Transcript Dynamic Causal Modelling - University College London

Dynamic Causal Modelling
Will Penny
Wellcome Department of Imaging Neuroscience,
University College London, UK
Cyclotron Research Centre,
University of Liege, April 2003
Outline
 Functional specialisation and integration
 DCM theory
 DCM for auditory word processing
 DCM for category effects
Outline
 Functional specialisation and integration
 DCM theory
 DCM for auditory word processing
 DCM for category effects
Attention to Visual Motion
Buchel et al. 1997
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, 4 100 scan sessions;
each session comprising 10 scans of 4 different condition
e.g. F A F N F A F N S .................
F – fixation
S – stationary dots
N – moving dots
A – attended moving dots
Experimental Factors
1. Photic Stimulation, S-F
2. Motion, N-S
3. Attention, A-N
Functional Specialisation
Q. In what areas does the
‘motion’ factor change activity ?
Univariate Analysis
Multivariate Analysis
Functional Integration
Attention
V5 activity
Q. In what areas does the
‘attention’ factor change this
correlation ?
SPM{Z}
time
V5 activity
Q. In what areas is activity
correlated with activity in V2 ?
attention
no attention
V2
V2 activity
Functional Integration
Q. In what areas is activity
correlated with activity in V2 ?
Q. In what areas does the
‘attention’ factor change this
correlation ?
PPI Question:
Psycho-Physiological
Interaction
Gitelman et al. 2003
Larger Networks:
Attention
V2
1. Structural Equation Modelling (SEM)
2. Dynamic Causal Modelling (DCM)
Activity = ‘Hemodynamic’ (SEM)
= ‘Neuronal’ (PPI/DCM)
Outline
 Functional specialisation and integration
 DCM theory
 DCM for auditory word processing
 DCM for category effects
Aim of DCM
To estimate and make inferences about
(1) the influence that one neural system exerts over another
(i.e. effective connectivity)
Z4
Z5
Z2
Z3
(2) how this is affected by the experimental context
DCM Theory




A Model of Neuronal Activity
A Model of Hemodynamic Activity
Fitting the Model
Making inferences
Model of Neuronal Activity
Set
u2
Z4
Z5
Z2
Z2
Z3
z  f ( z, u )
Stimuli
u1
Z1
Nonlinear,
systems-level
model
Bilinear Dynamics
z 4  a 44 z 4 
Set
u2
a 45 z 5  (a 42  u 2 b422 ) z 2
a 54
z5  a55 x5 
2
23
b
a53 z 3  a54 z 4
Stimuli
u1
b422
z 2  a 22 z 2 
a53
a 21 z1  (a 23  u 2 b232 ) z 3
c11
a 21
z1  a11 z1  c11u1
a 23
z3  a33 z 3  a35 z 5
z  Az  uBz  Cu
Bilinear Dynamics: Positive transients
Stimuli
u1
Set
u2
u1
+
Z1
+
-
u2
Z1
+
Z2
-
Z2
-
z  Az  uBz  Cu
DCM: A model for fMRI
z 4  a 44 z 4 
Set
u2
a 45 z 5  (a 42  u 2 b422 ) z 2
a 54
z5  a55 x5 
z4
b422
g (v4 , q4 )
a53 z 3  a54 z 4
y4
g (v5 , q5 )
a 21
a 21 z1  (a 23  u 2 b232 ) z 3
z3  a33 z 3  a35 z 5
z1
g (v2 , q2 )
g (v1 , q1 )
y2
y1
z3
g (v3 , q3 )
y3
z  Az  uBz  Cu
y  g ( z , v, q )
i
i
i
z1  a11 z1  c11u1
z2
a 23
y5
c11
z 2  a 22 z 2 
z5
Stimuli
u1
i
Causality:
set of differential
equations relating
change in one area
to change in
another
The hemodynamic model


f in  1
f
u
signal
s
s

s
s
0
volume
f in
activity
u(t)
f out  v,  
flow
0
fin
f in E  f in , E0 
 0 E0
v

f out  v, 
0
q
v
BOLD signal
y (t )   v, q, E0 
dHb
q
State Equations
Flow component
Balloon component
Activity-dependent signal
The rate of change of volume
s  u (t )  s/ s  ( f in  1) /  f
 0 v  f in  f out (v, )
Buxton,
Mandeville,
Hoge,
Mayhew.
Flow inducing signal
fin  s
The change in deoxyhemoglobin
 0 q  f in
E  f in , E 0 
 f out (v,  )q / v
E0
Output function: a mixture of intra- and extra-vascular signal
y (t )   (v, q, E0 )  V0 k1 (1  q )  k 2 (1  q / v )  k3 (1  v ) 
Impulse
response
Hemodynamics
BOLD
is
sluggish
Model estimation and inference
z  Az  uBz  Cu
y  g ( z , v, q )
i
i
i
i
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)  p(B|N) p(N)
Laplace
Approximation
Posterior Distributions
z  Az  uBz  Cu
P(A(ij)) = N
(mA(i,j),SAij))
mA
P(B(ij)) = N
(mB(i,j),SBij))
P(C(ij)) = N
(mC(i,j),SCij))
mB
mC
A1
A2
WA
Show connections for which
A(i,j) > Thresh
with probability > 90%
Practical Steps of DCM
Design matrix
1) Standard Analysis of fMRI Data
SPMs
2) Statistical Parametric Maps
Z4
Z5
Z2
3) Construction of a Connectivity Model
Z3
4) Evaluation of the Connectivity Model
Outline
 Functional specialisation and integration
 DCM theory
 DCM for auditory word processing
 DCM for category effects
Single word processing at different rates
Friston et al.
2003
SPM{F}
“Dog”
“Mountain”
“Gate”
Functional localisation of primary and secondary
auditory cortex and Wernicke’s area
Time Series
Auditory stimulus, u1
A2
A1
Adaptation variable, u2
WA
Dynamic Causal Model
Auditory stimulus, u1
u1 enters A1 and is also
allowed to affect all intrinsic
self-connections
A2
Model
allows for
full intrinsic
connectivity
A1
.
u1
Adaptation variable, u2
u2 is allowed to
affect all intrinsic
connections between
regions
.
WA
z  Az  uBz  Cu
Inferred Neural Network
Intrinsic connections
are feed-forward
A2
-.62 (99%)
.92
(100%)
A1
.47
(98%)
.38
(94%)
.37 (100%)
Neuronal saturation
with increasing
stimulus frequency
in A1 & WA
.37 (91%)
WA
-.51 (99%)
Time-dependent
change in A1-WA
connectivity
Outline
 Functional specialisation and integration
 DCM theory
 DCM for auditory word processing
 DCM for category effects
DCM: Category Effects
Mechelli et al. 2003
The fMRI data were originally acquired by Ishai et al. (1999; 2000) and provided by
the National fMRI Data Center (www.fmridc.org)
2x3 Factorial Design:
Tasks were
(1) passive viewing
(2) delayed matching
Stimuli were pictures of
(1) Houses
(2) Faces
(3) Chairs
Baselines involved scrambled pictures of Houses, Faces and Chairs
Results
Ishai et al. found that...
(1) all categories activated a distributed system including bilateral fusiform,
inferior occipital, mid-occipital and inferior temporal regions
(2) within this network, distinct regions in the occipital and temporal cortex
responded preferentially to Faces, House and Chairs
Medial
Fusiform
Lateral
Fusiform
Inferor
Temporal
L
R
p<0.05 (corrected)
QUESTION:
Are the category effects reported by Ishai et al.
(1999; 2000) in the occipital and temporal cortex
mediated by Bottom-up or Top-down mechanisms?
DCM Model
(1) V3 and the Superior Parietal area
(that did not show category effects)
(2) Temporal and Occipital areas
(that did show category effects)
Superior
Parietal
Category
Effects
Chair
responsive
area
Face
responsive
area
House
responsive
area
(3) Extrinsic connections
(4) Intrinsic Connections
V3
(5) Modulatory Connections
Visual Objects
DCM was used to estimate Extrinsic, Intrinsic and Modulatory connections
at the neuronal level using Bayesian framework. Inferences were made at 95%
Hypothesis
We hypothesised a significant influence of category on the intrinsic connections
which would account for the category effects observed in the occipital and
temporal cortex.
(i) One possibility was that this influence would be expressed through the
connections from V3 to the category-responsive areas – which would suggest
bottom-up modulation.
(ii) Another possibility was that the influence of object category on the connectivity
parameters was expressed in the connections from parietal cortex to the
category-responsive areas – thereby indicating top-down modulation.
(iii) Finally, it was possible that object-specificity was conferred by connections
from both V3 and parietal cortex.
DCM Results
The extrinsic connection from the experimental input to V3 was significant in all
subjects
Sup
Par
House
responsive
area
Medial
Fusiform
Face
responsive
area
Lateral
Fusiform
V3
Visual Objects
Chair
responsive
area
Inferior
Temporal
DCM Results
The intrinsic connections between V3, superior parietal and the categoryresponsive regions were significant
Sup
Par
House
responsive
area
Medial
Fusiform
Face
responsive
area
Lateral
Fusiform
V3
Visual Objects
Chair
responsive
area
Inferior
Temporal
DCM Results
The modulatory connections showed that category effects in the occipital and
temporal cortex were mediated by inputs from V3.
Sup
Par
House
responsive
area
Medial
Fusiform
Face
responsive
area
Lateral
Fusiform
V3
Visual Objects
Chair
responsive
area
Inferior
Temporal
Equivalent
top-down effect
was not
significant
DCM Results
The modulatory connections showed that category effects in the occipital and
temporal cortex were mediated by inputs from V3.
Sup
Par
House
responsive
area
Medial
Fusiform
Face
responsive
area
Lateral
Fusiform
V3
Visual Objects
Chair
responsive
area
Inferior
Temporal
Equivalent
top-down effect
was not
significant
DCM Results
The modulatory connections showed that category effects in the occipital and
temporal cortex were mediated by inputs from V3.
Sup
Par
House
responsive
area
Medial
Fusiform
Face
responsive
area
Lateral
Fusiform
V3
Visual Objects
Chair
responsive
area
Inferior
Temporal
Equivalent
top-down effect
was not
significant
Summary
 Studies of functional integration look at
experimentally induced changes in connectivity
 In PPI’s and DCM this connectivity is at the
neuronal level
 DCM: Neurodynamics and hemodynamics
 Inferences about large-scale neuronal networks