3 research outputs found
The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem
Objective: The purpose of this study is to introduce and evaluate the
unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the
electroencephalography (EEG) forward problem. Methods: This new approach for
source analysis does not use a geometry conforming volume triangulation, but
instead uses a structured mesh that does not resolve the geometry. The geometry
is described using level set functions and is incorporated implicitly in its
mathematical formulation. As no triangulation is necessary, the complexity of a
simulation pipeline and the need for manual interaction for patient specific
simulations can be reduced and is comparable with that of the FEM for
hexahedral meshes. In addition, it maintains conservation laws on a discrete
level. Here, we present the theory for UDG-FEM forward modeling, its
verification using quasi-analytical solutions in multi-layer sphere models and
an evaluation in a comparison with a discontinuous Galerkin (DG-FEM) method on
hexahedral and on conforming tetrahedral meshes. We furthermore apply the
UDG-FEM forward approach in a realistic head model simulation study. Results:
The given results show convergence and indicate a good overall accuracy of the
UDG-FEM approach. UDG-FEM performs comparable or even better than DG-FEM on a
conforming tetrahedral mesh while providing a less complex simulation pipeline.
When compared to DG-FEM on hexahedral meshes, an overall better accuracy is
achieved. Conclusion: The UDG-FEM approach is an accurate, flexible and
promising method to solve the EEG forward problem. Significance: This study
shows the first application of the UDG-FEM approach to the EEG forward problem.Comment: This work has been submitted to the IEEE for possible publication.
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A discontinuous Galerkin Method for the EEG Forward Problem using the Subtraction Approach
In order to perform electroencephalography (EEG) source reconstruction, i.e.,
to localize the sources underlying a measured EEG, the electric potential
distribution at the electrodes generated by a dipolar current source in the
brain has to be simulated, which is the so-called EEG forward problem. To solve
it accurately, it is necessary to apply numerical methods that are able to take
the individual geometry and conductivity distribution of the subject's head
into account. In this context, the finite element method (FEM) has shown high
numerical accuracy with the possibility to model complex geometries and
conductive features, e.g., white matter conductivity anisotropy. In this
article, we introduce and analyze the application of a discontinuous Galerkin
(DG) method, a finite element method that includes features of the finite
volume framework, to the EEG forward problem. The DG-FEM approach fulfills the
conservation property of electric charge also in the discrete case, making it
attractive for a variety of applications. Furthermore, as we show, this
approach can alleviate modeling inaccuracies that might occur in head
geometries when using classical FE methods, e.g., so-called "skull leakage
effects", which may occur in areas where the thickness of the skull is in the
range of the mesh resolution. Therefore, we derive a DG formulation of the FEM
subtraction approach for the EEG forward problem and present numerical results
that highlight the advantageous features and the potential benefits of the
proposed approach
Conditionally Gaussian Hypermodels for Cerebral Source Localization
Bayesian modeling and analysis of the MEG and EEG modalities provide a
flexible framework for introducing prior information complementary to the
measured data. This prior information is often qualitative in nature, making
the translation of the available information into a computational model a
challenging task. We propose a generalized gamma family of hyperpriors which
allows the impressed currents to be focal and we advocate a fast and efficient
iterative algorithm, the Iterative Alternating Sequential (IAS) algorithm for
computing maximum a posteriori (MAP) estimates. Furthermore, we show that for
particular choices of the scalar parameters specifying the hyperprior, the
algorithm effectively approximates popular regularization strategies such as
the Minimum Current Estimate and the Minimum Support Estimate. The connection
between priorconditioning and adaptive regularization methods is also pointed
out. The posterior densities are explored by means of a Markov Chain Monte
Carlo (MCMC) strategy suitable for this family of hypermodels. The computed
experiments suggest that the known preference of regularization methods for
superficial sources over deep sources is a property of the MAP estimators only,
and that estimation of the posterior mean in the hierarchical model is better
adapted for localizing deep sources.Comment: 30 page