Mean field modelling of human EEG: application to epilepsy

Aggregated electrical activity from brain regions recorded via an electroencephalogram (EEG), reveal that the brain is never at rest, producing a spectrum of ongoing oscillations that change as a result of different behavioural states and neurological conditions. In particular, this thesis focusses on pathological oscillations associated with absence seizures that typically affect 2–16 year old children. Investigation of the cellular and network mechanisms for absence seizures studies have implicated an abnormality in the cortical and thalamic activity in the generation of absence seizures, which have provided much insight to the potential cause of this disease. A number of competing hypotheses have been suggested, however the precise cause has yet to be determined. This work attempts to provide an explanation of these abnormal rhythms by considering a physiologically based, macroscopic continuum mean-field model of the brain's electrical activity. The methodology taken in this thesis is to assume that many of the physiological details of the involved brain structures can be aggregated into continuum state variables and parameters. The methodology has the advantage to indirectly encapsulate into state variables and parameters, many known physiological mechanisms underlying the genesis of epilepsy, which permits a reduction of the complexity of the problem. That is, a macroscopic description of the involved brain structures involved in epilepsy is taken and then by scanning the parameters of the model, identification of state changes in the system are made possible. Thus, this work demonstrates how changes in brain state as determined in EEG can be understood via dynamical state changes in the model providing an explanation of absence seizures. Furthermore, key observations from both the model and EEG data motivates a number of model reductions. These reductions provide approximate solutions of seizure oscillations and a better understanding of periodic oscillations arising from the involved brain regions. Local analysis of oscillations are performed by employing dynamical systems theory which provide necessary and sufficient conditions for their appearance. Finally local and global stability is then proved for the reduced model, for a reduced region in the parameter space. The results obtained in this thesis can be extended and suggestions are provided for future progress in this area.