A model of feedback control for the charge-balanced suppression of epileptic seizures

Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying 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. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage

A continuous mapping of sleep states through association of EEG with a mesoscale cortical model

Here we show that a mathematical model of the human sleep cycle 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 dimensionality reduction. We first show that LLE can distinguish between traditional sleep stages when applied to EEG data. It reliably separates 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. Lastly, we show that this method gives consistent results for various subjects over a full night of sleep and can be done in real time

A Simple Statistical Method for the Automatic Detection of Ripples in Human Intracranial EEG.

High frequency oscillations (HFOs) are a promising biomarker of epileptic tissue, but detection of these electrographic events remains a challenge. Automatic detectors show encouraging results, but they typically require optimization of multiple parameters, which is a barrier to good performance and broad applicability. We therefore propose a new automatic HFO detection algorithm, focusing on simplicity and ease of implementation. It requires tuning of only an amplitude threshold, which can be determined by an iterative process or directly calculated from statistics of the rectified filtered data (i.e. mean plus standard deviation). The iterative approach uses an estimate of the amplitude probability distribution of the background activity to calculate the optimum threshold for identification of transient high amplitude events. We tested both the iterative and non-iterative approaches using a dataset of visually marked HFOs, and we compared the performance to a commonly used detector based on the root-mean-square. When the threshold was optimized for individual channels via ROC curve, all three methods were comparable. The iterative detector achieved a sensitivity of 99.6%, false positive rate (FPR) of 1.1%, and false detection rate (FDR) of 37.3%. However, in an eight-fold cross-validation test, the iterative method had better sensitivity than the other two methods (80.0% compared to 64.4 and 65.8%), with FPR and FDR of 1.3, and 49.4%, respectively. The simplicity of this algorithm, with only a single parameter, will enable consistent application of automatic detection across research centers and recording modalities, and it may therefore be a powerful tool for the assessment and localization of epileptic activity

Inter-hemispheric oscillations in human sleep

Sleep is generally categorized into discrete stages based on characteristic electroencephalogram (EEG) patterns. This traditional approach represents sleep architecture in a static way, but it cannot reflect variations in sleep across time and across the cortex. To investigate these dynamic aspects of sleep, we analyzed sleep recordings in 14 healthy volunteers with a novel, frequency-based EEG analysis. This approach enabled comparison of sleep patterns with low inter-individual variability. We then implemented a new probability dependent, automatic classification of sleep states that agreed closely with conventional manual scoring during consolidated sleep. Furthermore, this analysis revealed a previously unrecognized, interhemispheric oscillation during rapid eye movement (REM) sleep. This quantitative approach provides a new way of examining the dynamic aspects of sleep, shedding new light on the physiology of human slee