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Multivariate Matching Pursuit Decomposition and Normalized Gabor Entropy for Quantification of Preictal Trends in Epilepsy

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Mathematics and Statistics Department, Louisiana Tech University, Ruston, LA 71272, USA
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Biomedical Engineering Department, Louisiana Tech University, Ruston, LA 71272, USA
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(6), 419; https://doi.org/10.3390/e20060419
Received: 1 April 2018 / Revised: 20 May 2018 / Accepted: 26 May 2018 / Published: 31 May 2018
(This article belongs to the Special Issue Entropy in Signal Analysis)
Quantification of the complexity of signals recorded concurrently from multivariate systems, such as the brain, plays an important role in the study and characterization of their state and state transitions. Multivariate analysis of the electroencephalographic signals (EEG) over time is conceptually most promising in unveiling the global dynamics of dynamical brain disorders such as epilepsy. We employed a novel methodology to study the global complexity of the epileptic brain en route to seizures. The developed measures of complexity were based on Multivariate Matching Pursuit (MMP) decomposition of signals in terms of time–frequency Gabor functions (atoms) and Shannon entropy. The measures were first validated on simulation data (Lorenz system) and then applied to EEGs from preictal (before seizure onsets) periods, recorded by intracranial electrodes from eight patients with temporal lobe epilepsy and a total of 42 seizures, in search of global trends of complexity before seizures onset. Out of five Gabor measures of complexity we tested, we found that our newly defined measure, the normalized Gabor entropy (NGE), was able to detect statistically significant (p < 0.05) nonlinear trends of the mean global complexity across all patients over 1 h periods prior to seizures’ onset. These trends pointed to a slow decrease of the epileptic brain’s global complexity over time accompanied by an increase of the variance of complexity closer to seizure onsets. These results show that the global complexity of the epileptic brain decreases at least 1 h prior to seizures and imply that the employed methodology and measures could be useful in identifying different brain states, monitoring of seizure susceptibility over time, and potentially in seizure prediction. View Full-Text
Keywords: Multivariate Matching Pursuit; Gabor entropy; complexity; Lorenz system; epilepsy Multivariate Matching Pursuit; Gabor entropy; complexity; Lorenz system; epilepsy
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Liu, R.; Karumuri, B.; Adkinson, J.; Hutson, T.N.; Vlachos, I.; Iasemidis, L. Multivariate Matching Pursuit Decomposition and Normalized Gabor Entropy for Quantification of Preictal Trends in Epilepsy. Entropy 2018, 20, 419.

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