1. Dynamic Causal Modelling for M/EEG
Stefan Kiebel
Wellcome Trust Centre for Neuroimaging
UCL

2. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

3. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

4. Electroencephalography (EEG)
amplitude (μV)
time
time (ms)
trial type 1
channels
trial type 2
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
channels

5. M/EEG analysis at sensor level
time
trial type 1
Approach: Reduce evoked response to a few variables, e.g.:
The average over a few channels
in peri-stimulus time.
channels
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
trial type 2
Different approach that tells us more about the neuronal dynamics of localized brain sources?
channels

6. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

7. Dynamic Causal Modelling
Build a model for spatiotemporal data:
???
Assume that both ERPs are
generated by temporal dynamics
of a network of a few sources A1 A2
Describe temporal dynamics
by differential equations
Dynamic
Causal
Modelling
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Each source projects to the sensors,
following physical laws
Solve for the model parameters
using Bayesian model inversion

8. Mismatch negativity (MMN)
mode 1
Oddball paradigm
standards
deviants
mode 2
pseudo-random auditory sequence
80% standard tones – 500 Hz
20% deviant tones – 550 Hz
time
preprocessing
mode 3
raw data
convert to matlab file
filter
epoch
down sample
artifact correction
average
data reduction to principal spatial modes
(explaining most of the variance)
128 EEG
scalp electrodes
ERPs / ERFs
time (ms)

9. Model for mismatch negativity
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Garrido et al., PNAS, 2008

10. Macro- and meso-scale macro-scale meso-scale micro-scale 10
external granular
layer
external pyramidal
layer
internal granular
layer
internal pyramidal
layer
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
AP generation zone
synapses 10

11. The generative model Source dynamics f Spatial forward model g
states x
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Evoked response
parameters θ
data y
Input u

12. Neural mass equations and connectivity
State equations
Extrinsic lateral connections
spiny stellate cells
inhibitory interneurons
pyramidal cells
Extrinsic
forward connections
Intrinsic connections
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Extrinsic backward connections
neuronal (source) model 12

13. Spatial model Depolarisation of pyramidal cells Sensor data
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system… 13

14. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

15. Bayesian model inversion
Specify generative forward model
(with prior distributions of parameters)
Measured data
Expectation-Maximization algorithm
Iterative procedure:
Compute model response using current set of parameters
Compare model response with data
Improve parameters, if possible
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Posterior distributions of parameters
Model evidence 15

16. Model comparison: Select
Which model is the best?
Model 1
Model comparison: Select
model with
highest
model
evidence
data y
Model 2
...
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
best?
Model n

17. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

18. Mismatch negativity (MMN)
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Garrido et al., PNAS, 2008

19. Mismatch negativity (MMN)
time (ms)
time (ms)
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Garrido et al., PNAS, 2008

20. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

21. Another (MMN) example Forward and Forward - F Backward - B Backward -
IFG
IFG
IFG
Forward and
Forward - F
Backward - B
Backward - FB
STG
STG
STG
STG
STG
STG
STG A1 A1 A1 A1 A1 A1
input
input
input
Forward
Forward
Forward
Backward
Backward
Backward
Lateral
Lateral
Lateral
modulation of effective connectivity

22. Group model comparison
Bayesian Model Comparison
Group level
log-evidence
Forward (F)
Backward (B)
Forward and Backward (FB)
subjects
Garrido et al., (2007), NeuroImage

23. Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling
3 Bayesian model inversion
4 Examples

24. Evoked and induced responses
Several events can induce the activity changes of neuronal populations. These changes could be either phase-locked to the stimulus onset (i.e. evoked activities) or non phase-locked (induced responses). To extract evoked potentials, people usually apply average technique to eliminate the non-stationary components, both the noise and the induced responses. In order to obtain the induced responses, the data were projected into the time frequency domain trail by trail and then average across trails.
Trends Cogn Sci Apr;3(4):

25. Time-series data in channel space Dynamic power data in source space
Modelling of induced responses
Inversion of electromagnetic model L
input
Time-series data in channel space
Dynamic power data in source space
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Aim: Explain dynamic power spectrum of each source as function of power input from other sources.
Chen et al., Neuroimage, 2008

26. Face data (EEG): Network of four sourcesLF RF LV RV
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
input

27. Observed power spectraLV RV LF RF
Time (ms)
observed
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
Frequency (Hz)

28. Single subject results: Coupling functionsLF RF RV LV RV RF
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
input
Chen et al., Neuroimage, 2008

29. Observed and fitted power spectraLV RV LF RF
Time (ms)
observed
Frequency (Hz)
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system…
fitted

30. 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 models
and 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.
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system… 30

31. Thanks to Karl Friston Marta Garrido CC Chen Jean Daunizeau 31
1- Modelling: capture data tendencies/regularities
But: model quality <-> predictive ability
=> Parameters estimation
2- 2 forms of uncertainty:
- stochastic
- epistemological (=> reducible)
-> Definition of “noise”
3- - Model sufficiently complex -> perfect data fit but suboptimal predictions
- Model too simple -> poor data fit …
4- Link modelling to some measure of the uncertainty which is propagated through the model:
model relevance is related to the quality of the information we can extract from the data about the modelled system… 31