QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.

Experimental investigation of thermal structures in regular three-dimensional falling films

Interfacial waves on the surface of a falling liquid film are known to modify heat and mass transfer. Under non-isothermal conditions, the wave topology is strongly influenced by the presence of thermocapillary (Marangoni) forces at the interface which leads to a destabilization of the film flow and potentially to critical film thinning. In this context, the present study investigates the evolution of the surface topology and the evolution of the surface temperature for the case of regularly excited solitary-type waves on a falling liquid film under the influence of a wall-side heat flux. Combining film thickness (chromatic confocal imaging) and surface temperature information (infrared thermography), interactions between hydrodynamics and thermocapillary forces are revealed. These include the formation of rivulets, film thinning and wave number doubling in spanwise direction. Distinct thermal structures on the films’ surface can be associated to characteristics of the surface topology.

Evidence for distinct dehydrogenase and isomerase sites within a single 3β-hydroxysteroid dehydrogenase/5-ene-4-ene isomerase protein

Complementary DNA encoding human 3β-hydroxysteroid dehydrogenase/5-ene-4-ene isomerase (30-HSD) has been expressed in transfected GH4C1 with use of the cytomegalovirus promoter. The activity of the expressed protein clearly shows that both dehydrogenase and isomerase enzymatic activities are present within a single protein. However, such findings do not indicate whether the two activities reside within one or two closely related catalytic sites. With use of [3H]-5-androstenedione, the intermediate compound in dehydroepiandrosterone (DHEA) transformation into 4-androstenedione by 3β-HSD, the present study shows that 4MA (N,N-diethyl-4-rnethyl-3-oxo-4-aza-5α-androstane-17β-carboxamide) and its analogues inhibit DHEA oxidation competitively while they exert a noncompetitive inhibition of the isomerization of 5-androstenedione to 4-androstenedione with an approximately 1000-fold higher Ki value. The present results thus strongly suggest that dehydrogenase and isomerase activities are present at separate sites on the 3β-HSD protein. In addition, using 5α-dihydrotestosterone (DHT) and 5α-androstane-3β,17β-diol as substrates for dehydrogenase activity only, we have found that dehydrogenase activity is reversibly and competitively inhibited by 4MA. Such data suggest that the irreversible step in the transformation of DHEA to 4-androstenedione is due to a separate site possessing isomerase activity that converts the 5-ene-3-keto to a much more stable 4-ene-3-keto configuration. © 1991 American Chemical Society.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Globcurrent: Sentinel-3 synergy in action

The ESA Data User Element (DUE) funded GlobCurrent project (http://www.globcurrent.org) aims to: (i) advance the quantitative estimation of ocean surface currents from satellite sensor synergy; and (ii) demonstrate impact in user-led scientific, operational and commercial applications that, in turn, will improve and strengthen the uptake of satellite measurements. Today, a synergetic approach for quantitative analysis can build on high-resolution imaging radar and spectrometer data, infrared radiometer data and radar altimeter measurements. It will further integrate Sentinel-3 in combination with Sentinel-1 SAR data. From existing and past missions, it is often demonstrated that sharp gradients in the sea surface temperature (SST) field and the ocean surface chlorophyll-a distribution are spatially correlated with the sea surface roughness anomaly fields at small spatial scales, in the sub-mesocale (1-10 km) to the mesoscale (30-80 km). At the larger mesoscale range (>50 km), information derived from radar altimeters often depict the presence of coherent structures and eddies. The variability often appears largest in regions where the intense surface current regimes (>100 - 200 km) are found. These 2-dimensional structures manifested in the satellite observations represent evidence of the upper ocean (~100-200 m) dynamics. Whereas the quasi geostrophic assumption is valid for the upper ocean dynamics at the larger scale (>100 km), possible triggering mechanisms for the expressions at the mesoscale-to-submesoscale may include spiraling tracers of inertial motion and the interaction of the wind-driven Ekman layer with the quasi-geostrophic current field. This latter, in turn, produces bands of downwelling (convergence) and upwelling (divergence) near fronts. A regular utilization of the sensor synergy approach with the combination of Sentinel-3 and Sentinel-1 will provide a highly valuable data set for further research and development to better relate the 2-dimensional surface expressions and the upper ocean dynamics.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

Mixed-dimensional coupling in finite element models

In many finite element analysis models it would be desirable to combine reduced- or lower-dimensional element types with higher-dimensional element types in a single model. In order to achieve compatibility of displacements and stress equilibrium at the junction or interface between the differing element types, it is important in such cases to integrate into the analysis some scheme for coupling the element types. A novel and effective scheme for establishing compatibility and equilibrium at the dimensional interface is described and its merits and capabilities are demonstrated. Copyright (C) 2000 John Wiley & Sons, Ltd.

Three-Dimensional Analysis of Seepage below and around Hydraulic Structures

This paper investigates the problem of seepage under the floor of hydraulic structures considering the compartment of flow that seeps through the surrounding banks of the canal. A computer program, utilizing a finite-element method and capable of handling three-dimensional (3D) saturated–unsaturated flow problems, was used. Different ratios of canal width/differential head applied on the structure were studied. The results produced from the two-dimensional (2D) analysis were observed to deviate largely from that obtained from 3D analysis of the same problem, despite the fact that the porous medium was isotropic and homogeneous. For example, the exit gradient obtained from 3D analysis was as high as 2.5 times its value obtained from 2D analysis. Uplift force acting upwards on the structure has also increased by about 46% compared with its value obtained from the 2D solution. When the canal width/ differential head ratio was 10 or higher, the 3D results were comparable to the 2D results. It is recommended to construct a core of low permeability soil in the banks of canal to reduce the seepage losses, uplift force, and exit gradient.

Three dimensional number density mapping in the plume of a low temperature laser ablated magnesium plasma

Simultaneous optical absorption and laser-induced fluorescence measurements have been used to map the three-dimensional number densities of ground-state ions and neutrals within a low-temperature KrF laser-produced magnesium plasma expanding into vacuum. Data is reported for the symmetry plane of the plasma, which includes the laser interaction point at a delay of 1 μs after the ∼30 ns KrF laser ablation pulse and for a laser fluence of 2 J cm−2 on target. The number density distributions of ion and neutral species within this plane indicate that two distinct regions exist within the plume; one is a fast component containing ions and neutrals at maximum densities of ∼3×1013 cm−3 and ∼4×1012 cm−3, respectively and the second is a high-density region containing slow neutral species, at densities up to ∼1×1015 cm−3.

Reliability Assessment of 3-D Space Frame Structures Applying Stochastic Finite Element Analysis

Throughout design development of satellite structure, stress engineer is usually challenged with randomness in applied loads and material properties. To overcome such problem, a risk-based design is applied which estimates satellite structure probability of failure under static and thermal loads. Determining probability of failure can help to update initially applied factors of safety that were used during structure preliminary design phase. These factors of safety are related to the satellite mission objective. Sensitivity-based analysis is to be implemented in the context of finite element analysis (probabilistic finite element method or stochastic finite element method (SFEM)) to determine the probability of failure for satellite structure or one of its components.

Three-dimensional graphene-Co3O4 cathodes for rechargeable Li-O2 batteries

A three-dimensional (3D) graphene-Co₃O₄ electrode was prepared by a two-step method in which graphene was initially deposited on a Ni foam with Co₃O₄ then grown on the resulting graphene structure. Cross-linked Co₃O₄ nanosheets with an open pore structure were fully and vertically distributed throughout the graphene skeleton. The free-standing and binder-free monolithic electrode was used directly as a cathode in a Li-O₂ battery. This composite structure exhibited enhanced performance with a specific capacity of 2453 mA h g^-1 at 0.1 mA cm^-2 and 62 stable cycles with 583 mA h g^-1 (1000 mA h g_carbon^-1). The excellent electrochemical performance is associated with the unique architecture and superior catalytic activity of the 3D electrode.