1. DCM for ERP/ERF: theory and practice
Giovanna Moretto
and
Friederike Schüür

2. Dynamical Causal Modelling
A sophisticated technique to investigate effective connectivity of the brain for fMRI and EEG / MEG data:
EEG / MEG data:
The goal of DCM is to explain evoked responses as the output of an interacting network consisting of a few areas that receive an input stimulus. ?

3. Terminology: effective connectivity?
Functional specialisation:
Identification of a particular brain region with a specific function.
Functional integration:
Identifying interactions among specialised neural populations & how these depend on the context.
Functional connectivity:
Is defined as correlations between remote neuro-physiological events.
Effective connectivity:
Refers explicitly to the influence that one neuronal system exerts over another, either at a synaptic (i.e. synaptic efficacy) or population level.

4. Different analyses for different purposes …
Functional Connectivity
Effective Connectivity
Structural Equation Modelling
Psycho-physiological interactions
Kalman Filtering
Volterra Series
Dynamical Causal Modelling (DCM)
Seed-voxel correlation analysis
Eigenimage analysis
Independent component analysis
Psycho-physiological interactions

5. Introduction Example: Mismatch Negativity (EEG) Dynamical Causal Model
Outline
Introduction Example: Mismatch Negativity (EEG)
Dynamical Causal Model
Single Source
Network of Sources
Spatial Expression in Sensors
Model Inversion
Example in detail: Mismatch Negativity (EEG)
DCM in SPM
Only about Evoked Responses for an EEG data set (also possible for steady state responses and induced responses).
Principle for e.g. induced responses is highly similar as well as DCM for MEG data sets.
Only for Evoked responses and only for EEG … principle is the same for all others and once this is understood easy to integrate the differences.

6. Introduction Example: Mismatch Negativity
Oddball paradigm
standards
deviants
pseudo-random auditory sequence
80% standard tones – 500 Hz
20% deviant tones – 550 Hz
time
SPM
data
convert to matlab file
filter
epoch
down sample
artifact correction
average
ERPs of 12 subjects,
2 conditions
(standard + deviant)
raw data
preprocessing
128 EEG
scalp electrodes

7. Grand Mean (average over subjects)
DCM:
1) Models the difference between two evoked responses …
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standards
deviants
MMN
2) … as a modulation of some of the inter-aereal connections.

8. How can the MMN be explained?
Build a model to test hypotheses:
Assume that both ERPs are generated by temporal dynamics of a few sources A1 A2
Describe temporal dynamics by differential equations
Dynamic
Causal
Modelling
Each source projects to the sensors, following physical laws
Solve for the model‘s parameters using Bayesian model inversion

9. Why? What are we interested in … ?
STG
input
IFG A1
STG
input
IFG
1.41 (99%)
0.93 (55%)
First, to find the best model …
Second, to determine the coupling parameters …
2.41 (100%)
4.50 (100%)
5.40 (100%)
1.74 (96%)

10. The Theory in more detail … Overview
Single Source
Network of Sources
Spatial Expression in Sensors
Model Inversion

11. Single Source State equations neuronal (source) model
spiny stellate cells
inhibitory interneurons
pyramidal cells
Input
Intrinsic connections
DCM adopts a neural mass model to explain source activity in terms of the ensemble dynamics of interacting inhibitory and excitatory subpopulations of neurons. This model emulates the activity of a source using three neural subpopulations each assigned to one of three cortical layers.
Excitatory subpopulation  granular layer
Inhibitory sub-population  supra granular layer
Pyramidal cells  infra-granular layer
see Jansen & Rit (1995) and David & Friston (2003)
neuronal (source) model

12. Spatial Expression in Sensors
In more detail … Overview
Single Source
Network of Sources
Spatial Expression in Sensors
Model Inversion

13. Extrinsic Connectivity
State equations
Extrinsic lateral connections
spiny stellate cells
inhibitory interneurons
pyramidal cells
Extrinsic
forward connections
Intrinsic connections
X  neural states of cortical sources
U  exogenous inputs
H  systems response
Extrinsic backward connections
neuronal (source) model

14. Spatial Expression in Sensors
Overview
Single Source
Network of Sources
Spatial Expression in Sensors
Model Inversion

15. Spatial Forward Model Depolarisation of pyramidal cells Spatial model
Sensor data
Spatial model
L  lead field matrix; accounts for passive conduction of electromagnetic field
Relation scalp data h and source activity: linear & instantaneous (assumption)
Reduce dimensionality of sensor data (modes later on) while retaining max. amount of information  projection to subspace defined by principle eigenvestors (modes)
“In summary, our DCM comprises a state-equation that is based on neurobiological heuristics and an observer equation based on an electromagnetic forward model. By integrating the state-equation and passing the ensuing states through the observer equation, we generate a predicted measurement.”
Default: Each area that is part of the model is modeled by one equivalent current dipole (ECD).

16. Spatial Expression in Sensors
Overview
Single Source
Network of Sources
Spatial Expression in Sensors
Model Inversion

17. Model Inversion Data Predicted data
input 50
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time (ms)
Observed (adjusted) 1
Predicted data
We need to estimate the extrinsic connectivity parameters and their modulation from data. 50
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150
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time (ms)
Predicted
First 60ms look weird but that’s because we decided not to model first (early) responses.

18. DCM: Model Inversion Data Predicted data (model)
Expectation-Maximization algorithm
Iterative procedure:
Compute model response using current set of parameters
Compare model response with data
Improve parameters, if possible
Output: Posterior distributions of parameters
Make inferences on parameters

19. The Practical Part … The buttons …
But actually, the practical part of DCM still involves a lot of theory, as we will see …

20. Back to the example: MMN
Oddball paradigm
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-50 50
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150
200
250
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400 -4 -3 -2 -1 1 2 3 4 ms m V
standards
deviants
MMN
standards
deviants
time
Before the DCM:
A. Collect, pre-process, and average EEG data.
B. Make required assumptions based on already existing literature …
e.g. for the location of the sources.
Switch presenter …

21. Assumptions …
MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002).
“We argue that the right IFG mediates auditory deviance detection in case of low discriminability between a sensory memory trace and auditory input. This prefrontal mechanism might be part of top-down modulation of the deviance detection system in the STG.”

22. Assumptions …
MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002).
Assumed Sources:
Left A1
Right A1
Left STG
Right STG
Right IFG
STG A1
IFG
DCM requited prior knowledge, e.g. about source numbers and locations
Find the coordinates of the sources … (in mm in MNI coordinates).

23. DCM specification … IFG STG STG A1 A1 input Opitz et al., 2002
rIFG
lA1
rA1
lSTG
rSTG A1 A1
Make a schematic model and determine which connections should be included …
input
Doeller et al., 2003
modulation of effective connectivity

24. Alternative Models for Comparison …
IFG
IFG
IFG
Forward and
Forward - F
Backward - B
Backward - FB
STG
STG
STG
STG
STG
STG A1 A1 A1 A1 A1 A1
left and right primary auditory cortices (A1),
left and right superior temporal
gyrus (STG) and right inferior frontal gyrus (IFG),
(A1) were chosen as cortical input stations
for processing the auditory information.
input
input
input
Forward
Forward
Forward
Backward
Backward
Backward
Lateral
Lateral
Lateral
modulation of effective connectivity

25. Finally … SPM! DCM for Evoked Responses
Also for steady-state responses (SSR) and induces responses (IND) …

26. Choose nr. of components
Choose time window
Trial indices
Choose nr. of components
Model between trial effects
Data must be spm format
To reduce amount of data: projection to sub-space, modes is factors you extract that you keep (the more the more information but the more data, later vectors carry only little additional information)

27. How to spatially model ER
Sources’ coordinates
Onset time for modelling
Sources’ names
Animated
Tight priors on location but not orientation (can compensate up to a certain extent for inaccuracies)
Early responses are not modelled because the propagation of the stimulus impulse through the input nodes causes a delay
For modelling first response only A matrix is used, for second the modulation (B-matrix)

28. e.g. from left A1 to left STG
input
IFG
modulation of
effective connectivity
e.g. from left A1 to left STG
Specify extrinsic connections
Input to
Intrinsic connections: modelled by H which reflects the max. post synaptic potential
Modulatory effect
Intrinsic connections
from
Invert DCM

29. Wait …

30. Coupling B
Posterior means for gain modulations
Probability ≠ prior means

31. Why? What are we interested in … ?
STG
input
IFG A1
STG
input
IFG
1.41 (99%)
0.93 (55%)
First, to find the best model …
Second, to determine the coupling parameters …
2.41 (100%)
4.50 (100%)
5.40 (100%)
1.74 (96%)

32. Log evidence = accuracy - complexity
Forward (F)
Backward (B)
Forward and Backward (FB)

33. Why? What are we interested in … ?
STG
input
IFG A1
STG
input
IFG
1.41 (99%)
0.93 (55%)
First, to find the best model …
Second, to determine the coupling parameters …
2.41 (100%)
4.50 (100%)
5.40 (100%)
1.74 (96%)

34. ERP (sources) … right A1 Activity of interneuron populations50
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200
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0.2
0.4
0.6
0.8
right A1 A1
STG
input
IFG
modulation of
effective connectivity
Activity of interneuron populations
Activity of pyramidal cells
trial 1 (pop. 1)
trial 2 (pop. 1)
trial 1 (pop. 2)
trial 2 (pop. 2)
trial 1 (pop. 3)
trial 2 (pop. 3)

35. Response … Decided not to model early responses condition 150
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150
200
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time (ms)
Observed (adjusted) 1
Predicted
Observed (adjusted) 2
condition 1
condition 2

36. DCM output Forward and Backward - FB IFG STG STG A1 A1 input Forward
reconstructed responses at source level (ERPs (sources))
1.41 (99%)
0.93 (55%)
STG
STG
coupling changes (coupling B)
probability that a change occurred (coupling B)
2.41 (100%)
5.40 (100%)
1.74 (96%)
4.50 (100%) A1 A1
input
Forward
Backward
standard
Lateral
deviant

37. Conclusions
DCM is a sophisticated technique to investigate effective connectivity
Combines a biologically plausible neuronal mass model with a spatial forward model to generate a predicted data set
Allows us to estimate connectivity parameters & how they are modulated between conditions
And to compute the model evidence in order to single out the best model of the ones proposed.
Underlying theory is complex, but SPM analysis is comparatively simple.
But: requires a lot of previous knowledge.
DCM is not a method to do ERP source reconstruction but knowledge about possible sources is a prerequisite for applying DCM to a data set.
DCM is not exploratory!

38. References:
Jansen BH, Rit VG, (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics 73:357–366
David O, Friston KJ (2003). A neural mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage 20:1743–1755
Kiebel SJ, Garrido MI, Moran RJ, Friston KJ (2008). Dynamic causal modeling for EEG and MEG. Cognitive Neurodynamics (2008) 2:121–136
SPM8 Manual:

39. Special Thanks to
Rosalyn Moran

40. Thanks for your attention ….
Any questions?