Hyperspherical manifold for EEG signals of epileptic seizures. (English) Zbl 1251.92025

Ahmad, Tahir; Ramachandran, Vinod

J. Appl. Math. 2012, Article ID 926358, 22 p. (2012).

Summary: 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 a priori 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 is then 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.

MSC:

92C55	Biomedical imaging and signal processing
92C50	Medical applications (general)
60A10	Probabilistic measure theory
60B99	Probability theory on algebraic and topological structures

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