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Nonlinear dynamics and generalized synchronization: clinical applications in epilepsy and dementia

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

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  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, 23-5-2005

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

  5. 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 14-4-1629 / 8-7-1695

  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: 1-101. (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: 236-251 1 department of clinical neurophysiology, VU University Medical Centre 2 MEG Centre, VU University Medical Centre

  11. time-delay embedding L L 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 likelihood rx 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

  20. 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

  21. 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

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

  23. 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

  24. oogknipperen

  25. propofol

  26. Visual Working Memory Task Response: items remembered

  27. 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

  28. Changes in synchronization entropy during working memory task

  29. Nonlinear synchronization in EEG andwhole-head MEG recordings of healthy subjectsStam CJ, Breakspear M, van Cappellen van Walsum AM, van Dijk BW. Human Brain Mapping 2003; 19: 63-78.

  30. Alzheimer’s disease: a dysconnection syndrome? ?

  31. 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

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

  33. Alzheimer gamma band (20-50 Hz)

  34. Dynamics of functional connectivity in Alzheimer’s disease Alzheimer patients (N = 24) Control subjects (N = 19) 21 channel EEG, no-task, eyes-closed Synchronization rate: rate of change of synchronization Synchronization likelihood: mean level of synchronization * * * *

  35. Dynamics of functional connectivity Control subject Alzheimer patient

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

  37. 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)

  38. Detrended fluctuation analysis of synchronization likelihood SL 8-13 Hz DFA 8-13 Hz SL 13-30 Hz DFA 13-30 Hz

  39. Detrended fluctuation analysis

  40. 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: 708-715

  41. 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?

  42. 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

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

  44. The ‘Kevin Bacon’ game

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