Skip to main content
SpringerLink
Log in

Identifying Influential Nodes in a Network Model of Epilepsy

  • Published:
Journal of Nonlinear Science Aims and scope Submit manuscript

Abstract

A significant proportion of individuals with epilepsy suffer from intractable forms of the disease. Current evidence suggests that pathological brain connectivity could be a major contributor to the propagation of focal seizures, constituting a possible cause for some forms of intractable epilepsy. Currently, however, the precise network structures that underpin epileptic brain connectivity are poorly understood. In this study, we use a computational model to simulate focal seizure spread in the macaque cortical connectome. We then use the results to propose a novel network centrality measure (called “Ictogenic Centrality”) that accurately identifies which nodes are most effective in propagating seizures. In the framework presented, ictogenic centrality outperforms other standard centrality measures in correctly identifying ictogenic nodes, exhibiting high accuracy (0.947), specificity (0.939), and sensitivity (0.964). Ictogenic centrality is degree based and relies on only a single free parameter, making it useful and efficient to compute for large networks. Our results suggest that baseline brain connectivity may predispose the temporal and frontal lobes toward ictogenicity even in the absence of any overtly pathological network reorganization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Bakker, R., Wachtler, T., Diesmann, M.: Cocomac 2.0 and the future of tract-tracing databases. Front. Neuroinform. 6, 30 (2012)

    Google Scholar 

  • Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    MathSciNet  MATH  Google Scholar 

  • Bartolomei, F., Lagarde, S., Wendling, F., McGonigal, A., Jirsa, V., Guye, M., Bénar, C.: Defining epileptogenic networks: contribution of seeg and signal analysis. Epilepsia 58(7), 1131–1147 (2017)

    Google Scholar 

  • Benjamin, O., Fitzgerald, T.H.B., Ashwin, P., Tsaneva-Atanasova, K., Chowdhury, F., Richardson, M.P., Terry, J.R.: A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy. J. Math. Neurosci. 2(1), 1 (2012)

    MathSciNet  MATH  Google Scholar 

  • Bergey, G.K., Morrell, M.J., Mizrahi, E.M., Goldman, A., King-Stephens, D., Nair, D., Srinivasan, S., Jobst, B., Gross, R.E., Shields, D.C., et al.: Long-term treatment with responsive brain stimulation in adults with refractory partial seizures. Neurology 84(8), 810–817 (2015)

    Google Scholar 

  • Bernhardt, B.C., Bonilha, L., Gross, D.W.: Network analysis for a network disorder: the emerging role of graph theory in the study of epilepsy. Epilepsy Behav. 50, 162–170 (2015)

    Google Scholar 

  • Bonilha, L., Nesland, T., Martz, G.U., Joseph, J.E., Spampinato, M.V., Edwards, J.C., Tabesh, A.: Medial temporal lobe epilepsy is associated with neuronal fibre loss and paradoxical increase in structural connectivity of limbic structures. J. Neurol. Neurosurg. Psychiatry 89(9), 903–909 (2012)

    Google Scholar 

  • Bonilha, L., Jensen, J.H., Baker, N., Breedlove, J., Nesland, T., Lin, J.J., Drane, D.L., Saindane, A.M., Binder, J.R., Kuzniecky, R.I.: The brain connectome as a personalized biomarker of seizure outcomes after temporal lobectomy. Neurology 84(18), 1846–1853 (2015)

    Google Scholar 

  • 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. Cerebral Cortex 16(9), 1296–1313 (2005)

    Google Scholar 

  • Buckmaster, P.S., Zhang, G.F., Yamawaki, R.: Axon sprouting in a model of temporal lobe epilepsy creates a predominantly excitatory feedback circuit. J. Neurosci. 22(15), 6650–6658 (2002)

    Google Scholar 

  • Chen, N., Liu, C., Yan, N., Wei, H., Zhang, J., Ge, Y., Meng, F.: A macaque model of mesial temporal lobe epilepsy induced by unilateral intrahippocampal injection of kainic acid. PLoS ONE 8(8), e72336 (2013)

    Google Scholar 

  • Chen, N., Gao, Y., Yan, N., Liu, C., Zhang, J.-G., Xing, W.-M., Kong, D.-M., Meng, F.-G.: High-frequency stimulation of the hippocampus protects against seizure activity and hippocampal neuronal apoptosis induced by kainic acid administration in macaques. Neuroscience 256, 370–378 (2014)

    Google Scholar 

  • Chen, Y.-C., Zhu, G.-Y., Wang, X., Shi, L., Jiang, Y., Zhang, X., Zhang, J.-G.: Deep brain stimulation of the anterior nucleus of the thalamus reverses the gene expression of cytokines and their receptors as well as neuronal degeneration in epileptic rats. Brain Res. 1657, 304–311 (2017)

    Google Scholar 

  • Cossu, M., Cardinale, F., Castana, L., Citterio, A., Francione, S., Tassi, L., Benabid, A.L., Lo Russo, G.: Stereoelectroencephalography in the presurgical evaluation of focal epilepsy: a retrospective analysis of 215 procedures. Neurosurgery 57(4), 706–718 (2005)

    Google Scholar 

  • Crossley, N.A., Mechelli, A., Scott, J., Carletti, F., Fox, P.T., McGuire, P., Bullmore, E.T.: The hubs of the human connectome are generally implicated in the anatomy of brain disorders. Brain 137(8), 2382–2395 (2014)

    Google Scholar 

  • Crunelli, V., Leresche, N.: Childhood absence epilepsy: genes, channels, neurons and networks. Nat. Rev. Neurosci. 3(5), 371 (2002)

    Google Scholar 

  • Da Silva, F.L., Blanes, W., Kalitzin, S.N., Parra, J., Suffczynski, P., Velis, D.N.: Epilepsies as dynamical diseases of brain systems: basic models of the transition between normal and epileptic activity. Epilepsia 44(12), 72–83 (2003)

    Google Scholar 

  • de Solla Price, D.: A general theory of bibliometric and other cumulative advantage processes. J. Am. Soc. Inf. Sci. 27(5), 292–306 (1976)

    Google Scholar 

  • Deco, G., Jirsa, V.K., McIntosh, A.R., Sporns, O., Kotter, R.: Key role of coupling, delay, and noise in resting brain fluctuations. Proc. Natl. Acad. Sci. USA 106, 10302–10307 (2009)

    Google Scholar 

  • Elsharkawy, A.E., Behne, F., Oppel, F., Pannek, H., Schulz, R., Hoppe, M., Pahs, G., Gyimesi, C., Nayel, M., Issa, A., et al.: Long-term outcome of extratemporal epilepsy surgery among 154 adult patients. J. Neurosurg. 108(4), 676–686 (2008)

    Google Scholar 

  • Engel Jr., J., Wiebe, S., French, J., Sperling, M., Williamson, P., Spencer, D., Gumnit, R., Zahn, C., Westbrook, E., Enos, B.: Practice parameter: temporal lobe and localized neocortical resections for epilepsy. Epilepsia 44(6), 741–751 (2003)

    Google Scholar 

  • Englot, D.J.: A modern epilepsy surgery treatment algorithm: Incorporating traditional and emerging technologies. Epilepsy Behav. 80, 68–74 (2018)

    Google Scholar 

  • Englot, D.J., Birk, H., Chang, E.F.: Seizure outcomes in nonresective epilepsy surgery: an update. Neurosurg. Rev. 40, 181–194 (2017)

    Google Scholar 

  • Fisher, R., Salanova, V., Witt, T., Worth, R., Henry, T., Gross, R., Oommen, K., Osorio, I., Nazzaro, J., Labar, D., et al.: Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy. Epilepsia 51(5), 899–908 (2010)

    Google Scholar 

  • Frässle, S., Lomakina, E.I., Kasper, L., Manjaly, Z.M., Leff, A., Pruessmann, K.P., Buhmann, J.M., Stephan, K.E.: A generative model of whole-brain effective connectivity. NeuroImage 179, 505–529 (2018)

    Google Scholar 

  • Ghosh, A., Rho, Y., McIntosh, A.R., Kötter, R., Jirsa, V.K.: Noise during rest enables the exploration of the brain’s dynamic repertoire. PLoS Computat. Biol. 4(10), e1000196 (2008)

    MathSciNet  Google Scholar 

  • Goodfellow, M., Rummel, C., Abela, E., Richardson, M.P., Schindler, K., Terry, J.R.: Estimation of brain network ictogenicity predicts outcome from epilepsy surgery. Sci. Rep. 6, 29215 (2016)

    Google Scholar 

  • Goulas, A., Bastiani, M., Bezgin, G., Uylings, H.B.M., Roebroeck, A., Stiers, P.: Comparative analysis of the macroscale structural connectivity in the macaque and human brain. PLoS Comput. Biol. 10(3), e1003529 (2014)

    Google Scholar 

  • Hindmarsh, J., Cornelius, P.: The development of the Hindmarsh–Rose model for bursting. In: Coombes, S., Bressloff, P.C. (eds.) Bursting: The Genesis of Rhythm in the Nervous System, pp. 3–18. World Scientific (2005)

  • Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. B 221(1222), 87–102 (1984)

    Google Scholar 

  • 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(12), e1004642 (2015)

    Google Scholar 

  • Hwang, D.-U., Chavez, M., Amann, A., Boccaletti, S.: Synchronization in complex networks with age ordering. Phys. Rev. Lett. 94(13), 138701 (2005)

    Google Scholar 

  • Ji, G.-J., Zhang, Z., Qiang, X., Zang, Y.-F., Liao, W., Guangming, L.: Generalized tonic-clonic seizures: aberrant interhemispheric functional and anatomical connectivity. Radiology 271(3), 839–847 (2014)

    Google Scholar 

  • Jirsa, V.K., Stacey, W.C., Quilichini, P.P., Ivanov, A.I., Bernard, C.: On the nature of seizure dynamics. Brain 137(8), 2210–2230 (2014)

    Google Scholar 

  • Jirsa, V.K., Proix, T., Perdikis, D., Woodman, M.M., Wang, H., Gonzalez-Martinez, J., Bernard, C., Bénar, C., Guye, M., Chauvel, P., et al.: The virtual epileptic patient: individualized whole-brain models of epilepsy spread. Neuroimage 145, 377–388 (2017)

    Google Scholar 

  • Kaiser, M., Hilgetag, C.C.: Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2(7), e95 (2006)

    Google Scholar 

  • Kale, P., Zalesky, A., Gollo, L.L.: Estimating the impact of structural directionality: how reliable are undirected connectomes? Netw. Neurosci. 2(2), 1–51 (2018)

    Google Scholar 

  • Kalitzin, S.N., Velis, D.N., da Silva, F.H.L.: Stimulation-based anticipation and control of state transitions in the epileptic brain. Epilepsy Behav. 17(3), 310–323 (2010)

    Google Scholar 

  • Khambhati, A.N., Davis, K.A., Lucas, T.H., Litt, B., Bassett, D.S.: Virtual cortical resection reveals push-pull network control preceding seizure evolution. Neuron 91(5), 1170–1182 (2016)

    Google Scholar 

  • Kim, J.B., Suh, S., Seo, W.-K., Oh, K., Koh, S.-B., Kim, J.H.: Altered thalamocortical functional connectivity in idiopathic generalized epilepsy. Epilepsia 55(4), 592–600 (2014)

    Google Scholar 

  • Klinger, N.V., Mittal, S.: Clinical efficacy of deep brain stimulation for the treatment of medically refractory epilepsy. Clin. Neurol. Neurosurg. 140, 11–25 (2016)

    Google Scholar 

  • Kötter, R.: Online retrieval, processing, and visualization of primate connectivity data from the cocomac database. Neuroinformatics 2(2), 127–144 (2004)

    Google Scholar 

  • Kötter, R., Wanke, E.: Mapping brains without coordinates. Philos. Trans. R. Soc. B: Biol. Sci. 360(1456), 751–766 (2005)

    Google Scholar 

  • Kwan, P., Sander, J.W.: The natural history of epilepsy: an epidemiological view. J. Neurol. Neurosurg. Psychiatry 75(10), 1376–1381 (2004)

    Google Scholar 

  • Liao, W., Zhang, Z., Pan, Z., Mantini, D., Ding, J., Duan, X., Luo, C., Guangming, L., Chen, H.: Altered functional connectivity and small-world in mesial temporal lobe epilepsy. PLoS ONE 5(1), e8525 (2010)

    Google Scholar 

  • Lytton, W.W.: Computer modelling of epilepsy. Nat. Rev. Neurosci. 9(8), 626 (2008)

    Google Scholar 

  • Manford, M., Hart, Y.M., Sander, J.W.A.S., Shorvon, S.D.: The national general practice study of epilepsy: the syndromic classification of the international league against epilepsy applied to epilepsy in a general population. Arch. Neurol. 49(8), 801–808 (1992)

    Google Scholar 

  • Maynard, L.M., Leach, J.L., Horn, P.S., Spaeth, C.G., Mangano, F.T., Holland, K.D., Miles, L., Faist, R., Greiner, H.M.: Epilepsy prevalence and severity predictors in MRI-identified focal cortical dysplasia. Epilepsy Res. 132, 41–49 (2017)

    Google Scholar 

  • 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. 105(16), 6179–6184 (2008)

    Google Scholar 

  • Mormann, F., Andrzejak, R.G., Elger, C.E., Lehnertz, K.: Seizure prediction: the long and winding road. Brain 130(2), 314–333 (2006)

    Google Scholar 

  • Morrell, M.J.: Responsive cortical stimulation for the treatment of medically intractable partial epilepsy. Neurology 77(13), 1295–1304 (2011)

    Google Scholar 

  • Newman, M.: Networks. Oxford University Press, Oxford (2018)

    MATH  Google Scholar 

  • Oh, S.W., Harris, J.A., Ng, L., Winslow, B., Cain, N., Mihalas, S., Wang, Q., Lau, C., Kuan, L., Henry, A.M., et al.: A mesoscale connectome of the mouse brain. Nature 508(7495), 207 (2014)

    Google Scholar 

  • Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: bringing order to the web. Technical report, Stanford InfoLab (1999)

  • Pecora, L.M., Carroll, T.L.: Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80(10), 2109 (1998)

    Google Scholar 

  • Petkov, G., Goodfellow, M., Richardson, M.P., Terry, J.R.: A critical role for network structure in seizure onset: a computational modeling approach. Front. Neurol. 5, 261 (2014)

    Google Scholar 

  • Prayson, R.A., Estes, M.L.: Cortical dysplasia: a histopathologic study of 52 cases of partial lobectomy in patients with epilepsy. Hum. Pathol. 26(5), 493–500 (1995)

    Google Scholar 

  • Proix, T., Bartolomei, F., Chauvel, P., Bernard, C., Jirsa, V.K.: Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy. J. Neurosci. 34(45), 15009–15021 (2014)

    Google Scholar 

  • Proix, T., Bartolomei, F., Guye, M., Jirsa, V.K.: Individual brain structure and modelling predict seizure propagation. Brain 140(3), 641–654 (2017)

    Google Scholar 

  • Semah, F., Broglin, D., Arzimanoglou, A., Cavalcanti, D., Baulac, M.: Is the underlying cause of epilepsy a major prognostic factor for recurrence? Neurology 51, 1256–1262 (1998)

    Google Scholar 

  • Shah, P., Bernabei, J., Kini, L., Ashourvan, A., Boccanfuso, J., Archer, R., Oechsel, K., Lucas, T.H., Bassett, D.S., Davis, K., et al.: High interictal connectivity within the resection zone is associated with favorable post-surgical outcomes in focal epilepsy patients. bioRxiv, pp. 459008 (2018)

  • Sinha, N., Dauwels, J., Kaiser, M., Cash, S.S., Brandon Westover, M., Wang, Y., Taylor, P.N.: Predicting neurosurgical outcomes in focal epilepsy patients using computational modelling. Brain 140(2), 319–332 (2016)

    Google Scholar 

  • Sørensen, A.T., Kokaia, M.: Novel approaches to epilepsy treatment. Epilepsia 54(1), 1–10 (2013)

    Google Scholar 

  • Spencer, S.S.: Neural networks in human epilepsy: evidence of and implications for treatment. Epilepsia 43(3), 219–227 (2002)

    MathSciNet  Google Scholar 

  • Sveinbjornsdottir, S., Duncan, J.S.: Parietal and occipital lobe epilepsy: a review. Epilepsia 34(3), 493–521 (1993)

    Google Scholar 

  • Taylor, P.N., Baier, G.: A spatially extended model for macroscopic spike-wave discharges. J. Comput. Neurosci. 31(3), 679–684 (2011)

    Google Scholar 

  • Taylor, P.N., Goodfellow, M., Wang, Y., Baier, G.: Towards a large-scale model of patient-specific epileptic spike-wave discharges. Biol. Cybern. 107(1), 83–94 (2013)

    Google Scholar 

  • Terry, J.R., Benjamin, O., Richardson, M.P.: Seizure generation: the role of nodes and networks. Epilepsia 53(9), e166–e169 (2012)

    Google Scholar 

  • Vaessen, M.J., Jansen, J.F.A., Braakman, H.M.H., Hofman, P.A.M., De Louw, A., Aldenkamp, A.P., Backes, W.H.: Functional and structural network impairment in childhood frontal lobe epilepsy. PLoS ONE 9(3), e90068 (2014)

    Google Scholar 

  • van Diessen, E., Zweiphenning, W.J.E.M., Jansen, F.E., Stam, C.J., Braun, K.P.J., Otte, W.M.: Brain network organization in focal epilepsy: a systematic review and meta-analysis. PLoS ONE 9(12), e114606 (2014)

    Google Scholar 

  • Velasco, A.L., Velasco, F., Jiménez, F., Velasco, M., Castro, G., Carrillo-Ruiz, J.D., Fanghänel, G., Boleaga, B.: Neuromodulation of the centromedian thalamic nuclei in the treatment of generalized seizures and the improvement of the quality of life in patients with lennox–gastaut syndrome. Epilepsia 47(7), 1203–1212 (2006)

    Google Scholar 

  • Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440 (1998)

    MATH  Google Scholar 

  • Wendling, F., Bartolomei, F., Bellanger, J.J., Chauvel, P.: Epileptic fast activity can be explained by a model of impaired gabaergic dendritic inhibition. Eur. J. Neurosci. 15(9), 1499–1508 (2002)

    Google Scholar 

  • Wendling, F., Chauvel, P., Biraben, A., Bartolomei, F.: From intracerebral eeg signals to brain connectivity: identification of epileptogenic networks in partial epilepsy. Front. Syst. Neurosci. 4, 154 (2010)

    Google Scholar 

  • World Health Organization: Neurological disorders: public health challenges. http://www.who.int/mental_health/neurology/neurological_disorders_report_web.pdf, p. 189 (2006). Accessed 11 Apr 2019

Download references

Acknowledgements

Special thanks to Bill Stacey and Steve Gliske for their helpful comments on this paper.

Funding

This work was supported by National Institutes of Health [R01-NS094399], the National Science Foundation [1560061], and the Ohio Wesleyan Summer Science Research Program.

Author information

Authors and Affiliations

  1. Ohio Wesleyan University, 61 South Sandusky Street, Delaware, OH, 43015, USA

    Joseph Emerson

  2. Wesleyan University, 45 Wyllys Avenue, Middletown, CT, 06459, USA

    Amber Afelin

  3. Vacaville, USA

    Viesulas Sliupas

  4. Gonzaga University, 502 East Boone Avenue, Spokane, WA, 99258, USA

    Christian G. Fink

Authors
  1. Joseph Emerson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amber Afelin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Viesulas Sliupas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christian G. Fink
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian G. Fink.

Additional information

Communicated by Paul Newton.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Emerson, J., Afelin, A., Sliupas, V. et al. Identifying Influential Nodes in a Network Model of Epilepsy. J Nonlinear Sci 30, 2283–2308 (2020). https://doi.org/10.1007/s00332-019-09545-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00332-019-09545-4

Keywords

Mathematics Subject Classification

Search

Navigation