Modeling Phase Transitions in the Brain

by Steyn-ross, D. Alistair; Steyn-ross, Moira

• ISBN13: 9781441907950
• ISBN10: 1441907955
• Format: Hardcover
• Copyright: 2010-01-30
• Publisher: Springer Verlag

Summary

The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states.Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf--Turing interactions leading to cortical waves.

Author Biography

Alistair Steyn-Ross and Moira Steyn-Ross are computational and theoretical physicists in the Department of Engineering, University of Waikato, New Zealand. They share a long standing interest in the application of physics-based methods to gain insight into the emergent behavior of complex biological systems such as single neurons and interacting neural populations.

Table of Contents

Foreword	p. v
List of Contributors	p. xi
Acronyms	p. xv
Introduction	p. xxiii
Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles	p. 1
Introduction	p. 1
Phase transitions in single neurons	p. 2
H.R. Wilson spiking neuron model	p. 3
Type-I and type-II subthreshold fluctuations	p. 5
Theoretical fluctuation statistics for approach to criticality	p. 7
The anesthesia state	p. 11
Effect of anesthetics on bioluminescence	p. 11
Effect of propofol anesthetic on EEG	p. 13
SWS-REM sleep transition	p. 15
Modeling the SWS-REM sleep transition	p. 17
The hypnic jerk and the wake-sleep transition	p. 20
Discussion	p. 23
References	p. 24
Generalized state-space models for modeling nonstationary EEG time-series	p. 27
Introduction	p. 27
Innovation approach to time-series modeling	p. 28
Maximum-likelihood estimation of parameters	p. 28
State-space modeling	p. 30
State-space representation of ARMA models	p. 30
Modal representation of state-space models	p. 32
The dynamics of AR(1) and ARMA(2,1) processes	p. 33
State-space models with component structure	p. 35
State-space GARCH modeling	p. 36
State prediction error estimate	p. 36
State-space GARCH dynamical equation	p. 37
Interface to Kalman filtering	p. 38
Some remarks on practical model fitting	p. 38
Application examples	p. 40
Transition to anesthesia	p. 41
Sleep stage transition	p. 43
Temporal-lobe epilepsy	p. 45
Discussion and summary	p. 48
References	p. 51
Spatiotemporal instabilities in neural fields and the effects of additive noise	p. 53
Introduction	p. 53
The basic model	p. 54
Model properties and the extended model	p. 57
Linear stability in the deterministic system	p. 58
Specific model	p. 60
Stationary (Turing) instability	p. 61
Oscillatory instability	p. 63
External noise	p. 66
Stochastic stability	p. 68
Noise-induced critical fluctuations	p. 70
Nonlinear analysis of the Turing instability	p. 71
Deterministic analysis	p. 71
Stochastic analysis at order ¿(¿3/2)	p. 74
Stochastic analysis at order (¿5/2)	p. 76
Conclusion	p. 77
References	p. 78
Spontaneous brain dynamics emerges at the edge of instability	p. 81
Introduction	p. 81
Concept of instability, noise, and dynamic repertoire	p. 82
Exploration of the brain's instabilities during rest	p. 86
Dynamical invariants of the human resting-state EEG	p. 89
Time-series analysis	p. 90
Spatiotemporal analysis	p. 93
Final remarks	p. 94
References	p. 97
Limited spreading: How hierarchical networks prevent the transition to the epileptic state	p. 99
Introduction	p. 99
Self-organized criticality and avalanches	p. 100
Epilepsy as large-scale critical synchronized event	p. 101
Hierarchical cluster organization of neural systems	p. 101
Phase transition to the epileptic state	p. 103
Information flow model for brain/hippocampus	p. 103
Change during epileptogenesis	p. 104
Spreading in hierarchical cluster networks	p. 105
Model of hierarchical cluster networks	p. 105
Model of activity spreading	p. 107
Spreading simulation outcomes	p. 107
Discussion	p. 111
Outlook	p. 112
References	p. 114
Bifurcations and state changes in the human alpha rhythm: Theory and experiment	p. 117
Introduction	p. 117
An overview of alpha activity	p. 118
Basic phenomenology of alpha activity	p. 119
Genesis of alpha activity	p. 120
Modeling alpha activity	p. 121
Mean-field models of brain activity	p. 122
Outline of the extended Liley model	p. 124
Linearization and numerical solutions	p. 128
Obtaining physiologically plausible dynamics	p. 129
Characteristics of the model dynamics	p. 130
Determination of state transitions in experimental EEG	p. 136
Surrogate data generation and nonlinear statistics	p. 137
Nonlinear time-series analysis of real EEG	p. 137
Discussion	p. 138
Metastability and brain dynamics	p. 140
References	p. 141
Inducing transitions in mesoscopic brain dynamics	p. 147
Introduction	p. 147
Mesoscopic brain dynamics	p. 148
Computational methods	p. 149
Internally-induced phase transitions	p. 150
Noise-induced transitions	p. 150
Neuromodulatory-induced phase transitions	p. 155
Attention-induced transitions	p. 156
Externally-induced phase transitions	p. 162
Electrical stimulation	p. 162
Anesthetic-induced phase transitions	p. 167
Discussion	p. 170
References	p. 173
Phase transitions in physiologically-based multiscale mean-field brain models	p. 179
Introduction	p. 179
Mean-field theory	p. 181
Mean-field modeling	p. 181
Measurements	p. 184
Corticothalamic mean-field modeling and phase transitions	p. 184
Corticothalamic connectivities	p. 184
Corticothalamic parameters	p. 185
Specific equations	p. 187
Steady states	p. 187
Transfer functions and linear waves	p. 189
Spectra	p. 189
Stability zone, instabilities, seizures, and phase transitions	p. 191
Mean-field modeling of the brainstem and hypothalamus, and sleep transitions	p. 194
Ascending Arousal System model	p. 194
Summary and discussion	p. 198
References	p. 198
A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep	p. 203
Introduction	p. 203
Methods	p. 204
Continuum model of cortical activity	p. 204
Modeling the transition to REM sleep	p. 207
Modeling the slow oscillation of SWS	p. 208
Experimental Methods	p. 209
Results	p. 210
Discussion	p. 212
Appendix	p. 215
Mean-field cortical equations	p. 215
Comparison of model mean-soma potential and experimentally-measured local-field potential	p. 217
Spectrogram and coscalogram analysis	p. 217
References	p. 219
What can a mean-field model tell us about the dynamics of the cortex?	p. 223
Introduction	p. 223
A mean-field model of the cortex	p. 224
Stationary states	p. 226
Hopf bifurcations	p. 227
Stability analysis	p. 227
Stability of the stationary states	p. 228
Dynamic simulations	p. 229
Breathing modes	p. 230
Response to localized perturbations	p. 233
K-complex revisited	p. 237
Spiral waves	p. 240
Conclusions	p. 241
References	p. 241
Phase transitions, cortical gamma, and the selection and read-out of information stored in synapses	p. 243
Introduction	p. 243
Basis of simulations	p. 244
Results	p. 245
Nonspecific flux, transcortical flux, and control of gamma activity	p. 245
Transition to autonomous gamma	p. 246
Power spectra	p. 248
Selective resonance near the threshold for gamma oscillation	p. 248
Synchronous oscillation and traveling waves	p. 251
Comparisons to experimental results, and an overview of cortical dynamics	p. 252
Comparability to classic experimental data	p. 253
Intracortical regulation of gamma synchrony	p. 253
Synchrony, traveling waves, and phase cones	p. 254
Phase transitions and null spikes	p. 255
Implications for cortical information processing	p. 257
Appendix	p. 260
Model equations	p. 260
Hilbert transform and null spikes	p. 264
References	p. 265
Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion	p. 271
Introduction	p. 271
Continuum modeling of the cortex	p. 272
Reversal potentials	p. 272
Gap-junction diffusion	p. 273
Theory	p. 274
Input from chemical synapses	p. 274
Input from electrical synapses	p. 280
Results	p. 282
Stability predictions	p. 282
Slow-soma stability	p. 284
Fast-soma stability	p. 284
Grid simulations	p. 287
Slow-soma simulations	p. 288
Fast-soma simulations	p. 290
Response to inhibitory diffusion and subcortical excitation	p. 290
Discussion	p. 294
Appendix	p. 297
References	p. 298
Index	p. 301
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