Classical ERP analysis
Analyse averages over channels and select interesting peri-
stimulus times
Analyse averages over channels and select interesting peri-
stimulus times
condition 1condition 1
Difference between
selected data
Difference between
selected dataAnalysis of variance (Anova),
over subjects
Analysis of variance (Anova),over subjects
Analysis at channel level.but not in brain space
Analysis at channel level.but not in brain space
time
chan
nels
chan
nels condition 2condition 2
Source reconstruction
0
1
RL
Reconstruct brain sources which generated the observed channel data
Reconstruct brain sources which generated the observed channel data
Analysis at source level, but typically no model about dynamics
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
Develop mechanistic model for the full data, not only for selected or averaged
part
Use network modelUse network model
Explain differences in responses by change of a few interpretable parameters
in generating network
Explain differences in responses by change of a few interpretable parameters
in generating network
condition 1condition 1
condition 2condition 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..
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
Increase in backward
connection A2->A1
modulation
input
Four steps through the model
Single sourceSingle source
Network of sourcesNetwork of sources
Spatial expression in sensorsSpatial expression in sensors
Single neuronal populationSingle neuronal population
Neural mass model
tt
Hth
uhx i
exp)(
1
01
0
1
exp1
2
)(
erx
e
xSuo
h
t0
x
uo
0
Input synapses
Dendrites and somas
Axons
iu xou
State-space model
Neuronal convolution
212
2
21
2
xx
uH
x
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
xxxS
Hx
xx
xxxS
Hx
xx
xxx
xxCuxIS
Hx
xx
xxxIS
Hx
xx
1 2Cu
Intrinsic connections
neuronal (source) model
State equations
,,uxfx
Extrinsic connectivity
Extrinsicforward
connections
spiny 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
xx
xxx
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
DataData
Model inversion: possible?
ModelModel
Can we estimate extrinsic connectivity parameters and its
modulation from data?
Can we estimate extrinsic connectivity parameters and its
modulation from data?
input
modulation
DataDataSpecify generative forward model
(with prior distributions on unknown parameters)
Specify generative forward model (with prior distributions on
unknown parameters)
Expectation-Maximization algorithmExpectation-Maximization algorithm
Iterative procedure:Iterative procedure: Compute model response using current set of parameters
Compute model response using current set of parameters
Compare model response with dataCompare model response with data
Improve parameters, if possibleImprove parameters, if possible
DCM: The basic approach
Output: Posterior distributions of parameters Output: Posterior distributions of parameters
Make inferences on parametersMake 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 data
preprocessing
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
2.4
1 (
10
0%
) 4.5
0 (1
00
%) 5
.40
(1
00
%) 1
.74
(96
%)
1.4
1 (
99
%)
standard
deviant
0.9
3 (5
5%
)
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
2.1
7 (
10
0%
) 17
.95
(10
0%
) 2.6
5 (
10
0%
) 1.5
8 (1
00
%)
0.6
0 (
10
0%
) 1.4
0 (1
00
%)
group
Neumann and Lohmann, 2003
)|()...|()|(),...,|(...
)|()|( )()|()|(),|(
)()|( )|(
111
12
1221
11
ypypypyyp
ypyppypypyyp
pypyp
NNN
DCM output
Parameters at group level?
lo
g-e
vid
en
ce
(log
-evi
denc
e no
rmal
ized
to
the
nu
ll m
ode
l) Bayesian Model Comparison
subjects
Forward (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