Phase Resetting in Medicine and Biology: Stochastic Modelling and Data Analysis

Գրքի շապիկի երեսը
Springer Science & Business Media, 15 հնվ, 2007 թ. - 329 էջ
Synchronization processes are of great interest and importance in biology, medicine and physics. In particular, for the comprehension of brain function ing it appears inevitable that one should analyze neuronal synchronization processes. This book presents a new understanding of how a stimulus in fluences synchronization patterns of a population of oscillators. On the one hand, a variety of stimulation-induced dynamical phenomena will be pre sented; on the other hand, new data analysis tools will be developed which will serve as a link between theory and experiment. In this way it will be possible to use the theory presented here as a basis for the design and evalu and ation of stimulation experiments and stimulation techniques in medicine biology. We shall focus particularly on applications concerning the analysis of magnetoencephalography (MEG) and electroencephalography (EEG) data as well as deep brain stimulation techniques used in Parkinsonian patients. This book addresses graduate students, professors and scientists in vari ous fields including biology, mathematics, medicine, neuroscience, physiology and physics. Besides mathematically involved parts, the book also provides the reader with numerous illustrations and explications of the deep dynamical principles governing stimulation-induced desynchronization and synchroniza tion processes. Therefore this book will be of interest to a general readership, and those who are not familiar with mathematics should not be deterred by the formulas.
 

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Introduction
1
12 Physiological Motivation
3
122 Deep Brain Stimulation
5
13 Stochastic Approach
6
14 Synergetics
9
Resetting an Ensemble of Oscillators
11
221 Macroscopic Level
12
222 Cluster of Oscillators
19
631 Excitation of Higher Order
165
632 Excitation of Lower Order
169
64 Couplings Determine Reaction to Stimulation
172
641 Rapid Recovery
173
642 Harmonic Early Response
174
65 Vulnerability and Recovery
176
651 Phase Errors Versus Duration Errors
177
652 Protective Effect of Couplings
181

23 Stochastic Model
21
24 FokkerPlanck Equation
22
241 Stationary Solution
23
242 Fourier Transformation
24
25 Spontaneous Behavior
25
26 Black Holes Without Noise
26
27 Ensemble Dynamics During Stimulation
28
272 Stimulation Induced Frequency Shift
37
273 Stimulation Mechanism with Higher Harmonics
39
28 Firing Patterns
46
29 Summary and Discussion
51
Synchronization Patterns
55
33 Clustering
57
34 Populations of Neurons
58
341 Model Neuron
59
342 Neuronal Interactions
60
35 Populations of Phase Oscillators
61
36 Slaving Principle and Center Manifold
64
361 Center Manifold Theorem
66
362 Strategy
69
372 One Cluster
71
373 Two Clusters
75
374 Three Clusters
77
375 Four Clusters
78
38 Complexity of Synchronized States
79
382 Phase and Frequency Shifts
82
383 Cluster Variables
84
384 Frozen States
86
385 Transient Behavior
88
386 Coupling Mechanism
90
39 Neural Coding
93
310 Summary
96
Stochastic Model
98
42 Derivation of the Model Equation
100
43 Fourier Transformation
105
44 Summary and Discussion
106
Clustering in the Presence of Noise
107
53 Comparison with the Ensembles Dynamics
108
54 Noisy Cluster States
109
541 Linear Problem
110
542 FirstMode Instability
111
543 SecondMode Instability
117
544 ThirdMode Instability
118
545 FourthMode Instability
119
546 TwoMode Instability
120
55 Scaling of Noisy Cluster States
127
56 The Experimentalists Inverse Problem
130
562 Firing Patterns
132
57 Neural Coding Revisited
135
58 Summary and Discussion
137
6 Single Pulse Stimulation
145
62 How Stimulation Affects Order Parameters
147
621 Cluster Variables and Order Parameters
148
622 Uniform and Partial Desynchronization
149
623 Stimulating a OneCluster State
150
624 Stimulating a TwoCluster State
159
63 Transient Mode Excitation and Early Response
163
653 Partial Desynchronization and Transient Phenomena
183
66 Black Hole and Recovery
185
67 Subcritical Long Pulses
187
671 Spiraling Towards the Desynchronized State
189
672 Excitation of Higher Order
191
673 Excitation of Lower Order
195
Periodic Stimulation
202
72 Smooth Periodic Stimulation
204
1 Phase Locking
205
2 Phase Locking
207
723 Changes of the Synchronization Pattern
210
73 Pulsatile Periodic Stimulation
212
74 Annihilation of Rhythms
214
75 Summary and Discussion
215
Data Analysis
219
82 Phases and Amplitudes
220
821 Marker Events
221
822 Reconstruction of the Modes Dynamics
222
823 Slaving Principle and Transients
224
83 Tracking Down the Black Holes
225
84 MEG and EEG Analysis
226
841 Triggered Averaging
227
m Transients
229
m Transients with Delay
236
m Transients
238
m Transients
240
m Transients With Delay
242
m Phase Synchronization
244
849 SelfSynchronization Versus Transients
248
8410 The Flow of Synchronized Cerebral Activity
249
8411 Inverse Problems
250
85 Summary and Discussion
251
Modelling Perspectives
256
911 TimeDelayed Interactions
258
912 Anatomy of Interacting Clusters
260
93 Chaotic Oscillators
261
94 Macroscopic Versus Microscopic
262
Neurological Perspectives
265
102 Parkinsonian Resting Tremor
266
1022 Stereotactic Treatment
270
11 Epilogue
275
112 Experimental Electrical and Magnetic Stimulation
279
113 Therapeutic Stimulation
280
Appendices
282
A Numerical Analysis of the Partial Differential Equations
285
B Phase and Frequency Shifts Occurring in Chap 3
287
B2 Three Clusters
288
C SingleMode Instability
291
C3 ThirdMode Instability
292
D TwoMode Instability
293
D3 Linear Problem Type I
294
D5 Singularities
295
References
297
Author Index
321
Subject Index
325
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