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Elasticity reconstruction from experimental MR displacement data: Initial experience with an overlapping subzone finite element inversion process
Abstract
The determination of the elastic property distribution in heterogeneous gel samples with a finite element based reconstruction scheme is considered. The algorithm operates on small overlapping subzones of the total field to allow for a high degree of spatial discretization while maintaining computational tractability. By including a Maxwellian-type viscoelastic property in the model physics and optimizing the spatial distribution of this property in the same manner as elasticity, a Young's modulus image is obtained which reasonably reflects the true distribution within the gel. However, the image lacks the clarity and accuracy expected based on simulation experience. Preliminary investigations suggest that transient effects in the data are the cause of a significant mismatch between the inversion model, which assumes steady-state conditions, and the actual displacements as measured by a phase contrast MR technique.
... As of yet, no direct correlation has been found between mechanical property contrast and a molecular contrast immediately discernible through standard MR imaging sequences. This necessitates the development of indirect imaging processes, most commonly algorithms which operate on the displacement or strain images that can be detected directly through MR phenomenon (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). The reconstructive nature of these methods renders them sensitive to the accuracy with which they can account for behavior observed in the imaged data; that is, the final elastographic image produced by such indirect imaging algorithms can only be as good as the fundamental assumptions which underlie the reconstruction approach. ...
... Regardless of the way in which Eq. [1] is incorporated into the inversion process, it is, by nature, a 3D relationship that can only be simplified to two dimensions under special circumstances. It has been found previously (14) that the data-model match between the assumed medium behavior and the true physics of the material in question is critical to the performance of nonlinear optimizationbased inversion schemes. It is easy to imagine, therefore, that inaccuracies in the assumption of 2D behavior in the imaging region for MRE could represent a significant compromise in the quality of the reconstructed property image. ...
... To implement this formulation discretely, the Young's modulus distribution is described on the same basis set as the dis-placement variables, so that E ϭ k E k k . The derivative terms, ץu/ץE k , required for solution in this manner can then be generated from the formulation of the discrete forward calculation, Eq. [7], so that: [14] where ץA/ץE k has terms ␣ץ ij /ץE k , corresponding to ␣ ij in Eq. [9]. ...
Accurate characterization of harmonic tissue motion for realistic tissue geometries and property distributions requires knowledge of the full three-dimensional displacement field because of the asymmetric nature of both the boundaries of the tissue domain and the location of internal mechanical heterogeneities. The implications of this for magnetic resonance elastography (MRE) are twofold. First, for MRE methods which require the measurement of a harmonic displacement field within the tissue region of interest, the presence of 3D motion effects reduces or eliminates the possibility that simpler, lower-dimensional motion field images will capture the true dynamics of the entire stimulated tissue. Second, MRE techniques that exploit model-based elastic property reconstruction methods will not be able to accurately match the observed displacements unless they are capable of accounting for 3D motion effects. These two factors are of key importance for MRE techniques based on linear elasticity models to reconstruct mechanical tissue property distributions in biological samples. This article demonstrates that 3D motion effects are present even in regular, symmetric phantom geometries and presents the development of a 3D reconstruction algorithm capable of discerning elastic property distributions in the presence of such effects. The algorithm allows for the accurate determination of tissue mechanical properties at resolutions equal to that of the MR displacement image in complex, asymmetric biological tissue geometries. Simulation studies in a realistic 3D breast geometry indicate that the process can accurately detect 1-cm diameter hard inclusions with 2.5× elasticity contrast to the surrounding tissue. Magn Reson Med 45:827–837, 2001. © 2001 Wiley-Liss, Inc.
... [12][13][14] The development of numerical models is also useful for the reconstruction process of the mechanical properties in MRE, for instance by identification process. [15][16][17][18][19][20][21] Because of the viscoelastic nature of soft tissues, both the elasticity and the viscosity play a major role in the shear wave properties. 22 It is therefore essential to properly implement the influence of viscosity and heterogeneity of the medium in such numerical tools. ...
... The identification of models is a powerful method to extract the mechanical properties in MRE but needs accurate forward simulations with relatively low computation costs. [15][16][17][18][19][20][21] As it offers the possibility to identify the mechanical property distribution from an experimental wave field, the proposed 2D-FEM is a perfect candidate for the robust mapping of the mechanical properties in MRE. ...
Dynamic elastography is a virtual palpation tool that aims at investigating the
mechanical response of biological soft tissues in vivo. The objective of this study
is to develop a finite element model (FEM) with low computational cost for
reproducing realistically wave propagation for magnetic resonance elastography
in heterogeneous soft tissues. Based on the first‐order shear deformation theory
for moderately thick structures, this model is developed and validated through
comparison with analytical formulations of wave propagating in heterogeneous,
viscoelastic infinite medium. This 2D‐FEM is then compared to experimental
data and a 3D‐FEM using a commercial software. Our FEM is a powerful
promising tool for investigations of magnetic resonance elastography.
KEYWORDS
finite element model, heterogeneity, magnetic resonance elastography, shear deformation theory,
shear wave propagation, viscoelasticity
... [12][13][14] The development of numerical models is also useful for the reconstruction process of the mechanical properties in MRE, for instance by identification process. [15][16][17][18][19][20][21] Because of the viscoelastic nature of soft tissues, both the elasticity and the viscosity play a major role in the shear wave properties. 22 It is therefore essential to properly implement the influence of viscosity and heterogeneity of the medium in such numerical tools. ...
... The identification of models is a powerful method to extract the mechanical properties in MRE but needs accurate forward simulations with relatively low computation costs. [15][16][17][18][19][20][21] As it offers the possibility to identify the mechanical property distribution from an experimental wave field, the proposed 2D-FEM is a perfect candidate for the robust mapping of the mechanical properties in MRE. ...
... In this paper, we develop and implement a generalized adjoint method based on a Lagrangian that no longer requires the stiffness matrix to be self-adjoint, but reverts back to the classic adjoint scheme when the stiffness matrix is selfadjoint. We present the details of implementation via the finite element method in a common mathematical framework for three widely used mechanical models in MRE: compressible viscoelasticity [42], [34], incompressible viscoelasticity [32], [43] and poroelasticity [44], [45]. Numerical experiments with data from simulations, tissue mimicking phantoms and in vivo brain data show that the generalized adjoint algorithm preserves efficiency of the gradient calculation. ...
... In order to implement (20), an upper bound on λ needs to be imposed for numerical stability. Previous studies [42], [34] have shown that both viscoelastic approaches are able to recover accurate shear moduli provided the longitudinal wave is modeled accurately. ...
We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradientand Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.
... The literature on the theoretical physics of elasticity imaging is quite limited but a comprehensive analysis of the problem of reconstruction of 3D elastic modulus distribution is given in the book by A.R. Skovoroda [83]. This problem was analyzed by several authors [51,[84][85][86][87][88][89][90][91][92][93][94][95][96], however, in the following discussion we will closely follow the logic and concepts developed by Skovoroda. ...
... Elastic modulus reconstruction in an inhomogeneous material can be posed in a number of ways [51,[83][84][85][86][87][88][89][90][91][92][93][94][95][100][101][102]. These approaches can be generally grouped into two categories: direct and indirect (model-based) reconstruction techniques. ...
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, 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 ul-trasound 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 ultra-sound 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.
... The method used in the reconstruction algorithm involves an optimization approach that is more robust to measurement noise. [14,15]. Here, the equivalent optimization problem was solved using Conjugate Gradient (CG) optimization methods based on an adjoint residual calculation. ...
... This approach generates a high degree of spatial discretization and, utilizes the data-rich environment obtained from MRI. The image reconstructions show that the zoned inversion strategy is capable of producing accurate elasticity modulus distribution images from displacement data obtained from MR even in the presence of high noise [14,15,24,25]. ...
Magnetic resonance elastography (MRE) is a recent development in magnetic resonance imaging techniques which provides a method of imaging with contrast related to mechanical tissue properties. This paper discusses one artifact due to the geometry of the actuator for tissue mimicking phantoms. The elimination of artifacts in cancer imaging systems is essential to limiting chances of the misrepresentation of cancerous cells or normal tissue. One potential reason for artifact producing in MRE imaging can be due to constraints applied by actuation systems. Two experiments have been carried out to demonstrate the possibility of creating artifacts due to actuator geometry which can cause the erroneous data. Two different types of actuation approaches that are being used for the breast cancer and phantom imaging in MRE are evaluated. The reconstruction results obtained from simulation and real MR data sets for these two types of actuators are also compared. Copyright© (2010) by the International Society for Research in Science and Technology.
... The literature on the theoretical physics of elasticity imaging is quite limited but a comprehensive analysis of the problem of reconstruction of 3D elastic modulus distribution is given in the book by A.R. Skovoroda [83]. This problem was analyzed by several authors [51,[84][85][86][87][88][89][90][91][92][93][94][95][96], however, in the following discussion we will closely follow the logic and concepts developed by Skovoroda. ...
... Elastic modulus reconstruction in an inhomogeneous material can be posed in a number of ways [51,[83][84][85][86][87][88][89][90][91][92][93][94][95][100][101][102]. These approaches can be generally grouped into two categories: direct and indirect (model-based) reconstruction techniques. ...
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, 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 ul-trasound 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 ultra-sound 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.
... The method used in the reconstruction algorithm involves an optimization approach that is more robust to measurement noise. [14,15]. Here, the equivalent optimization problem was solved using Conjugate Gradient (CG) optimization methods based on an adjoint residual calculation. ...
... This approach generates a high degree of spatial discretization and, utilizes the data-rich environment obtained from MRI. The image reconstructions show that the zoned inversion strategy is capable of producing accurate elasticity modulus distribution images from displacement data obtained from MR even in the presence of high noise [14,15,24,25]. ...
Magnetic resonance Elastography (MRE) is a recent development in magnetic resonance imaging techniques which provides a method of imaging with contrast related to mechanical tissue properties. This paper discusses one artifact due to the geometry of the actuator for tissue mimicking phantoms. The elimination of artifacts in cancer imaging systems is essential to limiting chances of the misrepresentation of cancerous cells or normal tissue. One potential reason for artifact producing in MRE imaging can be due to constrains applied by actuation systems. Two experiments have been carried out to demonstrate the possibility of creating artifacts due to actuator geometry which can cause the erroneous data. Two different types of actuation approaches that are being used for the breast cancer and phantom imaging in MRE are evaluated. The reconstruction results obtained from simulation and real MR data sets for these two types of actuators are also compared.
... The literature on the theoreti- cal physics of elasticity imaging is quite limited but a com- prehensive analysis of the problem of reconstruction of 3D elastic modulus distribution is given in the book by A.R. Skovoroda [83]. This problem was analyzed by several authors [51,[84][85][86][87][88][89][90][91][92][93][94][95][96], however, in the following discussion we will closely follow the logic and concepts developed by Skovoroda. ...
... Elastic modulus reconstruction in an inhomogeneous ma- terial can be posed in a number of ways [51,[83][84][85][86][87][88][89][90][91][92][93][94][95][100][101][102]. These approaches can be generally grouped into two categories: direct and indirect (model-based) reconstruction techniques. ...
Radiation force is a universal phenomenon in any wave motion, electromagnetic or acoustic. Radiation force is produced by a change in the density of energy of the propagating wave. The concept of radiation pressure follows from Maxwell?s equations (1871), while the idea of electromagnetic wave (light) pressure can be traced back to Johannes Kepler (1619). Acoustic radiation force was first experimentally demonstrated by August Kundt (1874) and its physical bases were analyzed in classical works of Lord Rayleigh (1902), L. Brillouin, and P. Langevin. Until recently, main biomedical application of acoustic radiation force was in measuring acoustic power of therapeutic devices, but during the last 15 years it became one of the hottest areas of biomedical ultrasonics with numerous new applications ranging from acoustical tweezers, targeted drug and gene delivery, manipulating of cells in suspension, increasing the sensitivity of biosensors and immunochemical tests, assessing viscoelastic properties of fluids and biological tissue, and monitoring lesions during therapy. The widest new area of applications of radiation force is related to medical imaging in general and elasticity imaging specifically. Remote excitation of shear stress in a given site in the body using radiation force of focused ultrasound offers numerous new possibilities for medical diagnostics.
... If, for example, the measured displacements are used, then the measured displacements on the boundary are treated as exact, while the interior measured displacements are not (a best fit to these is all that is required), and so the measured boundary displacements are overweighted. Kallel et al. [15] and Oberai et al. [16] applied their iterative inversion methods to quasi-static compression elastography and Van Houten et al. [17][18][19][20] and Fu et al. [21] to time harmonic elastography using MRI and ultrasound, respectively. All of these iterative inversion methods use a finite element-based algorithm. ...
... A space-time regularization procedure is applied to stabilize the hydrostatic stress by weakly penalizing the L 2 norms of both the magnitude and the gradients of the hydrostatic stress field. We solve for the best shear modulus and hydrostatic stress fields fitting Equation (18) in a least squares sense subject to the regularization on the hydrostatic stress by minimizing ...
In order to image the shear modulus in soft tissue, for medical diagnosis, given one component of measured displacements as a function of time on an imaging plane, two related direct finite element-based inversion algorithms are presented. One algorithm is based on the governing equations expressed in the frequency domain, and the other is in the time domain. The algorithms consider the complete equations of isotropic, small deformation, elasto-dynamics, where the hydrostatic stress is also treated as an unknown. The algorithms reconstruct both the shear modulus and hydrostatic stress fields, and regularization is used to stabilize the hydrostatic stress recovery. An algorithm is also developed for reconstructing the second displacement component, while simultaneous finding a smooth approximation to the measured displacement component to reduce noise. Shear modulus reconstruction results from both algorithms, using experimental ultrasound measurements on a tissue-mimicking phantom, are presented, and the merits and drawbacks of each algorithm are discussed.
... NLI is an iterative technique that minimizes an objective function which compares a heterogeneous nearly incompressible viscoelastic computational model with the measured displacement data of tissue under external harmonic excitation (Van Houten et al 1999, Van Houten et al 2000, McGarry et al 2012. NLI inversions reported here applied the same parameters commonly used for in vivo brain imaging (Schwarb et al 2019, McIlvain et al 2020, Delgorio et al 2021. ...
Objective:
Magnetic resonance elastography (MRE) of the brain has shown promise as a sensitive neuroimaging biomarker for neurodegenerative disorders; however, the accuracy of performing MRE of the cerebral cortex warrants investigation due to the unique challenges of studying thinner and more complex geometries.
Approach:
A series of realistic, whole-brain simulation experiments are performed to examine the accuracy of MRE to measure the viscoelasticity (shear stiffness, μ, and damping ratio, ξ) of cortical structures predominantly effected in aging and neurodegeneration. Variations to MRE spatial resolution and the regularization of a nonlinear inversion (NLI) approach are examined.
Main results:
Higher-resolution MRE displacement data (1.25 mm isotropic resolution) and NLI with a low soft prior regularization weighting provided minimal measurement error compared to other studied protocols. With the optimized protocol, an average error in μ and ξ was 3% and 11%, respectively, when compared with the prescribed ground truth. Mid-line structures, as opposed to those on the cortical surface, generally display greater error. Varying model boundary conditions and reducing the thickness of the cortex by up to 0.67 mm (which is a realistic portrayal of neurodegenerative pathology) results in no loss in reconstruction accuracy.
Significance:
These experiments establish quantitative guidelines for the accuracy expected of in vivo MRE of the cortex, with the proposed method providing valid MRE measures for future investigations into cortical viscoelasticity and relationships with health, cognition, and behavior.
... Van Houten et al (cf. [7,[36][37][38][39]) also present a finite element based Newton -Raphson iterative scheme to find the elastic moduli λ and µ by solving a similar optimization problem. In their works, a clever domain decomposition approach, termed subzoning which is similar to our technique called localization, is used which reduces the computational costs tremendously. ...
This paper deals with an inverse problem for recovering the viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a viscoelastic partial differential equation whose solution can approximately simulate MRE data, the inverse problem is transformed to a least square variational problem. This is to search for viscoelastic coefficients of this equation such that the solution to a boundary value problem of this equation fits approximately to MRE data with respect to the least square cost function. By computing the Gateaux derivatives of the cost function, we minimize the cost function by the projected gradient method is proposed for recovering the unknown coefficients. The reconstruction results based on simulated data and real experimental data are presented and discussed.
... Retrieved mechanical parameter distributions, corresponding to each subzone distribution, are finally averaged to form the final solution. This reconstruction method has been applied to phantoms, brain [176,203,264,265] and breast [266,267] data, and has proven its capacity to reconstruct multiple variables at various actuation frequencies using elastic and viscoelastic physical models (compressible elastic [268], compressible viscoelastic [269], and nearly incompressible viscoelastic [176, 184, 203, 231, 264-266, 268, 270-272]). Additionally, poroelastic models have been introduced for accurate consideration of the biphasic nature of entangled solid-liquid structures in biological tissues [168,184,211,270,271,273]). ...
Changes in biomechanical properties of biological soft tissues are often associated with physiological dysfunctions. Since biological soft tissues are hydrated, viscoelasticity is likely suitable to represent its solid-like behavior using elasticity and fluid-like behavior using viscosity. Shear wave elastography is a non-invasive imaging technology invented for clinical applications that has shown promise to characterize various tissue viscoelasticity. It is based on measuring and analyzing velocities and attenuations of propagated shear waves. In this review, principles and technical developments of shear wave elastography for viscoelasticity characterization from organ to cellular levels are presented, and different imaging modalities used to track shear wave propagation are described. At a macroscopic scale, techniques for inducing shear waves using an external mechanical vibration, an acoustic radiation pressure or a Lorentz force are reviewed along with imaging approaches proposed to track shear wave propagation, namely ultrasound, magnetic resonance, optical, and photoacoustic means. Then, approaches for theoretical modeling and tracking of shear waves are detailed. Following it, some examples of applications to characterize the viscoelasticity of various organs are given. At a microscopic scale, a novel cellular shear wave elastography method using an external vibration and optical microscopy is illustrated. Finally, current limitations and future directions in shear wave elastography are presented.
... ρ was constant and assumed to be 1000 kg m −3 . A stabilized incompressible finite element formulation was used to allow very high values of λ to be used without numerical issues (Van Houten et al 2000). λ = 161 kPa was prescribed corresponding to a Poisson ratio of 0.49. ...
Intrinsic activation MR elastography (IA-MRE) is a novel technique which seeks to estimate brain mechanical properties non-invasively and without external mechanical drivers. The method eliminates actuation hardware and patient discomfort while capitalizing on the brain's intrinsic low frequency motion. This study explores low frequency actuation (1 Hz) MR elastography in phantoms and analyzes performance of non-linear inversion (NLI) of viscoelastic and poroelastic mechanical models as a framework for assessing clinical results from IA-MRE. We present results from four gelatin phantoms and report stiffness resolution of 6 mm (two measurement voxels) with a stiffness contrast ratio of 4.21 relative to the background and 9 mm (three measurement voxels) with a lower stiffness contrast ratio of near 1.77. Stiffness edge resolution was also evaluated using edge spread and line spread functions and yielded a stiffness edge response distance of 9 mm. The intraclass correlation coefficient was high (0.93) between mechanical testing and poroelastic estimates, although quantitative agreement was affected by model-data mismatch. Viscoelastic MRE at low frequencies has issues with non-uniqueness due to small inertial forces, and performed worse than poroelastic MRE in terms of inclusion detection and consistency with mechanical testing. These results present the first evaluation of MR elastography using displacement measurements from an actuation frequency less than 5 Hz and support the validity of brain IA-MRE to recover spatially resolved stiffness changes. They provide a baseline of performance in terms of standard metrics for future animal and human brain stiffness studies and analyses based on intrinsic motion.
... Estimating accurate and relevant mechanical properties, an inverse problem, is a large obstacle in MRE and an active area of research. [21,22,16,5,19,1] Inversion algorithms vary by their underlying mechanical assumptions, actuation frequency, complexity of numerical estimation, and computational time. Applications of machine learning in the field of MRE is appealing because it removes many constraints of the inversion algorithm such as an initial guess of estimated properties, spatial filtering, partial volume effects, actuation frequency limitations on mechanical models, and model data mismatch for different tissues. ...
Traditionally, nonlinear inversion, direct inversion, or wave estimation methods have been used for reconstructing images from MRE displacement data. In this work, we propose a convolutional neural network architecture that can map MRE displacement data directly into elastograms, circumventing the costly and computationally intensive classical approaches. In addition to the mean squared error reconstruction objective, we also introduce a secondary loss inspired by the MRE mechanical models for training the neural network. Our network is demonstrated to be effective for generating MRE images that compare well with equivalents from the nonlinear inversion method.
... These types of models have been analysed in literature (Liu and Bilston 2000, Bilston et al. 2001, Banks et al. 2011), but have shortcomings in predicting creep (Maxwell model) or stress relaxation (Kelvin-Voigt model) (Liu et al. 2006, Banks et al. 2011. While the Maxwell constitutive equation was found to be better suited for modelling fluids (Houten et al. 2000;Sinkus et al. 2005a), the Kelvin-Voigt constitutive equation was employed for purposes similar to ours, modelling soft tissues subjected to elastography testing (Sinkus et al. 2005a, Huwart et al. 2006, Huwart et al. 2008) (albeit not considering the effects of large deformations on the wave behaviour). However, the Kelvin-Voigt model is not able to accurately capture the power-law dependence on frequency that is usually observed in tissues (Chui et al. 2004, Nicolle et al. 2010, Nicolle 2015. ...
Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.
... A value of ξ < 1 results in an oscillatory decay response to a step input, ξ = 1 is critical damping and ξ > 1 is known as overdamping (Cook et al 2007). NLI-MRE is an iterative technique that minimizes an objective function which compares the viscoelastic computational model in equation (1) with the measured displacement data of tissue under external harmonic excitation (Van Houten et al 1999, 2000, Van Houten et al 2001. The objective function, Φ, is given by: ...
This study evaluated non-linear inversion MRE (NLI-MRE) based on viscoelastic governing equations to determine its sensitivity to small, low contrast inclusions and interface changes in shear storage modulus and damping ratio. Reconstruction parameters identical to those used in recent in vivo MRE studies of mechanical property variations in small brain structures were applied. NLI-MRE was evaluated on four phantoms with contrast in stiffness and damping ratio. Image contrast to noise ratio was assessed as a function of inclusion diameter and property contrast, and edge and line spread functions were calculated as measures of imaging resolution. Phantoms were constructed from silicone, agar, and tofu materials. Reconstructed property estimates were compared with independent mechanical testing using dynamic mechanical analysis (DMA). The NLI-MRE technique detected inclusions as small as 8mm with a stiffness contrast as low as 14%. Storage modulus images also showed an interface edge response distance of 11mm. Damping ratio images distinguished inclusions with a diameter as small as 8mm, and yielded an interface edge response distance of 10mm. Property differences relative to DMA tests were in the 15%-20% range in most cases. In this study, NLI-MRE storage modulus estimates resolved the smallest inclusion with the lowest stiffness contrast, and spatial resolution of attenuation parameter images was quantified for the first time. These experiments and image quality metrics establish quantitative guidelines for the accuracy expected in vivo for MRE images of small brain structures, and provide a baseline for evaluating future improvements to the NLI-MRE pipeline.
... Given the size of the minimization problem in practical applications (10 4 -10 6 unknowns), computational load must be considered. An efficient algorithm has been developed, which divides the domain O into a set of overlapping subzones and seeks minimization on the individual subzones with appropriate boundary values prescribed on the zone surface [49,50,61]. The minimization Problem (7) becomes ...
A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.
... A number of studies on simulated objects and gel phantoms were dedicated to validating reconstruction procedures. Simulated phantoms were for instance used by Van Houten et al. [42][43][44] in order to assess the performance of a subzone-based FEM non-linear inversion algorithm. Heterogeneous objects consisting of a soft matrix containing several inclusions of various stiffness were simulated. ...
This thesis deals with two aspects of low field (0.2 T) Magnetic Resonance Imaging (MRI) : the research of new constrats due to the interaction between Nuclear Magnetic Resonance (NMR) and acoustics (elastography, spin-phonon interaction) and enhancement of the signal-to-noise ratio by Dynamic Nuclear Polarization (DNP). Magnetic Resonance Elastography (MRE) allows to assess some viscoelastic properties of tissues by visualization of the propagation of low frequency acoustic strain waves. A review on MRE is given, as well as a study on local measurement of the acoustic absorption coefficient. The next part is dedicated to MRI-ultrasound interaction. First, the ultrasonic transducer was calibrated for power and acoustic field using the comparison of two methods : the radiation force method (balance method) and laser interferometry. Then, we tried to modify the T1 contrast of tissues by spin-phonon interaction due to the application of ultrasound at the resonance frequency at 0.2 T, which is about 8.25 MHz. No modification of T1 contrast has been obtained, but the acoustic streaming phenomenon has been observed in liquids. MRI visualization of this streaming could make possible to calibrate transducers as well as to assess some mechanical properties of viscous fluids. The goal of the last part was to set up DNP experiments at 0.2 T in order to enhance the NMR signal. This double resonance method is based on the polarization transfer of unpaired electrons of free radicals to the surrounding protons of water. This transfer occurs by cross relaxation during the saturation of an electronic transition using Electronic Paramagnetic Resonance (EPR). Two EPR cavities operating at 5.43 GHz have been tested on oxo-TEMPO free radicals (nitroxide). An enhancement of the NMR signal by a factor 30 was obtained during these preliminary experiments.
... Poor quality datasets with low signal-to-noise ratio tend to provide unreliable tissue property estimates, with different biases depending on the inversion algorithms applied. While most studies use some form of direct numerical inversion, recent work is exploring the use of finite-element inversion techniques that have the potential to be more robust, e.g., Van Houten et al. 75 The term elastography is also often applied to qualitative elastography, typically using ultrasound, where relative stiffness of different tissue regions is estimated from the effect of static mechanical compression on local tissue deformation. 37 ...
The ability to measure and quantify the properties of skeletal muscle in vivo as a method for understanding its complex physiological and pathophysiological behavior is important in numerous clinical settings, including rehabilitation. However, this remains a challenge to date due to the lack of a "gold standard" technique. Instead, there are a myriad of measuring techniques each with its own set of pros and cons. This review discusses the current state-of-the-art in elastography imaging techniques, i.e., ultrasound and magnetic resonance elastography, as applied to skeletal muscle, and briefly reviews other methods of measuring muscle mechanical behavior in vivo. While in vivo muscle viscoelastic properties can be measured, these techniques are largely limited to static or quasistatic measurements. Emerging elastography techniques are able to quantify muscle anisotropy and large deformation effects on stiffness, but, validation and optimization of these newer techniques is required. The development of reliable values for the mechanical properties of muscle across the population using these techniques are required to enable them to become more useful in rehabilitation and other clinical settings.
... For the complete equations of elasto-dynamics with 2D or 3D displacement data, finite element based inverse methods have been proposed to image tissue elasticity by either an iterative optimization approach ( [21], [36], [59], [58], [85], [87], [89], [90]) or non-iterative solving [62]. The iterative methods avoid the computation of numerical derivatives from noisy measured data, which makes them very robust. ...
... Besides the Direct Inversion method and the Arrival Time method, other algorithms have also been developed. Some are based on finite element methods including iterative methods, [14], [45], [46], [47], [64] and [65], and non-iterative methods [51]. The finite element based iterative methods use the full elastic equation system as the basis for their algorithm, and the goal is to find the elastic modulus that minimizes the difference between the computed and measured displacements in a least squares sense. ...
... Magnetic Resonance Elastography (MRE) can directly visualise and measure tissue elasticity in vivo [23,24,5,25,26]. MRE acquisition requires application of mechanical waves to tissue within the MRI and sophisticated inverse problem methods to identify an elastic modulus map of the tissue. ...
... The assembled data are movies of the displacement components. This coupled process is called MR elastography; see [10,15,17,19,21,23,24,[29][30][31][32]. Biomechanical imaging functionals are calculated from these movie data. ...
In this paper, we establish sensitivity results that are relevant for imaging stiffness in tissue but may also be useful in other contexts. The data are the displacement at a single frequency throughout the imaging domain. The goal is to determine how the quantities—(1) amplitude of displacement, or alternatively (2) the displacement itself, the average displacement, the phase or the phase gradient—change within a homogeneous stiff inclusion embedded within a homogeneous background. The results are easily interpreted formulas that show the dependence on the radius of the inclusion, the frequency and the stiffness contrast between the inclusion and the background. Our assumptions are: (1) the displacement satisfies the Helmholtz equation with the variable stiffness parameter; (2) the experiment produces a plane wave in the absence of any inclusions; (3) in 3D, the inclusion is spherical; (4) in 2D the inclusion is a circular disc; and alternatively in 3D the inclusion is an infinite circular cylinder. Our method of analysis is to use series expansions of the solution expanded about the center of the inclusion.
... This data can then be used to reconstruct images of electrical conductivity and permittivity which may be better pathologic indicators [1,2] . Other examples are near infrared tomography [3,4] , microwave tomography [5,6] and elastography [7][8][9][10][11][12][13][14][15] . These emerging methods of characterizing tissue have yet to be realized and questions regarding resolution, diagnostic value, and overall capability have yet to be fully reported. ...
Medicine today relies on palpation as a first line of investigation in
the detection and diagnosis of breast cancer. Tissue stiffness (e.g. a
lump found in breast tissue) can signal the growth of a potential life
threatening cell mass. As such, elastographic imaging techniques (i.e.
direct imaging of tissue stiffness) have recently become of great
interest to scientists. In this paper, a new method called Modality
Independent Elastography (MIE) will be investigated within the context
of a mammographic imaging alternative/complement. This new approach uses
measures of image similarity in conjunction with computational models to
reconstruct images of tissue stiffness. The real strength in MIE is that
any imaging modality (e.g. magnetic resonance, computed tomography,
ultrasound) in which the image intensity data remains consistent from a
pre- to a post-deformed state could be used in this paradigm. Results
illustrate: (1) the encoding of stiffness information within the context
of a regional image similarity criterion, (2) the methodology for an
iterative elastographic imaging framework and (3) successful elasticity
reconstructions.
... Furthermore, they invoke the locally constant assumption and recover the elastic parameter by simple algebraic inversion (see [2, 3, 9, 11, 14, 24–26, 29, 30, 32]). Finite element based methods have also been developed to handle the complete equations of elasto-dynamics with 3D displacement field by either an optimization approach (see35363738) or direct solving (see [27]). In this work, however, we develop finite difference based numerical methods to reconstruct the shear modulus from single component displacement data. ...
The goal of elastography is to image the shear stiffness of tissue for cancer diagnosis and the focus of this paper is on single frequency elastographic data. Assuming that the measured displacement of the propagating shear wave satisfies the acoustic wave equation, the shear modulus μ can be recovered by solving a first-order partial differential equation in the inverse problem. To capture possible exponential growth and decay of the targeted parameter μ numerically in a stable manner, we propose a log-elastographic nonlinear scheme and a linear finite difference based elliptic scheme. Both methods are shown to be convergent at first order and their performances are compared with the performances of a semi-implicit upwind scheme and the direct inversion model previously investigated (see [23]). We present shear modulus reconstructions from synthetic data with and without noise.
The white matter tracts of brain tissue consist of highly-aligned, myelinated fibers; white matter is structurally anisotropic and is expected to exhibit anisotropic mechanical behavior. In vivo mechanical properties of tissue can be imaged using magnetic resonance elastography (MRE). MRE can detect and monitor natural and disease processes that affect tissue structure; however, most MRE inversion algorithms assume locally homogenous properties and/or isotropic behavior, which can cause artifacts in white matter regions. A heterogeneous, model-based transverse isotropic implementation of a subzone-based nonlinear inversion (TI-NLI) is demonstrated. TI-NLI reconstructs accurate maps of the shear modulus, damping ratio, shear anisotropy, and tensile anisotropy of in vivo brain tissue using standard MRE motion measurements and fiber directions estimated from diffusion tensor imaging (DTI). TI-NLI accuracy was investigated with using synthetic data in both controlled and realistic settings: excellent quantitative and spatial accuracy was observed and cross-talk between estimated parameters was minimal. Ten repeated, in vivo, MRE scans acquired from a healthy subject were co-registered to demonstrate repeatability of the technique. Good resolution of anatomical structures and bilateral symmetry were evident in MRE images of all mechanical property types. Repeatability was similar to isotropic MRE methods and well within the limits required for clinical success. TI-NLI MRE is a promising new technique for clinical research into anisotropic tissues such as the brain and muscle.
We performed functional intrinsic Magnetic Resonance Elastography (fiMRE) as well as Time of Flight angiography and BOLD fMRI on 7 healthy human subjects to monitor shear stiffness and arterial dilation during periods of prolonged visual stimulation. FiMRE activation with increased stiffness was observed to occur almost equally within brain white and gray matter (49.7±14.0% and 40.9±12.2%, respectively), while activation with decreased stiffness was significantly (p=0.018) more likely to occur in white matter than gray matter (50.8±11.4% and 37.0±4.5%, respectively). At the low mechanical activation and block design frequencies used in this intrinsic MRE (iMRE) approach, the aggregate stiffness change across the entire BOLD activation region was not significant. However, we observed significant reduction in shear stiffness (1.40 ± 0.15 to 0.68 ± 0.22 [kPa], p < 0.001) in areas adjacent to the Posterior Cerebral Artery, where vasodilation is evident, in the V1 region. In addition, we observed significant shear stiffness increase (1.29 ± 0.12 to 0.62 ± 0.16 [kPa], p < 0.001) in areas adjacent to the Middle Temporal or V5 region of the visual cortex. These results show that iMRE can measure intrinsic cerebro-mechanical reactions due to visual stimulation as well as the differential physiological response detected in distinct regions of the visual cortex.
In the present study we analyze the biomechanical properties of life-form parenchyma, derive the relationship between MR displacement-phase image and the elasticity of life-form parenchyma, thereby study the local frequency estimation(LFE) algorithm. Finally the algorithm is relized by Matlab, and the inversion results of phantom MRE image demonstrate the effectiveness of the LFE algorithm, which would form a basis for subsequent research on liver fibrosis classification .
Rationale and Objectives
Hydrocephalus (HC) is caused by accumulating cerebrospinal fluid resulting in enlarged ventricles and neurological symptoms. HC can be treated via a shunt in a subset of patients; identifying which individuals will respond through noninvasive imaging would avoid complications from unsuccessful treatments. This preliminary work is a longitudinal study applying MR Elastography (MRE) to HC patients with a focus on normal pressure hydrocephalus (NPH).
Materials and Methods
Twenty-two ventriculomegaly patients were imaged and subsequently received a lumbar drain placement for cerebrospinal fluid (CSF) drainage. NPH lumbar drain responders and NPH syndrome nonresponders were categorized by clinical presentation. Displacement images were acquired using intrinsic activation (IA) MRE and poroelastic inversion recovered shear stiffness and hydraulic conductivity values. A stable IA-MRE inversion protocol was developed to produce unique solutions for both recovered properties, independent of initial estimates.
Results
Property images showed significantly increased shear modulus (p = 0.003 in periventricular region, p = 0.005 in remaining cerebral tissue) and hydraulic conductivity (p = 0.04 in periventricular region) in ventriculomegaly patients compared to healthy volunteers. Baseline MRE imaging did not detect significant differences between NPH lumbar drain responders and NPH syndrome nonresponders; however, MRE time series analysis demonstrated consistent trends in average poroelastic shear modulus values over the course of the lumbar drain process in responders (initial increase, followed by a later decrease) which did not occur in nonresponders.
Conclusion
These findings are indicative of acute mechanical changes in the brain resulting from CSF drainage in NPH patients.
Mechanical‐wave stimulation/excitation is usually the key aspect that determines the quality of elasticity imaging. This chapter discusses the exogenous harmonic‐wave stimulation and its applications in estimating mechanical properties of elastic and viscoelastic media. It briefly summarizes the equations that describe local displacements associated with shear waves as a function of the spatially varying complex shear modulus. Cylindrical waves and surface waves are widely used to mechanically excite tissues. Wave speed in an elastic material is constant with frequency. In contrast, viscoelastic materials are dispersive; that is the wave speed changes substantially with frequency. Dispersive behavior is determined by the components of the materials and their mechanical couplings. In standard rheological models, these components are represented by springs and dash‐pots. Shear‐wave and surface‐wave imaging offer quantitative estimates of intrinsic viscoelastic properties of dispersive tissues. Coupling dispersion behavior with rheological models parameterizes measurements as needed for imaging.
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.
Magnetic resonance elastography (MRE) is a method for measuring the mechanical properties of soft tissue in vivo, non-invasively, by imaging propagating shear waves in the tissue. The speed and attenuation of waves depends on the elastic and dissipative properties of the underlying material. Tissue mechanical properties are essential for biomechanical models and simulations, and may serve as markers of disease, injury, development, or recovery. MRE is already established as a clinical technique for detecting and characterizing liver disease. The potential of MRE for diagnosing or characterizing disease in other organs, including brain, breast, and heart is an active research area. Studies involving MRE in the pre-clinical setting, in phantoms and artificial biomaterials, in the mouse, and in other mammals, are critical to the development of MRE as a robust, reliable, and useful modality.
In the present study we analyze the biomechanical properties of life-form parenchyma, derive the relationship between MR displacement-phase image and the elasticity of life-form parenchyma, thereby study the local frequency estimation(LFE) algorithm. Finally the algorithm is relized by Matlab, and the inversion results of phantom MRE image demonstrate the effectiveness of the LFE algorithm, which would form a basis for subsequent research on liver fibrosis classification.
Differences of elasticity in tissue phantoms with inclusions of different elasticity were mapped by means of MR elastography (MRE). This new magnetic resonance imaging technique is based on the phase shift of the MR signal by switching a motion sensitizing magnetic field gradient simultaneously with the coupling of a shear wave. Wave patterns showing snapshots of the shear wave that propagates through the investigated substance were depicted in tomographic phase images. It was investigated wether a visualization of differences in elasticity of soft tissues was possible on the basis of differences in the wavelength. For this purpose, tissue phantoms with cylindrical inclusions were produced from agar gels, with agar concentrations between 1.0 and 1.5 %. The diameters of the inclusions were of the order of a few centimetres. For diameters as small as 4 cm, there were still distinct differences in the wavelength between the matrix and the inclusion. The results of our study suggest that this technique has the potential for future application as an additional imaging method for tumor detection.
The biomechanical integrity of the human heart is critically important, with various diseases affecting the active or passive stiffness of the myocardium. Although manual palpation is an integral part of many diagnostic procedures and is of undisputed clinical value, its applicability is limited to superficial regions. Furthermore, it remains a qualitative not quantitative method. These limits, however, may be overcome with elastography, an exciting new imaging modality that enables noninvasive assessment of biomechanical properties deep inside the body. The general concept is based on the intertwined relationship between the local propagation properties of shear waves and the underlying, intrinsic mechanical shear parameters. Elasticity imaging already has demonstrated very promising results in breast cancer, liver fibrosis staging, and neurodegenerative diseases. However, its application to the cardiovascular system is rather novel, and its challenges include data acquisition and mechanical parameter reconstruction. This article discusses the requirements for performing quantitative elastography of the heart, as well as current developments and future perspectives.
Magnetic resonance elastography is a technique where mechanical properties of materials are estimated by fitting a mechanical model to an MRI-acquired displacement field. These models have been primarily limited to viscoelasticity and linear elasticity, and only recently has poroelasticity been utilized as an applied model. To validate these estimates, the same material is measured via an independent dynamic mechanical analysis device. However, these devices only apply analytic viscoelastic models. In some cases, there is a model mismatch if a viscoelastic mechanical analysis is being compared to a poroelastic model in elastography. Thus, a poroelastic dynamic mechanical analysis technique is needed to properly measure porous media and compare the results with the appropriate elastography technique. A finite element technique was implemented on a TA-Q800 Dynamic Mechanical Analysis machine similar to the algorithm used in the corresponding MR elastography method. A viscoelastic version of the finite element code was created to validate the theory and show results similar to those obtained by the analytic DMA solution. Also, differences were seen that can be attributed to inertial forces not accounted for by an analytical solution. A poroelastic algorithm was then applied, showing great promise in the ability to measure properties of porous tissues.
Die Magnetresonanzelastographie (MRE) stellt ein nichtinvasives Verfahren dar, welches die Bestimmung der in vivo Scherelastizität weicher Gewebe ermöglicht. Im Rahmen diese Arbeit wurden Methoden zur Bestimmung isotroper und anisotroper Scherelastizitäten anhand von MRE Wellenbildern entwickelt und evaluiert. Alle in dieser Arbeit vorgestellten Methoden basieren auf planarer MRE, d.h. auf der Aufnahme einer einzelnen Auslenkungskomponente innerhalb der Bildschicht. Dadurch wird die MRE erheblich beschleunigt. Allerdings stellen sich dadurch auch besondere Anforderungen an die Datenauswertung zur Bestimmung aussagekräftiger elastischer Kenngrößen. Anhand von planaren MRE-Experimenten an Gewebephantomen und menschlicher Skelettmuskulatur sowie mittels numerischer Simulation wird gezeigt, dass bei Beachtung weniger experimenteller Randbedingungen und einer darauf abgestimmten Datenauswertung, korrekte Elastizitäten ermittelt werden können. Ein besonderer Schwerpunkt der Arbeit liegt in der Analyse experimenteller Einflüsse wie Bildrauschen und -auflösung auf die ermittelten elastischen Kenngrößen. Des Weiteren werden Methoden zur Bestimmung anisotroper Elastizitäten sowie zur Analyse von Streueffekten im MRE-Wellenbild vorgestellt. Die behandelten Einflüsse auf die Amplituden und Wellenlängen im MRE-Bild, werden vergleichend diskutiert und zusammengefasst, um ein einfaches Verfahrensprotokoll zur Analyse experimenteller in vivo MRE-Daten zu entwickeln. Alle in dieser Arbeit verwendeten Methoden und Programme sind im Anhang zusammengefasst und auf Anforderung erhältlich.
Dispersive material properties provide valuable metrics for characterizing the nature of soft tissue lesions. Magnetic Resonance Elastography (MRE) targets non-invasive breast cancer diagnosis and is capable of imaging the damping properties of soft tissue. 3D time-harmonic displacement data obtained via MRI is used to drive a reconstruction algorithm capable of deducing the distribution of mechanical properties in the tissue. To make the most of this diagnostic capability, characterization of the damping behavior of tissue is made more sophisticated by the use of a Rayleigh damping model. To date, time-harmonic motion attenuation in tissue as found in dynamic MRE has been characterized by a single parameter model that takes the form of an imaginary component of a complex valued shear modulus. A more generalized damping formulation for the time-harmonic case, known commonly as Rayleigh or proportional damping, includes an additional parameter that takes the form of an imaginary component of a complex valued density. The effects of these two different damping mechanisms can be shown to be independent across homogeneous distributions and mischaracterization of the damping structure can be shown to lead to artifacts in the reconstructed attenuation profile. We have implemented a Rayleigh damping reconstruction method for MRE and measured the dispersive properties of actual patient data sets with impressive results. Reconstructions show a close match with varying tissue structure. The reconstructed values for real shear modulus and overall damping levels are in reasonable agreement with values established in the literature or measured by mechanical testing, and in the case of malignant lesions, show good correspondence with contrast enhanced MRI. There is significant medical potential for an algorithm that can accurately reconstruct soft tissue material properties through non invasive MRI scans. Imaging methods that help identify invasive regions through reconstruction of dispersive soft tissue properties could be applied to pathologies in the brain, lung, liver and kidney as well.
In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method (c-FEM) inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.
A nonlinear inversion scheme formulated on small subzones of the total region of interest (ROI) is developed. The algorithm reconstructs the distribution of a linear elastic stiffness term and a Maxwellian damping parameter over the entire ROI through a least squares optimization. The subzones are generated in a hierarchical manner based on progressive error minimization and processed in an automated, sweeping fashion until certain performance criterion are met. Simulation results show that the algorithm works well to minimize global error and is capable of simultaneously reconstructing both property parameter distributions even in the presence of random noise, although initial experience suggests that the elastic property image is superior to its attenuation coefficient counterpart.
A number of novel imaging modalities have been developed to interrogate the mechanical properties of tissue. A subset of these methods utilize acoustic radiation force to mechanically excite tissue and form images from the local responses of tissue to these excitations. These methods are attractive because of the ability to focus and steer the excitatory beams and to control their spatial and temporal characteristics using techniques similar to those employed in conventional ultrasonic imaging. These capabilities allow for a wide variety of imaging methods whose features are only beginning to be explored. However, radiation force based methods also present significant challenges. Tissue and transducer heating limit the tissue displacements achievable with radiation force applications and restrict image frame rates and fields-of-view. The small tissue displacements are difficult to detect and may be obscured by physiologic tissue motion. We review the fundamental limits of imaging methods based on radiation force generated by patient safety concerns and the impact of these limits on achievable image signal-to-noise ratios and frame rates. We also review our progress to date in the development and clinical evaluation of one class of radiation force imaging methods employing very brief impulses of radiation force.
A significant effort has been expended to measure the accuracy of the shear modulus estimates. Conversely, very little effort has been expended to establish the reproducibility of the method in a clinical context. Previously we established the reproducibility in phantoms to be 3% for repeated measurements without moving the phantom and 5% when the phantom was moved,however, the clinical reproducibility has not been demonstrated. The reproducibility of the method was estimated by scanning subjects' heels repeatedly on a GE 1.5T scanner using previously described methods. Three subjects were scanned three times on different days (termed non-consecutive) and three subjects were scanned three times in the same session without changing the position of the foot (termed consecutive). The average difference between mean values within the field of view for the non-consecutive group was 7.75% +/- 3.76% and for the consecutive group it was 5.30% +/- 4.16%. These values represent remarkably good reproducibility considering the 20% variation in shear modulus observed within individual heels and the several hundred percent changes observed between normal and pathologic tissues. The variation in repeated examinations was caused by four factors: positioning error between examinations accounted for 4.8%, computational noise 3.0%, and the combination of MR noise and patient motion during the examination, 5.3%. Each of these sources of variation can be reduced in relatively straightforward ways if necessary but the current level of reproducibility is sufficient for most current applications.
NMR characterization of biological tissues or materials (MR elastography) is a challenging and promising area of research. A review of ongoing progress in acoustic wave detection and characterization using NMR is given. After recalling some basic physical principles of acoustics (strain–stress relationship, viscoelasticity), NMR methods for shear or longitudinal wave detection are described, emphasizing pioneer works. Both spectroscopic and imaging methods are summarized, as well as a variety of procedures that allow reconstruction of (visco)elastic properties from NMR data. Emergent MR elastography (MRE) techniques were applied on inert materials for validation purposes. Relevant results were obtained on biological samples and in humans in vivo. The clinical use of MRE dedicated to virtual palpation is nowadays clearly envisaged. MR elastography is also compared to another developing approach, namely ultrasonic elastography which exhibits complementary advantages and drawbacks.
Gives a bibliographical review of the finite element methods (FEMs) applied in biomedicine from the theoretical as well as practical points of view. The bibliography at the end of the paper contains 748 references to papers, conference proceedings and theses/dissertations dealing with the finite element analyses and simulations in biomedicine that were published between 1985 and 1999.
Elasticity imaging is a novel domain which is currently gaining significant interest in the medical field. Most inversion techniques are based on the homogeneity assumption, i.e. the local spatial derivatives of the complex-shear modulus are ignored. This analysis presents an analytic approach in order to overcome this limitation, i.e. first order spatial derivatives of the real-part of the complex-shear modulus are taken into account. Resulting distributions in a gauged breast lesion phantom agree very well with the theoretical expectations. An in-vivo example of a cholangiocarcinoma demonstrates that the new approach provides maps of the viscoelastic properties which agree much better with expectations from anatomy.
Early diagnosis of breast cancer, which is critical for favorable clinical outcomes, is difficult because tumors and healthy tissue respond similarly to X rays and ultrasound. One physical property that clearly distinguishes healthy from cancerous tissue is mechanical stiffness or hardness. Researchers have attempted to combine external mechanical stimulation and Magnetic Resonance Imaging (MRI) to quantitatively measure the Young's modulus of tissue throughout both the breast and the prostate. This technique, Magnetic Resonance Elastography (MRE) has been called "palpation at a distance." One of the most challenging technical aspects of MRE is the efficient solution of the "inverse problem," i.e., quantitatively determining Young's modulus from MRI-measured tissue displacement data. Creare developed analytical techniques to improve the efficiency and robustness of the inverse problem solution. One technique, which utilizes an incompressible formulation of the tissue equations of motion, an adjoint method for calculating the gradient of the goodness-of-fit metric, and a quasi-Newton minimization algorithm, appears to provide a substantial improvement in efficiency over techniques used previously.
This paper considers an inverse problem of shear stiffness imaging in a linear isotropic two-dimensional acoustic media, where the targeted parameter is the shear modulus μ. For given single component displacement data, the mathematical model to recover the shear modulus appears to be a first-order partial differential equation while a much simpler algebraic model, called the direct inversion, can be derived by eliminating the first derivative terms of the shear modulus from the partial differential equation model. The objective of this paper is to establish a theoretical bound on the relative difference between the true value of the modulus and the approximated value reconstructed from the direct inversion. We exhibit a quantitative estimate of the relative error and present reconstruction examples by the direct inversion from simulated data. We demonstrate that the relative error of the numerical solution is well bounded by the theoretical error estimate.
A method has been developed for detecting and imaging the relative "stiffness," or elasticity of tissues. Externally applied vibration at low frequencies (10-1000 Hz) is used to induce oscillations within soft tissues, and the motion is detected by Doppler ultrasound. The results are displayed in a format resembling conventional Doppler color flow mapping, and are termed "sonoelasticity images." Preliminary experiments indicate that these novel images may be useful for detecting hard tumors in the prostate, liver, breast, and other organs.
Evaluation of internal displacement and strain distributions in tissue under externally applied forces is a necessary step in elasticity imaging. To obtain a quantitative image of the elastic modulus, strain and displacement fields must be measured with reasonable accuracy and inverted based on an accurate theoretical model of soft tissue mechanics. In this paper, results of measured internal strain and displacement fields from gel-based phantoms are compared with theoretical predictions of a linear elastic model. In addition, some aspects of elasticity reconstruction based on measured displacement and strain fields are discussed.< >
Sonoelasticity is a rapidly evolving medical imaging technique for visualizing hard tumors in tissues. In this novel diagnostic technique, a low‐frequency vibration is externally applied to excite internal vibrations within the tissue under inspection. A small stiff inhomogeneity in a surrounding tissue appears as a disturbance in the normal vibration eigenmode pattern. By employing a properly designed Doppler detection algorithm, a real‐time vibration image can be made. A theory for vibrations, or shear wave propagation in inhomogeneous tissue has been developed. A tumor is modeled as an elastic inhomogeneity inside a lossy homogeneous elastic medium. A vibration source is applied at a boundary. The solutions for the shear wave equation have been found both for the cases with tumor (inhomogeneous case) and without tumor (homogenous case). The solutions take into account varying parameters such as tumor size, tumor stiffness, shape of vibration source, lossy factor of the material, and vibration frequency. The problem of the lowest detectable change in stiffness is addressed using the theory, answering one of the most critical questions in this diagnostic technique. Some experiments were conducted to check the validity of the theory, and the results showed a good correspondence to the theoretical predictions. These studies provide basic understanding of the phenomena observed in the growing field of clinical Sonoelasticity imaging for tumor detection.
A newly developed magnetic resonance imaging technique can directly visualize propagating acoustic strain waves in tissue-like materials. By estimating the local wavelength of the acoustic wave pattern, quantitative values of shear modulus can be calculated and images generated that depict tissue elasticity or stiffness. Since tumors are significantly stiffer than normal tissue (the basis of their detection by palpation), this technique may have potential for 'palpation by imaging,' with possible application to the detection of tumors in breast, liver, kidney, and prostate. We describe the local wavelength estimation algorithm, study its properties, and show a variety of sample results.
In the magnetic resonance imaging (MRI) technique the local tissue characterization is accomplished by measurements of the standard NMR parameters.The present report is concerned with physical factors influencing the MRI tissue characteristics. The effect of mechanical waves on the NMR parameters has been discussed.
The propagation of shear waves in ex vivo tissue samples, agar/gel phantoms, and human volunteers was investigated. A moving coil apparatus was constructed to generate low acoustic frequency shear perturbations of 50 to 400 Hz. Oscillating gradients phase-locked with the shear stimulus were used to generate a series of phase contrast images of the shear waves at different time-points throughout the wave cycle. Quantitative measurements of wave velocity and attenuation were obtained to evaluate the effects of temperature, frequency, and tissue anisotropy. Results of these experiments demonstrate significant variation in shear wave behavior with tissue type, whereas frequency and anisotropic behavior was mixed. Temperature-dependent behavior related mainly to the presence of fat. Propagation velocities ranged from 1 to 5 m/sec, and attenuation coefficients of from 1 to 3 nepers/unit wavelength, depending on tissue type. These results confirm the potential of elastic imaging attributable to the intrinsic variability of elastic properties observed in normal tissue, although some difficulty may be experienced in clinical implementation because of viscous attenuation in fat.
In elasticity imaging, a surface deformation is applied to an
object using small pistons, and the resulting induced strains in the
interior of the object are measured using ultrasonic imaging. Two
important problems are considered: (1) the forward problem of
determining the strains induced by a known deformation of an object with
known elasticity; and (2) the inverse problem of reconstructing
elasticity from measured strains and the equations of equilibrium. The
method of finite differences is used to solve the forward problem for a
given piston configuration; some nontrivial issues arise in determining
boundary conditions. The finite difference equations are then rearranged
into a linear system of equations which formulates the inverse problem;
this system can be solved for the unknown elasticities. This formulation
of the inverse problem is completely consistent with the forward
problem; this is useful for iterative methods in which the deformation
is adaptively changed. A comparison between simulated and actual
measured results demonstrate the feasibility of the proposed procedure
Most algorithms for the least-squares estimation of non-linear parameters have centered about either of two approaches. On the one hand, the model may be expanded as a Taylor series and corrections to the several parameters calculated at each iteration on the assumption of local linearity. On the other hand, various modifications of the method of steepest-descent have been used. Both methods not infrequently run aground, the Taylor series method because of divergence of the successive iterates, the steepest-descent (or gradient) methods because of agonizingly slow convergence after the first few iterations. In this paper a maximum neighborhood method is developed which, in effect, performs an optimum interpolation between the Taylor series method and the gradient method, the interpolation being based upon the maximum neighborhood in which the truncated Taylor series gives an adequate representation of the nonlinear model. The results are extended to the problem of solving a set of nonlinear algebraic e
Acoustic shear waves of low frequency can be detected and measured using a phase contrast based magnetic resonance imaging
technique called MR Elastography or phase measurement based ultrasound techniques. Spatio-temporal variations of displacements
caused by the propagating waves can be used to estimate local values of the elasticity of the object being imaged. The currently
employed technique for estimating the elasticity from the wave displacement maps, the local frequency estimator (LFE), has
fundamental resolution limits and also has problems with shadowing and other refraction-related artifacts. These problems
can be overcome with an inverse approach using Green’s function integrals which directly solve the wave equation problem for
the propagating wave. The complete measurements of wave displacements as a function of space and time over the object of interest
obtained by the above techniques permit an iterative approach to inversion of the wave equation to obtain elasticity and attenuation
maps.
A method is introduced to measure internal mechanical displacement and strain by means of MRI. Such measurements are needed to reconstruct an image of the elastic Young's modulus. A stimulated echo acquisition sequence with additional gradient pulses encodes internal displacements in response to an externally applied differential deformation. The sequence provides an accurate measure of static displacement by limiting the mechanical transitions to the mixing period of the simulated echo. Elasticity reconstruction involves definition of a region of interest having uniform Young's modulus along its boundary and subsequent solution of the discretized elasticity equilibrium equations. Data acquisition and reconstruction were performed on a urethane rubber phantom of known elastic properties and an ex vivo canine kidney phantom using <2% differential deformation. Regional elastic properties are well represented on Young's modulus images. The long-term objective of this work is to provide a means for remote palpation and elasticity quantitation in deep tissues otherwise inaccessible to manual palpation.
Contenido: Introducción; Análisis de tensión; Tensión y dislocación; Relaciones de la tensión; Formulación de problemas de elasticidad; Problemas en dos dimensiones; Torsión de barras cilíndricas; Métodos de energía; Notación cartesiana de tensores; Tensores de tensión; Tensión, dislocación a gobierno de las ecuaciones de elasticidad; Vector y notación bivalente en elasticidad; Coordinadas ortogonales curvilíneas; Funciones de dislocación y tensión.
We describe a new method for quantitative imaging of strain and elastic modulus distributions in soft tissues. The method is based on external tissue compression, with subsequent computation of the strain profile along the transducer axis, which is derived from cross-correlation analysis of pre- and post-compression A-line pairs. The strain profile can then be converted to an elastic modulus profile by measuring the stresses applied by the compressing device and applying certain corrections for the nonuniform stress field. We report initial results of several phantom and excised animal tissue experiments which demonstrate the ability of this technique to quantitatively image strain and elastic modulus distributions with good resolution, sensitivity and with diminished speckle. We discuss several potential clinical uses of this technique.
An approach to ultrasonic tissue characterization, using textural features of the B-scan image, is described. Portions of a B-scan image, 64 X 64 pixels spatially by 8 bits deep, are acquired from regions of interest and subjected to computer analysis. A systematic approach to defining a set of 93 textural features of a B-scan is described and methods and criteria for selecting optimum combinations of these are discussed. As a test of its power, the approach has been applied to the discrimination between the B-scan textures corresponding to livers and spleens of normal humans and various measures of "success" have been quantified both on a "training set only" and on a "training set plus test set" basis. The overall test probability of success of 82% on a single image and 94% on a subject yielding multiple images indicates the potential of the techniques for conditions where a subtle but uniform change in parenchymal texture may be present.
A finite element reconstruction algorithm for optical data based on a diffusion equation approximation is presented. A frequency domain approach is adopted and a unified formulation for three combinations of boundary observables and conditions is described. A multidetector, multisource measurement and excitation strategy is simulated, which includes a distributed model of the light source that illustrates the flexibility of the methodology to modeling adaptations. Simultaneous reconstruction of both absorption and scattering coefficients for a tissue-like medium is achieved for all three boundary data types. The algorithm is found to be computationally practical, and can be implemented without major difficulties in a workstation computing environment. Results using simulated data suggest that qualitative images can be produced that readily highlight the location of absorption and scattering heterogeneities within a circular background region of close to 4 cm in diameter over a range of contrast levels. Absorption images appear to more closely identify the true size of the heterogeneity; however, both the absorption and scattering reconstructions have difficulty with sharp transitions at increasing depth. Quantitatively, the reconstructions are not accurate, suggesting that absolute optical imaging involving simultaneous recovery of both absorption and scattering profiles in multicentimeter tissues geometries may prove to be extremely difficult.
A nuclear magnetic resonance imaging (MRI) method is presented for quantitatively mapping the physical response of a material
to harmonic mechanical excitation. The resulting images allow calculation of regional mechanical properties. Measurements
of shear modulus obtained with the MRI technique in gel materials correlate with independent measurements of static shear
modulus. The results indicate that displacement patterns corresponding to cyclic displacements smaller than 200 nanometers
can be measured. The findings suggest the feasibility of a medical imaging technique for delineating elasticity and other
mechanical properties of tissue.
Sonoelasticity is a rapidly evolving medical imaging technique for visualizing hard tumors in tissues. In this novel diagnostic technique, a low-frequency vibration is externally applied to excite internal vibrations within the tissue under inspection. A small stiff inhomogeneity in a surrounding tissue appears as a disturbance in the normal vibration eigenmode pattern. By employing a properly designed Doppler detection algorithm, a real-time vibration image can be made. A theory for vibrations, or shear wave propagation in inhomogeneous tissue has been developed. A tumor is modeled as an elastic inhomogeneity inside a lossy homogeneous elastic medium. A vibration source is applied at a boundary. The solutions for the shear wave equation have been found both for the cases with tumor (inhomogeneous case) and without tumor (homogeneous case). The solutions take into account varying parameters such as tumor size, tumor stiffness, shape of vibration source, lossy factor of the material, and vibration frequency. The problem of the lowest detectable change in stiffness is addressed using the theory, answering one of the most critical questions in this diagnostic technique. Some experiments were conducted to check the validity of the theory, and the results showed a good correspondence to the theoretical predictions. These studies provide basic understanding of the phenomena observed in the growing field of clinical Sonoelasticity imaging for tumor detection.
Changes in tissue elasticity are generally correlated with its pathological state. In many cases, despite the difference in elasticity, the small size of a lesion or its location deep in the body preclude its detection by palpation. In general, such a lesion may or may not possess echogenic properties that would make it ultrasonically detectable. Elastography is an ultrasonic method for imaging the elasticity of compliant tissues. The method estimates the local longitudinal strain of tissue elements by ultrasonically assessing the one dimensional local displacements. This information can be combined with first order theoretical estimates of the local stress to yield a quantitative measure of the local elastic properties of tissue. The elasticity information is displayed in the form of a gray scale image called an elastogram. An experimental system for elastography in phantoms based on a single element transducer has been described previously [1]. Here we introduce a new elastography system based on a linear array transducer that is suitable for in vivo scanning. We describe tissue mimicking phantom experiments and preliminary in vivo breast and muscle elastograms confirming the feasibility of performing elastography in vivo. An elastogram of a breast containing an 8 mm palpable cancer nodule clearly shows the lesion. Elastograms and their corresponding sonograms show some similarities and differences in the depiction of tissue structures.
We describe a phase contrast based MRI technique with high sensitivity to cyclic displacement that is capable of quantitatively imaging acoustic strain waves in tissue-like materials. A formalism for considering gradient waveforms as basis functions to measure arbitrary cyclic motion waveforms is introduced. Experiments with tissue-like agarose gel phantoms show that it is possible to measure small cyclic displacements at a submicron level by an appropriate choice of the applied gradient basis function and to use this capability to observe the spatial and temporal pattern of displacements caused by acoustic strain waves. The propagation characteristics of strain waves are determined by the mechanical properties of the media. It is therefore possible to use this technique to noninvasively estimate material properties such as elastic modulus.
Electrical impedance imaging is a technique which is under investigation as a noninvasive method of tracking subsurface temperature distributions and/or associated cellular response during hyperthermia. In previous work, a finite element image reconstruction algorithm for converting surface potential distributions recorded at discrete electrode positions into spatial maps of conductivity values was developed. This paper reports on a series of significant improvements in the basic image reconstruction approach. Specifically, the ability to recover both the resistive and capacitive components of tissue electrical impedance have been incorporated. In addition, the image enhancement schemes of (1) total variation minimization, (2) dual meshing, and (3) spatial low-pass filtering, have been added. Through a series of simulation studies involving both phantom-like and clinically-relevant geometries having discrete regions and continuously-varying electrical property profiles, a significantly improved ability to recover spatial images of electrical properties in the impedance imaging context is demonstrated. The results show that the new algorithm is much more tolerant of measurement noise with levels up to 1% causing relatively modest degradations in image quality (compared to 0.1% which was needed previously in order to produce high quality images). The recovered electrical properties, themselves, both resistive and capacitive, are also found to be quantitative in value with errors in the 10-20% range occurring in the majority of cases, although deviations can reach 40% or more when noise levels as high as 10% are used. Temperature estimation simulations show that maximum temperature errors are significantly reduced (to approximately 2 degrees C relative to more than 10 degrees C in previous thermal simulations) with the new algorithm; however, temperature accuracies of better than 0.5 degree C on average are still found to be difficult to achieve with electrical impedance imaging even when the enhanced image reconstruction approach is used.
A least-squares strain estimator (LSQSE) for elastography is proposed. It is shown that with such an estimator, the signal-to-noise ratio in an elastogram (SNRe) is significantly improved. This improvement is illustrated theoretically using a modified strain filter and experimentally using a homogeneous gel phantom. It is demonstrated that the LSQSE results in an increase of the elastographic sensitivity (smallest, strain that could be detected), thereby increasing the strain dynamic range. Using simulated data, it is shown that a tradeoff exists between the improvement in SNRe and the reduction of strain contrast and spatial resolution.
To noninvasively quantify tissue elasticity for differentiating malignancy of soft tissue, we previously proposed a two-dimensional (2-D) mechanical inverse problem in which simultaneous partial differential equations (PDE's) represented the target distribution globally of relative shear moduli with respect to reference shear moduli such that the relative values could be determined from strain distributions obtained by conventional ultrasound (US) or nuclear magnetic resonance (NMR) imaging-based analysis. Here, we further consider the analytic solution in the region of interest, subsequently demonstrating that the problem is inevitably ill-conditioned in real-world applications, i.e., noise in measurement data and improper configurations of mechanical sources/reference regions make it impossible to guarantee the existence of a stable and unique target global distribution. Next, based on clarification of the inherent problematic conditions, we describe a newly developed numerical-based implicit-integration approach that novelly incorporates a computationally efficient regularization method designed to solve this differential inverse problem using just low-pass filtered spectra derived from strain measurements. To evaluate method effectiveness, reconstructions of the global distribution are carried out using intentionally created ill-conditioned models. The resultant reconstructions indicate the robust solution is highly suitable, while also showing it has high potential to be applied in the development of an effective yet versatile diagnostic tool for quantifying the distribution of elasticity in various soft tissues.
A finite element-based nonlinear inversion scheme for magnetic resonance (MR) elastography is detailed. The algorithm operates on small overlapping subzones of the total region of interest, processed in a hierarchical order as determined by progressive error minimization. This zoned approach allows for a high degree of spatial discretization, taking advantage of the data-rich environment afforded by the MR. The inversion technique is tested in simulation under high-noise conditions (15% random noise applied to the displacement data) with both complicated user-defined stiffness distributions and realistic tissue geometries obtained by thresholding MR image slices. In both cases the process has proved successful and has been capable of discerning small inclusions near 4 mm in diameter. Magn Reson Med 42:779-786, 1999.
A new method to reconstruct the elastic modulus of soft tissue subjected to an external static compression is presented. In this approach the Newton-Raphson method is used to vary a finite element (FE) model of the elasticity equations to fit, in a least squared sense, a set of axial tissue displacement fields estimated using a correlation technique applied to ultrasound signals. The ill-conditioning of the Hessian matrix is eliminated using the Tikhonov regularization technique. This regularization provides a compromise between fidelity to the observed data and a priori information of the solution. Using an echographic image formation model, it is shown that the method converges within a few iterations (8-10) and that strain images artifacts which are common in elastography are significantly reduced after the resolution of the inverse problem.
An imaging system that can display both the amplitude and phase maps of internal vibration in soft tissues for forced low-frequency vibration is described. In this method, low-frequency sinusoidal vibration of frequency under several hundred hertz is applied from the surface of the sample and the resulting movement in it is measured from the Doppler frequency shift of the simultaneously transmitted probe ultrasonic waves. Basic experiments are carried out by using 3.0-MHz ultrasonic waves. The two-dimensional maps of the amplitude and phase of internal vibration are shown, and the velocities of vibration are measured for some samples as well as in vivo.< >
Elasticity reconstructive imaging using static displacement and strain estimations
- T L Chenevert
- S Y Emelianov
- A R Skovoroda
L. Chenevert, S. Y. Emelianov, and A. R. Skovoroda, ''Elasticity
reconstructive imaging using static displacement and strain estimations,''
in Proc. of the Int. Soc. of Magnetic Resonance in Medicine, 461.
An overlapping subzone technique for MR based elastic property reconstruction
- Van Houten
Geenleaf “Reconstruction of elasticity and attenuation maps in shear wave imaging: An inverse approach ” inLecture Notes in Computer Science-Medical Image Computing and Computer-Assisted Intervention
- A V Manduca
- D T Dutt
- R Borup
- R L Muthupillai
- J F Ehman