DCM for ERP/ERF: theory and practice Giovanna Moretto and Friederike Schüür

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.

Different analyses for different purposes … Functional Connectivity Effective Connectivity Structural Equation Modelling Psycho-physiological interactions Kalman Filtering Volterra Series Dynamical Causal Modelling (DCM) Seed-voxel correlation analysis Eigenimage analysis Independent component analysis Psycho-physiological interactions

Introduction Example: Mismatch Negativity (EEG) Dynamical Causal Model Outline Introduction Example: Mismatch Negativity (EEG) Dynamical Causal Model Single Source Network of Sources Spatial Expression in Sensors Model Inversion Example in detail: Mismatch Negativity (EEG) DCM in SPM Only about Evoked Responses for an EEG data set (also possible for steady state responses and induced responses). Principle for e.g. induced responses is highly similar as well as DCM for MEG data sets. Only for Evoked responses and only for EEG … principle is the same for all others and once this is understood easy to integrate the differences.

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

Grand Mean (average over subjects) DCM: 1) Models the difference between two evoked responses … -100 -50 50 100 150 200 250 300 350 400 -4 -3 -2 -1 1 2 3 4 ms m V standards deviants MMN 2) … as a modulation of some of the inter-aereal connections.

How can the MMN be explained? Build a model to test hypotheses: Assume that both ERPs are generated by temporal dynamics of a few sources A1 A2 Describe temporal dynamics by differential equations Dynamic Causal Modelling Each source projects to the sensors, following physical laws Solve for the model‘s parameters using Bayesian model inversion

Why? What are we interested in … ? STG input IFG A1 STG input IFG 1.41 (99%) 0.93 (55%) First, to find the best model … Second, to determine the coupling parameters … 2.41 (100%) 4.50 (100%) 5.40 (100%) 1.74 (96%)

The Theory in more detail … Overview Single Source Network of Sources Spatial Expression in Sensors Model Inversion

Single Source State equations neuronal (source) model spiny stellate cells inhibitory interneurons pyramidal cells Input Intrinsic connections DCM adopts a neural mass model to explain source activity in terms of the ensemble dynamics of interacting inhibitory and excitatory subpopulations of neurons. This model emulates the activity of a source using three neural subpopulations each assigned to one of three cortical layers. Excitatory subpopulation  granular layer Inhibitory sub-population  supra granular layer Pyramidal cells  infra-granular layer see Jansen & Rit (1995) and David & Friston (2003) neuronal (source) model

Spatial Expression in Sensors In more detail … Overview Single Source Network of Sources Spatial Expression in Sensors Model Inversion

Extrinsic Connectivity State equations Extrinsic lateral connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic forward connections Intrinsic connections X  neural states of cortical sources U  exogenous inputs H  systems response Extrinsic backward connections neuronal (source) model

Spatial Expression in Sensors Overview Single Source Network of Sources Spatial Expression in Sensors Model Inversion

Spatial Forward Model Depolarisation of pyramidal cells Spatial model Sensor data Spatial model L  lead field matrix; accounts for passive conduction of electromagnetic field Relation scalp data h and source activity: linear & instantaneous (assumption) Reduce dimensionality of sensor data (modes later on) while retaining max. amount of information  projection to subspace defined by principle eigenvestors (modes) “In summary, our DCM comprises a state-equation that is based on neurobiological heuristics and an observer equation based on an electromagnetic forward model. By integrating the state-equation and passing the ensuing states through the observer equation, we generate a predicted measurement.” Default: Each area that is part of the model is modeled by one equivalent current dipole (ECD).

Spatial Expression in Sensors Overview Single Source Network of Sources Spatial Expression in Sensors Model Inversion

Model Inversion Data Predicted data input 50 100 150 200 250 -8 -6 -4 -2 2 4 6 time (ms) Observed (adjusted) 1 Predicted data We need to estimate the extrinsic connectivity parameters and their modulation from data. 50 100 150 200 250 -8 -6 -4 -2 2 4 6 time (ms) Predicted First 60ms look weird but that’s because we decided not to model first (early) responses.

DCM: Model Inversion Data Predicted data (model) Expectation-Maximization algorithm Iterative procedure: Compute model response using current set of parameters Compare model response with data Improve parameters, if possible Output: Posterior distributions of parameters Make inferences on parameters

The Practical Part … The buttons … But actually, the practical part of DCM still involves a lot of theory, as we will see …

Back to the example: MMN Oddball paradigm -100 -50 50 100 150 200 250 300 350 400 -4 -3 -2 -1 1 2 3 4 ms m V standards deviants MMN standards deviants time Before the DCM: A. Collect, pre-process, and average EEG data. B. Make required assumptions based on already existing literature … e.g. for the location of the sources. Switch presenter …

Assumptions … MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002). “We argue that the right IFG mediates auditory deviance detection in case of low discriminability between a sensory memory trace and auditory input. This prefrontal mechanism might be part of top-down modulation of the deviance detection system in the STG.”

Assumptions … MMN could be generated by a temporofrontal network (Doeller et al. 2003; Opitz et al. 2002). Assumed Sources: Left A1 Right A1 Left STG Right STG Right IFG STG A1 IFG DCM requited prior knowledge, e.g. about source numbers and locations Find the coordinates of the sources … (in mm in MNI coordinates).

DCM specification … IFG STG STG A1 A1 input Opitz et al., 2002 rIFG lA1 rA1 lSTG rSTG A1 A1 Make a schematic model and determine which connections should be included … input Doeller et al., 2003 modulation of effective connectivity

Alternative Models for Comparison … IFG IFG IFG Forward and Forward - F Backward - B Backward - FB STG STG STG STG STG STG A1 A1 A1 A1 A1 A1 left and right primary auditory cortices (A1), left and right superior temporal gyrus (STG) and right inferior frontal gyrus (IFG), (A1) were chosen as cortical input stations for processing the auditory information. input input input Forward Forward Forward Backward Backward Backward Lateral Lateral Lateral modulation of effective connectivity

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

Choose nr. of components Choose time window Trial indices Choose nr. of components Model between trial effects Data must be spm format To reduce amount of data: projection to sub-space, modes is factors you extract that you keep (the more the more information but the more data, later vectors carry only little additional information)

How to spatially model ER Sources’ coordinates Onset time for modelling Sources’ names Animated Tight priors on location but not orientation (can compensate up to a certain extent for inaccuracies) Early responses are not modelled because the propagation of the stimulus impulse through the input nodes causes a delay For modelling first response only A matrix is used, for second the modulation (B-matrix)

e.g. from left A1 to left STG input IFG modulation of effective connectivity e.g. from left A1 to left STG Specify extrinsic connections Input to Intrinsic connections: modelled by H which reflects the max. post synaptic potential Modulatory effect Intrinsic connections from Invert DCM

Wait …

Coupling B Posterior means for gain modulations Probability ≠ prior means

Why? What are we interested in … ? STG input IFG A1 STG input IFG 1.41 (99%) 0.93 (55%) First, to find the best model … Second, to determine the coupling parameters … 2.41 (100%) 4.50 (100%) 5.40 (100%) 1.74 (96%)

Log evidence = accuracy - complexity Forward (F) Backward (B) Forward and Backward (FB)

Why? What are we interested in … ? STG input IFG A1 STG input IFG 1.41 (99%) 0.93 (55%) First, to find the best model … Second, to determine the coupling parameters … 2.41 (100%) 4.50 (100%) 5.40 (100%) 1.74 (96%)

ERP (sources) … right A1 Activity of interneuron populations 50 100 150 200 -0.2 0.2 0.4 0.6 0.8 right A1 A1 STG input IFG modulation of effective connectivity Activity of interneuron populations Activity of pyramidal cells trial 1 (pop. 1) trial 2 (pop. 1) trial 1 (pop. 2) trial 2 (pop. 2) trial 1 (pop. 3) trial 2 (pop. 3)

Response … Decided not to model early responses condition 1 50 100 150 200 250 -8 -6 -4 -2 2 4 6 time (ms) Observed (adjusted) 1 Predicted Observed (adjusted) 2 condition 1 condition 2

DCM output Forward and Backward - FB IFG STG STG A1 A1 input Forward reconstructed responses at source level (ERPs (sources)) 1.41 (99%) 0.93 (55%) STG STG coupling changes (coupling B) probability that a change occurred (coupling B) 2.41 (100%) 5.40 (100%) 1.74 (96%) 4.50 (100%) A1 A1 input Forward Backward standard Lateral deviant

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!

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: http://www.fil.ion.ucl.ac.uk/spm/doc/manual.pdf

Special Thanks to Rosalyn Moran

Thanks for your attention …. Any questions?