Forward problem solution of electromagnetic source imaging using a new BEM formulation with high-order elements

Gençer, N.G.; Tanzer, İhsan Oğuz

doi:10.1088/0031-9155/44/9/314

Cited by 37 publications

(30 citation statements)

References 30 publications

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“…There is a large body of literature describing BEM implementations using the double-layer potential formulation for forward and inverse EEG problems [8,12,[18][19][20][21][22].…”

Section: G Existing Workmentioning

confidence: 99%

“…Triangulation is used in the vast majority of cases. Higher-order surface elements [22] are rarely used for the EEG problem, despite their potential to improve the modeling accuracy, because of the lack of algorithms to generate curved meshes from the available data (mostly volumes of anatomical MRI [27,28]). As a triangulated surface is not regular, some caution is needed in the application of the continuous equations derived above (cf Appendix D).…”

Section: A Discretization Of the Boundariesmentioning

confidence: 99%

“…, N . This set of equations can be expressed more concisely in matrix form The matrix A should be truncated 4 like in (22), to account for the zero conductivity σ N +1 = 0.…”

Section: G Symmetric Approachmentioning

confidence: 99%

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A common formalism for the Integral formulations of the forward EEG problem

Kybic

Clerc

Abboud

et al. 2005

IEEE Trans. Med. Imaging

393

334

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Abstract-The forward electro-encephalography (EEG) problem involves finding a potential V from the Poisson equation ∇ · (σ∇V ) = f , in which f represents electrical sources in the brain, and σ the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the Boundary Element Method (BEM) using a suitable integral formulation. Most previous work uses the same integral formulation, corresponding to a double-layer potential. In this article we present a conceptual framework based on a well-known theorem (Theorem 1) that characterizes harmonic functions defined on the complement of a bounded smooth surface. This theorem says that such harmonic functions are completely defined by their values and those of their normal derivatives on this surface. It allows us to cast the previous BEM approaches in a unified setting and to develop two new approaches corresponding to different ways of exploiting the same theorem. Specifically, we first present a dual approach which involves a single-layer potential. Then, we propose a symmetric formulation, which combines single and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a spherical geometry with known analytical solution, and the symmetric formulation achieves a significantly higher accuracy than the alternative methods. Additionally, we present results with realistically shaped meshes. Beside providing a better understanding of the foundations of BEM methods, our approach appears to lead also to more efficient algorithms.

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“…There is a large body of literature describing BEM implementations using the double-layer potential formulation for forward and inverse EEG problems [8,12,[18][19][20][21][22].…”

Section: G Existing Workmentioning

confidence: 99%

Section: A Discretization Of the Boundariesmentioning

confidence: 99%

See 1 more Smart Citation

A common formalism for the Integral formulations of the forward EEG problem

Kybic

Clerc

Abboud

et al. 2005

IEEE Trans. Med. Imaging

393

334

View full text Add to dashboard Cite

show abstract

“…Each row of A is calculated by visiting all elements of the mesh for surface integration. On each element, the surface integral is approximated by a weighted sum of potentials at the Gauss-Legendre quadrature points [12,21]. For elements close to the field node, recursive integration [17] is used for better accuracy.…”

Section: Accelerated Bem For Eegmentioning

confidence: 99%

Parallel implementation of the accelerated BEM approach for EMSI of the human brain

Ataseven

Akalin-Acar

Acar

et al. 2008

Med Biol Eng Comput

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Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable values. This is achieved using a parallel cluster of personal computers on a local area network. We used eight workstations and implemented a parallel version of the accelerated BEM approach that distributes the computation and the BEM matrix efficiently to the processors. The performance of the solver is evaluated in terms of the CPU operations and memory usage for different number of processors. Once the transfer matrix is computed, for a 12,294 node mesh, a single FP solution takes 676 ms on a single processor and 72 ms on eight processors. It was observed that workstation clusters are cost effective tools for solving the complex BEM models in a clinically acceptable time.

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“…Meshes created for cortex, white matter, scalp and skull meshes are presented. The BEM formulation [9] which employs triangular, quadratic, isoparametric elements will be used to solve the forward problem of EMSI.…”

Section: Introductionmentioning

confidence: 99%

Development of realistic head models for electromagnetic source imaging of the human brain

Akahn

Acar

Gençer

2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-In this work, a methodology is developed to solve the forward problem of electromagnetic source imaging using realistic head models. For this purpose, first segmentation of the 3 dimensional MR head images is performed. Then triangular, quadratic meshes are formed for the interfaces of the tissues. Thus, realistic meshes, representing scalp, skull, CSF, brain and eye tissues, are formed. At least 2000 nodes for the scalp and 5000 for the cortex are needed to obtain reasonable geometrical approximation. Solution of the forward problem using our previous Boundary Element Method (BEM) formulation with quadratic elements remains to be made.Keywords -BEM, realistic head model, segmentation, mesh generation. I. INTRODUCTIONElectrical activities of the human brain due to body functions can be measured with electrodes placed on the scalp (EEG) and with magnetic sensors (MEG) placed near the scalp surface. The representation of electrical activity of the brain using electrical and magnetic measurements is called electromagnetic source imaging (EMSI). The source of an electrical activity is usually modeled by electrical dipoles and the purpose of EMSI is to obtain information about the spatiotemporal behavior of these dipoles. An essential part of obtaining EMSIs is the solution of the electric and magnetic fields (the forward problem) for a given dipoleassuming a head model. The solution of the inverse problem (i.e., given the measured data, finding the location and direction of dipoles) is based on the comparison of the measured and calculated fields. To increase accuracy in EMSIs, the human head must be modeled accurately. The purpose of this study is twofold: 1) to obtain an accurate head model, 2) to solve the forward problem of EMSI for this model.In the earliest studies, head models with simple geometries having analytical solutions for a dipole inside the conductor model were used. The simplest head model is the homogeneous sphere. Other homogenous head models that may represent the head shape are prolate spheroid (eggshape). In order to represent layers like skull, scalp and cerebrospinal fluid (CSF), concentric and eccentric spheres models were used. Such models also have analytical solutions for a dipole inside conductor model [1]. . Thereafter a coarsening algorithm is used to represent the tissues with less number of triangles [7]. Finally, the resulting mesh is corrected topologically [8]. Up to this step linear elements are used. After obtaining the coarse mesh, the elements are converted to quadratic elements using the original segmentation data.In this study, the segmentation and mesh generation algorithms are explained. Meshes created for cortex, white matter, scalp and skull meshes are presented. The BEM formulation [9] which employs triangular, quadratic, isoparametric elements will be used to solve the forward problem of EMSI. II. SEGMENTATIONSegmentation is a process of classifying elements having the same properties in one group. In this work, segmentation of scalp, skull, CSF, eyes, gray m...

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Forward problem solution of electromagnetic source imaging using a new BEM formulation with high-order elements

Cited by 37 publications

References 30 publications

A common formalism for the Integral formulations of the forward EEG problem

A common formalism for the Integral formulations of the forward EEG problem

Parallel implementation of the accelerated BEM approach for EMSI of the human brain

Development of realistic head models for electromagnetic source imaging of the human brain

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