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

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

Introduction: EEG/MEG as Neuroimaging techniques Source localisation Introduction: EEG/MEG as Neuroimaging techniques MRI EEG MEG spatial resolution (mm) invasivity weak strong 5 10 15 20 temporal resolution (ms) 1 102 103 104 105 sEEG MEG EEG fMRI MRI(a,d) PET SPECT OI OI

Data importation/convertion EEG/MEG Source localisation MEEG functionalities in SPM8 Data Preperation 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 New MEEG data format based on “object-oriented” coding More stable interfacing and user-friendly  and a bit harder for developers  5

“Usual“ preprocessing EEG/MEG Source localisation MEEG functionalities in SPM8 Data Preperation “Usual“ preprocessing Filtering Re-referencing Epoching Artefact and bad channel rejection Averaging Displaying … 6

MEEG functionalities in SPM8 EEG/MEG Source localisation MEEG functionalities in SPM8 Data Preprocessing Source reconstruction Scalp Data Analysis Statistical Parametric Mapping Dynamic Causal Modelling 7

MEEG “usual” results MEG experiment of Face perception4 EEG/MEG Source localisation MEEG “usual” results MEG experiment of Face perception4 100 200 300 400 time (ms) Right temporal evoked signal faces scrambled M170 Energy changes (Faces - Scrambled, p<0.01) 0.1 0.2 0.4 0.6 0.8 time (s) 10 20 30 40 35 45 15 25 0.7 0.5 0.3 -0.1 1 2 3 -2 -3 -1 frequency (Hz) 4Electrophysiology 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… 9

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

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

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

Forward model: formulation EEG/MEG Source localisation Forward model: formulation Forward model data forward operator dipole parameters noise

Forward model: imaging/distributed model EEG/MEG Source localisation Forward model: imaging/distributed model data gain matrix dipole amplitudes noise

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

Inverse problem: an ill-posed 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) Existence Unicity Stability Inverse problem

Inverse problem: an ill-posed 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) Existence Unicity Stability Inverse problem

Inverse problem: an ill-posed 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) Existence Unicity Stability Inverse problem Introduction of prior knowledge (regularization) is needed

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

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

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

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

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

Y J μ1 μq λ1 λk Bayesian inference: graphical representation EEG/MEG Source localisation Bayesian inference: graphical representation Y J μ1 μq λ1 λk prior likelihood

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

Bayesian inference: model comparison EEG/MEG Source localisation Bayesian inference: model comparison At convergence model Mi Fi 1 2 3

Outline EEG/MEG Introduction Forward model Inverse problem Source localisation Outline Introduction Forward model Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

Conclusion: At the end of the day... 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 R L

Conclusion: Summary EEG/MEG • EEG/MEG source reconstruction: Source localisation Conclusion: Summary Forward model Inverse problem • 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

EEG/MEG Source localisation Change speaker… Again !

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

but a priori fixed number of sources considered EEG/MEG Source localisation ECD approach: principle Forward model data forward operator dipole parameters noise but a priori fixed number of sources considered  iterative fitting of the 6 parameters of each dipole 32

ECD solution: variational Bayes (VB) approach EEG/MEG Source localisation ECD solution: variational Bayes (VB) approach Dipole locations s and dipole moments w generated data using ε is white observation noise with precision γy. The locations s and moments w are drawn from normal distributions with precisions γs and γw. These are drawn from a prior gamma distribution. 33

“Classical” VB ECD solution: “classical” vs. VB approaches EEG/MEG Source localisation ECD solution: “classical” vs. VB approaches “Classical” VB Hard constraints Yes Soft constraints No Noise accommodation (in general) Model comparison YES 34

ECD solution: when and how to apply VB-ECD? 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 35

EEG/MEG Source localisation 36

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

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

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

Main references 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