Dynamic Causal Model for evoked responses in M/EEG Rosalyn Moran

Overview Dynamic Causal Modelling – Motivation Dynamic Causal Modelling – Generative model Bayesian model inversion/selection Example

Overview Dynamic Causal Modelling – Motivation Dynamic Causal Modelling – Generative model Bayesian model inversion/selection Example

Mismatch negativity (MMN) – DCM Motivation standards deviants Paradigm pseudo-random auditory sequence 80% standard tones – 500 Hz 20% deviant tones – 550 Hz time Raw data (128 sensors) Preprocessing (SPM8) Evoked responses (here: single sensor) μV time (ms)

Dynamic Causal Modelling- Motivation amplitude (μV) time time (ms) standard sensors deviant sensors

Dynamic Causal Modelling- Motivation time standard Conventional approach: Reduce evoked response to a few variables. sensors deviant Alternative approach that tells us about communication among brain sources? sensors

Dynamic Causal Modelling- Motivation Build a generative model for spatiotemporal data and fit to evoked responses. ??? Assume that both ERs are generated by temporal dynamics of a network of a few sources A1 A1 Describe temporal dynamics by differential equations Dynamic Causal Modelling Each source projects to the sensors, following physical laws Solve for the model parameters using Bayesian model inversion 7

DCM does not localise active sources Raw data (128 sensors) Preprocessing (SPM8) Evoked responses (here: single sensor) μV time (ms) MNI coordinates from the literature Source Localisation DCM

Overview Dynamic Causal Modelling – Motivation Dynamic Causal Modelling – Generative model Bayesian model inversion/selection Example

The Generative model fMRI ERPs Neural state equation: inputs Hemodynamic forward model: neural activityBOLD (nonlinear) Electric/magnetic forward model: neural activityEEG MEG LFP (linear) Neural state equation: fMRI 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 inputs

The Generative model Source dynamics f Spatial forward model g states x Evoked response parameters θ data y Input u

Macro- and meso-scale macro-scale meso-scale micro-scale 12 external granular layer external pyramidal layer internal granular layer internal pyramidal layer AP generation zone synapses 12

meso-scale 13 AP generation zone external granular layer external pyramidal layer synapses internal granular layer internal pyramidal layer AP generation zone 13

Neural mass equations and connectivity State equations Extrinsic lateral connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic forward connections Intrinsic connections Extrinsic backward connections neuronal (source) model 14

Overview Dynamic Causal Modelling – Motivation Dynamic Causal Modelling – Generative model Bayesian model inversion/selection Example

Model selection & Hypothesis Testing ... Model n Model selection: data y STG STG STG A1 A1 A1 best?

Model selection & Hypothesis Testing ... Model n Model selection: data y STG STG STG A1 A1 A1 17

Model selection & Hypothesis Testing ... Model n Model selection: data y STG STG STG STG A1 A1 A1 A1 18

Bayesian Statistics prior knowledge new data posterior  likelihood ∙ prior Bayes theorem allows one to formally incorporate prior knowledge into computing statistical probabilities. In DCM for ERPs priors include time constants, PSP, delays etc. The “posterior” probability of the parameters given the data is an optimal combination of prior knowledge and new data, weighted by their relative precision.

Define likelihood model Bayesian Inversion Neural Parameters: Dynamic Model Define likelihood model Observer function: Forward Spatial Model Specify priors Inference on models Invert model Inference on parameters Make inferences

Bayesian Inversion Specify generative forward model (with prior distributions of parameters) Evoked responses Expectation-Maximization algorithm Iterative procedure: Compute model response using current set of parameters Compare model response with data Improve parameters, if possible Posterior distributions of parameters Model evidence 21

Bayesian Model Selection Model evidence: Approximation: Free Energy accounts for both accuracy and complexity of the model allows for inference about structure (generalisability) of the model Fixed Effects Model selection via log Group Bayes factor: Random Effects Model selection via Model probability:

Overview Dynamic Causal Modelling – Motivation Dynamic Causal Modelling – Generative model Bayesian model inversion/selection Example

Mismatch negativity (MMN) – DCM Motivation standards deviants Paradigm pseudo-random auditory sequence 80% standard tones – 500 Hz 20% deviant tones – 550 Hz time Raw data (128 sensors) Preprocessing (SPM8) Evoked responses (here: single sensor) μV Garrido et al., (2007), NeuroImage time (ms)

Models for Deviant Response Generation Model for mismatch negativity Models for Deviant Response Generation Garrido et al., (2007), NeuroImage

Group model comparison Bayesian Model Comparison Group level log-evidence Forward (F) Backward (B) Forward and Backward (FB) subjects Garrido et al., (2007), NeuroImage

Models for Deviant Response Generation Temporal Hypotheses Do forward and backward connections operate as a function of time? Models for Deviant Response Generation Peristimulus time 1 Peristimulus time 2 Garrido et al., PNAS, 2008 27

Grand mean ERPs Bayesian model comparison among DCMs of grand mean ERPs. (A) Grand mean ERP responses, i.e., averaged over all subjects, to the deviant tone overlaid on a whole-scalp map of 128 EEG electrodes. (B) Overlapped ERP responses to deviant tones from all 128 sensors over the peristimulus interval [0, 400] (in milliseconds). (C) Differences in negative free-energy or log-evidence comparing the model with backward connections (FB) against the model without (F). The gray patch indicates the interval chosen to model the ERPs for each individual subject (see Fig. 3). Garrido M. I. et.al. PNAS 2007;104:20961-20966 ©2007 by National Academy of Sciences

Model Fit time (ms) time (ms) Garrido et al., PNAS, 2008

Bayesian model comparison across subjects Bayesian model comparison across subjects. (A) Comparison of the model with backward connections (FB) against the model without (F), across all subjects over the peristimulus interval 180–260 ms. The dots correspond to differences in log-evidence for 11 subjects over time. The solid line shows the average log-evidence differences over subjects [this is proportional to the log-group Bayes factor (Bf) or to the differences in the free energy of the two models (ΔF); see Materials and Methods for details]. The points outside the gray zone imply very strong inference (≥99% confidence that one model is more likely), i.e., model FB supervenes over F for positive points and the converse for negative points. (B) Histogram showing the number of subjects in each of seven levels of inference on models with and without backward connections across the peristimulus interval 180–260 ms. Garrido M. I. et.al. PNAS 2007;104:20961-20966 ©2007 by National Academy of Sciences

Summary DCM enables testing hypotheses about how brain sources communicate. DCM is based on a neurobiologically plausible generative model of evoked responses. Differences between conditions are modelled as modulation of connectivity. Inference: Bayesian model selection 31