Source localization for EEG and MEG

Source localization for EEGand MEG

Methods for Dummies 2006

FIL

Bahador Bahrami

Before we start …

•SPM5 and source localization:

•On-going work in progress

•MFD and source localization:

•This is the first on this topic

•Main references for this talk:

•Jeremie Mattout’s slides from SPM course

•Slotnick S.D. chapter in Todd Handy’s ERP handbook

•Rimona Weil’s wonderful help (thanks Rimona!)

Outline

•Theoretical

•Source localization stated as a problem

•Solution to the problem and their limitations

•Practical*

•How to prepare data

•Which buttons to press

•What to avoid

•What to expect

* Subject to change along with the development of SPM 5

Source localization as a problem

Any field potential vector could be consistent with aninfinite number of possible dipoles

The possibilities only increase with tri-poles andquadra-poles

ERP and MEG give us

And source localization aims to infer

among

How do we know which one iscorrect?

We can’t. There is no correct answer.

We can only see which one is better

Can we find the best answer?

Source localization is an ILL-DEFINED PROBLEM

Only among the alternatives that you have considered.

HUNTING forbest possible solution

Step ONE: How does your data look like?

MEG sensor location

MEG data

Source Reconstruction

Registration

HUNTING forbest possible solution

then

And on and on and on and …

FORWARD MODEL

Step Two

HUNTING forbest possible solution

Forward Model

Experimental DATA

Which forward solutions fit the DATA better (less error)?

Inverse Solution

HUNTING forbest possible solution

Forward

Inverse Solution

DATA

Iterative Process

Until solution stops getting better (error stabilises)

iteration

error

Components of the source reconstruction process

Source model

Forward model

Inverse method

Registration

‘Imaging’

‘ECD’

Data

Anatomy

Recipe for Source localization inSPM5

•Ingredients

–MEG converter has given you

•.MAT data file (contains experimental data)

•sensloc file (sensors locations)

•sensorient (sensors orientations)

•fidloc (fiducial locations in MEG space)

–fidloc in MRI space (we will see shortly)

–Structural T1 MRI scan

All in the same folder

fidloc in MRI space

Nasion

Left Tragus

Right Tragus

Nasion

Left Tragus

Right Tragus

Get these using SPM Display button

Save it as a MAT file in the same directory as the data

Components of the source reconstruction process

Source model

Forward model

Inverse solution

Registration

Source model

Source model

Templates

Individual MRI

Compute transformation T

Apply inverse transformation T-1

Individual mesh

- Individual MRI

- Template mesh

- spatial normalization into MNI template

- inverted transformation applied to the template mesh

- individual mesh

functions

output

Scalp Mesh

iskull mesh

Components of the source reconstruction process

Registration

Registration

Rigid transformation (R,t)

Individual MRI space

fiducials

Individual sensor space

fiducials

- sensor locations

- fiducial locations

(in both sensor & MRI space)

- individual MRI

input

- registration of the EEG/MEG data intoindividual MRI space

- registrated data

- rigid transformation

functions

output

Forward model

Foward model

Compute for

each dipole

Compute for

each dipole

Individual MRI space

Model of the

head tissue properties

Model of the

head tissue properties

Forward operator

- sensor locations

- individual mesh

input

- single sphere

- three spheres

- overlapping spheres

- realistic spheres

- forward operator K

functions

output

BrainStorm

Inverse solution

Inverse solution (1) - General principles

1 dipole source

per location

Cortical mesh

General Linear Model

Y = KJ+ E

[nxt]

[nxp]

[nxt]

[pxt]

n : number of sensors

p : number of dipoles

t : number of time samples

Under-determined GLM

Regularized solution

: min( ||Y – KJ||2 + λf(J) )

data fit

priors

Inverse solution (2) - Parametric empirical Bayes

2-level hierarchical model

E2 ~ N(0,Cp)

E1 ~ N(0,Ce)

Y = KJ + E1

J = 0 + E2

Sensor level

Source level

Gaussian variables

with unknown variance

Gaussian variables

with unknown variance

Linear parametrizationof the variances

Gaussian variables

with unknown variance

Gaussian variables

with unknown variance

Ce = 1.Qe1 + … + q.Qeq

Cp = λ1.Qp1 + … + λk.Qpk

Q: variance components

(,λ): hyperparameters

Q: variance components

(,λ): hyperparameters

Inverse solution (3) - Parametric empirical Bayes

Bayesian inference on model parameters

Inference on J and (,λ)

Model M

Qe1 , … , Qeq

Qp1 , … , Qpk

,λ

F = log( p(Y|M) ) =  log( p(Y|J,M) ) + log( p(J|M) ) dJ

E-step: maximizing F wrt J

J = CJKT[Ce + KCJ KT]-1Y

M-step: maximizing of F wrt (,λ)

Ce + KCJKT = E[YYT]

Maximizing the log-evidence

data fit

priors

Expectation-Maximization (EM)

MAP estimate

ReML estimate

Inverse solution (4) - Parametric empirical Bayes

Bayesian model comparison

B12 =

p(Y|M1)

p(Y|M2)

Model evidence

• Relevance of model M is quantified by its evidence p(Y|M) maximized by the EM scheme

Model comparison

• Two models M1 and M2 can be compared by the ratio of their evidence

Bayes factor

Model selection using a

‘Leaving-one-prior-out-strategy‘

Model selection using a

‘Leaving-one-prior-out-strategy‘

Inverse solution (5) - implementation

- preprocessed data

- forward operator

- individual mesh

- priors

input

- compute the MAP estimate of J

- compute the ReML estimate of (,λ)

- interpolate into individual MRI voxel-space

- inverse estimate

- model evidence

functions

output

- iterative forward and inverse computation

ECD approach

HUNTING forbest possible solution

Forward

Inverse Solution

DATA

Iterative Process

Until solution stops getting better (error stabilises)

iteration

error

Types of Analysis

•Evoked

–The evoked response is a reproducible response which occurs after eachstimulation and is phase-locked with the stimulus onset.

•Induced

–The induced response is usually characterized in the frequency domain andcontrary to the evoked response, is not phased-locked with the stimulus onset.

•The evoked response is obtained (on the scalp) as the stimulus or event-locked average over trials. This is then the input data for the 'evoked' casein source reconstruction.

•One can also reconstruct the evoked power in some frequency band (overthe time window), this is what is obtained when choosing 'both' in sourcereconstruction.

Jeremie says: