Modeling Phase Transitions in the Brain (eBook)

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