Applied Maths Seminar: Breakspear -- Bimodal and extremum statistics in human EEG : Measurement and implications

Although nonlinear dynamics are known to determine the behaviour of individual neurons,
an emerging consensus is that large-scale neocortical activity can be characterised as a
Gaussian process.  This view arises from both modelling and behavioural studies of the
brain.  Hence nonlinearity at this scale is seen to herald pathological states such as
seizures.  We analysed the temporal fluctuations in human electrocencephalographic (EEG)
recordings acquired from healthy human subjects and estimated the likely probability
distribution function(s) across a range of temporal scales.  At many time scales (e.g.
20 Hz) such fluctuations deviate significantly from fitted Gaussian distributions, with
a bias towards a power-law scaling at the high amplitude end, reflecting extremal events
in the EEG which would not be expected to occur in a Gaussian field.  Fits to the data
can be better captured by the exponential family of noise distributions.  Within the
traditional alpha range (~10 Hz), activity typically shows a distinct bimodal
distribution.  Hence, whilst Gaussian models capture much of the signal variation in
macroscopic brain signals, they are unable to explain these distinct phenomena.  Are
such deviations from a Gaussian model important and what alternative models, such as
fractional kinetics, should be explored?