Abstract
The electro-encephalogram is a time-varying signal that measures electrical activity in the brain. A conceptually intuitive non-linear technique, multidimensional probability evolution (MDPE), is introduced. It is based on the time evolution of the probability density function within a multi-dimensional state space. A synthetic recording is employed to illustrate why MDPE is capable of detecting changes in the underlying dynamics that are invisible to linear statistics. If a nonlinear statistic cannot outperform a simple linear statistic such as variance, then there is no reason to advocate its use. Both variance and MDPE were able to detect the seizure in each of the ten scalp EEG recordings investigated. Although MDPE produced fewer false positives, there is no firm evidence to suggest that MDPE, or any other non-linear statistic considered, outperforms variance-based methods at identifying seizures.
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Albano, A. M., Cellucci, C. J., Harner, R. N., andRapp, P. E. (2000): ‘Optimization of embedding parameters for prediction of seizure onset with mutual information’, in:Mees, A. I. (Ed.): ‘Nonlinear dynamics and statistics: proceedings of an Issac Newton Institute’ (Birkhauser, Boston, 2000), pp. 435–451
Arnhold, J., Grassberger, P., Lehnertz, K., andElger, C. (1999): ‘A robust method for detecting interdependences: application to intracranially recorded EEG’,Physica D,134, pp. 419–430
Blanco, S., Quian Quiroga, R., Rosso, O. A., andKochen, S. (1995): ‘Time-frequency analysis of electroencephalogram series’,Phys. Rev. E.,51, pp. 2624–2631
Blinowska, K. J., andMalinowski, M. (1991): ‘Non-linear and linear forecasting of the EEG time series’,Biol. Cybern.,66, pp. 159–165
Casdagli, M., Iasemidis, L. D., Savit, R. S., Gilmore, R. L., Roper, S. N., andSackellares, J. C. (1996): ‘Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy’,Physica D,99, pp. 381–399
Casdagli, M. C. (1997): ‘Characterizing non-linearity in weather and epilepsy data’,Fields Inst. Commun.,11, pp. 201–222
Casdagli, M. C., Iasemidis, L. D., Savit, R. S., Gilmore, R. L., Roper, S. N., andSackellares, J. C. (1997): ‘Non-linearity in invasive EEG recordings from patients temporal lobe epilepsy’,Electroencephalogr. Clin. Neurophys.,102, pp. 98–105
Chatfield, C. (1989): ‘The analysis of time series, 4th edn’ (Chapman and Hall, London. New York, 1989)
Eckmann, J. P., andRuelle, D. (1992): ‘Fundamental limitations for estimating dimensions and Liapunov exponents in dynamical systems’,Physica D,56, pp. 185–187
Esteller, R., Vachtsevanos, G., Echauz, J., D'Alessandro, M., Henry, T., Pennell, P., Epstein, C., Bakay, R., Bowen, C., Shor, R., andLitt, B. (1999): ‘Accumulated energy is a state-dependent predictor of seizures in mesial temporal lobe epilepsy’,Epilepsia,40, pp. 173–173
Grassberger, P., andProcaccia, I. (1983): ‘Characterization of strange attractors’,Phys. Rev. Lett.,50, pp. 346–349
Hernández, J. L., Valdés, J. L., Biscay, R., Jiménez, J. C., andValdés, P. (1995): ‘EEG predictability: adequacy of non-linear forecasting methods’,Int. J. Biomed. Comput.,38, pp. 197–206
Hively, L. M. (1999): ‘Detecting dynamical change in nonlinear time series’,Phys. Lett. A.,258, pp. 103–114
Iasemidis, L. D., andSackellares, J. C. (1996): ‘Chaos theory and epilepsy’,The Neuroscientist,2, pp. 118–126
Iasemidis, L. D., Principe, J. C., andSackellares, J. C. (1999): ‘Measurement and quantification of spatio-temporal dynamics of human epileptic seizures’ inAkay, M. (Ed.): ‘Nonlinear signal processing’ (IEEE Press, 1999)
Larter, R., andSpeelman, B. (1999): ‘A coupled ordinary differential equation lattice model for the simulation of epileptic seizures’,Chaos,9, pp. 795–804
Le Van Quyen, M., Martinerie, J., Baulac, M., andVarela, F. (1999): ‘Anticipating epileptic seizures in real time by a non-linear analysis of similarity between EEG recordings’,NeuroReport,10, pp. 2149–2155
Le Van Quyen, M., Martinerie, J., Baulac, M., andVarela, F. (2000): ‘Spatio-temporal characterizations of non-linear changes in intracranial activities prior to human temporal lobe seizures’,Eur. J. Neurosci.,12, pp. 2124–2134
Le Van Quyen, M., Martinerie, J., Navarro, V., Boon, P. D'Havé, M., Adam, C., Renault, B., Varela, F., andBaulac, M. (2001): ‘Anticipation of epileptic seizures from standard EEG recordings’,The Lancet,357, pp. 183–188
Lehnertz, K., andElger, C. E. (1998): ‘Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity’,Phys. Rev. Lett.,80, pp. 5019–5022
Lerner, D. E. (1996): ‘Monitoring changing dynamics with correlation integrals: case study of an epileptic seizure’,Physica D,97, pp. 563–576
Martinerie, J., Adam, C., Le Van Quyen, M., Baulac, M., Clemenceau, S., Renault, B., andVarela, F. J. (1998): ‘Epileptic seizures can be anticipated by non-linear analysis’,Nature Med.,4, pp. 1173–1176
McGrogan, N. (2001): ‘Neural network detection of epileptic seizures in the electroencephalogram’. PhD thesis, University of Oxford
Murro, A. M. (1991): ‘Computerized seizure detection of complex partial seizures’,Electroenceph. Clin. Neurophysiol.,79, pp. 330–333
Packard, N., Crutchfield, J., Farmer, J. D., andShaw, R. (1980): ‘Geometry from a time series’,Phys. Rev. Lett.,45, pp. 712–716
Press, W. H., Flannery, B. P., Teukolsky, S. A., andVetterling, W. T. (1992): ‘Numerical recipes in C’ (CUP, Cambridge, 1992), 2nd edn
Rosenstein, M. T., Collins, J. J., andDe Luca, C. J. (1994): ‘Reconstruction expansion as a geometry-based framework for choosing proper time delays’,Physica D,73, pp. 82–98
Sackellares, J. C., Iasemidis, L. D., Shiau, D., Gilmore, R. L., andRoper, S. N. (2000): ‘Epilepsy—when chaos fails’ inLehnertz, K., andElger, C. E. (Eds): ‘Chaos in the brain?’ (World Scientific, Singapore, 2000)
Sauer, T., Yorke, J. A., andCasdagli, M. (1991): ‘Embedology’,J. Stats. Phys.,65, pp. 579–616
Schreiber, T. (2000): ‘Is nonlinearity evident in time series of brain electrical activity?’ inLehnertz, K., Elger, C. E., Arnhold, J., andGrassberger, P. (Eds): ‘Chaos in brain?’ (World Scientific, Singapore, 2000)
Smith, L. A. (1988): ‘Intrinsic limits on dimension calculations’,Phys. Lett. A.,133, pp. 283–288
Smith, L. A. (1992): ‘Identification and prediction of low-dimensional dynamics’,Physica D,58, pp. 50–76
Smith, I. A. (1997): ‘The maintenance of uncertainty’ inCini, G. (Ed.): ‘Nonlinearity in geophysics and astrophysics’, Vol. CXXXIII, International School of Physics ‘Enrico Fermi’ (Società Italiana di Fisica, Bologna, Italy, 1997), pp. 177–246
Takens, F. (1981): ‘Detecting strange attractors in fluid turbulence’ inRand, D., andYoung, L. S. (Eds): ‘Dynamical systems and turbulence, Vol. 898’ (Springer-Verlag, New York, 1981), p. 366
Theiler, J. (1995): ‘On the evidence for low-dimensional chaos in an epileptic electroencephalogram’,Phys. Lett. A,196, pp. 335–341
Widman, G., Schreiber, T., Rehberg, B., Hoeft, A., andElger, C. E. (2000): ‘Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity’,Phys. Rev. E.,62, pp. 4898–4903
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McSharry, P.E., He, T., Smith, L.A. et al. Linear and non-linear methods for automatic seizure detection in scalp electro-encephalogram recordings. Med. Biol. Eng. Comput. 40, 447–461 (2002). https://doi.org/10.1007/BF02345078
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DOI: https://doi.org/10.1007/BF02345078