Kentucky-Austria International Cooperative Research
Applications
Analysis of Noninvasive Brain Scanning
Douglas, Haase, LodderResearch Issues. About 600,000 Americans suffer a stroke each year and 160,000 of them die. Stroke is the third leading cause of death and a major cause of severe, long-term disability. Studies indicate that oxidative stress and the inflammatory cascade, working together, are important in the pathogenetic cascade of neurodegeneration in stroke, suggesting that therapeutic efforts aimed at both of these mechanisms may be beneficial. Hyperbaric oxygen (HBO) is a model of oxidative stress. HBO administration produces many similar oxidative and inflammatory effects in the brain. O2 at high pressures acts as aneurotoxic agent leading to convulsions. The mechanism of this neurotoxicity is not known; however, oxygen free radicals and nitric oxide (NO) have been suggested as contributors. Therapeutic efforts are complicated by the lack of a good, noninvasive analytical method for assaying the effects of oxidative stress and the inflammatory cascade in vivo. Near-infrared spectrometry has been used successfully to monitor cerebral oxygenation, oxidative processes and inflammation in the brain in vivo and in vitro. Studies currently underway test the hypothesis that a computer algorithm can determine duration of HBO exposure using hyperspectral sensor data from the brain, free from significant interferences from whole blood, sample temperature, positioning of probe, and hair.
Related Research. Aneurysm, a source of stroke and subsequent brain damage, has been studied using NIR spectrometry and chemometrics. Atherosclerotic plaque that can lead to ischemic stroke has also been studied. Intermittent carotid occlusion has been used to create ischemia- reperfusion injury in whole gerbil brains while the NIR spectrum of the brain was monitored in vivo.
Research Approach. Using wire wrapped, self constructed MAReNIR scanners, we generate a large number (100's) of high resolution JPEG images. Data must be extended from the images. A correlation matrix is formed from the vectors extracted (based on particular frequencies of interest). The largest 15-20 moments (or from clusters of nearly identical moments) are determined. A nice feature of the problem is that exactness is unnecessary. Hence, getting close to the moment values is good enough. Once the moments are determined, we can evaluate if an emergency HBO situation is developing and offer a warning. We are trying to develop cost effective algorithms and codes on parallel machines to do the moments' calculation and evaluation in 15-20 wall clock seconds after the JPEG images become available for use.
Electromagnetics
Langer, LodderResearch Issues. The Linz group has developed the codes NGSolve and FEPP for solving the 3D Maxwell equations in the magnetostatic and the eddy current cases. The former code is a parallel code, the latter is a serial one. In order to develop efficient numerical methods for the electromagnetic scattering it is extremely important to have fast solvers for the time- harmonic Maxwell equations. The coupling of finite element method with the boundary element method BEM) is highly desirable. The development of efficient parallel algebraic multigrid solvers for Maxwell equations is an interesting research issue. The first version of an AMG for edge finite element schemes arising from the approximation of Maxwell's equations were derived by the Linz group and implemented in the parallel AMG package PEBBLES.
Related Research. Transmission-mode near-field scanning microscopes (NSM) in the near- infrared and microwave spectral regions are being modeled to provide understanding of near- field optics and imaging. Near-field spectrometric imaging involves the electromagnetic scattering characteristics of objects illuminated by the near field of a sub-wavelength-sized aperture. In this project, some unusual phenomena are being investigated, including a near- field focusing effect, as well as an impedance-based image-shape effect. Two computational models have been used to characterize NSMs; moment-method and finite-difference time- domain models. These two models are being applied to the analysis of the NSM for various configurations, and experimental near-field imaging measurements are compared with numerical predictions.
Research Approach. We are going to develop a coupled boundary and finite element tearing and interconnecting method for the Maxwell equations. This development should result in an highly efficient, fast and robust Maxwell solver that can be used in electromagnetic scattering.
Ocean Simulation
Douglas, Haase, ZulehnerResearch Issues. Ocean simulation is needed in various application fields as climate modeling, long-term weather forecast and contamination distribution. Although the basic equations are well known the complexity of them is still too high. Therefore, some simplifications have to be made in order to derive models that can be handled on computers nowadays. The ocean model and its spectral element discretization by Iskandarani and Haidevogel leads to Stokes problems, i.e., a special case of the saddle point problems in each time step of the time discretization. The efficient parallel solution of the time dependent huge problem is still a challenge that requires modern mathematical techniques as well as experience in the efficient realization on supercomputers.
Related Research. Douglas and Haase accelerated the ocean simulation code by Iskandarani during the last 3 years by a factor of three. The gain in performance has been achieved by using alternating Schwarz method (ASM) type preconditioners for the huge system of equations. This code realizes the 3D structure of the ocean by several stacked 2D layers plus some additional coupling terms. Iskandarani discussed with Haase the scheme for a full 3D ocean simulation based on (large) 3D spectral elements during his visit in Linz in November, 2002.
Research Approach. We plan three research activities in the ocean simulation. First, the ASM preconditioner in the stacked 2D layer model has to be improved by a adding an appropriate coarse global mesh to it. This will avoid the sensitivity of the preconditioner with respect to the chosen time step in the time discretization. As a result larger time steps are admissible and therefore less computations are necessary in sum. The second improvement contains a redesign of the ocean simulation code from an explicit to an implicit time discretization scheme which allows much larger time steps. Here, the solver for the systems of equations in each time step has to bere designed and the results from the saddle point problems will be used therein. The real 3D ocean simulation is the third activity. The 3D simulation require completely new 3D preconditioners for the high order 3D spectral elements and here we have to combine solution methods for saddle point problems with domain decomposition methods for higher order elements. Clearly, all the improvement have to be realized on parallel supercomputers.
Virtual Mouse
Douglas, Lodder, HaaseResearch Issues. How do you simulate an entire creature on the metabolic scale? Being able to predict how certain classes of mice react will be a novel and groundbreaking new method for drug discovery.
Related Research. The Virtual Cell project at the University of Connecticut Medical Center is producing a database of known reactions at the cellular level. We can use the database instead of computing similar reactions. In the long term, we would like all calculations at the grid nodes to be database lookups.
Research Approach. A very large grid will be laid over the physical domain of a mouse. At each grid node is a chemical reaction that can be simulated using a program like Gaussian or NWChem unless the reaction is already known and in a database. Between nodes is a simple heat and mass transfer problem that is solved between time steps. A multiscale (or multigrid) approach will significantly speed up the calculations.
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