Source localization for EEG and MEG. Methods for Dummies 2006 FIL Bahador Bahrami. Before we start …. SPM5 and source localization: Ongoing 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
Methods for Dummies 2006
FIL
Bahador Bahrami
* Subject to change along with the development of SPM 5
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Any field potential vector could be consistent with an infinite number of possible dipoles
The possibilities only increase with tripoles and quadrapoles
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among
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We can’t. There is no correct answer.
Source localization is an ILLDEFINED 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
Step ONE: How does your data look like?
Source Reconstruction
Registration
If
then
If
then
If
then
If
Step Two
then
FORWARD MODEL
And on and on and on and …
Forward Model
Experimental DATA
Inverse Solution
Which forward solutions fit the DATA better (less error)?
error
iteration
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
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
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
Source model
Compute transformation T
Individual MRI
Templates
Apply inverse transformation T1
Individual mesh
functions
output
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
Forward model
Model of the
head tissue properties
Individual MRI space
Foward model
Compute for
each dipole
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K
n
Forward operator
functions
input
output
BrainStorm
Inverse solution
1 dipole source
per location
Y = KJ+ E
[nxt]
[nxt]
[nxp]
[pxt]
: min( Y – KJ2 + 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
Underdetermined 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
2level 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
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+
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 logevidence
F = log( p(YM) ) = log(p(YJ,M) ) + log( p(JM) )dJ
data fit
priors
ExpectationMaximization (EM)
Estep: maximizing F wrt J
MAP estimate
Mstep: maximizing of F wrt (,λ)
Ce + KCJKT = E[YYT]
ReML estimate
p(YM1)
p(YM2)
B12 =
Inverse solution (4)  Parametric empirical Bayes
Bayesian model comparison
Model evidence
Model comparison
Bayes factor
Model selection using a
‘Leavingoneprioroutstrategy‘
ECD approach
Inverse solution (5)  implementation
input
functions
output
error
iteration
Forward
DATA
Inverse Solution
Iterative Process
Until solution stops getting better (error stabilises)
Jeremie says:
Conclusion  Summary
MRI space
Data space
Registration
Forward model
PEB inverse solution
EEG/MEG preprocessed data
SPM
Forward model
Inverse solution
Source model
Registration
Important!
Repeated for each condition
The same for all conditions.
Therefore, only done ONCE for each subject
Thank you MFD!