J. Daunizeau Wellcome Trust Centre for Neuroimaging, London, UK

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

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

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

4. Introductionstructural, functional and effective connectivity structural connectivity functional connectivity effective connectivity O. Sporns 2007, Scholarpedia • 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

5. • DCM: Bayesian inference priors on parameters parameter estimate: model evidence: IntroductionDCM: a parametric statistical approach • DCM: model structure 24 2 likelihood 4 1 3 u

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

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

8. Neural ensembles dynamicssystems of neural populations macro-scale meso-scale micro-scale Golgi Nissl external granular layer EI external pyramidal layer EP internal granular layer internal pyramidal layer II mean-field firing rate synaptic dynamics

9. Neural ensembles dynamicsfrom micro- to meso-scale: mean-field treatment : post-synaptic potential of jth neuron within itsensemble mean-field firing rate ensemble density p(x) mean firing rate (Hz) S(x) H(x) membrane depolarization (mV) mean membrane depolarization (mV)

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

11. inhibitory interneurons spiny stellate cells pyramidal cells Neural ensembles dynamicsintrinsic connections within the cortical column Golgi Nissl external granular layer external pyramidal layer internal granular layer intrinsic connections internal pyramidal layer

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

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

14. Neural ensembles dynamicssystems of neural populations macro-scale meso-scale micro-scale Golgi Nissl external granular layer EI external pyramidal layer EP internal granular layer internal pyramidal layer II mean-field firing rate synaptic dynamics

15. Neural ensembles dynamicsthe observation function likelihood function?

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

17. Bayesian inferenceforward and inverse problems forward problem likelihood posterior distribution inverse problem

18. generative modelm Bayesian inferencelikelihood and priors likelihood prior posterior

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

20. Bayesian inferencethe variational Bayesian approach free energy : functional of q approximate (marginal) posterior distributions:

21. Bayesian inferencea note on causality 1 2 1 2 3 1 2 3 1 2 time 3 3 u

22. Bayesian inferencekey model parameters 1 2 3 u state-state coupling input-state coupling input-dependent modulatory effect

23. Bayesian inferencemodel comparison for group studies m1 differences in log- model evidences m2 subjects fixed effect assume all subjects correspond to the same model random effect assume different subjects might correspond to different models

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

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

26. ConclusionDCM for EEG/MEG: variants 250 0 input depolarization 1st and 2d order moments 200 -20 150 -40  second-order mean-field DCM 100 -60 50 -80 0 -100 0 100 200 300 0 100 200 300 time (ms) time (ms) time (ms) auto-spectral density LA auto-spectral density CA1 cross-spectral density CA1-LA  DCM for steady-state responses frequency (Hz) frequency (Hz) frequency (Hz) 0 -20 -40  DCM for induced responses -60 -80  DCM for phase coupling -100 0 100 200 300

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