Elsevier

Neurocomputing

Volume 70, Issues 10–12, June 2007, Pages 1843-1847
Neurocomputing

Comparison of dynamical states of random networks with human EEG

https://doi.org/10.1016/j.neucom.2006.10.115Get rights and content

Abstract

Existing models of EEG have mainly focused on relations to network dynamics characterized by firing rates [L. de Arcangelis, H.J. Herrmann, C. Perrone-Capano, Activity-dependent brain model explaining EEG spectra, arXiv:q-bio.NC/0411043 v1, 23 Nov 2004; D.T. Liley, D.M. Alexander, J.J. Wright, M.D. Aldous, Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons, Network 10(1) (1999) 79–92; O. David, J.K. Friston, A neural mass model for MEG/EEG: coupling and neuronal dynamics, NeuroImage 20 (2003) 1743–1755]. Generally, these models assume that there exists a linear mapping between network firing rates and EEG states. However, firing rate is only one of several descriptors for network activity states. Other relevant descriptors are synchrony and irregularity of firing patterns [N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, J. Comput. Neurosci. 8(3) (2000) 183–208]. To develop a better understanding of the EEG we need to relate these state descriptors to EEG states. Here, we try to go beyond the firing rate based approaches described in [D.T. Liley, D.M. Alexander, J.J. Wright, M.D. Aldous, Alpha rhythm emerges from large-scale networks of realistically coupled multicompartmental model cortical neurons, Network 10(1) (1999) 79–92; O. David, J.K. Friston, A neural mass model for MEG/EEG: coupling and neuronal dynamics, NeuroImage 20 (2003) 1743–1755] and relate synchronicity and irregularity in the network to EEG states. We show that the transformation between network activity and EEG can be approximately mediated by linear kernel with the shape of an α- or γ-function, allowing us a comparison between EEG states and network activity space. We find that the simulated EEG generated from asynchronous irregular type network activity is closely related to the human EEG recorded in the awake state, evaluated using power spectral density characteristics.

Introduction

Cortical activity can be recorded at various levels of details ranging from in vivo intracellular recording (microscopic activity) to global population activity such as LFP, ECoG, and EEG (macroscopic activity). While there is a good understanding of the origin of the microscopic activity, very little is known about the origin of the macroscopic activity. It has long been speculated that the macroscopic cortical activity is generated as a consequence of network activity [5], [11], [10]. In fact, several modeling studies have been able to relate network dynamics to EEG states by assuming a linear mapping between the network firing rates and oscillations in the EEG [1], [7], [4]. However, network dynamics is not only characterized by firing rates, but also by synchronization in neural populations and irregularity of single-neuron firing patterns [3]. To understand how cortical background activity states generate the EEG we need to relate these state descriptors to EEG states. We show that the mapping between the population activity in the network can be approximated by a linear kernel described by either an α-function or a γ-function. The simulated EEG (see materials and methods) corresponding to asynchronous irregular (AI) and synchronous irregular states showed a good match with the human EEG  especially in theta and delta bands. Heterogeneous network simulations resembled the human background EEG even better  also in the alpha and beta bands.

Section snippets

Networks

We performed simulations of homogeneous and heterogeneous networks consisting of 50,000 leaky integrate and fire type neurons (80% excitatory and 20% inhibitory neurons), representing 0.5mm2 slice of cortex [2]. The neurons were connected randomly with a connection probability of 0.1. In a homogeneous network all neurons had identical passive properties. To introduce heterogeneity into the network, the passive properties (membrane capacity C and conductivity at resting condition Grest) and the

Network activity dynamics

A large random network of integrate and fire neurons exhibits a continuum of activity states, depending on the intensity of external excitatory inputs (νext), and on the recurrent inhibition/excitation balance (g). The firing pattern of individual neurons varies between regular (R) (CVISI0) and irregular (I) (CVISI1), population activity varies between synchronous (S) (ρnet1) and asynchronous (A) (ρnet0). Still, the network activity state can be attributed to one of four characteristic

Discussion

Here we presented a first attempt to relate the spiking activity of cortical network, to the macroscopic activity of the brain, as captured by the scalp EEG. Generally, the models AI state very closely resembles cortical activity in vivo in awake, behaving animals. Therefore, we assumed that healthy human EEG recordings correspond to an AI state in the cortical network model.

Our comparison of Sim-EEG based on AI state networks and recorded EEG from awake humans supports this assumption. For

Acknowledgments

We acknowledge stimulating discussions with Dr. Tonio Ball. This work was supported by the DFG GraKo-843 and the German Federal Ministry of Education and Research (BMBF Grant 01GQ0420 to BCCN Freiburg).

Ralph Meier was born in Germany in 1976. He obtained his Diploma in Biology at the Albert-Ludwigs- University of Freiburg in 2003. Then he obtained his Ph.D. in cooperation with the Center for Epilepsy, Freiburg and the Neurobiology & Biophysics Department at the University Freiburg, Germany in 2006. Currently he is a post-doctoral fellow at the Bernstein Center for Computational Neuroscience, Freiburg. His research is focused on understanding the dynamics of large scale neuronal networks,

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Cited by (2)

Ralph Meier was born in Germany in 1976. He obtained his Diploma in Biology at the Albert-Ludwigs- University of Freiburg in 2003. Then he obtained his Ph.D. in cooperation with the Center for Epilepsy, Freiburg and the Neurobiology & Biophysics Department at the University Freiburg, Germany in 2006. Currently he is a post-doctoral fellow at the Bernstein Center for Computational Neuroscience, Freiburg. His research is focused on understanding the dynamics of large scale neuronal networks, emergence of epileptiform activity and the development of scientific software.

Arvind Kumar was born in India in 1976. He did his M.E. (Electrical Engg.) from Birla Institute of Technology and Science, Pilani, India in 1999. After a short association with Indian Institute of Technology, Delhi, India, as a senior research fellow, he moved to the University of Freiburg, Germany, where he obtained his Ph.D. in 2006. Currently he is a post-doctoral fellow at Deptartment of Neuroscience, Brown University Providence, USA. His research is focused on understanding the dynamics of neuronal networks and modeling of cortical activity.

Andreas Schulze-Bonhage was born in 1960 in Berlin, Germany. He studied medicine at the University of Münster and consecutively worked there at the Institute of Neuroanatomy and Neurophysiology. After his training as a neurologist, he joined the Epilepsy Centre at the University of Bonn as a research fellow and consultant. After visits at the Montreal Neurological Institute and of the Cleveland Clinic Foundation, he became head of the newly founded epilepsy centre at the University of Freiburg. His research interests focus on clinical epileptology, brain imaging and EGG time series evaluation.

Ad Aertsen was born in 1948 in Holland, where he obtained his M.Sc. (University Utrecht) and Ph.D. (University Nijmegen) degrees in Physics. After associations with the University of Pennsylvania (Philadelphia), the Max-Planck-Institute for Biological Cybernetics (Tuebingen), the Hebrew University (Jerusalem), the Ruhr-University (Bochum), and the Weizmann Institute of Science (Rehovot), he is now Professor of Neurobiology and Biophysics at the Albert-Ludwigs-University in Freiburg, Germany (www.brainworks.uni-freiburg.de) and Coordinator of the Bernstein Center for Computational Neuroscience (www.bccn-freiburg.de). His research interests focus on the analysis and modeling of activity in biological neural networks and the associated development of neurotechnology.

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