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EEG/MEG source reconstruction. Jean Daunizeau Vladimir Litvak Wellcome Trust Centre for Neuroimaging 9 / 05 / 2008. Outline. Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion. Outline. Introduction Forward problem

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Eeg meg source reconstruction

EEG/MEGsource reconstruction

Jean Daunizeau

Vladimir Litvak

Wellcome Trust Centre for Neuroimaging

9 / 05 / 2008


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Introduction

EEG/MEG and neuroimaging

MRI

MEG

EEG

invasivity

weak

strong

OI

EEG

20

spatial resolution (mm)

MEG

SPECT

15

OI

PET

10

fMRI

sEEG

5

MRI(a,d)

1

10

102

103

104

105

temporal resolution (ms)


Introduction

forward/inverse problems : definitions

 Forward problem = modelling

  • Inverse problem = estimation of the model parameters


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Forward problem

physical model of bioelectrical activity

current dipole


Forward problem

the general linear model

noise

dipoles

gain matrix

measurements

Y = KJ + E1


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Inverse problem

an ill-posed problem

  • Jacques Hadamard (1865-1963)

    • Existence

    • Unicity

    • Stability


Inverse problem

an ill-posed problem

  • Jacques Hadamard (1865-1963)

    • Existence

    • Unicity

    • Stability


Inverse problem

cortically distributed current dipoles


Inverse problem

regularization

Spatial and

temporal

constraints

Adequacy with

other

modalities

Data fit

data fit

constraint

(regularization term)

W = I : minimum norm method

W =Δ : LORETA (maximum smoothness)


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Bayesian inference

principle

posterior pdf

likelihood

prior pdf

model evidence


Bayesian inference

hierarchical generative model

sensor level

source level

Q : (known) variance components

(λ,μ) : (unknown) hyperparameters


Bayesian inference

hierarchical generative model

λ1

λq

J

μ1

Y

μq


Bayesian inference

SPM implementations

IID

COH

prior covariance structure

ARD/GS

generative model M


Outline

Introduction

Forward problem

Inverse problem

Bayesian inference applied to the EEG/MEG inverse problem

Conclusion


Conclusion

at the end of the day…

Individual reconstructions in MRI template space

L

R

SPM machinery

RFX analysis

p < 0.01 uncorrected

R

L


Conclusion

summary

• EEG/MEG source reconstruction:

1. forward problem;

2. inverse problem (ill-posed).

• Prior information is mandatory

to solve the inverse problem.

• Bayesian inference is well suited for:

1. introducing such prior information…

2. … and estimating their weight wrt the data

3. providing us with a quantitative feedback

on the adequacy of the model.


Many thanks to

Karl Friston, Stephan Kiebel, Jeremie Mattout


Bayesian inference

expectation-maximization (EM)

average over J

model associated with F

generative model M


Bayesian inference

expectation-maximization (EM)

M-step

E-step

EM / ReML algorithm


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