Bayesian selection of dynamic causal models for fMRI
Will Penny
Olivier David, Karl Friston, Lee Harrison, Andrea Mechelli, Klaas Stephan
The brain as a dynamical system ? Bridging the gap between models and data, HBM Workshop, Budapest, Hungary, June 16 2004.
V1
V5
SPC
V1
V5
SPC
Wellcome Department of Imaging Neuroscience, ION, UCL, UK.
Single region
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u1
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a11c
Multiple regions
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0
0
z a z uc
z a a z u
u2
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a11
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c
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Modulatory inputs
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0 0 0
0 0
z a z z ucu
z a a z b z u
u2
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u1
a11
a22
c
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Reciprocal connections
1 11 12 1 1 12
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0 0
0 0
z a a z z ucu
z a a z b z u
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DCM for fMRI
Neurodynamics:
i ii
z Az u B z Cu
InputsChange inNeuronalActivity
NeuronalActivity
IntrinsicConnectivityMatrix
ModulatoryConnectivityMatrices
InputConnectivityMatrix
V1
V5
SPC
Hemodynamics
( , , )
( )
g z
y b
x x h
x
Hemodynamic variables
For each region:
[ , , , ]s f v qx
Hemodynamic parameters
Seconds
Dynamics
Model Comparison I
{ , , , }θ A B C h
( | , ) ( | )( | , )
( | )
p m p mp m
p m
y θ θθ y
y
V1
V5
SPC
( | ) ( | , ) ( | )p m p m p m dy y θ θ θ
Model, m Parameters:
PriorPosterior Likelihood
Evidence
Laplace, AIC, BIC approximations
Model fit + complexity
Model Comparison II
{ , , , }θ A B C h
( | , ) ( | )( | , )
( | )
p m p mp m
p m
y θ θθ y
y
V1
V5
SPC
Model, mParameters:
PriorPosterior Likelihood
( | ) ( )( | )
( )
p m p mp m
p
yy
y
PriorPosterior Evidence
Parameter Parameter
Model Model
Model Comparison III
V1
V5
SPC
( | ) ( | , ) ( | )p m i p m i p m i d y y θ θ θ
( | ) ( | , ) ( | )p m j p m j p m j d y y θ θ θ
Model, m=i
V1
V5
SPC
Model, m=j
Model Evidences:
Bayes factor:
( | )
( | )ij
p m iB
p m j
y
y
1 to 3: Weak3 to 20: Positive20 to 100: Strong>100: Very Strong
Attention to Visual MotionAttention to Visual Motion
STIMULISTIMULI
250 radially moving dots at 4.7 degrees/s250 radially moving dots at 4.7 degrees/s
PRE-SCANNINGPRE-SCANNING
5 x 30s trials with 5 speed changes (reducing to 1%)5 x 30s trials with 5 speed changes (reducing to 1%)
Task - detect change in radial velocityTask - detect change in radial velocity
SCANNINGSCANNING (no speed changes)(no speed changes)
6 normal subjects, 4 100 scan sessions;6 normal subjects, 4 100 scan sessions;
each session comprising 10 scans of 4 different conditioneach session comprising 10 scans of 4 different condition
1. Photic2. Motion3. Attention
Experimental Factors
Buchel et al. 1997
Specify regions of interest
Identify regions of Interest eg. V1, V5, SPC
GLM analysis
V1
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SPC
Motion
Photic
Att
Model 1
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V5
SPC
Motion
Photic
Att
Model 1V1
V5
Estimation
SPC
Time (seconds)
V1
V5
SPC
Motion
Photic
Att
Model 1
Motion
Photic
Att
V1
V5
SPC
Model 2
Bayes Factor B12 > 1019
VeryStrong
V1
V5
SPC
Motion
Photic
Att
Model 1
V1
V5
SPC
Motion
Photic
Att
Model 3
Bayes Factor B13=3.6
Positive
V1
V5
SPC
Motion
Photic
Att
Model 1
Motion
Photic
Att
Att
V1
V5
SPC
Model 4
Bayes Factor B14=2.8
Weak
Further Applications
FGleft
FGright
LGleft
LGright
RVF LVF
LD|LVF
LD LD
LD: Letter decision
LVF: left visual field
FG:
1. Klaas Stephan et al. HBM 04 – Poster TH154, Thurs 1pm
Dominant right->left modulation during letter tasks
LG and FG important for hemispheric integration (not MOG)
2. Olivier David et al. BIOMAG 04 – DCM for ERPs
Fusiform gyrus
LG: Lingual gyrus
