On estimating phenomenological model states for epileptic seizure prediction

The prediction of epileptic seizure, like the disease itself, is a very old but largely unresolved problem. The prediction may greatly improve the quality of life for an epileptic patient. A low-cost measurement like an Electroencephalogram (EEG) involves the non-invasive monitoring of the brain voltage signals to detect epileptic seizures. This study aims to find ways to estimate the internal states of the neuron population by looking at the measured EEG signals so that the seizure onset may be predicted in advance. If one may estimate the states of the neural population, then by relating to the bifurcation horizon, one may find the seizure onset time. To find such states, one needs an estimator/observer of a neuronal state space model. Most of the neuronal models, be it biological or phenomenological, are non-linear. If a linear or any other approximation is used for the observer design, the bifurcation horizon may not be accurate enough. The biological models of neural population have the barrier of determining all the physiological parameters of a patient, which may be a bit limiting. A phenomenological neuron model, like Epileptor, is adapted, which is a non-linear and discontinuous model; estimating its states may help in finding the bifurcation parameters. However, the non-linearities are of Lipschitz and monotonic class. Using Linear Matrix Inequality solutions, a Lipschitz Non-linear model-based Observer is developed and tested in simulation, without using approximations of any kind. The simulation shows high fidelity of the observer to the model at hand, estimating the states, and helping in determining the bifurcation parameters.