On the Inverse EEG Problem for a 1D Current Distribution
Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which live...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/715785 |
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| _version_ | 1832547491038363648 |
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| author | George Dassios George Fragoyiannis Konstantia Satrazemi |
| author_facet | George Dassios George Fragoyiannis Konstantia Satrazemi |
| author_sort | George Dassios |
| collection | DOAJ |
| description | Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases. |
| format | Article |
| id | doaj-art-2a83f123dfd74edf9b42e20b48957388 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2a83f123dfd74edf9b42e20b489573882025-02-03T06:44:32ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/715785715785On the Inverse EEG Problem for a 1D Current DistributionGeorge Dassios0George Fragoyiannis1Konstantia Satrazemi2Department of Chemical Engineering, University of Patras and ICE/HT-FORTH, Patras, GreeceDepartment of Chemical Engineering, University of Patras and ICE/HT-FORTH, Patras, GreeceDepartment of Chemical Engineering, University of Patras and ICE/HT-FORTH, Patras, GreeceAlbanese and Monk (2006) have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.http://dx.doi.org/10.1155/2014/715785 |
| spellingShingle | George Dassios George Fragoyiannis Konstantia Satrazemi On the Inverse EEG Problem for a 1D Current Distribution Journal of Applied Mathematics |
| title | On the Inverse EEG Problem for a 1D Current Distribution |
| title_full | On the Inverse EEG Problem for a 1D Current Distribution |
| title_fullStr | On the Inverse EEG Problem for a 1D Current Distribution |
| title_full_unstemmed | On the Inverse EEG Problem for a 1D Current Distribution |
| title_short | On the Inverse EEG Problem for a 1D Current Distribution |
| title_sort | on the inverse eeg problem for a 1d current distribution |
| url | http://dx.doi.org/10.1155/2014/715785 |
| work_keys_str_mv | AT georgedassios ontheinverseeegproblemfora1dcurrentdistribution AT georgefragoyiannis ontheinverseeegproblemfora1dcurrentdistribution AT konstantiasatrazemi ontheinverseeegproblemfora1dcurrentdistribution |