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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
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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
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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
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MEG experimentMEG experiment
Faces (F) vs. Scrambled faces (S)Faces (F) vs. Scrambled faces (S)
M170
SF
150-190ms
fT
RL
Example data
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averageaverage
. . . single trialssingle trials
estimated event-related potential/field (ERP/ERF)
estimated event-related potential/field (ERP/ERF)
ERP/ERF
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Forward model
Sensor dataSensor data Current densityCurrent density Neuronalactivity
Neuronalactivity
Magnetic fieldMagnetic field Interactions between areas
Interactions between areas
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Inverse problems
Sensor dataSensor data Current densityCurrent density Neuronalactivity
Neuronalactivity
Source reconstruction
Source reconstruction
Effective connectivity
Effective connectivity
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Dynamics f
ERP/ERF
Input u
Spatial forward model g
Generative model
),( xgy ),,( uxfx
data y
parameters θ
states x
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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
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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
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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
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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
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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
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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
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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
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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
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Connectivity parameters
ie,
ieH ,
4,,1
LBFC ,,
c ,, 21
Within-areaparameters
Between-areaparameters
Inputparameters
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Spatial forward modelDepolarisation ofpyramidal cells
Spatial model
Sensor data
),,( uxfx
K
),( 00 xgKxy
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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
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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?
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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:
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One area - one dipole
A1 A1
OF OF
PC
STG
input
ForwardBackward
Lateral
Left A1
Right A1
Left OF
Right OF
PC
Right STG
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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
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Parameters
ie,
ieH ,
4,,1
LBFC ,,
c ,, 21
Within-areaparameters
Between-areaparameters
Inputparameters
locmom ,
Spatialparameters
G
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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
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Observation equationObservation equation:
4,,1
))(),),(((),( 0 VdiagXxgvecNyp X
)),(( 0XXxgvecy
low-frequency drift termXX
Normal likelihood
))(,0(~ N
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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
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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
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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
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forward
backward
forward & backward
Model comparison
Garrido et al., in preparationGarrido et al., in preparation
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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
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Fit to scalp data
observedpredicted
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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.