1. CRIS Workshop: Computational Neuroscience and Bayesian Modelling
Monday 25th October; 2-5PM; Building 26, room 135; Clayton Campus
Effective and functional connectivity
Karl Friston, Wellcome Centre for Neuroimaging, UCL
Abstract
This talk will highlight the fundamental difference between effective and functional connectivity by demonstrating the nature of biophysical models used to infer effective connectivity. I will use DCM studies of reciprocal connections in the brain to illustrate what can be achieved using anatomically and physiologically informed models of distributed neuronal interactions. The examples chosen will focus on functional asymmetries in forward and backward connections and try to cover (i) different data features (e.g., fMRI and ERPs) and (ii) different scales (macroscopic and microscopic).

2. Functional and Effective connectivity
Dynamic Causal Modelling
DCM and fMRI
DCM and EEG
DCM and DTI

3. Functional connectivity Effective connectivity
Statistical dependence between systems
Effective connectivity
Causal influence among systems
DAG
DCM
Tests for conditional independence:
Structural causal modeling
Bayesian model comparison:
Dynamic causal modeling
Bayesian networks
DCM
PCA and ICA
Path analysis (SEM)
Ganger causality (MAR)

4. Functional and Effective connectivity
Dynamic Causal Modelling
DCM and fMRI
DCM and EEG
DCM and DTI

5. Forward models and their inversion
Observed data
Forward model (measurement)
Model inversion
Forward model (neuronal)
input

6. Model specification and inversion
Design experimental inputs
Neural dynamics
Define likelihood model
Observer function
Specify priors
Invert model
Inference on parameters
Inference on models
Inference

7. The bilinear (neuronal) model
Input
Dynamic perturbation
Structural perturbation
average
connectivity
bilinear and nonlinear
connectivity
exogenous causes

8. Functional and Effective connectivity
Dynamic Causal Modelling
DCM and fMRI
DCM and EEG
DCM and DTI

9. Output: a mixture of intra- and extravascular signal
Hemodynamic models
for fMRI
basically, a convolution
signal
The plumbing
flow
volume
dHb
sec
Output: a mixture of intra- and extravascular signal

10. A toy example u2 x3 u1 x1 x2 – – Neural population activity
0.4
0.3
0.2
0.1 10 20 30 40 50 60 70 80 90
100 u2
0.6
0.4
A toy example x3
0.2 10 20 30 40 50 60 70 80 90
100
0.3
0.2
0.1
BOLD signal change (%) 10 20 30 40 50 60 70 80 90
100 u1 x1 x2 3 2 1 – – 10 20 30 40 50 60 70 80 90
100 4 3 2 1 -1 10 20 30 40 50 60 70 80 90
100 3 2 1 10 20 30 40 50 60 70 80 90
100

11. An fMRI study of attention
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)
4 100 scan sessions;
each comprising 10 scans of 4 conditions
F A F N F A F N S
F - fixation point
A - motion stimuli with attention (detect changes)
N - motion stimuli without attention
S - no motion
V5+
PPC
Buchel et al 1999

12. 1) Hierarchical architecture
3) Attentional modulation of prefrontal connections
sufficient to explain regionally specific attentional effects
Attention
.43
.53
Photic
SPC
.40
.49
.62 V1
.92
.35
IFG
.53
2) Segregation of motion information to V5
Motion V5
.73
Friston et al 1999

13. Functional and Effective connectivity
Dynamic Causal Modelling
DCM and fMRI
DCM and EEG
DCM and DTI

14. neuronal mass models of distributed sources
input
Inhibitory cells in supragranular layers
Exogenous input
Excitatory spiny cells in granular layers
State equations
Output equation
Excitatory pyramidal cells in infragranular layers
Measured response

15. FB F Comparing models (with and without backward connections)
ERPs
log-evidence A1
STG
IFG
FB vs. F
IFG
IFG FB F
STG
STG
STG
STG
200
400
without
with A1 A1 A1 A1
input
input
Garrido et al 2007

16. Functional and Effective connectivity
Dynamic Causal Modelling
DCM and fMRI
DCM and EEG
DCM and DTI

17. Probabilistic constraints (priors) on effective connectivity LD LD
LD|LVF FG
(x3) FG
(x4)
Probabilistic constraints (priors) on effective connectivity LD LD LG
(x1) LG
(x2)
LD|RVF
RVF
stim.
LVF
stim.
BVF
stim. FG FG
DTI data and tractography LG LG
Probabilistic structural connectivity

18. Model-space search (scoring)
Optimizing structural constraints
Model-space search (scoring)

19. Model-space search - results1

20. Thank you And thanks to CC Chen Jean Daunizeau Marta Garrido
Lee Harrison
Stefan Kiebel
Andre Marreiros
Rosalyn Moran
Will Penny
Klaas Stephan
And many others