Epilepsy Detection and Monitoring - Quantitative EEG Analysis Methods and Clinical Applications - page 144

6.2 Epilepsy as a Dynamic Disease

The EEG is a complex signal. Its statistical properties depend on both time and space
[11]. Characteristics of the EEG, such as the existence of limit cycles (alpha activity,
ictal activity), instances of bursting behavior (during light sleep), jump phenomena
(hysteresis), amplitude-dependent frequency behavior (the smaller the amplitude the
higher the EEG frequency), and existence of frequency harmonics (e.g., under photic
driving conditions), are among the long catalog of properties typical of nonlinear
systems. The presence of nonlinearities in EEGs recorded from an epileptogenic
brain further supports the concept that the epileptogenic brain is a nonlinear system.
By applying techniques from nonlinear dynamics, several researchers have provided
evidence that the EEG of the epileptic brain is a nonlinear signal with deterministic
and perhaps chaotic properties [12-14].
The EEG can be conceptualized as a series of numerical values (voltages) over
time and space (gathered from multiple electrodes). Such a series is called a
multivariate time series . The standard methods for time-series analysis (e.g., power
analysis, linear orthogonal transforms, and parametric linear modeling) not only
fail to detect the critical features of a time series generated by an autonomous (no
external input) nonlinear system, but may falsely suggest that most of the series is
random noise [15]. In the case of a multidimensional, nonlinear system such as the
EEG generators, we do not know, or cannot measure, all of the relevant variables.
This problem can be overcome mathematically. For a dynamical system to exist, its
variables must be related over time. Thus, by analyzing a single variable (e.g., volt-
age) over time, we can obtain information about the important dynamic features of
the whole system. By analyzing more than one variable over time, we can follow the
dynamics of the interactions of different parts of the system under investigation.
Neuronal networks can generate a variety of activities, some of which are character-
ized by rhythmic or quasirhythmic signals. These activities are reflected in the corre-
sponding local EEG field potential. An essential feature of these networks is that
variables of the network have both a strong nonlinear range and complex interac-
tions. Therefore, they belong to a general class of nonlinear systems with complex
dynamics. Characteristics of the dynamics depend strongly on small changes in the
control parameters and/or the initial conditions. Thus, real neuronal networks
behave like nonlinear complex systems and can display changes between states such
as small-amplitude, quasirandom fluctuations and large-amplitude, rhythmic oscil-
lations. Such dynamic state transitions are observed in the brain during the
transition between interictal and epileptic seizure states.
One of the unique properties of the brain as a system is its relatively high degree
of plasticity. It can display adaptive responses that are essential to implementing
higher functions such as memory and learning. As a consequence, control parame-
ters are essentially plastic, which implies that they can change over time depending
on previous conditions. In spite of this plasticity, it is necessary for the system to stay
within a stable working range in order for it to maintain a stable operating point. In
the case of the patient with epilepsy, the most essential difference between a normal
and an epileptic network can be conceptualized as a decrease in the distance between
operating and bifurcation points.