EEG/MEG Source Localisation

EEG/MEG Source LocalisationSPM Course – Wellcome Trust Centre for Neuroimaging – Oct. 2008

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Jérémie Mattout, Christophe Phillips

Jean DaunizeauGuillaume FlandinKarl FristonRik HensonStefan KiebelVladimir Litvak

OutlineEEG/MEGEEG/MEG

Source localisationSource localisation

1. Introduction

2. Forward model

3. Inverse problem

4. Bayesian inference applied to the EEG/MEG inverse problem

5. Conclusion

EEG/MEGEEG/MEGSource localisationSource localisation Introduction: overview

EEG/MEGEEG/MEGSource localisationSource localisation

EEG/MEG source reconstruction process

Forwardmodel

Inverseproblem

Introduction: overview



1. Introduction

2. Forward model

3. Inverse problem


5. Conclusion

EEG/MEGEEG/MEGSource localisationSource localisation Forward model: formulation

EJfY

Forwardmodel

data sourceparameters

noiseforwardoperator


source biophysical model: current dipole

EEG/MEG source models

EquivalentCurrent

Dipoles (ECD)

Imaging orDistributed

Forward model: source space

- few dipoles withfree location and orientation

- many dipoles withfixed location and orientation

EEG/MEGEEG/MEGSource localisationSource localisation Forward model: imaging/distributed model

EKJY

data dipoleamplitudes

noisegain matrix



1. Introduction

2. Forward model

3. Inverse problem


5. Conclusion


« Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? »

Jacques Hadamard (1865-1963)

Inverse problem: an ill-posed problem

Inverseproblem

1. Existence2. Unicity3. Stability

EEG/MEGEEG/MEGSource localisationSource localisation Inverse problem: an ill-posed problem




Inverseproblem

EEG/MEGEEG/MEGSource localisationSource localisation Inverse problem: an ill-posed problem




Inverseproblem

Introduction of prior knowledge (regularization) is needed

EEG/MEGEEG/MEGSource localisationSource localisation Inverse problem: regularization

Data fit

Adequacywith other

modalities

Spatial and temporal priors

W = I : minimum norm

W = Δ : maximum smoothness (LORETA)

data fit prior(regularization term)



1. Introduction

2. Forward model

3. Inverse problem


5. Conclusion

EEG/MEGEEG/MEGSource localisationSource localisation Bayesian inference: probabilistic formulation

likelihood prior

posteriorevidence

Forwardmodel

Inverseproblem posterior

likelihood

EEG/MEGEEG/MEGSource localisationSource localisation Bayesian inference: hierarchical linear model

sensor (1st) level

source (2nd) level

Q : (known) variance components

(λ,μ) : (unknown) hyperparameters

likelihood

prior

qeqee QQC 1

1

kpkpp QQC 1

1

EEG/MEGEEG/MEGSource localisationSource localisation Bayesian inference: variance components

Multiple Sparse Priors(MSP)

…

# dipoles

# d

ipo

les

Minimum Norm(IID)

Maximum Smoothness(LORETA)

kpkpp QQC 1

1

EEG/MEGEEG/MEGSource localisationSource localisation Bayesian inference: iterative estimation scheme

M-step estimate while keeping constants

E-step estimate while keeping constants,J

Expectation-Maximization (EM) algorithm

J,

EEG/MEGEEG/MEGSource localisationSource localisation Bayesian inference: model comparison

)()()|(log McomplexityMaccuracyMYpF

model Mi

Fi

1 2 3

At convergence



1. Introduction

2. Forward model

3. Inverse problem


5. Conclusion

EEG/MEGEEG/MEGSource localisationSource localisation Conclusion: At the end of the day...

Somesthesic data Bilateral auditory tone

EEG/MEGEEG/MEGSource localisationSource localisation Conclusion: At the group level...

RL

Individual reconstructions in MRI template space

Group resultsp < 0.01 uncorrectedR L

EEG/MEGEEG/MEGSource localisationSource localisation Conclusion: Summary

• Prior information is mandatory

• EEG/MEG source reconstruction:1. forward model2. inverse problem (ill-posed)

• Bayesian inference is used to:1. incorpoate such prior information…2. … and estimating their weight w.r.t the data3. provide a quantitative feedback on model adequacy

Forwardmodel

Inverseproblem


source biophysical model: current dipole

EEG/MEG source models

EquivalentCurrent

Dipoles (ECD)

Imaging orDistributed

Equivalent Current Dipole (ECD) solution

few dipoles with free

location and orientation

many dipoles with fixed location and orientation

EEG/MEGEEG/MEGSource localisationSource localisation ECD approach: principle

EJfY

Forwardmodel

data dipoleparameters

noiseforwardoperator

but a priori fixed number of sources considered iterative fitting of the 6 parameters of each dipole


The locations s and moments w are drawn from normal distributions with precisions γs and γw.

E is white observation noise with precision γy.

w s

Y

w s

yThese are drawn from a prior gamma distribution.

EwsgEJfY )()(

Dipole J with location s and moment w

generated data Y using

ECD solution: variational Bayes (VB) approach

EEG/MEGEEG/MEGSource localisationSource localisation ECD solution: “classical” vs. VB approaches

“Classical” VB

Hard constraints Yes Yes

Soft constraints No Yes

Noise accommodation

No (in general)

Yes

Model comparison

No YES


• can be applied to single time-slice data or average over time (MEG and EEG)

• useful for comparing several few-dipole solutions for selected time points (N100, N170, etc.)

• although not dynamic, can be used for building up intuition about underlying generators, or using as a motivation for DCM source models

• implemented in Matlab and available in SPM8b

ECD solution: when and how to apply VB-ECD?

EEG/MEGEEG/MEGSource localisationSource localisation Example 1: somestesic stimulation

Scalp distribution, 21ms post-stimulus

ERP data over 64 channels VB-ECD solution

EEG/MEGEEG/MEGSource localisationSource localisation Example 2: auditory oddball

Oddball stimuli Standard stimuli

Scalp potential for auditory stimulations

Main referencesEEG/MEGEEG/MEG


Litvak and Friston (2008) Electromagnetic source reconstruction for group studies

Friston et al. (2008) Multiple sparse priors for the M/EEG inverse problem

Kiebel et al. (2008) Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG

Mattout et al. (2007) Canonical Source Reconstruction for MEG

Daunizeau and Friston (2007) A mesostate-space model for EEG and MEG

Henson et al. (2007) Population-level inferences for distributed MEG source localization under multiple constraints: application to face-evoked fields

Friston et al. (2007) Variational free energy and the Laplace approximation

Mattout et al. (2006) MEG source localization under multiple constraints

Friston et al. (2006) Bayesian estimation of evoked and induced responses

Phillips et al. (2005) An empirical Bayesian solution to the source reconstruction problem in EEG


),0(~),( CNMJp

)exp(kk

),(~ Nk

- Log-normal hyperpriors- Enforces the non-negativity of the hyperparameters- Enables Automatic Relevance Determination (ARD)

Bayesian inference: multiple sparse priors


SubjectsMRI Anatomical warping

Corticalmesh

Canonicalmesh

[Un]-normalisingspatial transformation

MNI Space

Forward model: canonical mesh


From Sensor to MRI space

MRI derived meshes

MEG

Full setup

EEG

RigidTransformation

HeadShape

SurfaceMatching

+

HeadShape

Forward model: coregistration

EEG/MEG Source Localisation

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