1. 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,

2. Nonlinear dynamics and generalized synchronization: clinical applications in epilepsy and dementia
Introduction
Functional connectivity
Synchronization likelihood
Applications
Seizure detection
Cognition
Normal
disturbed
Small-world networks in Alzheimer’s disease

3. Mechanisms of higher brain functions (cognition)
The brain shows local specialization
Complex tasks require cooperation between multiple brain areas
Synchronization is a key mechanism for functional integration
Synchronization results in the formation of functional networks with temporal and spatial structure

4. Functional integration in the brain:
- synchronous networks (‘binding’)
- dynamic changes
Cognitive dysfunction:
‘breakdown of binding’
tijd

5. ? ‘Functional connectivity’
How do distributed systems in the brain integrate their
activity under normal and pathological conditions? A ? B
‘Functional connectivity’
Dynamics of Synchronization:
Diminished:
Dysconnection /
Cognitive dysfunction
Excessive:
seizures
Normal:
‘fragile binding’

6. Synchronization of oscillators
Christiaan Huygens /

7. Synchronization: Adjustment of rhythms of (self sustained)
oscillating objects through weak interactions

8. Synchronization of chaotic oscillators
Complete / identical synchronization
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:
(intermittent) lag synchronization
(intermittent) phase synchronization
Generalized synchronization

9. Characterization of interdependencies between time series

10. Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets
C.J. Stam1, B.W. van Dyk2
Physica D, 2002; 163:
1 department of clinical neurophysiology, VU University Medical Centre
2 MEG Centre, VU University Medical Centre

11. time-delay embedding L L x(t) x(t+L) x(t+2*L) x(t+2*L) x(t+L) x(t)
Time series
x(t)
x(t+L)
x(t+2*L)
x(t+2*L)
Trajectory in state space
x(t+L)
x(t)

12. Generalized synchronization
State of the response system Is a (non linear)
function of the state of the driver system X Y
Y=F(X)

13. Synchronization likelihood
Measure of the synchronization between two signals X Y
Y=F(X)

14. Synchronization likelihood
SL between X and Y at time i is the likelihood that Ya,b resembles Yi, given that Xa,b resembles Xi Xi Xa Xb X Yi Ya Yb Y
t=i

15. Synchronization likelihoodrx X Xi
Pref = ry Yi Y
SL =

16. Nonlinearly coupled
non-identical Henon systems

17. Linear and nonlinear components of coupling:
multichannel surrogate data testing

18. The influence of different noise levels
on synchronization estimate

19. Bias in synchronization estimates due to filtering
5 Hz low pass
unfiltered

22. Nonlinear dynamics and generalized synchronization: clinical applications in epilepsy and dementia
Introduction
Functional connectivity
Synchronization likelihood
Applications
Seizure detection
Cognition
Normal
disturbed
Small-world networks in Alzheimer’s disease

23. 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

25. Seizure detection in neonates with synchronization likelihood
Altenburg et al., Clin Neurophysiol. 2003;114: 50-5.
Smit et al., Neuropediatrics 2004; 35: 1-7.

26. 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

27. oogknipperen

28. propofol

29. Visual
Working
Memory
Task
Response:
items remembered

30. 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

31. Changes in
synchronization
entropy during
working memory
task

32. 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:

33. Alzheimer’s disease: a dysconnection syndrome?

34. Generalized synchronization in Alzheimer’s disease
Subjects:
20 AD patients
MMSE: 21.3
20 healthy controls
Recording:
151 channel MEG
Condition:
eyes closed,
no task

36. Control gamma band (20-50 Hz)
synchronous
neural networks

37. Alzheimer gamma band (20-50 Hz)

38. Dynamics of functional connectivity in Alzheimer’s 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 * * * *

39. Dynamics of
functional
connectivity
Control subject
Alzheimer patient

40. Are fluctuations of global synchronization levels scale-free?

41. Detrended fluctuation analysis (DFA)
Plot of
Log(fluctuation) / Log(timescale)
Time series
integration
Fluctuation at
timescale t
Scaling (self similarity) exponent:
slope of linear fit through
Log(fluctuation) / Log(timescale)

42. Detrended fluctuation analysis of synchronization likelihood
SL 8-13 Hz
DFA 8-13 Hz
SL Hz
DFA Hz

43. Detrended fluctuation analysis

44. Disturbed fluctuations of resting state EEG synchronization in Alzheimer’s 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:

47. Interim conclusions: Results so far: Questions:
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?

48. Nonlinear dynamics and generalized synchronization: clinical applications in epilepsy and dementia
Introduction
Functional connectivity
Synchronization likelihood
Applications
Seizure detection
Cognition
Normal
disturbed
Small-world networks in Alzheimer’s disease

49. How to analyze a complex system as the brain?
Graph theory
Chaos theory
Information theory
Self-organized criticality

50. The ‘Kevin Bacon’ game

51. Cp: Cluster coefficient Lp: Pathlength : vertex : edge
Fig. 1
Graph F E D C A B
Cp: Cluster coefficient
Lp: Pathlength
: vertex
: edge

52. 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:
1011 neurons
104 synapses / neuron
Typically any two neurons are only 2 to 3 synapses away

54. ‘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

55. Neuro anatomical networks:
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)

56. C/Crandom = 2.08
L/Lrandom = 1.09

59. Questions: Is it possible to detect functional networks with EEG ?
Can these networks be characterized with graph theoretical measures?
What changes occur in Alzheimer’s disease ?
Loss of ‘clustering’ (cluster coefficient C) ?
Loss of ‘integration’ (path length L) ?
How does this correlate with cognitive dysfunction ?

60. ‘Small-world’ networks in Alzheimer’s disease
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

62. Application of graph analysis to EEG:1 2 3 4 C
threshold L

63. Synchronization matrix
Alzheimer patients
Control subjects

64. Synchronization matrix converted to ‘graph’
Alzheimer patients
Control subjects

67. Graph splitting and fragmentationB C
T=0.029
T=0.034
T=0.045
Fully connected
Splitting off
Fragmentation

69. 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)

70. Networks Normalized for K (edges / vertex)
Alzheimer patients
Control subjects

73. ‘small-world’ networks?
C/Crandom
L/Lrandom
Present study AD
1.93
0.97 *
Controls
2.13
0.89
Stam, 2004
1.89
1.19
Salvador, 2005
2.08
1.09
Hilgetag, 2000
Macaque visual ctx
1.85
1.02
Cat whole ctx
1.99
1.07
Watts & Strogatz, 1998
C. Elegans
5.6
1.18

74. 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

75. Acknowledgements: Afdeling KNF Afdeling neurologie MEG centrum
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