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. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

3. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

4. EEG/MEG Source localisation Introduction: overview

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

6. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

7. EEG/MEG Source localisation Forward model: formulation Forward model datasource parameters noiseforward operator

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

9. EEG/MEG Source localisation Forward model: imaging/distributed model datadipole amplitudes noisegain matrix

10. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

11. EEG/MEG Source localisation « 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) Inverse problem: an ill-posed problem Inverse problem 1.Existence 2.Unicity 3.Stability

12. 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) 1.Existence 2.Unicity 3.Stability Inverse problem

13. 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) 1.Existence 2.Unicity 3.Stability Inverse problem Introduction of prior knowledge (regularization) is needed

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

15. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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

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

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

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

20. EEG/MEG Source localisation Bayesian inference: model comparison model M i FiFi 1 2 3 At convergence

21. Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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

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

24. EEG/MEG Source localisation Conclusion: Summary Prior information is mandatory EEG/MEG source reconstruction: 1. forward model 2. inverse problem (ill-posed) 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 Forward model Inverse problem

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

26. EEG/MEG Source localisation ECD approach: principle Forward model datadipole parameters noiseforward operator but a priori fixed number of sources considered  iterative fitting of the 6 parameters of each dipole

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

28. EEG/MEG Source localisation ECD solution: “classical” vs. VB approaches “Classical”VB Hard constraintsYes Soft constraintsNoYes Noise accommodation No (in general) Yes Model comparison NoYES

29. EEG/MEG Source localisation 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 ECD solution: when and how to apply VB-ECD?

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

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

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

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

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