Journal of Theoretical Biology 242 (2006) 171–187 Travelling waves and EEG patterns during epileptic seizure: Analysis with an integrate-and-fire neural network Mauro Ursino à , Giuseppe-Emiliano La Cara Department of Electronics, Computer Science, and Systems, University of Bologna, viale Risorgimento 2, I-40136 Bologna, Cesena, Italy Received 1 July 2005; received in revised form 9 December 2005; accepted 20 February 2006 Available online 19 April 2006 Abstract Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50  50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio- temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low- amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level. r 2006 Elsevier Ltd. All rights reserved. Keywords: Epilepsy; EEG; Neural networks; Integrate-and-fire neurons; Mathematical modelling 1. Introduction The electroencephalogram (EEG) plays an important diagnostic role in epilepsy today. It may help in the classification of seizures and may provide important prognostic information. However, understanding the me- chanisms which relate EEG changes to patterns of neuronal activity in the cortex, and the neurophysiological and neurobiological factors involved, is still a difficult issue. Epileptic seizures are characterized by various events of electrical activity (cortical EEG), which may rapidly change with time and may exhibit a different frequency content. Drake et al. (1998) reported that seizure patients have a decreased power at high frequencies (8.25–30 Hz) relative to lower frequencies (0.25–8 Hz). Inouye et al. observed a change of power spectrum in alpha frequency (Inouye et al., 1990) and structural changes in EEG frequency composition (Inouye et al., 1994) just before the occurrence of spike and wave complexes during seizure. Low-amplitude patterns at high frequencies (40–100 Hz), named electrodecremental events, appear as a key phe- nomenon at focal seizure onset (Fisher et al., 1992). These patterns are characterized by a decrease of signal voltage ARTICLE IN PRESS www.elsevier.com/locate/yjtbi 0022-5193/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2006.02.012 à Corresponding author. Tel.: +39 051 2093008; fax: +39 051 2093073. E-mail address: mursino@deis.unibo.it (M. Ursino).