1 Jean Daunizeau Wellcome Trust Centre for Neuroimaging 23 / 10 / 2009 EEG-MEG source reconstruction

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

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

4 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 BayesSPMConclusionInverseForward Introduction

5  Forward problem = modelling  Inverse problem = estimation of the model parameters BayesInverseForward Introduction Forward and inverse problems: definitions SPMConclusion

6 current dipole BayesInverseForward Introduction Physical model of bioelectrical activity SPMConclusion

7 measurements noise dipoles gain matrix Y = KJ + E 1 BayesInverseForward Introduction Fields propagation through head tissues SPMConclusion

8 Jacques Hadamard ( ) 1.Existence 2.Unicity 3.Stability BayesForward Introduction An ill-posed problem InverseSPMConclusion

9 Jacques Hadamard ( ) 1.Existence 2.Unicity 3.Stability BayesForward Introduction An ill-posed problem InverseSPMConclusion

10 BayesForward Introduction Imaging solution: cortically distributed dipoles InverseSPMConclusion

11 BayesForward Introduction Imaging solution: cortically distributed dipoles InverseSPMConclusion

12 Data fit Adequacy with other modalities Spatial and temporal constraints W = I : minimum norm method W = Δ : LORETA (maximum smoothness) data fitconstraint (regularization term) BayesForward Introduction Regularization InverseSPMConclusion

13 likelihoodpriors posterior model evidence Forward Introduction Priors and posterior InverseBayesSPMConclusion

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

15 YJμ1μ1 μqμq λ1λ1 λqλq Forward Introduction Hierarchical generative model: graph InverseBayesSPMConclusion

16 Forward Introduction Variational Bayesian inversion (VB, EM, ReML) InverseBayesSPMConclusion free energy : functional of q  approximate (marginal) posterior distribution:

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

18 Source reconstruction for group studies canonical meshes! Forward Introduction Group studies InverseBayesSPMConclusion

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

20 Forward Introduction Dynamic Causal Modelling (DCM) InverseBayesSPMConclusion GolgiNissl internal granular layer internal pyramidal layer external pyramidal layer external granular layer action potentials generation zone synapses macro-scalemeso-scalemicro-scale PC EI II firing rate membrane potential (mV) time (s)

21 Forward Introduction InverseBayesSPMConclusion

22 Prior information is mandatory to solve the inverse problem. EEG/MEG source reconstruction: 1. forward problem; 2. inverse problem (ill-posed). 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. Forward Introduction InverseBayesSPMConclusion

23 R L individual reconstructions in MRI template space RFX analysis p < 0.01 uncorrected RL 2nd level group analysis Forward Introduction InverseBayesSPMConclusion

24 Many thanks to Karl Friston, Stephan Kiebel, Jeremie Mattout and Vladimir Litvak Forward Introduction InverseBayesSPMConclusion