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Einrichtungen >> Technische Fakultät (TF) >> Department Informatik (INF) >> Lehrstuhl für Informatik 10 (Systemsimulation) >>
Parallele Löser und effiziente Diskretisierungsmethoden für bioelektrische Feldberechnungen

The reconstruction of the bioelectric field in the human brain from non-invasive measurements like electroencephalographic recordings (EEG) has the potential to become a powerful tool in neurology.
From a mathematical point of view, the reconstruction can be considered as an inverse problem, which can be solved by repeated numerical simulations of the potential distribution, that we call forward problem, for assumed dipolar current sources in the brain.
The sources to be localized during the inverse problem and to be modeled in the forward problem are electrolytic currents within the dendrites of the large pyramidal cells of activated neurons in the cortex sheet of the human brain. The resulting primary current is generally formulated as a mathematical dipole.
In our project we are interested in the modelling of the mathematical dipoles and the efficient solution of the forward and inverse problem.
Prof. Dr. Ulrich Rüde

Prof. Dr.-Ing. Harald Köstler, Akad. Dir., Dr. rer. nat. Carsten Wolters

inverse problems; multigrid; singularities; bioelectric field problem

Laufzeit: 1.1.2006 - 31.12.2014

Köstler, Harald
Telefon +49 9131 85 28359, Fax +49 9131 85 28928, E-Mail: harald.koestler@fau.de
Köstler, Harald: An accurate multigrid solver for computing singular solutions of elliptic problems. In: The Center for Applied Scientific Computing-Lawrence ; Livermore National Laboratory ; Los Alamos National Laboratory ; Front Range Scientific Computations, Inc. (Veranst.) : Abstracts Of the 12th Copper Mountain Conference on Multigrid Methods (12th Copper Mountain Conference on Multigrid Method Copper Mountain 3.4.2005 -- 8.4.2005). 2005, S. 1-11.
Köstler, Harald: Extrapolation Techniques for Computing Accurate Solutions of Elliptic Problems with Singular Solutions.Vortrag: 12th Copper Mountain Conference on Multigrid Methods, Copper Mountain, 07.04.2005
Freundl, Christoph ; Köstler, Harald: Using ParExPDE for the numerical solution of bioelectric field problems. In: Hülsemann, Frank ; Kowarschik, Markus ; Rüde, Ulrich (Hrsg.) : 18th Symposium Simulationstechnique ASIM 2005 Proceedings (18th Symposium Simulationstechnique ASIM 2005 Erlangen 12.9. -15.9.2005). Erlangen : SCS Publishing House, 2005, S. 89-94. - ISBN 3-936150-41-9
Köstler, Harald ; Rüde, Ulrich: An accurate multigrid solver for computing singular solutions of elliptic problems. In: Numerical Linear Algebra with Applications 13 (2006), Nr. 2-3, S. 231-249
Mohr, Marcus ; Popa, Constantin ; Rüde, Ulrich: Analysis of a Preconditioned CG Method for an Inverse Bioelectric Field Problem. In: Ion, Stelian ; Marinoschi, Gabriela ; Popa, Constantin (Hrsg.) : Mathematical Modelling of Environmental and Life Sciences Problems (Proc. of 4th workshop, Sept 2005, Constanta, Romania) (4th Workshop on Mathematical Modelling of Environmental and Life Sciences Problems Constanta, Romania Sept 2005). Bukarest : Editura Academiei Romane, 2006, S. 135-146.
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