Haskins fMRI Workshop Part III: Across Subjects Analysis - Univariate, Multivariate, Connectivity
Brain Connectivity Inference for fMRI data
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Transcript of Brain Connectivity Inference for fMRI data
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