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dc.contributor.authorKybic, Jan
dc.contributor.authorClerc, Maureen
dc.contributor.authorAbboud, Toufic
dc.contributor.authorFaugeras, Olivier
dc.contributor.authorKeriven, Renaud
dc.contributor.authorPapadopoulo, Théo
dc.date.accessioned2012-02-23T08:44:52Z
dc.date.available2012-02-23T08:44:52Z
dc.date.issued2005-01
dc.identifier.citationKYBIC, J. - CLERC, M. - ABBOUD, T. - FAUGERAS, O. - KERIVEN, R. - et al.: A Common Formalism for the Integral Formulations of the Forward EEG Problem. IEEE Transactions on Medical Imaging. 2005, vol. 24, no. 1, p. 12-28. ISSN 0278-0062. DOI: 10.1109/TMI.2004.837363eng
dc.identifier.urihttp://hdl.handle.net/10467/9185
dc.description.abstractThe forward electroencephalography (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. 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.eng
dc.language.isocescze
dc.publisherIEEEcze
dc.rights© 2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.eng
dc.subjectBoundary Element Methodeng
dc.subjectPoisson equationeng
dc.subjectintegral methodeng
dc.subjectEEGeng
dc.titleA common formalism for the integral formulations of the forward EEG problemcze
dc.typečlánek z tištěného periodikacze
dc.identifier.doi10.1109/TMI.2004.837363
dc.identifier.doihttp://dx.doi.org/10.1109/TMI.2004.837363


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