Journal of Applied Mathematics

Hyperspherical Manifold for EEG Signals of Epileptic Seizures

Tahir Ahmad and Vinod Ramachandran

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 926358, 22 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495232

Digital Object Identifier
doi:10.1155/2012/926358

Zentralblatt MATH identifier
1251.92025

Citation

Ahmad, Tahir; Ramachandran, Vinod. Hyperspherical Manifold for EEG Signals of Epileptic Seizures. J. Appl. Math. 2012 (2012), Article ID 926358, 22 pages. doi:10.1155/2012/926358. https://projecteuclid.org/euclid.jam/1355495232


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