Nonlinear dynamics and generalized synchronization: clinical
applications in epilepsy and dementia C.J. Stam Department of
clinical neurophysiology VU University Medical Center Amsterdam
Oscillations and Instability; control, near and far from
equilibrium in biology Leiden, 23-5-2005
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Nonlinear dynamics and generalized synchronization: clinical
applications in epilepsy and dementia I.Introduction Functional
connectivity Synchronization likelihood II.Applications Seizure
detection Cognition Normal disturbed III.Small-world networks in
Alzheimers disease
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Mechanisms of higher brain functions (cognition) 1.The brain
shows local specialization 2.Complex tasks require cooperation
between multiple brain areas 3.Synchronization is a key mechanism
for functional integration 4.Synchronization results in the
formation of functional networks with temporal and spatial
structure
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Functional integration in the brain: - synchronous networks
(binding) - dynamic changes tijd Cognitive dysfunction: breakdown
of binding
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AB Dynamics of Synchronization: Functional connectivity
Excessive: seizures Normal: fragile binding Diminished:
Dysconnection / Cognitive dysfunction How do distributed systems in
the brain integrate their activity under normal and pathological
conditions? ?
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Christiaan Huygens 14-4-1629 / 8-7-1695 Synchronization of
oscillators
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Synchronization: Adjustment of rhythms of (self sustained)
oscillating objects through weak interactions
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Synchronization of chaotic oscillators Synchronization of chaos
refers to a process wherein two (or many) systems (either
equivalent or nonequivalent) adjust a given property of their
motion to a common behavior due to a coupling or to a forcing
(periodical or noisy) S. Boccaletti e.a. Physics reports 2002; 366:
1-101. Complete / identical synchronization (intermittent) lag
synchronization (intermittent) phase synchronization Generalized
synchronization
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Characterization of interdependencies between time series
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Synchronization likelihood: an unbiased measure of generalized
synchronization in multivariate data sets C.J. Stam 1, B.W. van Dyk
2 Physica D, 2002; 163: 236-251 1 department of clinical
neurophysiology, VU University Medical Centre 2 MEG Centre, VU
University Medical Centre
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x(t)x(t+L)x(t+2*L) L x(t) x(t+L) x(t+2*L) time-delay embedding
Trajectory in state space L Time series
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Generalized synchronization X Y State of the response system Is
a (non linear) function of the state of the driver system
Y=F(X)
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Synchronization likelihood X Y Measure of the synchronization
between two signals Y=F(X)
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Synchronization likelihood X Y SL between X and Y at time i is
the likelihood that Y a,b resembles Y i, given that X a,b resembles
X i XiXi XaXa XbXb YiYi YaYa t=i YbYb
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YiYi XiXi ryry rxrx Synchronization likelihood X Y P ref = SL
=
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Nonlinearly coupled non-identical Henon systems
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Linear and nonlinear components of coupling: multichannel
surrogate data testing
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The influence of different noise levels on synchronization
estimate
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5 Hz low passunfiltered Bias in synchronization estimates due
to filtering
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Nonlinear dynamics and generalized synchronization: clinical
applications in epilepsy and dementia I.Introduction Functional
connectivity Synchronization likelihood II.Applications Seizure
detection Cognition Normal disturbed III.Small-world networks in
Alzheimers disease
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Seizure detection in the neonatal intensive care unit Seizure
occur frequently in neurologically compromized neonates Up to 85%
of the seizures are subclinical Current methods for seizure
detection have limitations: Gotman CFM
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Seizure detection in neonates with synchronization likelihood
Altenburg et al., Clin Neurophysiol. 2003;114: 50-5. Smit et al.,
Neuropediatrics 2004; 35: 1-7.
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Towne et al., Neurology 2000 236 coma patients no clinical
symptoms of seizures EEG: 8% of these patients is in non convulsive
status epilepticus (NCSE) NCSE: silent epidemic in intensive care
patients
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oogknipperen
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propofol
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Visual Working Memory Task Response: items remembered
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synchronization likelihood during retention interval: increase
in 2-6 Hz synchronization decrease of 6-10 Hz synchronization 2-6
Hz: theta working memory 6-10 Hz: lower alpha attention
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Changes in synchronization entropy during working memory
task
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Nonlinear synchronization in EEG and whole-head MEG recordings
of healthy subjects Stam CJ, Breakspear M, van Cappellen van Walsum
AM, van Dijk BW. Human Brain Mapping 2003; 19: 63-78.
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Alzheimers disease: a dysconnection syndrome? ?
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Generalized synchronization in Alzheimers disease Subjects: 20
AD patients MMSE: 21.3 20 healthy controls Recording: 151 channel
MEG Condition: eyes closed, no task
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Control gamma band (20-50 Hz) synchronous neural networks
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Alzheimer gamma band (20-50 Hz)
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Dynamics of functional connectivity in Alzheimers disease
Alzheimer patients (N = 24) Control subjects (N = 19) 21 channel
EEG, no-task, eyes-closed Synchronization likelihood: mean level of
synchronization Synchronization rate: rate of change of
synchronization ** **
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Alzheimer patientControl subject Dynamics of functional
connectivity
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Are fluctuations of global synchronization levels
scale-free?
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Detrended fluctuation analysis (DFA) Time series integration
Fluctuation at timescale t Plot of Log(fluctuation) /
Log(timescale) Scaling (self similarity) exponent: slope of linear
fit through Log(fluctuation) / Log(timescale)
Disturbed fluctuations of resting state EEG synchronization in
Alzheimers disease C.J. Stam, T. Montez, B.F. Jones, S.A.R.B.
Rombouts, Y. van der Made, Y.A.L. Pijnenburg, Ph. Scheltens Clin
Neurophysiol, 2005; 116: 708-715
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Interim conclusions: Results so far: Synchronisation analysis
can detect and characterize functional networks Networks change:
Cognitive tasks Brain pathology Questions: What is an optimal
network? How can we detect / characterize an optimal network?
Slide 48
Nonlinear dynamics and generalized synchronization: clinical
applications in epilepsy and dementia I.Introduction Functional
connectivity Synchronization likelihood II.Applications Seizure
detection Cognition Normal disturbed III.Small-world networks in
Alzheimers disease
Slide 49
How to analyze a complex system as the brain? Graph theory
Information theory Self-organized criticality Chaos theory
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The Kevin Bacon game
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Fig. 1 A B C D E F : vertex: edge Graph Cp: Cluster coefficient
Lp: Pathlength
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The enigma of the small-world phenomenon Most networks are
sparsely connected Most connections are local (high Cluster
coefficient) The distance between any two network elements is
small: how is this possible? Example: 10 11 neurons 10 4 synapses /
neuron Typically any two neurons are only 2 to 3 synapses away
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small-world networks: High cluster coefficient C Short path
length L Realistic model real complex networks optimal
configuration: Sparse connectivity Maximal communication between
all parts of the network Balance local specialisation / global
integration
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Experimental evidence for the existence of small-world networks
in the brain: Neuro anatomical networks: C. Elegans (Watts and
Strogatz, 1998) Visual cortex cat (Scannell et al., 1994) Animal
model / database (Hilgetag et al., 2000) Functional neural
networks: Animal model / strychnine (Stephan et al., 2000) fMRI
(Dodel et al., 2002; Eguiluz et al., 2004) MEG (Stam, 2004)
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C/C random = 2.08 L/L random = 1.09
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Questions: Is it possible to detect functional networks with
EEG ? Can these networks be characterized with graph theoretical
measures? What changes occur in Alzheimers disease ? Loss of
clustering (cluster coefficient C) ? Loss of integration (path
length L) ? How does this correlate with cognitive dysfunction
?
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Small-world networks in Alzheimers disease Alzheimer N = 15
69.6 (7.9) MMSE = 21.4 (4.0) Controls (subjective complaints) N =
13 70.6 (7.7) MMSE = 28.4 (1.1) EEG 21 channels Beta band (13-30
Hz) Rest / eyes closed
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Application of graph analysis to EEG: C L threshold 12 3 4
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Alzheimer patients Synchronization matrix Control subjects
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Alzheimer patients Synchronization matrix converted to graph
Control subjects
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T=0.029T=0.034T=0.045 Fully connectedSplitting offFragmentation
Graph splitting and fragmentation A BC
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Problem: Mean synchronisation is lower in AD than controls
Applying the same threshold means that AD networks will have less
connections Increased path length in Ad might be a trivial
consequence of the smaller number of supra threshold connections
Solution: compute C and L as a function of K (edges / vertex)
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Alzheimer patientsControl subjects Networks Normalized for K
(edges / vertex)
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small-world networks? C/C random L/L random Present
studyAD1.930.97 * Controls2.130.89 Stam, 2004Controls1.891.19
Salvador, 2005Controls2.081.09 Hilgetag, 2000Macaque visual ctx
1.851.02 Cat whole ctx1.991.07 Watts & Strogatz, 1998 C.
Elegans5.61.18
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Conclusions: Synchronization likelihood analysis can track
fragile binding in EEG and MEG Healthy subjects: Frequency specific
changes in synchronization in working memory task Scale-free
fluctuations of SL Alzheimer patients: Lower synchronization
Disturbed fluctuations of SL Disturbed spatial patterns
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Acknowledgements: Afdeling KNF R.L.M. Strijers E.M. Vriens H.E.
Ronner W. de Rijke L.S. Smit laboranten Afdeling neurologie H.W.
Berendse Y.A.L. Pijnenburg Ph. Scheltens M.C. Visser MEG centrum
B.W. van Dijk T. Montez J.C. de Munck J. Verbunt K. Cover
Kinderneurologie R.J. Vermeulen J. Altenburg Neonatale IC W.P.F.
Fetter Intensive care A.R.J. Girbes J.J. Spijkstra Neurochirurgie
W.P. VanderTop UMC F.S.S. Leijten W Spetgens Overige R. Ferri S.
Micheloyannis M. Breakspear G. Nolte J. Terry