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EEG/MEG Source Localisation SPM Short Course – Wellcome Trust Centre for Neuroimaging – May 2008 ? ? Jérémie Mattout, Christophe Phillips Jean Daunizeau Guillaume Flandin Karl Friston Rik Henson Stefan Kiebel Vladimir Litvak

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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EEG/MEG Source localisation spatial resolution (mm) invasivity weakstrong temporal resolution (ms) sEEG MEG EEG fMRI MRI(a,d) PET SPECT OI MRI EEG MEG OI Introduction: EEG/MEG as Neuroimaging techniques

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MEEG functionalities in SPM8 EEG/MEG Source localisation Data Preperation New MEEG data format based on object-oriented coding More stable interfacing and user-friendly and a bit harder for developers Data importation/convertion Import most common MEG/EEG data formats into one single data format Include associated data, e.g. electrode location and sensor setup

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MEEG functionalities in SPM8 EEG/MEG Source localisation Data Preperation Usual preprocessing Filtering Re-referencing Epoching Artefact and bad channel rejection Averaging Displaying …

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MEEG functionalities in SPM8 EEG/MEG Source localisation Data Preprocessing Scalp Data Analysis Statistical Parametric Mapping Dynamic Causal Modelling Source reconstruction

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Energy changes (Faces - Scrambled, p<0.01) time (s) frequency (Hz) time (ms) Right temporal evoked signal faces scrambled M170 MEG experiment of Face perception 4 4 Electrophysiology and haemodynamic correlates of face perception, recognition and priming, R.N. Henson, Y. Goshen-Gottstein, T. Ganel, L.J. Otten, A. Quayle, M.D. Rugg, Cereb. Cortex, EEG/MEG Source localisation MEEG usual results

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EEG/MEG Source localisation Change speaker…

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EEG/MEG Source localisation EEG/MEG source reconstruction process Forward model Inverse problem Introduction: overview

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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EEG/MEG Source localisation source biophysical model: current dipole EEG/MEG source models Equivalent Current Dipoles (ECD) Imaging or Distributed Forward model: source space - few dipoles with free location and orientation - many dipoles with fixed location and orientation

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EEG/MEG Source localisation Forward model: formulation Forward model datadipole parameters noiseforward operator

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EEG/MEG Source localisation Forward model: imaging/distributed model datadipole amplitudes noisegain matrix

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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EEG/MEG Source localisation « Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? » Jacques Hadamard ( ) Inverse problem: an ill-posed problem Inverse problem 1.Existence 2.Unicity 3.Stability

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EEG/MEG Source localisation Inverse problem: an ill-posed problem « Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? » Jacques Hadamard ( ) 1.Existence 2.Unicity 3.Stability Inverse problem

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EEG/MEG Source localisation Inverse problem: an ill-posed problem « Will it ever happen that mathematicians will know enough about the physiology of the brain, and neurophysiologists enough of mathematical discovery, for efficient cooperation to be possible ? » Jacques Hadamard ( ) 1.Existence 2.Unicity 3.Stability Inverse problem Introduction of prior knowledge (regularization) is needed

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EEG/MEG Source localisation Inverse problem: regularization Data fit Adequacy with other modalities Spatial and temporal priors W = I : minimum norm W = Δ : maximum smoothness (LORETA) data fitprior (regularization term)

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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EEG/MEG Source localisation Bayesian inference: probabilistic formulation likelihoodprior posterior evidence Forward model Inverse problem posterior likelihood

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EEG/MEG Source localisation Bayesian inference: hierarchical linear model sensor (1 st ) level source (2 nd ) level Q : (known) variance components (λ,μ) : (unknown) hyperparameters likelihood prior

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EEG/MEG Source localisation Bayesian inference: variance components Multiple Sparse Priors (MSP) … # dipoles Minimum Norm (IID) Maximum Smoothness (LORETA)

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EEG/MEG Source localisation Bayesian inference: graphical representation Y J μ1μ1 μqμq λ1λ1 λkλk likelihood prior

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EEG/MEG Source localisation Bayesian inference: iterative estimation scheme M-step E-step Expectation-Maximization (EM) algorithm

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EEG/MEG Source localisation Bayesian inference: model comparison model M i FiFi At convergence

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Outline EEG/MEG Source localisation 1.Introduction 2.Forward model 3.Inverse problem 4.Bayesian inference applied to the EEG/MEG inverse problem 5.Conclusion

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EEG/MEG Source localisation Conclusion: At the end of the day... R L Individual reconstructions in MRI template space Group results p < 0.01 uncorrected RL

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EEG/MEG Source localisation Conclusion: Summary Prior information is mandatory EEG/MEG source reconstruction: 1. forward model 2. inverse problem (ill-posed) Bayesian inference is used to: 1. incorpoate such prior information… 2. … and estimating their weight w.r.t the data 3. provide a quantitative feedback on model adequacy Forward model Inverse problem

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EEG/MEG Source localisation Change speaker… Again !

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EEG/MEG Source localisation source biophysical model: current dipole EEG/MEG source models Equivalent Current Dipoles (ECD) Imaging or Distributed Equivalent Current Dipole (ECD) solution few dipoles with free location and orientation many dipoles with fixed location and orientation

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EEG/MEG Source localisation ECD approach: principle Forward model datadipole parameters noiseforward operator but a priori fixed number of sources considered iterative fitting of the 6 parameters of each dipole

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EEG/MEG Source localisation The locations s and moments w are drawn from normal distributions with precisions γ s and γ w. ε is white observation noise with precision γ y. These are drawn from a prior gamma distribution. Dipole locations s and dipole moments w generated data using ECD solution: variational Bayes (VB) approach

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EEG/MEG Source localisation ECD solution: classical vs. VB approaches ClassicalVB Hard constraintsYes Soft constraintsNoYes Noise accommodation No (in general) Yes Model comparison NoYES

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EEG/MEG Source localisation can be applied to single time-slice data or average over time (MEG and EEG) useful for comparing several few-dipole solutions for selected time points (N100, N170, etc.) although not dynamic, can be used for building up intuition about underlying generators, or using as a motivation for DCM source models implemented in Matlab and (very soon) available in SPM8 ECD solution: when and how to apply VB-ECD?

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EEG/MEG Source localisation

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EEG/MEG - Log-normal hyperpriors - Enforces the non-negativity of the hyperparameters - Enables Automatic Relevance Determination (ARD) Bayesian inference: multiple sparse priors

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EEG/MEG Source localisation Subjects MRI Anatomical warping Cortical mesh Canonical mesh [Un]-normalising spatial transformation MNI Space Forward model: canonical mesh

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EEG/MEG Source localisation From Sensor to MRI space MRI derived meshes MEG Full setup EEG Rigid Transformation HeadShape Surface Matching + HeadShape Forward model: coregistration

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Main references EEG/MEG Source localisation Friston et al. (2008) Multiple sparse priors for the M/EEG inverse problem Kiebel et al. (2008) Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG Mattout et al. (2007) Canonical Source Reconstruction for MEG Daunizeau and Friston (2007) A mesostate-space model for EEG and MEG Henson et al. (2007) Population-level inferences for distributed MEG source localization under multiple constraints: application to face-evoked fields Friston et al. (2007) Variational free energy and the Laplace approximation Mattout et al. (2006) MEG source localization under multiple constraints Friston et al. (2006) Bayesian estimation of evoked and induced responses Phillips et al. (2005) An empirical Bayesian solution to the source reconstruction problem in EEG

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