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 handbookTodd 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

Source localization as a problem

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Any field potential vector could be consistent with an infinite number of possible dipoles The possibilities only increase with tri-poles and quadra-poles

ERP and MEG give us

And source localization aims to infer + - among

How do we know which one is correct? We can’t. There is no correct answer. We can only see which one is better Can we find the best answer? Source localization is an ILL-DEFINED PROBLEM Only among the alternatives that you have considered.

HUNTING for best possible solution Step ONE: How does your data look like? MEG sensor location MEG data Source Reconstruction Registration

HUNTING for best possible solution If then If then If then If then And on and on and on and … FORWARD MODEL Step Two

HUNTING for best possible solution Forward Model Experimental DATA Which forward solutions fit the DATA better (less error)? Inverse Solution

HUNTING for best possible solution Forward Inverse Solution DATA Iterative Process Until solution stops getting better (error stabilises) iteration error

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

fidloc in MRI space Nasion Left Tragus Right Tragus X X X Y Y Y Z Z Z Nasion Left Tragus Right Tragus 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 Source model Forward model Inverse solution Registration

Source model

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

Scalp Mesh iskull mesh

Components of the source reconstruction process Registration

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

Forward model

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

Inverse solution

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

Inverse solution (2) - Parametric empirical Bayes 2-level hierarchical model E 2 ~ N ( 0,C p ) E 1 ~ N ( 0,C e ) Y = KJ + E 1 J = 0 + E 2 Sensor level Source level Gaussian variables with unknown variance Gaussian variables with unknown variance Linear parametrization of the variances Gaussian variables with unknown variance Gaussian variables with unknown variance C e =  1.Q e 1 + … +  q.Q e q C p = λ 1.Q p 1 + … + λ k.Q p k Q: variance components ( , λ ): hyperparameters Q: variance components ( , λ ): hyperparameters

Inverse solution (3) - Parametric empirical Bayes Bayesian inference on model parameters Inference on J and ( , λ) Model M Q e 1, …, Q e q Q p 1, …, Q p k + JK + ,λ,λ F = log ( p(Y|M) ) =  log ( p(Y|J,M) ) + log ( p(J|M) ) dJ E-step: maximizing F wrt J J = C J K T [C e + KC J K T ] -1 Y ^ M-step: maximizing of F wrt ( , λ) C e + KC J K T = E[YY T ] Maximizing the log-evidence data fitpriors Expectation-Maximization (EM) MAP estimate ReML estimate

Inverse solution (4) - Parametric empirical Bayes Bayesian model comparison B 12 = p(Y|M 1 ) p(Y|M 2 ) Model evidence Relevance of model M is quantified by its evidence p(Y|M) maximized by the EM scheme Model comparison Two models M 1 and M 2 can be compared by the ratio of their evidence Bayes factor Model selection using a ‘Leaving-one-prior-out-strategy‘ Model selection using a ‘Leaving-one-prior-out-strategy‘

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

HUNTING for best possible solution Forward Inverse Solution DATA Iterative Process Until solution stops getting better (error stabilises) iteration error

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:

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

Important! Source model Forward model Inverse solution Registra tion The same for all conditions. Therefore, only done ONCE for each subject Repeated for each condition

Considerations Source localization project is still ongoing Unable to incorporate prior assumptions about source (e.g., from fMRI blobs) Source localization only for conditions Not for contrasts Source localization is a single subject analysis (no way to look at group effects)

Thank you Rimona! Thank you MFD!