instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
A new topological classifier for detecting the emergence of epileptic seizures

According to the World Health Organization (WHO), epilepsy is a chronic brain disorder characterized by recurrent seizures, which may vary from a brief lapse of attention or muscle jerks to severe and prolonged convulsions. The seizures are caused by sudden, usually brief, excessive electrical discharges in a group of brain cells (neurons). Unfortunately, to the best of our knowledge, monitoring the electrical activity of each single neuron is not feasible, but it is possible to capture the electrical activity of the whole brain (or of a part of it). Currently, the standard technique used to record the signals through the positioning of certain number of electrodes on the scalp, is the electroencephalogram (EEG), whose direct observation helps neurologists in diagnosing epilepsy; the use of methods for the automatic diagnosis is still far from be a reality. In the last decades several methods have been proposed in literature -- linear and non-linear analysis, applications of chaos theory and dynamical systems modelling, but none of them is suitable. The intrinsic non- linearity and the non-stationarity of EEG signals request for more suitable methods capable of extracting global information, both structural and functional, characterizing the brain cluster of neurons involved in the hyper-synchronous activity

In this talk we describe a method suitable to automatically classify EEG signals that record epileptic seizures from those recording the activity of an healthy brain. This step is very important and preliminary to reconstruct the abstract structural and functional components of the brain because it allows us to characterize the transition phase from an healthy to an epileptic state of the system. The proposed method uses the topological data analysis (TDA) combining two powerful instruments, persistent homology and persistent entropy measure for analysing the set of EEG signals and construct a topological classifier. The contribution of this work is twofold: from the one hand, we describe how the Persistent Entropy (PE for short) can be used to discriminate the epileptic state versus non epileptic states. From the other hand, we conjecture that the Vietoris-Rips filtration helps to understand which region plays the role of trigger for an epileptic seizure. 

(M. Rucco, M. Piangerelli and E. Merelli )