American Institute of Mathematical Sciences

Advanced
2013, 10(3): 579-590. doi: 10.3934/mbe.2013.10.579

Identifying preseizure state in intracranial EEG data using diffusion kernels

Dominique Duncan 1, , Ronen Talmon 2, , Hitten P. Zaveri 3, and  Ronald R. Coifman 4,

1. 

101 AKW, 51 Prospect St. New Haven, CT 06511, United States
2. 

103 AKW, 51 Prospect St. New Haven, CT 06511, United States
3. 

716 LLCI, 15 York St. New Haven, CT 06520, United States
4. 

108A AKW, 51 Prospect St. New Haven, CT 06511, United States

Received  July 2012 Revised  December 2012 Published  April 2013

The goal of this study is to identify preseizure changes in intracranial EEG (icEEG). A novel approach based on the recently developed diffusion map framework, which is considered to be one of the leading manifold learning methods, is proposed. Diffusion mapping provides dimensionality reduction of the data as well as pattern recognition that can be used to distinguish different states of the patient, for example, interictal and preseizure. A new algorithm, which is an extension of diffusion maps, is developed to construct coordinates that generate efficient geometric representations of the complex structures in the icEEG data. In addition, this method is adapted to the icEEG data and enables the extraction of the underlying brain activity.
    The algorithm is tested on icEEG data recorded from several electrode contacts from a patient being evaluated for possible epilepsy surgery at the Yale-New Haven Hospital. Numerical results show that the proposed approach provides a distinction between interictal and preseizure states.
Keywords: epilepsy, diffusion maps, Intracranial EEG, seizure prediction, nonlinear independent component analysis.
Mathematics Subject Classification: 68T10, 65F15, 92B99, 92C20, 00A6.
Citation: Dominique Duncan, Ronen Talmon, Hitten P. Zaveri, Ronald R. Coifman. Identifying preseizure state in intracranial EEG data using diffusion kernels. Mathematical Biosciences & Engineering, 2013, 10 (3) : 579-590. doi: 10.3934/mbe.2013.10.579
References:
[1]

R. G. Andrzejak, F. Mormann, R. Kreuz, C. Rieke, A. Kraskov, C. E. Elger and K. Lehnertz, Testing the null hypothesis of the nonexistence of a preseizure state, Phys. Rev. E, 67 (2003), 10901. doi: 10.1103/PhysRevE.67.010901.

[2]

J. Britz, D. Van De Ville and C. M. Michel, BOLD correlates of EEG topography reveal rapid resting-state network dynamics, NeuroImage, 52 (2010), 1162-1170. doi: 10.1016/j.neuroimage.2010.02.052.

[3]

R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comp. Harm. Anal., 21 (2006), 5-30. doi: 10.1016/j.acha.2006.04.006.

[4]

D. Duncan, R. B. Duckrow, R. R. Coifman and H. P. Zaveri, Intracranial EEG Evaluation of a Resting State Network, Challenges of Modern Technology, 1 (2010), 27-29.

[5]

M. G. Frei, H. P. Zaveri, S. Arthurs, G. K. Bergey, C. C. Jouny, K. Lehnertz, J. Gotman, I. Osorio, T. I. Netoff, W. J. Freeman, J. Jefferys, G. Worrell, M. Le Van Quyen, S. J. Schiff and F. Mormann, Controversies in epilepsy: Debates held during the fourth international workshop on seizure prediction, Epilepsy and Behavior, 19 (2010), 4-16. doi: 10.1016/j.yebeh.2010.06.009.

[6]

I. I. Goncharova, H. P. Zaveri, R. B. Duckrow, E. J. Novotny and S. S. Spencer, Spatial distribution of intracranially recorded spikes in medial and lateral temporal epilepsies, Epilepsia, 50 (2009), 2575-85. doi: 10.1111/j.1528-1167.2009.02258.x.

[7]

W. A. Hauser, J. F. Annegers and W. A. Rocca, Descriptive epidemiology of epilepsy: Contributions of population-based studies from Rochester, Minnesota, Mayo. Clin. Proc., 71 (1996), 576-586. doi: 10.4065/71.6.576.

[8]

D. Kushnir, A. Haddad and R. R. Coifman, Anisotropic diffusion on sub-manifolds with application to earth structure classification, Appl. Comp. Harm. Anal., 32 (2012), 280-294. doi: 10.1016/j.acha.2011.06.002.

[9]

P. Kwan and M. J. Brodie, Early identification of refractory epilepsy, N. Engl. J. Med., 342 (2000), 314-319. doi: 10.1056/NEJM200002033420503.

[10]

F. Mormann, R. G. Andrzejak, C. E. Elger and K. Lehnertz, Seizure prediction: the long and winding road, Brain, 130 (2007), 314-333. doi: 10.1093/brain/awl241.

[11]

X. Papademetris, A. P. Jackowski, R. T. Schultz, L. H. Staib and J. S. Duncan, Integrated intensity and point-feature non-rigid registration, in "Medical Image Computing and Computer-Assisted Intervention" (Eds. C. Barillot, D. Haynor and P. Hellier) Saint-Malo: Springer, (2004), 763-770.

[12]

M. R. Portnoff, Time-frequency representation of digital signals and systems based on short-time Fourier analysis, IEEE Trans. Signal Process, ASSP-28, 55-69. doi: 10.1109/TASSP.1980.1163359.

[13]

A. Schulze-Bonhage, H. Feldwisch-Drentrup and M. Ihle, Epilepsy and behavior, Elsevier, 22 (2011), S88-S93. doi: 10.1016/j.yebeh.2003.11.021.

[14]

A. Singer and R. R. Coifman, Non-linear independent component analysis with diffusion maps, Appl. Comp. Harm. Anal., 25 (2008), 226-239. doi: 10.1016/j.acha.2007.11.001.

[15]

E. Susman, Brain stimulation reduces seizures in refractory adult epilepsy, Neurology Today, 9 (2009), 22-23. doi: 10.1097/01.NT.0000345158.91024.42.

[16]

R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking, submitted to PNAS, (2012).

[17]

R. Talmon, D. Kushnir, R. R. Coifman, I. Cohen and S. Gannot, Parametrization of linear systems using diffusion kernels, IEEE Trans. Signal Process, 60 (2012). doi: 10.1109/TSP.2011.2177973.

show all references

References:
[1]

R. G. Andrzejak, F. Mormann, R. Kreuz, C. Rieke, A. Kraskov, C. E. Elger and K. Lehnertz, Testing the null hypothesis of the nonexistence of a preseizure state, Phys. Rev. E, 67 (2003), 10901. doi: 10.1103/PhysRevE.67.010901.

[2]

J. Britz, D. Van De Ville and C. M. Michel, BOLD correlates of EEG topography reveal rapid resting-state network dynamics, NeuroImage, 52 (2010), 1162-1170. doi: 10.1016/j.neuroimage.2010.02.052.

[3]

R. R. Coifman and S. Lafon, Diffusion maps, Appl. Comp. Harm. Anal., 21 (2006), 5-30. doi: 10.1016/j.acha.2006.04.006.

[4]

D. Duncan, R. B. Duckrow, R. R. Coifman and H. P. Zaveri, Intracranial EEG Evaluation of a Resting State Network, Challenges of Modern Technology, 1 (2010), 27-29.

[5]

M. G. Frei, H. P. Zaveri, S. Arthurs, G. K. Bergey, C. C. Jouny, K. Lehnertz, J. Gotman, I. Osorio, T. I. Netoff, W. J. Freeman, J. Jefferys, G. Worrell, M. Le Van Quyen, S. J. Schiff and F. Mormann, Controversies in epilepsy: Debates held during the fourth international workshop on seizure prediction, Epilepsy and Behavior, 19 (2010), 4-16. doi: 10.1016/j.yebeh.2010.06.009.

[6]

I. I. Goncharova, H. P. Zaveri, R. B. Duckrow, E. J. Novotny and S. S. Spencer, Spatial distribution of intracranially recorded spikes in medial and lateral temporal epilepsies, Epilepsia, 50 (2009), 2575-85. doi: 10.1111/j.1528-1167.2009.02258.x.

[7]

W. A. Hauser, J. F. Annegers and W. A. Rocca, Descriptive epidemiology of epilepsy: Contributions of population-based studies from Rochester, Minnesota, Mayo. Clin. Proc., 71 (1996), 576-586. doi: 10.4065/71.6.576.

[8]

D. Kushnir, A. Haddad and R. R. Coifman, Anisotropic diffusion on sub-manifolds with application to earth structure classification, Appl. Comp. Harm. Anal., 32 (2012), 280-294. doi: 10.1016/j.acha.2011.06.002.

[9]

P. Kwan and M. J. Brodie, Early identification of refractory epilepsy, N. Engl. J. Med., 342 (2000), 314-319. doi: 10.1056/NEJM200002033420503.

[10]

F. Mormann, R. G. Andrzejak, C. E. Elger and K. Lehnertz, Seizure prediction: the long and winding road, Brain, 130 (2007), 314-333. doi: 10.1093/brain/awl241.

[11]

X. Papademetris, A. P. Jackowski, R. T. Schultz, L. H. Staib and J. S. Duncan, Integrated intensity and point-feature non-rigid registration, in "Medical Image Computing and Computer-Assisted Intervention" (Eds. C. Barillot, D. Haynor and P. Hellier) Saint-Malo: Springer, (2004), 763-770.

[12]

M. R. Portnoff, Time-frequency representation of digital signals and systems based on short-time Fourier analysis, IEEE Trans. Signal Process, ASSP-28, 55-69. doi: 10.1109/TASSP.1980.1163359.

[13]

A. Schulze-Bonhage, H. Feldwisch-Drentrup and M. Ihle, Epilepsy and behavior, Elsevier, 22 (2011), S88-S93. doi: 10.1016/j.yebeh.2003.11.021.

[14]

A. Singer and R. R. Coifman, Non-linear independent component analysis with diffusion maps, Appl. Comp. Harm. Anal., 25 (2008), 226-239. doi: 10.1016/j.acha.2007.11.001.

[15]

E. Susman, Brain stimulation reduces seizures in refractory adult epilepsy, Neurology Today, 9 (2009), 22-23. doi: 10.1097/01.NT.0000345158.91024.42.

[16]

R. Talmon and R. R. Coifman, Differential stochastic sensing: intrinsic modeling of random time series with applications to nonlinear tracking, submitted to PNAS, (2012).

[17]

R. Talmon, D. Kushnir, R. R. Coifman, I. Cohen and S. Gannot, Parametrization of linear systems using diffusion kernels, IEEE Trans. Signal Process, 60 (2012). doi: 10.1109/TSP.2011.2177973.

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