respectively. The proposed technique presented better results than other methods from the literature, which were included in this work for comparison. Moreover, the algorithm presented low variation (σ=0:03 mm) due to the variation of the input parameters. Therefore, even for a wide range of different parameters configuration, similar results are presented for the proposed approach, which is an important feature and makes this technique easier to work with. Since this method is based on basic physics, it is simple, intuitive, easy to learn and easy to adapt.

Carotid plaque elasticity estimation using ultrasound elastography, MRI, and inverse FEA - A numerical feasibility study

The material properties of atherosclerotic plaques govern the biomechanical environment, which is associated with rupture-risk. We investigated the feasibility of noninvasively estimating carotid plaque component material properties through simulating ultrasound (US) elastography and in vivo magnetic resonance imaging (MRI), and solving the inverse problem with finite element analysis. 2D plaque models were derived from endarterectomy specimens of nine patients. Nonlinear neo-Hookean models (tissue elasticity C1) were assigned to fibrous intima, wall (i.e., media/adventitia), and lipid-rich necrotic core. Finite element analysis was used to simulate clinical cross-sectional US strain imaging. Computer-simulated, single-slice in vivo MR images were segmented by two MR readers. We investigated multiple scenarios for plaque model elasticity, and consistently found clear separations between estimated tissue elasticity values. The intima C1 (160 kPa scenario) was estimated as 125.8 ± 19.4 kPa (reader 1) and 128.9 ± 24.8 kPa (reader 2). The lipid-rich necrotic core C1 (5 kPa) was estimated as 5.6 ± 2.0 kPa (reader 1) and 8.5 ± 4.5 kPa (reader 2). A scenario with a stiffer wall yielded similar results, while realistic US strain noise and rotating the models had little influence, thus demonstrating robustness of the procedure. The promising findings of this computer-simulation study stimulate applying the proposed methodology in a clinical setting.

Visualizing the stress distribution within vascular tissues using intravascular ultrasound elastography: a preliminary investigation

A methodology for computing the stress distribution of vascular tissue using finite element-based, intravascular ultrasound (IVUS) reconstruction elastography is described. This information could help cardiologists detect life-threatening atherosclerotic plaques and predict their propensity to rupture. The calculation of vessel stresses requires the measurement of strain from the ultrasound images, a calibrating pressure measurement and additional model assumptions. In this work, we conducted simulation studies to investigate the effect of varying the model assumptions, specifically Poisson's ratio and the outer boundary conditions, on the resulting stress fields. In both simulation and phantom studies, we created vessel geometries with two fibrous cap thicknesses to determine if we could detect a difference in peak stress (spatially) between the two. The results revealed that (i) Poisson's ratios had negligible impact on the accuracy of stress elastograms, (ii) the outer boundary condition assumption had the greatest effect on the resulting modulus and stress distributions and (iii) in simulation and in phantom experiments, our stress imaging technique was able to detect an increased peak stress for the vessel geometry with the smaller cap thickness. This work is a first step toward understanding and creating a robust stress measurement technique for evaluating atherosclerotic plaques using IVUS elastography.

Characterization of the nonlinear elastic properties of soft tissues using the supersonic shear imaging (SSI) technique: inverse method, ex vivo and in vivo experiments

Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed.

Shear wave speed and dispersion measurements using crawling wave chirps

This article demonstrates the measurement of shear wave speed and shear speed dispersion of biomaterials using a chirp signal that launches waves over a range of frequencies. A biomaterial is vibrated by two vibration sources that generate shear waves inside the medium, which is scanned by an ultrasound imaging system. Doppler processing of the acquired signal produces an image of the square of vibration amplitude that shows repetitive constructive and destructive interference patterns called "crawling waves." With a chirp vibration signal, successive Doppler frames are generated from different source frequencies. Collected frames generate a distinctive pattern which is used to calculate the shear speed and shear speed dispersion. A special reciprocal chirp is designed such that the equi-phase lines of a motion slice image are straight lines. Detailed analysis is provided to generate a closed-form solution for calculating the shear wave speed and the dispersion. Also several phantoms and an ex vivo human liver sample are scanned and the estimation results are presented.

A regularization-free elasticity reconstruction method for ultrasound elastography with freehand scan

BACKGROUND

In ultrasound elastography, reconstruction of tissue elasticity (e.g., Young's modulus) requires regularization and known information of forces and/or displacements on tissue boundaries. In practice, it is challenging to choose an appropriate regularization parameter; and the boundary conditions are difficult to obtain in vivo. The purpose of this study is to develop a more applicable algorithm that does not need any regularization or boundary force/displacement information.

METHODS

The proposed method adopts the bicubic B-spline as the tissue motion model to estimate the displacement fields. Then the estimated displacements are input to the finite element inversion scheme to reconstruct the Young's modulus of each element. In the inversion, a modulus boundary condition is used instead of force/displacement boundary conditions. Simulation and experiments on tissue-mimicking phantoms are carried out to test the proposed method.

RESULTS

The simulation results demonstrate that Young's modulus reconstruction of the proposed method has a relative error of -3.43 ± 0.43% and root-squared-mean error of 16.94 ± 0.25%. The phantom experimental results show that the target hardening artifacts in the strain images are significantly reduced in the Young's modulus images. In both simulation and phantom studies, the size and position of inclusions can be accurately depicted in the modulus images.

CONCLUSIONS

The proposed method can reconstruct tissue Young's modulus distribution with a high accuracy. It can reduce the artifacts shown in the strain image and correctly delineate the locations and sizes of inclusions. Unlike most modulus reconstruction methods, it does not need any regularization during the inversion procedure. Furthermore, it does not need to measure the boundary conditions of displacement or force. Thus this method can be used with a freehand scan, which facilitates its usage in the clinic.

Quantitative sparse array vascular elastography: the impact of tissue attenuation and modulus contrast on performance

Quantitative sparse array vascular elastography visualizes the shear modulus distribution within vascular tissues, information that clinicans could use to reduce the number of strokes each year. However, the low transmit power sparse array (SA) imaging could hamper the clinical usefulness of the resulting elastograms. In this study, we evaluated the performance of modulus elastograms recovered from simulated and physical vessel phantoms with varying attenuation coefficients (0.6, 1.5, and [Formula: see text]) and modulus contrasts ([Formula: see text], [Formula: see text], and [Formula: see text]) using SA imaging relative to those obtained with conventional linear array (CLA) and plane-wave (PW) imaging techniques. Plaques were visible in all modulus elastograms, but those produced using SA and PW contained less artifacts. The modulus contrast-to-noise ratio decreased rapidly with increasing modulus contrast and attenuation coefficient, but more quickly when SA imaging was performed than for CLA or PW. The errors incurred varied from 10.9% to 24% (CLA), 1.8% to 12% (SA), and [Formula: see text] (PW). Modulus elastograms produced with SA and PW imagings were not significantly different ([Formula: see text]). Despite the low transmit power, SA imaging can produce useful modulus elastograms in superficial organs, such as the carotid artery.

The Gaussian shear wave in a dispersive medium

In "imaging the biomechanical properties of tissues," a number of approaches analyze shear wave propagation initiated by a short radiation force push. Unfortunately, it has been experimentally observed that the displacement-versus-time curves for lossy tissues are rapidly damped and distorted in ways that can confound simple tracking approaches. This article addresses the propagation, decay and distortion of pulses in lossy and dispersive media, to derive closed-form analytic expressions for the propagating pulses. The theory identifies key terms that drive the distortion and broadening of the pulse. Furthermore, the approach taken is not dependent on any particular viscoelastic model of tissue, but instead takes a general first-order approach to dispersion. Examples with a Gaussian beam pattern and realistic dispersion parameters are given along with general guidelines for identifying the features of the distorting wave that are the most compact.

A tracer-kinetic field theory for medical imaging

Dynamic imaging data are currently analyzed with a tracer-kinetic theory developed for individual time curves measured over whole organs. The assumption is that voxels represent isolated systems which all receive indicator through the same arterial inlet. This leads to well-known systematic errors, but also fails to exploit the spatial structure of the data. In this study, a more general theoretical framework is developed which makes full use of the specific structure of image data. The theory encodes the fact that voxels receive indicator from their immediate neighbors rather than from an upstream arterial input. This results in a tracer-kinetic field theory where the tissue parameters are functions of space which can be measured by analyzing the temporal and spatial patterns in the concentrations. The implications are evaluated through a number of field models for common tissue types. The key benefits of a tracer-kinetic field theory are that: 1) long-standing systematic errors can be corrected, specifically the issue of bolus dispersion and the contamination of large-vessel blood flow on tissue perfusion measurements; 2) additional tissue parameters can be measured that characterize convective or diffusive exchange between voxels; 3) the need to measure a separate arterial input function can be eliminated.

Mechanical characterization of tissue-engineered cartilage using microscopic magnetic resonance elastography

Knowledge of mechanical properties of tissue-engineered cartilage is essential for the optimization of cartilage tissue engineering strategies. Microscopic magnetic resonance elastography (μMRE) is a recently developed MR-based technique that can nondestructively visualize shear wave motion. From the observed wave pattern in MR phase images the tissue mechanical properties (e.g., shear modulus or stiffness) can be extracted. For quantification of the dynamic shear properties of small and stiff tissue-engineered cartilage, μMRE needs to be performed at frequencies in the kilohertz range. However, at frequencies greater than 1 kHz shear waves are rapidly attenuated in soft tissues. In this study μMRE, with geometric focusing, was used to overcome the rapid wave attenuation at high frequencies, enabling the measurement of the shear modulus of tissue-engineered cartilage. This methodology was first tested at a frequency of 5 kHz using a model system composed of alginate beads embedded in agarose, and then applied to evaluate extracellular matrix development in a chondrocyte pellet over a 3-week culture period. The shear stiffness in the pellet was found to increase over time (from 6.4 to 16.4 kPa), and the increase was correlated with both the proteoglycan content and the collagen content of the chondrocyte pellets (R(2)=0.776 and 0.724, respectively). Our study demonstrates that μMRE when performed with geometric focusing can be used to calculate and map the shear properties within tissue-engineered cartilage during its development.

A direct vulnerable atherosclerotic plaque elasticity reconstruction method based on an original material-finite element formulation: theoretical framework

The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time elasticity reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for elasticity reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3 ± 15.56%, 98.85 ± 72.42%, 103.29 ± 111.86% and 95.3 ± 10.49%, respectively, to values smaller than 2.6 × 10(-8) ± 5.7 × 10(-8)% (i.e. close to the exact solutions) when including modified-Xfem method into our direct elasticity reconstruction method.

Framework to co-register longitudinal virtual histology-intravascular ultrasound data in the circumferential direction

Considerable efforts have been directed at identifying prognostic markers for rapidly progressing coronary atherosclerotic lesions that may advance into a high-risk (vulnerable) state. Intravascular ultrasound (IVUS) has become a valuable clinical tool to study the natural history of coronary artery disease (CAD). While prospectively IVUS studies have provided tremendous insight on CAD progression, and its association with independent markers (e.g., wall shear stress), they are limited by the inability to examine the focal association between spatially heterogeneous variables (in both circumferential and axial directions). Herein, we present a framework to automatically co-register longitudinal (in-time) virtual histology-intravascular ultrasound (VH-IVUS) imaging data in the circumferential direction (i.e., rotate follow-up image so circumferential basis coincides with corresponding baseline image). Multivariate normalized cross correlation was performed on paired images (n = 636) from five patients using three independent VH-IVUS defined parameters: artery thickness, VH-IVUS defined plaque constituents, and VH-IVUS perivascular imaging data. Results exhibited high correlation between co-registration rotation angles determined automatically versus manually by an expert reader ( r(2) = 0.90). Furthermore, no significant difference between automatic and manual co-registration angles was observed ( 91.31 ±1.04(°) and 91.07 ±1.04(°), respectively; p = 0.48) and Bland-Altman analysis yielded excellent agreement ( bias = 0.24(°), 95% CI +/- 16.33(°)). In conclusion, we have developed, verified, and validated an algorithm that automatically co-registers VH-IVUS imaging data that will allow for the focal examination of CAD progression.

Biomechanics of atherosclerotic coronary plaque: site, stability and in vivo elasticity modeling

Coronary atheroma develop in local sites that are widely variable among patients and are considerably variable in their vulnerability for rupture. This article summarizes studies conducted by our collaborative laboratories on predictive biomechanical modeling of coronary plaques. It aims to give insights into the role of biomechanics in the development and localization of atherosclerosis, the morphologic features that determine vulnerable plaque stability, and emerging in vivo imaging techniques that may detect and characterize vulnerable plaque. Composite biomechanical and hemodynamic factors that influence the actual site of development of plaques have been studied. Plaque vulnerability, in vivo, is more challenging to assess. Important steps have been made in defining the biomechanical factors that are predictive of plaque rupture and the likelihood of this occurring if characteristic features are known. A critical key in defining plaque vulnerability is the accurate quantification of both the morphology and the mechanical properties of the diseased arteries. Recently, an early IVUS based palpography technique developed to assess local strain, elasticity and mechanical instabilities has been successfully revisited and improved to account for complex plaque geometries. This is based on an initial best estimation of the plaque components' contours, allowing subsequent iteration for elastic modulus assessment as a basis for plaque stability determination. The improved method has also been preliminarily evaluated in patients with successful histologic correlation. Further clinical evaluation and refinement are on the horizon.

An H∞ strategy for strain estimation in ultrasound elastography using biomechanical modeling constraint

The purpose of ultrasound elastography is to identify lesions by reconstructing the hardness characteristics of tissue reconstructed from ultrasound data. Conventional quasi-static ultrasound elastography is easily applied to obtain axial strain components along the compression direction, with the results inverted to represent the distribution of tissue hardness under the assumption of constant internal stresses. However, previous works of quasi-static ultrasound elastography have found it difficult to obtain the lateral and shear strain components, due to the poor lateral resolution of conventional ultrasound probes. The physical nature of the strain field is a continuous vector field, which should be fully described by the axial, lateral, and shear strain components, and the clinical value of lateral and shear strain components of deformed tissue is gradually being recognized by both engineers and clinicians. Therefore, a biomechanical-model-constrained filtering framework is proposed here for recovering a full displacement field at a high spatial resolution from the noisy ultrasound data. In our implementation, after the biomechanical model constraint is integrated into the state-space equation, both the axial and lateral displacement components can be recovered at a high spatial resolution from the noisy displacement measurements using a robust H∞ filter, which only requires knowledge of the worst-case noise levels in the measurements. All of the strain components can then be calculated by applying a gradient operator to the recovered displacement field. Numerical experiments on synthetic data demonstrated the robustness and effectiveness of our approach, and experiments on phantom data and in-vivo clinical data also produced satisfying results.

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.

Towards an elastographic atlas of brain anatomy

Cerebral viscoelastic constants can be measured in a noninvasive, image-based way by magnetic resonance elastography (MRE) for the detection of neurological disorders. However, MRE brain maps of viscoelastic constants are still limited by low spatial resolution. Here we introduce three-dimensional multifrequency MRE of the brain combined with a novel reconstruction algorithm based on a model-free multifrequency inversion for calculating spatially resolved viscoelastic parameter maps of the human brain corresponding to the dynamic range of shear oscillations between 30 and 60 Hz. Maps of two viscoelastic parameters, the magnitude and the phase angle of the complex shear modulus, |G*| and φ, were obtained and normalized to group templates of 23 healthy volunteers in the age range of 22 to 72 years. This atlas of the anatomy of brain mechanics reveals a significant contrast in the stiffness parameter |G*| between different anatomical regions such as white matter (WM; 1.252±0.260 kPa), the corpus callosum genu (CCG; 1.104±0.280 kPa), the thalamus (TH; 1.058±0.208 kPa) and the head of the caudate nucleus (HCN; 0.649±0.101 kPa). φ, which is sensitive to the lossy behavior of the tissue, was in the order of CCG (1.011±0.172), TH (1.037±0.173), CN (0.906±0.257) and WM (0.854±0.169). The proposed method provides the first normalized maps of brain viscoelasticity with anatomical details in subcortical regions and provides useful background data for clinical applications of cerebral MRE.

Reconstruction of elasticity: a stochastic model-based approach in ultrasound elastography

Background

The convectional strain-based algorithm has been widely utilized in clinical practice. It can only provide the information of relative information of tissue stiffness. However, the exact information of tissue stiffness should be valuable for clinical diagnosis and treatment.

Methods

In this study we propose a reconstruction strategy to recover the mechanical properties of the tissue. After the discrepancies between the biomechanical model and data are modeled as the process noise, and the biomechanical model constraint is transformed into a state space representation the reconstruction of elasticity can be accomplished through one filtering identification process, which is to recursively estimate the material properties and kinematic functions from ultrasound data according to the minimum mean square error (MMSE) criteria. In the implementation of this model-based algorithm, the linear isotropic elasticity is adopted as the biomechanical constraint. The estimation of kinematic functions (i.e., the full displacement and velocity field), and the distribution of Young’s modulus are computed simultaneously through an extended Kalman filter (EKF).

Results

In the following experiments the accuracy and robustness of this filtering framework is first evaluated on synthetic data in controlled conditions, and the performance of this framework is then evaluated in the real data collected from elastography phantom and patients using the ultrasound system. Quantitative analysis verifies that strain fields estimated by our filtering strategy are more closer to the ground truth. The distribution of Young’s modulus is also well estimated. Further, the effects of measurement noise and process noise have been investigated as well.

Conclusions

The advantage of this model-based algorithm over the conventional strain-based algorithm is its potential of providing the distribution of elasticity under a proper biomechanical model constraint. We address the model-data discrepancy and measurement noise by introducing process noise and measurement noise in our framework, and then the absolute values of Young’s modulus are estimated through the EFK in the MMSE sense. However, the initial conditions, and the mesh strategy will affect the performance, i.e., the convergence rate, and computational cost, etc.

The ultrasound elastography inverse problem and the effective criteria

The elastography (elasticity imaging) is one of the recent state-of-the-art methods for diagnosis of abnormalities in soft tissue. The idea is based on the computation of the tissue elasticity distribution. This leads to the inverse elasticity problem; in that, displacement field and boundary conditions are known, and elasticity distribution of the tissue is aimed for computation. We treat this problem by the Gauss-Newton method. This iterative method results in an ill-posed problem, and therefore, regularization schemes are required to deal with this issue. The impacts of the initial guess for tissue elasticity distribution, contrast ratio between elastic modulus of tumor and normal tissue, and noise level of the input data on the estimated solutions are investigated via two different regularization methods. The numerical results show that the accuracy and speed of convergence vary when different regularization methods are applied. Also, the semi-convergence behavior has been observed and discussed. At the end, we signify the necessity of a clever initial guess and intelligent stopping criteria for the iterations. The main purpose here is to highlight some technical factors that have an influence on elasticity image quality and diagnostic accuracy, and we have tried our best to make this article accessible for a broad audience.

The intravascular ultrasound elasticity-palpography technique revisited: a reliable tool for the in vivo detection of vulnerable coronary atherosclerotic plaques

Critical to the detection of vulnerable plaques (VPs) is quantification of their mechanical properties. On the basis of intravascular ultrasound (IVUS) echograms and strain images, E. I. Céspedes, C. L. de Korte CL and A. F. van der Steen (Ultrasound Med Biol 2000;26:385-396) proposed an elasticity-palpography technique (E-PT) to estimate the apparent stress-strain modulus palpogram of the thick endoluminal layer of the arterial wall. However, this approach suffers from major limitations because it was developed for homogeneous, circular and concentric VPs. The present study was therefore designed to improve the E-PT by considering the anatomic shape of the VP. This improved E-PT was successfully applied to six coronary lesions of patients imaged in vivo with IVUS. Our results indicate that the mean relative error of the stress-strain modulus decreased from 61.02 ± 9.01% to 15.12 ± 12.57% when the IE-PT was used instead of the E-PT. The accuracy of the stress-strain modulus palpograms computed using the improved theoretical framework was also investigated with respect to noise, which may affect prediction of plaque vulnerability.

MREJ: MRE elasticity reconstruction on ImageJ

Magnetic resonance elastography (MRE) is a promising method for health evaluation and disease diagnosis. It makes use of elastic waves as a virtual probe to quantify soft tissue elasticity. The wave actuator, imaging modality and elasticity interpreter are all essential components for an MRE system. Efforts have been made to develop more effective actuating mechanisms, imaging protocols and reconstructing algorithms. However, translating MRE wave images into soft tissue elasticity is a nontrivial issue for health professionals. This study contributes an open-source platform - MREJ - for MRE image processing and elasticity reconstruction. It is established on the widespread image-processing program ImageJ. Two algorithms for elasticity reconstruction were implemented with spatiotemporal directional filtering. The usability of the method is shown through virtual palpation on different phantoms and patients. Based on the results, we conclude that MREJ offers the MRE community a convenient and well-functioning program for image processing and elasticity interpretation.

Incorporating endorectal MR elastography into multi-parametric MRI for prostate cancer imaging: Initial feasibility in volunteers

PURPOSE

To investigate the tolerability and technical feasibility of performing endorectal MR elastography (eMRE) in human volunteers within the representative age group commonly affected by prostate cancer.

MATERIALS AND METHODS

Endorectal MRE was conducted on seven volunteers in a 1.5 Tesla (T) MR imager using a rigid endorectal coil. Another five volunteers were imaged on a 3T MR imager using an inflatable balloon type endorectal coil. Tolerability was accessed for vibration amplitudes of ±1-50 μm and for frequencies of 100-300 Hz.

RESULTS

All 12 volunteers tolerated the displacements necessary to successfully perform eMRE. Shear waves with frequencies up to 300 Hz could propagate across the entire prostate using both coil designs.

CONCLUSION

The results of this study motivate further investigation of eMRE in prostate cancer patients to help determine if there is an added value of integrating eMRE into existing multi-parametric prostate MRI exams.

US elastography-derived shear wave velocity helps distinguish acutely inflamed from fibrotic bowel in a Crohn disease animal model

PURPOSE

To determine if acoustic radiation force impulse elastography-derived bowel wall shear wave velocity (SWV) allows distinction of acutely inflamed from fibrotic intestine in a Crohn disease animal model.

MATERIALS AND METHODS

University Committee on the Use and Care of Animals approval was obtained. An acute inflammation Crohn disease model was produced by treating eight Lewis rats with a single administration of trinitrobenzenesulfonic acid (TNBS) enema, with imaging performed 2 days later in the surviving six rats. Colonic fibrosis in an additional eight Lewis rats was achieved by administering repeated TNBS enemas during 4 weeks, with imaging performed in the surviving seven rats 7 days later to allow acute inflammation resolution. Nine transcutaneous bowel wall SWV measurements were obtained from the colon in all rats without and with applied strain. Mean SWVs without and with applied strain were compared between animal cohorts by using the Student t test, and receiver operating characteristic (ROC) curves were created to assess diagnostic performance.

RESULTS

Mean bowel wall SWVs were significantly higher for fibrotic versus acute inflammation cohort of rats at 0% (3.4 ± 1.1 vs 2.3 ± 0.5 m/sec; P = .047) and 30% (6.3 ± 2.2 vs 3.6 ± 0.9 m/sec; P = .02) applied strain. Both acute inflammation and fibrotic cohort of rats demonstrated linear increases in mean SWV with increasing applied strain, with significantly different mean slopes (P = .02) and y-intercepts (P = .02). The area under the ROC curve of the SWV ratio (mean SWV/applied strain) for differentiating histopathologically confirmed fibrotic from inflamed bowel was 0.971.

CONCLUSION

Bowel wall SWV helps distinguish acutely inflamed from fibrotic intestine in a Crohn disease animal model.

Noninvasive vascular elastography using plane-wave and sparse-array imaging

Stroke may occur when an atherosclerotic plaque ruptures in the carotid artery. Noninvasive vascular elastography (NIVE) visualizes the strain distribution within the carotid artery, which is related to its mechanical properties that govern plaque rupture. Strain elastograms obtained from the transverse plane of the carotid artery are difficult to interpret, because strain is estimated in Cartesian coordinates. Sparsearray (SA) elastography overcomes this problem by transforming shear and normal strain to polar coordinates. However, the SA's transmit power may be too weak to produce useful elastograms in the clinical setting. Consequently, we are exploring other imaging methods to solve this potential problem. This study evaluated the quality of elastograms produced with SA imaging, plane-wave (PW) imaging, and compounded-plane-wave (CPW) imaging. We performed studies on simulated and physical vessel phantoms, and the carotid artery of a healthy volunteer. All echo imaging was performed with a linear transducer array that contained 128 elements, operating at 5 MHz. In SA imaging, 7 elements were fired during transmission, but all 128 elements were active during reception. In PW imaging, all 128 elements were active during both transmission and reception. We created CPW images by steering the acoustic beam within the range of -15° to 15° in increments of 5°. SA radial and circumferential strain elastograms were comparable to those produced using PW and CPW imaging. Additionally, side-lobe levels incurred during SA imaging were 20 dB lower than those produced during PW imaging, and 10 dB lower than those computed using CPW imaging. Overall, SA imaging performs well in vivo; therefore, we plan to improve the technique and perform preclinical studies.

A four-criterion selection procedure for atherosclerotic plaque elasticity reconstruction based on in vivo coronary intravascular ultrasound radial strain sequences

Plaque elasticity (i.e., modulogram) and morphology are good predictors of plaque vulnerability. Recently, our group developed an intravascular ultrasound (IVUS) elasticity reconstruction method which was successfully implemented in vitro using vessel phantoms. In vivo IVUS modulography, however, remains a major challenge as the motion of the heart prevents accurate strain field estimation. We therefore designed a technique to extract accurate strain fields and modulograms from recorded IVUS sequences. We identified a set of four criteria based on tissue overlapping, RF-correlation coefficient between two successive frames, performance of the elasticity reconstruction method to recover the measured radial strain, and reproducibility of the computed modulograms over the cardiac cycle. This four-criterion selection procedure (4-CSP) was successfully tested on IVUS sequences obtained in twelve patients referred for a directional coronary atherectomy intervention. This study demonstrates the potential of the IVUS modulography technique based on the proposed 4-CSP to detect vulnerable plaques in vivo.

In vivo measurement of volumetric strain in the human brain induced by arterial pulsation and harmonic waves

Motion-sensitive phase contrast magnetic resonance imaging and magnetic resonance elastography are applied for the measurement of volumetric strain and tissue compressibility in human brain. Volumetric strain calculated by the divergence operator using a biphasic effective-medium model is related to dilatation and compression of fluid spaces during harmonic stimulation of the head or during intracranial passage of the arterial pulse wave. In six volunteers, phase contrast magnetic resonance imaging showed that the central cerebrum expands at arterial pulse wave to strain values of (2.8 ± 1.9)·10(-4). The evolution of volumetric strain agrees well with the magnitude of the harmonic divergence measured in eight volunteers by magnetic resonance elastography using external activation of 25 Hz vibration frequency. Intracranial volumetric strain was proven sensitive to venous pressure altered by abdominal muscle contraction. In eight volunteers, an increase in volumetric strain due to abdominal muscle contraction of approximately 45% was observed (P = 0.0001). The corresponding compression modulus in the range of 9.5-13.5 kPa demonstrated that the compressibility of brain tissue at 25 Hz stimulation is much higher than that of water. This pilot study provides the background for compression-sensitive magnetic resonance imaging with or without external head stimulation. Volumetric strain may be sensitive to fluid flow abnormalities or pressure imbalances between vasculature and parenchyma as seen in hydrocephalus.