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Beginning in 1988, techniques for analyzing nonlinear chaotic systems were ap-
plied by Iasemidis and Sackellares toward the study of the dynamical characteristics
of EEG signals from patients with medically refractory epilepsy [15,14]. Later, they
showed that, from a dynamical perspective, seizures evolve in a distinctive way over
minutes to hours [11, 9]. Specifically, seizures are preceded by a preictal transition,
detectable in the EEG, which has characteristic spatiotemporal dynamical proper-
ties. The seizure onset represents an abrupt phase transition from a complex to a
less complex (more ordered) state. The spontaneous formation of organized spatial,
temporal, or spatiotemporal patterns is often present in various physical, chemical,
or biological systems, and the study of these dynamical changes represents one of
the most fascinating and challenging areas of scientific investigation [21]. The pri-
mary common denominator in such abrupt changes of the state of a deterministic
system as above lies in the nonlinear nature of the system.
From analysis of the spatiotemporal dynamics of invasive EEG recordings in
patients with medically intractable temporal lobe epilepsy, Sackellares, Iasemidis,
and others first discovered and characterized a preictal transition process [10,8]. The
onset of this transition precedes the seizure for periods ranging from 0.5 to 1.5 h. In
their observations, the preictal dynamical transition was characterized by
1. progressive convergence of the mean short-term Lyapunov exponents (STL-
max) among specific anatomical areas (mean value entrainment), and
2. progressive phase locking of the STLmax profiles among various electrode sites
(phase entrainment).
In initial studies, preictal entrainment of EEG dynamics among electrode sites
was detected by visual inspection of STLmax versus time plots. More recently,
methods have been developed that provide objective criteria for dynamical entrain-
ment among electrode pairs [11, 9]. Based on these findings, an approach is devel-
oped for the automatic detection of the preictal state and prediction of impending
seizures.
The discovery of the preictal dynamical transition in temporal lobe epilepsy has
also been reported by other researchers. Using a modification of the correlation di-
mension, Elger and Lehnertz reported long-lasting and marked transitions toward
low-dimensional states up to 25 min before the occurrence of epileptic seizures [2].
These findings were interpreted by them as evidence for a continual increase in
the degree of synchronicity preceding the occurrence of an epileptic seizure. Mar-
tinerie et al. also found evidence for a reduction in the correlation dimension cal-
culated from intracranial EEG recordings, beginning 2-6 min prior to seizures [26].
Both studies analyzed intracranial EEG recordings in patients with unilateral mesial
temporal epilepsy. The investigators utilized an estimate of the signal complexity
(integral correlation dimension). However, we have found that this measure is not
reliable when applied to continuous, real-time EEG recordings.
Motivated by the studies of synchrony in communication among various brain
structures [36, 37], synchronization measures have recently been applied to EEG
data from epilepsy patients [28, 29, 30, 24]. In particular, Mormann et al. used a
measure of phase synchronization called mean phase coherence, which is based on
