Biomedical Engineering Reference
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nents during the second and fourth epochs, when noise components were propa-
gated across channels. However, partial coherences [Figure 14.4(c)] show relation-
ships only between channels 1 and 2 and between channels 2 and 3 during the second
and fourth epochs, when signals were directly related between these channels. Partial
coherence is close to zero during the first and third epochs because the spectral com-
ponents are common to all three channels and noise components are independent;
thus, no direct relationships should be observed between channels. Partial coherence
is close to zero for channels 1 and 3 during the second epoch because a noise compo-
nent added to channel 2 was not present in channel 1, and it is also close to zero dur-
ing the fourth epoch because a noise component added to channel 2 was not present
in channel 3. Thus, there were no direct relationships between signals 1 and 3. The
small patches in the plots of partial coherence for channels 1 and 3 are edge effects
from analyzing windows with concatenated signals.
SDTF [Figure 14.5(a)] does not differentiate direct flows from indirect ones.
There are visible flows 1
→
2 and 2
→
3 (direct flows), as well as 1
→
3 (indirect
flow), during the second epoch, and flows 3
→
2 and 2
→
1 (direct flows), as well as
3
1 (indirect flow) during the fourth epoch. SdDTF plots [Figure 14.5(b)] illus-
trate the effect of multiplying SDTF by partial coherence. Only direct flows 1
→
→
2
and 2
→
3 are observed during the second epoch, and only direct flows 3
→
2 and 2
→
1 are observed during the fourth epoch. The indirect flows 1
→
3 and 3
→
1 seen
in SDTF are eliminated in the SdDTF plots (the thin patch in 3
1 is an edge effect
from concatenated signals), yielding a more precise estimate of the changing rela-
tionships between signals.
To evaluate the statistical significance of event-related changes in SdDTF, that is,
event-related causality (ERC), new statistical methodology was developed for com-
paring prestimulus (baseline) with poststimulus SdDTF values. The main difference
between this methodology and other statistical methods is that both the baseline and
poststimulus epochs are treated as nonstationary (for more details, see [148]).
→
14.4.2 Application of ERC to Cortical Function Mapping
Application of ERC to human ECoG signals recorded during language tasks has
yielded interesting observations that are generally consistent with the putative func-
tional neuroanatomy and dynamics of human language. In particular,
Korzeniewska et al. [148] applied ERC analyses to an auditory word repetition task
in which the patient heard a series of spoken words and repeated each one aloud.
Previous observations of event-related high-gamma activity during this and other
language tasks led us to focus our ERC analyses on the causal interactions between
signals in high-gamma frequencies [80, 81, 88].
Integrals of ERC calculated for high-gamma interactions (82 to 100 Hz) during
auditory word repetition are illustrated in Figure 14.6. The magnitude of this inte-
gral is represented by the width of the arrow, and each arrow illustrates an increase
of ERC in the frequency range 82 to 100 Hz. This frequency range was empirically
derived based on the mean ERC over all time points and all pairs of analyzed chan-
nels. Its boundaries were defined by local minima of the averaged ERC. This was
done in lieu of choosing an arbitrary frequency range in order to avoid artificial
summation of flows related to different frequency bands.
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