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

Overview 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 M/EEG + fMRI 3.3 Full fusion of M/EEG + fMRI?

1. A PEB Framework for MEG/EEG (Bayesian inference) (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

1. A PEB Framework for MEG/EEG (Covariance Components/Priors) Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ = Hyper-parameters 1. Sensor components, (error): # sensors # sensors “IID” (white noise): Empty-room: 2. Source components, (priors/regularisation): # sources # sources Multiple Sparse Priors (MSP): “IID” (min norm): Friston et al (2008) Neuroimage

1. A PEB Framework for MEG/EEG (Hyperpriors) When multiple Q’s are correlated, estimation of hyperparameters λ can be difficult (eg local maxima), and they can become negative (improper for covariances) Prestim Baseline Anti-Averaging Smoothness Depth-Weighting Sensor priors projected to sensors Source priors To overcome this, one can: 1) impose positivity on hyperparameters: 2) impose weak, shrinkage hyperpriors: uninformative priors are then “turned-off” (cf. “Automatic Relevance Detection”) Henson et al (2007) Neuroimage

1. A PEB Framework for MEG/EEG (Generative Model) Source and sensor space Fixed Variable Data Friston et al (2008) Neuroimage

1. A PEB Framework for MEG/EEG (Estimation/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 3. Maximal F approximates Bayesian (log) “model evidence” for a model, m: Accuracy Complexity (…where and are the posterior mean and covariance of hyperparameters) 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 model evidence, so can compare constraints

Overview 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?

2. Group Inversion (Covariance Components) Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ = Hyper-parameters 1. Sensor components, (error): # sensors # sensors “IID” (white noise): Empty-room: 2. Source components, (priors/regularisation): # sources # sources Multiple Sparse Priors (MSP): “IID” (min norm): Friston et al (2008) Neuroimage

2. Group Inversion (Covariance Components) Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ = Hyper-parameters 1. Sensor components, (error): # sensors # sensors “IID” (white noise): Empty-room: 2. Optimise Multiple Sparse Priors by pooling across participants # sources Litvak & Friston (2008) Neuroimage

2. Group Inversion (one subject) (Generative Model) Source and sensor space Fixed Variable Data Litvak & Friston (2008) Neuroimage

2. Group Inversion (multiple subjects) (Generative Model) Source and sensor space Fixed Variable Data Litvak & Friston (2008) Neuroimage

Litvak & Friston (2008) Neuroimage 2. Group Inversion (multiple subjects) (Re-referencing leadfield matrices) Concatenate data across subjects …having projected to an “average” leadfield matrix Common source-level priors: Subject-specific sensor-level priors: Litvak & Friston (2008) Neuroimage

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

2. Group Inversion (Generative Model) MMN + 3 fMRI priors MMN + 3 fMRI priors (Group) Henson et al (submitted) Frontiers

Overview 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?

3. Types of Multimodal Integration “Neural” Activity Causes (hidden): (inversion) Generative (Forward) Models: Balloon Model Head Model Head Model ? Data: fMRI MEG EEG ? (future) Henson (2010) Biomag

3. Types of Multimodal Integration “Neural” Activity Causes (hidden): Symmetric Integration (Fusion) Generative (Forward) Models: Balloon Model Head Model Head Model ? Data: fMRI MEG EEG ? (future) Asymmetric Integration Daunizeau et al (2007), Neuroimage

3.1 Fusion of MEG+EEG (Sensor Components) Specifying (co)variance components (priors/regularisation): C = Sensor/Source covariance Q = Covariance components λ = Hyper-parameters 1. Sensor components, (error): # sensors # sensors “IID” (white noise): Empty-room: 2. Source components, (priors/regularisation): # sources # sources Multiple Sparse Priors (MSP): “IID” (min norm): Friston et al (2008) Neuroimage

3.1 Fusion of MEG+EEG (Sensor Components) 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): # sensors # sensors E.g, white noise for 2 modalities: 2. Source components, (priors/regularisation): # sources # sources Multiple Sparse Priors (MSP): “IID” (min norm): Henson et al (2009) Neuroimage

3.1 Basic Model for MEG or EEG (Generative Model) Source and sensor space Fixed Variable Data Henson et al (2009) Neuroimage

3.1 Fusion of MEG+EEG (Generative Model) Source and sensor space Fixed Variable Data Henson et al (2009) Neuroimage

3.1 Fusion of MEG+EEG (Theory) 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

3.1 Fusion of MEG+EEG (Application) ERs from 12 subjects for 3 simultaneously-acquired Neuromag sensor-types: Magnetometers (MEG, 102) (Planar) Gradiometers (MEG, 204) Electrodes (EEG, 70) fT μV RMS fT/m Faces Scrambled ms ms ms Faces - Scrambled 150-190ms Henson et al (2009) Neuroimage

3.1 Fusion of MEG+EEG Henson et al (2009) Neuroimage +31 -51 -15 +19 -48 -6 MEG mags MEG grads Faces Scrambled Faces – Scrambled, 150-190ms +43 -67 -11 +44 -64 -4 EEG FUSED IID noise for each modality; common MSP for sources Henson et al (2009) Neuroimage (fixed number of spatial+temporal modes)

3.1 Fusion of MEG+EEG (Conclusions) 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

3.2 Asymmetric 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): # sensors # sensors “IID” (white noise): Empty-room: 2. Source components, (priors/regularisation): # sources # sources Multiple Sparse Priors (MSP): “IID” (min norm): Friston et al (2008) Neuroimage

3.2 Asymmetric 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): # sensors # sensors “IID” (white noise): Empty-room: 2. Each suprathreshold fMRI cluster becomes a separate prior # sources “IID” (min norm): fMRI Priors: # sources # sources Henson et al (2010) Hum. Brain Map.

3.2 Basic model for MEG or EEG (Generative Model) Source and sensor space Fixed Variable Data Friston et al (2008) Neuroimage

3.2 Asymmetric Integration of M/EEG+fMRI (Generative Model) Source and sensor space Fixed Variable Data Henson et al (2010) Hum. Brain Map.

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 Gray matter segmentation Cortical surface extraction … 2. Projection onto the cortical surface using the Voronoï diagram … 3D geodesic Voronoï diagram 3. Prior covariance components Henson et al (2010) Hum. Brain Map.

3.2 Integration of M/EEG+fMRI (Application) 1 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Magnetometers (MEG) * * * * 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Magnetometers (MEG) * * * * 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Magnetometers (MEG) * * * * 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Magnetometers (MEG) * * * * 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Magnetometers (MEG) * * * * 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) IID sources and IID noise (L2 MNM) Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) None Global Local (Valid) Local (Invalid) Henson et al (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) IID sources and IID noise (L2 MNM) Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) None Global Local (Valid) Local (Invalid) Henson et al (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) 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 (2010) Hum. Brain Map.

3.2 Fusion of MEG+fMRI (Application) Right Posterior Fusiform (rPF) Right Medial Fusiform (rMF) Right Lateral Fusiform (rLF) +26 -76 -11 +32 -45 -12 +41 -43 -24 Differential Response (Faces vs Scrambled) R Left occipital pole (lOP) -27 -93 0 Differential Response (Faces vs Scrambled) Gradiometers (MEG) (5 Local Valid Priors) Left Lateral Fusiform (lLF) L -43 -47 -21 Differential Response (Faces vs Scrambled) NB: Priors affect variance, not precise timecourse… Henson et al (2010) Hum. Brain Map. 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 does not necessarily increase model evidence, particularly in conjunction with valid priors Can counteract superficial bias of, e.g, minimum-norm Affects variance but not not precise timecourse Henson et al (2010) Hum. Brain Map.

3.3 Fusion of fMRI and MEG/EEG? “Neural” 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? Source and sensor space Fixed Variable Data Henson (submitted) Frontiers

3.3 Fusion of fMRI and MEG/EEG? Source and sensor space Fixed Variable Data Henson (submitted) Frontiers

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 M/EEG is advantageous Unclear that fusion of fMRI and M/EEG is advantageous

The End

3.2. Fusion of MEG+fMRI fMRI hyperparameters Henson et al (2010) Magnetometers (MEG) Gradiometers (MEG) Electrodes (EEG) ln(λ)+32 Participant fMRI hyperparameters Local Valid ln(λ)+32 Participant Local Invalid Henson et al (2010) Prior 4. Prior 5.