Measuring Activation and Causality using multiple Prior Information Pedro A. Valdés-Sosa Cuban Neuroscience Center

Mapping

Brain Maps

Multimodal T1-Nissl-cryotomy-PET-myelin stain

Localization versus Connectivity Hiparcus ( II BC) Jackson US air Traffic Luria

Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity

Brain Tomographies Physical Model of some brain characteristic Prediction of measurement Direct Problem Image of some brain characteristic measurement Inverse Problem a Priori Information

EEG/MEG Forward Problem Primary current j EEG/MEG v

EEG inverse Problem Bayesian Inference!!

Methods for Regression Data VARETA LORETA ICA Non Negative Matrix Factorization In fact can be unified or combined

L0 Norm “Sparsness” AIC, BIC, TIC, RIC “subset selection”“Matching Purusit”“Dipoles”

L1 Norm “Sparseness” “Lasso”“Basis Pursuit”“FOCUSS” Connection with ICA

Fast LARS Algorithm (Friedman, Hastie, Tibshirani) Regularization path for diabetes data

L2 Norm “Minimum Norm” “Ridge”“Frames”“Minimum Norm”

Simplest EEG inverse Problem Bayesian Inference!!

Multiple Priors SparsenessMinimal Norm Non smoothDipoles=FOCUSSMinimum Norm SmoothVARETALORETA

Which inverse solution to choose?: let the data decide combining all solutions

Bayesian Model Averaging For 69 compartments

Simulations with Bayesian Model Averaging

BMA during concurrent EEG/fMRI

Combining Priors Fused Lasso VARETA-LORETA

Combining penalties (L1,I) (L1,L)

Between LORETA and VARETA LORETA VARETA Solution Chosen

Further Combination: Multiple Priors plus (semi) Non Negative Matrix Factorization Non Negative Matrix Factorizations used for data reduction Equivalent to Cluster Analysis

Multiple Priors plus (semi) Non Negative Matrix Factorization

Fast Non-negative LARS Algorithm (Morup) Regularization paths for diabetes data

Results for a Simulation 64 Channels, 1 Patch complex time series BIC Regularization path

Results of a Simulation

Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity

Effective vs. Functional Connectivity (Karl Friston)

Statistical Analysis of Causal Modeling "Beyond such discarded fundamentals as 'matter' and 'force' lies still another fetish amidst the inscrutable arcana of modern science, namely, the category of cause and effect.“ Karl Pearson (1911)

Granger (Non) Causality for TWO time series Granger Non Causality t t-1 t =1,…,N

Granger Causality of EEG signals Freiwald et al. (1999) J. Neurosci. Methods. 94: C3 C4 t t-1

What happens when you have a LOT of time series? 12…p12…p … t t-1 t =1,…,N Long history: Bressler, Baccala, Kaminski, Eichler, Goebel

Problems with the Multivariate Autoregressive Model for Brain Manifolds p→∞p→∞ # of parameters likelihood

Regions of Interest Alemán-Gómez Y. et al. PS0103

Point influence Measures is the simple test

 38 Spike and Wave

 39 Spike and Wave

What happens when you have a LOT of time series? 12…p12…p … t t-1 t =1,…,N Long history: Bressler, Baccala, Kaminski, Eichler, Goebel

a) Teat CG as a Random Field Concept applied to correlation fields by Worsley Usual SPM: RF is the brain New Idea RF is Cartesian product of Brain by Brain = = X

Granger Causality must be measured on a MANIFOLD

Influence Measures defined on a Manifold An influence field is a multiple test and all for a given

Discretization of the Continuos AR Model

Influence Fields and Bayesian Estimation Influence field likelihood prior

Influence Fields Outield Infield

Priors for Influence Fields maximal SMOOTHNESS Valdés-Sosa PA Neuroinformatics (2004) 2:1-12 Valdés-Sosa PA et al. Phil. Trans R. Soc. B (2005) 360: Minimum norm I Minimum spatial laplacian L prior

vs FFA Amigdala Fear Static + Fear Dynamic Neutral Neural basis of emotional expression processing

Emotional Network (Dipole)

Cuban Neuroscience Center Concurrent EEG-fMRI recordings Fine time scale

Cuban Neuroscience Center Concurrent EEG-fMRI (  Rhythm)

Basis of concurrent EEG/MEG-fMRI analysis-voxel level Trujillo et al. IJBEM (2001)  BOLD  Vasomotor Feed Forward Signal  VFFS  Ensemble of Postsynaptic Potentials  ePSP  net Primary Current Density  nPCD  EEG/MEG

EEG/MEG-fMRI-voxel Inverese solution Association  BOLD  VFF S  ePSP  nPCD  EEG/MEG

correlationlog BOLD-log j

First order Autoregressive Model for fMRI and EEG

Estimated A for fMRI-EEG (f,s) using L1 regularizer

EEG-fMRI influence Fields Maximal Evidence dipole MN non smooth smooth nonsmooth+smooth dipole+MN

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Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity