Shlomo Ta'asan

Multiplex assessment of serum biomarker concentrations in well-appearing children with inflicted traumatic brain injury.

Proper diagnosis of mild inflicted traumatic brain injury (ITBI) is difficult; children often present without a history of trauma and with nonspecific symptoms, such as vomiting. Previous studies suggest that biomarkers may be able to screen for brain injury in this population, but these studies focused on only a few biomarkers. We hypothesized that using multiplex bead technology we would be able to identify multiple differences in the serum biomarker profile between in children with ITBI and those without brain injury. We compared the concentrations of 44 serum biomarkers in 16 infants with mild ITBI and 20 infants without brain injury. There were significant group differences in the concentrations of nine of the 44 markers. Vascular cellular adhesion molecule (VCAM) (p < 0.00) and IL-6 (IL-6) (p < 0.00) had the most significant group differences; IL-6 was higher after ITBI, whereas VCAM was lower. Using VCAM and IL-6 in classification algorithms, we could discriminate the groups with a sensitivity and specificity of 87% and 90%, respectively. The results suggest significant changes in the serum biomarker profile after mild ITBI. Future research is needed to determine whether these biomarkers can screen for brain injury in infants with nonspecific symptoms.

Extracting Grain Boundary and Surface Energy from Measurement of Triple Junction Geometry

Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials generates large sets of dihedral angles from which maps of the grain boundary energy may be extracted. A preliminary analysis has been performed for a sample of magnesia based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. We apply Herrings relation at each triple junction, based on the assumption of local equilibrium at the junction. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. Discretizing the misorientation and employing multiscale statistical analysis on large data sets allows (relative) grain boundary energy as a function of boundary character to be extracted from triple junction geometry. A similar analysis of thermal grooves allows the anisotropy of the surface energy to be measured in MgO.

Extracting the relative grain boundary free energy and mobility functions from the geometry of microstructures

This paper describes a method for extracting, from measurements of a polycrystal, the relative excess free energy and the relative mobility of the grain boundaries as functions of the crystallographic type (five degrees of freedom) and relevant thermodynamic variables. The method requires the simultaneous measurement of both the geometry and the crystallography of a large number of grain boundary intersections; the crystallographic information may be obtained from orientation imaging microscopy (OIM). For simplicity, the intersections will be assumed to be triple junctions (three intersecting boundaries). The energies and mobilities are obtained as ratios to respective standards that must be determined independently. In section 2, the authors review Herring`s equation relating the grain boundary energies at a triple junction to the intersection angles. In section 3 they present the equation connecting the mobilities. In section 4, the mathematical method will be illustrated for the energy case, using the simplifying assumption that the energy is independent of the grain boundary inclination and that the misorientation can be specified by one angle as in a fiber texture. The illustration comprises 1.3 {times} 10{sup 5} randomly generated triple junctions with an assumed hypothetical free energy function.

Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady state that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Mesoscale Simulation of Grain Growth

Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.

New insights into mathematical modeling of the immune system

In order to understand the integrated behavior of the immune system, there is no alternative to mathematical modeling. In addition, the advent of experimental tools such as gene arrays and proteomics poses new challenges to immunologists who are now faced with more information than can be readily incorporated into existing paradigms of immunity. We review here our ongoing efforts to develop mathematical models of immune responses to infectious disease, highlight a new modeling approach that is more accessible to immunologists, and describe new ways to analyze microarray data. These are collaborative studies between experimental immunologists, mathematicians, and computer scientists.

Towards a Statistical Theory of Texture Evolution in Polycrystals

Most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundary network play a crucial role in determining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing an arrangement of grains—a texture—that provides for a desired set of material properties. One of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening. Here we propose an upscaling procedure suitable for large complex systems. The procedure is based on numerical experimentation combined with stochastic tools and consists of large-scale numerical simulations of a system at a microscopic level, statistical analysis of the microscopic data, and formulation of the model based on stochastic characteristics predicted by the statistical analysis. This approach promises to be valuable in establishing the effective model of microstructural evolution in realistic two- and three-dimensional systems. To test ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one-dimensional network of grain boundaries. Despite the simplicity of its formulation, this model exhibits highly nontrivial behavior characterized by growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher-dimensional simulations. Here we focus on the grain deletion events which are common to all coarsening systems.

The Surface Energy of MgO: Multiscale Reconstruction from Thermal Groove Geometry

The surface energy of MgO is determined using experimental data collected from equilibrated thermal grooves circumscribing island grains. Local equilibrium assumptions at each groove require that the Herring equations be satisfied at each data site, thereby yielding a large and overdetermined system of equations involving the surface energy γ. This inverse problem is then solved using a new technique that is statistical in nature and multiscale in implementation. The resulting discrete solution represents a statistically significant representation of the surface energy of MgO as a function of surface orientation. Comparisons to results derived from a more traditional approach, along with suggested further applications, are discussed.

On the multigrid waveform relaxation method

The multigrid waveform relaxation method is an efficient method for solving certain classes of time-dependent partial differential equations (PDEs). This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier–Laplace analysis, practical convergence rate estimates of the multigrid waveform relaxation are obtained. Experimental results show that the analysis yields accurate performance prediction.

NUMERICAL ANALYSIS OF THE VERTEX MODELS FOR SIMULATING GRAIN BOUNDARY NETWORKS

Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics describe macroscopic properties. The formation of various statistical distributions is extremely complex and is strongly influenced by topological changes in the network. This work is an attempt to elucidate the role of these changes by conducting a thorough numerical investigation of one of the simplest types of grain growth simulation models, the vertex model. While having obvious limitations in terms of its ability to represent realistic systems, the vertex model enables full control over topological transitions and retains essential geometric features of the network. We formulate a self-consistent vertex model and investigate the role of microscopic parameters on mesoscale network behavior. This study sheds light on several important questions, such as how statistics are affected by the choice of temporal and spatial resolution and rules governing topological c...