Quantitative analysis of EEG signals: Time-frequency methods and ...

1987) is that coherence gives the correlation as a function of frequency, thus allowing the
study of spatial correlations between dierent frequency bands. There is an extensive
literature about the use of coherence in EEGs. This section will only show some examples
and for a more complete review I suggest the work of Lopes da Silva (1993a).
Lopes da Silva et al. (1973a) computed thalamo-cortical and cortico-cortical coherences
for checking the validity of the assumption of a thalamic pacemaker of cortical
alpha rhythms, as proposed by Andersen and Andersson (1968). They found that
cortico-cortical coherences were higher than the thalamo-cortical ones, thus stressing
the importance of cortical mechanisms in the spread of alpha rhythms, in disagreement
with the thalamic pacemaker theory.
Storm van Leeuwen et al. (1978) used coherence analysis for dierentiating alpha
and murhythms. It is interesting to remark that since these frequencies are very similar,
this is a very dicult task to achieve with normal spectrograms.
Other interesting application of coherence is for the denition of characteristic \lengths
of synchrony" between neuronal populations. This is achieved by establishing lengths
with signicant coherence. Following this approach, after studying 189 children, Thatcher
et al. (1986) proposed a \two-compartmental model" stating that two separate sources
of EEG coherences are present: the rst one determined by short length axonal connections
and the second one by long distance connections.
Bullock and coworkers (1989, 1995a, 1995b) criticize the use of scalp electrodes for
measuring spatial structure of synchrony and they studied the spatial structure of coherence
with intracranial electrodes. In contradiction with previous reports of population
synchrony of the order of several centimeters, they reported that coherence varied in
the order of a few millimeters, thus showing a microstructure of the cell populations.
Furthermore, due to this small range structure, they criticize the view of the EEG as a
linear superposition of independent oscillators.
Several attempts were performed in order to analyze epileptic seizures with coherence
analysis. Gerch and Goddard (1970) used coherence for identifying the location of an
epileptic focus in a cat brain. By seeing a signicant decrease of coherence between two
channels after the subtraction of the eect of a third one (this method called partial
coherence), they deduce that the third one was driving the other two, thus being the
focus of the seizure.
Brazier (1972), introduced the measurement of time delays between channels (see
eq. 12) in order to follow routes of propagation and establish the origin of seizure activity.
Gotman (1983, 1987) proposed a modication of this algorithm by calculating the time
delay from the slope of a straight linettedto the phase spectrum when the coherence
is signicant. He showed that time delays most often indicate a lead from the side of
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