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Dynamic Causal Modelling for EEG/MEG:principles
Adapted from the DCM course slides ofJ. Daunizeau
Overview
1 DCM: introduction
2 Neural states dynamics
3 Bayesian inference
4 Conclusion
Overview
1 DCM: introduction
2 Neural states dynamics
3 Bayesian inference
4 Conclusion
Introductionstructural, functional and effective connectivity
• structural connectivity= presence of axonal connections
• functional connectivity = statistical dependencies between regional time series
• effective connectivity = causal (directed) influences between neuronal populations
! connections are recruited in a context-dependent fashion
O. Sporns 2007, Scholarpedia
structural connectivity functional connectivity effective connectivity
u1 u1 X u2
A B
u2u1
A B
u2u1
localizing brain activity:functional segregation
effective connectivity analysis:functional integration
Introductionfrom functional segregation to functional integration
« Where, in the brain, didmy experimental manipulation
have an effect? »
« How did my experimental manipulationpropagate through the network? »
?
( , , )x f x u neural states dynamics
Electromagneticobservation model:spatial convolution
• simple neuronal model• realistic observation model
• realistic neuronal model• simple observation model
fMRIfMRI EEG/MEGEEG/MEG
inputs
IntroductionDCM: evolution and observation mappings
Hemodynamicobservation model:temporal convolution
IntroductionDCM: a parametric statistical approach
,
, ,
y g x
x f x u
• DCM: model structure
1
2
4
3
24
u
, ,p y m likelihood
• DCM: Bayesian inference
ˆ ,E y m
, ,p y m p y m p m p m d d
model evidence:
parameter estimate:
priors on parameters
Overview
1 DCM: introduction
2 Neural states dynamics
3 Bayesian inference
4 Conclusion
Neural ensembles dynamicsDCM for M/EEG: systems of neural populations
Golgi Nissl
internal granularlayer
internal pyramidallayer
external pyramidallayer
external granularlayer
mean-field firing rate synaptic dynamics
macro-scale meso-scale micro-scale
EP
EI
II
Neural ensembles dynamicsDCM for M/EEG: synaptic dynamics
1iK
time (ms)m
embr
ane
depo
lariz
atio
n (m
V)
1 22 2
2 / / 2 / 1( ) 2i e i e i eS
post-synaptic potential
1eK
IPSP
EPSP
Neural ensembles dynamicsDCM for M/EEG: extrinsic connections between brain regions
extrinsicforward
connections
spiny stellate cells
inhibitory interneurons
pyramidal cells
0( )F S
0( )LS
0( )BS extrinsic backward connections
extrinsiclateral connections
1 2
3 4
7 82 2
8 3 0 8 7
1 42 2
4 1 0 4 1
0 5 6
2 5
2 25 0 2 1 5 2
3 6
2 26 4 7 6 3
(( ) ( )) 2
(( ) ( ) ) 2
(( ) ( ) ( )) 2
( ) 2
e B L e e
e F L u e e
e B L e e
i i i
I S
I S u
S Sx
S
Overview
1 DCM: introduction
2 Neural states dynamics
3 Bayesian inference
4 Conclusion
Bayesian inferenceforward and inverse problems
,p y m
forward problem
likelihood
,p y m
inverse problem
posterior distribution
Bayesian paradigmderiving the likelihood function
- Model of data with unknown parameters:
y f e.g., GLM: f X
- But data is noisy: y f
- Assume noise/residuals is ‘small’:
22
1exp2
p
4 0.05P
→ Distribution of data, given fixed parameters:
2
2
1exp2
p y y f
f
Likelihood:
Prior:
Bayes rule:
Bayesian paradigmlikelihood, priors and the model evidence
generative model m
Overview
1 DCM: introduction
2 Neural states dynamics
3 Bayesian inference
4 Conclusion
• Suitable experimental design:– any design that is suitable for a GLM – preferably multi-factorial (e.g. 2 x 2)
• e.g. one factor that varies the driving (sensory) input• and one factor that varies the modulatory input
• Hypothesis and model:– define specific a priori hypothesis– which models are relevant to test this hypothesis?– check existence of effect on data features of interest– there exists formal methods for optimizing the experimental design
for the ensuing bayesian model comparison[Daunizeau et al., PLoS Comp. Biol., 2011]
Conclusionplanning a compatible DCM study