M/EEG source analysis Rik Henson MRC CBU, Cambridge (with thanks to Christophe

Jeremie Mattout, Gareth Barnes, Jean Daunizeau, Stefan Kiebel and Karl

Estimation

Multimodal integration

Estimation

Multimodal integration

Evidence
Bayesian Perspective
Forward Problem
Inverse Problem
Data
Parameters
Model

of sensors
geometry of head
conductivity of head
(source space)

Head not spherical; Conductivity not homogeneous
Boundary (or Finite) Element Models:

Pros: Realistic

Other approaches (for MEG): Fit local spheres to each sensor;
Single shell, spherical approx (Nolte)

large changes in conductivity:
Scalp (skin-air boundary)
Outer Skull (bone-skin boundary)
Inner Skull

(Represented as tessellated triangular meshes)

Extracting these surfaces from an MRI is difficult, eg, because CSF-bone T1-contrast is poor (use PD?)…

A fourth important surface (for some solutions) is:
Cortex (WM-GM boundary)

Extracting this surface from an MRI is very difficult because so convoluted (though FreeSurfer)…

why not warp Template surfaces from an MNI brain based

Henson et al (2009), Neuroimage

why not warp Template surfaces from an MNI brain based

“Canonical”

(Also provides a 1-to-1 mapping across subjects, so source solutions can be written directly to MNI space, and group-inversion applied; see later)

Given that surfaces are part of the forward model (m), can use the model evidence to determine whether Canonical Meshes are sufficient

Henson et al (2009), Neuroimage

Mattout et al (2007), Comp Int & Neuro

Individual Canonical Template
(Inverse-Normalised)

Dipoles (ECD) anywhere in brain:
is linear in but

Estimation

Multimodal integration

volume) until fit to sensor data is maximised (i.e, error

Kiebel et al (2008), Neuroimage

offers a natural answer to question of the number of

Kiebel et al (2008), Neuroimage

a source localisation (inverse) method that includes temporal constraints on

David et al (2011), Journal of Neuroscience

Estimation

Multimodal integration

Leadfields n sensors x p sources
E = Error

…linear Forward Model for MEG/EEG:

Fact that p>>n means under-determined problem (cf. GLM and ECD)…
…so some form of regularisation needed, e.g,“Weighted L2-norm”…

Inverse Problem: Distributed

Given p sources fixed in location (e.g, on a cortical mesh)…

(Free orientations can be simulated by having 2-3 columns in L per location)

Solution”

(error) covariance
Prior:
C(j) = p x p Source (prior) covariance
Posterior:
Inverse Problem:

Parametric Empirical Bayesian (PEB) 2-level hierarchical form:

Maximum A Posteriori (MAP) estimate:

cf Classical Tikhonov:

= Sensor/Source covariance
Q = Covariance components
λ = Hyper-parameters

2. Source components,

“IID” (white noise):

Empty-room:

“IID” (min norm):

Multiple Sparse
Priors (MSP):

Friston et al (2008) Neuroimage

Inverse Problem:
Covariance Components (Priors)

of hyperparameters λ can be difficult (eg local maxima), and

To overcome this, one can:

uninformative priors are then “turned-off” (cf. “Automatic Relevance Detection”)

1) impose positivity on hyperparameters:

2) impose weak, shrinkage hyperpriors:

Inverse Problem: HyperPriors

of hyperparameters λ can be difficult (eg local maxima), and

To overcome this, one can:

uninformative priors are then “turned-off” (cf. “Automatic Relevance Detection”)

1) impose positivity on hyperparameters:

2) impose weak, shrinkage hyperpriors:

Inverse Problem: HyperPriors

(DAG) model

estimates of the hyperparameters (λ) by maximising the variational “free

2. Obtain Maximum A Posteriori (MAP) estimates of parameters (sources, J):

3. Maximal F approximates Bayesian (log) “model evidence” for a model, m:

Complexity

(…where and are the posterior mean and covariance of hyperparameters)

Accuracy

Inverse Problem: Estimation

Problem: Multiple Sparse Priors
…
Friston et al (2008) Neuroimage

Problem: Multiple Sparse Priors
Friston et al (2008) Neuroimage

extent that multiple (100’s) of sparse priors possible (MSP)…
…(or multiple

Inverse Problem: PEB Summary

Estimation

Multi-modal and multi-subject integration

(error):
C = Sensor/Source covariance
Q = Covariance components
λ =

2. Source components, (priors/regularisation):

“IID” (white noise):

Empty-room:

“IID” (min norm):

Multiple Sparse
Priors (MSP):

Friston et al (2008) Neuroimage

= Sensor/Source covariance
Q = Covariance components
λ = Hyper-parameters

“IID” (white noise):
Empty-room:
2.

Litvak & Friston (2008) Neuroimage

Multi-subject Integration (Group Inversion)

before)

(2008) Neuroimage
…having projected to an “average” leadfield matrix
Multi-subject Integration: Leadfield

integration of M/EEG + fMRI

3. Full fusion of M/EEG +

Neuroimage

Integration

integration of M/EEG + fMRI

3. Full fusion of M/EEG +

= Sensor/Source covariance
Q = Covariance components
λ = Hyper-parameters

2. Source components,

“IID” (white noise):

Empty-room:

“IID” (min norm):

Multiple Sparse
Priors (MSP):

Friston et al (2008) Neuroimage

Symmetric Integration of MEG+EEG

Sensor error covariance for ith modality
Qij = jth component for

2. Source components, (priors/regularisation):

“IID” (min norm):

Multiple Sparse
Priors (MSP):

E.g, white noise for 2 modalities:

Henson et al (2009) Neuroimage

Symmetric Integration of MEG+EEG

before)

modalities:
Where data / leadfields scaled to have same average /

mi = Number of spatial modes
(e.g, ~70% of #sensors)

(note: common sources and source priors, but separate error components)

Symmetric Integration of MEG+EEG

(MEG, 102)
(Planar) Gradiometers
(MEG, 204)
Electrodes
(EEG, 70)
Henson et al (2009)

150-190ms

Faces - Scrambled

ms

ms

ms

Symmetric Integration of MEG+EEG

MEG mags

EEG

FUSED

+31 -51 -15

+19 -48 -6

+43 -67 -11

+44 -64 -4

Henson et al (2009) Neuroimage

IID noise for each modality; common MSP for sources

(fixed number of spatial+temporal modes)

Scrambled

150-190ms

Faces – Scrambled,

Faces

Symmetric Integration of MEG+EEG

the conditional precision of the source estimates relative to inverting

Symmetric Integration of MEG+EEG

integration of M/EEG + fMRI

3. Full fusion of M/EEG +

(error):
C = Sensor/Source covariance
Q = Covariance components
λ

2. Source components, (priors/regularisation):

“IID” (white noise):

Empty-room:

“IID” (min norm):

Multiple Sparse
Priors (MSP):

Friston et al (2008) Neuroimage

Sensor components, (error):
C = Sensor/Source covariance
Q =

“IID” (white noise):

Empty-room:

“IID” (min norm):

fMRI Priors:

# sources

# sources

2. Each suprathreshold fMRI cluster becomes a separate prior

Asymmetric Integration of M/EEG+fMRI

M/EEG+fMRI

Integration of M/EEG+fMRI

and connected component labelling
…
2. Projection onto the cortical surface using

…

3. Prior covariance components

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

clusters from SPM of fMRI data from separate group of

1

2

3

4

5

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

None Global Local (Valid) Local (Invalid) Valid+Invalid

Electrodes (EEG)

Negative Free Energy (a.u.)
(model evidence)

*

*

*

*

*

*

*

Gradiometers (MEG)

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Gradiometers (MEG)

None Global Local (Valid) Local (Invalid) Valid+Invalid

Electrodes (EEG)

Negative Free Energy (a.u.)
(model evidence)

*

*

*

*

*

*

*

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Gradiometers (MEG)

None Global Local (Valid) Local (Invalid) Valid+Invalid

Electrodes (EEG)

Negative Free Energy (a.u.)
(model evidence)

*

*

*

*

*

*

*

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Gradiometers (MEG)

None Global Local (Valid) Local (Invalid) Valid+Invalid

Electrodes (EEG)

Negative Free Energy (a.u.)
(model evidence)

*

*

*

*

*

*

*

Henson et al (2010) Hum. Brain Map.

Gradiometers (MEG)

None Global Local (Valid) Local (Invalid) Valid+Invalid

Electrodes (EEG)

Negative Free Energy (a.u.)
(model evidence)

*

*

*

*

*

*

*

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

IID sources and IID noise (L2 MNM)

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

IID sources and IID noise (L2 MNM)

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

L2-norm
None

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

IID sources and IID noise (L2 MNM)

Henson et al (2010) Hum. Brain Map.

None

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

IID sources and IID noise (L2 MNM)

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

Local Valid Priors)
Differential Response
(Faces vs Scrambled)
Differential Response
(Faces vs

Right Posterior Fusiform (rPF) Right Medial Fusiform (rMF) Right Lateral Fusiform (rLF)

Left occipital pole (lOP)

-27 -93 0

+26 -76 -11

+41 -43 -24

+32 -45 -12

-43 -47 -21

Left Lateral Fusiform (lLF)

Differential Response
(Faces vs Scrambled)

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

valid priors increases model evidence further
Helpful if some fMRI regions

Henson et al (2010) Hum. Brain Map.

Asymmetric Integration of M/EEG+fMRI

integration of M/EEG + fMRI

3. Full fusion of M/EEG +

of fMRI + MEG/EEG?

Henson (2010) Biomag

Al (2011) Frontiers

and sensor space

option of Canonical Meshes)

2. …but offers unique Bayesian approaches

plus valid (Qv) or invalid (Qi) focal prior

plus valid (Qv) or invalid (Qi) focal prior

general, temporal correlation of signal (sources) and noise (sensors) will

then turns out that EM can simply operate on prewhitened data (covariance), where Y size n x t:

Valid
Local
Invalid
Henson et al (2010)

3 fMRI priors (Group)
Multi-subject Integration: Results