Dynamic Causal Modelling for EEG and MEG Stefan Kiebel
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
Mismatch negativity (MMN) Paradigm standards deviants pseudo-random auditory sequence time! 80% standard tones 500 Hz 20% deviant tones 550 Hz Raw data (e.g., 128 sensors) Preprocessing (Statistical Parametric Mapping) Evoked responses (shown: single sensor) µv time (ms) Garrido et al., NeuroImage, 2007
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
Electroencephalography (EEG) amplitude (µv) time (ms) Modelling aim: Eplain all data with few parameters How to: Assume data are caused by few interacting brain sources
Probabilistic inference Forward problem p(y θ,m) Likelihood Posterior distribution p(θ y,m) Inverse problem
Cognitive neuroscience Conventional analysis: Which regions are involved in task? DCM analysis: How do regions communicate? STG STG STG STG A1 A1 A1 A1 Input (s)mulus) Input (s)mulus)
Model for auditory evoked response Garrido et al., PNAS, 2007
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
The DCM approach DCM: model structure θ 24 (, ϕ) (,, θ ) y = g + ε & = f u ( θϕ,, m) p y likelihood 4 3 2 1 u DCM: Bayesian inference parameter estimate: model evidence: ˆ θ = E θ y, m priors on parameters ( ) (,, ) ( ) ( ) p y m = p yθϕm p θm p ϕm dϕdθ
Inference at meso-scale macro-scale meso-scale micro-scale eternal granular layer eternal pyramidal layer internal granular layer internal pyramidal layer Firing rate Synaptic dynamics
Neural mass equations and connectivity Etrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells 4 γ 3 γ 2 1 4 0 1 4 4 1 2 ) ) ( ) (( e e L F e e Cu S I A A H τ τ γ τ + + + = = 1 γ 2 γ ) ( 0 A F S ( 0 ) A L S ( 0 ) A B S Etrinsic backward connections Intrinsic connections Etrinsic lateral connections ( ),u,θ f = 0 2 7 8 0 3 8 8 7 2 )) ( ) (( e e L B e e S I A A H τ τ γ τ + + = = 2 3 6 7 4 6 6 3 2 2 5 1 2 0 5 5 2 6 5 0 2 ) ( 2 )) ( ) ( ) (( i i i i e e L B e e S H S S A A H τ τ γ τ τ τ γ τ = = + + = = = Jansen & Rit, Biol Cybern,1995 David et al., NeuroImage, 2006
Source activity over time Forward Backward Lateral Input u = f (, u, θ ) states parameters θ
Spatial forward model y=g(,φ)+ε Kiebel et al., NeuroImage, 2006 Daunizeau et al., NeuroImage, 2009
The generative model Source dynamics Spatial forward model = f (, u, θ ) states parameters θ y=g(,φ)+ε Evoked responses Input u David et al., NeuroImage, 2006 Kiebel et al., Human Brain Mapping, 2009
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
Probabilistic inference Forward problem p(y θ,m) Likelihood Posterior distribution p(θ y,m) Inverse problem
Bayesian inference Evoked responses Specify generative forward model (with prior distributions of parameters) Variational (Bayesian) algorithm Iterative procedure: 1. Compute model response using current set of parameters 2. Compare model response with data 3. Improve parameters, if possible 1. Posterior distributions of parameters p( ϑ y, m) 2. Model evidence p( y m)
0.01 0.005 Observed (adjusted) 1 0.01 0.005 Predicted Fitted data 0.01 0 Observed (adjusted) 1 time (ms) 0.01 0 Predicted 1.5 1 0.5 mode 1 1.5 1 0.5 mode 2-0.005-0.005 0-0.5 0-0.5-1 -1-0.010 0 50 100 150 200 250 time (ms) -0.005 time (ms) -0.010 0 50 100 150 200 250 channels -0.005-1.5 1.5 1 50 100 150 200 mode 3-1.5 1.5 1 50 100 150 200 mode 4 0.5 0.5-0.01 0 50 100 150 200 250 time (ms) -0.01 0 50 100 150 200 250 channels 0-0.5-1 0-0.5-1 -1.5 50 100 150 200-1.5 50 100 150 200 0.01 Observed (adjusted) 2 0.01 Predicted 1.5 1 mode 5 1.5 1 mode 6 0.5 0.5 0.005 0.005 0-0.5 0-0.5-1 -1 0-0.005-0.01 0 50 100 150 200 250 time (ms) time (ms) 0-0.005-0.01 0 50 100 150 200 250 channels -1.5 1.5 1 0.5 0-0.5-1 50 100 150 200 mode 7-1.5 1.5 1 0.5 0-0.5-1 50 100 150 200 mode 8 trial 1 (predicted) trial 1 (observed) trial 2 (predicted) trial 2 (observed) -1.5 50 100 150 200-1.5 50 100 150 200 time (ms)
best? Model selection: Which model is the best? data y Model 1 Model 2 p( y m1 ) p θ y, m ) ( 1 p( y m2 ) p θ y, m ( 2 ) Model selection: Select model with highest model evidence... p( y mi ) best? Model n p( y mn ) p θ y, m ( n ) Stephan et al., NeuroImage, 2009 Penny et al., PLoS Comp Biol, 2010
Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications
Auditory evoked potential Garrido et al., PNAS, 2007
Auditory evoked potential time (ms) time (ms) Garrido et al., PNAS, 2007
Mismatch negativity: EEG IFG IFG IFG Forward - F Backward - B Forward and Backward - FB STG STG STG STG STG STG STG A1 A1 A1 A1 A1 A1 input input input Forward Backward Lateral Forward Backward Lateral Forward Backward Lateral modulation of effective connectivity Garrido et al., NeuroImage, 2007
MMN: Group model comparison Bayesian Model Comparison Group level! log-evidence Forward (F) subjects Backward (B) Forward and Backward (FB) Garrido et al., NeuroImage, 2007
Patient study: EEG, MMN Boly et al., Science, 2011
Patient study: EEG Boly et al., Science, 2011
DCM for EEG/MEG variants auto-spectral density LA auto-spectral density CA1 cross-spectral density CA1-LA DCM for steady-state responses frequency (Hz) frequency (Hz) frequency (Hz) DCM for induced responses DCM for phase coupling
Summary Dynamic Causal Modelling tests hypotheses about how brain sources communicate. Differences between conditions or groups are modelled as modulation of connectivity. Bayesian model comparison to identify best model among alternative, plausible models.
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