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 EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion EEG/MEG Introduction: EEG/MEG as Neuroimaging techniques Source localisation MRI MEG EEG spatial resolution (mm) OI EEG 20 invasivity MEG weak strong SPECT 15 OI PET 10 fMRI 5 sEEG MRI(a,d) 1 10 102 103 104 105 temporal resolution (ms) 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 MEEG functionalities in SPM8 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 EEG/MEG Source localisation Data Preperation MEEG functionalities in SPM8 “Usual“ preprocessing • Filtering • Re-referencing • Epoching • Artefact and bad channel rejection • Averaging • Displaying •… EEG/MEG Source localisation MEEG functionalities in SPM8 Data Preprocessing Source reconstruction Scalp Data Analysis Statistical Parametric Mapping Dynamic Causal Modelling EEG/MEG MEEG “usual” results Source localisation MEG experiment of Face perception4 Right temporal evoked signal Energy changes (Faces - Scrambled, p<0.01) 45 faces scrambled 3 40 2 frequency (Hz) 35 100 200 M170 4Electrophysiology 300 time (ms) 400 1 30 25 0 20 -1 15 -2 10 -3 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 time (s) 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, 2003. EEG/MEG Source localisation Change speaker… EEG/MEG Source localisation Introduction: overview Forward model Inverse problem EEG/MEG source reconstruction process EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion EEG/MEG Source localisation Forward model: source space source biophysical model: current dipole Equivalent Current Dipoles (ECD) - few dipoles with EEG/MEG source models free location and orientation Imaging or Distributed - many dipoles with fixed location and orientation EEG/MEG Forward model: formulation Source localisation Forward model Y f J E data forward operator dipole noise parameters EEG/MEG Source localisation Forward model: imaging/distributed model Y KJ E data gain matrix dipole noise amplitudes EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion 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 (1865-1963) 1. Existence 2. Unicity 3. Stability Inverse problem 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 (1865-1963) 1. Existence 2. Unicity 3. Stability Inverse problem 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 (1865-1963) 1. Existence 2. Unicity 3. Stability Inverse problem Introduction of prior knowledge (regularization) is needed EEG/MEG Source localisation Inverse problem: regularization Spatial and temporal priors Adequacy with other modalities Data fit data fit W = I : minimum norm W = Δ : maximum smoothness (LORETA) prior (regularization term) EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion EEG/MEG Bayesian inference: probabilistic formulation Source localisation Forward model likelihood Inverse problem posterior likelihood posterior evidence prior EEG/MEG Source localisation Bayesian inference: hierarchical linear model pY J , Μ sensor (1st) level likelihood pJ Μ source (2nd) level prior q Ce 1Qe1 qQe C p 1Q k Q 1 p k p Q : (known) variance components (λ,μ) : (unknown) hyperparameters EEG/MEG Source localisation Bayesian inference: variance components p( J M ) ~ N (0, C p ) C p 1Q k Q 1 p k p # dipoles # dipoles … Minimum Norm (IID) Maximum Smoothness (LORETA) Multiple Sparse Priors (MSP) EEG/MEG Bayesian inference: graphical representation Source localisation λ1 λk J μ1 prior pJ Μ p J 1 ,, k , Q1p ,, Q pk Y likelihood μq pY J , Μ p Y J , 1 ,, q , Qe1 ,, Qeq , K EEG/MEG Source localisation Bayesian inference: iterative estimation scheme Expectation-Maximization (EM) algorithm E-step qˆ ( J M ) arg max F q( J M ) p( J Y , ˆ, ˆ , M ) M-step (ˆ, ˆ ) arg max F , p(Y J , M ) p( J M ) ln p(Y M ) F ln q ( J M ) q( J M ) p( J Y , M ) p(Y M ) ln q ( J M ) q( J M ) EEG/MEG Bayesian inference: model comparison Source localisation At convergence F ln p(Y | M ) accuracy(M ) complexity(M ) Fi 1 2 3 model Mi EEG/MEG Source localisation Outline 1. Introduction 2. Forward model 3. Inverse problem 4. Bayesian inference applied to the EEG/MEG inverse problem 5. Conclusion EEG/MEG Source localisation Conclusion: At the end of the day... Individual reconstructions in MRI template space L R R L Group results p < 0.01 uncorrected EEG/MEG Source localisation Conclusion: Summary • EEG/MEG source reconstruction: 1. forward model 2. inverse problem (ill-posed) • Prior information is mandatory • 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 EEG/MEG Source localisation Change speaker… Again ! EEG/MEG Source localisation Equivalent Current Dipole (ECD) solution source biophysical model: current dipole few dipoles with free location and orientation Equivalent Current Dipoles (ECD) EEG/MEG source models Imaging or Distributed many dipoles with fixed location and orientation EEG/MEG ECD approach: principle Source localisation Forward model Y f J E data forward operator dipole noise parameters but a priori fixed number of sources considered iterative fitting of the 6 parameters of each dipole EEG/MEG ECD solution: variational Bayes (VB) approach Source localisation w s Dipole locations s and dipole moments w generated data using w s ε is white observation noise with precision γy. y y G( s ) w y The locations s and moments w are drawn from normal distributions with precisions γs and γw. These are drawn from a prior gamma distribution. EEG/MEG Source localisation ECD solution: “classical” vs. VB approaches “Classical” VB Hard constraints Yes Yes Soft constraints No Yes Noise accommodation No Yes Model comparison (in general) No YES EEG/MEG Source localisation ECD solution: when and how to apply VB-ECD? • 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 EEG/MEG Source localisation EEG/MEG Source localisation Bayesian inference: multiple sparse priors p( J , M ) ~ N (0, C ) k exp(k ) k ~ N (,) - Log-normal hyperpriors - Enforces the non-negativity of the hyperparameters - Enables Automatic Relevance Determination (ARD) EEG/MEG Source localisation Forward model: canonical mesh MNI Space Canonical mesh Subjects MRI Anatomical warping [Un]-normalising spatial transformation Cortical mesh EEG/MEG Forward model: coregistration Source localisation From Sensor to MRI space EEG HeadShape Rigid Transformation + Surface Matching HeadShape MRI derived meshes MEG Full setup EEG/MEG Source localisation Main references 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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