Skip to main content
Log in

Application of correlation dimension and pointwise dimension for non-linear topographical analysis of focal onset seizures

  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

For many patients who are candidates for epilepsy surgery, non-invasive evaluation fails to provide sufficient information to permit surgical treatment. Since there are also definite risks and considerable costs associated with invasive procedures, new (non-invasive) techniques are required. This study provides empirical evidence that a non-linear approach applied to ictal surface electroencephalograms (EEGs) can help to delineate the area of seizure onset and may prove useful in complementing visual analysis of the EEG. Multichannel EEGs, recorded from eight patients with different drug-resistant localisation-related epilepsies, were analysed using the concept of correlation dimension and two extensions based on the pointwise dimension. The latter also provided results in cases where assessment of the correlation dimension was not feasible. Comparative values between 2 and 6 were accepted as the result of the algorithms, mostly 3–4 for the EEG channels strongly reflecting epileptic activity, and 4–6 for the other signals. The proportion of accepted pointwise values was usually 200–800% for strong epileptic EEG activity compared to the other data. The approach permitted the characterisation of the scalp area reflecting epileptic activity. The results obtained were in perfect concordance with those obtained during pre-surgical work-up and confirmed by the post-operative outcome.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Argyris, J., Faust, G. andHaase, M. (1994): ‘An exploration of chaos’ (Amsterdam: Elsevier Science B.V., North Holland)

    MATH  Google Scholar 

  • Albano, A.M., Muench, J., Schwartz, C., Mees, A.I. andRapp, P.E. (1988): ‘Singular-value decomposition and the Grassberger-Procaccia algorithm’,Phys. Rev. A,38(2), pp. 3017–3026

    Article  MathSciNet  Google Scholar 

  • Blanco, S., Figliola A., Kochen S. andRosso O.A. (1997): ‘Using non-linear dynamic metric tools for characterizing brain structures’,IEEE Eng. Med. Biol., July/August, pp. 83–92

  • Bullmore, E.T., Brammer, M.J., Bourlon, P., Alarcon, G., Polkey, C.E., Elwes, R. andBinnie, C.D. (1994): ‘Fractal analysis of electroencephalographic signals intracerebrally recorded during 35 epileptic seizures: evaluation of a new method for synoptic visualisation of ictal events’,Electroenceph. Clin. Neurophysiol.,91, 337–345

    Article  Google Scholar 

  • Casdagli, M.C., Iasemidis, L.D., Sackellares, J., Roper, S.N., Gilmore, R.L. andSavit, R.S. (1996): ‘Characterizing non-linearity in invasive EEG recordings from temporal lobe epilepsy’,Physica D,99, pp. 381–399

    Article  MATH  Google Scholar 

  • Cerutti, S., Carrault, G., Cluitmans, P.J.M., Kinie, A., Lipping, T., Nikolaidis, N., Pitas, I. and Signorini, M. G. (1996): ‘Non-linear algorithms for processing biological signals’,Comput. Meth. Programs Biomed.,51, pp. 51–73

    Article  Google Scholar 

  • Chen, J.J., Tsai, J.J., Sheu, C.H., Lin, H.Y. andYeh, J.G. (1997): ‘Application of dipole modeling in localization of mesio-temporal epileptogenic focus’,Proc. National Sci. Council Repub. China B,21(2), pp. 61–70

    MATH  Google Scholar 

  • Engel, J. (Ed.) (1987): ‘Surgical treatment of the epilepsies’, (Raven Press: New York)

    Google Scholar 

  • Farmer, J.D., Ott, E. andYorke, J.A. (1983): ‘The dimension of chaotic attractors’,Physica D,7, pp. 153–180

    Article  MathSciNet  Google Scholar 

  • Feucht, M., Möller, U., Witte, H., Schmidt, K., Arnold, M., Benninger, F., Steinberger, K. andFriedrich, M.H. (1998): ‘Non-linear dynamics of 3 Hz spike-and-wave discharges recorded during typical absence seizures in children’,Cerebral Cortex,8(6), pp. 524–533

    Article  Google Scholar 

  • Frank, G. W., Lookman, T., Nerenberg, M. A., Essex, C., Lemieux, J. andBlume, W. (1990): ‘Chaotic time series analysis of epileptic seizures’,Physica D,46, pp. 427–438

    Article  MATH  Google Scholar 

  • Graf, K. E. andElbert, T. (1990): ‘Dimensional analysis of the waking EEG’ in Basar, E. (ed): ‘Chaos in brain function’ (Springer: Berlin) pp. 135–152

    Google Scholar 

  • Grassberger, P. andProcaccia, I. (1983): ‘Measuring the strangeness of strange attractors’,Physica D,9, pp. 189–208

    Article  MATH  MathSciNet  Google Scholar 

  • Heyden, M.J., Diks, C., Pijn, J.P. andVelis, D.N. (1996): ‘Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy’,Phys. Lett. A,216, pp. 283–288

    Article  Google Scholar 

  • Holzfuss, J. andMayer-Kress, G. (1986): ‘An approach to error-estimation in the application of dimension algorithms’ inMayer-Kress, G. (ed.): ‘Dimensions and entropies in chaotic systems’ Springer Series in Synergetics 32 (Springer: New York)

    Google Scholar 

  • Jansen, B.H. (1996): ‘Non-linear dynamics and quantitative EEG analysis’,Electroenceph. Clin. Neurophysiol.Suppl.,45, 39–56

    Google Scholar 

  • Koebbe, M. andMayer-Kress, G. (1992): ‘Use of recurrence plots in the analysis of time series data’, inCasdagli, M. andEubank, S. (eds.): ‘Non-linear modeling and forecasting’, SFI Studies in the Sciences of Complexity, Proc. Vol. XII, (Addison-Wesley), pp. 361–378

  • Krajca, V., Petránek, S. Patáková, I. andVärri, A. (1991): ‘Automatic identification of significant graphoelements in multichannel EEG recordings by adaptive segmentation and fuzzy clustering’,Int. J. Biomed. Comput.,28, pp. 71–89

    Article  Google Scholar 

  • Krajca, V., Petránek, S., Pietilä, T. andFrey, H. (1993): ‘“Wave-Finder”: a new system for an automatic processing of long-term EEG-recording’, inRother, M. andZwiener, U (Eds.), ‘Quantitative EEG analysis—clinical utility and new methods’ (Universitätsverlag: Jena)

    Google Scholar 

  • Krystal, A.D., Zaidman, C., Greenside, H.S., Weiner, R.D. andCoffey, C.E. (1997): ‘The largest Lyapunov exponent of the EEG during ECT seizures as a measure of ECT seizure adequacy’,Electroenceph. Clin. Neurophysiol.,103, pp. 599–606

    Article  Google Scholar 

  • Lehnertz, K. andElger, C.E. (1995): ‘Spatio-temporal dynamics of the primary epileptogenetic area in temporal lobe epilepsy characterized by neuronal complexity loss’,Electroenceph. Clin. Neurophysiol.,95, pp. 108–117

    Article  Google Scholar 

  • Lehnertz, K. andElger, C.E. (1997): ‘Neuronal complexity loss in the temporal lobe epilepsy: effects of carbamazepine on the dynamics of the epileptic focus’,Electroenceph. Clin. Neurophysiol.,103, pp. 376–380

    Article  Google Scholar 

  • Lerner, D.E. (1996): ‘Monitoring changing dynamics with correlation integrals: Case study of an epileptic seizure’,Physica D,97, pp. 563–576

    Article  Google Scholar 

  • Lopes da Silva, F.H., Pijn, J.P. andWadman, W.J. (1994): ‘Dynamics of local neuronal networks: control parameters and state bifurcations in epileptogenesis’,Prog. Brain Res.,102, pp. 359–370

    Article  Google Scholar 

  • Manuca, R., Casdagli, M.C. andSavit, R.S. (1998): ‘Nonstationarity in epileptic EEG and implications for neural dynamics’,Math. Biosci.,147(1), pp. 1–22

    Article  MATH  Google Scholar 

  • Mars, N.J.I., Thompson, P.M. andWilkus, R.J. (1985): ‘Spread of epileptic seizure activity in humans’,Epilepsia,26, pp. 85–94

    Article  Google Scholar 

  • Pijn, J.P.M., van Neerven, J., Noest, A. andLopes da Silva, F.H. (1991): ‘Chaos or noise in EEG signals; dependence on state and brain site’,Electroenceph. Clin. Neurophysiol.,79, pp. 371–81

    Article  Google Scholar 

  • Pijn, J.P.M., Demetrios, N.V., v.d. Heyden, M.J., DeGoede, J., v. Jeelen, C.W.M. andLopes da Silva, F.H. (1997): ‘Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings’,Brain Topography,9(4), pp. 249–270

    Article  Google Scholar 

  • Popivanov, D., Mineva, A. andDushanova, J. (1998): ‘Tracking EEG signal dynamics during mental tasks’,IEEE Eng. Med. Biol., March/April, pp. 89–95

    Article  Google Scholar 

  • Pritchard, W.S., Kriebel, K.K. andDuke, D.W. (1996): ‘On the validity of estimating EEG correlation dimensions from a spatial embedding’,Psychophysiol,33(5), pp. 362–368

    Article  Google Scholar 

  • Rapp, P.E., Albano, A.M., Guzmann, G.C., Greenbaum, N.N. andBashore, T.R. (1986): ‘Experimental studies of chaotic neural behaviour: Cellular activity and electroencephalographic signals’, inOthmar, H.G. (ed.): ‘Nonlinear oscillations in biology and chemistry’, Springer Lecture Notes Biomath, 66, pp. 175–197

  • Rapp, P.E., Zimmermann, I.D., Vining, E.P., Cohen, N., Albano, A.M. andJiménez-Montano, M.A. (1994): ‘The non-random structure of neural spike trains increases during focal seizures’,J. Neurosci.,14(8), pp. 4731–4739

    Google Scholar 

  • Sarnthein, J., Abarbanel, H.D.I. andPockberger, H. (1997): ‘Non-linear analysis of epileptic activity in rabbit neocortex’,Biol. Cybern.,78, pp. 37–44.

    Article  Google Scholar 

  • Seri, S., Cerquiglini, A., Pisani, F., Michel, C.M., Marqui, R.D.P. andCuratolo, P. (1998): ‘Frontal lobe epilepsy associated with tuberous sclerosis: Electroencephalographic-magnetic resonance image fusioning’,J. Child Neurol.,13(1), pp. 33–38

    Article  Google Scholar 

  • Skinner, J.E., Carpeggiani, C., Landisman, C.E. andFulton, K.W. (1991): ‘Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial iscemia’,Circ. Res.,68(4), pp. 966–976

    Google Scholar 

  • Takens, F. (1980): ‘Detecting strange attractors in turbulence’, in Rand, D. A. and Young, L. S. (Eds.): Springer Lecture Notes Math 898, pp. 366–381

  • Theiler, J. (1986): ‘Spurious dimension from correlation algorithms applied to limited time-series data’,Phys. Rev. A,34(3), pp. 2427–2432

    Article  Google Scholar 

  • Theiler, T., Eubank, S., Longtin, A., Galdrikian, B. andFarmer, J.D. (1992): ‘Testing for non-linearity in time series: The method of surrogate data’,Physica D,58, pp. 77–94

    Article  Google Scholar 

  • Theiler, J. andRapp, P.E. (1996): ‘Re-examination of the evidence for low-dimensional, non-linear structure in the human electroencephalogram’,Electroenceph. Clin. Neurophysiol.,98, 213–222

    Article  Google Scholar 

  • Zaveri, H.P., Williams, W.J., Iasemidis, L.D. andSackellares, J.C. (1992): ‘Time-frequency representation of electrocorticograms in temporal lobe epilepsy’,IEEE Trans. Biomed. Eng.,39(5), pp. 502–509

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Feucht.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feucht, M., Möller, U., Witte, H. et al. Application of correlation dimension and pointwise dimension for non-linear topographical analysis of focal onset seizures. Med. Biol. Eng. Comput. 37, 208–217 (1999). https://doi.org/10.1007/BF02513289

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02513289

Keywords

Navigation