Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 150

ber of estimated ICs equals the total number of recording electrodes. If that number
is considerably greater than the true number of independent sources contributing to
the recorded signals, ICs containing spurious activity will appear because of overfit-
ting. Contrarily, if the total number of ICs is considerably smaller than the true num-
ber of underlying sources, valuable information will be lost because of underfitting.
This important limitation (that the number of independent components is arbitrarily
defined) could explain why, until now, ICA has not been able to clearly and un-
equivocally disentangle event-related electrical brain responses into physiologically
meaningful independent constituents [Mouraux and Iannetti, 2008]. Another prob-
lem that has to be considered when applying ICA is the amount of available data
needed to correctly estimate the unmixing matrix (see Sect. 3.6.2).

4.1.7.3 Analysis of non-phase locked responses

A given sensory or internally generated stimulus or a motor response can provoke
not only the time-locked event-related response, but can also induce changes in the
ongoing EEG/MEG activities. These effects can be quantified by observing the rel-
ative changes: (i) in the power of specific frequency bands—known as event-related
synchronization ERS or desynchronization ERD [Pfurtscheller and Lopes da Silva,
1999], (ii) the changes in the phase distribution—known as phase resetting [Sayers
et al., 1974], (iii) phase synchrony [Engel and Singer, 2001], and (iv) phase cluster-
ing [Kalitzin et al., 2002].

4.1.7.3.1 Event-related synchronization and desynchronization To introduce
the ERD and ERS measures we have to realize that in the spontaneous ongoing brain
activity (recorded as EEG) rhythmic components are present (see Sect. 4.1.2) . The
measure of ERD is defined as the relative decrease and ERS as the relative increase of
power in a given frequency band relative to some baseline level. Thus mathematically
both effects can be described by the same formula:

S f − R f

ERD / ERS = (4.17)

R f

with ERD relating to negative values and ERS to the positive values; S f is the band
power in the analysis time; and R f is the band power in the baseline time. The base-
line time should be selected in such a way that the signal can be considered as not
affected by the processes under investigation. The baseline epoch should contain
only the spontaneous activity.
The physiological interpretation of ERD/ERS is explicitly expressed in their
names. The EEG signal can be observed mainly due to synchronous activity of neu-
rons under the electrode which corresponds to the area of cortex of the order of a few
squared centimeters. The amplitude of the rhythmic oscillation is proportional to the
number of synchronously active neurons ( Sect. 4.1.1) . In this sense the ERD and ERS
observed in EEG measure the level of synchronization of huge ensembles of corti-
cal neurons. However, one should be aware of the spatial scale of the physiological
processes reflected in the ERD/ERS. Especially in the case of ERD one can imagine