EEG/MEG source reconstructionEEG/MEG source reconstructionin SPM5in SPM5

EEG/MEG source reconstructionEEG/MEG source reconstructionin SPM5in SPM5

Jérémie Mattout / Christophe Phillips / Karl FristonJérémie Mattout / Christophe Phillips / Karl Friston

With thanks toWith thanks to

John Ashburner, Guillaume Flandin, Rik Henson, Stefan KiebelJohn Ashburner, Guillaume Flandin, Rik Henson, Stefan Kiebel

Outline

Introduction- EEG/MEG inverse problem- 3D reconstruction in SPM5

I - Source model

II - Data registration

III - Head model and forward computation

IV - Inverse estimation

Demo

Introduction - EEG/MEG inverse problem

Introduction - EEG/MEG inverse problem

Jacques Hadamard (1865-1963)

1. Existence2. Unicity3. Stability

“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?”

Introduction - EEG/MEG inverse problem

Data Y Current density J

Inverse problem (ill-posed)Inverse problem (ill-posed)

Forward problem (well-posed)Y = K(J) + E

Forward problem (well-posed)Y = K(J) + E

• incorporate multiple constraints/prior information• estimate the optimal contribution of those priors• evaluate the relevance of the priors/model

Bayesian framework

Parametric empirical Bayes

Bayesian model comparison

PreprocessingPreprocessing ProjectionProjection SPM5-engineSPM5-engine

EEG/MEG Raw data

EEG/MEG Raw data

Single Trials- epoching- artefacts- filtering- averagin

Single Trials- epoching- artefacts- filtering- averagin

2D - scalp2D - scalp SPM{t}SPM{F}

SPM{t}SPM{F}

Mass univariateanalysis

Mass univariateanalysis

3D - brain3D - brain

DCMDCMspm_eeg_inv_*.m

Introduction - 3D Reconstruction in SPM5

SourcesSources

‘Imaging’‘Imaging’‘Equivalent Current Dipoles’ (ECD)

‘Equivalent Current Dipoles’ (ECD)

3D Projection3D Projection

Introduction - 3D Reconstruction in SPM5

MEG dataMEG data

EEG dataEEG data

(1) Source model(1) Source model

(3) Forward model(3) Forward model

(4) Inverse method(4) Inverse method

(2) Registration(2) Registration

ECDECD ImagingImaging

DataDataAnatomyAnatomy

Introduction - 3D Reconstruction in SPM5

D =

data: [151x2188x5 spm_file_array]channels: [1x1 struct]scale: [1x1 struct]filter: [1x1 struct]events: [1x1 struct]reref: []descrip: []datatype: 'int16'fname: 'fmbe_emer01_TCS.mat'fnamedat: 'fmbe_emer01.dat'Nchannels: 151Nevents: 5Nsamples: 2188Radc: 625path: [1x76 char]inv: {1x7 cell}modality: 'MEG'

D.inv{1} =

method: 'Imaging'mesh: [1x1 struct]datareg: [1x1 struct]forward: [1x1 struct]inverse: [1x1 struct]comment: {'MN + Smoothness'}date: [2x11 char]

Introduction - 3D Reconstruction in SPM5

Data structureData structure

D = spm_eeg_ldata;

Outline

Introduction- EEG/MEG inverse problem- 3D reconstruction in SPM5

I - Source model

II - Data registration

III - Head model and forward computation

IV - Inverse estimation

Demo

Compute transformation TCompute transformation T

Apply inverse transformation T-1Apply inverse transformation T-1

- Individual MRI- Template mesh

input- spatial normalization into MNI template1

- inverted transformation applied to the template mesh2

- inner-skull and scalp binary masks

- cortical mesh- inner-skull mesh- scalp mesh

functions output

1Unified segmentation, J. Ashburner and K.J. Friston, NeuroImage, 2005.2Canonical source reconstruction for EEG & MEG, J. Mattout and K.J. Friston, in preparation.

- wmeshTemplate_3004d.mat- wmeshTemplate_4004d.mat- wmeshTemplate_5004d.mat- wmeshTemplate_7004d.mat

Individual MRI

Individual mesh

Templates

I - Source Model (Meshes)

D.inv{1} =

method: 'Imaging'mesh: [1x1 struct]datareg: [1x1 struct]forward: [1x1 struct]inverse: [1x1 struct]comment: {'MN + Smoothness'}date: [2x11 char]

D.inv{1}.mesh =

sMRI: [1x87 char]nobias: [1x86 char]def: [1x94 char]invdef: [1x98 char]msk_iskull: [1x92 char]msk_scalp: [1x91 char]msk_flags: ''tess_ctx: [1x95 char]Ctx_Nv: 4004Ctx_Nf: 8000tess_iskull: [1x108 char]Iskull_Nv: 2002Iskull_Nf: 4000tess_scalp: [1x106 char]Scalp_Nv: 2002Scalp_Nf: 4000CtxGeoDist: [1x101 char]

I - Source Model (Meshes)

Outline

Introduction- EEG/MEG inverse problem- 3D reconstruction in SPM5

I - Source model

II - Data registration

III - Head model and forward computation

IV - Inverse estimation

Demo

Rigid transformation (R,t)Rigid transformation (R,t)

fiducialsfiducials

- sensor locations- fiducial locations(in sensor & MRI space)- structural MRI- (scalp mesh)

input

- registration of the EEG/MEG data into MRI space3- registered data- transformation matrix

functions output

EEG/MEGsensor space

MRI space

3A method for registration of 3d-shapes, P.J. Besl and N.D. McKay, IEEE Trans. Pat. Anal. And Mach. Intel., 1992.

- Landmarks (MEG/EEG)- ICP Surface matching (EEG)

II - Data Registration

D.inv{1} =

method: 'Imaging'mesh: [1x1 struct]datareg: [1x1 struct]forward: [1x1 struct]inverse: [1x1 struct]comment: {'MN + Smoothness'}date: [2x11 char]

D.inv{1}.datareg =

sens: [1x98 char]fid: [1x94 char]fidmri: [1x94 char]hsp: ''scalpvert: ''sens_coreg: [1x104 char]fid_coreg: [1x100 char]hsp_coreg: ''eeg2mri: [1x87 char]

II - Data Registration

Outline

Introduction- EEG/MEG inverse problem- 3D reconstruction in SPM5

I - Source model

II - Data registration

III - Head model and forward computation

IV - Inverse estimation

Demo

Compute foreach dipole

Compute foreach dipole

+

p

n

- sensor locations- cortical mesh- scalp mesh

input - single sphere- three spheres- overlapping spheres- realistic spheres

- forward operator

functions

output

BrainSTorm

K

K

MRI space

Forward operator

http://neuroimage.usc.edi/brainstorm

Head model

III - Head model & Forward computation

D.inv{1} =

method: 'Imaging'mesh: [1x1 struct]datareg: [1x1 struct]forward: [1x1 struct]inverse: [1x1 struct]comment: {'MN + Smoothness'}date: [2x11 char]

D.inv{1}.forward =

bst_options: [1x1 struct]bst_channel: [1x100 char]bst_tess: [1x97 char]gainmat: [1x103 char]pcagain: [1x107 char]

III - Head model & Forward computation

Outline

Introduction- EEG/MEG inverse problem- 3D reconstruction in SPM5

I - Source model

II - Data registration

III - Head model and forward computation

IV - Inverse estimation

Demo

2-level hierarchical model

Linear parameterization of the variances

Linear parameterization of the variances

Gaussian variableswith unknown variance

Gaussian variableswith unknown variance

1EKJY

20 EJ

)CΝ(0,~e1

E

)CΝ(0,~p2

E

ne

1ee Q.Q.C 1 n

ee m

p1

pp Q.Q.C 1 mpp

Single trialSingle trial

Sensors

Sources

Q: variance components: hyperparameters

IV - Parametric Empirical Bayes (Inverse)

Bayesian inference on model parameters

Model MModel M + +

E-step: maximizing F wrt J

M-step: maximizing of F wrt

Maximizing the log-evidenceMaximizing the log-evidence

data fit priors

Expectation-Maximization (EM)Expectation-Maximization (EM)

ne

1e Q,,Q

mp

1p Q,,Q K

dJMJpMJYpMYpF ))|(log()),|(log())|(log(

InferenceInference

YKKKJ TT 1

pep CCCˆ

TT YYEKK pe CC

Bayesian Model ComparisonBayesian Model Comparison 21 FF ?

MAP estimate

ReML estimate

),,(],,[ NQYYREMLFJ T

IV - Parametric Empirical Bayes (Inverse)

J

Log(Bayes factor) = F1-F21

4Comparing dynamic causal models, W.D. Penny, K.E. Stephan, A. Mechelli, K. Friston, NeuroImage, 2004.

Evoked and induced activityEvoked and induced activity

Synchronized oscillations in time,but not in phase with the stimulation

Events

Average

FT

- =

t

Evoked resp. Induced resp.

t

s

IV - Parametric Empirical Bayes (Inverse)

Multiple trialsMultiple trialsdata & constraints

},,{

],[11

1

T

pe

n

KKQQQ

yyY

evoked energy induced energy

),,)((

],,,[11 NQYSVSSSYREML

FEJTTT

r

eeee

),,~

))((~

(

],,[11 NQYSVSSSIYREML

FETTT

rr

iii

Tkk

yi

Tyii

YGIYE

GVtrCMMEE~

)(~

)(ˆˆ

1)(

)(

Te

Tye

Tyee

SSYMSJ

YGYE

GVtrCMMEE

ˆ

)(ˆˆ

)(

)(

TTT

ip

i

pp

ie

i

ee

peT

eT

pT

p

SSWWSSG

QC

QC

CKCKC

CKKCKCM

111

1

)(ˆ

)(

))11((~

Nkkk IIYY )1( Nk IYY

IV - Parametric Empirical Bayes (Inverse)

ExampleExample Energy changes (Faces - Scrambled, p<0.01)

0.1 0.2 0.4 0.6 0.8

time (s)

10

20

30

40

35

45

15

25

0.70.50.30-0.1

0

1

2

3

-2

-3

-1frequ

ency

(Hz)

100 200 300 400

time (ms)

Right temporal evoked signal

facesscrambled

M170

Time-frequency subspace

0 200time (ms)

400

MEG experimentof Face perception4

4Electrophysiology and haemodynamic correlates of face perception, recognition and priming, R.N. Henson, Y. Goshen-Gottstein, T. Ganel, L.J. Otten, A. Quayle, M.D. Rugg, Cereb. Cortex, 2003.

IV - Parametric Empirical Bayes (Inverse)

ExampleExample

IV - Parametric Empirical Bayes (Inverse)

ExampleExample

IV - Parametric Empirical Bayes (Inverse)

- preprocessed data- forward operator- mesh- constraints

input

- compute the MAP estimate of J1

- compute the ReML estimate of 1

- model evidence2,4

- source dynamic1,2

- power3

functions output

1An empirical Bayesian solution to the source reconstruction problem in EEG, C. Phillips, J. Mattout, M.D. Rugg, P. Maquet and K.J. Friston, NeuroImage, 2005.2MEG source localization under multiple constraints: an extended Bayesian framework, J. Mattout, C. Phillips, M.D. Rugg and K.J. Friston, NeuroImage (in press).3Bayesian estimation of evoked and induced responses, K.J. Friston, R.N. Henson, C. Phillips and J. Mattout, Hum. Brain Mapp. (in press).4Variational free energy and the Laplace approximation, K.J. Friston, J. Mattout, N. Trujillo-Barreto, J. Ashburner and W. Penny (in preparation).

IV - Parametric Empirical Bayes (Inverse)

D.inv{1} =

method: 'Imaging'mesh: [1x1 struct]datareg: [1x1 struct]forward: [1x1 struct]inverse: [1x1 struct]comment: {'MN + Smoothness'}date: [2x11 char]

D.inv{1}.inverse =

activity: 'evoked'contrast: [0.5000 0.5000 1 0 0]woi: [150 190]priors: [1x1 struct]dim: 4004resfile: 'fmbe_emer01_TCS_remlmat_150_190ms_evoked_11H3.mat'LogEv: 9.8269e+003

IV - Parametric Empirical Bayes (Inverse)