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Cortical Entropy Changes with General Anaesthesia: Experiment and Theory.

Cortical Entropy Changes with General Anaesthesia: Experiment and Theory. JW Sleigh 1 , DA Steyn-Ross 2 , M Steyn-Ross 2 , T Sampson 2 , G Ludbrook 3 , C Grant 3 , D Williams 3 . 1 Department of Anaesthesia, Waikato Clinical School, Hamilton, NZ

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Cortical Entropy Changes with General Anaesthesia: Experiment and Theory.

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  1. Cortical Entropy Changes with General Anaesthesia: Experiment and Theory. JW Sleigh1, DA Steyn-Ross2, M Steyn-Ross2, T Sampson2, G Ludbrook3, C Grant3, D Williams3. 1Department of Anaesthesia, Waikato Clinical School, Hamilton, NZ 2Department of Physics and Engineering, University of Waikato, Hamilton, NZ 3Department of Anaesthesia, University of Adelaide, Adelaide SA, Australia.

  2. Approximate Entropy as an Electroencephalographic measure of Anesthetic Drug Effect during Desflurane Anesthesia Jorgen Bruhn, M.D.,Heiko R6peke, M.D., Andreas Hoaft, M.D., Ph.D. 204 -210 0 1991 Quantification of EEG irregularity by use of the entropy of the power spectrum T. Inouye, K. Shinosaki, H. Sakamoto, S. Toi, S. Ukai, A. lyama, Y. Katsuda and M. Hirano Department of Neuropsychiatry, Osaka University Medical Schoo4 Fukwhima-ku, Osaka 553 (Japan) (Accepted for publication: 7 December 1990)

  3. Plan of Talk • A Brief History of Entropy • Thermodynamic vs Information • Spectral entropy, correlation times, and thermodynamic entropy • Introduce Cortical Model • Mesoscopic modelling • EEG and Anaesthesia • Data collection and analysis • Conclusions

  4. (1)The Heat MacroscopeClausius 1865 (hntroph) - Transformation • 1st law - Quantity is constant but exchangeable • 2nd law - Quality is degraded: Dispersal of energy dS=dE/T

  5. (2)The Heat MicroscopeBoltzmann /Maxwell (1876) W is number of arrangements to achieve the same state • (eg teenager’s bedroom) S = kB  logeW

  6. MICROSTATES (1) + +  (2) +  + (3)  + + (1)    MACROSTATE Voltage of 2 volts S = k  Log(3) Voltage of 0 volts S = k  Log(1) Microstates and Macrostates

  7. (3)Information, not HeatShannon (1948) • “No one really knows what entropy is, so in a debate you will always have the advantage” • J von Neumann to Claude Shannon H = –pilog(pi)

  8. How to Calculate Shannon Entropy/Uncertainty/Ignorance (H) Narrow Distribution H=0.81 H = –pilog(pi) pi Broad Distribution H=0.94 pi

  9. How do general anaesthetic drugs work? (Campagna, NEJM 2003;348:2110-24)----- Microscopic explanations ----- • Enhance inhibition? • GABA/Cl- • K+ Leakage • Reduce excitation? • Nicotinic receptors • NMDA antagonism

  10. Isoflurane vs XenonDe Sousa et al, Anesthesiology, 2000:92;1055 Isoflurane: IPSC Isoflurane: EPSC Xenon: IPSC & EPSC % Charge Transfer

  11. Entropy and Anaesthesia?Axiom: Consciousness has something to do with “information processing” in the cortex

  12. Scale Substances Molecules Bosons, Fermions Measurement Temperature, Pressure, Entropy Velocities, Positions Quantum states Microscopic Macroscopic ABSTRACTION vs DETAIL Mesoscopic

  13. SCALE • Nervous • System • Neurons / Synapses / Networks • Ion channels / proteins • MEASUREMENT • Aesthesia / Consciousness • Distribution of potential / Field Potentials / EEG • Charge / ionic currents Macroscopic Mesoscopic Microscopic

  14. “Ceaselessly Colliding”Entropy = energy diffusionMoleculesNeurons

  15. Molecular heterogeneity of kinetic energy . Dispersed by collisions. Entropy is measure of this dispersal. Entropy measures energy and inter-molecular interactions. Neuronal heterogeneity of charge. Dispersed by synaptic events. Entropy is measure of this dispersal – of cortical activity. => Entropy measure of consciousness ??? Thermodynamics & Corticodynamics“Thermal agitation” vs “Neural agitation”

  16. Entropyis a monotonic function of energy There is noupper limit to molecular velocity. More heat => more kinetic energy => more collisions => more entropy Entropy is not a monotonic function of energy There isan upper limit to the neuronal firing rate More synaptic events more information processing …???Rate and timing codes… “Population inversion & negative temperature” Thermodynamic entropy vs Cortical entropy(differences = purpose?)

  17. “Population Inversion”Ceiling vs No Ceiling Uncertainty Entropy Probability Temperature

  18. Spectral Entropy & Synaptic Agitation Ornstein –Uhlenbeck processes dv/dt = Kinetic Energy = Damping + Diffusion (input) dhe/dv = Electrical energy = Drift matrix + Diffusion • Thermodynamics: Gas • Temperature  Velocity of molecules  1/Drift. • --- Lorentzian spectrum ---- • Spectral Entropy  log(Drift) •  Spectral Entropy of KE = (Temperature) • Synaptic Excitibility: • Drift term  Intensity of inputs into dendritic tree • --- Lorentzian spectrum ---- Spectral Entropy  log(Drift) •  Spectral Entropy of the EEG = (synaptic activity)

  19. Unconsciousness = loss of EEG high frequencies AWAKE ASLEEP AWAKE Frequency (Hz) Time (sec)

  20. EEG & Power Spectrum - Alert Patient Freedom Spectral Entropy = 0.9 Correlation Time < 10msec

  21. EEG & Power Spectrum - Anaesthetised Prison Awake Spectral Entropy = 0.4 Asleep Correlation Time = 125msec

  22. Example of changes in spectral entropy with anaesthesia AWAKE ASLEEP

  23. Theory & Experimental Results Deep GA 0.74(0.02) Awake 0.90(0.03) Loss-of-Consciousness 0.69(0.06) Increasing Anaesthetic Effect

  24. Conclusions / Musings • Spectral entropy measures corticodynamic entropy / activity: NOT a direct measure of “information processing” • What is “information processing”? How does xenon disrupt information processing without disrupting activity? • What are the “microstates”? • http://www.phys.waikato.ac.nz/cortex/(ASR thesis: pgs 71, 126, 166)

  25. Temperature T: result of transfer of kinetic energy of molecules by collisions S = E / T Cooling reduces the available energy states and slows dispersion Excitibility : result of transfer of voltage changes by synapses S = E /  Anaesthesia reduces the synaptic efficiency Coma = “Freezing” Thermodynamics & Corticodynamics“Thermal agitation” vs “Neural agitation”

  26. Spectral Entropy vs Log Correlation TimeHSpectral Entropy = –Ln(Tcorrel)

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