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Modern network science of neurological disorders

Key Points

  • Healthy structural and functional brain networks are characterized by a cost-effective architecture, which has an optimal balance between local and global connectivity, and a hierarchical modular structure.

  • Normal brain-network organization arises during development under genetic control and is correlated with cognitive function.

  • Local brain lesions give rise to widespread changes to networks, whereas global brain disorders preferentially affect highly connected hub regions.

  • In many neurological disorders, the most consistent changes concern a breakdown of the hierarchical modular structure and, in particular, a loss of highly connected hub areas.

  • The pattern of network changes in neurological disorders may be explained by a hypothetical scenario of 'hub overload and failure'.

Abstract

Modern network science has revealed fundamental aspects of normal brain-network organization, such as small-world and scale-free patterns, hierarchical modularity, hubs and rich clubs. The next challenge is to use this knowledge to gain a better understanding of brain disease. Recent developments in the application of network science to conditions such as Alzheimer's disease, multiple sclerosis, traumatic brain injury and epilepsy have challenged the classical concept of neurological disorders being either 'local' or 'global', and have pointed to the overload and failure of hubs as a possible final common pathway in neurological disorders.

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Figure 1: Organization of normal brain networks.
Figure 2: Simulation of the widespread effects of local lesions.
Figure 3: Network changes in Alzheimer's disease.
Figure 4: Future clinical use of network modelling in epilepsy surgery.
Figure 5: Hub overload and failure as final common pathway of brain disease.

References

  1. Barabasi, A. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999). A classic study that introduces a model of scale-free networks that arise from growth by preferential attachment.

    CAS  PubMed  Google Scholar 

  2. Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440–442 (1998). This paper showed for the first time how clustering and short paths could be combined in small-world networks. It was a major starting point for much of the recent interest in complex-network studies.

    CAS  PubMed  Google Scholar 

  3. Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Rev. Neurosci. 10, 186–198 (2009).

    CAS  Google Scholar 

  4. Stam, C. J. & van Straaten, E. C. W. The organization of physiological brain networks. Clin. Neurophysiol. 123, 1067–1087 (2012).

    CAS  PubMed  Google Scholar 

  5. van den Heuvel, M. P. & Hulshoff Pol, H. E. Exploring the brain network: a review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20, 519–534 (2010).

    CAS  PubMed  Google Scholar 

  6. Bullmore, E. & Sporns, O. The economy of brain network organization. Nature Rev. Neurosci. 13, 336–349 (2012). This review discusses in detail how the organization of brain networks can be understood in terms of connection cost and information-processing efficiency.

    CAS  Google Scholar 

  7. Sporns, O. Structure and function of complex brain networks. Dialogues Clin. Neurosci. 15, 247–262 (2013).

    PubMed  PubMed Central  Google Scholar 

  8. Meunier, D., Lambiotte, R. & Bullmore, E. T. Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010).

    PubMed  PubMed Central  Google Scholar 

  9. Hoff, G. E. A.-J., van den Heuvel, M. P., Benders, M. J. N. L., Kersbergen, K. J. & De Vries, L. S. On development of functional brain connectivity in the young brain. Front. Hum. Neurosci. 7, 650 (2013).

    PubMed  PubMed Central  Google Scholar 

  10. Bassett, D. S. & Bullmore, E. T. Human brain networks in health and disease. Curr. Opin. Neurol. 22, 340–347 (2009).

    PubMed  PubMed Central  Google Scholar 

  11. Filippi, M. et al. Assessment of system dysfunction in the brain through MRI-based connectomics. Lancet Neurol. 12, 1189–1199 (2013).

    PubMed  Google Scholar 

  12. Hulshoff Pol, H. & Bullmore, E. Neural networks in psychiatry. Eur. Neuropsychopharmacol. 23, 1–6 (2013).

    CAS  PubMed  Google Scholar 

  13. Sharp, D. J., Scott, G. & Leech, R. Network dysfunction after traumatic brain injury. Nature Rev. Neurol. 10, 156–166 (2014).

    Google Scholar 

  14. Tijms, B. M. et al. Alzheimer's disease: connecting findings from graph theoretical studies of brain networks. Neurobiol. Aging 34, 2023–2036 (2013).

    PubMed  Google Scholar 

  15. van den Heuvel, M. P. & Sporns, O. Network hubs in the human brain. Trends Cogn. Sci. 17, 683–696 (2013). One of the first studies to introduce the concept of a rich club — a subgraph of strongly interconnected hubs — in the context of brain networks.

    PubMed  Google Scholar 

  16. Heimans, J. J. & Reijneveld, J. C. Factors affecting the cerebral network in brain tumor patients. J. Neurooncol. 108, 231–237 (2012).

    PubMed  PubMed Central  Google Scholar 

  17. Rehme, A. K. & Grefkes, C. Cerebral network disorders after stroke: evidence from imaging-based connectivity analyses of active and resting brain states in humans. J. Physiol. 591, 17–31 (2013).

    CAS  PubMed  Google Scholar 

  18. Xu, H. et al. Reduced efficiency of functional brain network underlying intellectual decline in patients with low-grade glioma. Neurosci. Lett. 543, 27–31 (2013).

    CAS  PubMed  Google Scholar 

  19. de Haan, W., Mott, K., van Straaten, E. C. W., Scheltens, P. & Stam, C. J. Activity dependent degeneration explains hub vulnerability in Alzheimer's disease. PLoS Comput. Biol. 8, e1002582 (2012). A simulation study that shows how synaptic damage due to excessive neural activity can give rise to a cascade of events that result in damage to hub regions, as observed in AD.

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Honey, C. J. & Sporns, O. Dynamical consequences of lesions in cortical networks. Hum. Brain Mapp. 29, 802–809 (2008).

    PubMed  Google Scholar 

  21. van Dellen, E. et al. Local polymorphic delta activity in cortical lesions causes global decreases in functional connectivity. Neuroimage 83, 524–532 (2013).

    CAS  PubMed  Google Scholar 

  22. Kandel, E. R., Markram, H., Matthews, P. M., Yuste, R. & Koch, C. Neuroscience thinks big (and collaboratively). Nature Rev. Neurosci. 14, 659–664 (2013).

    CAS  Google Scholar 

  23. He, Y. & Evans, A. Graph theoretical modeling of brain connectivity. Curr. Opin. Neurol. 23, 341–350 (2010).

    PubMed  Google Scholar 

  24. Sporns, O. Networks of the Brain. (MIT Press, 2010).

    Google Scholar 

  25. Gómez-Gardeñes, J., Zamora-López, G., Moreno, Y. & Arenas, A. From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex. PLoS ONE 5, e12313 (2010).

    PubMed  PubMed Central  Google Scholar 

  26. van den Heuvel, M. P. & Sporns, O. Rich-club organization of the human connectome. J. Neurosci. 31, 15775–15786 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Pan, R. K. & Sinha, S. Modular networks emerge from multiconstraint optimization. Phys. Rev. 76, 045103 (2007).

    Google Scholar 

  28. Fornito, A. et al. Genetic influences on cost-efficient organization of human cortical functional networks. J. Neurosci. 31, 3261–3270 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Smit, D. J. A. et al. Endophenotypes in a dynamically connected brain. Behav. Genet. 40, 167–177 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. van den Heuvel, M. P. et al. Genetic control of functional brain network efficiency in children. Eur. Neuropsychopharmacol. 23, 19–23 (2013).

    CAS  PubMed  Google Scholar 

  31. Meunier, D., Stamatakis, E. A. & Tyler, L. K. Age-related functional reorganization, structural changes, and preserved cognition. Neurobiol. Aging 35, 42–54 (2014).

    PubMed  Google Scholar 

  32. Wu, K. et al. Age-related changes in topological organization of structural brain networks in healthy individuals. Hum. Brain Mapp. 33, 552–568 (2012).

    CAS  PubMed  Google Scholar 

  33. Boersma, M. et al. Network analysis of resting state EEG in the developing young brain: structure comes with maturation. Hum. Brain Mapp. 32, 413–425 (2011).

    PubMed  Google Scholar 

  34. Boersma, M. et al. Growing trees in child brains: graph theoretical analysis of electroencephalography-derived minimum spanning tree in 5- and 7-year-old children reflects brain maturation. Brain Connect. 3, 50–60 (2013).

    PubMed  Google Scholar 

  35. Nijhuis, E. H. J., van Cappellen van Walsum, A.-M. & Norris, D. G. Topographic hub maps of the human structural neocortical network. PLoS ONE 8, e65511 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Schoonheim, M. M. et al. Gender-related differences in functional connectivity in multiple sclerosis. Mult. Scler. 18, 164–173 (2012).

    PubMed  Google Scholar 

  37. Schoonheim, M. M. et al. Functional connectivity changes in multiple sclerosis patients: a graph analytical study of MEG resting state data. Hum. Brain Mapp. 34, 52–61 (2013).

    PubMed  Google Scholar 

  38. Wu, K. et al. Topological organization of functional brain networks in healthy children: differences in relation to age, sex, and intelligence. PLoS ONE 8, e55347 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. Li, Y. et al. Brain anatomical network and intelligence. PLoS Comput. Biol. 5, e1000395 (2009). This study demonstrates a direct connection between the topological properties of structural brain networks and intelligence.

    PubMed  PubMed Central  Google Scholar 

  40. van den Heuvel, M. P., Stam, C. J., Kahn, R. S. & Hulshoff Pol, H. E. Efficiency of functional brain networks and intellectual performance. J. Neurosci. 29, 7619–7624 (2009). This study shows that shorter paths of functional brain networks, especially in relation to hub regions, are strongly associated with higher intelligence.

    CAS  PubMed  PubMed Central  Google Scholar 

  41. Douw, L. et al. Cognition is related to resting-state small-world network topology: an magnetoencephalographic study. Neuroscience 175, 169–177 (2011).

    CAS  PubMed  Google Scholar 

  42. Langer, N. et al. Functional brain network efficiency predicts intelligence. Hum. Brain Mapp. 33, 1393–1406 (2012).

    PubMed  Google Scholar 

  43. Crossley, N. A. et al. Cognitive relevance of the community structure of the human brain functional coactivation network. Proc. Natl Acad. Sci. USA 110, 11583–11588 (2013). This is the most extensive study on the cognitive relevance of subnetworks or modules in brain networks.

    CAS  PubMed  Google Scholar 

  44. van der Flier, W. M. et al. Optimizing patient care and research: the Amsterdam Dementia Cohort. J. Alzheimers. Dis. 41, 313–327 (2014).

    PubMed  Google Scholar 

  45. Olde Dubbelink, K. T. et al. Disrupted brain network topology in Parkinson's disease: a longitudinal magnetoencephalography study. Brain 137, 197–207 (2014). A prospective MEG study that shows a progressive network disorganization and loss of hubs in PD.

    PubMed  Google Scholar 

  46. Agosta, F. et al. Brain network connectivity assessed using graph theory in frontotemporal dementia. Neurology 81, 134–143 (2013).

    PubMed  Google Scholar 

  47. Skidmore, F. et al. Connectivity brain networks based on wavelet correlation analysis in Parkinson fMRI data. Neurosci. Lett. 499, 47–51 (2011).

    CAS  PubMed  Google Scholar 

  48. Baggio, H.-C. et al. Functional brain networks and cognitive deficits in Parkinson's disease. Hum. Brain Mapp. 35, 4620–4634 (2014).

    PubMed  Google Scholar 

  49. Stam, C. J. Use of magnetoencephalography (MEG) to study functional brain networks in neurodegenerative disorders. J. Neurol. Sci. 289, 128–134 (2010).

    CAS  PubMed  Google Scholar 

  50. Fornito, A. & Bullmore, E. T. Connectomics: a new paradigm for understanding brain disease. Eur. Neuropsychopharmacol. http://dx.doi.org/10.1016/j.euroneuro.2014.02.011 (2014).

  51. Xie, T. & He, Y. Mapping the Alzheimer's brain with connectomics. Front. Psychiatry 2, 77 (2011).

    PubMed  Google Scholar 

  52. Iturria-Medina, Y. Anatomical brain networks on the prediction of abnormal brain states. Brain Connect. 3, 1–21 (2013).

    PubMed  Google Scholar 

  53. Reid, A. T. & Evans, A. C. Structural networks in Alzheimer's disease. Eur. Neuropsychopharmacol. 23, 63–77 (2013).

    CAS  PubMed  Google Scholar 

  54. Stam, C. J. et al. The trees and the forest: characterization of complex brain networks with minimum spanning trees. Int. J. Psychophysiol. 92, 129–138 (2014).

    CAS  PubMed  Google Scholar 

  55. Delbeuck, X., van der Linden, M. & Collette, F. Alzheimer's disease as a disconnection syndrome? Neuropsychol. Rev. 13, 79–92 (2003).

    CAS  PubMed  Google Scholar 

  56. Heringa, S. M. et al. Multiple microbleeds are related to cerebral network disruptions in patients with early Alzheimer's disease. J. Alzheimers. Dis. 38, 211–221 (2014).

    PubMed  Google Scholar 

  57. de Haan, W. et al. Disruption of functional brain networks in Alzheimer's disease: what can we learn from graph spectral analysis of resting-state magnetoencephalography? Brain Connect. 2, 45–55 (2012).

    PubMed  Google Scholar 

  58. Wang, L. et al. Amnestic mild cognitive impairment: topological reorganization of the default-mode network. Radiology 268, 501–514 (2013).

    PubMed  Google Scholar 

  59. He, Y., Chen, Z. & Evans, A. Structural insights into aberrant topological patterns of large-scale cortical networks in Alzheimer's disease. J. Neurosci. 28, 4756–4766 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  60. Sanz-Arigita, E. J. et al. Loss of 'small-world' networks in Alzheimer's disease: graph analysis of fMRI resting-state functional connectivity. PLoS ONE 5, e13788 (2010).

    PubMed  PubMed Central  Google Scholar 

  61. Tijms, B. M. et al. Single-subject grey matter graphs in Alzheimer's disease. PLoS ONE 8, e58921 (2013). The first study to show abnormal structural brain networks in AD at the single-subject level.

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Lo, C.-Y. et al. Diffusion tensor tractography reveals abnormal topological organization in structural cortical networks in Alzheimer's disease. J. Neurosci. 30, 16876–16885 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  63. Reijmer, Y. D. et al. Disruption of cerebral networks and cognitive impairment in Alzheimer disease. Neurology 80, 1370–1377 (2013).

    PubMed  Google Scholar 

  64. de Haan, W. et al. Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory. BMC Neurosci. 10, 101 (2009).

    PubMed  PubMed Central  Google Scholar 

  65. Stam, C. J. et al. Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. Brain 132, 213–224 (2009). This study uses MEG to demonstrate abnormal functional network organization in AD and points out the importanceof hub connections in the disease process.

    CAS  PubMed  Google Scholar 

  66. de Waal, H. et al. The effect of souvenaid on functional brain network organisation in patients with mild Alzheimer's disease: a randomised controlled study. PLoS ONE 9, e86558 (2014).

    PubMed  PubMed Central  Google Scholar 

  67. Supekar, K., Menon, V., Rubin, D., Musen, M. & Greicius, M. D. Network analysis of intrinsic functional brain connectivity in Alzheimer's disease. PLoS Comput. Biol. 4, e1000100 (2008).

    PubMed  PubMed Central  Google Scholar 

  68. Brier, M. R. et al. Functional connectivity and graph theory in preclinical Alzheimer's disease. Neurobiol. Aging 35, 757–768 (2014).

    PubMed  Google Scholar 

  69. Seo, E. H. et al. Whole-brain functional networks in cognitively normal, mild cognitive impairment, and Alzheimer's disease. PLoS ONE 8, e53922 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  70. Yao, Z. et al. Abnormal cortical networks in mild cognitive impairment and Alzheimer's disease. PLoS Comput. Biol. 6, e1001006 (2010).

    PubMed  PubMed Central  Google Scholar 

  71. Vecchio, F. et al. Human brain networks in cognitive decline: a graph theoretical analysis of cortical connectivity from EEG data. J. Alzheimers. Dis. 41, 113–127 (2014).

    PubMed  Google Scholar 

  72. Zhao, X. et al. Disrupted small-world brain networks in moderate Alzheimer's disease: a resting-state fMRI study. PLoS ONE 7, e33540 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  73. Liu, Z. et al. Altered topological patterns of brain networks in mild cognitive impairment and Alzheimer's disease: a resting-state fMRI study. Psychiatry Res. 202, 118–125 (2012).

    PubMed  Google Scholar 

  74. Stam, C. J., Jones, B. F., Nolte, G., Breakspear, M. & Scheltens, P. Small-world networks and functional connectivity in Alzheimer's disease. Cereb. Cortex 17, 92–99 (2007).

    CAS  PubMed  Google Scholar 

  75. de Haan, W. et al. Disrupted modular brain dynamics reflect cognitive dysfunction in Alzheimer's disease. Neuroimage 59, 3085–3093 (2012).

    CAS  PubMed  Google Scholar 

  76. Chen, G. et al. Modular reorganization of brain resting state networks and its independent validation in Alzheimer's disease patients. Front. Hum. Neurosci. 7, 456 (2013).

    PubMed  PubMed Central  Google Scholar 

  77. Ciftçi, K. Minimum spanning tree reflects the alterations of the default mode network during Alzheimer's disease. Ann. Biomed. Eng. 39, 1493–1504 (2011).

    PubMed  Google Scholar 

  78. Tahaei, M. S., Jalili, M. & Knyazeva, M. G. Synchronizability of EEG-based functional networks in early Alzheimer's disease. IEEE Trans. Neural Syst. Rehabil. Eng. 20, 636–641 (2012).

    PubMed  Google Scholar 

  79. Minati, L. et al. Widespread alterations in functional brain network architecture in amnestic mild cognitive impairment. J. Alzheimers. Dis. 40, 213–220 (2014).

    PubMed  Google Scholar 

  80. Buckner, R. L. et al. Cortical hubs revealed by intrinsic functional connectivity: mapping, assessment of stability, and relation to Alzheimer's disease. J. Neurosci. 29, 1860–1873 (2009). Demonstration of the correlation between topological properties, in particular node degree, and spatial patterns of amyloid deposition in AD.

    CAS  PubMed  PubMed Central  Google Scholar 

  81. Shu, N. et al. Disrupted topological organization in white matter structural networks in amnestic mild cognitive impairment: relationship to subtype. Radiology 265, 518–527 (2012).

    PubMed  Google Scholar 

  82. Binnewijzend, M. A. A. et al. Brain network alterations in Alzheimer's disease measured by eigenvector centrality in fMRI are related to cognition and CSF biomarkers. Hum. Brain Mapp. 35, 2383–2393 (2014).

    PubMed  Google Scholar 

  83. He, Y. et al. Impaired small-world efficiency in structural cortical networks in multiple sclerosis associated with white matter lesion load. Brain 132, 3366–3379 (2009). A report of structural network abnormalities in MS and their relationship with white-matter lesions.

    PubMed  PubMed Central  Google Scholar 

  84. Shu, N. et al. Diffusion tensor tractography reveals disrupted topological efficiency in white matter structural networks in multiple sclerosis. Cereb. Cortex 21, 2565–2577 (2011).

    PubMed  Google Scholar 

  85. Liu, Y. et al. Altered topological organization of white matter structural networks in patients with neuromyelitis optica. PLoS ONE 7, e48846 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  86. Tewarie, P. et al. Cognitive and clinical dysfunction, altered MEG resting-state networks and thalamic atrophy in multiple sclerosis. PLoS ONE 8, e69318 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  87. Tewarie, P. et al. Functional brain network analysis using minimum spanning trees in multiple sclerosis: an MEG source-space study. Neuroimage 88, 308–318 (2014).

    CAS  PubMed  Google Scholar 

  88. Van Schependom, J. et al. Graph theoretical analysis indicates cognitive impairment in MS stems from neural disconnection. Neuroimage. Clin. 4, 403–410 (2014).

    Google Scholar 

  89. Caeyenberghs, K. et al. Brain connectivity and postural control in young traumatic brain injury patients: a diffusion MRI based network analysis. Neuroimage. Clin. 1, 106–115 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  90. Pollonini, L. et al. Information communication networks in severe traumatic brain injury. Brain Topogr. 23, 221–226 (2010).

    PubMed  Google Scholar 

  91. Tsirka, V. et al. Mild traumatic brain injury: graph-model characterization of brain networks for episodic memory. Int. J. Psychophysiol. 79, 89–96 (2011).

    PubMed  Google Scholar 

  92. Messé, A. et al. Specific and evolving resting-state network alterations in post-concussion syndrome following mild traumatic brain injury. PLoS ONE 8, e65470 (2013).

    PubMed  PubMed Central  Google Scholar 

  93. Nakamura, T., Hillary, F. G. & Biswal, B. B. Resting network plasticity following brain injury. PLoS ONE 4, e8220 (2009).

    PubMed  PubMed Central  Google Scholar 

  94. Pandit, A. S. et al. Traumatic brain injury impairs small-world topology. Neurology 80, 1826–1833 (2013). This study relates global brain-network abnormalities to cognitive deficits in traumatic brain injury, and also indicates a special role of hub-like structures

    PubMed  PubMed Central  Google Scholar 

  95. Han, K. et al. Disrupted modular organization of resting-state cortical functional connectivity in U.S. military personnel following concussive 'mild' blast-related traumatic brain injury. Neuroimage 84, 76–96 (2014).

    PubMed  Google Scholar 

  96. Achard, S. et al. Hubs of brain functional networks are radically reorganized in comatose patients. Proc. Natl Acad. Sci. USA 109, 20608–20613 (2012). This study shows that hub reorganization may be the most salient feature of brain networks that are in states of impaired consciousness.

    CAS  PubMed  Google Scholar 

  97. Caeyenberghs, K. et al. Graph analysis of functional brain networks for cognitive control of action in traumatic brain injury. Brain 135, 1293–1307 (2012).

    PubMed  Google Scholar 

  98. Caeyenberghs, K., Leemans, A., Leunissen, I., Michiels, K. & Swinnen, S. P. Topological correlations of structural and functional networks in patients with traumatic brain injury. Front. Hum. Neurosci. 7, 726 (2013).

    PubMed  PubMed Central  Google Scholar 

  99. Bernhardt, B. C., Hong, S., Bernasconi, A. & Bernasconi, N. Imaging structural and functional brain networks in temporal lobe epilepsy. Front. Hum. Neurosci. 7, 624 (2013).

    PubMed  PubMed Central  Google Scholar 

  100. Guye, M., Bettus, G., Bartolomei, F. & Cozzone, P. J. Graph theoretical analysis of structural and functional connectivity MRI in normal and pathological brain networks. MAGMA 23, 409–421 (2010).

    PubMed  Google Scholar 

  101. Onias, H. et al. Brain complex network analysis by means of resting state fMRI and graph analysis: will it be helpful in clinical epilepsy? Epilepsy Behav. http://dx.doi.org/10.1016/j.yebeh.2013.11.019 (2013).

  102. Minati, L., Varotto, G., D'Incerti, L., Panzica, F. & Chan, D. From brain topography to brain topology: relevance of graph theory to functional neuroscience. Neuroreport 24, 536–543 (2013).

    PubMed  Google Scholar 

  103. van Diessen, E., Diederen, S. J. H., Braun, K. P. J., Jansen, F. E. & Stam, C. J. Functional and structural brain networks in epilepsy: what have we learned? Epilepsia 54, 1855–1865 (2013).

    PubMed  Google Scholar 

  104. Bernhardt, B. C., Chen, Z., He, Y., Evans, A. C. & Bernasconi, N. Graph-theoretical analysis reveals disrupted small-world organization of cortical thickness correlation networks in temporal lobe epilepsy. Cereb. Cortex 21, 2147–2157 (2011).

    PubMed  Google Scholar 

  105. Bonilha, L. et al. Medial temporal lobe epilepsy is associated with neuronal fibre loss and paradoxical increase in structural connectivity of limbic structures. J. Neurol. Neurosurg. Psychiatry 83, 903–909 (2012).

    PubMed  PubMed Central  Google Scholar 

  106. Bonilha, L. et al. Presurgical connectome and postsurgical seizure control in temporal lobe epilepsy. Neurology 81, 1704–1710 (2013). This study illustrates the clinical importance of presurgical network changes in epilepsy for predicting surgical outcome.

    PubMed  PubMed Central  Google Scholar 

  107. DeSalvo, M. N., Douw, L., Tanaka, N., Reinsberger, C. & Stufflebeam, S. M. Altered structural connectome in temporal lobe epilepsy. Radiology 270, 842–848 (2014).

    PubMed  Google Scholar 

  108. Vaessen, M. J. et al. White matter network abnormalities are associated with cognitive decline in chronic epilepsy. Cereb. Cortex 22, 2139–2147 (2012).

    PubMed  Google Scholar 

  109. Xue, K. et al. Diffusion tensor tractography reveals disrupted structural connectivity in childhood absence epilepsy. Epilepsy Res. 108, 125–138 (2014).

    PubMed  Google Scholar 

  110. Ponten, S. C., Bartolomei, F. & Stam, C. J. Small-world networks and epilepsy: graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures. Clin. Neurophysiol. 118, 918–927 (2007). This is one of the first reports of pathological functional-network regularization during seizures recorded with depth electrodes.

    CAS  PubMed  Google Scholar 

  111. Kramer, M. A., Kolaczyk, E. D. & Kirsch, H. E. Emergent network topology at seizure onset in humans. Epilepsy Res. 79, 173–186 (2008).

    PubMed  Google Scholar 

  112. Schindler, K. A., Bialonski, S., Horstmann, M.-T., Elger, C. E. & Lehnertz, K. Evolving functional network properties and synchronizability during human epileptic seizures. Chaos 18, 033119 (2008).

    PubMed  Google Scholar 

  113. Takahashi, H., Takahashi, S., Kanzaki, R. & Kawai, K. State-dependent precursors of seizures in correlation-based functional networks of electrocorticograms of patients with temporal lobe epilepsy. Neurol. Sci. 33, 1355–1364 (2012).

    PubMed  Google Scholar 

  114. Ponten, S. C., Douw, L., Bartolomei, F., Reijneveld, J. C. & Stam, C. J. Indications for network regularization during absence seizures: weighted and unweighted graph theoretical analyses. Exp. Neurol. 217, 197–204 (2009).

    CAS  PubMed  Google Scholar 

  115. Gupta, D., Ossenblok, P. & van Luijtelaar, G. Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy: a MEG study. Med. Biol. Eng. Comput. 49, 555–565 (2011).

    PubMed  Google Scholar 

  116. Chavez, M., Valencia, M., Navarro, V., Latora, V. & Martinerie, J. Functional modularity of background activities in normal and epileptic brain networks. Phys. Rev. Lett. 104, 118701 (2010).

    CAS  PubMed  Google Scholar 

  117. Horstmann, M.-T. et al. State dependent properties of epileptic brain networks: comparative graph-theoretical analyses of simultaneously recorded EEG and MEG. Clin. Neurophysiol. 121, 172–185 (2010).

    PubMed  Google Scholar 

  118. Bartolomei, F., Bettus, G., Stam, C. J. & Guye, M. Interictal network properties in mesial temporal lobe epilepsy: a graph theoretical study from intracerebral recordings. Clin. Neurophysiol. 124, 2345–2353 (2013).

    CAS  PubMed  Google Scholar 

  119. Quraan, M. A., McCormick, C., Cohn, M., Valiante, T. A. & McAndrews, M. P. Altered resting state brain dynamics in temporal lobe epilepsy can be observed in spectral power, functional connectivity and graph theory metrics. PLoS ONE 8, e68609 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  120. van Dellen, E. et al. Long-term effects of temporal lobe epilepsy on local neural networks: a graph theoretical analysis of corticography recordings. PLoS ONE 4, e8081 (2009).

    PubMed  PubMed Central  Google Scholar 

  121. Clemens, B. et al. Neurophysiology of juvenile myoclonic epilepsy: EEG-based network and graph analysis of the interictal and immediate preictal states. Epilepsy Res. 106, 357–369 (2013).

    CAS  PubMed  Google Scholar 

  122. Douw, L. et al. Epilepsy is related to θ band brain connectivity and network topology in brain tumor patients. BMC Neurosci. 11, 103 (2010).

    PubMed  PubMed Central  Google Scholar 

  123. Douw, L. et al. 'Functional connectivity' is a sensitive predictor of epilepsy diagnosis after the first seizure. PLoS ONE 5, e10839 (2010).

    PubMed  PubMed Central  Google Scholar 

  124. Kuhnert, M.-T., Elger, C. E. & Lehnertz, K. Long-term variability of global statistical properties of epileptic brain networks. Chaos 20, 043126 (2010).

    PubMed  Google Scholar 

  125. Morgan, R. J. & Soltesz, I. Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures. Proc. Natl Acad. Sci. USA 105, 6179–6184 (2008). A detailed simulation of seizures in neural networks that demonstrates the importance of network topology, and in particular the presence of hubs, for the spreading of epileptic activity.

    CAS  PubMed  Google Scholar 

  126. Lee, U., Kim, S. & Jung, K. Y. Classification of epilepsy types through global network analysis of scalp electroencephalograms. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73, 041920 (2006).

    PubMed  Google Scholar 

  127. Ortega, G. J., Sola, R. G. & Pastor, J. Complex network analysis of human ECoG data. Neurosci. Lett. 447, 129–133 (2008).

    CAS  PubMed  Google Scholar 

  128. van Dellen, E. et al. Epilepsy surgery outcome and functional network alterations in longitudinal MEG: a minimum spanning tree analysis. Neuroimage 86, 354–363 (2014).

    PubMed  Google Scholar 

  129. Wilke, C., Worrell, G. & He, B. Graph analysis of epileptogenic networks in human partial epilepsy. Epilepsia 52, 84–93 (2011). One of the best illustrations that surgical removal of nodes with high centrality in functional brain networks is associated with a favourable surgical outcome in epilepsy.

    PubMed  Google Scholar 

  130. Amini, L. et al. Comparison of five directed graph measures for identification of leading interictal epileptic regions. Physiol. Meas. 31, 1529–1546 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  131. Varotto, G., Tassi, L., Franceschetti, S., Spreafico, R. & Panzica, F. Epileptogenic networks of type II focal cortical dysplasia: a stereo-EEG study. Neuroimage 61, 591–598 (2012).

    PubMed  Google Scholar 

  132. Kim, J.-Y., Kang, H.-C., Kim, K., Kim, H. D. & Im, C.-H. Localization of epileptogenic zones in Lennox-Gastaut syndrome (LGS) using graph theoretical analysis of ictal intracranial EEG: a preliminary investigation. Brain Dev. http://dx.doi.org/10.1016/j.braindev.2014.02.006 (2014).

  133. van Diessen, E., Otte, W. M., Braun, K. P. J., Stam, C. J. & Jansen, F. E. Improved diagnosis in children with partial epilepsy using a multivariable prediction model based on EEG network characteristics. PLoS ONE 8, e59764 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  134. Ibrahim, G. M. et al. Neocortical pathological high-frequency oscillations are associated with frequency-dependent alterations in functional network topology. J. Neurophysiol. 110, 2475–2483 (2013).

    PubMed  Google Scholar 

  135. van Diessen, E. et al. Are high frequency oscillations associated with altered network topology in partial epilepsy? Neuroimage 82, 564–573 (2013).

    PubMed  Google Scholar 

  136. Liao, W. et al. Altered functional connectivity and small-world in mesial temporal lobe epilepsy. PLoS ONE 5, e8525 (2010).

    PubMed  PubMed Central  Google Scholar 

  137. Song, M. et al. Impaired resting-state functional integrations within default mode network of generalized tonic–clonic seizures epilepsy. PLoS ONE 6, e17294 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  138. Vlooswijk, M. C. G. et al. Loss of network efficiency associated with cognitive decline in chronic epilepsy. Neurology 77, 938–944 (2011). An MRI study that shows the relationship between network changes and cognitive distrubances in chronic epilepsy.

    CAS  PubMed  Google Scholar 

  139. Vaessen, M. J. et al. Abnormal modular organization of functional networks in cognitively impaired children with frontal lobe epilepsy. Cereb. Cortex 23, 1997–2006 (2013).

    CAS  PubMed  Google Scholar 

  140. Liao, W. et al. Relationship between large-scale functional and structural covariance networks in idiopathic generalized epilepsy. Brain Connect. 3, 240–254 (2013).

    PubMed  PubMed Central  Google Scholar 

  141. Vaessen, M. J. et al. Functional and structural network impairment in childhood frontal lobe epilepsy. PLoS ONE 9, e90068 (2014).

    PubMed  PubMed Central  Google Scholar 

  142. Zhang, Z. et al. Altered functional–structural coupling of large-scale brain networks in idiopathic generalized epilepsy. Brain 134, 2912–2928 (2011).

    PubMed  Google Scholar 

  143. van Wijk, B. C. M., Stam, C. J. & Daffertshofer, A. Comparing brain networks of different size and connectivity density using graph theory. PLoS ONE 5, e13701 (2010).

    PubMed  PubMed Central  Google Scholar 

  144. Erdo˝s, P. & Rényi, A. On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5, 17–61 (in Russian, with an English summary) (1960).

    Google Scholar 

  145. Rapoport, A. A. Contribution to the theory of random and biased nets. Bull. Math. Biol. 19, 257–277 (1957).

    Google Scholar 

  146. Estrada, E. The Structure of Complex Networks. (Oxford Univ. Press, 2011).

    Google Scholar 

  147. Newman, M. E. J. Networks: An Introduction. (Oxford Univ. Press, 2010).

    Google Scholar 

  148. Barrat, A., Barthelemy, M. & Vespignani, A. Dynamical Processes on Complex Networks. (Cambridge Univ. Press, 2008).

    Google Scholar 

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Acknowledgements

The author thanks his colleagues, who participated in many of the studies described here and contributed to the ideas expressed in this Review.

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Correspondence to Cornelis J. Stam.

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C.J.S. is an unpaid advisor for Danone research.

PowerPoint slides

Glossary

Small-world networks

Networks characterized by a combination of high clustering (which represents local connectedness) and short path lengths (that is, short distances between any two nodes).

Scale-free networks

Networks in which the probability that a randomly chosen node has degree (number of connections) k is inversely proportional to k.

Hierarchical modularity

A type of network organization where each component (for instance, a module or cluster) is composed of smaller components but at the same time is part of a larger component.

Connectedness

A measure of the existence of connections (structural or functional) between network elements.

Degree distributions

The probability distribution (P(k)) of degrees over a network. P(k) is the probability P that a randomly chosen node has degree k.

Centrality

A measure of the relative importance of a node in a network. Various centrality measures exist (including degree, betweenness and eigenvector).

Multiconstraint optimization

Optimal network organization that takes into account multiple, often conflicting, constraints (for instance, wiring cost and path length).

Minimum spanning tree

An acyclic connected subnetwork that minimizes the cost function that is associated with edges.

Synchronizability

A property of a network that indicates whether a dynamical process on this network will reach a stable synchronized state.

Neuromyelitis optica

A demyelinating disorder that affects optic nerves.

Ictal state

Brain state during an epileptic seizure.

Cryptogenic localization-related epilepsy

Focal epilepsy that is putatively due to a local structural abnormality which cannot yet be demonstrated.

Absence epilepsy

A form of generalized epilepsy that is characterized by 3 Hz spike–wave discharges in the electroencephalogram.

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Stam, C. Modern network science of neurological disorders. Nat Rev Neurosci 15, 683–695 (2014). https://doi.org/10.1038/nrn3801

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