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

3

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

4

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

5

Forward problem = modelling

Inverse problem = estimation of the model parameters

BayesInverseForwardIntroduction

Forward and inverse problems: definitions

SPM Conclusion

6

current dipole

BayesInverseForwardIntroduction

Physical model of bioelectrical activity

SPM Conclusion

7

measurements

noise

dipoles

gain matrix

Y = KJ + E1

BayesInverseForwardIntroduction

Fields propagation through head tissues

SPM Conclusion

8

Jacques Hadamard (1865-1963)

1. Existence2. Unicity3. Stability

BayesForwardIntroduction

An ill-posed problem

Inverse SPM Conclusion

9

Jacques Hadamard (1865-1963)

1. Existence2. Unicity3. Stability

BayesForwardIntroduction

An ill-posed problem

Inverse SPM Conclusion

10

BayesForwardIntroduction

Imaging solution: cortically distributed dipoles

Inverse SPM Conclusion

11

BayesForwardIntroduction

Imaging solution: cortically distributed dipoles

Inverse SPM Conclusion

12

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

13

likelihood priors

posteriormodel evidence

ForwardIntroduction

Priors and posterior

Inverse Bayes SPM Conclusion

14

sensor level source level

Q : (known) variance components

(λ,μ) : (unknown) hyperparameters

ForwardIntroduction

Hierarchical generative model

Inverse Bayes SPM Conclusion

15

Y

J

μ1

μq

λ1 λq

ForwardIntroduction

Hierarchical generative model: graph

Inverse Bayes SPM Conclusion

16

generative model M

average over J

model associated with F

ForwardIntroduction

Restricted Maximum Likelihood (ReML)

Inverse Bayes SPM Conclusion

17

generative model M

prior covariance structure

IID

COH

ARD/GS

ForwardIntroduction

Imaging source reconstruction in SPM

Inverse Bayes SPM Conclusion

18

Source reconstruction for group studies

canonical meshes!

ForwardIntroduction

Group studies

Inverse Bayes SPM Conclusion

19

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

20

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

21

• 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

22

RL

individual reconstructions in MRI template space

RFX analysisp < 0.01 uncorrectedR L

SPM machinery

ForwardIntroduction Inverse Bayes SPM Conclusion

23

Many thanks to…

Karl FristonStephan KiebelJeremie Mattout

Christophe PhillipsVladimir Litvak

Guillaume Magic Flandin

ForwardIntroduction Inverse Bayes SPM Conclusion