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) EEG data ‘Imaging’ 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 Individual MRI Templates Apply inverse transformation T-1 Individual mesh input - Individual MRI - Template mesh functions - spatial normalization into MNI template - inverted transformation applied to the template mesh output - individual mesh Registration fiducials fiducials Rigid transformation (R,t) Individual sensor space Individual MRI space input - sensor locations - fiducial locations (in both sensor & MRI space) - individual MRI functions - registration of the EEG/MEG data into individual MRI space output - registrated data - rigid transformation Foward model p Compute for each dipole K + n Forward operator Individual MRI space Model of the head tissue properties functions input - sensor locations - individual mesh - single sphere - three spheres - overlapping spheres - realistic spheres BrainStorm output - forward operator K Inverse solution (1) - General principles General Linear Model 1 dipole source per location Cortical mesh Under-determined GLM Regularized solution Y = KJ+ E [nxt] [nxp][pxt] [nxt] n : number of sensors p : number of dipoles t : number of time samples ||Y – KJ||2 + λf(J) ) J^ : min( J data fit priors Inverse solution (2) - Parametric empirical Bayes 2-level hierarchical model Gaussian Gaussian variables variables with with unknown unknown variance variance Y = KJ + E1 E1 ~ N(0,Ce) J = 0 + E2 Sensor level E2 ~ N(0,Cp) Source level Linear parametrization of the variances Ce = 1.Qe1 + … + q.Qeq Cp = λ1.Qp1 + … + λk.Qpk Q: variance components (,λ): hyperparameters Inverse solution (3) - Parametric empirical Bayes Bayesian inference on model parameters + Model M + J Q e1 , … , Q eq Qp1 , … , Qpk ,λ K 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 M-step: maximizing of F wrt (,λ) J^ = CJKT[Ce + KCJ KT]-1Y MAP estimate 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 - preprocessed data - forward operator - individual mesh - priors functions - compute the MAP estimate of J - compute the ReML estimate of (,λ) - interpolate into individual MRI voxel-space ECD approach - iterative forward and inverse computation output - inverse estimate - model evidence Conclusion - Summary MRI space Data space Registration Forward model EEG/MEG preprocessed data PEB inverse solution SPM