

Preprint 90/2003
Efficient Computation of Lead Field Bases and Influence Matrix for the FEM-based EEG and MEG Inverse Problem. Part I: Complexity Considerations
Carsten H. Wolters, Lars Grasedyck, and Wolfgang Hackbusch
Contact the author: Please use for correspondence this email.
Submission date: 06. Nov. 2003
published in: Inverse problems, 20 (2004) 4, p. 1099-1116
DOI number (of the published article): 10.1088/0266-5611/20/4/007
Bibtex
with the following different title: Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem
Keywords and phrases: eeg/meg, algebraic multigrid method, source reconstruction, conductivity anisotropy and inhomogeneity, finite element method, inverse method, reciprocity, hierarchical matrices
Abstract:
The inverse problem in Electro- and Magneto-EncephaloGraphy (EEG/ MEG) aims at
reconstructing the underlying current distribution in the human brain using
potential differences and/or magnetic fluxes that are measured non-invasively
directly, or at a close distance, from the head surface. The simulation of EEG
and MEG fields for a given dipolar source in the brain using a volume-conduction
model of the head is called the forward problem. The Finite Element (FE) method,
used for the forward problem, is able to realistically model tissue conductivity
inhomogeneities and anisotropies, which is crucial for an accurate reconstruction
of the current distribution. So far, the computational complexity is quite large
when using the necessary high resolution FE models.
In this paper we will derive algorithms for the efficient computation
of EEG and MEG lead fields bases which exploit the fact that the
number of sensors is generally much smaller than the number of reasonable
dipolar sources.
The state-of-the-art forward approach will be speeded up by a factor
of more than 100 for a realistic choice of the number of
sensors and sources.
Our approaches can be applied to inverse reconstruction algorithms
in both continuous and discrete source parameter space for EEG and MEG.
In combination with algebraic multigrid solvers, the presented approach leads
to a highly efficient solution of FE-based source reconstruction problems.