EEG-MEG source reconstruction Jean Daunizeau Wellcome Trust Centre for Neuroimaging 23 / 10 / 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 (20Hz) individual meshes evoked responses • inverse modelling • 1st 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 (20Hz) individual meshes evoked responses • inverse modelling • 1st 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 + E1 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 Adequacy with other modalities Data fit 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 λ1 λq J μ1 Y μq 15 Introduction Forward Inverse Bayes SPM Conclusion Variational Bayesian inversion (VB, EM, ReML) ln p y m ln p , y m q S q D K L q ; p y , m free energy : functional of q approximate (marginal) posterior distribution: q , q 1 2 p 1 , 2 y , m p 1 or 2 y , m 2 q 1 o r 2 1 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) macro-scale meso-scale Golgi micro-scale Nissl external granular layer EI external pyramidal layer PC internal granular layer action potentials generation zone internal pyramidal layer II firing rate membrane potential (mV) synapses membrane potential (mV) time (s) 20 Introduction Forward Inverse Bayes SPM Conclusion 21 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. 22 Introduction Forward Inverse Bayes SPM Conclusion individual reconstructions in MRI template space L R 2nd level group analysis R L RFX analysis p < 0.01 uncorrected 23 Introduction Forward Inverse Bayes SPM Conclusion Many thanks to Karl Friston, Stephan Kiebel, Jeremie Mattout and Vladimir Litvak 24
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