1. Dynamic Causal Modelling
Will Penny
Karl Friston, Lee Harrison, Klaas Stephan, Andrea Mechelli
Wellcome Department of Imaging Neuroscience,
University College London, UK
Loughborough University
Nov 25th 2003

2. Outline Functional specialisation and integration DCM theory
Attention to visual motion fMRI study
Model comparison

3. Outline Functional specialisation and integration DCM theory
Attention Data
Model comparison

4. Attention to Visual Motion fMRI
Stimuli
250 radially moving dots at 4.7 degrees/s
Pre-Scanning
5 x 30s trials with 5 speed changes (reducing to 1%)
Task - detect change in radial velocity
Scanning (no speed changes)
6 normal subjects, 360 whole-brain scans, one every
3.2 seconds; each session comprising 4 different conditions
e.g. F A F N F A F N S
F – fixation
S – stationary dots
N – moving dots
A – attended moving dots
Buchel et al. 1997
Experimental Factors
Photic Stimulation, S,N,A
Motion, N,A
Attention, A

5. Functional Specialisation
Q. In what areas does the
‘motion’ factor change activity ?
Univariate Analysis
Spatial resolution – millimetres
Temporal resolution – seconds

6. Functional Integration
Multivariate Analysis
SPM
Q. In what areas is activity
correlated with activity in V2 ?
Q. In what areas does the
‘attention’ factor change this
correlation ?
V5 activity
300
600
900
Seconds
Attention V2
attention
V5 activity
no attention
V2 activity

7. Larger networks fMRI time series Structural Equation Modelling (SEM)
Y(4)t
Y(1)t
Y(2)t
Y(3)t
Multivariate Autoregressive (MAR)

8. Outline Functional specialisation and integration DCM theory
Attention Data
Model comparison

9. Aim of DCM To estimate and make inferences about
(1) the influence that one neural system exerts over another
(2) how this is affected by the experimental context Z2 Z4 Z3 Z5
Logothetis:
fMRI is most
strongly correlated
with Local Field Potential

10. DCM Theory A Model of Neuronal Activity
A Model of Hemodynamic Activity
Fitting the Model
Making inferences
Model Comparison

11. Model of Neuronal ActivityZ2 Z1 Z4 Z3 Z5
Stimuli u1
Set u2
Systems-level
model

12. Bilinear Dynamics
a53
Set u2
Stimuli u1

13. Bilinear dynamics: oscillatory transients
Stimuli u1
Set u2 u 1 Z 2 - + Z1 - - + Z2 -
Seconds -

14. Bilinear dynamics: positive transients
Stimuli u1
Set u2 u 1 Z 2 - + Z1 - + + Z2 - -

15. DCM: A model for fMRI
Set u2
Stimuli u1

16. The hemodynamic model
Buxton,
Mandeville,
Hoge,
Mayhew.

17. Impulse
response
Hemodynamics
BOLD is
sluggish

18. Neuronal Transients and BOLD: I
300ms
500ms
Seconds
Seconds
More enduring transients produce bigger BOLD signals

19. Neuronal Transients and BOLD: II
Seconds
Seconds
BOLD is sensitive to frequency
content of transients
Relative timings of transients are
amplified in BOLD
Seconds

20. Model estimation and inference
Unknown neural parameters, N={A,B,C}
Unknown hemodynamic parameters, H
Vague priors and stability priors, p(N)
Informative priors, p(H)
Observed BOLD time series, B.
Data likelihood, p(B|H,N) = Gauss (B-Y)
Bayesian inference p(N|B) a p(B|N) p(N)
Laplace
Approximation

21. Outline Functional specialisation and integration DCM theory
Attention Data
Model comparison

22. Results Attention Motion Photic Photic Motion Attention V1 V5 SPC
0.85
0.57
-0.02
1.36
0.70
0.84
0.23
SPC
P(B{Attention-V1,V5} |Data)
Attention
Motion
Photic

23. Outline Functional specialisation and integration DCM theory
Attention Data
Model comparison

24. First level of Bayesian Inference
We have data, y, and some parameters, b
First level of Inference: What are the best parameters ?
Parameters are of model, M, ….

25. First and Second Levels
The first level again, writing in dependence on M:
Second level of Inference: What’s the best model ?

26. Model Comparison We need to compute the Bayesian Evidence:
We can’t always compute it exactly, but we
can approximate it: Log p(y|M) ~ F(M)
Evidence = Accuracy - Complexity

27. Model 1 Model 3 Model 2 Model 4 Photic Photic Attention Motion MotionV1 V5
SPC
Motion
Photic
Attention
0.85
0.57
-0.02
1.36
0.03
0.70
0.23 V1 V5
SPC
Motion
Photic
Attention
0.85
0.57
-0.02
1.36
0.70
0.84
0.23 V1 V5
SPC
Motion
Photic
Attention
0.96
0.39
0.06
0.58 V1 V5
SPC
Motion
Photic
Attention
0.86
0.56
-0.02
1.42
0.55
0.75
0.89
Model 2
Model 4

28. Summary Studies of functional integration look at
experimentally induced changes in connectivity
In DCM this connectivity is at the
neuronal level
DCM: Neurodynamics and hemodynamics
Inferences about large-scale neuronal networks
Model comparison
Future Work: DCMs for EEG and fMRI