A network of networks model to study phase synchronization using structural connection matrix of human brain

Abstract The cerebral cortex plays a key role in complex cortical functions. It can be divided into areas according to their function (motor, sensory and association areas). In this paper, the cerebral cortex is described as a network of networks (cortex network), we consider that each cortical area is composed of a network with small-world property (cortical network). The neurons are assumed to have bursting properties with the dynamics described by the Rulkov model. We study the phase synchronization of the cortex network and the cortical networks. In our simulations, we verify that synchronization in cortex network is not homogeneous. Besides, we focus on the suppression of neural phase synchronization. Synchronization can be related to undesired and pathological abnormal rhythms in the brain. For this reason, we consider the delayed feedback control to suppress the synchronization. We show that delayed feedback control is efficient to suppress synchronous behavior in our network model when an appropriate signal intensity and time delay are defined.

[1]  W. Singer,et al.  Synchronization of Neural Activity across Cortical Areas Correlates with Conscious Perception , 2007, The Journal of Neuroscience.

[2]  Yoshiki Kuramoto,et al.  Self-entrainment of a population of coupled non-linear oscillators , 1975 .

[3]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.

[4]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[5]  Yong He,et al.  Diffusion Tensor Tractography Reveals Abnormal Topological Organization in Structural Cortical Networks in Alzheimer's Disease , 2010, The Journal of Neuroscience.

[6]  P. Brown,et al.  Cortico-cortical coupling in Parkinson's disease and its modulation by therapy. , 2005, Brain : a journal of neurology.

[7]  Alan C. Evans,et al.  Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. , 2007, Cerebral cortex.

[8]  A. Alexander,et al.  Diffusion tensor imaging of cerebral white matter: a pictorial review of physics, fiber tract anatomy, and tumor imaging patterns. , 2004, AJNR. American journal of neuroradiology.

[9]  Nikolaos Papanikolaou,et al.  Fiber tracking: A qualitative and quantitative comparison between four different software tools on the reconstruction of major white matter tracts , 2016, European journal of radiology open.

[10]  Hanshuang Chen,et al.  Enhancement of neuronal coherence by diversity in coupled Rulkov-map models , 2008 .

[11]  Pablo Varona,et al.  Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis , 2001, Biological Cybernetics.

[12]  R. Traub,et al.  A mechanism for generation of long-range synchronous fast oscillations in the cortex , 1996, Nature.

[13]  M. Rosenblum,et al.  Controlling synchronization in an ensemble of globally coupled oscillators. , 2004, Physical review letters.

[14]  H. Bergman,et al.  Pathological synchronization in Parkinson's disease: networks, models and treatments , 2007, Trends in Neurosciences.

[15]  W. Singer,et al.  Visuomotor integration is associated with zero time-lag synchronization among cortical areas , 1997, Nature.

[16]  Morten L. Kringelbach,et al.  Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs , 2016, Scientific Reports.

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

[18]  J. Kurths,et al.  Exploring Brain Function from Anatomical Connectivity , 2011, Front. Neurosci..

[19]  Gustavo Deco,et al.  Optimal Information Transfer in the Cortex through Synchronization , 2010, PLoS Comput. Biol..

[20]  Alex Arenas,et al.  From Modular to Centralized Organization of Synchronization in Functional Areas of the Cat Cerebral Cortex , 2010, PloS one.

[21]  Mariano Sigman,et al.  A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks , 2011, Proceedings of the National Academy of Sciences.

[22]  P. Basser,et al.  Diffusion tensor MR imaging of the human brain. , 1996, Radiology.

[23]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[24]  Henk Nijmeijer,et al.  Collective Almost Synchronisation in Complex Networks , 2012, PloS one.

[25]  李涛,et al.  Small-world brain networks in schizophrenia , 2012 .

[26]  M. Rosenblum,et al.  Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  S. Shipp.  Structure and function of the cerebral cortex , 2007, Current Biology.

[28]  Jürgen Kurths,et al.  Phase synchronization in ensembles of bursting oscillators. , 2004, Physical review letters.

[29]  N. Rulkov.  Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[30]  Ruedi Stoop,et al.  Beyond scale-free small-world networks: cortical columns for quick brains. , 2013, Physical review letters.

[31]  Antonio M. Batista,et al.  Delayed feedback control of bursting synchronization in a scale-free neuronal network , 2010, Neural Networks.

[32]  H. Freund,et al.  The cerebral oscillatory network of parkinsonian resting tremor. , 2003, Brain : a journal of neurology.

[33]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[34]  Chris G. Antonopoulos,et al.  Do Brain Networks Evolve by Maximizing Their Information Flow Capacity? , 2015, PLoS Comput. Biol..

[35]  Gerda de Vries,et al.  Bursting as an emergent phenomenon in coupled chaotic maps. , 2001 .

[36]  R Stoop,et al.  Multiple-time-scale framework for understanding the progression of Parkinson's disease. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  N. Tzourio-Mazoyer,et al.  Automated Anatomical Labeling of Activations in SPM Using a Macroscopic Anatomical Parcellation of the MNI MRI Single-Subject Brain , 2002, NeuroImage.

[38]  Jürgen Kurths,et al.  Suppression of phase synchronisation in network based on cat's brain. , 2016, Chaos.

[39]  R N Lemon,et al.  Synchronization in monkey motor cortex during a precision grip task. I. Task-dependent modulation in single-unit synchrony. , 2001, Journal of neurophysiology.

[40]  C. Stam,et al.  The organization of physiological brain networks , 2012, Clinical Neurophysiology.

[41]  Murilo S. Baptista,et al.  Chaotic, informational and synchronous behaviour of multiplex networks , 2015, Scientific Reports.

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

[43]  John Skvoretz,et al.  Node centrality in weighted networks: Generalizing degree and shortest paths , 2010, Soc. Networks.

[44]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.