Dynamic Causal Modelling for M/EEG Stefan Kiebel Wellcome Trust Centre for Neuroimaging UCL

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Electroencephalography (EEG) amplitude (μV) time time (ms) trial type 1 channels trial type 2 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… channels

M/EEG analysis at sensor level time trial type 1 Approach: Reduce evoked response to a few variables, e.g.: The average over a few channels in peri-stimulus time. channels 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… trial type 2 Different approach that tells us more about the neuronal dynamics of localized brain sources? channels

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Dynamic Causal Modelling Build a model for spatiotemporal data: ??? Assume that both ERPs are generated by temporal dynamics of a network of a few sources A1 A2 Describe temporal dynamics by differential equations Dynamic Causal Modelling 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Each source projects to the sensors, following physical laws Solve for the model parameters using Bayesian model inversion

Mismatch negativity (MMN) mode 1 Oddball paradigm standards deviants mode 2 pseudo-random auditory sequence 80% standard tones – 500 Hz 20% deviant tones – 550 Hz time preprocessing mode 3 raw data convert to matlab file filter epoch down sample artifact correction average data reduction to principal spatial modes (explaining most of the variance) 128 EEG scalp electrodes ERPs / ERFs time (ms)

Model for mismatch negativity 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Garrido et al., PNAS, 2008

Macro- and meso-scale macro-scale meso-scale micro-scale 10 external granular layer external pyramidal layer internal granular layer internal pyramidal layer 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… AP generation zone synapses 10

The generative model Source dynamics f Spatial forward model g states x 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Evoked response parameters θ data y Input u

Neural mass equations and connectivity State equations Extrinsic lateral connections spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic forward connections Intrinsic connections 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Extrinsic backward connections neuronal (source) model 12

Spatial model Depolarisation of pyramidal cells Sensor data 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… 13

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Bayesian model inversion Specify generative forward model (with prior distributions of parameters) Measured data Expectation-Maximization algorithm Iterative procedure: Compute model response using current set of parameters Compare model response with data Improve parameters, if possible 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Posterior distributions of parameters Model evidence 15

Model comparison: Select Which model is the best? Model 1 Model comparison: Select model with highest model evidence data y Model 2 ... 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… best? Model n

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Mismatch negativity (MMN) 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Garrido et al., PNAS, 2008

Mismatch negativity (MMN) time (ms) time (ms) 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Garrido et al., PNAS, 2008

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Another (MMN) example Forward and Forward - F Backward - B Backward - IFG IFG IFG Forward and Forward - F Backward - B Backward - FB STG STG STG STG STG STG STG A1 A1 A1 A1 A1 A1 input input input Forward Forward Forward Backward Backward Backward Lateral Lateral Lateral modulation of effective connectivity

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

Overview of the talk 1 M/EEG analysis 2 Dynamic Causal Modelling 3 Bayesian model inversion 4 Examples

Evoked and induced responses Several events can induce the activity changes of neuronal populations. These changes could be either phase-locked to the stimulus onset (i.e. evoked activities) or non phase-locked (induced responses). To extract evoked potentials, people usually apply average technique to eliminate the non-stationary components, both the noise and the induced responses. In order to obtain the induced responses, the data were projected into the time frequency domain trail by trail and then average across trails. Trends Cogn Sci. 1999 Apr;3(4):151-162

Time-series data in channel space Dynamic power data in source space Modelling of induced responses Inversion of electromagnetic model L input Time-series data in channel space Dynamic power data in source space 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Aim: Explain dynamic power spectrum of each source as function of power input from other sources. Chen et al., Neuroimage, 2008

Face data (EEG): Network of four sources LF RF LV RV 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… input

Observed power spectra LV RV LF RF Time (ms) observed 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… Frequency (Hz)

Single subject results: Coupling functions LF RF RV LV RV RF 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… input Chen et al., Neuroimage, 2008

Observed and fitted power spectra LV RV LF RF Time (ms) observed Frequency (Hz) 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… fitted

Summary DCM combines state-equations for neural mass dynamics with spatial forward model. Differences between responses acquired under different conditions are modelled as modulation of connectivity within and between sources. Bayesian model comparison allows one to compare many different models and identify the best one. Make inference about posterior distribution of parameters (e.g., effective connectivity, location of dipoles, etc.). Many extensions to DCM for M/EEG are available in SPM8. 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… 30

Thanks to Karl Friston Marta Garrido CC Chen Jean Daunizeau 31 1- Modelling: capture data tendencies/regularities But: model quality <-> predictive ability => Parameters estimation 2- 2 forms of uncertainty: - stochastic - epistemological (=> reducible) -> Definition of “noise” 3- - Model sufficiently complex -> perfect data fit but suboptimal predictions - Model too simple -> poor data fit … 4- Link modelling to some measure of the uncertainty which is propagated through the model: model relevance is related to the quality of the information we can extract from the data about the modelled system… 31