Abstract
A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The spontaneous emergence of coherence and synchronization across such scales is crucial to neural function, while its anomalies often relate to pathological conditions. Here we provide a numerical study of synchronization dynamics in the human connectome network. Our purpose is to provide a detailed characterization of the recently uncovered broad dynamic regime, interposed between order and disorder, which stems from the hierarchical modular organization of the human connectome. In this regime—similar in essence to a Griffiths phase—synchronization dynamics are trapped within metastable attractors of local coherence. Here we explore the role of noise, as an effective description of external perturbations, and discuss how its presence accounts for the ability of the system to escape intermittently from such attractors and explore complex dynamic repertoires of locally coherent states, in analogy with experimentally recorded patterns of cerebral activity.
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Notes
- 1.
Notice that this definition of \(\sigma \), that we call, “time variability” is closely related to the chimera index introduced by Shanahan [31]. While chimera indices are averaged between individual network moduli and measure the onset of local coherence, \(\sigma \) is defined at the global level and records fluctuations of the global order parameter.
References
Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C.J., Wedeen, V.J., Sporns, O.: Mapping the structural core of human cerebral cortex. PLoS Biol. 6(7), e159 (2008)
Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., Hagmann, P.: Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl. Acad. Sci. 106(6), 2035–2040 (2009)
Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–98 (2009)
Sporns, O.: Networks of the Brain. MIT Press, Cambridge (2010)
Kaiser, M.: A tutorial in connectome analysis: topological and spatial features of brain networks. NeuroImage 57(3), 892–907 (2011)
Meunier, D., Lambiotte, R., Bullmore, E.: Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010)
Zhou, C., Zemanova, L., Zamora-López, G., Hilgetag, C.C., Kurths, J.: Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett. 97(23) (2006)
Ivković, M., Amy, K., Ashish, R.: Statistics of weighted brain networks reveal hierarchical organization and Gaussian degree distribution. PLoS ONE 7(6), e35029 (2012)
Zhou, C., Zemanova, L., Zamora-López, G., Hilgetag, C.C., Kurths, J.: Structure-function relationship in complex brain networks expressed by hierarchical synchronization. New J. Phys. 9(6), 178–178 (2007)
Kaiser, M., Goerner, M., Hilgetag, C.: Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9, 110 (2007)
Kaiser, M., Hilgetag, C.C.: Optimal hierarchical modular topologies for producing limited sustained activation of neural networks. Front. Neuroinform. 4(8) (2010)
Moretti, P., Muñoz, M.A.: Griffiths phases and the stretching of criticality in brain networks. Nat. Commun. 4(2521) (2013)
Vojta, T.: Rare region effects at classical, quantum and nonequilibrium phase transitions. J. Phys. A 39(22), R143–R205 (2006)
Muñoz, M.A., Juhász, R., Castellano, C., Ódor, G.: Griffiths phases on complex networks. Phys. Rev. Lett. 105, 128701 (2010)
Steinmetz, P.N., Roy, A., Fitzgerald, P.J., Hsiao, S.S., Johnson, K.O., Niebur, E.: Attention modulates synchronized neuronal firing in primate somatosensory cortex. Nature 404(6774), 187–190 (2000)
Kandel, E.R., Schwartz, J.H., Jessell, T.M.: Principles of Neural Science. McGraw-Hill, New York (2000)
Buzsáki, G.: Rhythms of the Brain. Oxford University Press, NY (2006)
Breakspear, M., Stam, C.J.: Dynamics of a neural system with a multiscale architecture. Phil. Trans. R. Soc. Lond. B 360(1457), 1051–1074 (2005)
Villegas, P., Moretti, P., Muñoz, M.A.: Frustrated hierarchical synchronization and emergent complexity in the human connectome network. Sci. Rep. 4(5990) (2014)
Rosenblum, M.G., Pikovsky, A., Kurths, J.: Synchronization—A universal concept in nonlinear sciences. Cambridge University Press, Cambridge (2001)
Kuramoto, Y.: Self-entrainment of a population of coupled nonlinear oscillators. Lect. Not. Phys. 39, 420–422 (1975)
Strogatz, S.H.: From kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143(1), 1–20 (2000)
Acebrón, J.A., Bonilla, L.L., Pérez-Vicente, C.J., Ritort, F., Spigler, R.: The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005)
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)
Chialvo, D.R.: Emergent Complex Neural Dyn. Nat. Phys. 6, 744–750 (2010)
Deco, G., Jirsa, V.K.: Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. J. Neurosci. 32(10), 3366–3375 (2012)
Haimovici, A., Tagliazucchi, E., Balenzuela, P., Chialvo, D.R.: Brain organization into resting state networks emerges at criticality on a model of the human connectome. Phys. Rev. Lett. 110, 178101 (2013)
Cabral, J., Hugues, E., Sporns, O., Deco, G.: Role of local network oscillations in resting-state functional connectivity. NeuroImage 57(1), 130–139 (2011)
Duch, J., Arenas, A.: Community detection in complex networks using extremal optimization. Phys. Rev. E 72, 027104 (2005)
Newman, M.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Shanahan, M.: Metastable chimera states in community-structured oscillator networks. Chaos 20(1), 013108 (2010)
Eckmann, J.P., Feinerman, O., Gruendlinger, L., Moses, E., Soriano, J., Tlusty, T.: The physics of living neural networks. Phys. Rep. 449(1–3), 54–76 (2007)
Arenas, A., Díaz-Guilera, A., Pérez-Vicente, C.: Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006)
Wildie, M., Shanahan, M.: Metastability and chimera states in modular delay and pulse-coupled oscillator networks. Chaos 22(4), 043131 (2012)
Acknowledgments
We acknowledge financial support from J. de Andalucía P09-FQM-4682 and the Spanish MINECO FIS2012-37655-C02-01 and FIS2013-43201-P.
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Villegas, P., Hidalgo, J., Moretti, P., Muñoz, M.A. (2016). Complex Synchronization Patterns in the Human Connectome Network. In: Battiston, S., De Pellegrini, F., Caldarelli, G., Merelli, E. (eds) Proceedings of ECCS 2014. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-29228-1_7
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