Will Penny,Wellcome Trust Centre for Neuroimaging,University College London

Brain Connectivity Inference for fMRI data

fNIRS Conference, UCL, 26-28 October 2012

Wellcome Trust Centre for Neuroimaging at UCL

Methods Physics

Attention

Language Memory

Emotion

Vision fMRI MEG

TheoreticalNeurobiology

Statistical Parametric Mapping (SPM)

Realignment Smoothing

Normalisation

General linear model

Statistical parametric mapImage time-series

Parameter estimates

Design matrix

Template

Kernel

Random Field Theory

p <0.05

Statisticalinference

SPM for NIRS Sungho Tak

Chul Ye et al. Neuroimage (2009)

),,( uxFx Neural state equation:

inputs

Dynamic Causal Modelling (DCM)

),,( uxFx Neural state equation:

Neural model:8 state variables per region

nonlinear state equationpropagation delays

MEGMEG

inputs

Dynamic Causal Modelling (DCM)

Neuronal Model for EEG/MEG

Jansen & Ritt, Biol Cyb, 1995 David & Friston Neuroimage, 2006

Shipp, Current Biology, 2010

Predictive Coding

),,( uxFx Neural state equation:

Electric/magneticforward model:

neural activityEEGMEGLFP

(linear)

Neural model:8 state variables per region

nonlinear state equationpropagation delays

MEGMEG

inputs

Dynamic Causal Modelling (DCM)

),,( uxFx Neural state equation:

Electric/magneticforward model:

neural activityEEGMEGLFP

(linear)

Neural model:1 state variable per regionbilinear state equationno propagation delays

Neural model:8 state variables per region

nonlinear state equationpropagation delays

fMRIfMRI MEGMEG

inputs

Dynamic Causal Modelling (DCM)

Single region 1 11 1 1z a z cu

u2

u1

z1

z2

z1

u1

a11c

Neuronal Model for fMRI

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

u1 u2

z1

z2

a11

a22

c

a12

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

),,( uxFx Neural state equation:

Electric/magneticforward model:

neural activityEEGMEGLFP

(linear)

Neural model:1 state variable per regionbilinear state equationno propagation delays

Neural model:8 state variables per region

nonlinear state equationpropagation delays

fMRIfMRI MEGMEG

inputs

Hemodynamicforward model:neural activityBOLD(nonlinear)

Dynamic Causal Modelling (DCM)

Hemodynamics

( , , )

( )

g z

y b

x x h

x

Hemodynamic variables

For each region:

[ , , , ]s f v qx

Hemodynamic parameters

Seconds

Dynamics

Bayesian InferenceIntegrate Neuronaland Hemodynamicequations

Approximate posteriorfrom Variational Bayes

Same inferencealgorithms forfMRI/MEG

V1

V5

SPC

Motion

Photic

Att

Model 1V1

V5

Bayesian Inference

SPC

Time (seconds)

Posterior Inference

B321

P(B

3 21|y

)g

How muchattention (input 3) changes connection fromV1 (region 1) to V5 (region 2)

V1

V5

SPC

Motion

Photic

Att

Model 1

V1

V5

SPC

Motion

Photic

Att

Model 3

Bayes Factor B13=3.6

Positive

),,( uxFx Neural state equation:

Hemodynamic and Optical

Forward Model ?

Neural model:1 state variable per regionbilinear state equationno propagation delays

fMRIfMRI NIRSNIRS

inputs

Dynamic Models of Brain Interactions

Multiple state variables per region ?

• Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. NeuroImage 19:1273-1302.

• O David et al. Dynamic Causal Modelling of Evoked Responses in EEG and MEG. NeuroImage, 30:1255-1272, 2006.

• Friston K, Penny W (2011) Post hoc Bayesian model selection. Neuroimage 56: 2089-2099.

• Penny WD, Stephan KE, Mechelli A, Friston KJ (2004a) Comparing dynamic causal models. NeuroImage 22:1157-1172.

• Penny WD, Stephan KE, Daunizeau J, Joao M, Friston K, Schofield T, Leff AP (2010) Comparing Families of Dynamic Causal Models. PLoS Computational Biology 6: e1000709.

• Penny WD (2012) Comparing dynamic causal models using AIC, BIC and free energy. Neuroimage, 59: 319-330.

• Stephan KE, Weiskopf N, Drysdale PM, Robinson PA, Friston KJ (2007) Comparing hemodynamic models with DCM. NeuroImage 38:387-401.

• Stephan KE, Penny WD, Moran RJ, den Ouden HEM, Daunizeau J, Friston KJ (2010) Ten simple rules for Dynamic Causal Modelling. NeuroImage 49: 3099-3109.

Papers