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:

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Source localization for EEG and MEG

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Source localization for eeg and meg

Source localization for EEG and MEG

Methods for Dummies 2006

FIL

Bahador Bahrami


Before we start

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

    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

    Source localization as a problem


    Source localization for eeg and meg

    +

    -


    Source localization for eeg and meg

    +

    -


    Source localization for eeg and meg

    +

    -

    +

    -

    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

    ERP and MEG give us


    And source localization aims to infer

    +

    -

    And source localization aims to infer

    among


    How do we know which one is correct

    +

    -

    +

    -

    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.


    Hunting for best possible solution

    MEG sensor location

    MEG data

    HUNTING for best possible solution

    Step ONE: How does your data look like?

    Source Reconstruction

    Registration


    Hunting for best possible solution1

    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 solution2

    HUNTING for best possible solution

    Forward Model

    Experimental DATA

    Inverse Solution

    Which forward solutions fit the DATA better (less error)?


    Hunting for best possible solution3

    error

    iteration

    HUNTING for best possible solution

    Forward

    DATA

    Inverse Solution

    Iterative Process

    Until solution stops getting better (error stabilises)


    Source localization for eeg and meg

    Components of the source reconstruction process

    Source model

    ‘ECD’

    ‘Imaging’

    Forward model

    Registration

    Inverse method

    Data

    Anatomy


    Recipe for source localization in spm5

    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

    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


    Source localization for eeg and meg

    Components of the source reconstruction process

    Forward model

    Inverse solution

    Source model

    Registration


    Source localization for eeg and meg

    Source model


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    Scalp Mesh

    iskull mesh


    Source localization for eeg and meg

    Components of the source reconstruction process

    Registration


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    Forward model


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    Inverse solution


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    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


    Source localization for eeg and meg

    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‘


    Source localization for eeg and meg

    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


    Hunting for best possible solution4

    error

    iteration

    HUNTING for best possible solution

    Forward

    DATA

    Inverse Solution

    Iterative Process

    Until solution stops getting better (error stabilises)


    Types of analysis

    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:


    Source localization for eeg and meg

    Conclusion - Summary

    MRI space

    Data space

    Registration

    Forward model

    PEB inverse solution

    EEG/MEG preprocessed data

    SPM


    Source localization for eeg and meg

    Forward model

    Inverse solution

    Source model

    Registration

    Important!

    Repeated for each condition

    The same for all conditions.

    Therefore, only done ONCE for each subject


    Considerations

    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 Rimona!

    Thank you MFD!


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