Non-linear analysis of epileptic seizures. I. Correlation-dimension measurements for absence epilepsy and near-periodic signals.

The study of six absence seizures from two patients confirmed the efficacy, in the search for low correlation dimensions, of using scaled-structure analysis, combined with the appropriate checking procedures. The analysis is directed towards characterizing an attractor not only by its correlation dimension, but also by its "quality" and by the probability for genuine identification. For near-periodic dynamics, we warn against: (1) artefacts that appear at high values of the correlation integral, in the form of apparent Grassberger-Procaccia scaling at very low values of the dimension (near-periodicity artefact); (2) erroneous interpretation of phase-randomization data, owing to destruction of the artefact by randomization rather than any evidence for low-dimensional dynamics. In single-channel analyses of two patients and six seizures altogether, high-quality attractors were found only for one seizure in two channels, at correlation dimensions 4.7 and 6, respectively. Furthermore, no attractor of measurable dimension was found from multichannel space reconstructions over durations approaching those of typical seizures. Both these results show that in an absence seizure, spatial extension of low-dimensional dynamics must be lost over such durations.