EEG Signal Analysis in Anesthesia - Quantitative EEG Analysis Methods and Clinical Applications - page 235

gesting a repetition of the original signal voltage. The autocorrelation of signal x
(i.e., correlation of x versus x ) is denoted as γ XX ( τ ) where τ is the offset time interval

or lag.
Empirically, it is known that the EEG has a mean voltage of zero, over time: It is
positive as often as it is negative. However, the EEG and its derived statistical mea-
surements seldom have a true Gaussian probability distribution. This observation
complicates the task of a researcher or of some future automated EEG alarm system
that seeks to identify changes in the EEG over time. Strictly speaking, non-Gaussian
signals should not be compared using the common statistical tests, such as t -tests or
analysis of variance that are appropriate for normally distributed data. Instead,
there are three options: nonparametric statistical tests, a transform to convert
non-Gaussian EEG data to a normal (Gaussian) distribution, or higher order
spectral statistics (see later discussion).
Transforming non-Gaussian data by taking its logarithm is frequently all that is
required to allow analysis of the EEG as a normal distribution [31]. For example, a
brain ischemia detection system may try to identify when slow wave activity has sig-
nificantly increased. A variable such as “delta” power (described later), which mea-
sures slow wave activity, has a highly non-Gaussian distribution; thus, directly
comparing this activity at different times requires the nonparametric
Kruskal-Wallis or Friedman's test. However, a logarithmic transform of delta
power may produce a nearly normal p ( x ) curve; therefore, the more powerful para-
metric analysis of variance with repeated measures could be used appropriately to
detect changes in log(delta power) over time. Log transformation is not a panacea,
however, and whenever statistical comparisons of qEEG are to be made, the data
should be examined to verify the assumption of normal distribution.

9.4.1 Clinical Applications of Time-Domain Methods
Historically (predigital computer), intraoperative EEG analysis used analog, time
domain-based methods. In 1950 Faulconer and Bickford noted that the electrical
power in the EEG (power voltage 2 /resistance) was associated

with changes in the rate of thiopental or diethyl ether administration. Using analog
technology, they computed a power parameter as (essentially) a moving average of
the square of EEG voltage and used it to control the flow of diethyl ether to a vapor-
izer. This system was reported to successfully control depth of anesthesia in 50
patients undergoing laparotomy [17]. Digital total power (TP

= voltage × current =

sum of the squared
values of all the EEG samples in an epoch) was later used by several investigators,
but it is known have several problems, including its sensitivity to electrode location
and its insensitivity to important changes in frequency distribution as well as a
highly non-Gaussian distribution. Arom et al. reported that a decrease in TP may
predict neurological injury following cardiac surgery [32], but this finding has not
been replicated.
More comprehensive time domain-based approaches to analysis of the EEG
were reported by Burch [33], and by Klein [34] who estimated an “average” fre-
quency by detecting the number of times the EEG voltage crosses the zero voltage
level per second. Investigators have not reported strong clinical correlations with
zero crossing frequency (ZXF). The ZXF does not correlated with depth of anesthe-

=