J. Daunizeau Wellcome Trust Centre for Neuroimaging, London, UK UZH – Foundations of Human Social Behaviour, Zurich, Switzerland Dynamic Causal Modelling: basics

Overview 1 DCM: introduction 2 Neural ensembles dynamics 3 Bayesian inference 4 Conclusion

Overview 1 DCM: introduction 2 Neural ensembles dynamics 3 Bayesian inference 4 Conclusion

Introduction structural, functional and effective connectivity structural connectivity = presence of axonal connections functional connectivity = statistical dependencies between regional time series effective connectivity = causal (directed) influences between neuronal populations ! connections are recruited in a context-dependent fashion O. Sporns 2007, Scholarpedia structural connectivityfunctional connectivityeffective connectivity

Introduction DCM: a parametric statistical approach DCM: model structure  24 u likelihood DCM: Bayesian inference model evidence: parameter estimate: priors on parameters

Introduction DCM for EEG-MEG: auditory mismatch negativity S-D: reorganisation of the connectivity structure rIFG rSTG rA1 lSTG lA1 rIFG rSTG rA1 lSTG lA1 standard condition (S) deviant condition (D) t ~ 200 ms … … S SS D S S S S D S sequence of auditory stimuli

Overview 1 DCM: introduction 2 Neural ensembles dynamics 3 Bayesian inference 4 Conclusion

Neural ensembles dynamics systems of neural populations GolgiNissl internal granular layer internal pyramidal layer external pyramidal layer external granular layer mean-field firing ratesynaptic dynamics macro-scalemeso-scalemicro-scale EP EI II

Neural ensembles dynamics from micro- to meso-scale: mean-field treatment S(x)H(x) : post-synaptic potential of j th neuron within its ensemble mean-field firing rate mean membrane depolarization (mV) mean firing rate (Hz) membrane depolarization (mV) ensemble density p(x)

Neural ensembles dynamics synaptic dynamics time (ms) membrane depolarization (mV) post-synaptic potential IPSP EPSP

Neural ensembles dynamics intrinsic connections within the cortical column GolgiNissl internal granular layer internal pyramidal layer external pyramidal layer external granular layer spiny stellate cells inhibitory interneurons pyramidal cells intrinsic connections

Neural ensembles dynamics from meso- to macro-scale: neural fields local (homogeneous) density of connexions local wave propagation equation:

Neural ensembles dynamics extrinsic connections between brain regions extrinsic forward connections spiny stellate cells inhibitory interneurons pyramidal cells extrinsic backward connections extrinsic lateral connections

Neural ensembles dynamics systems of neural populations GolgiNissl internal granular layer internal pyramidal layer external pyramidal layer external granular layer macro-scalemeso-scalemicro-scale EP EI II mean-field firing ratesynaptic dynamics

likelihood function? Neural ensembles dynamics the observation function

Overview 1 DCM: introduction 2 Neural ensembles dynamics 3 Bayesian inference 4 Conclusion

Bayesian inference forward and inverse problems forward problem likelihood inverse problem posterior distribution

generative model m likelihood prior posterior Bayesian inference likelihood and priors

Principle of parsimony : « plurality should not be assumed without necessity » “Occam’s razor” : model evidence p(y|m) space of all data sets y=f(x) x Bayesian inference model comparison Model evidence:

free energy : functional of q approximate (marginal) posterior distributions: Bayesian inference the variational Bayesian approach

time Bayesian inference a note on causality 12 3 u

12 3 u Bayesian inference key model parameters state-state coupling input-state coupling input-dependent modulatory effect

Bayesian inference model comparison for group studies m1m1 m2m2 differences in log- model evidences subjects fixed effect random effect assume all subjects correspond to the same model assume different subjects might correspond to different models

1 DCM: introduction 2 Neural ensembles dynamics 3 Bayesian inference 4 Conclusion Overview

Conclusion back to the auditory mismatch negativity S-D: reorganisation of the connectivity structure rIFG rSTG rA1 lSTG lA1 rIFG rSTG rA1 lSTG lA1 standard condition (S) deviant condition (D) t ~ 200 ms … … S SS D S S S S D S sequence of auditory stimuli

Conclusion DCM for EEG/MEG: variants  DCM for steady-state responses  second-order mean-field DCM  DCM for induced responses  DCM for phase coupling time (ms) inputdepolarization time (ms) auto-spectral density LA auto-spectral density CA1 cross-spectral density CA1-LA frequency (Hz) 1 st and 2d order moments

Many thanks to: Karl J. Friston (London, UK) Rosalyn Moran (London, UK) Stefan J. Kiebel (Leipzig, Germany)