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

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

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

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

Source model Compute transformation T Apply inverse transformation T-1 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

Registration Rigid transformation (R,t) Individual MRI space fiducials Individual sensor space fiducials Rigid transformation (R,t) 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

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

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

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

+ Inverse solution (3) - Parametric empirical Bayes Qe1 , … , Qeq Bayesian inference on model parameters Model M Qe1 , … , Qeq Qp1 , … , Qpk + J K ,λ 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) J = CJKT[Ce + KCJ KT]-1Y ^ E-step: maximizing F wrt J MAP estimate M-step: maximizing of F wrt (,λ) Ce + KCJKT = E[YYT] ReML estimate

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 B12 = p(Y|M1) p(Y|M2) Bayes factor Model selection using a ‘Leaving-one-prior-out-strategy‘

Inverse solution (5) - implementation input functions output iterative forward and inverse computation ECD approach 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

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