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An electrophysiological validation of stochastic DCM for fMRI The goal of Dynamic Causal Modelling (DCM) of neuroimaging data is to study experimentally induced changes in effective connectivity among brain regions. In this work, we assess the predictive validity of stochastic DCM of fMRI data (Daunizeau et al., 2012), in terms of its ability to explain changes in the frequency spectrum of concurrently acquired EEG signal. First, we use a neural field model to show how dense lateral connections induce a separation of time scales, whereby fast (and high spatial frequency) modes are enslaved by slow (low spatial frequency) modes. This slaving effect is such that the frequency spectrum of fast modes (which dominate EEG signals) is controlled by the amplitude of slow modes (which dominate fMRI signals). This means we expect the frequency modulation of EEG to follow temporal variations of slow neural states driving fMRI BOLD signal changes (as in Kilner et al., 2005). Second, we use conjoint empirical EEG-fMRI data – acquired in epilepsy patients – to demonstrate the electrophysiological underpinning of (spontaneous) neural fluctuations inferred from stochastic DCM for fMRI.

J. Daunizeau Brain and Spine Institute, Paris, France Wellcome Trust Centre for Neuroimaging, London, UK

Overview 1

Dynamic Causal Modelling (DCM): introduction

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Stochastic DCM for fMRI

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Separation of time scales in neural fields

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Predicting EEG frequency modulation from sDCM for fMRI

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Conclusion

Overview 1

Dynamic Causal Modelling (DCM): introduction

2

Stochastic DCM: motivation

3

Separation of time scales in neural fields

4

Predicting EEG frequency modulation from sDCM for fMRI

5

Conclusion

DCM for fMRI: introduction structural, functional and effective connectivity structural connectivity

functional connectivity

effective connectivity

O. Sporns 2007, Scholarpedia

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structural connectivity = presence of axonal connections

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functional connectivity = statistical dependencies between regional time series

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effective connectivity = causal (directed) influences between neuronal populations ! connections are recruited in a context-dependent fashion

DCM for fMRI: introduction functional integration and the neural code

activation studies: functional segregation

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effective connectivity studies: functional integration

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“where did the experimental manipulation have a specific effect?”

“how did the experimental manipulation propagate through the network?”

DCM for fMRI: introduction neural states dynamics a24

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gating effect

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driving input

f f 2 f 2 f x2 x  f ( x, u )  f  x0 ,0   x  u  ux  2  ... x u xu x 2 0

nonlinear state equation: m n  (i ) ( j)  x   A   ui B   x j D  x  Cu i 1 j 1   Stephan et al., 2009

DCM for fMRI: introduction the neuro-vascular coupling u t

m n   x   A   ui B (i )   x j D ( j )  x  Cu i 1 j 1  

experimentally controlled stimulus

neural states dynamics

vasodilatory signal

s  x   s   ( f  1)

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s flow induction (rCBF)

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 ( h)  { ,  , ,  , E0 }  ( n)  { A, B(i ) , C, D( j ) }

Balloon model changes in volume

 v  f  v1/  v

 ( q, v ) 

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hemodynamic states dynamics

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changes in dHb 1/   q  f E ( f,E0 ) E q0 v q / v

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S    q  V0  k1 1  q   k2 1    k3 1  v   S0  v  

k1  4.30 E0TE k2   r0 E0TE k3  1  

BOLD signal change observation

DCM for fMRI: introduction the variational Bayesian approach to model inversion



ln p  y m   ln p  , y m   S  q   DKL q   ; p  y, m  q



free energy : functional of q

mean-field: approximate marginal posterior distributions:

q   , q   1

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   , 

p 1 ,2 y, m  2

p 1 or 2 y, m  1

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DCM for fMRI: introduction example: audio-visual associative learning auditory cue

visual outcome

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cue-dependent surprise

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cue-independent surprise Den Ouden et al., 2010

Overview 1

Dynamic Causal Modelling (DCM): introduction

2

Stochastic DCM: motivation

3

Separation of time scales in neural fields

4

Predicting EEG frequency modulation from sDCM for fMRI

5

Conclusion

Stochastic DCM for fMRI the effect of state noise on network dynamics

2-regions DCM structure +

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state-space landscape of the normal rate of convergence   x 

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Daunizeau et al., 2012

Stochastic DCM for fMRI mediated influence: canonical model comparison u2

Model comparison: evidence against the full model

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Stochastic DCM for fMRI

SPMresults: .\20070914MP_sDCM\analysis

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Height threshold F = 11.230194 {p