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

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.

[1]  C. Elger,et al.  Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss. , 1995, Electroencephalography and clinical neurophysiology.

[2]  J Sarnthein,et al.  Nonlinear analysis of epileptic activity in rabbit neocortex , 1998, Biological Cybernetics.

[3]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[4]  Leonidas D. Iasemidis,et al.  Characterizing nonlinearity in invasive EEG recordings from temporal lobe epilepsy , 1996 .

[5]  Christopher Essex,et al.  Chaotic time series analyses of epileptic seizures , 1990 .

[6]  W. J. Williams,et al.  Cross Time-frequency Representation Of Electrocorticograms In Temporal Lobe Epilepsy , 1991 .

[7]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[8]  K. E. Graf,et al.  Dimensional analysis of the waking EEG , 1990 .

[9]  D. N Velis,et al.  Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy , 1996 .

[10]  F. H. Lopes da Silva,et al.  Chaos or noise in EEG signals; dependence on state and brain site. , 1991, Electroencephalography and clinical neurophysiology.

[11]  Jerome Engel,et al.  Surgical treatment of the epilepsies , 1993 .

[12]  S. Blanco,et al.  Using nonlinear dynamic metric tools for characterizing brain structures , 1997, IEEE Engineering in Medicine and Biology Magazine.

[13]  F. Busse.  An exploration of chaos: J. Argyris, G. Faust and M. Haase, Elsevier, Amsterdam, 1994, 722 pp., ISBN 0-444-82002-7 (hardbound), 0-444-82003-5 (paperback) , 1994 .

[14]  P. Rapp,et al.  Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram. , 1996, Electroencephalography and clinical neurophysiology.

[15]  Joachim Holzfuss,et al.  Approach to error-estimation in the application of dimension algorithms , 1986 .

[16]  J J Chen,et al.  Application of dipole modeling in localization of mesio-temporal epileptogenic focus. , 1997, Proceedings of the National Science Council, Republic of China. Part B, Life sciences.

[17]  P. Rapp,et al.  The algorithmic complexity of neural spike trains increases during focal seizures , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[18]  W. Pritchard,et al.  On the validity of estimating EEG correlation dimension from a spatial embedding. , 1996, Psychophysiology.

[19]  F Benninger,et al.  Nonlinear dynamics of 3 Hz spike-and-wave discharges recorded during typical absence seizures in children. , 1998, Cerebral cortex.

[20]  P. Thompson,et al.  Spread of Epileptic Seizure Activity in Humans , 1985, Epilepsia.

[21]  E T Bullmore,et al.  Fractal analysis of electroencephalographic signals intracerebrally recorded during 35 epileptic seizures: evaluation of a new method for synoptic visualisation of ictal events. , 1994, Electroencephalography and clinical neurophysiology.

[22]  M. Casdagli,et al.  Nonstationarity in epileptic EEG and implications for neural dynamics. , 1998, Mathematical biosciences.

[23]  S Cerutti,et al.  Non-linear algorithms for processing biological signals. , 1996, Computer methods and programs in biomedicine.

[24]  C M Michel,et al.  Frontal Lobe Epilepsy Associated With Tuberous Sclerosis: Electroencephalographic-Magnetic Resonance Image Fusioning , 1998, Journal of child neurology.

[25]  F. H. Lopes da Silva,et al.  Dynamics of local neuronal networks: control parameters and state bifurcations in epileptogenesis. , 1994, Progress in brain research.

[26]  F. H. Lopes da Silva,et al.  Nonlinear dynamics of epileptic seizures on basis of intracranial EEG recordings , 2005, Brain Topography.

[27]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[28]  Gottfried Mayer-Kress,et al.  Dimensions and Entropies in Chaotic Systems , 1986 .

[29]  Theodore R. Bashore,et al.  Experimental Studies of Chaotic Neural Behavior: Cellular Activity and Electroencephalographic Signals , 1986 .

[30]  D Popivanov,et al.  Tracking EEG signal dynamics during mental tasks. A combined linear/nonlinear approach. , 1998, IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society.

[31]  J E Skinner,et al.  Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial ischemia. , 1991, Circulation research.

[32]  H. Greenside,et al.  The largest Lyapunov exponent of the EEG during ECT seizures as a measure of ECT seizure adequacy. , 1997, Electroencephalography and clinical neurophysiology.

[33]  J. Yorke,et al.  Dimension of chaotic attractors , 1982 .

[34]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[35]  M. Koebbe.  Use of recurrence plots in analysis of time-series data , 1992 .

[36]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[37]  A Värri,et al.  Automatic identification of significant graphoelements in multichannel EEG recordings by adaptive segmentation and fuzzy clustering. , 1991, International journal of bio-medical computing.

[38]  David Lerner,et al.  Monitoring changing dynamics with correlation integrals: case study of an epileptic seizure , 1996 .

[39]  K Lehnertz,et al.  Neuronal complexity loss in temporal lobe epilepsy: effects of carbamazepine on the dynamics of the epileptogenic focus. , 1997, Electroencephalography and clinical neurophysiology.