EEGMEG source reconstruction r IFG l A 1

EEG-MEG source reconstruction r. IFG l. A 1 l. STG r. A 1 r. STG Jean Daunizeau Wellcome Trust Centre for Neuroimaging 08 / 05 / 2009 1

EEG/MEG data sensor locations structural MRI • anatomical templates • data convert • epoching • BEM forward modelling • spatial denormalisation gain matrix trials • baseline correction • averaging over trials • low pass filter (20 Hz) individual meshes evoked responses • inverse modelling • 1 st level contrast cortical sources • standard SPM analysis 2

EEG/MEG data sensor locations structural MRI • anatomical templates • data convert • epoching • BEM forward modelling • spatial denormalisation gain matrix trials • baseline correction • averaging over trials • low pass filter (20 Hz) individual meshes evoked responses • inverse modelling • 1 st level contrast cortical sources • standard SPM analysis 3

Introduction Forward Inverse Bayes SPM Conclusion 1. Introduction 2. Forward problem 3. Inverse problem 4. Bayesian inference applied to distributed source reconstruction 5. SPM variants of the EEG/MEG inverse problem 6. Conclusion 4

Introduction Forward Inverse Bayes SPM Conclusion Forward and inverse problems: definitions Forward problem = modelling Inverse problem = estimation of the model parameters 5

Introduction Forward Inverse Bayes SPM Conclusion Physical model of bioelectrical activity current dipole 6

Introduction Forward Inverse Bayes SPM Conclusion Fields propagation through head tissues noise dipoles gain matrix measurements Y = KJ + E 1 7

Introduction Forward Inverse Bayes SPM Conclusion An ill-posed problem Jacques Hadamard (1865 -1963) 1. Existence 2. Unicity 3. Stability 8

Introduction Forward Inverse Bayes SPM Conclusion An ill-posed problem Jacques Hadamard (1865 -1963) 1. Existence 2. Unicity 3. Stability 9

Introduction Forward Inverse Bayes SPM Conclusion Imaging solution: cortically distributed dipoles 10

Introduction Forward Inverse Bayes SPM Conclusion Imaging solution: cortically distributed dipoles 11

Introduction Forward Inverse Bayes SPM Conclusion Regularization Spatial and temporal constraints Data fit Adequacy with other modalities data fit constraint (regularization term) W = I : minimum norm method W = Δ : LORETA (maximum smoothness) 12

Introduction Forward Inverse Bayes SPM Conclusion Priors and posterior likelihood posterior priors model evidence 13

Introduction Forward Inverse Bayes SPM Conclusion Hierarchical generative model sensor level source level Q : (known) variance components (λ, μ) : (unknown) hyperparameters 14

Introduction Forward Inverse Bayes SPM Conclusion Hierarchical generative model: graph λ 1 λq J μ 1 Y μq 15

Introduction Forward Inverse Bayes SPM Conclusion Restricted Maximum Likelihood (Re. ML) average over J generative model M model associated with F 16

Introduction Forward Inverse Bayes SPM Conclusion Imaging source reconstruction in SPM IID COH generative model M ARD/GS prior covariance structure 17

Introduction Forward Inverse Bayes SPM Source reconstruction for group studies Conclusion Group studies canonical meshes! 18

Introduction Forward Inverse Bayes SPM Conclusion Equivalent Current Dipoles (ECD) Somesthesic stimulation (evoked potential) soft symmetry constraints! ECD moments prior precision ECD positions prior precision ECD moments EEG/MEG data ECD positions measurement noise precision 19

Introduction Forward Inverse Bayes SPM Conclusion Dynamic Causal Modelling (DCM) macroscopic scale mesoscopic scale microscopic scale system of ensembles (105~106 neuron ensemble neurons) mean-field response (due to ensemble dispersion) excitatory interneurons pyramidal cells effective connectivity (due to synaptic density) inhibitory interneurons 20

Introduction Forward Inverse Bayes SPM Conclusion • EEG/MEG source reconstruction: 1. forward problem; 2. inverse problem (ill-posed). • Prior information is mandatory to solve the inverse problem. • Bayesian inference is well suited for: 1. introducing such prior information… 2. … and estimating their weight wrt the data 3. providing us with a quantitative feedback on the adequacy of the model. 21

Introduction Forward Inverse Bayes SPM Conclusion individual reconstructions in MRI template space L R SPM machinery R L RFX analysis p < 0. 01 uncorrected 22

Introduction Forward Inverse Bayes SPM Conclusion Many thanks to… Karl Friston Stephan Kiebel Jeremie Mattout Christophe Phillips Vladimir Litvak Guillaume Magic Flandin 23