90 research outputs found
Research in Applied Mathematics, Fluid Mechanics and Computer Science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999
Review on solving the forward problem in EEG source analysis
Background. The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods. While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results. It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method. Conclusion. Solving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.peer-reviewe
Institute for Computational Mechanics in Propulsion (ICOMP)
The Institute for Computational Mechanics in Propulsion (ICOMP) is operated by the Ohio Aerospace Institute (OAI) and the NASA Lewis Research Center in Cleveland, Ohio. The purpose of ICOMP is to develop techniques to improve problem-solving capabilities in all aspects of computational mechanics related to propulsion. This report describes the accomplishments and activities at ICOMP during 1993
[Activity of Institute for Computer Applications in Science and Engineering]
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science
Topological photonics by breaking the degeneracy of line node singularities in semimetal-like photonic crystals
Degeneracy is an omnipresent phenomenon in various physical systems, which
has its roots in the preservation of geometrical symmetry. In electronic and
photonic crystal systems, very often this degeneracy can be broken by virtue of
strong interactions between photonic modes of the same energy, where the level
repulsion and the hybridization between modes causes the emergence of photonic
bandgaps. However, most often this phenomenon does not lead to a complete and
inverted bandgap formation over the entire Brillouin zone. Here, by
systematically breaking the symmetry of a two-dimensional square photonic
crystal, we investigate the formation of Dirac points, line node singularities,
and inverted bandgaps. The formation of this complete bandgap is due to the
level repulsion between degenerate modes along the line nodes of a
semimetal-like photonic crystal, over the entire Brillouin zone. Our numerical
experimentations are performed by a home-build numerical framework based on a
multigrid finite element method. The developed numerical toolbox and our
observations pave the way towards designing complete bandgap photonic crystals
and exploring the role of symmetry on the optical behaviour of even more
complicated orders in photonic crystal systems
[Research activities in applied mathematics, fluid mechanics, and computer science]
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995
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