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Brain Connectivity and Model Comparison

Brain Connectivity and Model Comparison. Will Penny. Wellcome Trust Centre for Neuroimaging, University College London, UK. 26 th November 20 10. Dynamic Causal Models. Neural state equation :. inputs. Dynamic Causal Models. Neural state equation :. MEG. Neural model:

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Brain Connectivity and Model Comparison

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  1. Brain Connectivity and Model Comparison Will Penny Wellcome Trust Centre for Neuroimaging, University College London, UK 26th November 2010

  2. Dynamic Causal Models Neural state equation: inputs

  3. Dynamic Causal Models Neural state equation: MEG Neural model: 8 state variables per region nonlinear state equation propagation delays inputs

  4. Dynamic Causal Models Electric/magnetic forward model:neural activityEEGMEG LFP (linear) Neural state equation: MEG Neural model: 8 state variables per region nonlinear state equation propagation delays inputs

  5. Dynamic Causal Models Electric/magnetic forward model:neural activityEEGMEG LFP (linear) Neural state equation: fMRI MEG Neural model: 1 state variable per region bilinear state equation no propagation delays Neural model: 8 state variables per region nonlinear state equation propagation delays inputs

  6. Dynamic Causal Models Hemodynamicforward model:neural activityBOLD (nonlinear) Electric/magnetic forward model:neural activityEEGMEG LFP (linear) Neural state equation: fMRI MEG Neural model: 1 state variable per region bilinear state equation no propagation delays Neural model: 8 state variables per region nonlinear state equation propagation delays inputs

  7. Dynamic Causal Models DCM for ERP/ERF DCM for Steady State Spectra DCM for fMRI DCM for Time Varying Spectra DCM for Phase Coupling

  8. Synchronization Gamma sync  synaptic plasticity, forming ensembles Theta sync  system-wide distributed control (phase coding) Pathological (epilepsy, Parkinsons) Phase Locking Indices, Phase Lag etc are useful characterising systems in their steady state

  9. Weakly Coupled Oscillators For studying synchronization among brain regions Relate change of phase in one region to phase in others Region 2 Region 1 ? ? Region 3

  10. One Oscillator

  11. Two Oscillators

  12. Two Coupled Oscillators 0.3

  13. Stronger coupling 0.6

  14. Mutual Entrainment 0.3 0.3

  15. DCM for Phase Coupling

  16. DCM for Phase Coupling

  17. DCM for Phase Coupling Phase interaction function is an arbitrary order Fourier series

  18. MEG Example Fuentemilla et al, Current Biology, 2010

  19. Delay activity (4-8Hz) Duzel et al. (2005) find different patterns of sensor-space theta-coupling in the delay period dependent on task. We are now looking at source space and how this coupling evolves.

  20. Data Preprocessing • Pick 3 regions based on source reconstruction • 1. Right MTL [27,-18,-27] mm • 2. Right VIS [10,-100,0] mm • 3. Right IFG [39,28,-12] mm • Project MEG sensor activity onto 3 regions •  with fewer sources than sensors and known location, • then pinv will do (Baillet et al., 2001)

  21. Data Preprocessing • Pick 3 regions based on source reconstruction • 1. Right MTL [27,-18,-27] mm • 2. Right VIS [10,-100,0] mm • 3. Right IFG [39,28,-12] mm • Project MEG sensor activity onto 3 regions •  with fewer sources than sensors and known location, • then pinv will do (Baillet et al., 2001) • Bandpass data into frequency range of interest • Hilbert transform data to obtain instantaneous phase

  22. Data Preprocessing • Pick 3 regions based on source reconstruction • 1. Right MTL [27,-18,-27] mm • 2. Right VIS [10,-100,0] mm • 3. Right IFG [39,28,-12] mm • Project MEG sensor activity onto 3 regions •  with fewer sources than sensors and known location, • then pinv will do (Baillet et al., 2001) • Bandpass data into frequency range of interest • Hilbert transform data to obtain instantaneous phase • Fit models to control data (10 trials) and memory data (10 trials). • Each trial comprises first 1sec of delay period.

  23. ? 2.46 IFG VIS ? 2.89 MTL Question Which connections are modulated by memory task? This question can be answered using Bayesian parameter inference

  24. MTL Master VIS Master IFG Master 1 IFG 3 5 VIS IFG VIS IFG VIS Master- Slave MTL MTL MTL IFG 6 VIS 2 IFG VIS 4 IFG VIS Partial Mutual Entrainment MTL MTL MTL 7 IFG VIS Total Mutual Entrainment MTL Q. How do we compare these hypotheses ? A. Bayesian Model Comparison

  25. LogBF model 3 versus model 1 > 20 LogEv Model

  26. 0.77 2.46 IFG VIS 0.89 2.89 MTL Model 3

  27. Control fIFG-fVIS fMTL-fVIS

  28. Memory fIFG-fVIS fMTL-fVIS

  29. Recordings from rats doing spatial memory task: Jones and Wilson, PLoS B, 2005

  30. Summary • Differential equation models of brain connectivity • Bayesian inference over parameters and models • DCM for Phase Coupling

  31. Hippocampus Septum Connection to Neurobiology: Septo-Hippocampal theta rhythm Denham et al. 2000: Wilson-Cowan style model

  32. Four-dimensional state space

  33. Hippocampus Septum Hopf Bifurcation A B A B

  34. For a generic Hopf bifurcation (Erm & Kopell…) See Brown et al. 04, for PRCs corresponding to other bifurcations

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