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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

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.

slide2

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)

plan of talk
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
1 the heat macroscope clausius 1865 hntroph transformation
(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

2 the heat microscope boltzmann maxwell 1876
(2)The Heat MicroscopeBoltzmann /Maxwell (1876)

W is number of arrangements to achieve the same state

  • (eg teenager’s bedroom)

S = kB  logeW

microstates and macrostates
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
3 information not heat shannon 1948
(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)

how to calculate shannon entropy uncertainty ignorance h
How to Calculate Shannon Entropy/Uncertainty/Ignorance (H)

Narrow Distribution

H=0.81

H = –pilog(pi)

pi

Broad Distribution

H=0.94

pi

how do general anaesthetic drugs work campagna nejm 2003 348 2110 24 microscopic explanations
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
isoflurane vs xenon de sousa et al anesthesiology 2000 92 1055
Isoflurane vs XenonDe Sousa et al, Anesthesiology, 2000:92;1055

Isoflurane: IPSC

Isoflurane: EPSC

Xenon: IPSC & EPSC

% Charge Transfer

slide11
Entropy and Anaesthesia?Axiom: Consciousness has something to do with “information processing” in the cortex
microscopic
Scale

Substances

Molecules

Bosons, Fermions

Measurement

Temperature, Pressure, Entropy

Velocities, Positions

Quantum states

Microscopic

Macroscopic

ABSTRACTION vs DETAIL

Mesoscopic

slide13

SCALE

  • Nervous
  • System
  • Neurons / Synapses / Networks
  • Ion channels / proteins
  • MEASUREMENT
  • Aesthesia / Consciousness
  • Distribution of potential / Field Potentials / EEG
  • Charge / ionic currents

Macroscopic

Mesoscopic

Microscopic

thermodynamics corticodynamics thermal agitation vs neural agitation
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”
thermodynamic entropy vs cortical entropy differences purpose
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?)
population inversion ceiling vs no ceiling
“Population Inversion”Ceiling vs No Ceiling

Uncertainty

Entropy

Probability

Temperature

spectral entropy synaptic agitation
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)
slide19

Unconsciousness = loss of EEG high frequencies

AWAKE

ASLEEP

AWAKE

Frequency (Hz)

Time (sec)

eeg power spectrum alert patient
EEG & Power Spectrum - Alert Patient

Freedom

Spectral Entropy = 0.9

Correlation Time < 10msec

eeg power spectrum anaesthetised
EEG & Power Spectrum - Anaesthetised

Prison

Awake

Spectral Entropy = 0.4

Asleep

Correlation Time = 125msec

theory experimental results
Theory & Experimental Results

Deep GA

0.74(0.02)

Awake

0.90(0.03)

Loss-of-Consciousness

0.69(0.06)

Increasing Anaesthetic Effect

conclusions musings
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)
thermodynamics corticodynamics thermal agitation vs neural agitation25
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”