1. Dynamic Causal Model
for evoked responses
in M/EEG
Rosalyn Moran

2. Overview Dynamic Causal Modelling – Motivation
Dynamic Causal Modelling – Generative model
Bayesian model inversion/selection
Example

3. Overview Dynamic Causal Modelling – Motivation
Dynamic Causal Modelling – Generative model
Bayesian model inversion/selection
Example

4. Mismatch negativity (MMN) – DCM Motivation
standards
deviants
Paradigm
pseudo-random auditory sequence
80% standard tones – 500 Hz
20% deviant tones – 550 Hz
time
Raw data
(128 sensors)
Preprocessing
(SPM8)
Evoked responses
(here: single sensor) μV
time (ms)

5. Dynamic Causal Modelling- Motivation
amplitude (μV)
time
time (ms)
standard
sensors
deviant
sensors

6. Dynamic Causal Modelling- Motivation
time
standard
Conventional approach: Reduce evoked response to a few variables.
sensors
deviant
Alternative approach that tells
us about communication among brain sources?
sensors

7. Dynamic Causal Modelling- Motivation
Build a generative model for spatiotemporal data
and fit to evoked responses.
???
Assume that both ERs are
generated by temporal dynamics
of a network of a few sources A1 A1
Describe temporal dynamics
by differential equations
Dynamic
Causal
Modelling
Each source projects to the sensors,
following physical laws
Solve for the model parameters
using Bayesian model inversion 7

8. DCM does not localise active sources
Raw data
(128 sensors)
Preprocessing
(SPM8)
Evoked responses
(here: single sensor) μV
time (ms)
MNI coordinates from the literature
Source Localisation
DCM

9. Overview Dynamic Causal Modelling – Motivation
Dynamic Causal Modelling – Generative model
Bayesian model inversion/selection
Example

10. The Generative model fMRI ERPs Neural state equation: inputs
Hemodynamic forward model: neural activityBOLD
(nonlinear)
Electric/magnetic
forward model: neural activityEEG MEG
LFP
(linear)
Neural state equation:
fMRI
ERPs
Neural model:
1 state variable per region
bilinear state equation
no propagation delays
Neural model:
8 state variables per region
nonlinear state equation
propagation delays
inputs

11. The Generative model Source dynamics f Spatial forward model g
states x
Evoked response
parameters θ
data y
Input u

12. Macro- and meso-scale macro-scale meso-scale micro-scale 12
external granular
layer
external pyramidal
layer
internal granular
layer
internal pyramidal
layer
AP generation zone
synapses 12

13. meso-scale 13 AP generation zone external granular layer
external pyramidal
layer
synapses
internal granular
layer
internal pyramidal
layer
AP generation zone 13

14. Neural mass equations and connectivity
State equations
Extrinsic lateral connections
spiny stellate cells
inhibitory interneurons
pyramidal cells
Extrinsic
forward connections
Intrinsic connections
Extrinsic backward connections
neuronal (source) model 14

15. Overview Dynamic Causal Modelling – Motivation
Dynamic Causal Modelling – Generative model
Bayesian model inversion/selection
Example

16. Model selection & Hypothesis Testing
...
Model n
Model selection:
data y
STG
STG
STG A1 A1 A1
best?

17. Model selection & Hypothesis Testing
...
Model n
Model selection:
data y
STG
STG
STG A1 A1 A1 17

18. Model selection & Hypothesis Testing
...
Model n
Model selection:
data y
STG
STG
STG
STG A1 A1 A1 A1 18

19. Bayesian Statistics
prior knowledge
new data
posterior  likelihood ∙ prior
Bayes theorem allows one to formally incorporate prior knowledge into computing statistical probabilities.
In DCM for ERPs priors include time constants, PSP, delays etc.
The “posterior” probability of the parameters given the data is an optimal combination of prior knowledge and new data, weighted by their relative precision.

20. Define likelihood model
Bayesian Inversion
Neural Parameters: Dynamic Model
Define likelihood model
Observer function:
Forward Spatial Model
Specify priors
Inference on models
Invert model
Inference on parameters
Make inferences

21. Bayesian Inversion Specify generative forward model
(with prior distributions of parameters)
Evoked responses
Expectation-Maximization algorithm
Iterative procedure:
Compute model response using current set of parameters
Compare model response with data
Improve parameters, if possible
Posterior distributions of parameters
Model evidence 21

22. Bayesian Model Selection
Model evidence:
Approximation: Free Energy
accounts for both accuracy and complexity of the model
allows for inference about structure (generalisability) of the model
Fixed Effects Model selection via
log Group Bayes factor:
Random Effects Model selection
via Model probability:

23. Overview Dynamic Causal Modelling – Motivation
Dynamic Causal Modelling – Generative model
Bayesian model inversion/selection
Example

24. Mismatch negativity (MMN) – DCM Motivation
standards
deviants
Paradigm
pseudo-random auditory sequence
80% standard tones – 500 Hz
20% deviant tones – 550 Hz
time
Raw data
(128 sensors)
Preprocessing
(SPM8)
Evoked responses
(here: single sensor) μV
Garrido et al., (2007), NeuroImage
time (ms)

25. Models for Deviant Response Generation
Model for mismatch negativity
Models for Deviant Response Generation
Garrido et al., (2007), NeuroImage

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

27. Models for Deviant Response Generation
Temporal Hypotheses
Do forward and backward connections operate as a function of time?
Models for Deviant Response Generation
Peristimulus time 1
Peristimulus time 2
Garrido et al., PNAS, 2008 27

28. Grand mean ERPs
Bayesian model comparison among DCMs of grand mean ERPs. (A) Grand mean ERP responses, i.e., averaged over all subjects, to the deviant tone overlaid on a whole-scalp map of 128 EEG electrodes. (B) Overlapped ERP responses to deviant tones from all 128 sensors over the peristimulus interval [0, 400] (in milliseconds). (C) Differences in negative free-energy or log-evidence comparing the model with backward connections (FB) against the model without (F). The gray patch indicates the interval chosen to model the ERPs for each individual subject (see Fig. 3).
Garrido M. I. et.al. PNAS 2007;104:
©2007 by National Academy of Sciences

29. Model Fit
time (ms)
time (ms)
Garrido et al., PNAS, 2008

30. Bayesian model comparison across subjects
Bayesian model comparison across subjects. (A) Comparison of the model with backward connections (FB) against the model without (F), across all subjects over the peristimulus interval 180–260 ms. The dots correspond to differences in log-evidence for 11 subjects over time. The solid line shows the average log-evidence differences over subjects [this is proportional to the log-group Bayes factor (Bf) or to the differences in the free energy of the two models (ΔF); see Materials and Methods for details]. The points outside the gray zone imply very strong inference (≥99% confidence that one model is more likely), i.e., model FB supervenes over F for positive points and the converse for negative points. (B) Histogram showing the number of subjects in each of seven levels of inference on models with and without backward connections across the peristimulus interval 180–260 ms.
Garrido M. I. et.al. PNAS 2007;104:
©2007 by National Academy of Sciences

31. Summary
DCM enables testing hypotheses about how brain sources communicate.
DCM is based on a neurobiologically plausible generative model of evoked responses.
Differences between conditions are modelled as modulation of connectivity.
Inference: Bayesian model selection 31