1. EEG/MEG Source Localisation
SPM Short Course – Wellcome Trust Centre for Neuroimaging – May 2008 ?
Jérémie Mattout, Christophe Phillips
Jean Daunizeau
Guillaume Flandin
Karl Friston
Rik Henson
Stefan Kiebel
Vladimir Litvak

2. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

3. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

4. Introduction: EEG/MEG as Neuroimaging techniques
Source localisation
Introduction: EEG/MEG as Neuroimaging techniques
MRI
EEG
MEG
spatial resolution (mm)
invasivity
weak
strong 5 10 15 20
temporal resolution (ms) 1
102
103
104
105
sEEG
MEG
EEG
fMRI
MRI(a,d)
PET
SPECT OI OI

5. Data importation/convertion
EEG/MEG
Source localisation
MEEG functionalities in SPM8
Data Preperation
Data importation/convertion
Import most common MEG/EEG data formats into one single data format
Include “associated data”, e.g. electrode location and sensor setup
New MEEG data
format based on
“object-oriented”
coding
More stable interfacing and user-friendly 
and a bit harder for developers  5

6. “Usual“ preprocessing
EEG/MEG
Source localisation
MEEG functionalities in SPM8
Data Preperation
“Usual“ preprocessing
Filtering
Re-referencing
Epoching
Artefact and bad channel rejection
Averaging
Displaying … 6

7. MEEG functionalities in SPM8
EEG/MEG
Source localisation
MEEG functionalities in SPM8
Data Preprocessing
Source reconstruction
Scalp Data Analysis
Statistical Parametric Mapping
Dynamic Causal Modelling 7

8. MEEG “usual” results MEG experiment of Face perception4 EEG/MEG
Source localisation
MEEG “usual” results
MEG experiment
of Face perception4
100
200
300
400
time (ms)
Right temporal evoked signal
faces
scrambled
M170
Energy changes (Faces - Scrambled, p<0.01)
0.1
0.2
0.4
0.6
0.8
time (s) 10 20 30 40 35 45 15 25
0.7
0.5
0.3
-0.1 1 2 3 -2 -3 -1
frequency (Hz)
4Electrophysiology and haemodynamic correlates of face perception, recognition and priming, R.N. Henson, Y. Goshen-Gottstein, T. Ganel, L.J. Otten, A. Quayle, M.D. Rugg, Cereb. Cortex, 2003.

9. EEG/MEG
Source localisation
Change speaker… 9

10. Introduction: overview
EEG/MEG
Source localisation
Introduction: overview
EEG/MEG source reconstruction process
Forward
model
Inverse
problem

11. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

12. Forward model: source space
EEG/MEG
Source localisation
Forward model: source space
source biophysical model: current dipole
EEG/MEG source models
Equivalent
Current
Dipoles (ECD)
Imaging or
Distributed
few dipoles with
free location and orientation
many dipoles with
fixed location and orientation

13. Forward model: formulation
EEG/MEG
Source localisation
Forward model: formulation
Forward
model
data
forward
operator
dipole
parameters
noise

14. Forward model: imaging/distributed model
EEG/MEG
Source localisation
Forward model: imaging/distributed model
data
gain matrix
dipole
amplitudes
noise

15. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

16. Inverse problem: an ill-posed problem
EEG/MEG
Source localisation
Inverse problem: an ill-posed problem
« Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? »
Jacques Hadamard ( )
Existence
Unicity
Stability
Inverse
problem

17. Inverse problem: an ill-posed problem
EEG/MEG
Source localisation
Inverse problem: an ill-posed problem
« Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? »
Jacques Hadamard ( )
Existence
Unicity
Stability
Inverse
problem

18. Inverse problem: an ill-posed problem
EEG/MEG
Source localisation
Inverse problem: an ill-posed problem
« Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? »
Jacques Hadamard ( )
Existence
Unicity
Stability
Inverse
problem
Introduction of prior knowledge (regularization) is needed

19. (regularization term)
EEG/MEG
Source localisation
Inverse problem: regularization
Data fit
Adequacy
with other
modalities
Spatial and
temporal priors
data fit
prior
(regularization term)
W = I : minimum norm
W = Δ : maximum smoothness (LORETA)

20. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

21. Bayesian inference: probabilistic formulation
EEG/MEG
Source localisation
Bayesian inference: probabilistic formulation
Forward
model
likelihood
Inverse
problem
posterior
likelihood
prior
posterior
evidence

22. Bayesian inference: hierarchical linear model
EEG/MEG
Source localisation
Bayesian inference: hierarchical linear model
source (2nd) level
sensor (1st) level
likelihood
prior
Q : (known) variance components
(λ,μ) : (unknown) hyperparameters

23. Multiple Sparse Priors
EEG/MEG
Source localisation
Bayesian inference: variance components
# dipoles
Minimum Norm
(IID)
Maximum Smoothness
(LORETA)
Multiple Sparse Priors
(MSP) …

24. Y J μ1 μq λ1 λk Bayesian inference: graphical representation EEG/MEG
Source localisation
Bayesian inference: graphical representation Y J μ1 μq λ1 λk
prior
likelihood

25. Bayesian inference: iterative estimation scheme
EEG/MEG
Source localisation
Bayesian inference: iterative estimation scheme
Expectation-Maximization (EM) algorithm
E-step
M-step

26. Bayesian inference: model comparison
EEG/MEG
Source localisation
Bayesian inference: model comparison
At convergence
model Mi Fi 1 2 3

27. Outline EEG/MEG Introduction Forward model Inverse problem
Source localisation
Outline
Introduction
Forward model
Inverse problem
Bayesian inference applied to the EEG/MEG inverse problem
Conclusion

28. Conclusion: At the end of the day...
EEG/MEG
Source localisation
Conclusion: At the end of the day... R L
Individual reconstructions in MRI template space
Group results
p < 0.01 uncorrected R L

29. Conclusion: Summary EEG/MEG • EEG/MEG source reconstruction:
Source localisation
Conclusion: Summary
Forward
model
Inverse
problem
• EEG/MEG source reconstruction:
1. forward model
2. inverse problem (ill-posed)
• Prior information is mandatory
• Bayesian inference is used to:
1. incorpoate such prior information…
2. … and estimating their weight w.r.t the data
3. provide a quantitative feedback on model adequacy

30. EEG/MEG
Source localisation
Change speaker…
Again !

31. Equivalent Current Dipole (ECD) solution
EEG/MEG
Source localisation
Equivalent Current Dipole (ECD) solution
source biophysical model: current dipole
EEG/MEG source models
Equivalent
Current
Dipoles (ECD)
Imaging or
Distributed
few dipoles with free location and orientation
many dipoles with fixed location and orientation

32. but a priori fixed number of sources considered
EEG/MEG
Source localisation
ECD approach: principle
Forward
model
data
forward
operator
dipole
parameters
noise
but a priori fixed number of sources considered
 iterative fitting of the 6 parameters of each dipole 32

33. ECD solution: variational Bayes (VB) approach
EEG/MEG
Source localisation
ECD solution: variational Bayes (VB) approach
Dipole locations s and dipole moments w generated data using
ε is white observation noise
with precision γy.
The locations s and moments w are
drawn from normal distributions with
precisions γs and γw.
These are drawn from a prior gamma distribution. 33

34. “Classical” VB ECD solution: “classical” vs. VB approaches
EEG/MEG
Source localisation
ECD solution: “classical” vs. VB approaches
“Classical” VB
Hard constraints
Yes
Soft constraints No
Noise accommodation
(in general)
Model comparison
YES 34

35. ECD solution: when and how to apply VB-ECD?
EEG/MEG
Source localisation
ECD solution: when and how to apply VB-ECD?
can be applied to single time-slice data or average over time (MEG and EEG)
useful for comparing several few-dipole solutions for selected time points (N100, N170, etc.)
although not dynamic, can be used for building up intuition about underlying generators, or using as a motivation for DCM source models
implemented in Matlab and (very soon) available in SPM8 35

36. EEG/MEG
Source localisation 36

37. Bayesian inference: multiple sparse priors
EEG/MEG
Source localisation
Bayesian inference: multiple sparse priors
Log-normal hyperpriors
Enforces the non-negativity of the hyperparameters
Enables Automatic Relevance Determination (ARD)

38. spatial transformation
EEG/MEG
Source localisation
Forward model: canonical mesh
MNI Space
Canonical
mesh
Subjects
MRI
[Un]-normalising
spatial transformation
Anatomical warping
Cortical
mesh

39. Forward model: coregistration
EEG/MEG
Source localisation
Forward model: coregistration
From Sensor to MRI space
HeadShape
Surface
Matching +
EEG
Rigid
Transformation
Full setup
MRI derived meshes
MEG

40. Main references EEG/MEG
Source localisation
Main references
Friston et al. (2008) Multiple sparse priors for the M/EEG inverse problem
Kiebel et al. (2008) Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG
Mattout et al. (2007) Canonical Source Reconstruction for MEG
Daunizeau and Friston (2007) A mesostate-space model for EEG and MEG
Henson et al. (2007) Population-level inferences for distributed MEG source localization under multiple constraints: application to face-evoked fields
Friston et al. (2007) Variational free energy and the Laplace approximation
Mattout et al. (2006) MEG source localization under multiple constraints
Friston et al. (2006) Bayesian estimation of evoked and induced responses
Phillips et al. (2005) An empirical Bayesian solution to the source reconstruction problem in EEG