Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

Jessica Margaret Dunn, David Abbott, Richard Masterton, Robert Anderssen

Abstract


The Brain Research Institute (BRI) uses various types of indirect measurements, including EEG and fMRI, to understand and assess brain activity and function. As well as the recovery of generic information about brain function, research also focuses on the utilisation of such data and understanding to study the initiation, dynamics, spread and suppression of epileptic seizures. To assist with the future focussing of this aspect of their research, the BRI asked the MISG 2010 participants to examine how the available EEG and fMRI data and current knowledge about epilepsy should be analysed and interpreted to yield an enhanced understanding about brain activity occurring before, at commencement of, during, and after a seizure. Though the deliberations of the study group were wide ranging in terms of the related matters considered and discussed, considerable progress was made with the following three aspects. (1) The science behind brain activity investigations depends crucially on the quality of the analysis and interpretation of, as well as the recovery of information from, EEG and fMRI measurements. A number of specific methodologies were discussed and formalised, including independent component analysis, principal component analysis, profile monitoring and change point analysis (hidden Markov modelling, time series analysis, discontinuity identification). (2) Even though EEG measurements accurately and very sensitively record the onset of an epileptic event or seizure, they are, from the perspective of understanding the internal initiation and localisation, of limited utility. They only record neuronal activity in the cortical (surface layer) neurons of the brain, which is a direct reflection of the type of electrical activity they have been designed to record. Because fMRI records, through the monitoring of blood flow activity, the location of localised brain activity within the brain, the possibility of combining fMRI measurements with EEG, as a joint inversion activity, was discussed and examined in detail. (3) A major goal for the BRI is to improve understanding about ``when'' (at what time) an epileptic seizure actually commenced before it is identified on an eeg recording, ``where'' the source of this initiation is located in the brain, and ``what'' is the initiator. Because of the general agreement in the literature that, in one way or another, epileptic events and seizures represent abnormal synchronisations of localised and/or global brain activity the modelling of synchronisations was examined in some detail.

References
  • C. M. Michel, G. Thut, S. Morand, A. Khateb, A. J. Pegna, R. Grave de Peralta, S. Gonzalez, M. Seeck and T. Landis, Electric source imaging of human brain functions, Brain Res. Rev., 36(2--3), 2001, 108--118. doi:10.1016/S0165-0173(01)00086-8
  • S. Ogawa, R. S. Menon, S. G. Kim and K. Ugurbil, On the characteristics of functional magnetic resonance imaging of the brain, Annu. Rev. Bioph. Biom., 27, 1998, 447--474. doi:10.1146/annurev.biophys.27.1.447
  • C. D. Binnie and H. Stefan, Modern electroencephalography: its role in epilepsy management, Clin. Neurophysiol., 110(10), 1999, 1671--1697. doi:10.1016/S1388-2457(99)00125-X
  • J. X. Tao, A. Ray, S. Hawes-Ebersole and J. S. Ebersole, Intracranial eeg substrates of scalp eeg interictal spikes, Epilepsia, 46(5), 2005, 669--76. doi:10.1111/j.1528-1167.2005.11404.x
  • S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. G. Kim, H. Merkle and K. Ugurbil, Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging, P. Natl. Acad. Sci. USA, 89(13), 1992, 5951--5955. doi:10.1073/pnas.89.13.5951
  • J. Engel Jr., Report of the ilae classification core group, Epilepsia, 47(9), 2006, 1558--1568. doi:10.1111/j.1528-1167.2006.00215.x
  • L. Lemieux, A. Salek-Haddadi, O. Josephs, P. Allen, N. Toms, C. Scott, K. Krakow, R. Turner and D. R. Fish, Event-related fmri with simultaneous and continuous eeg: description of the method and initial case report, NeuroImage, 14(3), 2001, 780--7. doi:10.1006/nimg.2001.0853
  • P. Federico, D. F. Abbott, R. S. Briellmann, A. S. Harvey and G. D. Jackson, Functional mri of the pre-ictal state, Brain, 128(8), 2005, 1811-7. doi:10.1093/brain/awh533
  • C. S. Hawco, A. P. Bagshaw, Y. Lu, F. Dubeau and J. Gotman, bold changes occur prior to epileptic spikes seen on scalp eeg, NeuroImage, 35(4), 2007, 1450--1458. doi:10.1016/j.neuroimage.2006.12.042
  • F. Moeller, H. R. Siebner, S. Wolff, H. Muhle, R. Boor, O. Granert, O. Jansen, U. Stephani and M. Siniatchkin, Changes in activity of striato-thalamo-cortical network precede generalized spike wave discharges, NeuroImage, 39(4), 2008, 1839--1849. doi:10.1016/j.neuroimage.2007.10.058
  • V. Osharina, E. Ponchel, A. Aarabi, R. Grebe and F. Wallois, Local haemodynamic changes preceding interictal spikes: A simultaneous electrocorticography (ecog) and near-infrared spectroscopy (nirs) analysis in rats, NeuroImage, 50(2), 2010, 600--607. doi:10.1016/j.neuroimage.2010.01.009
  • R. S. Fisher, W. Boas, W. Blume, C. Elger, P. Genton, P. Lee and J. Engel, Epileptic seizures and epilepsy: Definitions proposed by the international league against epilepsy (ilae) and the international bureau for epilepsy (ibe), Epilepsia, 46(4), 2005, 470--472. doi:10.1111/j.0013-9580.2005.66104.x
  • H. Berger, Electroencephalogram in humans, Arch. Psychiat. Nerven., 87, 1929, 527--570.
  • C. M. Michel, M. M. Murray, G. Lantz, S. Gonzalez, L. Spinelli and R. G. de Peralta, eeg source imaging, Clin. Neurophysiol., 115(10), 2004, 2195--2222. doi:10.1016/j.clinph.2004.06.001
  • P. L. Nunez and R. B. Silberstein, On the relationship of synaptic activity to macroscopic measurements: Does co-registration of eeg with fmri make sense?, Brain Topogr., 13(2), 2000, 79--96. doi:10.1023/A:1026683200895
  • S. Ogawa, T. M. Lee, A. R. Kay and D. W. Tank, Brain magnetic resonance imaging with contrast dependent on blood oxygenation, P. Natl. Acad. Sci. USA, 87(24), 1990, 9868--9872. doi:10.1073/pnas.87.24.9868
  • J. S. Gati, R. S. Menon, K. Ugurbil and B. K. Rutt, Experimental determination of the bold field strength dependence in vessels and tissue, Magn. Reson. Med., 38(2), 1997, 296--302. doi:10.1002/mrm.1910380220
  • P. A. Bandettini, E. C. Wong, R. S. Hinks, R. S. Tikofsky and J. S. Hyde, Time course EPI of human brain function during task activation, Magn. Reson. Med., 25(2), 1992, 390--397.
  • K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppelm, M. S. Cohen and R. Turner, Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation, P. Natl. Acad. Sci. USA, 89(12), 1992, 5675--5679. doi:10.1073/pnas.89.12.5675
  • J. Frahm, K. D. Merboldt and W. Hnicke, Functional mri of human brain activation at high spatial resolution, Magn. Reson. Med., 29(1), 1993, 139--144.
  • P. A. Bandettini, A. Jesmanowicz, E. C. Wong and J. S. Hyde, Processing strategies for time-course data sets in functional MRI of the human brain, Magn. Reson. Med., 30(2), 1993, 161--173.
  • K. J. Friston, P. Jezzard and R. Turner, Analysis of functional MRI time-series, Hum. Brain Mapp., 1(2), 1994, 153--171.
  • B. Biswal, F. Z. Yetkin, V. M. Haughton and J. S. Hyde, Functional connectivity in the motor cortex of resting human brain using echo-planar mri, Mag. Reson. Med., 34(4), 1995, 537--541. doi:10.1002/mrm.1910340409
  • K. J. Friston, J. Ashburner, C. D. Frith, J. Poline, J. D. Heather and R. S. J. Frackowiak, Spatial registration and normalization of images, Hum. Brain Mapp., 3(3), 1995, 165--189.
  • K. J. Friston, S. Williams, R. Howard, R. S. Frackowiak and R. Turner, Movement-related effects in fmri time-series, Magn. Reson. Med., 35(3), 1996, 346--355.
  • G. H. Glover, T. Q. Li and D. Ress, Image-based method for retrospective correction of physiological motion effects in fmri: Retroicor, Magn. Reson. Med., 44(1), 2000, 162--167. doi:10.1002/1522-2594(200007)44:13.0.CO;2-E
  • K. J. Friston, O. Josephs, G. Rees and R. Turner, Nonlinear event-related responses in fmri, Magn. Reson. Med., 39(1), 1998, 41--52. doi:10.1002/mrm.1910390109
  • K. Ugurbil, L. Toth and D. Kim, How accurate is magnetic resonance imaging of brain function?, Trends Neurosci., 26(2), 2003, 108--114. doi:10.1016/S0166-2236(02)00039-5
  • D. S. Kim, I. Ronen, C. Olman, S. G. Kim, K. Ugurbil and L. J. Toth, Spatial relationship between neuronal activity and bold functional mri, NeuroImage, 21(3), 2004, 876--885. doi:10.1016/j.neuroimage.2003.10.018
  • A. Connelly, G. D. Jackson, R. S. Frackowiak, J. W. Belliveau, F. Vargha-Khadem and D. G. Gadian, Functional mapping of activated human primary cortex with a clinical mr imaging system, Radiology, 188(1), 1993, 125--130.
  • L. Allison, Hidden Markov Models, Technical Report, School of Computer and Software Engineering, Monash University, 2000.
  • R. J. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control, Appl. Math.-Czech., 2004.
  • B. Bhavnagri, Discontinuities of plane functions projected from a surface with methods for finding these, Technical Report, 2009.
  • B. Bhavnagri, Computer Vision using Shape Spaces, Technical Report,1996, University of Adelaide.
  • B. Bhavnagri, A method for representing shape based on an equivalence relation on polygons, Pattern Recogn., 27(2), 1994, 247--260. doi:10.1016/0031-3203(94)90057-4
  • D. F. Abbott, A. B. Waites, A. S. Harvey and G. D. Jackson, Exploring epileptic seizure onset with fmri, NeuroImage, 36(S1) (344TH-PM), 2007.
  • M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, 197, 1977, 287--289.
  • S. H. Strogatz, SYNC - The Emerging Science of Spontaneous Order, Theia, New York, 2003.
  • J. W. Kim, J. A. Roberts and P. A. Robinson, Dynamics of epileptic seizures: Evolution, spreading, and suppression, J. Theor. Biol., 257(4), 2009, 527--532. doi:10.1016/j.jtbi.2008.12.009
  • Y. Kuramoto, T. Aoyagi, I. Nishikawa, T. Chawanya T and K. Okuda, Neural network model carrying phase information with application to collective dynamics, J. Theor. Phys., 87(5), 1992, 1119--1126.
  • V. B. Mountcastle, The columnar organization of the neocortex, Brain, 120(4), 1997, 701. doi:10.1093/brain/120.4.701
  • F. L. Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity, Epilepsia, 44(12), 2003, 72--83.
  • F. H. Lopes da Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Dynamical diseases of brain systems: different routes to epileptic seizures, ieee T. Bio-Med. Eng., 50(5), 2003, 540.
  • L.D. Iasemidis, Epileptic seizure prediction and control, ieee T. Bio-Med. Eng., 50(5), 2003, 549--558.
  • L. D. Iasemidis, D. S. Shiau, W. Chaovalitwongse, J. C. Sackellares, P. M. Pardalos, J. C. Principe, P. R. Carney, A. Prasad, B. Veeramani, and K. Tsakalis, Adaptive epileptic seizure prediction system, ieee T. Bio-Med. Eng., 50(5), 2003, 616--627.
  • K. Lehnertz, F. Mormann, T. Kreuz, R.G. Andrzejak, C. Rieke, P. David and C. E. Elger, Seizure prediction by nonlinear eeg analysis, ieee Eng. Med. Biol., 22(1), 2003, 57--63. doi:10.1109/MEMB.2003.1191451
  • K. Lehnertz, R. G. Andrzejak, J. Arnhold, T. Kreuz, F. Mormann, C. Rieke, G. Widman and C. E. Elger, Nonlinear eeg analysis in epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention, J. Clin. Neurophysiol., 18(3), 2001, 209.
  • B. Litt and K. Lehnertz, Seizure prediction and the preseizure period, Curr. Opin. Neurol., 15(2), 2002, 173. doi:10.1097/00019052-200204000-00008
  • B. Litt and J. Echauz, Prediction of epileptic seizures, Lancet Neurol., 1(1), 2002, 22--30. doi:10.1016/S1474-4422(02)00003-0
  • M. M{a}kiranta, J. Ruohonen, K. Suominen, J. Niinim{a}ki, E. Sonkaj{a}rvi, V. Kiviniemi, T. Sepp{a}nen, S. Alahuhta, V. J{a}ntti and O. Tervonen, {bold} signal increase preceeds eeg spike activity--a dynamic penicillin induced focal epilepsy in deep anesthesia, NeuroImage, 27(4), 2005, 715--724. doi:10.1016/j.neuroimage.2005.05.025
  • K. Lehnertz, F. Mormann, H. Osterhage, A. M{u}ller, J. Prusseit, A. Chernihovskyi, M. Staniek, D. Krug, S. Bialonski and C. E. Elger, State-of-the-art of seizure prediction, J. Clin. Neurophysiol., 24(2), 2007, 147. doi:10.1097/WNP.0b013e3180336f16
  • F. Mormann, T. Kreuz, C. Rieke, R. G. Andrzejak, A. Kraskov, P. David, C. E. Elger and K. Lehnertz, On the predictability of epileptic seizures, Clin. Neurophysiol., 116(3), 2005, 569--587. doi:10.1016/j.clinph.2004.08.025
  • F. Mormann, R. G. Andrzejak, C. E. Elger and K. Lehnertz, Seizure prediction: the long and winding road, Brain, 130(2), 2007, 314--333. doi:10.1093/brain/awl241
  • Z. Rogowski, I. Gath and E. Bental, On the prediction of epileptic seizures, Biol. Cybern., 42(1), 1981, 9--15.
  • Y. Salant, I. Gath, O. Henriksen, Prediction of epileptic seizures from two-channel eeg, Med. Biol. Eng. Comput., 36(5), 1998, 549--556. doi:10.1007/BF02524422
  • J. Gotman and D.J. Koffler, Interictal spiking increases after seizures but does not after decrease in medication, Evoked Potential, 72(1), 1989, 7--15.
  • J. Gotman and M. G. Marciani, Electroencephalographic spiking activity, drug levels, and seizure occurence in epileptic patients, Ann. Neurol., 17(6), 1985, 59--603.
  • A. Katz, D. A. Marks, G. McCarthy and S. S. Spencer, Does interictal spiking change prior to seizures?, Electroen. Clin. Neuro., 79(2), 1991, 153--156.
  • A. Granada, R. M. Hennig, B. Ronacher, A. Kramer and H. Herzel, Phase Response Curves: Elucidating the dynamics of couples oscillators, Method Enzymol., 454(A), 2009, 1--27. doi:10.1016/S0076-6879(08)03801-9 doi:10.1016/S0076-6879(08)03801-9
  • H. Kantz and T. Schreiber, Nonlinear time series analysis, 2004, Cambridge Univ Press.
  • M. V. L. Bennett and R. S Zukin, Electrical coupling and neuronal synchronization in the mammalian brain, Neuron, 41(4), 2004, 495 --511. doi:10.1016/S0896-6273(04)00043-1
  • L.D. Iasemidis, J. Chris Sackellares, H. P. Zaveri and W. J. Williams, Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures, Brain Topogr., 2(3), 1990, 187--201. doi:10.1007/BF01140588
  • M. Le Van Quyen, J. Martinerie, V. Navarro, M. Baulac and F. J. Varela, Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol., 18(3), 2001, 191.
  • J. Martinerie, C. Adam, M. Le Van Quyen, M. Baulac, S. Clemenceau, B. Renault and F. J. Varela, Epileptic seizures can be anticipated by non-linear analysis, Nat. Med., 4(10), 1998, 1173--1176. doi:10.1038/2667
  • A. Pikovsky, M. Rosenblum, J. Kurths and R. C. Hilborn, Synchronization: A universal concept in nonlinear science, Amer. J. Phys., 70, 2002, 655.
  • H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys. J., 12(1), 1972, 1--24.
  • D. Cumin and C. P. Unsworth, Generalising the Kuramoto model for the study of neuronal synchronisation in the brain, Physica D, 226(2), 2007, 181--196. doi:10.1016/j.physd.2006.12.004
  • F. K. Skinner, H. Bazzazi and S. A. Campbell, Two-cell to N-cell heterogeneous, inhibitory networks: Precise linking of multistable and coherent properties, J. Comput. Neurosci., 18(3), 2005, 343--352. doi:10.1007/s10827-005-0331-1
  • W. W. Lytton, Computer modelling of epilepsy, Nat. Rev. Neurosci., 9(8), 2008, 626--637. doi:10.1038/nrn2416
  • R. D. Traub, A. Bibbig, F. E. N. LeBeau, E. H. Buhl and M. A. Whittington, Cellular mechanisms of neuronal population oscillations in the hippocampus in vitro, Ann. Rev., 2004.
  • R. D. Traub, A. Draguhn, M. A. Whittington, T. Baldeweg, A. Bibbig, E. H. Buhl and D. Schmitz, Axonal gap junctions between principal neurons: A novel source of network oscillations, and perhaps epileptogenesis., Rev. Neuroscience, 13(1), 2002, 1. doi:10.1146/annurev.neuro.27.070203.144303
  • M. Scheffer, J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, E. H. van Nes, M. Rietkerk and G. Sugihara, Early-warning signals for critical transitions, Nature, 461(7260), 2009, 53--59. doi:10.1038/nature08227
  • K. Murphy, A Brief Introduction to Graphical Models and Bayesian Networks, 2008, http://www.cs.ubc.ca/murphyk/Bayes/bnintro.html.
  • R. C. Bradley, An elementary treatment of the Radon Nikodym Derivative, Am. Math. Mon., 96(5), 1989, 437--440.
  • S. Bretschneider, Estimating forecast variance with exponential smoothing, Int. J. Forecasting, 2, 1986, 349--355.
  • R. A. J. Masterton, D. F. Abbott, S. W. Flemin and G. D. Jackson, Measurement and reduction of motion and ballistocardiogram artefacts from simultaneous eeg and fmri recordings, NeuroImage, 37,(1), 2007, 202-211. doi:10.1016/j.neuroimage.2007.02.060
  • M. Moosmann, V. H. Schnfelder, K. Specht, R. Scheeringa, H. Nordby amd K. Hugdahl, Realignment parameter-informed artefact correction for simultaneous eeg-fmri recordings, NeuroImage, 45(4), 2009, 1144-1150. doi:10.1016/j.neuroimage.2009.01.024
  • A. Connes and M. A. Rieffel, Lect. Notes. Math, 1994, Academic Press, San Diego, California.
  • A. L. Carey and J. Phillips, Algebras almost commuting with Clifford algebras in a II$\infty $ factor, K-Theory, 4(5), 1991, 445--478.
  • A. L. Carey and D. E. Evans, Algebras Almost Commuting with Clifford Algebras, J. Funct. Anal., 88,(2), 1990, 279--298. doi:10.1007/BF00533214
  • J. D. Williams, J. B. Brich, W. H. Woodall and N. M. Ferry, Statistical monitoring of heteroscedastic does-response profiles from high-throughput screening, J. Agric. Biol. Envir. S., 12(2), 2007, 216--235. doi:10.1198/108571107X197779
  • M. A. Mahmoud and W. H. Woodall, Phase I analysis of linear profiles with calibration applications, Technometrics, 46, 2004, 277--391. doi:10.1198/004017004000000455
  • J. O. Ramsay and B. W. Silverman, Functional Data Analysis, 3rd Edition, 1997, Springer--Verlag, New York.
  • M. A. Mahmoud, P. A. Parker, W. H. Woodall and D. M. Hawkins, A change point method for linear profile data, Qual. Reliab. Eng. Int., 23, 2007, 247--268. doi:10.1002/qre.788
  • M. M. Gardner and J. C. Lu, Equipment Fault detection using Spatial Signatures, ieee T. Compon. Pack. C, 20, 1997, 295--304. doi:10.1109/3476.650961
  • J. Jin and J. Shi, Automatic feature extraction of waveform signals for in-process diagnostic performance improvement, J. Intell. Manuf., 12(3), 2001, 257--268.
  • J. Jin and J. Shi, Feature preserving data compression of stamping tonnage information using wavelet, Technometrics, 41(4), 1999, 327--339.
  • D. C. Montgomery, Introduction to Statistical Quality Control, 5th edition, 2005, John Wiley and Sons, New York.
  • K. J. Worsley, C. Liao, J. Aston, V. Petre, G. Duncan, F. Orales and A. Evans, A general statistical analysis for fmri data, NeuroImage, 15(1), 2002, 1--15. doi:10.1006/nimg.2001.0933
  • C. R. Genoves, A Bayesian time course model for functional magnetic resonance imaging data, J. Am. Stat. Assoc., 95, 2000, 691--719.
  • N. Lange and S.L. Zeger, Non-Linear Fourier time series analysis for human brain mapping by functional magnetic resonance imaging, J. R. Stat. Soc., 14, 1997, 1--29.
  • P. L. Purden, V. Solo, R. M. Weisskoff and E. Brown, Locally regularized spatiotemporal modelling and model comparison for functional MRI, NeuroImage, 14, 2001, 912--923. doi:10.1006/nimg.2001.0870
  • K. J. Worsley, Detecting activation in fmri data, Stat. Methods Med. Res., 12(5), 2003, 401--418. doi:10.1191/0962280203sm340ra
  • M. Neter, H. Kutner, C. J. Nachtsheim and W. Wasserman, Applied Linear Regression Models, 3rd Edition, 1996, IrwinS, Chicago.
  • L. Kang and S.L. Albin, On-line monitoring when the process yields a linear profile, J. Qual. Technol., 32, 2000, 418--426.
  • C. Aou and F. Tsung, Monitoring profiles based on nonparametric regression methods, J. Am. Stat. Assoc., 4, 2008, 1512--526. doi:10.1198/004017008000000433
  • A. Azzalini and A. W. Bowman, On the use of nonparametric regression for checking linear relationship, J. R. Stat. Soc., 1993, 549--557.
  • O. Mestek, J. Pavlik and M. Suchanek, Multivariate control charts for calibration curves, Fresen. J. Anal. Chem., 350, 1994, 344--351. doi:10.1007/BF00325603
  • A. Hyvarinen, Fast and robust fixed-point algorithms for independent component analysis, ieee T. Neural Networ., 10(3), 1999, 626--634. doi:10.1109/72.761722
  • C. F. Beckmann and S. A. Smith, Probabilistic independent component analysis for functional magnetic resonance imaging, ieee T. Med. Imaging, 23(2), 2004, 137--152. doi:10.1109/TMI.2003.822821
  • V. D. Calhoun, T. Adali, M. C. Stevens, K. A. Kiehl and J. J. Pekar, Semi-blind ica of fmri: a method for utilizing hypothesis-derived time courses in a spatial ica analysis, NeuroImage, 25(2), 2005, 527--538. doi:10.1016/j.neuroimage.2004.12.012
  • I. Daubechies, E. Roussos, S. Takerkart, M. Benharrosh, C. Golden, K. D'Ardenne, W. Richter, J. D. Cohen and J. Haxby, Independent component analysis for brain fmri does not select for independence, P. Natl. Acad. Sci. USA, 106(26), 2009. doi:10.1073/pnas.0903525106
  • K. Dolan, M. Majtanik and P. A. Tass, Phase resetting and transient desynchronization in networks of globally coupled phase oscillators with inertia, Physica D, 211(1-2), 2005, 128--138. doi:10.1016/j.physd.2005.08.009
  • T. Eichele, V. D. Calhoun, and S. Debener, Mining eeg-fmri using independent component analysis, Int. J. Psychophysiol., 73(1), 2009, 53--61. doi:10.1016/j.ijpsycho.2008.12.018
  • P. Bai, H. Shen, X. Huang and Y. Truong, A supervised singular value decomposition for independent component analysis of fmri, Stat. Sinica, 18(4), 2008, 1233-1252.
  • M. Bennett, M. F. Schatz, H. Rockwood and K. Wiesenfeld, Huygens's clocks, P. Roy. Soc. Lond. A Mat., 458(2019), 2002, 563--579. doi:10.1098/rspa.2001.0888
  • M. K. S. Yeung and S. H. Strogatz, Time delay in the Kuramoto model of coupled oscillators, Phys. Rev., 82(3), 1999, 648--651.
  • A. T. Winfree, The Geometry of Biological Time, 1990, Springer Verlag, New York.
  • K. Okuda and Y. Kuramoto, Mutual entrainment between populations of coupled oscillators, Prog. Theo. Phys., 86(6), 1991, 1159--1176.
  • J. L. P. Velazquez, Brain, behaviour and mathematics: Are we using the right approaches?, Physica D, 212(3-4), 2005, 161--182. doi:10.1016/j.physd.2005.10.005
  • J. W. Kim and P. A. Robinson, Controlling limit-cycle behaviors of brain activity, Physical Review E, 77(5), 2008. doi:10.1103/PhysRevE.77.051914
  • J. W. Kim and P. A. Robinson, Compact dynamical model of brain activity, Phys. Rev. E, 75(3), 2007. doi:10.1103/PhysRevE.75.031907
  • S. H. Strogatz, Exploring complex networks, Nature, 410(6825), 2001, 268--276.
  • J. A. Acebron, L. L. Bonilla, C. J. P. Vicente, F. Ritort and R. Spigler, The Kuramoto model: A simple paradigm for synchronization phenomena, Rev. Mod. Phys., 77(1), 2005, 137--185. doi:10.1103/RevModPhys.77.137
  • A. T. Winfree, Biological rhythms and behavior of populations of couple oscillators, J. Theor. Biol., 16(1), 1967, 15.
  • F. R. de Hoog, Why are simple models often appropriate in industrial mathematics?, In R. S. Anderssen, R. Braddock and L. Newham, Proceedings of the 18th World imacs/modsim Congress, Cairns, July 13-17, 2009, 23--36. doi:978-0-9758400-7-8
  • S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D, 143(1-4), 2000, 1--20.
  • Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, 1984, Springer Verlag, Berlin.
  • Y. Kuramoto, Collective synchronization of pulse-coupled oscillators and excitable units, Physica D, 50(1), 1991, 15--30.
  • S. K. Han, C. Kurrer and Y. Kuramoto, Dephasing and bursting in coupled neural oscillators, Phys. Rev. Lett., 75(17), 1995, 3190--3193. doi:10.1103/PhysRevLett.75.3190
  • T. D. Frank, A. Daffertshofer, C. E. Peper, P. J. Beek and H. Haken, Towards a comprehensive theory of brain activity: Coupled oscillator systems under external forces, Physica D, 144(1-2), 2000, 62--86.
  • M. Majtanik, K. Dolan and P. A. Tass, Desynchronization in networks of globally coupled neurons with dendritic dynamics, J. Bio. Phys., 32(3-4), 2006, 307--333. doi:10.1007/s10867-006-9018-8
  • M. Moazami-Goudarzi, J. Sarnthein, L. Michels, R. Moukhtieva and D. Jeanmonod, Enhanced frontal low and high frequency power and synchronization in the resting eeg of parkinsonian patients, NeuroImage, 41(3), 2008, 985--997. doi:10.1016/j.neuroimage.2008.03.032
  • J. L. P. Velazquez, R. F. Galan, L. G. Dominguez, Y. Leshchenko, S. Lo, J. Belkas and R. G. Erra. Phase response curves in the characterization of epileptiform activity, Phys. Rev. E, 76(6), 2007. doi:10.1103/PhysRevE.76.061912
  • C. Lin and M. Lin, The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain, Commun. Nonlinear Sci., 14(8), 2009, 3258--3260. doi:10.1016/j.cnsns.2009.01.007
  • A. Ghosh, D. Roy amd V. K. Jirsa, Simple model for bursting dynamics of neurons, Phys. Rev. E, 80(4), 2009. doi:10.1103/PhysRevE.80.041930

Keywords


EEG, fMRI, epileptic seizures, joint inversion, Change Point Monitoring, Time Series Analysis, Synchronization

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DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3638



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