Dynamic Causal Modelling for EEG/MEG:principles

Adapted from the DCM course slides ofJ. Daunizeau

Overview

1 DCM: introduction

2 Neural states dynamics

3 Bayesian inference

4 Conclusion

Overview

1 DCM: introduction

2 Neural states dynamics

3 Bayesian inference

4 Conclusion

Introductionstructural, functional and effective connectivity

• structural connectivity= presence of axonal connections

• functional connectivity = statistical dependencies between regional time series

• effective connectivity = causal (directed) influences between neuronal populations

! connections are recruited in a context-dependent fashion

O. Sporns 2007, Scholarpedia

structural connectivity functional connectivity effective connectivity

u1 u1 X u2

A B

u2u1

A B

u2u1

localizing brain activity:functional segregation

effective connectivity analysis:functional integration

Introductionfrom functional segregation to functional integration

« Where, in the brain, didmy experimental manipulation

have an effect? »

« How did my experimental manipulationpropagate through the network? »

?

( , , )x f x u neural states dynamics

Electromagneticobservation model:spatial convolution

• simple neuronal model• realistic observation model

• realistic neuronal model• simple observation model

fMRIfMRI EEG/MEGEEG/MEG

inputs

IntroductionDCM: evolution and observation mappings

Hemodynamicobservation model:temporal convolution

IntroductionDCM: a parametric statistical approach

,

, ,

y g x

x f x u

• DCM: model structure

1

2

4

3

24

u

, ,p y m likelihood

• DCM: Bayesian inference

ˆ ,E y m

, ,p y m p y m p m p m d d

model evidence:

parameter estimate:

priors on parameters

Overview

1 DCM: introduction

2 Neural states dynamics

3 Bayesian inference

4 Conclusion

Neural ensembles dynamicsDCM for M/EEG: systems of neural populations

Golgi Nissl

internal granularlayer

internal pyramidallayer

external pyramidallayer

external granularlayer

mean-field firing rate synaptic dynamics

macro-scale meso-scale micro-scale

EP

EI

II

Neural ensembles dynamicsDCM for M/EEG: synaptic dynamics

1iK

time (ms)m

embr

ane

depo

lariz

atio

n (m

V)

1 22 2

2 / / 2 / 1( ) 2i e i e i eS

post-synaptic potential

1eK

IPSP

EPSP

Neural ensembles dynamicsDCM for M/EEG: extrinsic connections between brain regions

extrinsicforward

connections

spiny stellate cells

inhibitory interneurons

pyramidal cells

0( )F S

0( )LS

0( )BS extrinsic backward connections

extrinsiclateral connections

1 2

3 4

7 82 2

8 3 0 8 7

1 42 2

4 1 0 4 1

0 5 6

2 5

2 25 0 2 1 5 2

3 6

2 26 4 7 6 3

(( ) ( )) 2

(( ) ( ) ) 2

(( ) ( ) ( )) 2

( ) 2

e B L e e

e F L u e e

e B L e e

i i i

I S

I S u

S Sx

S

Overview

1 DCM: introduction

2 Neural states dynamics

3 Bayesian inference

4 Conclusion

Bayesian inferenceforward and inverse problems

,p y m

forward problem

likelihood

,p y m

inverse problem

posterior distribution

Bayesian paradigmderiving the likelihood function

- Model of data with unknown parameters:

y f e.g., GLM: f X

- But data is noisy: y f

- Assume noise/residuals is ‘small’:

22

1exp2

p

4 0.05P

→ Distribution of data, given fixed parameters:

2

2

1exp2

p y y f

f

Likelihood:

Prior:

Bayes rule:

Bayesian paradigmlikelihood, priors and the model evidence

generative model m

Overview

1 DCM: introduction

2 Neural states dynamics

3 Bayesian inference

4 Conclusion

• Suitable experimental design:– any design that is suitable for a GLM – preferably multi-factorial (e.g. 2 x 2)

• e.g. one factor that varies the driving (sensory) input• and one factor that varies the modulatory input

• Hypothesis and model:– define specific a priori hypothesis– which models are relevant to test this hypothesis?– check existence of effect on data features of interest– there exists formal methods for optimizing the experimental design

for the ensuing bayesian model comparison[Daunizeau et al., PLoS Comp. Biol., 2011]

Conclusionplanning a compatible DCM study