Single-Channel EEG Analysis - Quantitative EEG Analysis Methods and Clinical Applications - page 81

Figure 3.22 A 30-second EEG segment at the onset of a right temporal lobe seizure, recorded from
12 bilaterally placed depth (hippocampal) electrodes, 8 subdural temporal electrodes, and 8
subdural orbitofrontal electrodes (according to nomenclature in Figure 3.21). The ictal discharge
begins as a series of low-amplitude sharp and slow wave complexes in the right depth electrodes
(RTD 1-3, more prominently RTD2) approximately 5 seconds into the record. Within seconds, it
spreads to RST1, the rest of the right hippocampus, and the temporal and frontal lobes. The seizure
lasted for 80 seconds (the full duration of this seizure is not shown in this figure).
3.2.2 Nonlinear Dynamic Measures of EEGs
From the dynamic systems theory perspective, a nonlinear system may be character-
ized by steady states that are chaotic attractors in the state space [55, 61, 62]. A state
space is created by treating each time-dependent variable of a system as one of the
components of a time-dependent state vector. For most dynamic systems, the state
vectors are confined to a subspace of the state space and create an object commonly
referred to as an attractor. The geometric properties of these attractors provide
information about the dynamics of a system. Among the well-known methods used
to study systems in the state space [63-65], the Lyapunov exponents and correlation
dimension are discussed further below and applied to EEG.
3.2.2.1 Reconstruction of the State Space: Embedding
A well-known technique for visualizing the dynamics of a multidimensional system
is to generate the state space portrait of the system. A state space portrait [66] is cre-
ated by treating each time-dependent variable of a system as a component of a vec-
tor in a vector space. Each vector represents an instantaneous state of the system.
These time-dependent vectors are plotted sequentially in the state space to represent
the evolution of the state of the system with time. One of the problems in analyzing
multidimensional systems in nature is the lack of knowledge of which observable
(variables of the system that can be measured) should be analyzed, as well as the
limited number of observables available due to experimental constraints. It turns
out that when the behavior over time of the variables of the system is related, which