EEG/MEG Source Localisation

1. EEG/MEG Source Localisation JérémieMattout & Christophe Phillips ? SPM Short Course – Wellcome Trust Centre for Neuroimaging – May 2007

2. EEG/MEG Source localisation Introduction Data Preprocessing Source reconstruction Scalp Data Analysis Statistical Parametric Mapping Dynamic Causal Modelling

3. Forward Computation (K) Inverse Computation EEG/MEG generative model EEG/MEG sources Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods EEG/MEG Source localisation Overview

4. Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods EEG/MEG Source localisation An ill-posed inverse problem • Jacques Hadamard (1865-1963) • Existence • Unicity • 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 ? »

5. Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods EEG/MEG Source localisation An ill-posed inverse problem • Jacques Hadamard (1865-1963) • Existence • Unicity • Stability Prior information is needed

6. ? Likelihood Posterior Priors EEG/MEG Source localisation Bayesian Formulation « 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 ? » Jacques Hadamard Bayes’ Rule Y: data J : sources M: model assumptions Gaussian densities: defined by their means and variances

7. Inversion EEG/MEG Source localisation General procedure

8. EEG/MEG Source localisation User interface File manager Current Analysis Meshing Co-registration Forward computation Inverse solution

9. EEG/MEG Source localisation Anatomical model – Source space Individual cortical mesh MNI Space Canonical mesh Subject’s MRI [Un]-normalising spatial transformation Anatomical warping Cortical mesh

10. EEG/MEG Source localisation Coregistration From Sensor to MRI space EEG fiducials HeadShape Rigid Transformation + Surface Matching Full setup HeadShape MRI derived meshes MEG

11. EEG/MEG sources EEG/MEG Source localisation Forward Computation Computing the operator K # dipoles 1 sphere 3 spheres K # sensors Lead field matrix

12. Head model Mesh shape and size EEG/MEG Source localisation Data Likelihood Linear Generative Model ModelM

13. EEG/MEG Source localisation Priors on the sources Incorporating Multiple Priors # dipoles … # dipoles IID (Minimum Norm) Spatial smoothness (LORETA) Multiple sparse priors (MSP)

14. Head model Mesh shape and size EEG/MEG Source localisation Parametric Empirical Bayesian Inference (I) Hierarchical model ModelMi 2nd Level … … 1st Level Likelihood Prior Posterior Evidence

15. - PEB inference yields posterior estimates: J, C,λandμ - Knowing J and C, Posterior Probability Maps (PPM) can be computed EEG/MEG Source localisation Parametric Empirical Bayesian Inference (II) EM/ReML algorithm M-step E-step ^ ^ ^ ^ ^ ^

16. p(Y|Mi) model Mi 3 1 2 EEG/MEG Source localisation Parametric Empirical Bayesian Inference (III) Model comparison

17. EEG/MEG Source localisation Conclusion First level analysis PEB PPM Second level analysis Individual summary statistics … RFX analysis p < 0.01 uncorrected SPM

18. To be continued…

19. Forward Computation (K) Inverse Computation EEG/MEG generative model EEG/MEG sources EEG/MEG Source localisation ECD approach Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods

20. EEG/MEG Source localisation Y = KJ + E Problem to solve: ECD approach: model • A priori fixed number of sources considered, (usually less than 5) •  over-determined but nonlinear problem • iterative fitting of the 6 parameters of each source K depends on the source location r → non-linear relationship with Y : Y = K(r) J + E J are the source intensity (incl. orientation) → linear relationship with Y, once K is fixed: J = K Y and Y = K J ^ - ^ ^

21. EEG/MEG Source localisation • The iterative optimisation procedure can only find a local minimum • thestarting location(s) used can influence the solution found ! Value of parameter 1D example of optimisation problem: Cost function Local minimum Local minimum Global minimum ECD approach: optimisation

22. EEG/MEG Source localisation ECD approach: results • For an ECD solution, initialise the dipoles • atmultiple random locationsand repeat the fitting procedure  cluster of solutions ? • at a«guessed» solutionspot, • then let the dipole free to move • keep the location fixed (also named « seeded-ECD ») • Eventually, • Simple focused solution: dipole coordinates • Time course of activity for each dipole

23. EEG/MEG Source localisation ECD approach: interpretation and limitation • How many dipoles ?The more sources, the better the fit… in a mathematical sense !!! • (Still the number of sources limited : 6xNs < Ne) • Moreover it is NOT possible to mathematically compare 2 models with different number of sources ! • Is a dipole, i.e. a punctual source, the right model for a patch of activated cortex ? • What about the influence of the noise ? Find the confidence interval. • Is the seeded-ECD a good approach ? Given that you find what you put in…

24. EEG/MEG Source localisation ECD approach: application epilepsy 2D EEG map of first peak, above F4 front L R back

26. EEG/MEG Source localisation Anatomically constrained spherical head models, or pseudo-spherical model. Forward Problem: analytical vs. numerical solution • The head is NOT spherical: •  cannot use the exact analytical solution because of model/anatomical errors. • Realistic model needs BEM solution: •  surfaces extraction •  computationnaly heavy •  errors for superficial sources • Could we combine the advantages of both solutions ?

27. EEG/MEG Source localisation Scalp (or brain) surface Best fitting sphere: centre and radii (scalp, skull, brain) Spherical transformation of source locations Leadfield for the spherical model Anatomically constrained spherical model

28. EEG/MEG Source localisation Anatomically constrained spherical model • Dipole: • defined by its polar coordinates (Rd,IRM, qd, fd ) • Fitted sphere: • defined by its centre and radius, (cSph,RSph) Direction (qd,fd) Fitted sphere Rscalp(qd,fd) Rd,IRM RSph Scalp surface cSph

29. EEG/MEG Source localisation Fitted sphere and scalp surface Application: scalp surface

30. EEG/MEG Source localisation Application: cortical surface

31. EEG/MEG Source localisation

32. EEG/MEG Source localisation Priors on the sources (II) Hyperpriors • Log-normal hyperpriors • Enforces the non-negativity of the scale parameters • Enables Automatic Relevance Determination (ARD)