Eduardo Martínez MontesEduardo Martínez Montes

Neurophysics Department Neurophysics Department Cuban Neuroscience CenterCuban Neuroscience Center

Source Localization for the EEG and MEG

EEG/MEG BETInverse ProblemInverse Problem

of the EEG/MEGof the EEG/MEG

Prior Information

or Constraints

Anatomical Mathematical

EEG generatorsEEG generators

EEG reflects the electrical activity of neuronal masses, with spatial and temporal synchrony.

Primary Current Density (PCD). Macroscopic temporal and spatial average of current density produced by Postsinaptic Potentials.

Main difficulties

. Geometry . Inhomogeneity . Anisotropy

Direct ProblemDirect ProblemEEG/MEGPCD

Model for the head

. Piece-wise isotropic

and homogeneous

Espherical Geometry

Realistic Geometry

POTENTIALMaxwell equations +Boundary conditions + 2nd Green Identity =Fredholm Eq. 2nd type

Drawbacks. Prior Model for DCP. Sensitivity to

conductivity ratios

Direct ProblemDirect ProblemLEAD FIELD

Reciprocity Theorem =

Fredholm Eq. 1st type

k -> lead field

Drawbacks

. Sensitivity to conductivity ratios

3( ) ( , ) ( )c

e e

R

V d r k r r j r r

Nunez, 1981; Riera and Fuentes, 1998

Inverse ProblemInverse Problem

of the EEG/MEGof the EEG/MEG

3, , ,s s g g gv r t K r r j r t d r

Continuum:

Drawback: The IP has analytical solution only for unrealistically simplehead geometries and prior assumptions.

3 3s t s g g t s tN N N N N N N N v = K j + eDiscrete:

Drawback: The problem is highly underdetermined (Ns<<Ng), with an ill-conditioned system matrix K that makes the solution very sensible to small measurement noise errors.

EEG/MEG PCD

3( ) ( , ) ( )c

e e

R

V d r k r r j r r

Different ApproachesDifferent Approaches

Dipolar - local minima, ad hoc number of dipoles, spread act.

BESA CURRY MUSIC

Distributed - non-uniq., ill-cond.,

point sources

Regularization

. Minimum Norm

. Weighted MN, FOCUSS, RWMN

. LORETA Bayesian Approach

. BMA Others

. LAURA, EPIFOCUS

. BeamformerChristoph et al., 2004

What’s wrong with IS methods?What’s wrong with IS methods?1- Ghost Sources:

2- Bias in the estimation of deep sources:

New methodologyNew methodology

Based on Bayesian ApproachAims to reduce the appearance of ghost sourcesAims to overcome the bias on the estimation of

the deep sources.

Bayesian Model Averaging (BMA)

Trujillo et al., 2004.

MN Methods: Tikhonov vs BayesMN Methods: Tikhonov vs Bayes

2 2ˆ min j

j v K j L j

TikhonovRegularization

P P P j v v j j

Bayes

Bayesian Model

v = K j+ e

ˆ max P j

j j v

2,N e 0 I 12,N Tj 0 L L

Why Bayes?Why Bayes?

Offers a natural way for introducing prior information in terms of probabilities

It is easy to construct very complicated models from much simpler ones

Bayesian Framework:Bayesian Framework:First LevelFirst Level

GivenGiven::

kM

v

Model +Data

ˆ max ,k kP Mj

j j v

,,

, ,

k kk

k

k k k

P M P MP M

P M

P M P M P M d

v j jj v

v

v v j j j

InferInfer::

ˆ ,k kE M j j v

Why Bayes Again?Why Bayes Again?

It accounts for uncertainty about model form by weighting the conditional posterior densities according to the posterior probabilities of each model.

Model Uncertainty:Model Uncertainty:

Model 22j

Model N ˆNj

Model 11j

DATA

Bayesian Framework:Bayesian Framework:Second LevelSecond Level

Averaging

Model

Model +Data

1M

NM

v

GivenGiven::

1

ˆ max

max ,N

k kk

P

P M P M

j

j

j j v

j v v

1

0

00

0

0 0

,

;

N

k kk

kk kk kN

r rr

k k

P P M P M

P MBP M

P MB

B P v M P v M

j v j v v

v

1

ˆ ,N

k kk

E E M P M

j j v j v v

Models and Dimensionality:Models and Dimensionality:

1M

2M

kM

1kM

NM

For 69 compartments2010N

3M 2kM

1

,N

k kk

E E M P M

j v j v v

Simulations Simulations

Previous Studies about Visual Previous Studies about Visual Steady-State responses:Steady-State responses:

A strong source has been reported in the primary visual cortex located in the medial region of the occipital hemispheric pole.

A second frontal source has also been observed and has been associated with the electroretinogram.

Some authors have predicted the activation of the thalamus, but it has not been yet detected with none of the inverse methods available.

Visual Steady-State ResponseVisual Steady-State Response

BMA:BMA:

BESA:BESA:LORETALORETA

Conclusions:Conclusions: A new Bayesian inverse solution method based on

model averaging is proposed The new method shows less blurring and

significantly less ghost sources than previous approaches

The new approach shows that the EEG might contain enough information for estimating deep sources even in the presence of cortical ones.

Ongoing Research:Ongoing Research:

Extension of the methodology to include spatial-temporal constraints

Use connectivity constraints for solving the EEG/MEG inverse problem

Estimation of causal models using the anatomical connectivity as prior information

ReferencesReferences

N.J. Trujillo-Barreto, L. Melie-García, E. Cuspineda, E. Martínez, P.A. Valdés-Sosa. Bayesian Inference and Model Averaging in EEG/MEG Imaging [abstract]. Presented at the 9th International Conference on Functional Mapping of the Human Brain, June 19-22, 2003, New York, NY. Available on CD-Rom in NeuroImage, Vol. 19, No. 2.

N.J. Trujillo-Barreto, E. Palmero, L. Melie, E. Martinez. MCMC for Bayesian Model Averaging in EEG/MEG Imaging [abstract]. Presented at the 9th International Conference on Functional Mapping of the Human Brain, June 19-22, 2003, New York, NY. Available on CD-Rom in NeuroImage, Vol. 19, No. 2.

N.J. Trujillo-Barreto, E. Aubert-Vázquez, P.A. Valdés-Sosa, (2004). Bayesian Model Averaging in EEG/MEG imaging. NeuroImage, 21: 1300–1319.

Nunez P., (1981) Electrics Fields of the Brain. New York: Oxford Univ. Press.

Riera JJ, Fuentes ME (1998). Electric lead field for a piecewise homogeneous volume conductor model of the head. IEEE Trans Biomed Eng 45:746 –753.

Christoph M. Michel, Micah M. Murray, Göran Lantz, Sara Gonzalez, Laurent Spinelli, Rolando Grave de Peralta, (2004). EEG source imaging. Clinical Neurophysiology, 115, 2195–2222.