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

u1

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

b21

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