Dynamic Causal Modellingfor evoked responses

Stefan Kiebel

Max Planck Institute forHuman Cognitive and Brain Sciences

Leipzig, Germany

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

pseudo-random auditory sequence

80% standard tones – 500 Hz

20% deviant tones – 550 Hz

time

standards deviants

Mismatch negativity (MMN)

time (ms)

μV

Paradigm

Raw data(e.g., 128 sensors)

Preprocessing (SPM8)

Evoked responses(here: single sensor)

Electroencephalography (EEG)

time

sens

ors

sens

ors

standard

deviant

time (ms)

amplitude (μV)

Analysis at sensor levelse

nsor

sse

nsor

s

standard

deviant

time

Conventional approach: Reduce evoked response to a few

variables.

Alternative approach?

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

Electroencephalography (EEG)

time (ms)

amplitude (μV)

Modelling aim: Explain all data with few

parameters

How?Assume data are caused

by few communicating brain sources

Connectivity models

A1 A1

STG

Input (stimulus)

STG

Conventional analysis: Which regions are involved in task?

A1 A1

STG

Input (stimulus)

STG

DCM analysis: How do regions communicate?

Macro- and meso-scale

internal granularlayer

internal pyramidallayer

external pyramidallayer

external granularlayer

AP generation zone synapses

macro-scale meso-scale micro-scale

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

The generative model

),,( uxfx

Source dynamics

states x parameters θ

Input u

Evoked response

data y

),( xgy

Spatial forward model g

David et al., NeuroImage, 2006Kiebel et al., Human Brain Mapping, 2009

Neural mass equations and connectivity

Extrinsicforward

connectionsspiny

stellate cells

inhibitory interneurons

pyramidal cells

4 3

214

014

41

2))()((ee

LF

e

e xxCuxSIAAHx

xx

1 2)( 0xSAF

)( 0xSAL

)( 0xSABExtrinsic backward connections

Intrinsic connections

neuronal (source) model

Extrinsic lateral connections

State equations

,,uxfx

0x

278

038

87

2))()((ee

LB

e

e xxxSIAAHx

xx

236

746

63

225

1205

52

650

2)(

2))()()((

iii

i

ee

LB

e

e

xxxSHx

xx

xxxSxSAAHx

xxxxx

David et al., NeuroImage, 2006Time (ms)

Am

plitu

de (a

.u.)

Model for auditory evoked response

Garrido et al., PNAS, 2007

Spatial model

0x

LL

Depolarisation ofpyramidal cells

Spatial model

Sensor data y

Kiebel et al., NeuroImage, 2006Daunizeau et al., NeuroImage, 2009

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

Bayesian model inversion

Evoked responsesSpecify generative forward model

(with prior distributions of parameters)

Expectation-Maximization algorithm

Iterative procedure: 1. Compute model response using current set of parameters

2. Compare model response with data3. Improve parameters, if possible

1. Posterior distributions of parameters

2. Model evidence )|( myp

),|( myp

Friston, PLoS Comp Biol, 2008

Model selection: Which model is the best?

)|( 1mypModel 1

data y

Model 2

...

Model n

)|( 2myp

)|( nmypbest?

Model selection:

Selectmodel with

highestmodel

evidence

),|( 1myp

),|( 2myp

),|( nmyp

)|( imyp

Fastenrath et al., NeuroImage, 2009Stephan et al., NeuroImage, 2009

best?

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling – Motivation

3 Dynamic Causal Modelling – Generative model

4 Bayesian model inversion

5 Examples

Auditory evoked response

Garrido et al., PNAS, 2007

Auditory evoked response

Garrido et al., PNAS, 2007

time (ms) time (ms)

A1 A1

STG STG

ForwardBackward

Lateral

STG

input

A1 A1

STG STG

ForwardBackward

Lateral

input

A1 A1

STG

ForwardBackward

Lateral

input

Forward - F Backward - BForward and

Backward - FB

STG

IFGIFGIFG

modulation of effective connectivity

Mismatch negativity

Garrido et al., (2007), NeuroImage

Bayesian Model Comparison

Forward (F)

Backward (B)

Forward and Backward (FB)

subjects

log

-evi

denc

e

Group level

Group model comparison

Garrido et al., (2007), NeuroImage

Summary

DCM enables testing hypotheses about how brain sources communicate.

DCM is based on a neurobiologically grounded, dynamic model of evoked responses.

Differences between conditions are modelled as modulation of connectivity.

Inference: Bayesian model selection

Thanks to: Marta GarridoJean DaunizeauKarl Friston

and the FIL methods group