Representation of bioelectric current sources using Whitney elements in the finite element method

Tanzer, İhsan Oğuz; Järvenpää, Seppo; Nenonen, Jukka; Somersalo, Erkki

doi:10.1088/0031-9155/50/13/004

Cited by 26 publications

(19 citation statements)

References 28 publications

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“…A rationale for this effect has been given in [60,25]. In future work, we are therefore planning to adapt other source modeling approaches such as the Venant [47,43,18,59,52], the partial integration [61,54,59,48,52], or the Whitney approach [46,35,36] to the DG-FEM framework. Until now, these have been formulated and evaluated only for the CG-FEM.…”

Section: Discussionmentioning

confidence: 99%

A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach

Engwer¹,

Vorwerk²,

Ludewig³

et al. 2017

SIAM J. Sci. Comput.

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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.

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Section: Discussionmentioning

confidence: 99%

A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach

Engwer¹,

Vorwerk²,

Ludewig³

et al. 2017

SIAM J. Sci. Comput.

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“…This combination yields a simple model of synthetic dipoles (Bauer et al, 2015; Pursiainen et al, 2011; Pursiainen, 2012; Tanzer et al, 2005) with dipole moment and position determined by

{\vec{q}}_{w} = \frac{{\vec{r}}_{P_{j}} - {\vec{r}}_{P_{i}}}{‖ {\overset{italicr}{true}}_{{italicP}_{italicj}} - {\overset{italicr}{true}}_{{italicP}_{italici}} ‖} a n d {\vec{r}}_{w} = \frac{1}{2} ({\vec{r}}_{P_{j}} + {\vec{r}}_{P_{i}}),

…”

Section: Methodsmentioning

confidence: 99%

Forward and inverse effects of the complete electrode model in neonatal EEG

Pursiainen

Lew

Wolters

2017

Journal of Neurophysiology

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The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.

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“…The primary sources are electrolytic currents within the dendrites of the large pyramidal cells of activated neurons in the human cortex. Even if there are also smoother models [33], most often the primary sources are formulated as a mathematical point current dipole [25,6,18]. The finite element (FE) method is often used for the solution of the forward problem, because it allows for a realistic representation of the complicated head volume conductor with its tissue conductivity inhomogeneities and anisotropies [45,3,1,34,4,15,19,37,26,39,7].…”

Section: Introductionmentioning

confidence: 99%

Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis

Lew

Wolters

Dierkes

et al. 2009

Applied Numerical Mathematics

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Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem.In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine.

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Representation of bioelectric current sources using Whitney elements in the finite element method

Cited by 26 publications

References 28 publications

A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach

A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach

Forward and inverse effects of the complete electrode model in neonatal EEG

Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis

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