EEGMEG Source Localisation Jrmie Mattout Christophe Phillips SPM

EEG/MEG Source Localisation Jérémie Mattout & Christophe Phillips ? SPM Short Course – Wellcome Trust Centre for Neuroimaging – May 2007

EEG/MEG Source localisation Introduction Data Preprocessing Source reconstruction Scalp Data Analysis Statistical Parametric Mapping Dynamic Causal Modelling

EEG/MEG Source localisation Overview Forward Computation (K) Inverse Computation EEG/MEG sources EEG/MEG generative model Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods

EEG/MEG Source localisation Equivalent Current Dipoles (ECD) An ill-posed inverse problem Imaging or Distributed Jacques Hadamard (1865 -1963) 1. Existence 2. Unicity 3. Stability EEG/MEG inverse methods « 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 ? »

EEG/MEG Source localisation Equivalent Current Dipoles (ECD) An ill-posed inverse problem Imaging or Distributed Jacques Hadamard (1865 -1963) 1. Existence 2. Unicity 3. Stability EEG/MEG inverse methods Prior information is needed

EEG/MEG Source localisation Bayesian Formulation « 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 Bayes’ Rule ? Posterior Y: data J : sources M: model assumptions Likelihood Priors Gaussian densities: defined by their means and variances

EEG/MEG Source localisation General procedure Inversion

EEG/MEG Source localisation User interface File manager Current Analysis Meshing Co-registration Forward computation Inverse solution

EEG/MEG Source localisation Anatomical model – Source space Individual cortical mesh MNI Space Canonical mesh Subject’s MRI Anatomical warping [Un]-normalising spatial transformation Cortical mesh

EEG/MEG Source localisation Coregistration From Sensor to MRI space EEG fiducials Head. Shape Rigid + Transformation Surface Matching Head. Shape MRI derived meshes MEG Full setup

EEG/MEG Source localisation Forward Computation Computing the operator K 3 spheres EEG/MEG sources 1 sphere # sensors # dipoles K Lead field matrix

EEG/MEG Source localisation Data Likelihood Linear Generative Model Mesh shape and size Head model M

EEG/MEG Source localisation Priors on the sources Incorporating Multiple Priors # dipoles … IID (Minimum Norm) Spatial smoothness (LORETA) Multiple sparse priors (MSP)

EEG/MEG Source localisation Parametric Empirical Bayesian Inference (I) Hierarchical model … Model Mi 2 nd Level … 1 st Level Mesh shape and size Likelihood Posterior Evidence Prior Head model

EEG/MEG Source localisation Parametric Empirical Bayesian Inference (II) EM/Re. ML algorithm M-step E-step ^ C, ^ λ^ and μ^ - PEB inference yields posterior estimates: J, ^ ^ - Knowing J and C, Posterior Probability Maps (PPM) can be computed

EEG/MEG Source localisation Parametric Empirical Bayesian Inference (III) Model comparison p(Y|Mi) 1 2 3 model Mi

EEG/MEG Source localisation Conclusion First level analysis PEB PPM Second level analysis Individual summary statistics … RFX analysis p < 0. 01 uncorrected SPM

To be continued…

EEG/MEG Source localisation ECD approach Forward Computation (K) Inverse Computation EEG/MEG sources EEG/MEG generative model Equivalent Current Dipoles (ECD) Imaging or Distributed EEG/MEG inverse methods

EEG/MEG Source localisation ECD approach: model Problem to solve: Y = KJ + E A priori fixed number of sources considered, (usually less than 5) over-determined but nonlinear problem iterative fitting of the 6 parameters of each source K depends on the source location r → non-linear relationship with Y : Y = K(r) J + E J are the source intensity (incl. orientation) ^ = K J^ → linear relationship with Y, once K is fixed: J^ = K - Y and Y

Source localisation ECD approach: optimisation 1 D example of optimisation problem: Cost function EEG/MEG Value of parameter Local minimum Global minimum The iterative optimisation procedure can only find a local minimum the starting location(s) used can influence the solution found !

EEG/MEG Source localisation ECD approach: results For an ECD solution, initialise the dipoles • at multiple random locations and repeat the fitting procedure cluster of solutions ? • at a «guessed» solution spot, • then let the dipole free to move • keep the location fixed (also named « seeded-ECD » ) Eventually, • Simple focused solution: dipole coordinates • Time course of activity for each dipole

EEG/MEG Source localisation ECD approach: interpretation and limitation • How many dipoles ? The more sources, the better the fit… in a mathematical sense !!! (Still the number of sources limited : 6 x. Ns < Ne) • Moreover it is NOT possible to mathematically compare 2 models with different number of sources ! • Is a dipole, i. e. a punctual source, the right model for a patch of activated cortex ? • What about the influence of the noise ? Find the confidence interval. • Is the seeded-ECD a good approach ? Given that you find what you put in…

EEG/MEG Source localisation ECD approach: application epilepsy 2 D EEG map of first peak, above F 4 front L R back

EEG/MEG Source localisation Forward Problem: analytical vs. numerical solution The head is NOT spherical: cannot use the exact analytical solution because of model/anatomical errors. Realistic model needs BEM solution: surfaces extraction computationnaly heavy errors for superficial sources Could we combine the advantages of both solutions ? Anatomically constrained spherical head models, or pseudo-spherical model.

EEG/MEG Source localisation Anatomically constrained spherical model Scalp (or brain) surface Best fitting sphere: centre and radii (scalp, skull, brain) Spherical transformation of source locations Leadfield for the spherical model

EEG/MEG Source localisation Anatomically constrained spherical model Dipole: defined by its polar coordinates (Rd, IRM, qd, fd ) Fitted sphere: defined by its centre and radius, (c. Sph, RSph) Fitted sphere Direction (qd, fd) Rscalp(qd, fd) Rd, IRM c. Sph RSph Scalp surface

EEG/MEG Source localisation Application: scalp surface Fitted sphere and scalp surface

EEG/MEG Source localisation Application: cortical surface

EEG/MEG Source localisation

EEG/MEG Source localisation Priors on the sources (II) Hyperpriors - Log-normal hyperpriors - Enforces the non-negativity of the scale parameters - Enables Automatic Relevance Determination (ARD)