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EEG_MEG source reconstruction

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					EEG-MEG source reconstruction




                                 Jean Daunizeau
          Wellcome Trust Centre for Neuroimaging

                                   23 / 10 / 2009


                                               1
 EEG/MEG data               sensor locations                                              structural MRI


                                                            • anatomical templates




                                                          individual
    • data convert                                         meshes
                            • BEM forward modelling                     • spatial denormalisation
    • epoching

    trials                                  gain matrix




• baseline correction        evoked
• averaging over trials                  • inverse modelling           cortical   • standard SPM analysis
                           responses                                   sources
• low pass filter (20Hz)                 • 1st level contrast

                                                                                                       2
 EEG/MEG data               sensor locations                                              structural MRI


                                                            • anatomical templates




                                                          individual
    • data convert                                         meshes
                            • BEM forward modelling                     • spatial denormalisation
    • epoching

    trials                                  gain matrix




• baseline correction        evoked
• averaging over trials                  • inverse modelling           cortical   • standard SPM analysis
                           responses                                   sources
• low pass filter (20Hz)                 • 1st level contrast

                                                                                                       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         priors




           posterior
                                          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)


                                  q
                                                     
 ln p  y m   ln p  , y m   S  q   DKL 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 

                                                                   q 1 or 2 
                 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      Source reconstructionBayes
               Forward     Inverse               SPM
                                       for group studies       Conclusion

                             Group studies




                                           canonical meshes!

                                                                            18
Introduction          Forward                 Inverse   Bayes         SPM              Conclusion

                             Equivalent Current Dipoles (ECD)

         soft symmetry constraints!                       Somesthesic stimulation (evoked potential)


   ECD moments            ECD positions
   prior precision        prior precision




                ECD                     ECD
                moments                 positions




              EEG/MEG data      measurement noise
                                    precision


                                                                                                       19
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




                                                                   membrane potential (mV)
                      firing rate




                                    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




                                                        RFX analysis
                      R         L                   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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posted:11/16/2011
language:English
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