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

Generative Models of M/EEG: Group inversion and MEG+EEG+fMRI multimodal integration Rik Henson (with much input from Karl Friston)

A Generative Model of M/EEG • 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? Overview

(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 1. A PEB Framework for MEG/EEG(Generative Model) (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 # 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(Generative Model) Fixed Variable Data 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 # sensors # sources # sources # sources # sources Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ= Hyper-parameters 2. Group Inversion 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 # 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

2. Group Inversion(Generative Model) MSP MMN MSP (Group) Litvak & Friston (2008) Neuroimage

“Neural” Activity Causes (hidden): 3. Types of Multimodal Integration (inversion) Balloon Model Head Model Head Model Generative (Forward) Models: ? Data: fMRI MEG EEG ? (future)

“Neural” Activity Causes (hidden): 3. Types of Multimodal Integration 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 # 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

# sensors # 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

Stack data and leadfields for d modalities: 3.1 Fusion of MEG+EEG(Theory) (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) 3.1 Fusion of MEG+EEG(Application) fT mV RMS fT/m Faces Scrambled ms ms ms Faces - Scrambled 150-190ms Henson et al (2009) Neuroimage

+19 -48 -6 +31 -51 -15 MEG mags MEG grads Faces Scrambled 3.1 Fusion of MEG+EEG 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) 3.1 Fusion of MEG+EEG(Conclusions) Henson et al (2009) Neuroimage

# sensors # sensors # sensors # sensors # sources # sources # sources # sources Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ= Hyper-parameters 3.2 Integration of M/EEG+fMRI 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 # 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(Generative Model)

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

1 2 3.2 Integration of M/EEG+fMRI (Application) 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.

Magnetometers (MEG) * * 3.2 Fusion of MEG+fMRI (Application) * * 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) 3.2 Fusion of MEG+fMRI (Application) 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) 3.2 Fusion of MEG+fMRI (Application) 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) 3.2 Fusion of MEG+fMRI (Application) 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

“Neural” Activity Causes (hidden): 3.3 Fusion of fMRI and MEG/EEG? 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

3.3 Fusion of fMRI and MEG/EEG? space (s) time (t)? Henson (2010) Biomag

Overall Conclusions • 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

The End

3. Fusion of MEG+EEG Henson et al (2009) Neuroimage

3. Fusion of MEG+EEG log(λx106) log(λx106) Hyperparameters Participant Participant EEG Grads Mags Grads Mags Henson et al (2009) Neuroimage

Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) ln(λ)+32 4. Fusion of MEG+fMRI Participant fMRI hyperparameters Local Valid ln(λ)+32 Participant Local Invalid Henson et al (in press) Human Brain Mapping Prior 4. Prior 5.

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