Theoretical foundation for digital space of flat electroencephalogram

Abstract

Epilepsy is one of the most common disorders of the brain characterized by recurrent seizures. Epileptic seizure, which is caused by abnormal electrical activity in brain can be measured by using Magnetoencephalogram (MEG) and Electroencephalogram (EEG). MEG measures magnetic field whereas EEG measures electrical potential during seizure. Fuzzy Topographic Topological Mapping (FTTM) is a mathematical model for solving neuromagnetic inverse problem. The model was developed to accommodate static simulated and experimental MEG signals and their transformed image. However, in this thesis, digital topology is adopted for FTTM, in particular with Khalimsky topology where the actual structure of digital objects can be visualized. The new construction is called FTTM digital and is denoted as FTTMdig. All four components of FTTMdig are shown to be homeomorphic as in the older versions of FTTM. In addition, real time recorded EEG signal during epileptic seizure is constructed to be topological space by inducing on metric space. Finally, this topological space of real time recorded EEG signal is incorporated with FTTMdig via relational topology. The integration of these two topologies is the key to the foundation of the novel Flat EEG.