Parallele Löser und effiziente Diskretisierungsmethoden für bioelektrische Feldberechnungen

Internally funded project


Project Details

Project leader:
Prof. Dr. Ulrich Rüde

Project members:
Prof. Dr. Harald Köstler

Contributing FAU Organisations:
Lehrstuhl für Informatik 10 (Systemsimulation)
Technische Fakultät

Start date: 01/01/2006
End date: 31/12/2014


Abstract (technical / expert description):

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.


Publications

Köstler, H., & Rüde, U. (2006). An accurate multigrid solver for computing singular solutions of elliptic problems. Numerical Linear Algebra With Applications, 13(2-3), 231-249. https://dx.doi.org/10.1002/nla.478
Mohr, M., Popa, C., & Rüde, U. (2006). Analysis of a Preconditioned CG Method for an Inverse Bioelectric Field Problem. In Mathematical Modelling of Environmental and Life Sciences Problems (Proc. of 4th workshop, Sept 2005, Constanta, Romania) (pp. 135-146). Constanta, Romania, RO: Bukarest: Editura Academiei Romane.
Köstler, H. (2005). An accurate multigrid solver for computing singular solutions of elliptic problems. In Abstracts Of the 12th Copper Mountain Conference on Multigrid Methods (pp. 1-11). Copper Mountain.
Freundl, C., & Köstler, H. (2005). Using ParExPDE for the numerical solution of bioelectric field problems. In 18th Symposium Simulationstechnique ASIM 2005 Proceedings (pp. 89-94). Erlangen: Erlangen: SCS Publishing House.
Köstler, H., & Rüde, U. (2004). Extrapolation Techniques for Computing Accurate Solutions of Elliptic Problems with Singular Solutions. In Computational Science - ICCS 2004 (pp. 410-417). Krakau: Berlin: Springer-Verlag.

Last updated on 2019-19-03 at 13:50