Dynamic causal Modelling for evoked responses

Stefan Kiebel

Wellcome Trust Centre for Neuroimaging

UCL

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling

3 Bayesian model inversion

4 Examples

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.

What else can we try to reduce the evoked response to a few

variables?

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling

3 Bayesian model inversion

4 Examples

Dynamic Causal Modelling

A1 A2

),,( uxfx

)|(

),|(

myp

myp

???Build a model for spatiotemporal data:

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

Describe temporal dynamics by differential equations

Each source projects to the sensors, following physical laws

Solve for the model‘s 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 data

preprocessing

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

connections

spiny stellate

cells

inhibitory interneurons

pyramidal cells

4 3

214

014

41

2))()((

ee

LF

e

e xxCuxSIAA

Hx

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 xxxSIAA

Hx

xx

236

746

63

225

1205

52

650

2)(

2))()()((

iii

i

ee

LB

e

e

xxxS

Hx

xx

xxxSxSAA

Hx

xx

xxx

Spatial model

0x

LL

Depolarisation ofpyramidal cells

Spatial model

Sensor data y

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling

3 Bayesian model inversion

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

Model comparison: Which model is the best?

)|( 1mypModel 1

data y

Model 2

...

Model n

)|( 2myp

)|( nmypbest?

Model comparison:

Selectmodel with

highestmodel

evidence

),|( 1myp

),|( 2myp

),|( nmyp

)|( imyp

Overview of the talk

1 M/EEG analysis

2 Dynamic Causal Modelling

3 Bayesian model inversion

4 Examples

Mismatch negativity (MMN)

Garrido et al., PNAS, 2008

Mismatch negativity (MMN)

Garrido et al., PNAS, 2008

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

Another (MMN) example

Bayesian Model Comparison

Forward (F)

Backward (B)

Forward and Backward (FB)

subjects

lo

g-ev

iden

ce

Group level

Group model comparison

Garrido et al., (2007), NeuroImage

Ongoing workCC Chen et al.: ‚Dynamic Causal Modelling of induced responses‘,

Neuroimage (in press).

CC Chen et al.: ‚Forward and backward connections in the brain: A DCM study of functional asymmetries in face processing‘, in preparation.

R Moran et al.: ‚A neural mass model of spectral responses in electrophysiology‘, Neuroimage (2007)

R Moran et al.: ‚Bayesian estimation of synaptic physiology from the spectral responses of neural masses‘, Neuroimage (in press)

Fastenrath et al., ‚Dynamic Causal Modelling for M/EEG: Spatial and temporal symmetry constraints‘, submitted

Daunizeau et al.: Dynamic Causal Modelling of distributed electromagnetic responses, in preparation

Marreiros et al.: ‚Population dynamics under the Laplace assumption‘, in preparation

Summary

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

Differences between evoked responses are modelled as modulation of connectivity between/within 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 will be available in SPM8.

Thanks to

Karl Friston

Marta Garrido

Jean Daunizeau