196 research outputs found

    Characterizing anisotropy in fibrous soft materials by MR elastography of slow and fast shear waves

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    The general objective of this work was to develop experimental methods based on magnetic resonance elastography (MRE) to characterize fibrous soft materials. Mathematical models of tissue biomechanics capable of predicting injury, such as traumatic brain injury (TBI), are of great interest and potential. However, the accuracy of predictions from such models depends on accuracy of the underlying material parameters. This dissertation describes work toward three aims. First, experimental methods were designed to characterize fibrous materials based on a transversely isotropic material model. Second, these methods are applied to characterize the anisotropic properties of white matter brain tissue ex vivo. Third, a theoretical investigation of the potential application of MRE to probe nonlinear mechanical behavior of soft tissue was performed. These studies provide new methods to characterize anisotropic and nonlinear soft materials as well as contributing significantly to our understanding of the behavior of specific biological soft tissues

    Dual-Probe Shear Wave Elastography in a Transversely Isotropic Phantom

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    This project aimed to evaluate the possibility of obtaining a full mechanical characterization of a transversely isotropic (TI) phantom with dual-probe SWE. A TI phantom was developed and mechanical tests were performed to verify its anisotropy. Moreover, multiple wave propagation modes calculated with dual-probe SWE showed a good agreement with the theoretical curves and indicated the possibility of measuring all the elasticity constants needed to fully characterize a TI tissueope

    Modeling and inversion of seismic data using multiple scattering, renormalization and homotopy methods

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    Seismic scattering theory plays an important role in seismic forward modeling and is the theoretical foundation for various seismic imaging methods. Full waveform inversion is a powerful technique for obtaining a high-resolution model of the subsurface. One objective of this thesis is to develop convergent scattering series solutions of the Lippmann-Schwinger equation in strongly scattering media using renormalization and homotopy methods. Other objectives of this thesis are to develop efficient full waveform inversion methods of time-lapse seismic data and, to investigate uncertainty quantification in full waveform inversion for anisotropic elastic media based on integral equation approaches and the iterated extended Kalman filter. The conventional Born scattering series is obtained by expanding the Lippmann-Schwinger equation in terms of an iterative solution based on perturbation theory. Such an expansion assumes weak scattering and may have the problems of convergence in strongly scattering media. This thesis presents two scattering series, referred to as convergent Born series (CBS) and homotopy analysis method (HAM) scattering series for frequency-domain seismic wave modeling. For the convergent Born series, a physical interpretation from the renormalization prospective is given. The homotopy scattering series is derived by using homotopy analysis method, which is based on a convergence control parameter hh and a convergence control operator HH that one can use to ensure convergence for strongly scattering media. The homotopy scattering scattering series solutions of the Lippmann-Schwinger equation, which is convergent in strongly scattering media. The homotopy scattering series is a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. The Fast Fourier Transform (FFT) is employed for efficient implementation of matrix-vector multiplication for the convergent Born series and the homotopy scattering series. This thesis presents homotopy methods for ray based seismic modeling in strongly anisotropic media. To overcome several limitations of small perturbations and weak anisotropy in obtaining the traveltime approximations in anisotropic media by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory, this study applies the homotopy analysis method to the eikonal equation. Then this thesis presents a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system. The new traveltime approximations are derived by using the linear and nonlinear operators in the retrieved zero-order deformation equation. Flexibility on variable anisotropy parameters is naturally incorporated into the linear differential equations, allowing a medium of arbitrarily anisotropy. This thesis investigates efficient target-oriented inversion strategies for improving full waveform inversion of time-lapse seismic data based on extending the distorted Born iterative T-matrix inverse scattering to a local inversion of a small region of interest (e. g. reservoir under production). The target-oriented approach is more efficient for inverting the monitor data. The target-oriented inversion strategy requires properly specifying the wavefield extrapolation operators in the integral equation formulation. By employing the T-matrix and the Gaussian beam based Green’s function, the wavefield extrapolation for the time-lapse inversion is performed in the baseline model from the survey surface to the target region. I demonstrate the method by presenting numerical examples illustrating the sequential and double difference strategies. To quantify the uncertainty and multiparameter trade-off in the full waveform inversion for anisotropic elastic media, this study applies the iterated extended Kalman filter to anisotropic elastic full waveform inversion based on the integral equation method. The sensitivity matrix is an explicit representation with Green’s functions based on the nonlinear inverse scattering theory. Taking the similarity of sequential strategy between the multi-scale frequency domain full waveform inversion and data assimilation with an iterated extended Kalman filter, this study applies the explicit representation of sensitivity matrix to the the framework of Bayesian inference and then estimate the uncertainties in the full waveform inversion. This thesis gives results of numerical tests with examples for anisotropic elastic media. They show that the proposed Bayesian inversion method can provide reasonable reconstruction results for the elastic coefficients of the stiffness tensor and the framework is suitable for accessing the uncertainties and analysis of parameter trade-offs

    On an inverse problem from magnetic resonance elastic imaging

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    The imaging problem of elastography is an inverse problem. The nature of an inverse problem is that it is ill-conditioned. We consider properties of the mathematical map which describes how the elastic properties of the tissue being reconstructed vary with the field measured by magnetic resonance imaging (MRI). This map is a nonlinear mapping, and our interest is in proving certain conditioning and regularity results for this operator which occurs implicitly in this problem of imaging in elastography. In this treatment we consider the tissue to be linearly elastic, isotropic, and spatially heterogeneous. We determine the conditioning of this problem of function reconstruction, in particular for the stiffness function. We further examine the conditioning when determining both stiffness and density. We examine the Frechet derivative of the nonlinear mapping, which enables us to describe the properties of how the field affects the individual maps to the stiffness and density functions. We illustrate how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. We present new results which show that the stiffness map is mildly ill-posed, whereas the density map suffers from medium ill-conditioning. Computational work has been done previously to study the sensitivity of these maps, but our work here is analytical. The validity of the Newton-Kantorovich and optimization methods for the computational solution of this inverse problem is directly linked to the Frechet differentiability of the appropriate nonlinear operator, which we justify

    A Structural Health Monitoring Concept on Ultrasonic Based Assessment of Aged Structures with Isotropic and Anisotropic Material Properties

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    Ultrasound is a technique widely applied in classical NDT where a lot of progress has been made in terms of signal processing, resolution, visualisation, and possibly more. With the introduction of the phased array technique, advanced computation and sensor signal processing also the characterisation of anisotropic materials has been facilitated. In par-allel SHM has emerged as a field of research very much looking into the automation of NDT in view of taking enhanced advantage of an engineering structure’s damage toler-ance and hence light weight potential. Ultrasonic guided waves are a field very much explored currently within the context of SHM and as such it is worth to determine what of the guided wave related techniques developed in NDT may be inheritable for SHM applications. Reverse Phase Matching (RPM) referred to anisotropic material properties and ray tracing are an interesting combination to be pursued in terms of finding an opti-mum sensor configuration for SHM through numerical simulation based on FEM, allowing to take better advantage of a polymer based composite materials potential such as CFRP by taking advantage of those materials’ inherent non-linear responses. The approach to be taken is illustrated with respect to an example, explaining on how to assess an ageing CFRP component in terms of its damage condition and an SHM system to be configured in the end. Finally a systematic is presented on how knowledge generated in NDT can be linked into a ‘SHM-toolbox’ to be used for the advancement of SHM systems to be de-veloped in the longer term.Ultraschall ist eine in der klassischen zerstörungsfreien PrĂŒfung (ZfP) weit verbreitete Technik, bei der vielfĂ€ltig Fortschritte hinsichtlich Signalverarbeitung, Auflösungsvermö-gen, Visualisierung und vermutlich weiterer Dinge erzielt wurden. Mit der EinfĂŒhrung des Phased Array sowie fortgeschrittener Rechner- und Signalverarbeitungstechnik ist auch die Charakterisierung anisotroper Werkstoffe erleichtert worden. Parallel dazu hat sich das Gebiet der ZustandsĂŒberwachung (Structural Health Monitoring (SHM)) als For-schungsfeld entwickelt, dies im Hinblick auf die Automatisierung der ZfP und der erwei-terten Nutzung des Potenzials der Schadenstoleranz bzw. des Leichtbaus von Bauteilen. GefĂŒhrte Wellen auf der Basis des Ultraschalls sind im Bereich des SHM ein derzeit breit untersuchtes Forschungsfeld und es ist somit wert zu ermitteln, inwieweit sich auf ge-fĂŒhrte Wellen beziehende Techniken aus der ZfP auf SHM-Anwendungen ĂŒbertragen werden können. Reverse Phase Matching (RPM) in Verbindung mit anisotropen Werk-stoffeigenschaften und Ray Tracing sind eine in diesem Sinne interessante, sich fĂŒgende und verfolgungswerte Kombination, um möglicherweise ĂŒber die Betrachtung inhĂ€renter nicht-linearer Werkstoffantworten auf der Basis einer numerischen Simulation (FEM) ein optimales Sensornetzwerk fĂŒr SHM zu bestimmen, womit das Potenzial eines Faserver-bundwerkstoffs wie CFK besser genutzt werden kann. Ein hierzu gewĂ€hlter Ansatz wird am Beispiel einer gealterten CFK-Struktur im Hinblick auf deren SchĂ€digungszustand er-lĂ€utert, fĂŒr den dann diesbezĂŒglich am Ende ein SHM-System konfiguriert werden kann. Abschließend wird eine Systematik vorgestellt, ĂŒber die in der ZfP generiertes Wissen mit einem ‘SHM-Werkzeugkasten’ so verknĂŒpft wird, dass lĂ€ngerfristig eine Weiterentwick-lung von SHM-Systemen ermöglicht wird

    Viscoelasticity Imaging of Biological Tissues and Single Cells Using Shear Wave Propagation

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    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

    Acoustic Waves

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    The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis

    Wave Propagation in Materials for Modern Applications

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    In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas
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