Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 104

potentials typically have amplitudes of 5-10 mV and a time span of 10-50 msec. In
order to obtain supra-threshold excitation, the amplitudes of many postsynaptic po-
tentials have to be superimposed.
The electrical activity of neurons, producing electric and magnetic fields conform-
ing approximately to that of a dipole, generates currents along the cell membrane in
the intra- and extracellular spaces. Macroscopic observation of these fields requires
the synchronization of electrical activity of a large number of dipoles oriented in
parallel [Nunez, 1981]. Indeed, pyramidal cells of the cortex are to a large degree
parallel and moreover, they are synchronized by virtue of common feeding by tha-
lamocortical connections [Lopes da Silva, 1996]. The condition of synchrony is ful-
filled by the PSPs, which are relatively long in duration. The contribution from action
potentials to the electric field measured extracranially is negligible. EEG comes from
the summation of synchronously generated postsynaptic potentials. The contribution
to the electric field of neurons acting synchronously is approximately proportional
to their number, and for these firing non-synchronously, as the square root of their
number. For example: if an electrode records action of 10 8 neurons (which is typi-
cal for a scalp electrode) and 1% of them are acting in synchrony, their contribution
will be 100 times bigger than the contribution of neurons acting asynchronously,
since

10 6
√ 10 8

100. Scalp potentials are mostly due to sources coherent at the scale
of at least several centimeters (roughly 10 8 neurons) with geometries encouraging
the superposition of potentials generated by many local sources. Nearly all EEGs
are believed to be generated by cortical sources [Nunez, 1981] by virtue of the fol-
lowing reasons: cortical proximity to scalp, relatively large sink-source separation in
pyramidal cells constituting cortex dipoles, property of the cortex to produce large
cortical layers, high synchrony of pyramidal cells fed by the common thalamic input.
MEG is closely related to EEG. The source of the MEG signal is the same electrical
activity of the synchronized neural populations as is the case for EEG.
The processes at the cellular level (action potential generation) are non-linear.
Non-linear properties can also be observed in the dynamics of well-defined neu-
ral populations. However, at the EEG level, non-linearities are the exception rather
than the rule. The lack of the traces of non-linear dynamics in EEG was demon-
strated by means of surrogate data [Achermann et al., 1994, Stam et al., 1999] and
by means of comparison of linear and non-linear forecasting [Blinowska and Mali-
nowski, 1991]. In the latter work it was demonstrated that also in the case of LFP,
recorded from implanted electrodes, the linear forecasting gave the same or better
results than non-linear. During epileptic seizures some EEG epochs of non-linear
character were found [Pijn et al., 1997]. Indeed during seizure large parts of the
brain became synchronized.
Since non-linear methods are very sensitive to noise and prone to systematic er-
rors, as was mentioned in Sect. 2.5.7, one should have good reason to apply them
to the EEG analysis. It is recommended to check first if the signal has non-linear
character and if the linear methods are not sufficient. Most functions can be locally
linearized and thus linear methods may also work quite well for non-linear signals.

=