Journal of Computational Neuroscience

, Volume 38, Issue 3, pp 559–575 | Cite as

A probabilistic method for determining cortical dynamics during seizures

  • Vera M. Dadok
  • Heidi E. Kirsch
  • Jamie W. Sleigh
  • Beth A. Lopour
  • Andrew J. Szeri


This work presents a probabilistic method for inferring the parameter ranges in a biologically relevant mathematical model of the cortex most likely to be producing seizures observed in an electrocorticogram (ECoG) signal from a human subject. Additionally, this method produces a probabilistic pathway of the temporal evolution of physiological state in the cortex over the course of individual seizures, leveraging a model of the cortex that describes cortical physiology. We describe ways in which these methods and results offer insights into seizure etiology and have the potential to suggest new treatment options. To directly account for the stochastic and noisy nature of the mathematical model and the ECoG signal, we use a probabilistic Bayesian framework to map features of ECoG segments onto a distribution of likelihoods over physiologically-relevant parameter states. A Hidden Markov Model (HMM) is then introduced to incorporate the belief that cortical physiology has both temporal continuity and also a degree of reproducibility between individual seizures. By inspecting the ratio of likelihoods between HMMs run under two possible parameter regions, both of which produce seizures in the model, we determine which physiological parameter regions are more likely to be causing the observed seizures. We show that between individual seizures, there is consistency in these likelihood ratios between hypothesized regions, in the temporal pathways calculated, and in the separation of seizure from non-seizure time segment likelihood maps.


Cortex Seizure Epilepsy HMM 



This work was partially supported by an NSF Graduate Research Fellowship and in part by the National Science Foundation through the research grant CMMI 1031811. We would also like to thank Kevin Haas and Prashanth Selvaraj for their suggestions and insights.

Conflict of interests

The authors declare that they have no conflict of interest.


  1. Aarabi, A., & He, B. (2014). Seizure prediction in hippocampal and neocortical epilepsy using a model-based approach. Clinical Neurophysiology, 125(5), 930–940.PubMedCentralPubMedCrossRefGoogle Scholar
  2. Bazhenov, M., Timofeev, I., Fröhlich, F., & Sejnowski, T.J. (2008). Cellular and network mechanisms of electrographic seizures. Drug Discovery Today: Disease Models, 5(1), 45–57.PubMedCentralPubMedGoogle Scholar
  3. Blenkinsop, A., Valentin, A., Richardson, M.P., & Terry, J.R. (2012). The dynamic evolution of focal-onset epilepsies -combining theoretical and clinical observations. European Journal of Neuroscience, 36(2), 2188–2200.PubMedCrossRefGoogle Scholar
  4. Blümcke, I., Thom, M., Aronica, E., Armstrong, D.D., Vinters, H.V., Palmini, A., Jacques, T.S., Avanzini, G., Barkovich, A.J., Battaglia, G., & et al. (2011). The clinicopathologic spectrum of Focal Cortical Dysplasias: A consensus classification proposed by an ad hoc task force of the ILAE Diagnostic Methods Commission. Epilepsia, 52(1), 158–174.PubMedCentralPubMedCrossRefGoogle Scholar
  5. Bojak, I., & Liley, D.T.J. (2005). Modeling the effects of anesthesia on the electroencephalogram. Physical Review E, 71(4), 041902.CrossRefGoogle Scholar
  6. Bojak, I., & Liley, D.T.J. (2007). Self-organized 40 Hz synchronization in a physiological theory of EEG. Neurocomputing, 70(10), 2085–2090.CrossRefGoogle Scholar
  7. Boon, P., Vonck, K., Vandekerckhove, T., D’have, M., Nieuwenhuis, L., Michielsen, G., Vanbelleghem, H., Goethals, I., Caemaert, J., Calliauw, L., & Reuck, J.D. (1999). Vagus nerve stimulation for medically refractory epilepsy; efficacy and cost-benefit analysis. Acta Neurochirurgica, 141(5), 447–453.PubMedCrossRefGoogle Scholar
  8. Brodie, M.J., Covanis, A., Gil-Nagel, A., Lerche, H., Perucca, E., Sills, G.J., & White, H.S. (2011). Antiepileptic drug therapy: Does mechanism of action matter? Epilepsy & Behavior, 21(4), 331–341.CrossRefGoogle Scholar
  9. Dadok, V.M., Kirsch, H.E., Sleigh, J.W., Lopour, B.A., & Szeri, A.J. (2013). A probabilistic framework for a physiological representation of dynamically evolving sleep state. Journal of Computational Neuroscience. doi: 10.1007/s10827-013-0489-x.
  10. Elliott, R.E., Morsi, A., Kalhorn, S.P., Marcus, J., Sellin, J., Kang, M., Silverberg, A., Rivera, E., Geller, E., Carlson, C., Devinsky, O., & Doyle, W.K. (2011). Vagus nerve stimulation in 436 consecutive patients with treatment-resistant epilepsy: Long-term outcomes and predictors of response. Epilepsy & Behavior, 20(1), 57– 63.CrossRefGoogle Scholar
  11. Englot, D.J., Chang, E.F., & Auguste, K.I. (2011). Vagus nerve stimulation for epilepsy: A meta-analysis of efficacy and predictors of response. Journal of Neurosurgery, 115(6), 1248–1255.PubMedCrossRefGoogle Scholar
  12. Foster, B.L., Bojak, I., & Liley, D.T.J. (2008). Population based models of cortical drug response: Insights from anaesthesia. Cognitive Neurodynamics, 2(4), 283–296.PubMedCentralPubMedCrossRefGoogle Scholar
  13. Freestone, D.R., Aram, P., Dewar, M., Scerri, K., Grayden, D.B., & Kadirkamanathan, V. (2011). A data-driven framework for neural field modeling. NeuroImage, 56(3), 1043–58.PubMedCrossRefGoogle Scholar
  14. Friston, K.J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling. Neuroimage, 19(4), 1273–1302.PubMedCrossRefGoogle Scholar
  15. Friston, K.J., Li, B., Daunizeau, J., & Stephan, K.E. (2011). Network discovery with DCM. NeuroImage, 56(3), 1202– 1221.PubMedCentralPubMedCrossRefGoogle Scholar
  16. Good, L.B., Sabesan, S., Marsh, S.T., Tsakalis, K., Treiman, D., & Iasemidis, L. (2009). Control of synchronization of brain dynamics leads to control of epileptic seizures in rodents. International Journal of Neural Systems, 19(03), 173–196.PubMedCentralPubMedCrossRefGoogle Scholar
  17. Jobst, B.C. (2010). Electrical stimulation in epilepsy: Vagus nerve and brain stimulation. Current Treatment Options in Neurology, 12(5), 443–453.PubMedCrossRefGoogle Scholar
  18. Kandel, E., Schwartz, J., & Jessell, T. (2000). Principles of neural science, vol 4. New York: McGraw-Hill.Google Scholar
  19. Kiebel, S.J., Garrido, M.I., Moran, R., Chen, C.-C., & Friston, K.J. (2009). Dynamic causal modeling for EEG and MEG Human Brain Mapping, 30(6), 1866–1876.Google Scholar
  20. Kostopoulos, G.K. (2009). Encyclopedia of basic epilepsy research. In Schwartzkroin, PA (Ed.) (pp. 1327–1336): Academic.Google Scholar
  21. Kramer, M.A., Kirsch, H.E., & Szeri, A.J. (2005). Pathological pattern formation and cortical propagation of epileptic seizures. Journal of the Royal Society Interface, 2(2), 113–127.PubMedCentralCrossRefGoogle Scholar
  22. Kramer, M.A., Szeri, A.J., Sleigh, J.W., & Kirsch, H.E. (2007). Mechanisms of seizure propagation in a cortical model. Journal of Computational Neuroscience, 22(1), 63–80.PubMedCrossRefGoogle Scholar
  23. Kuhlmann, L., Burkitt, A.N., Cook, M.J., Fuller, K., Grayden, D.B., Seiderer, L., & Mareels, I.M.Y. (2009). Seizure detection using seizure probability estimation: Comparison of features used to detect seizures. Annals of Biomedical Engineering, 37(10), 2129–2145.PubMedCrossRefGoogle Scholar
  24. Kwan, P., & Brodie, M.J. (2000). Early identification of refractory epilepsy. New England Journal of Medicine, 342(5), 314–319.PubMedCrossRefGoogle Scholar
  25. Liley, D.T.J., & Bojak, I. (2005). Understanding the transition to seizure by modeling the epileptiform activity of general anesthetic agents. Journal of Clinical Neurophysiology, 22(5), 300–313.PubMedGoogle Scholar
  26. Liley, D.T.J., Cadusch, P.J., & Wright, J.J. (1999). A continuum theory of electro-cortical activity. Neurocomputing, 26, 795–800.CrossRefGoogle Scholar
  27. Liley, D.T.J., Cadusch, P.J., & Dafilis, M.P. (2002). A spatially continuous mean field theory of electrocortical activity. Network: Computation in Neural Systems, 13(1), 67–113.CrossRefGoogle Scholar
  28. Lopour, B.A., & Szeri, A.J. (2010). A model of feedback control for the charge-balanced suppression of epileptic seizures. Journal of Computational Neuroscience, 28(3), 375–387.PubMedCentralPubMedCrossRefGoogle Scholar
  29. Lopour, B.A., Tasoglu, S., Kirsch, H.E., Sleigh, J.W., & Szeri, A.J. (2011). A continuous mapping of sleep states through association of EEG with a mesoscale cortical model. Journal of Computational Neuroscience, 30(2), 471–487.PubMedCentralPubMedCrossRefGoogle Scholar
  30. MacKay, D.J.C. (2010). Information theory, inference, and learning algorithms: Cambridge University Press.Google Scholar
  31. Moran, R., Pinotsis, D.A., & Friston, K. (2013). Neural masses and fields in dynamic causal modeling. Frontiers in Computational Neuroscience, 7(57), 1–12.Google Scholar
  32. Nevado-Holgado, A.J., Marten, F., Richardson, M.P., & Terry, J.R. (2012). Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: Application to epilepsy seizure evolution. Neuroimage, 59(3), 2374–2392.PubMedCrossRefGoogle Scholar
  33. Picot, M.C., Baldy-Moulinier, M., Daurès, J.P., Dujols, P., & Crespel, A. (2008). The prevalence of epilepsy and pharmacoresistant epilepsy in adults: A population-based study in a western European country. Epilepsia, 49 (7), 1230–1238.PubMedCrossRefGoogle Scholar
  34. Pinotsis, D.A., Moran, R.J., & Friston, K.J. (2012). Dynamic causal modeling with neural fields. NeuroImage, 59(2), 1261–74.PubMedCentralPubMedCrossRefGoogle Scholar
  35. Schelter, B., Winterhalder, M., Maiwald, T., Brandt, A., Schad, A., Timmer, J., & Schulze-Bonhage, A. (2006). Do false predictions of seizures depend on the state of vigilance? A report from two seizure-prediction methods and proposed remedies. Epilepsia, 47(12), 2058–2070.PubMedCrossRefGoogle Scholar
  36. Selvaraj, P., Sleigh, J.W., Freeman, W.J., Kirsch, H.E., & Szeri, A.J. (2013). Open loop optogenetic control of cortical epileptiform activity. Journal of Computational Neuroscience.  10.1007/s10827-013-0484-2.
  37. Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W., & Liley, D.T.J. (1999). Theoretical electroencephalogram stationary spectrum for a white-noise-driven cortex: Evidence for a general anesthetic-induced phase transition. Physical Review E, 60(6), 7299.CrossRefGoogle Scholar
  38. Steyn-Ross, M.L., Steyn-Ross, D.A., Sleigh, J.W., & Whiting, D.R. (2003). Theoretical predictions for spatial covariance of the electroencephalographic signal during the anesthetic-induced phase transition: Increased correlation length and emergence of spatial self-organization. Physical Review E, 68(2), 021,902.CrossRefGoogle Scholar
  39. Steyn-Ross, M.L., Steyn-Ross, D.A., & Sleigh, J.W. (2004). Modelling general anaesthesia as a first-order phase transition in the cortex. Progress in Biophysics & Molecular Biology, 85, 369–385.CrossRefGoogle Scholar
  40. Steyn-Ross, M.L., Steyn-Ross, D.A., & Sleigh, J.W. (2012). Gap junctions modulate seizures in a mean-field model of general anesthesia for the cortex. Cognitive Neurodynamics, 6(3), 215–225.PubMedCentralPubMedCrossRefGoogle Scholar
  41. Sun, F.T., Morrell, M.J., & Wharen, R.E. (2008). Responsive cortical stimulation for the treatment of epilepsy. Neurotherapeutics, 5(1), 68–74.PubMedCrossRefGoogle Scholar
  42. Tsimpiris, A., & Kugiumtzis, D. (2010). Measures of analysis of time series (MATS): A MATLAB toolkit for computation of multiple measures on time series data bases. Journal of Statistical Software, 33(5).Google Scholar
  43. Vaseghi, S.V. (2008). Advanced digital signal processing and noise reduction. Chichester: Wiley.Google Scholar
  44. Wang, Y., Goodfellow, M., Taylor, P.N., & Baier, G. (2012). Phase space approach for modeling of epileptic dynamics. Physical Review E, 85(6), 061,918.CrossRefGoogle Scholar
  45. Wendling, F. (2008). Computational models of epileptic activity: a bridge between observation and pathophysiological interpretation. Expert Review of Neurotherapeutics, 8(6), 889.PubMedCentralPubMedCrossRefGoogle Scholar
  46. Wilson, M.T., Sleigh, J.W., Steyn-Ross, D.A., & Steyn-Ross, M.L. (2006a). General anesthetic-induced seizures can be explained by a mean-field model of cortical dynamics. Anesthesiology, 104(3), 588–593.PubMedCrossRefGoogle Scholar
  47. Wilson, M.T., Steyn-Ross, D.A., Sleigh, J.W., Steyn-Ross, M.L., Wilcocks, L.C., & Gillies, I.P. (2006b). The K-complex and slow oscillation in terms of a mean-field cortical model. Journal of Computational Neuroscience, 21(3), 243– 257.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vera M. Dadok
    • 1
  • Heidi E. Kirsch
    • 3
  • Jamie W. Sleigh
    • 4
  • Beth A. Lopour
    • 5
  • Andrew J. Szeri
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA
  2. 2.Center for Neural Engineering and Prostheses, and Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of NeurologyUniversity of CaliforniaSan FranciscoUSA
  4. 4.Department of Anesthetics, Waikato Clinical SchoolUniversity of AucklandHamiltonNew Zealand
  5. 5.Department of Biomedical EngineeringUniversity of CaliforniaIrvineUSA

Personalised recommendations