Dynamic causal modelling of electromagnetic responses Karl Friston - Wellcome Trust Centre for Neuroimaging, Institute of Neurology, UCL In recent years, dynamic causal modelling has become established in the analysis of invasive and non-invasive electromagnetic signals. In this talk, I will briefly review the basic idea behind dynamic causal modelling – namely to equip a standard electromagnetic forward model, used in source reconstruction, with a neural mass or field model that embodies interactions within and between sources. A key point here is that the resulting forward or generative models can predict a large variety of data features – such as event or induced responses, or indeed their complex cross spectral density – using the same underlying neuronal model. Dynamic causal modelling brings a new perspective to characterising event and induced responses – empirical response components, previously reified as objects of study in their own right (such as the mismatch negativity or P300) now become data features that have to be explained in terms of neuronal dynamics and changes in distributed connectivity. In other words, dynamic causal modelling emphasises the neurobiological mechanisms that underlie responses – over all channels and peristimulus time – without particular regard for the phenomenology of classical response components. My hope is to incite some discussion of this shift in perspective and its implications.

One ring to rule them all, one ring to find them, one ring to bring them all, and in the darkness bind them

Overview The basic idea (functional and effective connectivity) Generative model and face validation An empirical example

Generative model Exogenous and endogenous fluctuations Neuronal dynamics Evoked responsesInduced responses

Model inversion Exogenous and endogenous fluctuations

Bayesian model inversion and parameter averaging Invert model of induced responses Inference on parameters and models Invert model of evoked responses Update priors We seek the posterior conditioned on both evoked and induced responses. Using Bayes rule we have: Giving the likelihood and prior for induced responses

State-space model Convolution kernel representation Functional Taylor expansion Spectral representation Convolution theorem Cross-spectral density CoherenceCross-correlation Cross-covariance Autoregressive representation Yule Walker equations Spectral representation Convolution theorem Directed transfer functions Granger causalityAuto-correlation Auto-regression coefficients Measures of functional connectivity or statistical dependence among observed responses Models of effective connectivity among hidden states causing observed responses

Effective connectivity Cross spectral density Volterra kernels Cross covariance functions Spectral factors Auto regression coefficients Director transfer functions Granger causality nonparametricparametric Modulation transfer functions Spectral measures

Overview The basic idea Generative model and face validation An empirical example

Early source (1)Higher source (2) Endogenous fluctuations Infragranular layer supragranular layer Deep pyramidal cells Inhibitory interneurons Superficial pyramidal cells Spiny stellate cells Forward extrinsic connections Backward extrinsic connections Intrinsic connections Granular layer Generative (conductance based neural mass) model based on the canonical microcircuit Inhibitory connections: k = E Excitatory connections: k = I Exogenous (subcortical) input Endogenous fluctuations

The effect of parameters on transfer functions – contribution analysis

peristimulus time (ms) Exogenous input peristimulus time (ms) Hidden neuronal states (conductance and depolarisation) source 1source 2 Predicted responses to sustained exogenous (stimulus) input

Transfer functions and spectral asymmetries Forward connections (gamma) backward connections (beta) Endogenous fluctuations

Simulated responses (sample estimates over16 trials) Predicted responses (expectation under known input)

Overview The basic idea Generative model and face validation An empirical example

From 32 Hz (gamma) to 10 Hz (alpha) t = 4.72; p = SPM t Right hemisphereLeft hemisphere Forward Backward Frequency (Hz) LVRV RF LF input FLBLFLBL FNBLFNBL FLBNFLBN FNBNFNBN Functional asymmetries in forward and backward connections Phenomenological DCM for induced responses (Chen et al 2008)

LVRV RF LF input Posterior predictions following inversion of event responses Estimates of dipole orientation Sensor level observations and DCM predictions

Posterior predictions following inversion of induced responses

Forward connections (gamma?) LVRV RF LF input LVRV RF LF input Backward connections (beta) Transfer functions and spectral asymmetries

Thank you And thanks to Gareth Barnes Andre Bastos CC Chen Jean Daunizeau Marta Garrido Lee Harrison Martin Havlicek Stefan Kiebel Marco Leite Vladimir Litvak Andre Marreiros Rosalyn Moran Will Penny Dimitris Pinotsis Krish Singh Klaas Stephan Bernadette van Wijk And many others

superficial deep Errors (superficial pyramidal cells) Expectations (deep pyramidal cells) frequency (Hz) spectral power Forward transfer function frequency (Hz) spectral power Backward transfer function Andre Bastos V4V1