1. M/EEG Analysis in SPM Rik Henson (MRC CBU, Cambridge)
Jeremie Mattout, Christophe Phillips, Stefan Kiebel, Olivier David, Vladimir Litvak, ... & Karl Friston (UCL, London)

2. Overview
As in the spirit of this talk series about Statistical Parametric Mapping, this talk is only about localising experimental M/EEG effects in space (sensors or sources) and/or time...
[plus a few words about testing effective connectivity]
...it does not review all the other types of analyses and information one can obtain from M/EEG...
...and nor does it cover M/EEG preprocessing (epoching, filtering, averaging, time-freq transformations, etc), since these procedures are fairly standard nowadays

3. Overview Random Field Theory for Space-Time images
Empirical Bayesian approach to the Inverse Problem
A Canonical Cortical mesh and Group Analyses
[ Dynamic Causal Modelling (DCM) ]

4. 1. Localising in Space/Freq/Time
Random Field Theory is a method for correcting for multiple statistical comparisons with N-dimensional spaces (for parametric statistics, eg Z-, T-, F- statistics)
When is there an effect in time, eg GFP (1D)?
Where is there an effect in time-frequency space (2D)?
Where is there an effect in time-sensor space (3D)?
Where is there an effect in time-source space (4D)?
Worsley Et Al (1996). Human Brain Mapping, 4:58-73

5. Where is an effect in time-sensor space (3D)?
F-statistic for ANOVA across EEG subjects (Henson et al, 2008, Neuroimage)
MEG data first requires sensor-level realignment, using e.g, SSS...
SPM{F}
Taylor & Henson (2008) Biomag

6. 1. Localising in Space/Freq/Time
Extended to 2D cortical mesh surface
RFT generally requires Gaussian smoothing, but exerts exact FWE control for sufficient smoothing
Nonparametric (permutation) methods of FWE control make fewer distributional assumptions (do not require smoothing), but do require exchangeability
Pantazis Et Al (2005) NeuroImage, 25:

7. Overview Random Field Theory for Space-Time images
Empirical Bayesian approach to the Inverse Problem
A Canonical Cortical mesh and Group Analyses
[ Dynamic Causal Modelling (DCM) ]

8. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

9. Weighted Minimum Norm, Regularisation
Linear system to be inverted:
Y = Data, n sensors x t=1 time-samples
J = Sources, p sources x t time-samples
L = Forward model, n sensors x p sources
E = Multivariate Gaussian noise, n x t
Ce= error covariance over sensors
Since n<p, need to regularise, eg “weighted minimum (L2) norm” (WMN):
(Tikhonov)
W = Weighting matrix
W = I minimum norm
W = DDT coherent
W = diag(LTL) depth-weighted
Wp = (LpTCy-1Lp) SAM
W = … ….
“L-curve” method
||Y – LJ||2
||WJ||2
= regularisation
(hyperparameter)
Phillips Et Al (2002) Neuroimage, 17, 287–301

10. Equivalent Bayesian Formulation
Equivalent “Parametric Empirical Bayes” formulation:
Y = Data, n sensors x t=1 time-samples
J = Sources, p sources x t time-samples
L = Forward model, n sensors x p sources
C(e) = covariance over sensors
C(j) = covariance over sources
Posterior is product of likelihood and prior:
W = Weighting matrix
W = I minimum norm
W = DDT coherent
W = diag(LTL) depth-weighted
Wp = (LpTCy-1Lp) SAM
W = … ….
Maximal A Posteriori (MAP) estimate is:
(Contrasting with Tikhonov):
Phillips Et Al (2005) Neuroimage,

11. Covariance Constraints (Priors)
How parameterise C(e) and C(j)?
“IID” constraint on sensors (Q(e)=I(n))
# sensors
Q = (co)variance components (Priors)
λ = estimated hyperparameters
Sparse priors on sources (Q1(j), Q2(j), …) …
# sources
# sources
“IID” constraint on sources (Q(j)=I(p))

12. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

13. Expectation-Maximisation (EM)
How estimate λ? …. Use EM algorithm:
…to maximise the (negative) “free energy” (F):
(Note estimation in nxn sensor space)
Once estimated hyperparameters (iterated M-steps), get MAP for parameters (single E-step):
(Can also estimate conditional covariance of parameters, allowing inference:)
Phillips et al (2005) Neuroimage

14. Multiple Constraints (Priors)
Multiple constraints: Smooth sources (Qs), plus valid (Qv) or invalid (Qi) focal prior Qs Qs
Qs,Qv
500 simulations
Qs,Qi
Qs,Qi,Qv
500 simulations Qv Qi
Mattout Et Al (2006) Neuroimage,

15. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

16. Model Evidence Friston Et Al (2007) Neuroimage, 34, 220-34
A (generative) model, M, is defined by the set of {Q(e), Q(j), L}:
The “model log-evidence” is bounded by the free energy:
Friston Et Al (2007) Neuroimage, 34,
(F can also be viewed the difference of an “accuracy” term and a “complexity” term):
Two models can be compared using the “Bayes factor”:
Also useful when comparing different forward models, ie L’s, Henson et al (2009b), NI

17. Model Comparison (Bayes Factors)
Multiple constraints: Smooth sources (Qs), plus valid (Qv) or invalid (Qi) focal prior
Log-Evidence
Bayes Factor Qs
205.2
7047
1.8
(1/9899)
Qs,Qv
214.1
Qs,Qv,Qi
214.7
(Qs,Qi)
204.9 Qs Qv Qi
Mattout Et Al (2006) Neuroimage,

18. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

19. Temporal Correlations
To handle temporally-extended solutions, first assume temporal-spatial factorisation:
Y = vectorised data, nt x 1
C(e) = spatial error covariance over sensors
V(e)= temporal error covariance over sensors
C(j) = spatial error covariance over sources
V(j) = temporal error covariance over sources ~
In general, temporal correlation of signal (sources) and noise (sensors) will differ, but can project onto a temporal subspace (via S) such that:
Friston Et Al (2006) Human Brain Mapping, 27:722–735
V typically Gaussian autocorrelations…
S typically an SVD into Nr temporal modes…
Then turns out that EM can simply operate on prewhitened data (covariance), where Y size n x t:

20. Localising Power (eg induced)
Friston Et Al (2006) Human Brain Mapping, 27:722–735

21. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

22. Automatic Relevance Detection (ARD)
When have many constraints (Q’s), pairwise model comparison becomes arduous
Moreover, when Q’s are correlated, F-maximisation can be difficult (eg local maxima), and hyperparameters can become negative (improper for covariances)
Note: Even though Qs may be uncorrelated in source space, they can become correlated when projected through L to sensor space (where F is optimised)
Prestim Baseline
Anti-Averaging
Smoothness
Depth-Weighting
Sensor-level
Source-level
Henson Et Al (2007) Neuroimage, 38,

23. Automatic Relevance Detection (ARD)
When have many constraints (Q’s), pairwise model comparison becomes arduous
Moreover, when Q’s are correlated, F-maximisation can be difficult (eg local maxima), and hyperparameters can become negative (improper for covariances)
To overcome this, one can:
1) impose positivity constraint on hyperparameters:
2) impose (sparse) hyperpriors on the (log-normal) hyperparameters:
Uninformative priors are then “turned-off” as (“ARD”)
Complexity
(…where η and Σλ are the posterior mean and covariance of hyperparameters)

24. Automatic Relevance Detection (ARD)
When have many constraints (Q’s), pairwise model comparison becomes arduous
Moreover, when Q’s are correlated, F-maximisation can be difficult (eg local maxima), and hyperparameters can become negative (improper for covariances)
Prestim Baseline
Anti-Averaging
Smoothness
Depth-Weighting
Sensor-level
Source-level
Henson Et Al (2007) Neuroimage, 38,

25. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

26. Multiple Sparse Priors (MSP)
So why not use ARD to select from a large number of sparse source priors….!?
Q(2)1 …
Q(2)N
Q(2)j
Left patch …
Q(2)j+1
Right patch …
Q(2)j+2
Bilateral patches … …
Friston Et Al (2008) Neuroimage

27. Multiple Sparse Priors (MSP)
So why not use ARD to select from a large number of sparse source priors….!
Friston Et Al (2008) Neuroimage
No depth bias!

28. 2. Parametric Empirical Bayes (PEB)
Weighted Minimum Norm & Bayesian equivalent
EM estimation of hyperparameters (regularisation)
Model evidence and Model Comparison
Spatiotemporal factorisation and Induced Power
Automatic Relevance Detection (hyperpriors)
Multiple Sparse Priors
MEG and EEG fusion (simultaneous inversion)

29. Fusion of MEG/EEG Henson Et Al (2009a), Neuroimage
Separate Error Covariance components for each of i=1..M modalities (Ci(e)):
Data and leadfields scaled
(with mi spatial modes):
Henson Et Al (2009a), Neuroimage

30. Fusion of MEG/EEG + Fused Henson Et Al (2009a), Neuroimage
Magnetometers (MEG)
Gradiometers (MEG)
Electrodes (EEG)
+ Fused
Henson Et Al (2009a), Neuroimage

31. Overview Random Field Theory for Space-Time images
Empirical Bayesian approach to the Inverse Problem
A Canonical Cortical mesh and Group Analyses
[ Dynamic Causal Modelling (DCM) ]

32. 3. Canonical Mesh & Group Analyses
A “canonical” (Inverse-normalised) cortical mesh
Group analyses in 3D
Use of fMRI spatial priors (in MNI space)
Group-based inversions

33. A “Canonical” Cortical Mesh
Given the difficulty in (automatically) creating accurate cortical meshes from MRIs, how about inverse-normalising a (quality) template mesh in MNI space?
Original
MRI
Spatial Normalisation
Normalised
MRI
Ashburner & Friston (2005) Neuroimage
Warps…
Template
MRI
(in “MNI”
space)

34. A “Canonical” Cortical Mesh
Individual
Canonical
Template
N=1
Apply inverse of warps from spatial normalisation of whole MRI to a template cortical mesh…
“Canonical”
Mattout Et Al (2007) Comp. Intelligence & Neuroscience

35. A “Canonical” Cortical Mesh
But warps from cortex not appropriate to skull/scalp, so use individually (and easily) defined skull/scalp meshes…
Free Energy/104
N=9
Canonical Cortex
Individual Skull
Individual Scalp
CanInd
Statistical tests of model evidence over N=9 MEG subjects show:
MSP > MMN
BEMs > Spheres (for CanInd)
(7000 > 3000 dipoles)
(Normal > Free for MSP)
Henson Et Al (2009b), Neuroimage

36. 3. Canonical Mesh & Group Analyses
A “canonical” (Inverse-normalised) cortical mesh
Group analyses in 3D
Use of fMRI spatial priors (in MNI space)
Group-based inversions

37. Group Analyses in 3D Taylor & Henson (2008), Biomag
Once have a 1-to-1 mapping from M/EEG source to MNI space, can create 3D normalised images (like fMRI) and use SPM machinery to perform group-level classical inference…
N=19, MNI space, Pseudowords>Words
ms with >95% probability
Smoothed,
Interpolated J
Taylor & Henson (2008), Biomag

38. 3. Canonical Mesh & Group Analyses
A “canonical” (Inverse-normalised) cortical mesh
Group analyses in 3D
Use of fMRI spatial priors (in MNI space)
Group-based inversions

39. fMRI spatial priors Human Brain Mapping Henson Et Al (2010)
Group fMRI results in MNI space can be used as spatial priors on individual source space...
...importantly each fMRI cluster is separate prior, so is “weighted” independently …
Thresholding and connected component labelling
Project onto cortical surface using Voronoï diagram …
Human Brain Mapping
Henson Et Al (2010) …
Prior covariance components

40. 3. Canonical Mesh & Group Analyses
A “canonical” (Inverse-normalised) cortical mesh
Group analyses in 3D
Use of fMRI spatial priors (in MNI space)
Group-based inversions

41. Group-based source priors
Concatenate data and leadfields over i=1..s subjects…
…projecting data and leadfields to a reference subject via A:
Common source-level priors:
Subject-specific sensor-level priors:
Litvak & Friston (2008), Neuroimage; Henson et al (2011), Frontiers

42. Group-based source priors
Litvak & Friston (2008), Neuroimage; Henson et al (2011), Frontiers

43. Group-based source priors
N=19, MNI space, Pseudowords>Words, ms with >95% probability
Group Inversion
Individual Inversions
Taylor & Henson (in prep)

44. Summary
SPM also implements Random Field Theory for principled correction of multiple comparisons over space/time/freq
SPM implements a variant of the L2-distributed norm that:
effectively automatically “regularises” in principled fashion
allows for multiple constraints (priors), valid & invalid
allows model comparison, or automatic relevance detection…
…to the extent that multiple (100’s) of sparse priors possible
also offers a framework for MEG+EEG fusion
SPM can also inverse-normalise a template cortical mesh that:
obviates manual cortex meshing
allows use of fMRI priors in MNI space
allows using group constraints on individual inversions

45. Overview Random Field Theory for Space-Time images
Empirical Bayesian approach to the Inverse Problem
A Canonical Cortical mesh and Group Analyses
Dynamic Causal Modelling (DCM)

46. Functional vs Effective Connectivity
Correlations:
A B C 1
0.49 1
B and C correlated because of common input from A, eg:
A = time-series
B = 0.5 * A + e1
C = 0.3 * A + e2 B
0.49
0.31
Effective connectivity
Functional connectivity A
-0.02
2=0.5, ns. C
Effective connectivity is model-dependent…
Real interest is changes in effective connectivity induced by (experimental) inputs

47. Basic DCM Approach 1. Neural dynamics 2. Observer function
Design experimental inputs
1. Neural dynamics
Define likelihood model
2. Observer function
Specify priors
Inference on models
Inference on parameters
Invert model
Make inferences

48. inhibitory interneurons
1. Neural Dynamics
Extrinsic
forward connections
Extrinsic backward connections
Intrinsic connections
Extrinsic lateral connections
Jansen & Rit (1995)
spiny stellate cells
inhibitory interneurons
pyramidal cells
David et al. (2006) NeuroImage

49. B A C 2. Observer Model y1 y2 Kiebel et al. (2006) NeuroImage
Measurements assumed to reflect currents in (large) pyramidal cells (x0) B A
One option is a small number of “equivalent current dipoles” (ECDs) C
Fix their locations, but allow orientations to be estimated as 3 parameters (q) y1 y2
Kiebel et al. (2006) NeuroImage

50. EEG example: MisMatch Negativity (MMN)
standards
deviants
Standards
(1kHz)
Deviants
(2kHz)
HEOG
VEOG
“MMN” = deviants – standards A1
STG
IFG
Doeller et al., 2003
=>Seed 5 ECDs
Garrido et al. (2007) NeuroImage

51. EEG example: MisMatch Negativity (MMN)
log evidence
subjects
Forward (F)
Backward (B)
Forward and Backward (FB)
IFG
IFG
IFG -
STG
STG
STG
STG
STG
STG A1 A1 A1 A1 A1 A1
input
input
input
Forward
Forward
Forward
Backward
Backward
Backward
Lateral
Lateral
Lateral
Garrido et al. (2007) NeuroImage

52. EEG example: MisMatch Negativity (MMN)
MisMatch reflects changes in forward and backward connections:
Invalid top-down predictions fail to suppress bottom-up prediction error?
Group-based posterior densities of connections in FB model:
IFG
0.93 (55%)
1.41 (99%)
STG
STG
frontal cortex
auditory cortex
prediction error
prediction
2.41 (100%)
4.50 (100%)
1.74 (96%)
5.40 (100%) A1 A1
Forward
Backward
Lateral
input
Garrido et al. (2007) NeuroImage

53. The End (Really)

54. If want to try… http://www.fil.ion.ucl.ac.uk/spm
SPM5 Manual (…/spm5/man/manual.pdf)

55. Future Directions
Variational Bayes (VB), relaxing Gaussian assumptions
e.g, VB for ECD (Kiebel et al, Neuroimage, 2007)
Dynamic Causal Modelling (DCM), for ECD or MSP
Multi-level heirarchical models (e.g, across subjects)
Nonstationary hyperparameters
Proper Data Fusion (single forward model from neural activity to both M/EEG and fMRI)

56. “Optimal” Regularisation
Single hyper-parameter for a coherent (smoothness) constraint on sources (cf. LORETA)
L-curve EM
500 simulations
C(e)
C(j)
Mattout Et Al (2006) Neuroimage,

57. Where is an effect in time-frequency (2D)?
Kilner Et Al (2005) Neuroscience Letters 374, 174–178

58. Expectation Maximisation
How estimate J and λ simultaneously…? Maximise the “free energy” (F):
Y = Data, n sensors x t time-samples
λ = hyperparameter(s)
q(J) = any distribution over J
using EM algorithm, where E-step:
Friston Et Al (2006) Neuroimage, 20,
and M-step is:
For Gaussian distributions, equivalent to ReML objective function:
In practice, this gives ReML estimates of λ, which can then be used to give MAP estimates of J (via Cj and Ce):

59. Temporal Correlations
To handle temporally-extended solutions, first assume temporal-spatial factorisation:
Y = vectorised data, nt x 1
C(e) = spatial error covariance over sensors
V(e)= temporal error covariance over sensors
C(j) = spatial error covariance over sources
V(j) = temporal error covariance over sources ~
In general, temporal correlation of signal (sources) and noise (sensors) will differ, but can project onto a temporal subspace (via S) such that:
Friston Et Al (2006) Human Brain Mapping, 27:722–735
V typically Gaussian autocorrelations…
S typically an SVD into Nr temporal modes…
Then turns out that EM can simply operate on prewhitened data (covariance), where Y size n x t:

60. Localising Power (eg induced)
Similarly, can extend over trials as well as samples, such that given i=1..N trials, Yi:
Y = [Y1 Y2 ... YN] = concatenated data, n x tN
Can be shown that expected energy for one trial in a time-frequency window defined by W:
W = time-frequency contrast matrix
and total energy (induced and evoked) across i=1..N trials becomes:
Friston Et Al (2006) Human Brain Mapping, 27:722–735

61. Localising Power (eg induced)
Friston Et Al (2006) Human Brain Mapping, 27:722–735

62. Where is an effect in time-sensor space (3D)?
SPM of F-statistic for EEG condition effect across subjects
(NB: MEG data requires sensor-level realignment, e.g SSS)
Henson Et Al (2008) Neuroimage