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Dynamic Causal Modelling for M/EEG. 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 - PowerPoint PPT Presentation
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Dynamic Causal Modelling for M/EEG
Stefan KiebelWellcome 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.
Different approach that tells us more about the neuronal
dynamics of localized brain sources?
Overview of the talk
1 M/EEG analysis
2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples
Dynamic Causal Modelling
A1 A2
),,( uxfx
)|(),|(
mypmyp
???Build a model for spatiotemporal data:
Assume that both ERPs are generated by temporal dynamics of a network of a few sources
Describe temporal dynamics by differential equations
Each source projects to the sensors, following physical laws
Solve for the model 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 datapreprocessing
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
connectionsspiny
stellate cells
inhibitory interneurons
pyramidal cells
4 3
214
014
41
2))()((ee
LF
e
e xxCuxSIAAHx
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 xxxSIAAHx
xx
236
746
63
225
1205
52
650
2)(
2))()()((
iii
i
ee
LB
e
e
xxxSHx
xx
xxxSxSAAHx
xxxxx
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)
Overview of the talk
1 M/EEG analysis
2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples
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
log
-evi
denc
e
Group level
Group model comparison
Garrido et al., (2007), NeuroImage
Overview of the talk
1 M/EEG analysis
2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples
Trends Cogn Sci. 1999 Apr;3(4):151-162
Evoked and induced responses
Modelling of induced responses
Time-series data in channel space
Inversion of electromagnetic
model Linput
Aim: Explain dynamic power spectrum of each source as function of power input from other
sources.
Dynamic power data in source space
Chen et al., Neuroimage, 2008
Face data (EEG): Network of four sources
LV RV
RFLF
inputmmz
mmymmx
88040
mmzmmymmx
83336
mmzmmy
mmx
108040
mmzmmy
mmx
183136
Observed power spectra
frequency
pst (
ms)
trial 1: source 1 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 1 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 2 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 2 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 3 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 3 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 4 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 4 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
observed
Frequency (Hz)
Tim
e (m
s)
LV RV LF RF
Single subject results: Coupling functions
LV RV
RFLF
input
RV
RF
Chen et al., Neuroimage, 2008
Observed and fitted power spectra
frequency
pst (
ms)
trial 1: source 1 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 1 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 2 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 2 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 3 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 3 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
frequency
pst (
ms)
trial 1: source 4 observed
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
channel
pst (
ms)
trial 1: source 4 predicted
20 40 60
-100
-50
0
50
100
150
200
250
300
350
400
observed
fitted
Frequency (Hz)
Tim
e (m
s)
LV RV LF RF
Summary
DCM combines state-equations for neural mass dynamics with spatial forward model.
Differences between responses acquired under different conditions are modelled as modulation of connectivity within and between 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 are available in SPM8.
Thanks to
Karl Friston
Marta Garrido
CC Chen
Jean Daunizeau
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