UC Berkeley

Using a mean-field, mesoscale model of the human cortex, we examine both feedback control for the suppression of seizures and the continuous mapping of sleep states to aid in seizure prediction. First, we verify the strong convergence of numerical solutions to the model, which consists of coupled stochastic partial differential equations. In doing this, we pay special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. We then develop a new model for the measurement of a cortical surface electrode based on extracellular currents flowing in the cortex. This model is used to simulate feedback with a new control algorithm that utilizes a charge-balanced signal. Not only does this succeed in suppressing the seizure oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage.

Next, we turn to a representation of the human sleep cycle contained within the mesoscale cortical model. We show that it can be used to obtain a detailed description of electroencephalogram (EEG) sleep stages, and we discuss how this analysis may aid in the prediction and prevention of seizures during sleep. The association between EEG data and the cortical model is found via locally linear embedding (LLE), a method of nonlinear dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates rapid eye movement (REM) and non-REM sleep and maps the EEG data to a low-dimensional output space where the sleep state changes smoothly over time. We also incorporate the concept of strongly connected components and use this as a method of automatic outlier rejection for EEG data. Then, by using LLE on a hybrid data set containing both sleep EEG and signals generated from the mesoscale cortical model, we quantify the relationship between the data and the mathematical model. This enables us to take any sample of sleep EEG data and associate it with a position among the continuous range of sleep states provided by the model; we can thus infer a trajectory of states as the subject sleeps. Because current sleep scoring consists of only five discrete stages, this technique may allow for tracking of sleep dynamics and a greater ability to predict the onset of seizures. We show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time.