DCM for ERP/ERF: theory and practice Melanie Boly Based on slides from Chris Phillips, Klaas Stephan and Stefan Kiebel

Dynamical Causal Modelling A sophisticated technique to investigate effective connectivity of the brain for fMRI and EEG / MEG data: ? ? EEG / MEG data: The goal of DCM is to explain evoked responses as the output of an interacting network consisting of a few areas that receive an input stimulus.

Terminology: effective connectivity? Functional specialisation: Identification of a particular brain region with a specific function. Functional integration: Identifying interactions among specialised neural populations & how these depend on the context. Functional connectivity: Is defined as correlations between remote neuro- physiological events. Effective connectivity: Refers explicitly to the influence that one neuronal system exerts over another, either at a synaptic (i.e. synaptic efficacy) or population level.

Effective connectivity in DCM  the influence that one neural system exerts over another how is this affected by experimental manipulations - how is this affected by experimental manipulations  considers the brain as a physical interconnected system  requires - an anatomical model of which regions are connected and - a mathematical model of how the different regions interact

Neural state equation: Electric/magnetic forward model: neural activity  EEG MEG LFP DCM: generative model for fMRI and ERPs Neural model: 1 state variable per region bilinear state equation no propagation delays Neural model: 8 state variables per region nonlinear state equation propagation delays fMRI ERPs inputs Hemodynamic forward model: neural activity  BOLD

Neural mass model of a cortical macrocolumn = Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Extrinsic inputsExtrinsic inputs Excitatory connection Inhibitory connection MEG/EEG signal MEG/EEG signal mean firing rate  mean postsynaptic potential (PSP) mean PSP  mean firing rate Function P Function S CONNECTIVITY ORGANISATION POPULATION DYNAMICS

Neural mass model of a cortical macrocolumn = Excitatory Interneurons H e,  e Pyramidal Cells H e,  e Inhibitory Interneurons Hi,  i Extrinsic inputsExtrinsic inputs Excitatory connection Inhibitory connection   e,  i : synaptic time constant (excitatory and inhibitory)  H e, H i : synaptic efficacy (excitatory and inhibitory)   1,…,   : intrinsic connection strengths  propagation delays 22 11 44 33 MEG/EEG signal MEG/EEG signal Parameters: Jansen & Rit (1995) Biol. Cybern. David et al. (2006) NeuroImage mean firing rate  mean postsynaptic potential (PSP) mean PSP  mean firing rate ~H ~~ Function P Function S

Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Bottom-up Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Top-down Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Excitatory Interneurons Pyramidal Cells Inhibitory Interneurons Lateral aFaF aBaB aLaL Excitatory connection Inhibitory connection Hierarchical Connections

neural mass model Excitatory IN Inhibitory IN Pyramidal cells Intrinsic Forward Backward Lateral Input u area model Extrinsic David et al., 2005 David and Friston, 2003 Model parameters (I) 1 2

neural mass model Layer 4 Supra-granular Infra-granular Intrinsic Forward Backward Lateral Input u area model Extrinsic David et al., 2005 David and Friston, 2003 Model parameters (I) 1 2    e,  i : synaptic time constant (excitatory and inhibitory)  H e, H i :synaptic efficacy (excitatory and inhibitory)   1,…,   : connectivity constants Connectivity matrices 22 11 33 44  e, H e  i, H i within-area parameters between-area parameters

Extrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic backward connections Intrinsic connections neuronal (source) model Extrinsic lateral connections State equations Hierarchical DCM for M/EEG mean PSP  mean firing rate Function S

Extrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic backward connections Intrinsic connections neuronal (source) model Extrinsic lateral connections State equations Output equation Lead field Hierarchical DCM for M/EEG

Electromagnetic forward model for M/EEG Depolarisation of pyramidal cells Forward model: lead field & gain matrix Scalp data Forward model

Practical Example …

Introduction Example: Mismatch Negativity pseudo-random auditory sequence 80% standard tones – 500 Hz 20% deviant tones – 550 Hz time standardsdeviants Oddball paradigm raw data preprocessing convert to matlab file filter epoch down sample artifact correction average 128 EEG scalp electrodes SPM ERPs of 12 subjects, 2 conditions (standard + deviant) data

Grand Mean (average over subjects) ms  V standards deviants MMN DCM: 1) Models the difference between two evoked responses … 2) … as a modulation of some of the inter-aereal connections.

Finally … SPM! DCM for Evoked Responses Also for steady-state responses (SSR) and induces responses (IND) …

Choose time window Choose nr. of components Trial indices

Spatial Forward Model Default: Each area that is part of the model is modeled by one equivalent current dipole (ECD). Depolarisation of pyramidal cells Sensor data Spatial model

STG A1 IFG MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002). Assumed Sources: 1.Left A1 2.Right A1 3.Left STG 4.Right STG 5.Right IFG Assumptions … Find the coordinates of the sources … (in mm in MNI coordinates).

Sources’ names Sources’ coordinates Onset time for modelling How to spatially model ER

A1 STG input STG IFG modulation of effective connectivity Opitz et al., 2002 Doeller et al., 2003 rIFG rSTG rA1lA1 lSTG DCM specification …

A1 STG input STG IFG modulation of effective connectivity Specify extrinsic connections Input Modulatory effect Intrinsic connections from to e.g. from left A1 to left STG Invert DCM

Extrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic backward connections Intrinsic connections neuronal (source) model Extrinsic lateral connections State equations Output equation Lead field Then.. Optimization of the parameters

Model Inversion: fit the data Data We need to estimate the extrinsic connectivity parameters and their modulation from data. Predicted data

Coupling B Probability ≠ prior means Posterior means for gain modulations

A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input A1 STG Forward Backward Lateral input Forward-FBackward-B Forward and Backward-FB STG IFG modulation of effective connectivity Alternative Models for Comparison …

MOG LG RVF stim. LVF stim. FG LD|RVF LD|LVF LD MOG LG RVF stim. LVF stim. FG LD LD|RVFLD|LVF MOG m2m2 m1m1 Stephan et al Group level BMS resistant to outliers

Exceedance probability Estimates of Dirichlet parameters Post. expectations of model probabilities Stephan et al. 2009

Conclusions DCM is a sophisticated technique to investigate effective connectivity Combines a biologically plausible neuronal mass model with a spatial forward model to generate a predicted data set Allows us to estimate connectivity parameters & how they are modulated between conditions And to compute the model evidence in order to single out the best model of the ones proposed. Underlying theory is complex, but SPM analysis is comparatively simple. But: requires a lot of previous knowledge. DCM is not a method to do ERP source reconstruction but knowledge about possible sources is a prerequisite for applying DCM to a data set. DCM is not exploratory!

10 simple rules for dynamic causal modelling : 1) Know what is causal about dynamic causal model - In EEG: inferences about conduction delays is allowed, not in fMRI 2) Know your hypothesis and how to test it - anatomy of the network – inference on model structure or parameters 3) Use Bayesian Model selection as a fist step - Results on connection parameters depend on the accuracy of the model 4) Motivate model space carefully - parametrize model space – test systematically different models (factorial) 5) Choose an appropriate method for group-level inference on model structure - fixed/ random effects – family-level inference

10 simple rules for dynamic causal modelling: 6) Know what you can do and what you can’t do with bayesian model selection - model defined for one particular data set, - cannot change regions in fMRI, cannot change preprocessing steps in general - test an appropriate set of models 7) Choose an appropriate method for group inference on parameters - RFX vs FFX, bayesian model averaging 8) Optimize design and data acquisition - in EEG: record electrodes on the scalp – do first feature selection 9) Use anatomical information and computational models to refine your DCM - can improve model evidence 10) Report the modelling approach and results in detail

References: Jansen BH, Rit VG, (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics 73:357–366 David O, Friston KJ (2003). A neural mass model for MEG/EEG: coupling and neuronal dynamics. Neuroimage 20:1743–1755 Kiebel SJ, Garrido MI, Moran RJ, Friston KJ (2008). Dynamic causal modeling for EEG and MEG. Cognitive Neurodynamics (2008) 2:121–136 SPM8 Manual:

Thanks to Marta Garrido & Rosalyn Moran