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Generative Models of M/EEG: Group inversion and MEG+EEG+fMRI multimodal integration Rik Henson

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### Overview

### 1. A PEB Framework for MEG/EEG(Generative Model)

### 2. Group Inversion

### 3. Types of Multimodal Integration

### 3. Types of Multimodal Integration

### 3.1 Fusion of MEG+EEG(Theory)

### 3.1 Fusion of MEG+EEG(Application)

### 3.1 Fusion of MEG+EEG

### 3.1 Fusion of MEG+EEG(Conclusions)

### 3.2 Integration of M/EEG+fMRI

### 3.2 Integration of M/EEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.2 Fusion of MEG+fMRI (Application)

### 3.3 Fusion of fMRI and MEG/EEG?

### 3. Fusion of MEG+EEG

### 4. Fusion of MEG+fMRI

Group inversion and MEG+EEG+fMRI multimodal integration

Rik Henson

(with much input from Karl Friston)

- Group inversion (optimising priors across subjects)
- Multimodal integration:
- 3.1 Symmetric integration (fusion) of MEG + EEG
- 3.2 Asymmetric integration of MEG + fMRI
- 3.3 Full fusion of MEG/EEG + fMRI?

(Linear) Forward Model for MEG/EEG (for one timepoint):

Y = Data n sensors

J = Sources p>>n sources

L = Leadfields n sensors x p sources

E= Error n sensors

(Gaussian) Likelihood:

C(e)= n x n Sensor (error) covariance

Prior:

C(j)= p x p Source (prior) covariance

Posterior:

Phillips et al (2005), Neuroimage

# sensors

# sensors

# sensors

# sources

# sources

# sources

# sources

1. A PEB Framework for MEG/EEG(Generative Model)

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q= Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Source components, (priors/regularisation):

Multiple Sparse

Priors (MSP):

“IID” (min norm):

Friston et al (2008) Neuroimage

1. A PEB Framework for MEG/EEG(Inversion)

1. Obtain Restricted Maximum Likelihood (ReML) estimates of the hyperparameters (λ) by maximising the variational “free energy” (F):

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

cf. Tikhonov

…and an estimate of their posterior covariance (inverse precision):

(relevant to MEG+EEG integration)

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

(relevant to MEG+fMRI integration)

Friston et al (2002) Neuroimage

1. A PEB Framework for MEG/EEG

Summary:

- Automatically “regularises” in principled fashion…
- …allows for multiple constraints (priors)…
- …to the extent that multiple (100’s) of sparse priors possible…
- …(or multiple error components or multiple fMRI priors)…
- …furnishes estimates of source precisions and model evidence

# sensors

# sensors

# sensors

# sources

# sources

# sources

# sources

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q = Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Source components, (priors/regularisation):

Multiple Sparse

Priors (MSP):

“IID” (min norm):

Friston et al (2008) Neuroimage

# sensors

# sensors

# sensors

# sources

# sources

2. Group Inversion

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q = Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Optimise Multiple Sparse Priors by pooling across participants

Litvak & Friston (2008) Neuroimage

2. Group Inversion (single subject)(Generative Model)

Litvak & Friston (2008) Neuroimage

2. Group Inversion (multiple subjects)(Generative Model)

Litvak & Friston (2008) Neuroimage

2. Group Inversion(Generative Model)

…projecting data and leadfields to a reference subject (0):

Common source-level priors:

Subject-specific sensor-level priors:

Litvak & Friston (2008) Neuroimage

Activity

Causes (hidden):

(inversion)

Balloon

Model

Head

Model

Head

Model

Generative (Forward)

Models:

?

Data:

fMRI

MEG

EEG

? (future)

Activity

Causes (hidden):

Symmetric

Integration

(Fusion)

Balloon

Model

Head

Model

Head

Model

Generative (Forward)

Models:

?

Data:

fMRI

MEG

EEG

? (future)

Asymmetric

Integration

Daunizeau et al (2007), Neuroimage

# sensors

# sensors

# sensors

# sources

# sources

# sources

# sources

3.1 Fusion of MEG+EEG(Theory)

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q= Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Source components, (priors/regularisation):

Multiple Sparse

Priors (MSP):

“IID” (min norm):

Friston et al (2008) Neuroimage

# sources

# sources

# sensors

# sensors

# sensors

# sources

# sources

3.1 Fusion of MEG+EEG(Theory)

Specifying (co)variance components (priors/regularisation):

Ci(e)= Sensor error covariance for ith modality

Qij= jth component for ith modality

λij= Hyper-parameters

1. Sensor components, (error):

E.g, white noise for 2 modalities:

2. Source components, (priors/regularisation):

Multiple Sparse

Priors (MSP):

“IID” (min norm):

Henson et al (2009) Neuroimage

3.1 Fusion of MEG+EEG(Generative Model)

Henson et al (2009) Neuroimage

3.1 Fusion of MEG+EEG(Generative Model)

Henson et al (2009) Neuroimage

Stack data and leadfields for d modalities:

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

- Where data / leadfields scaled to have same average / predicted variance:

mi = Number of spatial modes

(e.g, channels)

Henson et al (2009) Neuroimage

ERs from 12 subjects for 3 simultaneously-acquired Neuromag sensor-types:

Magnetometers

(MEG, 102)

(Planar) Gradiometers

(MEG, 204)

Electrodes

(EEG, 70)

fT

mV

RMS fT/m

Faces

Scrambled

ms

ms

ms

Faces - Scrambled

150-190ms

Henson et al (2009) Neuroimage

+31 -51 -15

MEG mags

MEG grads

Faces

Scrambled

Faces – Scrambled,

150-190ms

+43 -67 -11

+44 -64 -4

FUSED

EEG

IID noise for each modality; common MSP for sources

Henson et al (2009) Neuroimage

(fixed number of spatial+temporal modes)

Fusing magnetometers, gradiometers and EEG increased the conditional precision of the source estimates relative to inverting any one modality alone

- (when equating number of spatial+temporal modes)
- The maximal sources recovered from fusion were a plausible combination of the ventral temporal sources recovered by MEG and the lateral temporal sources recovered by EEG
- (Simulations show the relative scaling of mags and grads agrees with empty-room data)

Henson et al (2009) Neuroimage

# sensors

# sensors

# sensors

# sources

# sources

# sources

# sources

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q = Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Source components, (priors/regularisation):

Multiple Sparse

Priors (MSP):

“IID” (min norm):

Friston et al (2008) Neuroimage

# sensors

# sensors

# sensors

# sources

# sources

3.2 Integration of M/EEG+fMRI

Specifying (co)variance components (priors/regularisation):

C = Sensor/Source covariance

Q = Covariance components

λ= Hyper-parameters

1. Sensor components, (error):

“IID” (white noise):

Empty-room:

2. Each suprathreshold fMRI cluster becomes a separate prior

# sources

fMRI Priors:

“IID” (min norm):

# sources

Henson et al (in press) Human Brain Mapping

3.2 Integration of M/EEG+fMRI (Priors)

T1-weighted MRI

{T,F,Z}-SPM

Anatomical data

Functional data

…

1. Thresholding and connected component labelling

Cortical surfaceextraction

Gray matter segmentation

…

2. Projection onto the cortical surface using the Voronoï diagram

…

3D geodesicVoronoï diagram

3. Prior covariance components

Henson et al (in press) Human Brain Mapping

2

SPM{F} for faces versus scrambled faces,

15 voxels, p<.05 FWE

3

4

5

5 clusters from SPM of fMRI data from separate group of (18) subjects in MNI space

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

*

*

*

*

Gradiometers (MEG)

*

*

Negative Free Energy (a.u.)

(model evidence)

*

*

Electrodes (EEG)

*

*

*

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

(binarised, variance priors)

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

*

*

*

*

Gradiometers (MEG)

*

*

Negative Free Energy (a.u.)

(model evidence)

*

*

Electrodes (EEG)

*

*

*

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

(binarised, variance priors)

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

*

*

*

*

Gradiometers (MEG)

*

*

Negative Free Energy (a.u.)

(model evidence)

*

*

Electrodes (EEG)

*

*

*

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

(binarised, variance priors)

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

*

*

*

*

Gradiometers (MEG)

*

*

Negative Free Energy (a.u.)

(model evidence)

*

*

Electrodes (EEG)

*

*

*

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

(binarised, variance priors)

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

*

*

*

*

Gradiometers (MEG)

*

*

Negative Free Energy (a.u.)

(model evidence)

*

*

Electrodes (EEG)

*

*

*

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

(binarised, variance priors)

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

IID sources and IID noise (L2 MNM)

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

None Global Local (Valid) Local (Invalid)

Henson et al (in press) Human Brain Mapping

IID sources and IID noise (L2 MNM)

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

None Global Local (Valid) Local (Invalid)

Henson et al (in press) Human Brain Mapping

IID sources and IID noise (L2 MNM)

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

None Global Local (Valid) Local (Invalid)

fMRI priors counteract superficial bias of L2-norm

Henson et al (in press) Human Brain Mapping

IID sources and IID noise (L2 MNM)

Magnetometers (MEG)

Gradiometers (MEG)

Electrodes (EEG)

None Global Local (Valid) Local (Invalid)

fMRI priors counteract superficial bias of L2-norm

Henson et al (in press) Human Brain Mapping

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

+41 -43 -24

+32 -45 -12

+26 -76 -11

Differential Response

(Faces vs Scrambled)

Left occipital pole (lOP)

R

-27 -93 0

Differential Response

(Faces vs Scrambled)

Gradiometers (MEG)

(5 Local Valid Priors)

Left Lateral Fusiform (lLF)

-43 -47 -21

L

Differential Response

(Faces vs Scrambled)

NB: Priors affect variance, not precise timecourse…

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

3.2 Fusion of MEG+fMRI (Conclusions)

- Adding a single, global fMRI prior increases model evidence
- Adding multiple valid priors increases model evidence further
- Helpful if some fMRI regions produce no MEG/EEG signal (or arise from neural activity at different times)
- Adding invalid priors rarely increases model evidence, particularly in conjunction with valid priors
- Can counteract superficial bias of, e.g, minimum-norm
- Affects variance but not not precise timecourse
- (Adding fMRI priors to MSP has less effect)

Henson et al (in press) Human Brain Mapping

Activity

Causes (hidden):

Fusion of fMRI + MEG/EEG?

Balloon

Model

Head

Model

Head

Model

?

Data:

fMRI

MEG

EEG

? (future)

Henson (2010) Biomag

3.3 Fusion of fMRI and MEG/EEG?

Henson (2010) Biomag

- The PEB (in SPM8) framework is advantageous
- Group optimisation of MSPs can be advantageous
- Full fusion of MEG and EEG is advantageous
- Using fMRI as (spatial) priors on MEG is advantageous
- Unclear that fusion of fMRI and M/EEG is advantageous

Henson et al (2009) Neuroimage

log(λx106)

log(λx106)

Hyperparameters

Participant

Participant

EEG

Grads

Mags

Grads

Mags

Henson et al (2009) Neuroimage

Gradiometers (MEG)

Electrodes (EEG)

ln(λ)+32

Participant

fMRI hyperparameters

Local

Valid

ln(λ)+32

Participant

Local

Invalid

Henson et al (in press) Human Brain Mapping

Prior 4.

Prior 5.

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