A Mathematical Model of Intercranial Electrical Activity and EEG Signal Processing
Open Access
- Author:
- Kennah, Justin James
- Area of Honors:
- Electrical Engineering (Behrend)
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Sudarshan Rao Nelatury, Thesis Supervisor
Sudarshan Rao Nelatury, Thesis Honors Advisor
Thomas Lee Hemminger, Faculty Reader - Keywords:
- EEG
epilepsy
seizure
epileptor
neurostimulation - Abstract:
- A dynamic model characterizing the brain signals of an epileptic is simulated numerically. The model is a non-linear, state-space representation involving five variables that control various types of seizures. The electrical activity shows intermittent rapid discharges, spikes, waves and steady time course with possible alternations between normal and ictal (seizure) phases. \\ The first part of the thesis begins with a model of neural activity during normal and abnormal periods. The primary contribution of the thesis involves numerical solution of the pertinent differential equations using the Runge-Kutta fourth order algorithm. Following this, extensive simulation trials are made to understand the role of the parameters in triggering seizures, what impulsive inputs contribute to the abnormalities, and how they help in restoring the activity to a calm steady state. Several simulated waveforms are included showing the erratic behavior of the brain going through these episodes. Phase-plane plots reveal regions of high intensity seizures distinct from normal resting brain activity. The code was developed and the plots are shown using Matlab software. Of particular significance is the choice of initial conditions. The overall signal behavior can only be explained using ideas from deterministic chaos and bifurcation theory. A clear understanding of the model helps in the development of bio-feedback to control the symptoms. This would be a good topic for future research.