Dynamic Causal Modelling of Dynamic Causal Modelling of Evoked Responses in EEG/MEGEvoked Responses in EEG/MEGDynamic Causal Modelling of Dynamic Causal Modelling of

Evoked Responses in EEG/MEGEvoked Responses in EEG/MEG

Wellcome Dept. of Imaging Neuroscience

University College London

Stefan KiebeStefan Kiebell

Principles of organisation

Varela et al. 2001, Nature Rev Neuroscience

Varela et al. 2001, Nature Rev Neuroscience

Functional segregationFunctional segregation Functional integrationFunctional integration

Power of signal,source localisation

Power of signal,source localisation

Interactions between distant brain areas

Interactions between distant brain areas

EEG and MEG

MEGMEG

- ~1929 (Hans Berger)- Neurophysiologists- From 10-20 clinical system to 64, 127, 256 sensors- Potential V: ~10 µV

- ~1929 (Hans Berger)- Neurophysiologists- From 10-20 clinical system to 64, 127, 256 sensors- Potential V: ~10 µV

EEGEEG

- ~1968 (David Cohen)- Physicists- From ~ 30 to more than 150 sensors- Magnetic field B: ~10-13 T

- ~1968 (David Cohen)- Physicists- From ~ 30 to more than 150 sensors- Magnetic field B: ~10-13 T

MEG experimentMEG experiment

Faces (F) vs. Scrambled faces (S)Faces (F) vs. Scrambled faces (S)

M170

SF

150-190ms

fT

RL

Example data

averageaverage

. . . single trialssingle trials

estimated event-related potential/field (ERP/ERF)

estimated event-related potential/field (ERP/ERF)

ERP/ERF

Forward model

Sensor dataSensor data Current densityCurrent density Neuronalactivity

Neuronalactivity

Magnetic fieldMagnetic field Interactions between areas

Interactions between areas

Inverse problems

Sensor dataSensor data Current densityCurrent density Neuronalactivity

Neuronalactivity

Source reconstruction

Source reconstruction

Effective connectivity

Effective connectivity

Dynamics f

ERP/ERF

Input u

Spatial forward model g

Generative model

),( xgy ),,( uxfx

data y

parameters θ

states x

Neural mass modelNeuronal assembly

Time [ms] v [mV]

Mean firing rate m(t)

Mean firing rate m(t)

Mean membrane potential

v(t)

Mean membrane potential

v(t)

Mean firing rate m(t)

Mean firing rate m(t)

mh

00

0)exp()(

t

tttH

tp

)()()( thtmtv

Jansen‘s model for a cortical areaExcitatory

InterneuronsHe, e

PyramidalCellsHe, e

InhibitoryInterneurons

Hi, i

Extrinsic inputs

Excitatory connection

Inhibitory connection

e, i : synaptic time constant (excitatory and inhibitory) He, Hi: synaptic efficacy (excitatory and inhibitory) 1,…,: connectivity constants

21

34

MEG/EEGsignal

MEG/EEGsignal

Parameters:Parameters:

Jansen & Rit, Biol. Cybern., 1995Jansen & Rit, Biol. Cybern., 1995

11

121211

12))((

xv

vxvSpH

xeee

e

22

222322

12)(

xv

vxvSH

xiii

i

Output : y(t)=v1-v2

33

3232133

12)(

xv

vxvvSH

xeee

e

1v

2v 3v

Input : p(t) cortical noise

Jansen‘s model for a cortical area

Jansen & Rit, Biol. Cybern., 1995Jansen & Rit, Biol. Cybern., 1995

MEG/EEG signal = dendritic signal of pyramidal cells

Connectivity between areas

1 2

1 2 1 2 1 2

Cor

tex

Bottom-up Top-Down Lateral

Supra granularSupra granular

Layer IVLayer IV

Infra granularInfra granular

Felleman & Van Essen, Cereb. Cortex, 1991Felleman & Van Essen, Cereb. Cortex, 1991

Inh.Inter.

Inh.Inter.

Exc.Inter.

abu

Exc.Inter.

Pyr.Cells

Inh.Inter.

Pyr.Cells

Inh.Inter.

Exc.Inter.

atd

Exc.Inter.

Pyr.Cells

Inh.Inter.

Pyr.Cells

Exc.Inter.

ala

Exc.Inter.

Pyr.Cells

Inh.Inter.

Pyr.Cells

Pyramidal cellsInhibitory interneurons

Excitatory interneurons

Pyramidal cellsInhibitory interneurons

Area 1 Area 2 Area 1 Area 2 Area 1 Area 2

Connectivity between areas

Cor

tex

Supra granularSupra granular

Layer IVLayer IV

Infra granularInfra granular

Bottom-up Top-Down Lateral

David et al., NeuroImage, 2005David et al., NeuroImage, 2005

Connectivity model (no delay)

236

746

63

225

1205

52

650

2)(

2))()()((

iii

i

ee

LB

e

e

xxxS

Hx

xx

xxxSxSCC

Hx

xx

xxx

214

014

41

2))()((

ee

ULF

e

e xxuCxSICC

Hx

xx

Pyramidalcells

Excit. IN

Inhib. IN278

038

87

2))()((

ee

LB

e

e xxxSICC

Hx

xx

jth state for all areas

jx

LBFC ,,

Connectivitymatrices

Input

Input is modelled by an impulse at peri-stimulus time t=0 convolved

with some input kernel.

))1(2cos(),,()( 21 titbtu ci

Gamma functionLow-frequent

change in input

Propagation delaysThere is short delay within-area

between subareas (~2 ms).

There is delay between areas. We found that these delays are important

parameters (~10-30 ms).

1 2

ExcitatoryInterneurons

He, e

PyramidalCellsHe, e

InhibitoryInterneurons

Hi, i

21

34

Delayed differential equations

Connectivity parameters

ie,

ieH ,

4,,1

LBFC ,,

c ,, 21

Within-areaparameters

Between-areaparameters

Inputparameters

Spatial forward modelDepolarisation ofpyramidal cells

Spatial model

Sensor data

),,( uxfx

K

),( 00 xgKxy

Forward modelling

3 main approaches lead to forward model 3 main approaches lead to forward model

2D realistic model2D realistic modelSpherical modelSpherical model 3D realistic model3D realistic model

-Analytic solution (Sarvas 1987)-Isotropy and homogeneity

-Analytic solution (Sarvas 1987)-Isotropy and homogeneity

-Numerical solution (Mosher 1999)-2D meshes-Isotropy and homogeneity

-Numerical solution (Mosher 1999)-2D meshes-Isotropy and homogeneity

-Numerical solution (Marin 1998)-3D meshes

-Numerical solution (Marin 1998)-3D meshes

Linear equation

= x +

datadata Forward model K

Forward model K

Sources J(over time)

Sources J(over time)

Error

Error= x +

Spatiotemporal characterization of the sensor data in terms of brain sourcesSpatiotemporal characterization of the sensor data in terms of brain sources

Question: How to solve for sources J?Question: How to solve for sources J?

Spherical model

-Analytic solution (fast)-Easy to use-Good model for MEG (said to be less so for EEG)-Easy to parameterise-Seems to explains data well for early to medium latencies

-Analytic solution (fast)-Easy to use-Good model for MEG (said to be less so for EEG)-Easy to parameterise-Seems to explains data well for early to medium latencies

locmom ,Spatialparameters

Idea: Each area is spatially modelled by one equivalent current dipole.

Advantages of spherical model:

One area - one dipole

A1 A1

OF OF

PC

STG

input

ForwardBackward

Lateral

Left A1

Right A1

Left OF

Right OF

PC

Right STG

Modulation by context

MMN

ERP standardsERP deviantsdeviants - standards

Mismatch negativity (MMN)

Different responses for two auditory stimuli

G

Model: Explain 2nd ERP/ERF by modulation of connectivity

between areas

Gain modulation matrix

Parameters

ie,

ieH ,

4,,1

LBFC ,,

c ,, 21

Within-areaparameters

Between-areaparameters

Inputparameters

locmom ,

Spatialparameters

G

Network of areas MEG/EEG scalp data

Input (Stimuli)

Posterior distributions of parameters

Modulation of connectivityModulation of connectivity differences between ERP/ERFsdifferences between ERP/ERFs

Dynamic causal modelling

),( xgy

),,( uxfx

Observation equationObservation equation:

4,,1

))(),),(((),( 0 VdiagXxgvecNyp X

)),(( 0XXxgvecy

low-frequency drift termXX

Normal likelihood

))(,0(~ N

Estimation of model parameters

)(p

)()|()|( pypyp

)|( yp

Parameters• Neurodynamics

• Connections (stability)

Known parameters: Source locations Network connectionsGain matrix K

Source locations Network connectionsGain matrix K

Unknown parameters:

Synaptic time constants and efficaciesCoupling parametersPropagation delays between areasInput parametersSpatial parameters

Synaptic time constants and efficaciesCoupling parametersPropagation delays between areasInput parametersSpatial parameters

Bayesian estimationLikelihood:•Neural mass model•Spatial forward model

Likelihood:•Neural mass model•Spatial forward model

Priors:•Neurodynamic constants•Connections•Spatial parameters

Priors:•Neurodynamic constants•Connections•Spatial parameters

Expectation/Maximization

Model comparison

models

p(y|mi)

1 2 3

)|(

)|(),|(),|(

myp

mpmypmyp

dmpmypmyp )|(),|()|(

)(

)()|(log

mcomplexity

maccuracymyp

Which model is the best among a set of competing models?

Penny et al. 2004, NeuroImagePenny et al. 2004, NeuroImage

A1 A1

STG STG

IFGForwardBackward

Lateral

input

MMN

ERP standardsERP deviantsdeviants - standards

Inferior frontal gyrus

Superiortemporalgyrus

Primaryauditorycortex

Mismatch negativity

Garrido et al., in preparationGarrido et al., in preparation

forward

backward

forward & backward

Model comparison

Garrido et al., in preparationGarrido et al., in preparation

Somatosensory evoked potential

SI

SII SII

input

ForwardBackward

Lateral

27

.68

(1

00

%)

2.6

7 (

10

0%

)

3.57 (99%)

0.95 (53%)

mode 3

mode 1

mode 2

Contra SI

Contra SII

Ipsi SII

Fit to scalp data

observedpredicted

Conclusions

Dynamic Causal Modelling (DCM) for EEG/MEG is physiologically grounded model.

Dynamic Causal Modelling (DCM) for EEG/MEG is physiologically grounded model.

Context-induced differences in ERPs are modelled as modulation of connectivity between areas.

Context-induced differences in ERPs are modelled as modulation of connectivity between areas.

Spherical head model is useful spatial model.Spherical head model is useful spatial model.

DCM can alternatively be seen as source reconstruction device with temporal constraints.

DCM can alternatively be seen as source reconstruction device with temporal constraints.