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## Source localization for EEG and MEG

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**Source localization for EEG and MEG**Methods for Dummies 2006 FIL Bahador Bahrami**Before we start …**• SPM5 and source localization: • On-going work in progress • MFD and source localization: • This is the first on this topic • Main references for this talk: • Jeremie Mattout’s slides from SPM course • Slotnick S.D. chapter in Todd Handy’s ERP handbook • Rimona Weil’s wonderful help (thanks Rimona!)**Outline**• Theoretical • Source localization stated as a problem • Solution to the problem and their limitations • Practical* • How to prepare data • Which buttons to press • What to avoid • What to expect * Subject to change along with the development of SPM 5**+**-**+**-**+**- + - Any field potential vector could be consistent with an infinite number of possible dipoles The possibilities only increase with tri-poles and quadra-poles**+**- And source localization aims to infer among**+**- + - How do we know which one is correct? We can’t. There is no correct answer. Source localization is an ILL-DEFINED PROBLEM We can only see which one is better Can we find the best answer? Only among the alternatives that you have considered.**MEG sensor location**MEG data HUNTING for best possible solution Step ONE: How does your data look like? Source Reconstruction Registration**If**then If then If then If HUNTING for best possible solution Step Two then FORWARD MODEL And on and on and on and …**HUNTING for best possible solution**Forward Model Experimental DATA Inverse Solution Which forward solutions fit the DATA better (less error)?**error**iteration HUNTING for best possible solution Forward DATA Inverse Solution Iterative Process Until solution stops getting better (error stabilises)**Components of the source reconstruction process**Source model ‘ECD’ ‘Imaging’ Forward model Registration Inverse method Data Anatomy**Recipe for Source localization in SPM5**• Ingredients • MEG converter has given you • .MAT data file (contains experimental data) • sensloc file (sensors locations) • sensorient (sensors orientations) • fidloc(fiducial locations in MEG space) • fidloc in MRI space (we will see shortly) • Structural T1 MRI scan All in the same folder**X**Y Z Nasion Nasion Nasion X Y Z Left Tragus Left Tragus Left Tragus X Y Z Right Tragus Right Tragus Right Tragus fidloc in MRI space Get these using SPM Display button Save it as a MAT file in the same directory as the data**Components of the source reconstruction process**Forward model Inverse solution Source model Registration**Source model**Compute transformation T Individual MRI Templates Apply inverse transformation T-1 Individual mesh functions output • Individual MRI • Template mesh • spatial normalization into MNI template • inverted transformation applied to the template mesh • individual mesh**Scalp Mesh**iskull mesh**Components of the source reconstruction process**Registration**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**Model of the**head tissue properties Individual MRI space Foward model 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**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**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**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**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‘**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**error**iteration HUNTING for best possible solution Forward DATA Inverse Solution Iterative Process Until solution stops getting better (error stabilises)**Types of Analysis**• Evoked • The evoked response is a reproducible response which occurs after each stimulation and is phase-locked with the stimulus onset. • Induced • The induced response is usually characterized in the frequency domain and contrary to the evoked response, is not phased-locked with the stimulus onset. • The evoked response is obtained (on the scalp) as the stimulus or event-locked average over trials. This is then the input data for the 'evoked' case in source reconstruction. • One can also reconstruct the evoked power in some frequency band (over the time window), this is what is obtained when choosing 'both' in source reconstruction. Jeremie says: