Dynamic Causal Modelling for M/EEG

Dynamic Causal Modelling for M/EEG

Stefan KiebelWellcome Trust Centre for Neuroimaging

UCL

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling

3 Bayesian model inversion

4 Examples

Electroencephalography (EEG)

time

chan

nels

chan

nels

trial type 1

trial type 2

time (ms)

amplitude (μV)

M/EEG analysis at sensor levelch

anne

lsch

anne

ls

trial type 1

trial type 2

time

Approach: Reduce evoked response to a few variables, e.g.:The average over a few channels

in peri-stimulus time.

Different approach that tells us more about the neuronal

dynamics of localized brain sources?


1 M/EEG analysis



4 Examples

Dynamic Causal Modelling

A1 A2

),,( uxfx

)|(),|(

mypmyp

???Build a model for spatiotemporal data:

Assume that both ERPs are generated by temporal dynamics of a network of a few sources

Describe temporal dynamics by differential equations

Each source projects to the sensors, following physical laws

Solve for the model parameters using Bayesian model inversion

DynamicCausal

Modelling

pseudo-random auditory sequence

80% standard tones – 500 Hz

20% deviant tones – 550 Hz

time

standards deviants

Oddball paradigm

raw datapreprocessing

data reduction to

principal spatial

modes

(explaining most

of the variance)

• convert to matlab file

• filter

• epoch

• down sample

• artifact correction

• average

ERPs / ERFs

128 EEG scalp electrodes

mode 2

mode 1

mode 3

time (ms)

Mismatch negativity (MMN)

Model for mismatch negativity

Garrido et al., PNAS, 2008

Macro- and meso-scale

internal granularlayer

internal pyramidallayer

external pyramidallayer

external granularlayer

AP generation zone synapses

macro-scale meso-scale micro-scale

The generative model

),,( uxfx

Source dynamics f

states x parameters θ

Input u

Evoked response

data y

),( xgy

Spatial forward model g

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

Spatial model

0x

LL

Depolarisation ofpyramidal cells

Spatial model

Sensor data y


1 M/EEG analysis



4 Examples

Bayesian model inversion

Measured dataSpecify 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


1 M/EEG analysis



4 Examples



time (ms) time (ms)


1 M/EEG analysis



4 Examples

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

Another (MMN) example

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


1 M/EEG analysis



4 Examples

Trends Cogn Sci. 1999 Apr;3(4):151-162

Evoked and induced responses

Modelling of induced responses

Time-series data in channel space

Inversion of electromagnetic

model Linput

Aim: Explain dynamic power spectrum of each source as function of power input from other

sources.

Dynamic power data in source space

Chen et al., Neuroimage, 2008

Face data (EEG): Network of four sources

LV RV

RFLF

inputmmz

mmymmx

88040

mmzmmymmx

83336

mmzmmy

mmx

108040

mmzmmy

mmx

183136

Observed power spectra

frequency

pst (

ms)

trial 1: source 1 observed

20 40 60

-100

-50

0

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300

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400

channel

pst (

ms)

trial 1: source 1 predicted

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pst (

ms)


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ms)


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observed

Frequency (Hz)

Tim

e (m

s)

LV RV LF RF

Single subject results: Coupling functions

LV RV

RFLF

input

RV

RF

Chen et al., Neuroimage, 2008

Observed and fitted power spectra

frequency

pst (

ms)


20 40 60

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channel

pst (

ms)


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pst (

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pst (

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pst (

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pst (

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pst (

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ms)


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observed

fitted

Frequency (Hz)

Tim

e (m

s)

LV RV LF RF

Summary

DCM combines state-equations for neural mass dynamics with spatial forward model.

Differences between responses acquired under different conditions are modelled as modulation of connectivity within and between sources.

Bayesian model comparison allows one to compare many different modelsand identify the best one.

Make inference about posterior distribution of parameters (e.g., effective connectivity, location of dipoles, etc.).

Many extensions to DCM for M/EEG are available in SPM8.

Thanks to

Karl Friston

Marta Garrido

CC Chen

Jean Daunizeau

Dynamic Causal Modelling for M/EEG

Documents

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