Quantitative analysis of EEG signals: Time-frequency methods and ...
Quantitative analysis of EEG signals: Time-frequency methods and ...
Quantitative analysis of EEG signals: Time-frequency methods and ...
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<strong>and</strong> the Lorenz equations (a model <strong>of</strong> Rayleigh-Benard convection). By changing the<br />
control parameters <strong>of</strong> the models, they showed increases <strong>of</strong> the spectral entropy upon<br />
the disordering <strong>of</strong> the systems in their route to chaoticity.<br />
Inouye <strong>and</strong> coworkers (1991, 1993) introduced the spectral entropy to the <strong>analysis</strong><br />
<strong>of</strong> <strong>EEG</strong> <strong>signals</strong>. From the spectral entropy they dened an irregularity index<strong>and</strong> they<br />
reported in rest <strong>EEG</strong>s, more irregularityinanterior than in occipital areas. Furthermore,<br />
they reported a greater degree <strong>of</strong> <strong>EEG</strong> desynchronization during mental arithmetic in<br />
comparison with rest <strong>EEG</strong>. Stam <strong>and</strong> coworkers (Stam et al., 1993) instead, dened an<br />
accelaration spectrum entropy from the second derivative <strong>of</strong> the signal <strong>and</strong> they reported<br />
dierences <strong>of</strong> this measure in dementia, Parkinson disease (Jelles et al., 1995) <strong>and</strong> during<br />
mental activation (Thomeer et al., 1994).<br />
Blanco et al. (1998a) proposed a further improvement by dening the entropy from<br />
the Wavelet Transform due to its advantages over the Fourier transform. Among these,<br />
the most important one is that the time evolution <strong>of</strong> the entropy can be followed. Since<br />
the entropy is dened from the time-<strong>frequency</strong> representation <strong>of</strong> the signal, the nearly<br />
optimal time-<strong>frequency</strong> resolution <strong>of</strong> the Wavelet Transform is crucial for having an<br />
accurate measure. This is particularly important in the case <strong>of</strong> event-related potentials,<br />
in which the relevant response is limited to a fraction <strong>of</strong> a second. Furthermore, Wavelet<br />
Transform lacks <strong>of</strong> the requirement <strong>of</strong> stationarity.<br />
I showed the application <strong>of</strong> the Wavelet-entropy (WS) to the study <strong>of</strong> ERPs. WS<br />
proved to be a very useful tool for characterizing the event-related responses, furthermore,<br />
the information obtained with the WS probed not to be trivially related with the<br />
energy <strong>and</strong> consequently with the amplitude <strong>of</strong> the signal. This means that with this<br />
method, new information can be accessed with an approach dierent from the traditional<br />
<strong>analysis</strong> <strong>of</strong> amplitude <strong>and</strong> delays <strong>of</strong> the event-related responses.<br />
WS as a measure <strong>of</strong> resonance in the brain<br />
Following the resonance theory, the ERP can be seen as an evoked synchronization,<br />
<strong>frequency</strong> stabilization, <strong>frequency</strong> selective enhancement <strong>and</strong>/or phase reordering <strong>of</strong> the<br />
ongoing <strong>EEG</strong>, <strong>and</strong> it should not be interpreted as an additive component to a noisy<br />
background <strong>EEG</strong> (see sec. x1.3).<br />
WS appears as an ideal tool for measuring the synchronization <strong>of</strong> the <strong>EEG</strong> oscillations<br />
upon stimulation. In this context, synchronization means that the group <strong>of</strong> cells<br />
involved in the generation <strong>of</strong> the response react to the stimulation tuned in <strong>frequency</strong>.<br />
That means, they produce a narrow b<strong>and</strong> in the <strong>frequency</strong> domain <strong>and</strong> consequently<br />
they are correlated with a decrease in the entropy. Basar (1980) already mentioned<br />
the importance <strong>of</strong> the entropy for underst<strong>and</strong>ing the relation between the pre-stimulus<br />
ongoing <strong>EEG</strong> <strong>and</strong> the event-related responses by making an analogy with the concept<br />
97