EEG/MEG Source Localisation

1. EEG/MEG Source Localisation SPM Course – Wellcome Trust Centre for Neuroimaging – Oct. 2008 ? Jérémie Mattout, Christophe Phillips Jean Daunizeau Guillaume Flandin Karl Friston Rik Henson Stefan Kiebel Vladimir Litvak

2. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

3. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

4. EEG/MEG Source localisation Introduction: overview

5. Forward model Inverse problem EEG/MEG source reconstruction process EEG/MEG Source localisation Introduction: overview

6. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

7. Forward model EEG/MEG Source localisation Forward model: formulation data forward operator source parameters noise

8. EEG/MEG Source localisation Forward model: source space source biophysical model: current dipole Imaging or Distributed Equivalent Current Dipoles (ECD) EEG/MEG source models • many dipoles with • fixed location and orientation • few dipoles with • free location and orientation

9. EEG/MEG Source localisation Forward model: imaging/distributed model data gain matrix dipole amplitudes noise

10. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

11. Inverse problem EEG/MEG Source localisation Inverse problem: an ill-posed problem « 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 (1865-1963) • Existence • Unicity • Stability

12. Inverse problem EEG/MEG Source localisation Inverse problem: an ill-posed problem « 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 (1865-1963) • Existence • Unicity • Stability

13. Inverse problem EEG/MEG Source localisation Inverse problem: an ill-posed problem « 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 (1865-1963) • Existence • Unicity • Stability Introduction of prior knowledge (regularization) is needed

14. Spatial and temporal priors Adequacy with other modalities Data fit EEG/MEG Source localisation Inverse problem: regularization data fit prior (regularization term) W = I : minimum norm W =Δ : maximum smoothness (LORETA)

15. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

16. Forward model Inverse problem posterior EEG/MEG Source localisation Bayesian inference: probabilistic formulation likelihood posterior likelihood prior evidence

17. EEG/MEG Source localisation Bayesian inference: hierarchical linear model sensor (1st) level likelihood source (2nd) level prior Q : (known) variance components (λ,μ) : (unknown) hyperparameters

18. EEG/MEG Source localisation Bayesian inference: variance components # dipoles … # dipoles Minimum Norm (IID) Maximum Smoothness (LORETA) Multiple Sparse Priors (MSP)

19. EEG/MEG Source localisation Bayesian inference: iterative estimation scheme Expectation-Maximization (EM) algorithm E-step estimate while keeping constants M-step estimate while keeping constants

20. Fi model Mi 3 1 2 EEG/MEG Source localisation Bayesian inference: model comparison At convergence

21. EEG/MEG Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

22. EEG/MEG Source localisation Conclusion: At the end of the day... Bilateral auditory tone Somesthesic data

23. Individual reconstructions in MRI template space L R Group results p < 0.01 uncorrected R L EEG/MEG Source localisation Conclusion: At the group level...

24. Forward model Inverse problem EEG/MEG Source localisation Conclusion: Summary • EEG/MEG source reconstruction: 1. forward model 2. inverse problem (ill-posed) • Prior information is mandatory • Bayesian inference is used to: 1. incorpoate such prior information… 2. … and estimating their weight w.r.t the data 3. provide a quantitative feedback on model adequacy

25. EEG/MEG Source localisation Equivalent Current Dipole (ECD) solution source biophysical model: current dipole few dipoles with free location and orientation many dipoles with fixed location and orientation Imaging or Distributed Equivalent Current Dipoles (ECD) EEG/MEG source models

26. Forward model EEG/MEG Source localisation ECD approach: principle data forward operator dipole parameters noise buta priori fixed number of sources considered  iterative fitting of the 6 parameters of each dipole

27. EEG/MEG Source localisation ECD solution: variational Bayes (VB) approach Dipole J with location s and moment w generated data Yusing Eis white observation noise with precision γy. The locations s and moments w are drawn from normal distributions with precisions γs and γw. These are drawn from a prior gamma distribution.

28. EEG/MEG Source localisation ECD solution: “classical” vs. VB approaches

29. EEG/MEG Source localisation ECD solution: when and how to apply VB-ECD? • can be applied to single time-slice data or average over time (MEG and EEG) • useful for comparing several few-dipole solutions for selected time points (N100, N170, etc.) • although not dynamic, can be used for building up intuition about underlying generators, or using as a motivation for DCM source models • implemented in Matlab and available in SPM8b

30. ERP data over 64 channels VB-ECD solution Scalp distribution, 21ms post-stimulus EEG/MEG Source localisation Example 1: somestesic stimulation

31. Oddball stimuli Standard stimuli EEG/MEG Source localisation Example 2: auditory oddball Scalp potential for auditory stimulations

32. EEG/MEG Source localisation Main references Litvak and Friston (2008) Electromagnetic source reconstruction for group studies Friston et al. (2008) Multiple sparse priors for the M/EEG inverse problem Kiebel et al. (2008) Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG Mattout et al. (2007) Canonical Source Reconstruction for MEG Daunizeau and Friston (2007) A mesostate-space model for EEG and MEG Henson et al. (2007) Population-level inferences for distributed MEG source localization under multiple constraints: application to face-evoked fields Friston et al. (2007) Variational free energy and the Laplace approximation Mattout et al. (2006) MEG source localization under multiple constraints Friston et al. (2006) Bayesian estimation of evoked and induced responses Phillips et al. (2005) An empirical Bayesian solution to the source reconstruction problem in EEG

33. EEG/MEG Source localisation

34. EEG/MEG Source localisation Bayesian inference: multiple sparse priors • Log-normal hyperpriors • Enforces the non-negativity of the hyperparameters • Enables Automatic Relevance Determination (ARD)

35. EEG/MEG Source localisation Forward model: canonical mesh MNI Space Canonical mesh Subjects MRI [Un]-normalising spatial transformation Anatomical warping Cortical mesh

36. EEG/MEG Source localisation Forward model: coregistration From Sensor to MRI space EEG HeadShape + Surface Matching Rigid Transformation Full setup HeadShape MRI derived meshes MEG