1. Eduardo Martínez Montes Neurophysics Department Cuban Neuroscience Center Source Localization for the EEG and MEG

2. EEG/MEG BET Inverse Problem of the EEG/MEG Prior Information or Constraints AnatomicalMathematical

3. 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.

4. Main difficulties. Geometry. Inhomogeneity. Anisotropy Direct Problem EEG/MEGPCD Model for the head. Piece-wise isotropic and homogeneous Espherical Geometry Realistic Geometry

5. POTENTIAL Maxwell equations + Boundary conditions + 2 nd Green Identity = Fredholm Eq. 2 nd type Drawbacks. Prior Model for DCP. Sensitivity to conductivity ratios Direct Problem LEAD FIELD Reciprocity Theorem = Fredholm Eq. 1 st type k -> lead field Drawbacks. Sensitivity to conductivity ratios Nunez, 1981; Riera and Fuentes, 1998

6. Inverse Problem of the EEG/MEG Continuum: Drawback: The IP has analytical solution only for unrealistically simple head geometries and prior assumptions. Discrete: 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

7. Different 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. Beamformer Christoph et al., 2004

8. What’s wrong with IS methods? 1- Ghost Sources: 2- Bias in the estimation of deep sources:

9. 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.

10. MN Methods: Tikhonov vs Bayes Tikhonov Regularization Bayes Bayesian Model

11. 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

12. Bayesian Framework: First Level Given : Model + Data Infer :

13. Why Bayes Again? It accounts for uncertainty about model form by weighting the conditional posterior densities according to the posterior probabilities of each model.

14. Model Uncertainty: Model 2 Model N Model 1 DATA

15. Bayesian Framework: Second Level AveragingAveraging Model + Data Given :

16. Models and Dimensionality: For 69 compartments

17. What we need to do: 1- Measure the influence of anatomical brain areas in the generation of the EEG/MEG data under consideration 2- Summarize this information in order to obtain realistic posterior estimates of the electric activity inside the brain

18. Simulations (OW): TRUE LORETA BMA

19. Simulations

20. Previous Studies about Visual 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.

21. Visual Steady-State Response BMA: BESA:LORETA

22. Steady-State Somatosensorial:

23. Steady-State Auditivo:

24. 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.

25. 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

26. References 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.