Dynamic Causal Modelling for EEG and MEG. Stefan Kiebel

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1 Dynamic Causal Modelling for EEG and MEG Stefan Kiebel

2 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

3 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

4 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

5 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

6 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

7 Probabilistic inference Forward problem p(y θ,m) Likelihood Posterior distribution p(θ y,m) Inverse problem

8 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)

9 Model for auditory evoked response Garrido et al., PNAS, 2007

10 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

11 The DCM approach DCM: model structure θ 24 (, ϕ) (,, θ ) y = g + ε & = f u ( θϕ,, m) p y likelihood 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

12 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

13 Neural mass equations and connectivity Etrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells 4 γ 3 γ ) ) ( ) (( 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 = )) ( ) (( e e L B e e S I A A H τ τ γ τ + + = = ) ( 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

14 Source activity over time Forward Backward Lateral Input u = f (, u, θ ) states parameters θ

15 Spatial forward model y=g(,φ)+ε Kiebel et al., NeuroImage, 2006 Daunizeau et al., NeuroImage, 2009

16 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

17 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

18 Probabilistic inference Forward problem p(y θ,m) Likelihood Posterior distribution p(θ y,m) Inverse problem

19 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)

20 Observed (adjusted) Predicted Fitted data Observed (adjusted) 1 time (ms) Predicted mode mode time (ms) time (ms) channels mode mode time (ms) channels Observed (adjusted) Predicted mode mode time (ms) time (ms) channels mode mode 8 trial 1 (predicted) trial 1 (observed) trial 2 (predicted) trial 2 (observed) time (ms)

21 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

22 Overview 1 M/EEG analysis 2 Dynamic Causal Modelling Motivation 3 Dynamic Causal Modelling Generative model 4 Bayesian inference 5 Applications

23 Auditory evoked potential Garrido et al., PNAS, 2007

24 Auditory evoked potential time (ms) time (ms) Garrido et al., PNAS, 2007

25 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

26 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

27 Patient study: EEG, MMN Boly et al., Science, 2011

28 Patient study: EEG Boly et al., Science, 2011

29 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

30 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.

31 Thank you!

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