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Brain Connectivity and Model Comparison
Will Penny Wellcome Trust Centre for Neuroimaging, University College London, UK 26th November 2010
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Dynamic Causal Models Neural state equation: inputs
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Dynamic Causal Models MEG Neural state equation: inputs Neural model:
8 state variables per region nonlinear state equation propagation delays inputs
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Dynamic Causal Models MEG Neural state equation: inputs
Electric/magnetic forward model: neural activityEEG MEG LFP (linear) Neural state equation: MEG Neural model: 8 state variables per region nonlinear state equation propagation delays inputs
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Dynamic Causal Models fMRI MEG Neural state equation: inputs
Electric/magnetic forward model: neural activityEEG MEG 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
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Dynamic Causal Models fMRI MEG Neural state equation: inputs
Hemodynamic forward model: neural activityBOLD (nonlinear) Electric/magnetic forward model: neural activityEEG MEG 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
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Dynamic Causal Models DCM for ERP/ERF DCM for Steady State Spectra
DCM for fMRI DCM for Time Varying Spectra DCM for Phase Coupling
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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
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Weakly Coupled Oscillators
For studying synchronization among brain regions Relate change of phase in one region to phase in others Region 1 Region 3 Region 2 ?
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One Oscillator
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Two Oscillators
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Two Coupled Oscillators
0.3
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Stronger coupling 0.6
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Mutual Entrainment 0.3 0.3
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DCM for Phase Coupling
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DCM for Phase Coupling
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DCM for Phase Coupling Phase interaction function is an arbitrary order Fourier series
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MEG Example Fuentemilla et al, Current Biology, 2010
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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.
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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)
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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
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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.
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Question Which connections are modulated by memory task? MTL VIS IFG
2.89 2.46 ? This question can be answered using Bayesian parameter inference
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MTL VIS IFG 1 2 3 4 5 6 7 Master- Slave Partial Mutual Entrainment Total MTL Master VIS Master IFG Master Q. How do we compare these hypotheses ? A. Bayesian Model Comparison
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LogBF model 3 versus model 1 > 20
LogEv Model
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Model 3 MTL VIS IFG 2.89 2.46 0.89 0.77
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Control fIFG-fVIS fMTL-fVIS
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Memory fIFG-fVIS fMTL-fVIS
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Recordings from rats doing spatial memory task:
Jones and Wilson, PLoS B, 2005
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Summary Differential equation models of brain connectivity
Bayesian inference over parameters and models DCM for Phase Coupling
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Connection to Neurobiology: Septo-Hippocampal theta rhythm
Denham et al. 2000: Hippocampus Septum Wilson-Cowan style model
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Four-dimensional state space
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Hopf Bifurcation Hippocampus Septum A B A B
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For a generic Hopf bifurcation (Erm & Kopell…)
See Brown et al. 04, for PRCs corresponding to other bifurcations
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