| 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. | Projektleitung:
Prof. Dr. Ulrich Rüde
Beteiligte:
Prof. Dr.-Ing. Harald Köstler, Akad. Dir., Dr. rer. nat. Carsten Wolters
Stichwörter:
inverse problems; multigrid; singularities; bioelectric field problem
Laufzeit: 1.1.2006 - 31.12.2014
Kontakt:
Köstler, Harald
Telefon +49 9131 85 28359, Fax +49 9131 85 28928, E-Mail: harald.koestler@fau.de
| | Publikationen |
|---|
| 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. |
|