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The sleep-wake cycle: constraining steady states by electroencephalogram analysis

The sleep-wake cycle: constraining steady states by electroencephalogram analysis. Anthony L. Krensel. Modelling neurons and the brain EEG and stability analysis Constraints on sleep-wake states Physiology and the sleep-wake cycle. Cortex: “higher order” functions...

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The sleep-wake cycle: constraining steady states by electroencephalogram analysis

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  1. The sleep-wake cycle:constraining steady states by electroencephalogram analysis Anthony L. Krensel Modelling neurons and the brain EEG and stability analysis Constraints on sleep-wake states Physiology and the sleep-wake cycle

  2. Cortex: “higher order” functions... Thalamus: filters information to cortex Brainstem: functions include arousal Continuum Modelling: Modelling neural populations by average properties and significant connections The brain:

  3. Neuronal signalling Propagates down axon Receives signal Response to Signal Synapse: Terminals transmit neurochemicals, onto next neuron

  4. Neuronal signalling Propagates down axon Receives signal Response to Signal Synapse: Terminals transmit neurochemicals, onto next neuron

  5. The EEG EC Spectrum • Awake, eyes closed (EC) • Enhancement at low f (gold) • 1/f behaviour (green) • Strong alpha peak (red) • Small beta peak (orange) S2 Spectrum • Sleep, stage 2 (S2) • Enhancement at low f (gold) • 1/f behaviour (green) • Spindle peak/peaks (blue) 3

  6. The EIRS Model Cortex: • Excitatory (e) • Inhibitory (i) Thalamus: • Reticular nucleus (r) • Relay nuclei (s) Subthalamic Input (n) Can find steady state firing rates

  7. Steady State • Steady state firing rates  d/dt = 0 so , , , can be computed. • Nonlinear relationship: and • The linear gains are

  8. The EEG spectrum and Stability • Instability = power in single frequency diverges • First approximation to spectrum: given by squared modulus of transfer function:

  9. Stability Analysis  • Instability Dispersion relation • Most unstable case: k = 0

  10. EEG analysis • Examine very low frequency regime , , ,

  11. A constrained parameter space (EC)

  12. Constraining EC

  13. Constrained parameter space (S2)

  14. Constraining S2

  15. Qualitative Results • Firing rates change as expected • Reticular sleep-wake switch: active in sleep • Relay nuclei inputs increase • Strong intra-cortical connectivity increase

  16. Arousal projection to the cortex

  17. Inputs to the model

  18. 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.

  19. Acknowledgements • Prof. Peter Robinson • Dr. Peter Drysdale

  20. Extra equations (basic model equations)

  21. More equations

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