Applying ICA in EEG: Choice of the Window Length and of the Decorrelation Method - Biomedical Engineering Systems and Technologies - page 252

(a) (b) (c)

(d) (e) (f)
Fig. 4. Realistic activities and corresponding histograms. first pre-ictal: (a) & (d), second pre-
ictal: (b) & (e), second ictal: (c) & (f).

[18]. Such mixing matrices guarantee the dipolarity of the underlying sources to be re-
trieved, providing a framework where the influence issue of the initialization (whitening
or sphering) in such context can be addressed.

Realistic Sources. Macroscopic models describe the neuronal activity at the scale
of neuronal populations by modelling the interconnection of pyramidal cells with in-
hibitory or excitatory inter-neurons. They have been particularly used to successfully
generate realistic electrophysiological recordings [19, 20]. In this work we have chosen
the Wendling's model [17], described by a set of ten differential equations. It has been
shown that this model is able to reproduce normal background activity (inter-ictal), first
and second pre-ictal activities as well as first and second ictal activities. Parameter val-
ues to be chosen in order to get these distinct epileptic activities are detailed in [21].
In this paper, these simulated activities have been introduced as sources (see fig. 4),
excepted the normal background and the first ictal activities that have Gaussian-like
distribution and are then inadequate for the selected ICA algorithms.
In a realistic situation, the number of ictal sources to be retrieved is limited. In our
simulation, the number of realistic sources (from pre-ictal to ictal) has been chosen to
be an eighth of the number of channels n (from 1 for 8 channels to 6 for 48 channels).
The remaining background activities are simulated randomly as sub and super gaussian
like in the previous random data set.

Dipolar Mixing Matrix. The next step for obtaining realistic EEGs, after plausible
source generation, is the construction of a realistic mixing matrix. We obtained it using
the classical three spheres model of Rush & Driscoll and the Berg surface potential