EEG/MEG source reconstruction

1. EEG/MEGsource reconstruction Jérémie Mattout / Christophe Phillips / Karl Friston Wellcome Dept. of Imaging Neuroscience, Institute of Neurology, UCL, London

2. Estimating brain activity from scalp electromagnetic data Sources MEG data Source Reconstruction ‘Equivalent Current Dipoles’ (ECD) ‘Imaging’ EEG data

3. Components of the source reconstruction process Source model ‘ECD’ ‘Imaging’ Forward model Registration Inverse method Data Anatomy

4. Components of the source reconstruction process Forward model Inverse solution Source model Registration

5. Source model Compute transformation T Individual MRI Templates Apply inverse transformation T-1 Individual mesh input functions output • Individual MRI • Template mesh • spatial normalization into MNI template • inverted transformation applied to the template mesh • individual mesh

6. fiducials fiducials Rigid transformation (R,t) Individual sensor space Individual MRI space Registration input functions output • sensor locations • fiducial locations • (in both sensor & MRI space) • individual MRI • registration of the EEG/MEG data into individual MRI space • registrated data • rigid transformation

7. Model of the head tissue properties Individual MRI space Foward model p Compute for each dipole + K n Forward operator functions input output • single sphere • three spheres • overlapping spheres • realistic spheres • sensor locations • individual mesh • forward operator K BrainStorm

8. 1 dipole source per location Y = KJ+ E [nxt] [nxt] [nxp] [pxt] : min( ||Y – KJ||2 + λf(J) ) J J Inverse solution (1) - General principles General Linear Model Cortical mesh n : number of sensors p : number of dipoles t : number of time samples Under-determined GLM ^ Regularized solution data fit priors

9. E1 ~ N(0,Ce) Y = KJ + E1 E2 ~ N(0,Cp) J = 0 + E2 Ce = 1.Qe1 + … + q.Qeq Cp = λ1.Qp1 + … + λk.Qpk Inverse solution (2) - Parametric empirical Bayes 2-level hierarchical model Gaussian variables with unknown variance Gaussian variables with unknown variance Sensor level Source level Linear parametrization of the variances Q: variance components (,λ): hyperparameters

10. Qe1 , … , Qeq + + Model M Qp1 , … , Qpk J K ,λ ^ J = CJKT[Ce + KCJ KT]-1Y Inverse solution (3) - Parametric empirical Bayes Bayesian inference on model parameters Inference on J and (,λ) Maximizing the log-evidence F = log( p(Y|M) ) =  log(p(Y|J,M) ) + log( p(J|M) )dJ data fit priors Expectation-Maximization (EM) E-step: maximizing F wrt J MAP estimate M-step: maximizing of F wrt (,λ) Ce + KCJKT = E[YYT] ReML estimate

11. p(Y|M1) p(Y|M2) B12 = Inverse solution (4) - Parametric empirical Bayes Bayesian model comparison Model evidence • Relevance of model M is quantified by its evidence p(Y|M) maximized by the EM scheme Model comparison • Two models M1 and M2 can be compared by the ratio of their evidence Bayes factor Model selection using a ‘Leaving-one-prior-out-strategy‘

12. ECD approach • iterative forward and inverse computation Inverse solution (5) - implementation input functions output • preprocessed data • - forward operator • individual mesh • priors • - compute the MAP estimate of J • compute the ReML estimate of (,λ) • interpolate into individual MRI voxel-space • inverse estimate • model evidence

13. Conclusion - Summary MRI space Data space Registration Forward model PEB inverse solution EEG/MEG preprocessed data SPM