Hyperspherical Manifold for EEG Signals of Epileptic Seizures
The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst m...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/926358 |
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| _version_ | 1832563542465708032 |
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| author | Tahir Ahmad Vinod Ramachandran |
| author_facet | Tahir Ahmad Vinod Ramachandran |
| author_sort | Tahir Ahmad |
| collection | DOAJ |
| description | The mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling. |
| format | Article |
| id | doaj-art-1502184cd2944b22bea676c1072611a3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1502184cd2944b22bea676c1072611a32025-02-03T01:13:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/926358926358Hyperspherical Manifold for EEG Signals of Epileptic SeizuresTahir Ahmad0Vinod Ramachandran1Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 Skudai, Johor, MalaysiaIbnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia, 81310 Skudai, Johor, MalaysiaThe mathematical modelling of EEG signals of epileptic seizures presents a challenge as seizure data is erratic, often with no visible trend. Limitations in existing models indicate a need for a generalized model that can be used to analyze seizures without the need for apriori information, whilst minimizing the loss of signal data due to smoothing. This paper utilizes measure theory to design a discrete probability measure that reformats EEG data without altering its geometric structure. An analysis of EEG data from three patients experiencing epileptic seizures is made using the developed measure, resulting in successful identification of increased potential difference in portions of the brain that correspond to physical symptoms demonstrated by the patients. A mapping then is devised to transport the measure data onto the surface of a high-dimensional manifold, enabling the analysis of seizures using directional statistics and manifold theory. The subset of seizure signals on the manifold is shown to be a topological space, verifying Ahmad's approach to use topological modelling.http://dx.doi.org/10.1155/2012/926358 |
| spellingShingle | Tahir Ahmad Vinod Ramachandran Hyperspherical Manifold for EEG Signals of Epileptic Seizures Journal of Applied Mathematics |
| title | Hyperspherical Manifold for EEG Signals of Epileptic Seizures |
| title_full | Hyperspherical Manifold for EEG Signals of Epileptic Seizures |
| title_fullStr | Hyperspherical Manifold for EEG Signals of Epileptic Seizures |
| title_full_unstemmed | Hyperspherical Manifold for EEG Signals of Epileptic Seizures |
| title_short | Hyperspherical Manifold for EEG Signals of Epileptic Seizures |
| title_sort | hyperspherical manifold for eeg signals of epileptic seizures |
| url | http://dx.doi.org/10.1155/2012/926358 |
| work_keys_str_mv | AT tahirahmad hypersphericalmanifoldforeegsignalsofepilepticseizures AT vinodramachandran hypersphericalmanifoldforeegsignalsofepilepticseizures |