J. Daunizeau Motivation, Brain and Behaviour group, ICM, Paris, France
1 Jean Daunizeau Wellcome Trust Centre for Neuroimaging 08 / 05 / 2009 EEG-MEG source reconstruction...
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Transcript of 1 Jean Daunizeau Wellcome Trust Centre for Neuroimaging 08 / 05 / 2009 EEG-MEG source reconstruction...
1
Jean Daunizeau
Wellcome Trust Centre for Neuroimaging
08 / 05 / 2009
EEG-MEG source reconstruction
rIFG
rSTGrA1
lSTGlA1
2
EEG/MEG data
• baseline correction• averaging over trials• low pass filter (20Hz)
trials
• data convert• epoching
sensor locations
• inverse modelling• 1st level contrast
• standard SPM analysis
gain matrix
individualmeshes
evokedresponses
corticalsources
• spatial denormalisation
• anatomical templates
structural MRI
• BEM forward modelling
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EEG/MEG data
• baseline correction• averaging over trials• low pass filter (20Hz)
trials
• data convert• epoching
sensor locations
• inverse modelling• 1st level contrast
gain matrix
evokedresponses
• anatomical templates
• standard SPM analysis
individualmeshes
corticalsources
• spatial denormalisation
structural MRI
• BEM forward modelling
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1. Introduction
2. Forward problem
3. Inverse problem
4. Bayesian inference applied to distributed source reconstruction
5. SPM variants of the EEG/MEG inverse problem
6. Conclusion
Bayes SPM ConclusionInverseForwardIntroduction
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Forward problem = modelling
Inverse problem = estimation of the model parameters
BayesInverseForwardIntroduction
Forward and inverse problems: definitions
SPM Conclusion
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current dipole
BayesInverseForwardIntroduction
Physical model of bioelectrical activity
SPM Conclusion
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measurements
noise
dipoles
gain matrix
Y = KJ + E1
BayesInverseForwardIntroduction
Fields propagation through head tissues
SPM Conclusion
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Jacques Hadamard (1865-1963)
1. Existence2. Unicity3. Stability
BayesForwardIntroduction
An ill-posed problem
Inverse SPM Conclusion
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Jacques Hadamard (1865-1963)
1. Existence2. Unicity3. Stability
BayesForwardIntroduction
An ill-posed problem
Inverse SPM Conclusion
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BayesForwardIntroduction
Imaging solution: cortically distributed dipoles
Inverse SPM Conclusion
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BayesForwardIntroduction
Imaging solution: cortically distributed dipoles
Inverse SPM Conclusion
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Data fit
Adequacy withother
modalities
Spatial and temporalconstraints
W = I : minimum norm method
W = Δ : LORETA (maximum smoothness)
data fit constraint(regularization term)
BayesForwardIntroduction
Regularization
Inverse SPM Conclusion
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likelihood priors
posteriormodel evidence
ForwardIntroduction
Priors and posterior
Inverse Bayes SPM Conclusion
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sensor level source level
Q : (known) variance components
(λ,μ) : (unknown) hyperparameters
ForwardIntroduction
Hierarchical generative model
Inverse Bayes SPM Conclusion
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Y
J
μ1
μq
λ1 λq
ForwardIntroduction
Hierarchical generative model: graph
Inverse Bayes SPM Conclusion
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generative model M
average over J
model associated with F
ForwardIntroduction
Restricted Maximum Likelihood (ReML)
Inverse Bayes SPM Conclusion
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generative model M
prior covariance structure
IID
COH
ARD/GS
ForwardIntroduction
Imaging source reconstruction in SPM
Inverse Bayes SPM Conclusion
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Source reconstruction for group studies
canonical meshes!
ForwardIntroduction
Group studies
Inverse Bayes SPM Conclusion
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EEG/MEG data measurement noiseprecision
ECDpositions
ECDmoments
ECD momentsprior precision
ECD positionsprior precision
soft symmetry constraints! Somesthesic stimulation (evoked potential)
ForwardIntroduction
Equivalent Current Dipoles (ECD)
Inverse Bayes SPM Conclusion
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ensemble (105~106 neurons)
mean-field response(due to ensemble dispersion)
effective connectivity(due to synaptic density)
macroscopic scale mesoscopic scale microscopic scale
excitatoryinterneurons
pyramidalcells
inhibitoryinterneurons
system of ensembles neuron
ForwardIntroduction
Dynamic Causal Modelling (DCM)
Inverse Bayes SPM Conclusion
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• Prior information is mandatoryto solve the inverse problem.
• EEG/MEG source reconstruction:1. forward problem;2. inverse problem (ill-posed).
• Bayesian inference is well suited for:1. introducing such prior information…2. … and estimating their weight wrt the data3. providing us with a quantitative feedbackon the adequacy of the model.
ForwardIntroduction Inverse Bayes SPM Conclusion
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RL
individual reconstructions in MRI template space
RFX analysisp < 0.01 uncorrectedR L
SPM machinery
ForwardIntroduction Inverse Bayes SPM Conclusion
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Many thanks to…
Karl FristonStephan KiebelJeremie Mattout
Christophe PhillipsVladimir Litvak
Guillaume Magic Flandin
ForwardIntroduction Inverse Bayes SPM Conclusion