Biomedical Engineering Reference
In-Depth Information
9.4
Time-Domain EEG Algorithms
Analysis of the EEG can be accomplished by examining how its voltage changes
over time. This approach, known as time-domain analysis, can use either a strict
statistical calculation (i.e., the mean and variance of the sampled waveform, or the
median power frequency) or some ad hoc measurement based on the morphology of
the waveform. Most of the commonly used time-domain methods are grounded in
probabilistic analysis of “random” signals and, therefore, some background on sta-
tistical approaches to signals is useful.
Of necessity, the definitions of probability functions, expected values, and cor-
relation are given mathematically as well as descriptively. However, the reader need
not feel compelled to attain a deep understanding of the equations presented here to
continue on. A more detailed review of the statistical approach to signal processing
can be obtained from Chapter 3 or one of the standard texts [26-28]. At present the
only two time-domain statistical qEEGs in clinical use in anesthesia are entropy and
the burst suppression ratio. The family of entropy qEEG parameters derived from
communications theory is used to estimate the degree of chaos, or lack of predict-
ability, in a signal. Entropy is discussed further later in this chapter.
A few definitions related to the statistical approach to time-related data are
called for. The EEG is not a deterministic signal, which means that it is not possible
to exactly predict future values of the EEG. Although the exact future values of a
signal cannot be predicted, some statistical characteristics of certain types of signals
are predictable in a general sense. These roughly predictable signals are termed
sto-
chastic
. The EEG is such a nondeterministic, stochastic signal because its future val-
ues can only be predicted in terms of a probability distribution of amplitudes
already observed in the signal. This probability distribution,
p
(
x
), can be deter-
mined experimentally for a particular signal,
x
(
t
), by simply forming a histogram of
all observed values over a period of time. A signal such as that obtained by rolling
dice has a probability distribution that is rectangular or uniform [i.e., the likelihood
of all face values of a throw are equal and in the case of a single die,
p
(
x
) = 1/6 for
each possible value]; a signal with a bell-shaped, or normal probability distribution
is termed Gaussian. As illustrated in Figure 9.2, EEG amplitude histograms may
have a nearly Gaussian distribution. The concept of using statistics, such as the
mean, standard deviation, skewness, and so forth, to describe a probability
distribution will be familiar to many readers.
If the probability function
p
(
x
) of a stochastic signal
x
(
i
) does not change over
time, that process is deemed stationary. The EEG is not strictly stationary because
its statistical parameters may change significantly within seconds, or it may be sta-
ble for tens of minutes (quasistationary) [29, 30]. If the EEG is at least
quasistationary, then it may be reasonable to check it for the presence of
rhythmicity, where rhythmicity is defined as repetition of patterns in the signal.
Recurring patterns can be identified mathematically using the concept of correla-
tion. Correlation between two signals measures the likelihood of change in one sig-
nal leading to a consistent change in the other. In assessing the presence of rhythms,
autocorrelation is used, testing the match of the original signal against different
starting time points of the same signal. If rhythm is present, then at a particular off-
set time (equal to the interval of the rhythm), the correlation statistic increases, sug-
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