Dynamic Causal Model for evoked responses in MEG/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

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

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

sensors standard deviant time Conventional approach: Reduce evoked response to a few variables. Alternative approach that tells us about communication among brain sources? 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 Describe temporal dynamics by differential equations Each source projects to the sensors, following physical laws Solve for the model parameters using Bayesian model inversion Dynamic Causal Modelling A1

DCM uses priors for source locations time (ms) μVμV Raw data (128 sensors) Preprocessing (SPM8) Evoked responses (here: single sensor) Source Localisation DCM MNI coordinates from the literature

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

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

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

One Source

Granular Layer: Excitatory Cells Infragranular layer: Pyramidal Cells Supragranular Layer: Inhibitory Cells macro-scalemeso-scalemicro-scale The state of a neuron comprises a number of attributes, membrane potentials, conductances etc. Modelling these states can become intractable. Mean field approximations summarise the states in terms of their ensemble density. Neural mass models consider only point densities and describe the interaction of the means in the ensemble

Dynamics AP generation zone synapses AP generation zone Granular Layer: Excitatory Cells Infragranular layer: Pyramidal Cells Supragranular Layer: Inhibitory Cells

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

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

Model Selection & Hypothesis Testing data y Model 1 Model 2... Model n Model selection: best? STG A1 STG A1

Model Selection & Hypothesis Testing data y Model selection: Model 1 Model 2... Model n STG A1 STG A1

posterior  likelihood ∙ prior 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. new data prior knowledge Bayesian Statistics

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

Evoked responses Specify generative forward model (with prior distributions of parameters) Expectation-Maximization algorithm Iterative procedure: 1.Compute model response using current set of parameters 2.Compare model response with data 3.Improve parameters, if possible 1.Posterior distributions of parameters 2.Model evidence

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

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

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

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

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

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

Grand mean ERPs Garrido M. I. et.al. PNAS 2007;104: ©2007 by National Academy of Sciences

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

Bayesian model comparison across subjects Garrido M. I. et.al. PNAS 2007;104: ©2007 by National Academy of Sciences

Bayesian model comparison across subjects First : Forward and Backward Connections are required to produce a deviant, “mismatch” response Then this was refined to show: Forward Connections are sufficient to generate early components of the mismatch ERP but Forward and Backward connections are required to generate late components of the ERP

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 Posterior Connectivity Estimates

mPFC VTA LFP DCM for Induced Responses DCM for Phase Coupling Conductance Based Mean Field Models DCM for Steady State Responses