Abstract
Understanding the relationship between structural and functional organization represents one of the most important challenges in neuroscience. An increasing amount of studies show that this organization can be better understood by considering the brain as an interactive complex network. This approach has inspired a large number of computational models that combine experimental data with numerical simulations of brain interactions. In this paper, we present a summary of a data-driven computational model of synchronization between distant cortical areas that share a large number of overlapping neighboring (anatomical) connections. Such connections are derived from in vivo measures of brain connectivity using diffusion-weighted magnetic resonance imaging and are additionally informed by the presence of significant resting-state functionally correlated links between the areas involved. The dynamical processes of brain regions are simulated by a combination of coupled oscillator systems and a hemodynamic response model. The coupled oscillatory systems are represented by the Kuramoto phase oscillators, thus modeling phase synchrony between regional activities. The focus of this modeling approach is to characterize topological properties of functional brain correlation related to synchronization of the regional neural activity. The proposed model is able to reproduce remote synchronization between brain regions reaching reasonable agreement with the experimental functional connectivities. We show that the best agreement between model and experimental data is reached for dynamical states that exhibit a balance of synchrony and variations in synchrony providing the integration of activity between distant brain regions.









Similar content being viewed by others
References
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 (2005)
Arenas, A., Díaz-Guilera, A., Pérez Vicente, C.J.: Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102 (2006)
Balanov, A.G., Janson, N.B., Postnov, D.E., Sosnovtseva, O.V.: Synchronization: From Simple to Complex. Springer, Berlin (2009)
Barttfeld, P., Uhrig, L., Sitt, J.D., Sigman, M., Jarraya, B., Dehaene, S.: Signature of consciousness in the dynamics of resting-state brain activity. Proc. Natl. Acad. Sci. USA 112, 887 (2015)
Bergner, A., Frasca, M., Sciuto, G., Buscarino, A., Ngamga, E.J., Fortuna, L., Kurths, J.: Remote synchronization in star networks. Phys. Rev. E 85, 026208 (2012)
Biswal, B.B.: Toward discovery science of human brain function. Proc. Natl. Acad. Sci. USA 107, 4734 (2010)
Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S.: Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34, 537 (1995)
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1 (2002)
Bola, M., Sabel, B.A.: Dynamic reorganization of brain functional networks during cognition. NeuroImage 114, 398 (2015)
Breakspear, M., Roberts, J.A., Terry, J.R., Rodrigues, S., Mahant, N., Robinson, P.A.: A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb. Cortex 16, 1296 (2006)
Breakspear, M., Heitmann, S., Daffertshofer, A.: Generative models of cortical oscillations: neurobiological implications of the Kuramoto model. Front. Hum. Neurosci. 4, 190 (2010)
Bressler, S.L., Menon, V.: Large-scale brain networks in cognition: emerging methods and principles. Trends Cogn. Sci. 14, 277 (2010)
Bullmore, E.T., Bassett, D.S.: Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113 (2011)
Bullmore, E.T., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186 (2009)
Cabral, J., Hugues, E., Sporns, O., Deco, G.: Role of local network oscillations in resting-state functional connectivity. Neuroimage 57, 130 (2011)
Cabral, J., Hugues, E., Kringelbach, M.L., Deco, G.: Modeling the outcome of structural disconnection on resting-state functional connectivity. Neuroimage 62, 1342 (2012)
Cabral, J., Fernandes, H.M., Van Hartevelt, T.J., James, A.C., Kringelbach, M.L.: Structural connectivity in schizophrenia and its impact on the dynamics of spontaneous functional networks. Chaos 23, 046111 (2013)
Cabral, J., Luckhoo, H., Woolrich, M.W., Joensson, M., Mohseni, H., Baker, A., Kringelbach, M.L., Deco, G.: Exploring mechanisms of spontaneous functional connectivity in MEG: how delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations. Neuroimage 90, 423 (2014a)
Cabral, J., Kringelbach, M.L., Deco, G.: Exploring the network dynamics underlying brain activity during rest. Prog. Neurobiol. 114, 102 (2014b)
Carhart-Harris, R., Muthukumaraswamy, S., Roseman, L., Kaelen, M., Droog, W., Murphy, K., Tagliazucchi, E., Schenberg, E.E., Nest, T., Orban, C., Leech, R., Williams, L.T., Williams, T.M., Bolstridge, M., Sessa, B., McGonigle, J., Sereno, M.I., Nichols, D., Hellyer, P.J., Hobden, P., Evans, J., Singh, K.D., Wise, R.G., Curran, H.V., Feilding, A., Nutt, D.J.: Neural correlates of the LSD experience revealed by multimodal neuroimaging. Proc. Natl. Acad. Sci. USA 113, 4853 (2016)
Ciccarelli, O., Catani, M., Johansen-Berg, H., Clark, C., Thompson, A.: Diffusion-based tractography in neurological disorders: concepts, applications, and future developments. Lancet Neurol. 7, 715 (2008)
Clayden, J.D.: Imaging connectivity: MRI and the structural networks of the brain. Funct. Neurol. 28, 197 (2013)
Cole, D.M., Smith, S.M., Beckmann, C.F.: Advances and pitfalls in the analysis and interpretation of resting-state FMRI data. Front. Syst. Neurosci. 4, 8 (2010)
Damoiseaux, J.S., Rombouts, S.A.R.B., Barkhof, F., Scheltens, P., Stam, C.J., Smith, S.M., Beckmann, C.F.: Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. USA 103, 13848 (2006)
Dang-Vu, T.T., Schabus, M., Desseilles, M., Albouy, G., Boly, M., Darsaud, A., Gais, S., Rauchs, G., Sterpenich, V., Vandewalle, G., Carrier, J., Moonen, G., Balteau, E., Degueldre, C., Luxen, A., Phillips, C., Maquet, P.: Spontaneous neural activity during human slow wave sleep. Proc. Natl. Acad. Sci. USA 105, 15160 (2008)
Deco, G., Jirsa, V.K.: Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. J. Neurosci. 32, 3366 (2012)
Deco, G., Kringelbach, M.L.: Great expectations: using whole-brain computational connectomics for understanding neuropsychiatric disorders. Neuron 84, 892 (2014)
Deco, G., Jirsa, V.K., McIntosh, A.R.: Emerging concepts for the dynamical organization of resting-state activity in the brain. Nat. Rev. Neurosci. 12, 43 (2011)
Deco, G., Jirsa, V.K., McIntosh, A.R.: Resting brains never rest: computational insights into potential cognitive architectures. Trends Neurosci. 36, 268 (2013)
Demirtas, M., Deco, G.: Chapter 4—computational models of dysconnectivity in large-scale resting-state networks. In: Anticevic, A., Murray, J.D. (eds.) Computational Psychiatry, pp. 87–116. Academic Press, New York (2018)
Desjardins, A.E., Kiehl, K.A., Liddle, P.F.: Removal of confounding effects of global signal in functional MRI analyses. NeuroImage 13, 751 (2001)
Farooq, H., Xu, J., Nam, J.W., Keefe, D.F., Yacoub, E., Georgiou, T., Lenglet, C.: Microstructure imaging of crossing (MIX) white matter fibers from diffusion MRI. Sci. Rep. 6, 38927 (2016)
Felleman, D.J., Van Essen, D.C.: Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1 (1991)
FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445 (1961)
Friston, K., Dolan, R.J.: Computational and dynamic models in neuroimaging. NeuroImage 52, 752 (2010)
Friston, K., Mechelli, A., Turner, R., Price, C.J.: Nonlinear responses in fMRI: the balloon model, Volterra kernels, and other hemodynamics. NeuroImage 12, 466 (2000)
Greve, D.N., Brown, G.G., Mueller, B.A., Glover, G., Liu, T.T.: A survey of the sources of noise in fMRI. Psychometrika 78, 396 (2013)
Hauptmann, C., Omel’chenko, O.E., Popovych, O., Maistrenko, Y., Tass, P.: Control of spatially patterned synchrony with multisite delayed feedback. Phys. Rev. E 76, 066209 (2007)
Haynes, J.D., Rees, G.: Decoding mental states from brain activity in humans. Nat. Rev. Neurosci. 7, 523 (2006)
Heeger, D.J., Ress, D.: What does MRI tell us about neuronal activity? Nat. Rev. Neurosci. 3, 142 (2002)
Hellyer, P.J., Shanahan, M., Scott, G., Wise, R.J.S., Sharp, D.J., Leech, R.: The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention. J. Neurosci. 34, 451 (2014)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500 (1952)
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. USA 106, 2035 (2009)
Huang, Z., Dai, R., Wu, X., Yang, Z., Liu, D., Hu, J., Gao, L., Tang, W., Mao, Y., Jin, Y., Wu, X., Liu, B., Zhang, Y., Lu, L., Laureys, S., Weng, X., Northoff, G.: The self and its resting state in consciousness: an investigation of the vegetative state. Hum. Brain Mapp. 35, 1997 (2014)
Hutchings, F., Han, C.E., Keller, S.S., Weber, B., Taylor, P.N., Kaiser, M.: Predicting surgery targets in temporal lobe epilepsy through structural connectome based simulations. PLoS Comput. Biol. 11, e1004642 (2015)
Iturria-Medina, Y., Sotero, R.C., Canales-Rodríguez, E.J., Alemán-Gómez, Y., Melie-García, L.: Studying the human brain anatomical network via diffusion-weighted MRI and graph theory. NeuroImage 40, 1064 (2008)
Izhikevich, E.M.: Which model to use for cortical spiking neurons? IEEE Trans. Neural Netw. 15, 1063 (2004)
Jbabdi, S., Sotiropoulos, S.N., Haber, S.N., Van Essen, D.C., Behrens, T.E.: Measuring macroscopic brain connections in vivo. Nat. Neurosci. 18, 1546 (2015)
Jirsa, V.K., Haken, H.: Field theory of electromagnetic brain activity. Phys. Rev. Lett. 77, 960 (1996)
Kanwisher, N.: Functional specificity in the human brain: a window into the functional architecture of the mind. Proc. Natl. Acad. Sci. USA 107, 11163 (2010)
Keane, A., Dahms, T., Lehnert, J., Suryanarayana, S.A., Hövel, P., Schöll, E.: Synchronisation in networks of delay-coupled type-I excitable systems. Eur. Phys. J. B 85, 407 (2012)
Koch, M.A., Norris, D.G., Hund-Georgiadis, M.: An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage 16, 241 (2002)
Kruggel, F., von Cramon, D.Y., Descombes, X.: Comparison of filtering methods for fMRI datasets. NeuroImage 10, 530 (1999)
Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators. In: Araki, H. (ed.) International Symposium on Mathematical Problems in Theoretical Physics, vol. 39 of Lecture Notes in Physics, pp. 420–422. Springer, Berlin (1975)
Lehnert, J., Dahms, T., Hövel, P., Schöll, E.: Loss of synchronization in complex neural networks with delay. Europhys. Lett. 96, 60013 (2011)
Liang, X., Tang, M., Dhamala, M., Liu, Z.: Phase synchronization of inhibitory bursting neurons induced by distributed time delays in chemical coupling. Phys. Rev. E 80, 066202 (2009)
Liu, Y., Liang, M., Zhou, Y., He, Y., Hao, Y., Song, M., Yu, C., Liu, H., Liu, Z., Jiang, T.: Disrupted small-world networks in schizophrenia. Brain 131, 945 (2008)
Lowe, M.J.: A historical perspective on the evolution of resting-state functional connectivity with MRI. Magn. Reson. Mater. Phys. 23, 279 (2010)
Masoller, C., Torrent, M.C., García-Ojalvo, J.: Interplay of subthreshold activity, time-delayed feedback, and noise on neuronal firing patterns. Phys. Rev. E 78, 041907 (2008)
Masoller, C., Torrent, M.C., García-Ojalvo, J.: Dynamics of globally delay-coupled neurons displaying subthreshold oscillations. Phil. Trans. R. Soc. A Math. Phys. Eng. Sci. 367, 3255 (2009)
Mosekilde, E., Maistrenko, Y., Postnov, D.: Chaotic Synchronization: Applications to Living Systems. World Scientific, Singapore (2002)
Muldoon, S.F., Pasqualetti, F., Gu, S., Cieslak, M., Grafton, S.T., Vettel, J.M., Bassett, D.S.: Stimulation-based control of dynamic brain networks. PLoS Comput. Biol. 12, e1005076 (2016)
Nagumo, J., Arimoto, S., Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061 (1962)
Nicosia, V., Valencia, M., Chavez, M., Díaz-Guilera, A., Latora, V.: Remote synchronization reveals network symmetries and functional modules. Phys. Rev. Lett. 110, 174102 (2013)
Noirhomme, Q., Soddu, A., Lehembre, R., Vanhaudenhuyse, A., Boveroux, P., Boly, M., Laureys, S.: Brain connectivity in pathological and pharmacological coma. Front. Syst. Neurosci. 4, 160 (2010)
Onias, H., Viol, A., Palhano-Fontes, F., Andrade, K.C., Sturzbecher, M., Viswanathan, G.M., de Araujo, D.B.: Brain complex network analysis by means of resting state fMRI and graph analysis: will it be helpful in clinical epilepsy? Epilepsy Behav. 38, 71 (2014)
Pikovsky, A., Rosenblum, M.G., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)
Popovych, O., Yanchuk, S., Tass, P.: Delay- and coupling-induced firing patterns in oscillatory neural loops. Phys. Rev. Lett. 107, 228102 (2011)
Power, J.D., Mitra, A., Laumann, T.O., Snyder, A.Z., Schlaggar, B.L., Petersen, S.E.: Methods to detect, characterize, and remove motion artifact in resting state fMRI. Neuroimage 84, 320 (2014)
Rodrigues, F.A., Peron, T.K.D.M., Ji, P., Kurths, J.: The Kuramoto model in complex networks. Phys. Rep. 610, 1 (2016)
Rossoni, E., Chen, Y., Ding, M., Feng, J.: Stability of synchronous oscillations in a system of Hodgkin–Huxley neurons with delayed diffusive and pulsed coupling. Phys. Rev. E 71, 061904 (2005)
Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059 (2010)
Rubinov, M., Knock, S.A., Stam, C.J., Micheloyannis, S., Harris, A.W.F., Williams, L.M., Breakspear, M.: Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403 (2009)
Rudie, J.D., Brown, J.A., Beck-Pancer, D., Hernandez, L.M., Dennis, E.L., Thompson, P.M., Bookheimer, S.Y., Dapretto, M.: Altered functional and structural brain network organization in autism. NeuroImage Clin. 2, 79 (2013)
Sanz-Leon, P., Knock, S.A., Spiegler, A., Jirsa, V.K.: Mathematical framework for large-scale brain network modeling in The Virtual Brain. Neuroimage 111, 385 (2015)
Schall, J.D.: On building a bridge between brain and behavior. Annu. Rev. Psychol. 55, 23 (2004)
Schrouff, J., Perlbarg, V., Boly, M., Marrelec, G., Boveroux, P., Vanhaudenhuyse, A., Bruno, M.A., Laureys, S., Phillips, C., Pélégrini-Issac, M., Maquet, P., Benali, H.: Brain functional integration decreases during propofol-induced loss of consciousness. NeuroImage 57, 198 (2011)
Senthilkumar, D.V., Kurths, J., Lakshmanan, M.: Inverse synchronizations in coupled time-delay systems with inhibitory coupling. Chaos 19, 023107 (2009)
Seth, A.K., Chorley, P., Barnett, L.C.: Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling. NeuroImage 65, 540 (2013)
Shanahan, M.: Metastable chimera states in community-structured oscillator networks. Chaos 20, 013108 (2010)
Sporns, O.: Networks of the Brain. MIT Press, Cambridge (2011)
Sporns, O.: Structure and function of complex brain networks. Dialog. Clin. Neurosci. 15, 247 (2013)
Sporns, O., Tononi, G., Kötter, R.: The human connectome: a structural description of the human brain. PLoS Comput. Biol. 1, e42 (2005)
Strogatz, S.H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1 (2000)
Tagliazucchi, E., Carhart-Harris, R., Leech, R., Nutt, D., Chialvo, D.R.: Enhanced repertoire of brain dynamical states during the psychedelic experience. Hum. Brain Mapp. 35, 5442 (2014)
Talairach, J., Tournoux, P.: Co-planar Stereotaxic Atlas of the Human Brain. 3-Dimensional Proportional System: An Approach to Cerebral Imaging. Thieme, New York (1988)
Tognoli, E., Kelso, J.A.S.: The metastable brain. Neuron 81, 35 (2014)
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., Joliot, M.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15, 273 (2002)
Uhlhaas, P., Pipa, G., Lima, B., Melloni, L., Neuenschwander, S., Nikolic, D., Singer, W.: Neural synchrony in cortical networks: history, concept and current status. Front. Integr. Neurosci. 3, 17 (2009)
van den Heuvel, M.P., Hulshoff Pol, H.E.: Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20, 519 (2010)
Vása, F., Shanahan, M., Hellyer, P.J., Scott, G., Cabral, J., Leech, R.: Effects of lesions on synchrony and metastability in cortical networks. NeuroImage 118, 456 (2015)
Viol, A., Palhano-Fontes, F., Onias, H., de Araujo, D.B., Viswanathan, G.M.: Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca. Sci. Rep. 7, 7388 (2017)
Vuksanović, V., Hövel, P.: Functional connectivity of distant cortical regions: role of remote synchronization and symmetry in interactions. NeuroImage 97, 1 (2014)
Vuksanović, V., Hövel, P.: Dynamic changes in network synchrony reveal resting-state functional networks. Chaos 25, 023116 (2015)
Vuksanović, V., Hövel, P.: Large-scale neural network model for functional networks of the human cortex. In: Pelster, A., Wunner, G. (eds.) Selforganization in Complex Systems: The Past, Present, and Future of Synergetics, Proceedings of the International Symposium, Hanse Institute of Advanced Studies Delmenhorst, pp. 345–352. Springer, Berlin (2016a). (Understanding Complex Systems)
Vuksanović, V., Hövel, P.: Role of structural inhomogeneities in resting-state brain dynamics. Cogn. Neurodyn. 10, 361 (2016b)
Wang, Q.Y., Lu, Q.S.: Time delay-enhanced synchronization and regularization in two coupled chaotic neurons. Chin. Phys. Lett. 22, 543 (2005)
Wang, Q., Lu, Q., Chen, G.: Synchronization transition induced by synaptic delay in coupled fast-spiking neurons. Int. J. Bifur. Chaos 18, 1189 (2008)
Wang, Q., Lu, Q., Chen, G., Feng, Z., Duan, L.X.: Bifurcation and synchronization of synaptically coupled FHN models with time delay. Chaos Solitons Fractals 39, 918 (2009)
Wildie, M., Shanahan, M.: Hierarchical clustering identifies hub nodes in a model of resting-state brain activity. In: The 2012 International Joint Conference on Neural Networks (IJCNN), pp. 1–6. IEEE (2012)
Womelsdorf, T., Schoffelen, J.M., Oostenveld, R., Singer, W., Desimone, R.: Modulation of neuronal interactions through neuronal synchronization. Science 316, 1609 (2007)
Xia, M., Wang, J., He, Y.: Brainnet viewer: a network visualization tool for human brain connectomics. PLoS ONE 8, 1 (2013)
Acknowledgements
AV and PH acknowledge support by Deutsche Forschungsgemeinschaft under Grant No. HO4695/3-1 and within the framework of Collaborative Research Center 910. We thank Yasser Iturria-Medina for sharing the DW-MRI data including fiber lengths used in the study. We also thank Jason Bassett for helpful discussions.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Paul Newton.
A List of Cortical and Subcortical Regions
A List of Cortical and Subcortical Regions
See Table 1.
Rights and permissions
About this article
Cite this article
Hövel, P., Viol, A., Loske, P. et al. Synchronization in Functional Networks of the Human Brain. J Nonlinear Sci 30, 2259–2282 (2020). https://doi.org/10.1007/s00332-018-9505-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00332-018-9505-7