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contractions in his right thigh adductor muscles, followed by tonic-clonic move-
ments on his right side and right gaze deviation and nystagmus. The patient was
initially given 2 mg of Ativan IV followed by 20 mg/kg of phenytoin equivalence
IV and a second fosphenytoin bolus of 5 mg/kg. Approximately half an hour after
the beginning of the EEG recording, the patient was transferred to the ICU. The
patient did not respond to the fosphenytoin, so he was intubated and placed on a
propofol drip. Soon after, the EEG showed a burst suppression pattern. The last
EEG file was recorded when the patient remained off propofol. The etiology of the
patient's seizures was noted as encephalomalacia in the left frontal cortex likely
due to a prior stroke. The EEG was recorded using 24 scalp electrodes that were
placed according to the standard international 10-20 montage (see Fig. 17.1) at a
sampling rate of 200 Hz. Due to the emergency nature of the clinical situation, the
recorded EEG data were available in five separate files (A through E) with some
gaps (e.g., when recording was stopped in order to transport the patient) between
the recordings. These files were of 1.10, 3.54, 3.03, 3.03, and 2.81 h in duration re-
spectively (i.e., total duration of 13.51 h). The proprietary EEG data were converted
into 16-bit signed binary format for further off-line nonlinear dynamical analysis.
Each file was first analyzed separately using the measures of brain dynamics that
are described next.
17.2.2 Measures of Brain Dynamics
17.2.2.1 Measure of Chaos(
STL
max
)
Under certain conditions, through the method of delays described by Packard et
al. [14] and Takens [17], sampling of a single variable of a system over time can de-
termine all state variables of the system that are related to an observed state variable.
In the case of the EEG, this method can be used to reconstruct a multidimensional
state space of the brain's electrical activity from a single EEG electrode that refer-
entially records from a brain site. Thus, in such an embedding, each state in the state
space is represented by a vector
X
, whose components are the delayed versions
of the original single-channel EEG time series
x
(
t
)
(
t
)
, that is:
X
(
t
)=(
x
(
t
)
,
x
(
t
+
τ
)
,...,
x
(
t
+(
d
−
1
)
τ
))
,
(17.1)
where
, and
d
is a pos-
itive integer denoting the embedding dimension of the reconstructed state space.
Plotting
X
τ
is the time delay between successive components of
X
(
t
)
(
)
in the created state space produces the state portrait of a spatially dis-
tributed system using the subsystem (brain's portion) where
x
t
(
)
is recorded from.
The most complicated steady state a nonlinear deterministic system can exhibit is a
strange and chaotic attractor, whose complexity is measured by its dimension
D
, and
its chaoticity by its Kolmogorov entropy (
K
) and Lyapunov exponents (
Ls
) [4, 3].
A steady state is chaotic if at least the maximum of these Lyapunov exponents
(
L
max) is positive.
t
