EEG/MEG source reconstruction

1. EEG/MEGsource reconstruction Jean Daunizeau Vladimir Litvak Wellcome Trust Centre for Neuroimaging 9 / 05 / 2008

2. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

3. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

4. Introduction EEG/MEG and neuroimaging MRI MEG EEG invasivity weak strong OI EEG 20 spatial resolution (mm) MEG SPECT 15 OI PET 10 fMRI sEEG 5 MRI(a,d) 1 10 102 103 104 105 temporal resolution (ms)

5. Introduction forward/inverse problems : definitions  Forward problem = modelling • Inverse problem = estimation of the model parameters

6. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

7. Forward problem physical model of bioelectrical activity current dipole

8. Forward problem the general linear model noise dipoles gain matrix measurements Y = KJ + E1

9. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

10. Inverse problem an ill-posed problem • Jacques Hadamard (1865-1963) • Existence • Unicity • Stability

11. Inverse problem an ill-posed problem • Jacques Hadamard (1865-1963) • Existence • Unicity • Stability

12. Inverse problem cortically distributed current dipoles

13. Inverse problem 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)

14. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

15. Bayesian inference principle posterior pdf likelihood prior pdf model evidence

16. Bayesian inference hierarchical generative model sensor level source level Q : (known) variance components (λ,μ) : (unknown) hyperparameters

17. Bayesian inference hierarchical generative model λ1 λq J μ1 Y μq

18. Bayesian inference SPM implementations IID COH prior covariance structure ARD/GS generative model M

19. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

20. Conclusion at the end of the day… Individual reconstructions in MRI template space L R SPM machinery RFX analysis p < 0.01 uncorrected R L

21. Conclusion summary • 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. Many thanks to Karl Friston, Stephan Kiebel, Jeremie Mattout

23. Bayesian inference expectation-maximization (EM) average over J model associated with F generative model M

24. Bayesian inference expectation-maximization (EM) M-step E-step EM / ReML algorithm