bayesian selection of dynamic causal models for fmri
DESCRIPTION
SPC. V1. V5. SPC. V1. V5. Bayesian selection of dynamic causal models for fMRI. Will Penny Olivier David, Karl Friston, Lee Harrison, Andrea Mechelli, Klaas Stephan. Wellcome Department of Imaging Neuroscience, ION, UCL, UK. - PowerPoint PPT PresentationTRANSCRIPT
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
1 11 1 1z a z cu
u2
u1
z1
z2
z1
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a11c
Multiple regions
1 11 1 1
2 21 22 2 2
0
0
z a z uc
z a a z u
u2
u1
z1
z2
z1
z2
u1
a11
a22
c
a21
Modulatory inputs
1 11 1 1 12
2 21 22 2 21 2 2
0 0 0
0 0
z a z z ucu
z a a z b z u
u2
u1
z1
z2
u2
z1
z2
u1
a11
a22
c
a21
b21
Reciprocal connections
1 11 12 1 1 12
2 21 22 2 21 2 2
0 0
0 0
z a a z z ucu
z a a z b z u
u2
u1
z1
z2
u2
z1
z2
u1
a11
a22
c
a1
2
a21
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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
V5
SPC
Motion
Photic
Att
Model 1
V1
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