Long-term variability of global statistical properties of epileptic brain networks.

We investigate the influence of various pathophysiologic and physiologic processes on global statistical properties of epileptic brain networks. We construct binary functional networks from long-term, multichannel electroencephalographic data recorded from 13 epilepsy patients, and the average shortest path length and the clustering coefficient serve as global statistical network characteristics. For time-resolved estimates of these characteristics we observe large fluctuations over time, however, with some periodic temporal structure. These fluctuations can--to a large extent--be attributed to daily rhythms while relevant aspects of the epileptic process contribute only marginally. Particularly, we could not observe clear cut changes in network states that can be regarded as predictive of an impending seizure. Our findings are of particular relevance for studies aiming at an improved understanding of the epileptic process with graph-theoretical approaches.

[1]  K. Mardia.  Statistics of Directional Data , 1972 .

[2]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[3]  O. Bertrand,et al.  Oscillatory Synchrony between Human Extrastriate Areas during Visual Short-Term Memory Maintenance , 2001, The Journal of Neuroscience.

[4]  E. Bullmore,et al.  Adaptive reconfiguration of fractal small-world human brain functional networks , 2006, Proceedings of the National Academy of Sciences.

[5]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[6]  A. Schulze-Bonhage,et al.  Seizure anticipation by patients with focal and generalized epilepsy: A multicentre assessment of premonitory symptoms , 2006, Epilepsy Research.

[7]  D. Velis,et al.  Long-Term Effects of Temporal Lobe Epilepsy on Local Neural Networks: A Graph Theoretical Analysis of Corticography Recordings , 2009, PloS one.

[8]  A. Schulze-Bonhage,et al.  Do False Predictions of Seizures Depend on the State of Vigilance? A Report from Two Seizure‐Prediction Methods and Proposed Remedies , 2006, Epilepsia.

[9]  Fabrizio De Vico Fallani,et al.  Structure of the cortical networks during successful memory encoding in TV commercials , 2008, Clinical Neurophysiology.

[10]  José Luis Pérez Velazquez,et al.  Phase synchronization measurements using electroencephalographic recordings , 2007, Neuroinformatics.

[11]  Matthäus Staniek,et al.  Measuring Synchronization in the Epileptic Brain: a Comparison of Different Approaches , 2007, Int. J. Bifurc. Chaos.

[12]  F. Mormann,et al.  Seizure prediction: Any better than chance? , 2009, Clinical Neurophysiology.

[13]  Yong He,et al.  Disrupted small-world networks in schizophrenia. , 2008, Brain : a journal of neurology.

[14]  P. Pardalos,et al.  Performance of a seizure warning algorithm based on the dynamics of intracranial EEG , 2005, Epilepsy Research.

[15]  M. Hallett,et al.  Identifying true brain interaction from EEG data using the imaginary part of coherency , 2004, Clinical Neurophysiology.

[16]  G. Sandini,et al.  Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. , 2009, Brain : a journal of neurology.

[17]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[18]  K. Hlavácková-Schindler,et al.  Causality detection based on information-theoretic approaches in time series analysis , 2007 .

[19]  Steven J. Schiff,et al.  Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures , 2005, NeuroImage.

[20]  C. Stam,et al.  Disturbed functional connectivity in brain tumour patients: Evaluation by graph analysis of synchronization matrices , 2006, Clinical Neurophysiology.

[21]  C. Stam,et al.  Small-world network organization of functional connectivity of EEG slow-wave activity during sleep , 2007, Clinical Neurophysiology.

[22]  Edward T. Bullmore,et al.  Age-related changes in modular organization of human brain functional networks , 2009, NeuroImage.

[23]  M. Kramer,et al.  Emergent network topology at seizure onset in humans , 2008, Epilepsy Research.

[24]  K. Lehnertz,et al.  State dependent properties of epileptic brain networks: Comparative graph–theoretical analyses of simultaneously recorded EEG and MEG , 2010, Clinical Neurophysiology.

[25]  C. Stam,et al.  Small-world networks and epilepsy: Graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures , 2007, Clinical Neurophysiology.

[26]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[27]  C. Elger,et al.  Measuring nonstationarity by analyzing the loss of recurrence in dynamical systems. , 2002, Physical review letters.

[28]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[29]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[30]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[31]  J. A. Scott Kelso,et al.  Brain coordination dynamics: True and false faces of phase synchrony and metastability , 2009, Progress in Neurobiology.

[32]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[33]  Klaus Lehnertz,et al.  From brain to earth and climate systems: Small-world interaction networks or not? , 2011, Chaos.

[34]  Andreas A Ioannides,et al.  Dynamic functional connectivity , 2007, Current Opinion in Neurobiology.

[35]  C E Elger,et al.  Preoperative Evaluation for Epilepsy Surgery (Bonn Algorithm) , 2002, Zentralblatt fur Neurochirurgie.

[36]  J. Martinerie,et al.  Preictal state identification by synchronization changes in long-term intracranial EEG recordings , 2005, Clinical Neurophysiology.

[37]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[38]  H. Berendse,et al.  The application of graph theoretical analysis to complex networks in the brain , 2007, Clinical Neurophysiology.

[39]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[40]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[41]  J. Kurths,et al.  Phase synchronization: from theory to data analysis , 2003 .

[42]  C. Stam,et al.  Indications for network regularization during absence seizures: Weighted and unweighted graph theoretical analyses , 2009, Experimental Neurology.

[43]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[44]  R. Kahn,et al.  Efficiency of Functional Brain Networks and Intellectual Performance , 2009, The Journal of Neuroscience.

[45]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[46]  Klaus Lehnertz,et al.  Discerning nonstationarity from nonlinearity in seizure-free and preseizure EEG recordings from epilepsy patients , 2003, IEEE Transactions on Biomedical Engineering.

[47]  K. Tsakalis,et al.  Long-term prospective on-line real-time seizure prediction , 2005, Clinical Neurophysiology.

[48]  Kaspar Anton Schindler,et al.  EEG analysis with simulated neuronal cell models helps to detect pre-seizure changes , 2002, Clinical Neurophysiology.

[49]  J Martinerie,et al.  Functional modularity of background activities in normal and epileptic brain networks. , 2008, Physical review letters.

[50]  K. Lehnertz,et al.  Spatiotemporal Aspects of Synergetic Processes in the Auditory Cortex as Revealed by the Magnetoencephalogram , 1989 .

[51]  C. Stam,et al.  The functional connectivity of different EEG bands moves towards small-world network organization during sleep , 2008, Clinical Neurophysiology.

[52]  A. Kraskov,et al.  On the predictability of epileptic seizures , 2005, Clinical Neurophysiology.

[53]  K. Lehnertz,et al.  Synchronization phenomena in human epileptic brain networks , 2009, Journal of Neuroscience Methods.

[54]  Kaspar Anton Schindler,et al.  Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial EEG. , 2006, Brain : a journal of neurology.

[55]  C. Stam,et al.  Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis , 2006, Neuroscience Letters.

[56]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[57]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[58]  C. Stam,et al.  Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources , 2007, Human brain mapping.

[59]  Silke Dodel,et al.  Functional connectivity by cross-correlation clustering , 2002, Neurocomputing.

[60]  Huafu Chen,et al.  Altered Functional Connectivity and Small-World in Mesial Temporal Lobe Epilepsy , 2010, PloS one.

[61]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[62]  Kaspar Anton Schindler,et al.  Increasing synchronization may promote seizure termination: Evidence from status epilepticus , 2007, Clinical Neurophysiology.

[63]  C. Stam,et al.  Small-world networks and functional connectivity in Alzheimer's disease. , 2006, Cerebral cortex.

[64]  Chu Timone.  How do brain tumors alter functional connectivity? A magnetoencephalography study , 2006 .

[65]  F. Mormann,et al.  Epileptic seizures are preceded by a decrease in synchronization , 2003, Epilepsy Research.

[66]  Klaus Lehnertz,et al.  Evolving functional network properties and synchronizability during human epileptic seizures. , 2008, Chaos.

[67]  C. Wasterlain,et al.  Status epilepticus: pathophysiology and management in adults , 2006, The Lancet Neurology.

[68]  Xin-Ping Guan,et al.  Networking Property During Epileptic Seizure with Multi-channel EEG Recordings , 2006, ISNN.

[69]  H. W. Veen,et al.  Handbook of Biological Physics , 1996 .