1. Effective Connectivity
Lee Harrison
Wellcome Department of Imaging Neuroscience,
University College London, UK
SPM Short Course, May 2004

2. Outline Motivation & concepts Models of effective connectivity
An example

3. Outline Motivation & concepts Models of effective connectivity
An example

4. Functional Specialization
Q. In what areas does the
‘motion’ factor change activity ?
Univariate Analysis

5. Functional Integration
To estimate and make inferences about
the influence that one neural system exerts over another
(2) how this is affected by the experimental context Z2 Z4 Z3 Z5

6. Concepts Brain as a physical system System identification
Evoked response to input
System identification
Parameterised models
In terms of connectivity
Classification of models
Black box & hidden states

7. Concepts (continued) Linear vs nonlinear systems
Balance mathematical tractability and biological plausibility
Generalization of General Linear Model
Bilinear models
Inputs
Perturbing & contextual
Stochastic & deterministic
use of design matrix
Experimental design
22 factorial design

8. Concepts (continued) Linear vs nonlinear systems
Balance mathematical tractability and biological plausibility
Generalization of General Linear Model
Bilinear models
Inputs
Perturbing & contextual
Stochastic & deterministic
use of design matrix
Experimental design
22 factorial design

9. Model of Neuronal ActivityZ2 Z1 Z4 Z3 Z5
Stimuli u1
Set u2
Nonlinear,
systems-level
model

10. Bilinear Dynamics Z4 Z2 Psycho-physiological interaction Z5 Z1 Z3 Set
Stimuli u1
Set u2
Psycho-physiological interaction

11. Bilinear Dynamics a53 Psycho-physiological interaction Set Stimuli u2

12. Bilinear Dynamics: Positive transients
Stimuli u1
Set u2 u 1 Z 2 - + Z1 - + + Z2 - -

13. Concepts (continued) Linear vs nonlinear systems
Balance mathematical tractability and biological plausibility
Generalization of General Linear Model
Bilinear models
Inputs
Perturbing & contextual
Stochastic & deterministic
use of design matrix
Experimental design
22 factorial design

14. Outline Motivation & concepts Models of effective connectivity
An example

15. Practical steps 1) Standard Analysis of fMRI Data
Design matrix
1) Standard Analysis of fMRI Data
2) Statistical Parametric Maps
3) Anatomical model
4) Connectivity model
5) Estimation & inference of model parameters
SPMs Z2 Z4 Z3 Z5

16. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
An example

17. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
An example

18. Structural Equation Modellingy1 y2 y3

19. Inference in SEMs V1 V5 PPC V1 V5 PPC V1 V5 PPC V1 V5 PPC V1 V5 PPCvs V1 V5
PPC V1 V5
PPC V1 V5
PPC
PFC V1 V5
PPC
PFC vs
PPIV5xPFC
PPIV5xPFC
Attentional
set
Attentional
set

20. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
An example

21. Bilinear Convolution Model

22. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
An example

23. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
Dynamic Causal Modelling
An example

24. The DCM and its bilinear approximation
neuronal
changes
intrinsic
connectivity
induced
connectivity
induced
response
Input
u(t)
The bilinear model
activity
z2(t)
activity
z3(t)
activity
z1(t) y y y
Hemodynamic model

25. The hemodynamic model y

26. Overview Models of Constraints on Bayesian estimation
Hemodynamics in a single region
Neuronal interactions
Constraints on
Connections
Hemodynamic parameters
Bayesian estimation

27. Practical steps 1) Standard Analysis of fMRI Data
Design matrix
1) Standard Analysis of fMRI Data
2) Statistical Parametric Maps
3) Anatomical model
4) Connectivity model
5) Estimation & inference of model parameters
SPMs Z2 Z4 Z3 Z5

28. Outline Motivation & concepts Models of effective connectivity
Linear regression
Convolution
State-Space
An example
DCM for visual motion processing

29. A fMRI study of attentional modulation
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, scan sessions;
each session comprising 10 scans of 4 different condition
F A F N F A F N S
F - fixation point only
A - motion stimuli with attention (detect changes)
N - motion stimuli without attention
S - no motion
PPC
V5+
Buchel et al 1999

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

31. Summary Studies of functional integration look at
experimentally induced changes in connectivity
Neurodynamics and hemodynamics
DCM
Inferences about large-scale neuronal networks