Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Enabling Real-Time Ultrasound Imaging of Soft Tissue Mechanical Properties by Simplification of the Shear Wave Motion Equation

Ultrasound based shear wave elastography (SWE) is a technique used for non-invasive characterization and imaging of soft tissue mechanical properties. Robust estimation of shear wave propagation speed is essential for imaging of soft tissue mechanical properties. In this study we propose to estimate shear wave speed by inversion of the firstorder wave equation following directional filtering. This approach relies on estimation of first-order derivatives which allows for accurate estimations using smaller smoothing filters than when estimating second-order derivatives. The performance was compared to three current methods used to estimate shear wave propagation speed: direct inversion of the wave equation (DIWE), time-to-peak (TTP) and crosscorrelation (CC). The shear wave speed of three homogeneous phantoms of different elastic moduli (gelatin by weight of 5%, 7%, and 9%) were measured with each method. The proposed method was shown to produce shear speed estimates comparable to the conventional methods (standard deviation of measurements being 0.13 m/s, 0.05 m/s, and 0.12 m/s), but with simpler processing and usually less time (by a factor of 1, 13, and 20 for DIWE, CC, and TTP respectively). The proposed method was able to produce a 2-D speed estimate from a single direction of wave propagation in about four seconds using an off-the-shelf PC, showing the feasibility of performing real-time or near real-time elasticity imaging with dedicated hardware

Uterine leiomyomas: correlation between histologic composition and stiffness via magnetic resonance elastography — a Pilot Study

Objectives: To evaluate magnetic resonance elastography as a tool for characterizing uterine leimyomas.Material and methods: At total of 12 women with symptomatic leiomyomas diagnosed in physical and ultrasound examinationswere enrolled in this pilot study. Before surgery, all patients underwent magnetic resonance elastography ofthe uterus using a 1.5 T MR whole-body scanner (Optima, GE Healthcare, Milwaukee, WI, USA). Surgical specimens wereforwarded for histological examination. The findings were allocated into 3 categories depending on the percentage contentof connective tissue: below 15%, from 15 to 30% and more than 30%. The median stiffness of leiomyomas for each of thegroup was calculated. The U-Mann Whitney test was used for statistical analysis.Results: The stiffness of the leiomyomas ranged between 3.7–6.9 kPa (median value 4.9 kPa). The concentration of extracellularcomponents in the leiomyomas did not exceed 40%. An increasing trend of the stiffness with the growing percentageof extracellular component was observed. Stiffness of the leiomyomas obtained by MRE varies depending on microscopiccomposition.Conclusions: The value of stiffness shows a trend of increasing with the percentage of extracellular component of theleiomyoma. Further studies are required to assess the usefulness of MRE in diagnostics of uterine leiomyomas

Soft tissue viscoelastic properties: measurements, models and interpretation

The quantification of mechanical properties of soft tissues has been of great interest for more than two decades because they have the potential of being used as biomarkers for disease diagnosis. Indentation techniques, the most recognized techniques for characterizing mechanical properties, are widely used for basic science investigations in research labs. The use of elastography techniques coupled with imaging technologies has been growing rapidly in recent years, which is promising for clinical applications. Each technique produces different mechanical behaviors due to the interaction of the stimuli and the structure of the tissue. An appropriate model will parameterize these behaviors to reflect the corresponding tissue microscopic features with high fidelity. The objective of this thesis is to identify combinations of techniques and models that will yield mechanical parameters with diagnostic interpretations about tissue microenvironment. Three techniques for characterizing tissue viscoelastic properties were developed and validated, each offers strengths in a large variety of applications. Indentation based techniques measure low-frequency force-displacement curves under different loading profiles. Ultrasound-based techniques and optical based techniques measure the dispersion behaviors of the propagating wave velocities at mid-to-high frequency ranges. When a material is linear, isotropic, and contains only elastic components, the “intrinsic” elastic modulus of the material can be obtained independently of the technique used when corrections are properly made to eliminate the bias from boundary effects. If the material includes time-dependent components, models must be included in the analysis to provide parametric estimates. Classical models for viscoelastic solids such as the Kelvin-Voigt model do not fully represent mechanical measurements in tissues because they are not material continua. Tissue properties are determined in part by fluid movement in the open- and closed-cell compartments found within a viscoelastic collagen matrix that is actively maintained by the embedded cells to meet programmed needs. These biphasic (solid/fluid) media exhibit multifaceted deformation responses that are particularly difficult to model using a concise feature set. The Kelvin-Voigt fractional derivative (KVFD) model introduced in this study represents the measurement data of a broad range in both time and frequency domain with a small number of parameters, and it yields stable estimates for many types of phantoms and tissues. It is superior to the integer derivative models for the materials and techniques we used in this study. Moreover, the KVFD model provides a three-dimensional feature space of mechanical properties that properly characterizes the composition and structure of a material. This was validated through measurements on gelatin-cream emulsion samples exhibiting viscoelastic behavior, as well as ex vivo liver tissue samples. For the elastic property, KVFD parameter E_0 mainly represents the elasticity of the solid matrix and is approximately equal to the shear modulus no matter which technique is used. For the viscous property, when combined with different measurement techniques, KVFD model parameter α and τ represent different tissue components. The combination of these techniques and the KVFD model have the potential to be able to distinguish between healthy and pathological tissues described by the histological features

Sensitivity Analysis in Magnetic Resonance Elastography and a Local Wavelength Reconstruction based on Wave Direction

or the detection of early stage cancer. MRE utilizes interior data for its inverse problems, which greatly reduces the ill-posedness from which most traditional inverse problems suffer. In this thesis, we first establish a sensitivity analysis for viscoelastic scalar medium with complex wave number and compare it with the purely elastic case. Also we estimate the smallest detectable inclusion for breast and liver, which is about twice larger than using the purely elastic model. We also found the existence of optimal frequency (50 Hz) that maximizes the detectability when the Voigt model is used. Second, we propose a local wavelength reconstruction based on the wave direction estimate for purely elastic medium. The main observation is that the wave looks primarily like a plane wave on a small window. On the small window, we first estimate the wave direction by solving a one dimensional optimization problem related to the minimum variance of shifted identical signals. Then along the wave direction, we use a non-periodic Fourier transform to reconstruct the wave number. This algorithm is extremely resilient to the noise and combined with another direct inversion method, this hybrid reconstruction becomes accurate as well. Extensive test reconstruc- tions on simulated and experimental data provided by the Mayo Clinic are included in this thesis. For the viscoelastic medium, this local wavelength reconstruction method will need an additional parameter for a scaling factor which leads to a two dimensional minimization problem. A slight modification in the Fourier transform part will also need to be created which is left for future work

Sensitivity Anaylsis and Detectability for Magnetic Resonance Elastography

This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application. Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy between the full elastic model and the scalar model that provides a criterion when the simple scalar model is acceptable; 3) a theoretical limit of the smallest tumor that magnetic resonance elastography can reconstruct; 4) the existence of optimal frequency when the Voigt (viscoelastic) model is adopted; and 5) the limit behavior of the solution when the inclusion stiness or attenuation becomes innitely high. We expect that this detectability approach is extendable to many hybrid imaging techniques to quantify their sensitivities and cross-compare them to determine which modality is the most powerful in detecting early-stage cancer

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

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

Evaluierung von Rekonstruktionsalgorithmen für die Magnetresonanz-Elastographie (MRE)

Magnetresonanzelastographie (MRE) ist eine neue Methode, mit der Magnetresonanztomographie nicht invasiv die Elastizität menschlichen Gewebes zu messen. Die Palpation zeigt, wie wichtig eine Abschätzung von Elastizitätsunterschieden für die Diagnostik sein kann. Ziel der MRE ist es, Elastogramme zur Diagnose bereitzustellen. Elastogramme sind Bilder, die in jedem Bildpunkt die Elastizität des Gewebes zeigen, in dem die ursprünglichen Bilddaten mit dem Magnetresonanztomographen akquiriert wurden. Dazu wird eine Bildakquisitionsmethode benutzt, die Bewegungen im Gewebe misst. Mechanische Wellen werden mit einem Schwingungsgenerator von außen über die Haut in das darunter liegende Gewebe induziert, was eine Schwingung der Wasserstoffprotonen verursacht, die durch Wechselwirkung mit den Magnetfeldern des Tomographen die zu messenden Signale generieren. Diese Schwingungen und dadurch bedingte Wellenausbreitungen können den Bilddaten durch Nachverarbeitung entnommen werden. Aus diesen Daten wiederum können dann Elastizitätsverteilungen bzw. Elastogramme rekonstruiert werden. Der Aufbau einer solchen Untersuchung bedarf der Steuerung einer mechanischen Anregung, welche mit dem Bildgebungsvorgang synchronisiert ist. Die Ergebnisse von MRE-Untersuchungen in Phantomen, der Skelettmuskulatur, des Hirns und der Haut mit dem beschriebenen System zeigen, dass MRE in den entsprechenden Regionen des Körpers Elastizitätsmessungen ermöglicht. Weiterhin werden Rekonstruktionsalgorithmen für die Berechnung von Elastogrammen vorgestellt, auf die Bilddaten der genannten Untersuchungen angewendet und evaluiert. Es zeigt sich, dass zur Rekonstruktion der Daten physikalische Eigenschaften angenommen werden müssen, die das menschliche Gewebe nicht realistisch beschreiben. Anhand der Evaluierung der Rekonstruktionsmethoden der MRE-Daten zeigt sich, dass aber gerade für die Rekonstruktion noch Forschungsbedarf besteht, um auch die Zuverlässigkeit des Verfahrens garantieren zu können, die für eine diagnostische Beurteilung notwendig ist. Dennoch lassen sich Elastizitätsverteilungen visualisieren, so dass die Aussagekraft der Elastograme mit statistischen Auswertungen von MRE-Untersuchungen mit einer großen Anzahl Patienten überprüft werden muss. Die MRE verspricht, eine Möglichkeit zu bieten, Krankheiten, die Elastizitätsänderungen verursachen, zu identifizieren und deren Verlauf zu verfolgen