We present work in this dissertation on methods to map measured electrode signals from human subjects into the physiologically relevant parameter space of a mathematical model of the cortex, approaching two specific dynamical brain phenomena: sleep and seizures.
In the context of sleep, we develop a probabilistic method for mapping human sleep electroencephalogram (EEG) signals onto a state space based on a biologically plausible mathematical model of the cortex. From a noninvasive EEG signal, this method produces physiologically meaningful pathways of the cortical state over a night of sleep. We propose ways in which these pathways offer insights into sleep-related conditions, functions, and complex pathologies. To address explicitly the noisiness of the EEG signal and the stochastic nature of the mathematical model, we use a probabilistic Bayesian framework to map each EEG epoch to a distribution of likelihoods over all model sleep states. A Hidden Markov Model (HMM) is incorporated to improve the path results using the prior knowledge that cortical physiology has temporal continuity.
Next we adapt our probabilistic methodology to infer the parameter region in the mathematical model of the cortex most likely to be producing seizures observed in an electrocorticogram (ECoG) signal. This method produces a probabilistic pathway of the temporal evolution of physiological state in the cortex over the course of individual seizures. We describe ways in which these methods and results offer insights into seizure etiology and suggest potential new treatment options.
Once again, a probabilistic Bayesian framework is used to map features of EEG or ECoG segments onto a distribution of likelihoods over physiological parameter states. And again, a Hidden Markov Model (HMM) is introduced to incorporate the belief that cortical physiology has both temporal continuity and also a degree of reproducibility between individual seizures. However, for seizures, we additionally inspect the ratio of likelihoods between HMMs run under two possible parameter regions, both of which produce seizures in the model, to determine which physiological parameter regions are more likely to be causing the observed seizures. We show that between individual seizures, there is consistency in these likelihood ratios between hypothesized regions, in the temporal pathways calculated, and in the separation of seizure from non-seizure time segment likelihood maps. We also improve upon several of the underlying techniques for sampling the parameter state space, feature selection, and probability density estimation.
