A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation

Drechsler, Florian; Wolters, Carsten H.; Dierkes, Thomas; Si, Hang; Grasedyck, Lars

doi:10.1016/j.neuroimage.2009.02.024

Cited by 58 publications

(106 citation statements)

References 33 publications

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“…However, for realistic head modeling, numerical approximation methods are more and more frequently used such as the boundary element method (BEM) [Kybic et al, 2005], the finite difference method (FDM) [Hallez et al, 2005], the finite volume method (FVM) [Cook and Koles, 2006], or the finite element method (FEM). This article focuses on the FEM, which allows high accuracy in the numerical solution of elliptic partial differential equations since it is specifically tailored to the corresponding variational formulation and allows high flexibility in modeling the forward problem in geometrically complicated inhomogeneous and anisotropic head volume conductors [Bertrand et al, 1991;Buchner et al, 1997;Drechsler et al, 2009;Haueisen, 1996;Lew et al, 2009;Marin et al, 1998;Ramon et al, 2004;Schimpf et al, 2002;van den Broek et al, 1998;Wolters et al, 2006;Zhang et al, 2006]. The use of recently developed transfer matrix approaches [Gencer and Acar, 2004;Weinstein et al, 2000;Wolters et al, 2004] or reciprocity approaches [Hallez et al, 2005; and advances in efficient FEM solver techniques for source analysis [Lew et al, 2009] drastically reduced the time complexity of the computations.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity of beamformer source analysis to deficiencies in forward modeling

Steinsträter

Sillekens

Junghöfer

et al. 2010

Human Brain Mapping

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Beamforming approaches have recently been developed for the field of electroencephalography (EEG) and magnetoencephalography (MEG) source analysis and opened up new applications within various fields of neuroscience. While the number of beamformer applications thus increases fast-paced, fundamental methodological considerations, especially the dependence of beamformer performance on leadfield accuracy, is still quite unclear. In this article, we present a systematic study on the influence of improper volume conductor modeling on the source reconstruction performance of an EEG-data based synthetic aperture magnetometry (SAM) beamforming approach. A finite element model of a human head is derived from multimodal MR images and serves as a realistic volume conductor model. By means of a theoretical analysis followed by a series of computer simulations insight is gained into beamformer performance with respect to reconstruction errors in peak location, peak amplitude, and peak width resulting from geometry and anisotropy volume conductor misspecifications, sensor noise, and insufficient sensor coverage. We conclude that depending on source position, sensor coverage, and accuracy of the volume conductor model, localization errors up to several centimeters must be expected. As we could show that the beamformer tries to find the best fitting leadfield (least squares) with respect to its scanning space, this result can be generalized to other localization methods. More specific, amplitude, and width of the beamformer peaks significantly depend on the interaction between noise and accuracy of the volume conductor model. The beamformer can strongly profit from a high signal-to-noise ratio, but this requires a sufficiently realistic volume conductor model.

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Section: Introductionmentioning

confidence: 99%

Sensitivity of beamformer source analysis to deficiencies in forward modeling

Steinsträter

Sillekens

Junghöfer

et al. 2010

Human Brain Mapping

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“…The source term in both following approaches, i.e., in section 2.2 the partial integration approach [17] and in section 2.4 the adjoint approach [18], is assumed to be a square-integrable function on the head domain Ω, i.e., it is assumed to be in the Sobolev space 16], so that the right-hand side of the PDE in equation (1), i.e., the divergence of a dipole, loses even one more degree of regularity and is thus only in the Sobolev space…”

Section: Eeg Forward Problemmentioning

confidence: 99%

“…Constrained Delaunay tetrahedralization FE approach: Tetrahedral FE meshes of the four layer sphere model are generated using the software TetGen [34] 170 which uses a constrained Delaunay tetrahedralization (CDT) approach [35,36]. Using models generated with this approach, EEG source analysis was performed [25,16]. The meshing procedure starts with the preparation of a suitable boundary discretization of the model.…”

Section: Fem Mesh Generationmentioning

confidence: 99%

“…In the literature, tetrahedral [5,14] as well as regular hexahedral [10,11,7] 35 FE approaches have been used for tCS modeling. Constrained Delaunay tetrahedralizations (CDT) from given tissue surface representations [15,16] have the advantage that smooth tissue surfaces are well represented in the model, while on the other side, the generation of such models is difficult in practice and might lead to unrealistic model features. For example, holes in tissue com-40 partments such as the foramen magnum and the optic canals in the skull are often artificially closed to allow CDT meshing.…”

Section: Introductionmentioning

confidence: 99%

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Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

et al. 2016

Self Cite

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To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less Preprint submitted to NeuroImage April 4, 2016 flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45 degrees and a factor of 1.66, respectively.2

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“…However, with a FEM discretization, the punctual source introduces a numerical singularity which impacts on both the accuracy and the performance of the FEM forward solution. The direct method, subtraction method and saint Venant's method [4,5,7,9,10,14,15,20] are three approaches which can be used to improve the behavior of the FEM in this context. In the literatures, several studies investigate and compare the accuracy of these methods [9,10,[14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Fem Method for the Eeg Forward Problem and Improvement Based on Modification of the Saint Venant's Method

Medani¹,

Lautru²,

Schwartz³

et al. 2015

PIER

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Abstract-The finite-element method (FEM) is applied to solve the EEG forward problem. Two issues related to the implementation of this method are investigated. The first is the singularity due to the punctual dipole sources and the second is the numerical errors observed near the interface of different tissues. To deal with the singularity of the punctual dipole sources, three source modeling methods, namely, the direct, the subtraction and the Saint Venant's methods, are examined. To solve the problem of numerical instability near the interface of different tissues, a modification on the Saint Venant's method is introduced. The numerical results are compared with analytical solution in the case of the multilayer spherical head models. The advantages of the proposed method are highlighted.

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A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation

Cited by 58 publications

References 33 publications

Sensitivity of beamformer source analysis to deficiencies in forward modeling

Sensitivity of beamformer source analysis to deficiencies in forward modeling

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

Fem Method for the Eeg Forward Problem and Improvement Based on Modification of the Saint Venant's Method

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