# Eduardo Mart�nez Montes Neurophysics Department Cuban

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```							Source Localization for the EEG
and MEG

Eduardo Martínez Montes

Neurophysics Department
Cuban Neuroscience Center
EEG/MEG    Inverse Problem             BET
of the EEG/MEG

Prior Information
or Constraints

Anatomical                   Mathematical
EEG 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.
PCD
Direct Problem         EEG/MEG

Main difficulties
. Geometry . Inhomogeneity . Anisotropy

Model for the head                   Espherical
. Piece-wise                          Geometry
isotropic
and homogeneous                     Realistic
Geometry
Direct Problem
Maxwell equations +         Reciprocity Theorem =
Boundary conditions +       Fredholm Eq. 1st type
2nd Green Identity =
V (re )   k (re , r)  j(r)d 3r
Fredholm Eq. 2nd type
Rc

. Prior Model for DCP       Drawbacks
. Sensitivity to            . Sensitivity to conductivity
conductivity ratios         ratios

Nunez, 1981;   Riera and Fuentes, 1998
EEG/MEG            Inverse Problem                             PCD
of the EEG/MEG

V (re )   k (re , r)  j(r)d 3r
Rc

Continuum:          v  rs , t    K  rs , rg   j  rg , t  d 3rg
Drawback: The IP has analytical solution only for unrealistically simple

Discrete:         v Ns  Nt = K Ns 3 N g  j3 N g  Nt + e Ns  Nt
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.
Different Approaches
 BESA
   Dipolar - local minima, ad hoc number         CURRY
of dipoles, spread act.             MUSIC

 Regularization
   Distributed - non-uniq., ill-cond.,     . Minimum Norm
point sources             . Weighted MN,
FOCUSS, RWMN
. LORETA
 Bayesian Approach
. BMA
 Others
. LAURA, EPIFOCUS
Christoph et al., 2004
. Beamformer
What’s wrong with IS methods?
1- Ghost Sources:

2- Bias in the estimation of deep sources:
New methodology

 Based on Bayesian Approach
 Aims to reduce the appearance of ghost sources
 Aims to overcome the bias on the estimation of
the deep sources.

Bayesian Model Averaging (BMA)

Trujillo et al., 2004.
MN Methods: Tikhonov vs Bayes
v = K  j+e
Tikhonov
Regularization                         Bayes

Bayesian
Model
P  j v   P  v j  P  j

e    N  0,  I 
2         j        
N 0,       2
L L
T       1

j
j

ˆ  min v  K  j 2   L  j 2             ˆ  max P  j v 
j
j
            
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:
First Level
Given:                          Infer:

P  v j, M k  P  j M k 
P  j v, M k  
Pv Mk 
Model   Mk
+               P  v M k    P  v j, M k  P  j, M k  dj
Data    v
j

ˆ  max P  j v, M 
jk                k         
ˆ  E  j v, M 
jk           k
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 1          ˆ
j1

Model 2          ˆ
j2            DATA

Model N          ˆ
jN
Bayesian Framework:
Second Level
N
Given:           P  j v    P  j v, M k   P  M k v 
k 1

 k Bk 0                PMk 
P Mk v 
Model   M1                                                  ; k 
N
P M0 
 B
A
v                                     r   r0
r 0
e
r   B  P v M  P v M 
k0                       k                  0
a
g   ˆ  max  P  j v  
j
i             j
Model M N    n
                        
N

+          g      max P  j v , M k   P  M k v 
j
k 1
Data v                                         N
ˆ  E  j v   E  j v, M   P  M v 
j                     k        k
k 1
Models and Dimensionality:
N
E  j v    E  j v, M k   P  M k v 
                      
k 1

M1
M k 1
M2

M3   M k 2

For 69 compartments
20
N 10                                              MN
Mk
Simulations
 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.

BMA:

BESA:
LORETA
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:
 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
References
   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.
   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.

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