INB-Lunch-Seminar

Sleep oscillations and the complex dynamics of the sleeping brain -

insights from the time series analysis of the human sleep EEG

Eckehard Olbrich

The dynamical system approach to investigate brain activity is a
promising way to improve our understanding of the underlying mechanisms
and functions of brain activity. The sleeping brain is of particular
interest because it shows a rich repertoire of internally generated
dynamic patterns and transitions between states which correspond to
different levels of consciousness.

The dynamics of the sleeping brain is governed by multiple time scales:
The typical EEG oscillations in the frequency range from 1 to 40 Hz, the
so called slow oscillation (0.1-1 Hz), the transitions between the sleep
stages at a scale of 10s to a few minutes, the NREM-REM sleep cycle
(appr. 90 min) and the dynamics of sleep regulation with the
homoeostatic component and the 24h circadian rhythm.

The ultimate aim is to integrate these different time scales in one
dynamical model. This can be done either by starting from the
physiological mechanisms and constructing appropriate models or by
analyzing the dynamics using time series such as the EEG -- which is my
approach. Beginning from the sleep EEG means starting from the fastest
time scale: The sleep oscillations. They are described by modelling the
EEG using adaptive linear models. The slower dynamics appear then as
time dependence of the parameters of these models, whereas these
parameters can be related to the frequency and incidence of the sleep
oscillations.

The changes of event frequencies and incidences as a function of sleep
stage and cycle as well as effects of sleep deprivation can be
considered as indicators for specific changes in the underlying neural
networks, e.g. due to modulatory influences. Using a simple model
network of globally coupled populations of excitatory and inhibitory
neurons it is shown that

(1) varying of the excitatory-inhibitory coupling modulated the
frequency of the oscillatory eigenmode of the network while the change
of the excitatory-excitatory coupling mainly altered its damping.

(2) the modulation of the frequency and the damping constant of the
eigenmode of the network can be detected from the change of the
frequency and event density of the oscillatory patterns detected from an
EEG-like signal generated by the network.

By adding systematic inhomogeneities into the couplings simulations
revealed oscillatory patterns at multiple frequencies beyond the single
frequency mean field solution that can be analyzed using state space
models. Finally first results regarding the relationship between the
slow parameter dynamics related to the sleep oscillations and the
dynamics of sleep regulation are discussed.