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In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav. 22 (2011) S102-S109) and does not correspond directly to realistic neuronal processes (excitatory-inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another.

We aim to derive fully autonomous seizure suppression paradigms based on reactive control of neuronal dynamics. A previously derived computational model of seizure generation describing collective degrees of freedom and featuring bistable dynamics is used. A novel technique for real-time control of epileptogenicity is introduced. The reactive control reduces practically all seizures in the model. The study indicates which parameters provide the maximal seizure reduction with minimal intervention. An adaptive scheme is proposed that optimizes the stimulation parameters in nonstationary situations.

High-frequency oscillations (HFOs) are EEG field potentials with frequencies higher than 30 Hz; commonly the frequency band between 30 and 70 Hz is denominated the gamma band, but with the discovery of activities at frequencies higher than 70 Hz a variety of terms have been proposed to describe the latter (Gotman and Crone, 2011). In general we may consider that the term HFO encompasses activities from 30 to 600 Hz. The best practice is to indicate always explicitly the frequency range of the HFOs in any specific study. There are numerous types of HFOs: those in normal brain appear to facilitate synchronization and information transfer necessary for cognitive processes and memory, while a particular class of HFOs in the brain of animals and people with epilepsy appears to reflect fundamental mechanisms of epileptic phenomena and could serve as biomarkers of epileptogenesis and epileptogenicity in abnormal conditions such as epilepsy. A better understanding of the significance of HFOs depends on a deeper analysis of the mechanisms of generation of different kinds of HFOs, that typically are at the crossroads between intrinsic membrane properties and neuronal interactions, both chemical and electrical. There is still a lack of understanding of how specific information is carried by HFOs and can be operational in normal cognitive processes such as in working and long-term memory and abnormal conditions such as epilepsy. The complexity of these processes makes the development of relevant computational models of dynamical neuronal networks most compelling., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Epilepsy is a pathological condition of the human central nervous system in which normal brain functions are impaired by unexpected transitions to states called seizures. We developed a lumped neuronal model that has the property of switching between two states as a result of intrinsic or extrinsic perturbations, such as noisy fluctuations. In one version of the model, seizure risk is controlled by a single connectivity parameter representing excitatory couplings between two model lumps. We show that this risk can be reconstructed from calculation of the cross-covariance between the activities of the two neural populations during the nonictal phase. In a second simulation sequence, we use a system of 10 interconnected lumps with randomly generated connectivity matrices. We show again that the tendency to develop seizures can be inferred from the cross-covariances calculated during the nonictal states. Our conclusion is that the risk of epileptic transitions in biological systems can be objectively quantified. This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction., (Copyright © 2011 Elsevier Inc. All rights reserved.)

It has been shown that the analysis of electroencephalographic (EEG) signals submitted to an appropriate external stimulation (active paradigm) is efficient with respect to anticipating epileptic seizures [S. Kalitzin, Clin. Neurophysiol. 116, 718 (2005)]. To better understand how an active paradigm is able to detect properties of EEG signals by means of which proictal states can be identified, we performed a simulation study using a computational model of seizure generation of a hippocampal network. Applying the active stimulation methodology, we investigated (i) how changes in model parameters that lead to a transition from the normal ongoing EEG to an ictal pattern are reflected in the properties of the simulated EEG output signals and (ii) how the evolution of neuronal excitability towards seizures can be reconstructed from EEG data using an active paradigm, rather than passively, using only ongoing EEG signals. The simulations indicate that a stimulation paradigm combined with appropriate analytical tools, as proposed here, may yield information about the change in excitability that precedes the transition to a seizure. Such information is apparently not fully reflected in the ongoing EEG activity. These findings give strong support to the development and application of active paradigms with the aim of predicting the occurrence of a transition to an epileptic seizure.