Steyn-Ross Modeling Phase Transitions in the Brain

1. Auflage 2010
ISBN: 978-1-4419-0796-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 4, 306 Seiten

Reihe: Springer Series in Computational Neuroscience

Foreword by Walter J. Freeman. 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.

Autoren/Hrsg.

Steyn-Ross, Moira

Steyn-Ross, D. Alistair

Inhaltsverzeichnis

1;Foreword;5
2;List of Contributors;10
3;Acronyms;13
4;Contents;14
5;Introduction;20
6;1 Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles;27
6.1;D.A. Steyn-Ross, M.L. Steyn-Ross, M.T. Wilson, and J.W. Sleigh;27
6.2;1.1 Introduction;27
6.3;1.2 Phase transitions in single neurons;28
6.3.1;1.2.1 H.R. Wilson spiking neuron model;29
6.3.2;1.2.2 Type-I and type-II subthreshold fluctuations;31
6.3.3;1.2.3 Theoretical fluctuation statistics for approachto criticality;33
6.3.3.1;1.2.3.1 Fluctuation variance;35
6.3.3.2;1.2.3.2 Fluctuation spectrum;36
6.4;1.3 The anesthesia state;37
6.4.1;1.3.1 Effect of anesthetics on bioluminescence;37
6.4.2;1.3.2 Effect of propofol anesthetic on EEG;39
6.5;1.4 SWS--REM sleep transition;41
6.5.1;1.4.1 Modeling the SWS--REM sleep transition;43
6.6;1.5 The hypnic jerk and the wake--sleep transition;46
6.7;1.6 Discussion;49
6.8;References;50
7;2 Generalized state-space models for modeling nonstationary EEG time-series;53
7.1;A. Galka, K.K.F. Wong, and T. Ozaki;53
7.2;2.1 Introduction;53
7.3;2.2 Innovation approach to time-series modeling;54
7.4;2.3 Maximum-likelihood estimation of parameters;54
7.5;2.4 State-space modeling;56
7.5.1;2.4.1 State-space representation of ARMA models;56
7.5.2;2.4.2 Modal representation of state-space models;58
7.5.3;2.4.3 The dynamics of AR(1) and ARMA(2,1) processes;59
7.5.4;2.4.4 State-space models with component structure;61
7.6;2.5 State-space GARCH modeling;62
7.6.1;2.5.1 State prediction error estimate;62
7.6.2;2.5.2 State-space GARCH dynamical equation;63
7.6.3;2.5.3 Interface to Kalman filtering;64
7.6.4;2.5.4 Some remarks on practical model fitting;64
7.7;2.6 Application examples;66
7.7.1;2.6.1 Transition to anesthesia;67
7.7.2;2.6.2 Sleep stage transition;69
7.7.3;2.6.3 Temporal-lobe epilepsy;71
7.8;2.7 Discussion and summary;74
7.9;References;77
8;3 Spatiotemporal instabilities in neural fieldsand the effects of additive noise;79
8.1;Axel Hutt;79
8.2;3.1 Introduction;79
8.2.1;3.1.1 The basic model;80
8.2.2;3.1.2 Model properties and the extended model;83
8.3;3.2 Linear stability in the deterministic system;84
8.3.1;3.2.1 Specific model;86
8.3.2;3.2.2 Stationary (Turing) instability;87
8.3.3;3.2.3 Oscillatory instability;89
8.4;3.3 External noise;92
8.4.1;3.3.1 Stochastic stability;94
8.4.2;3.3.2 Noise-induced critical fluctuations;96
8.5;3.4 Nonlinear analysis of the Turing instability;97
8.5.1;3.4.1 Deterministic analysis;97
8.5.2;3.4.2 Stochastic analysis at order O(3/2);100
8.5.3;3.4.3 Stochastic analysis at order O(5/2);102
8.6;3.5 Conclusion;103
8.7;References;104
9;4 Spontaneous brain dynamics emerges at the edge of instability;107
9.1;V.K. Jirsa and A. Ghosh;107
9.2;4.1 Introduction;107
9.3;4.2 Concept of instability, noise, and dynamic repertoire;108
9.4;4.3 Exploration of the brain's instabilities during rest;112
9.5;4.4 Dynamical invariants of the human resting-state EEG;115
9.5.1;4.4.1 Time-series analysis;116
9.5.2;4.4.2 Spatiotemporal analysis;119
9.6;4.5 Final remarks;120
9.7;References;123
10;5 Limited spreading: How hierarchical networks prevent the transition to the epileptic state;125
10.1;M. Kaiser J. Simonotto;125
10.2;5.1 Introduction;125
10.2.1;5.1.1 Self-organized criticality and avalanches;126
10.2.2;5.1.2 Epilepsy as large-scale critical synchronized event;127
10.2.3;5.1.3 Hierarchical cluster organization of neural systems;127
10.3;5.2 Phase transition to the epileptic state;129
10.3.1;5.2.1 Information flow model for brain/hippocampus;129
10.3.2;5.2.2 Change during epileptogenesis;130
10.4;5.3 Spreading in hierarchical cluster networks;131
10.4.1;5.3.1 Model of hierarchical cluster networks;131
10.4.2;5.3.2 Model of activity spreading;133
10.4.3;5.3.3 Spreading simulation outcomes;133
10.4.3.1;5.3.3.1 Delay until large-scale activation;134
10.4.3.2;5.3.3.2 Robustness of sustained-activity cases;135
10.5;5.4 Discussion;137
10.6;5.5 Outlook;138
10.7;References;140
11;6 Bifurcations and state changes in the human alpha rhythm: Theory and experiment;143
11.1;D.T.J. Liley, I. Bojak, M.P. Dafilis, L. van Veen, F. Frascoli,and B.L. Foster;143
11.2;6.1 Introduction;143
11.3;6.2 An overview of alpha activity;144
11.3.1;6.2.1 Basic phenomenology of alpha activity;145
11.3.2;6.2.2 Genesis of alpha activity;146
11.3.3;6.2.3 Modeling alpha activity;147
11.4;6.3 Mean-field models of brain activity;148
11.4.1;6.3.1 Outline of the extended Liley model;150
11.4.2;6.3.2 Linearization and numerical solutions;154
11.4.3;6.3.3 Obtaining physiologically plausible dynamics;155
11.4.4;6.3.4 Characteristics of the model dynamics;156
11.5;6.4 Determination of state transitions in experimental EEG;162
11.5.1;6.4.1 Surrogate data generation and nonlinear statistics;163
11.5.2;6.4.2 Nonlinear time-series analysis of real EEG;163
11.6;6.5 Discussion;164
11.6.1;6.5.1 Metastability and brain dynamics;166
11.7;References;167
12;7 Inducing transitions in mesoscopic brain dynamics;172
12.1;Hans Liljenström;172
12.2;7.1 Introduction;172
12.2.1;7.1.1 Mesoscopic brain dynamics;173
12.2.2;7.1.2 Computational methods;174
12.3;7.2 Internally-induced phase transitions;175
12.3.1;7.2.1 Noise-induced transitions;175
12.3.1.1;7.2.1.1 A paleocortical network model;176
12.3.1.2;7.2.1.2 Simulating noise-induced phase transitions;178
12.3.2;7.2.2 Neuromodulatory-induced phase transitions;180
12.3.3;7.2.3 Attention-induced transitions;181
12.3.3.1;7.2.3.1 A neocortical network model;182
12.3.3.2;7.2.3.2 Simulating neurodynamical effects of visual attention;185
12.4;7.3 Externally-induced phase transitions;187
12.4.1;7.3.1 Electrical stimulation;187
12.4.1.1;7.3.1.1 Electrical pulses to olfactory cortex;187
12.4.1.2;7.3.1.2 Electroconvulsive therapy;188
12.4.2;7.3.2 Anesthetic-induced phase transitions;192
12.4.2.1;7.3.2.1 Neural network model with spiking neurons;192
12.4.2.2;7.3.2.2 Variation of network dynamics with channel-density composition;193
12.5;7.4 Discussion;195
12.6;References;198
13;8 Phase transitions in physiologically-based multiscale mean-field brain models;203
13.1;P.A. Robinson C.J. Rennie A.J.K. Phillips J.W. Kim J.A. Roberts;203
13.2;8.1 Introduction;203
13.3;8.2 Mean-field theory;205
13.3.1;8.2.1 Mean-field modeling;205
13.3.2;8.2.2 Measurements;208
13.4;8.3 Corticothalamic mean-field modeling and phase transitions;208
13.4.1;8.3.1 Corticothalamic connectivities;208
13.4.2;8.3.2 Corticothalamic parameters;209
13.4.3;8.3.3 Specific equations;211
13.4.4;8.3.4 Steady states;211
13.4.5;8.3.5 Transfer functions and linear waves;213
13.4.6;8.3.6 Spectra;213
13.4.7;8.3.7 Stability zone, instabilities, seizures, and phasetransitions;215
13.5;8.4 Mean-field modeling of the brainstem and hypothalamus,and sleep transitions;218
13.5.1;8.4.1 Ascending Arousal System model;218
13.6;8.5 Summary and discussion;222
13.7;References;222
14;9 A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep;226
14.1;J.W. Sleigh, M.T. Wilson, L.J. Voss, D.A. Steyn-Ross, M.L. Steyn-Ross, and X. Li;226
14.2;9.1 Introduction;226
14.3;9.2 Methods;227
14.3.1;9.2.1 Continuum model of cortical activity;227
14.3.2;9.2.2 Modeling the transition to REM sleep;230
14.3.3;9.2.3 Modeling the slow oscillation of SWS;231
14.3.4;9.2.4 Experimental Methods;232
14.3.4.1;9.2.4.1 Animals;232
14.3.4.2;9.2.4.2 Surgery;232
14.3.4.3;9.2.4.3 Data recording;232
14.3.4.4;9.2.4.4 Sleep staging;233
14.4;9.3 Results;233
14.5;9.4 Discussion;235
14.6;9.5 Appendix;238
14.6.1;9.5.1 Mean-field cortical equations;238
14.6.2;9.5.2 Comparison of model mean-soma potential and experimentally-measured local-field potential;240
14.6.3;9.5.3 Spectrogram and coscalogram analysis;240
14.7;References;242
15;10 What can a mean-field model tell us about the dynamics of the cortex?;245
15.1;M.T. Wilson, M.L. Steyn-Ross, D.A. Steyn-Ross, J.W. Sleigh, I.P. Gillies, and D.J. Hailstone;245
15.2;10.1 Introduction;245
15.3;10.2 A mean-field model of the cortex;246
15.4;10.3 Stationary states;248
15.5;10.4 Hopf bifurcations;249
15.5.1;10.4.1 Stability analysis;249
15.5.2;10.4.2 Stability of the stationary states;250
15.6;10.5 Dynamic simulations;251
15.6.1;10.5.1 Breathing modes;252
15.6.2;10.5.2 Response to localized perturbations;255
15.6.3;10.5.3 K-complex revisited;259
15.6.4;10.5.4 Spiral waves;262
15.7;10.6 Conclusions;263
15.8;References;263
16;11 Phase transitions, cortical gamma, and the selection and read-out of information stored in synapses;265
16.1;J.J. Wright;265
16.2;11.1 Introduction;265
16.3;11.2 Basis of simulations;266
16.4;11.3 Results;267
16.4.1;11.3.1 Nonspecific flux, transcortical flux, and control of gamma activity;267
16.4.2;11.3.2 Transition to autonomous gamma;268
16.4.3;11.3.3 Power spectra;270
16.4.4;11.3.4 Selective resonance near the threshold for gamma oscillation;270
16.4.5;11.3.5 Synchronous oscillation and traveling waves;273
16.5;11.4 Comparisons to experimental results, and an overview of cortical dynamics;274
16.5.1;11.4.1 Comparability to classic experimental data;275
16.5.2;11.4.2 Intracortical regulation of gamma synchrony;275
16.5.3;11.4.3 Synchrony, traveling waves, and phase cones;276
16.5.4;11.4.4 Phase transitions and null spikes;277
16.6;11.5 Implications for cortical information processing;279
16.7;11.6 Appendix;282
16.7.1;11.6.1 Model equations;282
16.7.2;11.6.2 Hilbert transform and null spikes;286
16.8;References;287
17;12 Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion;292
17.1;M.L. Steyn-Ross, D.A. Steyn-Ross, M.T. Wilson, and J.W. Sleigh;292
17.2;12.1 Introduction;292
17.2.1;12.1.1 Continuum modeling of the cortex;293
17.2.2;12.1.2 Reversal potentials;293
17.2.3;12.1.3 Gap-junction diffusion;294
17.3;12.2 Theory;295
17.3.1;12.2.1 Input from chemical synapses;295
17.3.1.1;12.2.1.1 Slow-soma limit;297
17.3.1.2;12.2.1.2 Fast-soma limit;299
17.3.1.3;12.2.1.3 Wave equations;299
17.3.1.4;12.2.1.4 Subcortical inputs;300
17.3.2;12.2.2 Input from electrical synapses;301
17.3.2.1;12.2.2.1 Slow-soma limit with gap junctions;303
17.3.2.2;12.2.2.2 Fast-soma limit with gap junctions;303
17.4;12.3 Results;303
17.4.1;12.3.1 Stability predictions;303
17.4.2;12.3.2 Slow-soma stability;305
17.4.3;12.3.3 Fast-soma stability;305
17.4.4;12.3.4 Grid simulations;308
17.4.5;12.3.5 Slow-soma simulations;309
17.4.6;12.3.6 Fast-soma simulations;311
17.4.7;12.3.7 Response to inhibitory diffusion and subcorticalexcitation;311
17.5;12.4 Discussion;315
17.6;Appendix;318
17.7;References;319
18;Index;321