Dynamic Causal Modelling for ERP/ERFs

Valentina Doria

Georg Kaegi

Methods for Dummies

19/03/2008

Classical ERP analysis

Analyse averages over channels and select interesting peri-

stimulus times

condition 1

Difference between

selected dataAnalysis of variance (Anova),

over subjects

Analysis at channel level.but not in brain space

time

chan

nels

chan

nels condition 2

Source reconstruction

0

1

RL

Reconstruct brain sources which generated the observed channel data

Analysis at source level, but typically no model about dynamics

Selected data

New approach

Develop mechanistic model for the full data, not only for selected or averaged

part

Use network model

Explain differences in responses by change of a few interpretable parameters

in generating network

condition 1

condition 2

Dynamic Causal Modelling for ERPs/ERFs

differences in the evoked responses

changes in effective connectivity

functional connectivity vs. effective connectivity

causal architecture of interactions

The aim of DCM is to estimate and make inferences about

the coupling among brain areas, and how that coupling is

influences by changes in the experimental contex.

estimated by perturbing the system and

measuring the response

neural mass model

Layer 4

Supra-granular

Infra-granular

IntrinsicForward

BackwardLateral

Input u

1

32

3 area model

,,.

uxftx

),( xgy

state eq.

output eq.

Extrinsic

M/EEGneuronal states

parameters

input

David et al., 2006

Dynamic Causal Modelling for ERPs/ERFs (II)

Dynamics f

Input u

Spatial forward model g

Generative model

),( xgy ),,( uxfx

data y

parameters θ

states x ERP/ERF

Generative forward model:an example

A1

A2

A4

inputForward

BackwardLateral

A3

4 areas, somewhere in the

brain, happily working together..

Modulation of extrinsic connectivity

A1

A2

A4

ForwardBackward

Lateral

A3

Increase in backward

connection A2->A1

modulation

input

Four steps through the model

Single source

Network of sources

Spatial expression in sensors

Single neuronal population

Neural mass model

ttHth

uhx i

exp)(

1

01

0

1

exp12)(

erx

exSuo

h

t0

x

uo

0

Input synapses

Dendrites and somas

Axons

iu xou

State-space model

Neuronal convolution

212

2

21

2xxuHx

xx

i

Single source

Input

spiny stellate

cells

inhibitory interneurons

pyramidal cells

4 3

236

746

63

225

125

52

650

214

014

41

278

038

87

2)(

2))((

2))((

2))((

iii

i

eee

e

eee

e

eee

e

xxxSHx

xx

xxxSHx

xxxxx

xxCuxISHx

xx

xxxISHx

xx

1 2Cu

Intrinsic connections

neuronal (source) model

State equations

,,uxfx

Extrinsic connectivity

Extrinsicforward

connectionsspiny

stellate cells

inhibitory interneurons

pyramidal cells

4 3

236

746

63

225

1205

52

650

214

014

41

278

038

87

2)(

2))()()((

2))()((

2))()((

iii

i

ee

LB

e

e

ee

LF

e

e

ee

LB

e

e

xxxS

Hx

xx

xxxSxSAA

Hx

xxxxx

xxCuxSIAA

Hx

xx

xxxSIAA

Hx

xx

1 2)( 0xSAF

)( 0xSAL

)( 0xSABExtrinsic backward connections

Intrinsic connections

neuronal (source) model

Extrinsic lateral connections

State equations

,,uxfx

Output equation

0, Lxxg y

Spatial forward model

Depolarisation ofpyramidal cells

Spatial model

Sensor data

),,( uxfx

LL

),( 00 xgxLy L

Dynamics f

Input u

Spatial forward model g

Generative model

),( xgy ),,( uxfx

data y

parameters θ

states x ERP/ERF

A1

A2

A4

ForwardBackward

Lateral

A3

Data

Model inversion: possible?

Model

Can we estimate extrinsic connectivity parameters and its

modulation from data?

input

modulation

DataSpecify generative forward model

(with prior distributions on unknown parameters)

Expectation-Maximization algorithm

Iterative procedure: Compute model response using current set of parameters

Compare model response with data

Improve parameters, if possible

DCM: The basic approach

Output: Posterior distributions of parameters

Make inferences on parameters

DCM specification

• DCM is specified by a graph of nodes (cortical areas) and edges

(connections). Differences in 2 ERPs/ERFs are explained by coupling

modulations, i.e., changes in connection strength.

• DCM doesn’t test all possible models.

• Is crucial to build a model biologically plausible!

• Different hypotheses Different models

• Bayesian model comparison identifies the best model/hypothesis within

the universe of models/hypothesis considered.

pseudo-random auditory sequence

80% standard tones – 1000 Hz

20% deviant tones – 2000 Hz

time

standards deviants

Oddball paradigm

DCM specification – put into contextmode 1

mode 2

mode 3

svd

raw datapreprocessing

data reduction to

principal spatial

modes

(explaining most

of the variance)

• convert to matlab file

• epoch

• down sample

• filter

• artifact correction

• average

ERPs / ERFs

A1 A1

STG

input

STG

IFG

A1A1

STGSTG

IFG

a plausible model…

DCM specification – areas and connections

Choice of nodes/areas?- source localization, prior knowledge from literature

Choice of edges/connections?

- anatomical or functional evidence

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

DCM specification – testing different models

A1 A1

STG

ForwardBackward

Lateral

input

Forward and Backward - FB

STG

IFG

2.41

(100

%) 4.50 (100%

) 5.40

(100

%) 1.74 (96%

)

1.41

(99%

)

standarddeviant

0.93 (55%)

DCM output single subject

reconstructed responses at source

level

coupling changes

probability that a change occured

1,| Nyp

subN

iii

1

1

subN

ii

1

A1 A1

STG

ForwardBackward

Lateral

input

Forward and Backward - FB

STG

IFG

2.17

(100

%) 17.95 (100%

) 2.65

(100

%) 1.58 (100%

)

0.60

(100

%) 1.40 (100%

)

group

Neumann and Lohmann, 2003

)|()...|()|(),...,|(...

)|()|( )()|()|(),|(

)()|( )|(

111

12

1221

11

ypypypyyp

ypyppypypyyp

pypyp

NNN

DCM output

Parameters at group level?

log

-evi

denc

e

(log-

evid

ence

nor

mal

ized

to th

e nu

ll m

odel

) Bayesian Model Comparison

subjectsForward (F)

Backward (B)

Forward and Backward (FB)

fmyp ln

)(lnlnln jiij mypmypB

subN

sisiNsub mypmyyyp

121 )(ln|,...,,ln

Penny et al., 2004

DCM output

DCM.F

add up log-evidences for group analysis

Summary

• DCM models ERPs on the basis of a network of interacting cortical areas. Differences in waveforms are explained by coupling changes among these areas.

• The specification of the DCM (areas and connections in the network) is a critical point. It should be biologically plausible and motivated by specific hypotheses.

• DCM can be used to test different hypotheses or models of connectivity.

STGA1 IFG