Biomedical Engineering Reference
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processing. Actually, such areas are largely used in neuroscience as a reference sys-
tem for sharing cortical activation patterns found with different neuroimaging
techniques.
As a result of this anatomically guided data reduction, we pass from the analysis
of about 3,000 time series to the evaluation of fewer than a hundred (the BAs
located in both cerebral hemispheres). These BA waveforms, related to the increase
or decrease of the spectral power of the cortical current density in the investigated
frequency band, can be successively averaged across the subjects of the studied pop-
ulation. The grand-average waveforms describe the time behavior of the spectral
power increase or decrease of the current density in the population during the task
examined.
13.4 Statistical Analysis: A Method to Assess Differences Between
Brain Activities During Different Experimental Tasks
When an experiment is being conducted for EEG measurements, typically the task is
repeated by the subject a variable number of times (often called trials) in order to
collect enough EEG data to allow a statistical validation of the results.
Let
S
be the matrix of the power spectra of the cortical sources computed, which
has a dimension equal to the number of sources times the frequency bin used times
the number of trials recorded. We compute the average of the power spectral values
related to
i
th dipole within the
j
th frequency band of interest (theta, 3 to 7 Hz;
alpha, 8 to 12 Hz; beta, 13 to 29 Hz; gamma, 30 to 40 Hz); this operation is
repeated for each
s
ource and each frequency band. Thus, for each frequency band
we have a matrix
S
j
(with dimension sources
x
trials) which represent the distribu-
tion along the number of trials of the mean spectral power of each cortical sources.
The aim of the procedure is to find the differences between the cortical power
distributions
related to two different experimental tasks performe
d
by the subject,
say, task
A
and task
B
. For this reason, we compute the matrices
S
j
re
late
d to
the
EEG data recorded during task
A
and task
B
, and we refer to them as
S
j
A
and
S
j
B
.
Then, we perform a statistical contrast between such spectral matrices
S
j
A
and
S
j
B
using appropriate univariate statistical tests (such as the Student's test with the cor-
rection for multiple comparisons).
For the
i
th source and the
j
th frequency band, we denote by
the
mean values of the cortical power spectra distributions. In the following we want to
verify the null hypothesis
H
0
that such mean values are statistically similar:
μ
ij
,
and
μ
ij
,
, ,
μμ
ij
ij
, ,
μμ
ij
ij
H
0
:
=
and
H
A
:
≠
,
A
B
A
B
where
H
A
is the alternative hypothesis, that such differences are instead significantly
different.
Under the assumptions that: (1) the two samples came from normal (Gaussian)
populations, and (2) the populations have equal variances, Student's
t-
value for
testing the previous hypotheses can be expressed as
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