Computational model prospective on the observation of proictal states in epileptic neuronal systems Stiliyan Kalitzin a, ⁎, Marcus Koppert a , George Petkov a , Demetrios Velis a , F. Lopes da Silva b, c a Foundation Epilepsy Institute of The Netherlands (SEIN), Heemstede, The Netherlands b Swammerdam Institute for Life Sciences, Faculty of Biology, University of Amsterdam, Amsterdam, The Netherlands c Department of Bioengineering, Instituto Superior Técnico, Lisbon Technical University, Lisbon, Portugal abstract article info Article history: Received 17 August 2011 Accepted 19 August 2011 Keywords: Epilepsy Seizures Computational models Neural networks Connectivity 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 non- ictal 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. © 2011 Elsevier Inc. All rights reserved. 1. Introduction Epilepsy is one of the most studied neurological conditions. There is, however, still no clear understanding of the causes of epileptic sei- zures in general. Various animal, in vitro, and computational models have shown similarities to certain forms of the clinical manifestations, yet no adequate concept for all of the forms of epilepsy has been accepted or even proven to exist. One particularly interesting feature of epileptic disorders is the in- termittent, sometimes abrupt manifestation of pathological states, or seizures. These states are characterized by a synchronous, oscillatory type of electroencephalographic activity that is associated with various clinical manifestations. Although the existence of such states has been explored in computational and experimental models, the transitions from and to these states remain largely uncharted territory. Likewise, the prospect of predicting these interruptions of the normal electro- physiological activity of the brain is still a standing challenge for re- searchers. We believe that the issues of seizure prediction and seizure generation are intrinsically connected. Most of the proposed methodol- ogy is based on phenomenological intuition; the majority of the tech- niques attempt to detect seizure-like properties of the EEG signals in some period (loosely dubbed as the prediction horizon) before the clin- ical event. But what are the reasons for this assumption? Transitions may occur between states with completely different dynamic profiles, and therefore, no gradual “deformation” of the signal features before the transition will necessarily be observed. In this article we attempt to classify first the possible transition sce- narios in a dynamic system [1,2]. For a more detailed presentation, see [3]. Here we provide a short summary. We recognize three generic classes of scenarios: (1) external parameter-driven transitions (defor- mation of the dynamical model); (2) transitions driven by external or internal perturbations in multistable systems (bifurcation of the state); and (3) transitions in systems with internal instability regions (intermittency models). These scenarios are schematically illustrated in Fig. 1. The type 1 models are nonautonomous in the sense that sei- zures are generated under the influence of external inputs that modu- late the system's parameters. These models do not account for the dynamics of the transitions between normal states and epileptic sei- zures as such; these only translate parameter variations into EEG signal features. As long as the dynamics of the model do not include the pa- rameters responsible for seizure generation as dynamic degrees of free- dom, this model cannot provide any useful information about seizure prediction. This said, the nonautonomous class of models can play an important role in understanding the causes of some epileptic conditions and the influence of the various endogenous and exogenous factors contributing to seizure generation. The second class of models are Epilepsy & Behavior 22 (2011) S102–S109 ⁎ Corresponding author at: Foundation Epilepsy Institute of The Netherlands (SEIN), Achterweg 5, Heemstede 2103SW, The Netherlands. E-mail address: skalitzin@sein.nl (S. Kalitzin). 1525-5050/$ – see front matter © 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.yebeh.2011.08.017 Contents lists available at SciVerse ScienceDirect Epilepsy & Behavior journal homepage: www.elsevier.com/locate/yebeh