Dynamic epileptic activity analysis based on geometric structure of electroencephalographic signals

Abstract

Epilepsy is a chronic brain disorder that affects people all over the world. It is characterized by recurring seizures which are caused by sudden and brief excessive electrical discharges in the brain. Epileptic seizures are notoriously difficult to model due to their erratic behavior and limited availability of clean data to work with. In this research, an emulated probability measure called the Delia measure is developed to normalize raw EEG data before being mapped to the surface of a unit hypersphere and modeled using a von-Mises Fisher distribution. By computing the parameters for the distribution using genetic algorithms, it is determined that seizures can be sorted in order of their spread, which is an indicator of seizure violence. The Delia measure values are also used in conjunction with information theory to yield the self- information and entropy of seizures. Based on the information content obtained, a Type-2 fuzzy graph and a crisp graph are generated to describe the information flow and electrode interconnectivity respectively. These graphs show that there is a distinct difference between focal and generalized seizures, and that seizure data can be segregated into multiple communities. G¨odel’s incompleteness theorem is also used in conjunction with non-Euclidean geometry to prove that no two seizures are the same. Together, these results verify that there exists a governing pattern for epileptic seizures.