The sleep-wake cycle:constraining steady states by

electroencephalogram analysis

Modelling neurons and the brainEEG and stability analysisConstraints on sleep-wake statesPhysiology and the sleep-wake cycle

Anthony L. Krensel

The brain:

Cortex: “higher order” functions... Thalamus: filters information to cortex Brainstem: functions include arousal

Continuum Modelling: Modelling neural populations by

average properties and significant connections

Neuronal signalling

Receives

signal

Propagates

down axon

Synapse:

Terminals transmit

neurochemicals,

onto next neuron

Response to

Signal

Neuronal signalling

Receives

signal

Propagates

down axon

Synapse:

Terminals transmit

neurochemicals,

onto next neuron

Response to

Signal

The EEG

S2

Spectrum

EC Spectrum

Awake, eyes closed (EC)

•Enhancement at low f (gold)

•1/f behaviour (green)

•Strong alpha peak (red)

•Small beta peak (orange)

Sleep, stage 2 (S2)

•Enhancement at low f (gold)

•1/f behaviour (green)

•Spindle peak/peaks (blue)

3

The EIRS Model

Cortex: ● Excitatory (e)● Inhibitory (i)

Thalamus:● Reticular nucleus (r)● Relay nuclei (s)

Subthalamic Input (n)

Can find steady state firing rates

Steady State

Steady state firing rates d/dt = 0

so , , , can be computed.

Nonlinear relationship: and

The linear gains are

The EEG spectrum and Stability

Instability = power in single frequency diverges

First approximation to spectrum: given by squared modulus of

transfer function:

Stability Analysis Instability Dispersion relation Most unstable case: k = 0

EEG analysis

Examine very low

frequency regime

,

, ,

A constrained parameter space (EC)

Constraining EC

Constrained parameter space (S2)

Constraining S2

Qualitative Results

Firing rates change as expected

Reticular sleep-wake switch: active in sleep

Relay nuclei inputs increase

Strong intra-cortical connectivity increase

Arousal projection to the cortex

Inputs to the model

Summary and the Future

Constrained EC/S2 states in x,y,z Demonstrated links to physiology of sleep-wake Found a thalamic reticular sleep-wake switch

Extend this work to encompass sleep cycle Results guide modelling of sleep-wake inputs Ultimately link EIRS model to existing brainstem

models: e.g. the Phillips-Robinson model, the Circadian Oscillator, etc.

Acknowledgements

Prof. Peter Robinson Dr. Peter Drysdale

Extra equations (basic model equations)

More equations