Jean Daunizeau Wellcome Trust Centre for Neuroimaging 23 / 10 / 2009

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

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

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

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

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

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

7. Introduction Forward Inverse Bayes SPM Conclusion noise dipoles gain matrix measurements Fields propagation through head tissues Y = KJ + E1

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

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

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

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

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

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

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

15. Introduction λ1 λq Forward Inverse Bayes SPM Conclusion J μ1 Y μq Hierarchical generative model: graph

16. Introduction Forward Inverse Bayes SPM Conclusion Variational Bayesian inversion (VB, EM, ReML) free energy : functional of q  approximate (marginal) posterior distribution:

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

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

19. 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 ECD positions measurement noise precision EEG/MEG data

20. Introduction Forward Inverse Bayes SPM Conclusion Dynamic Causal Modelling (DCM) macro-scale meso-scale micro-scale Golgi Nissl external granular layer EI external pyramidal layer PC internal granular layer action potentials generation zone internal pyramidal layer II synapses firing rate membrane potential (mV) membrane potential (mV) time (s)

21. Introduction Forward Inverse Bayes SPM Conclusion

22. Introduction • EEG/MEG source reconstruction: 1. forward problem; 2. inverse problem (ill-posed). Forward Inverse Bayes SPM Conclusion • 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.

23. Introduction individual reconstructions in MRI template space Forward Inverse Bayes SPM Conclusion L R 2nd level group analysis RFX analysis p < 0.01 uncorrected R L

24. Introduction Forward Inverse Bayes SPM Conclusion Many thanks to Karl Friston, Stephan Kiebel, Jeremie Mattout and Vladimir Litvak