Understanding Neural Ensembles Dynamics through Dynamic Causal Modelling

1. Dynamic Causal Modelling for event-related responses J. Daunizeau Motivation, Brain and Behaviour group, ICM, Paris, France Wellcome Trust Centre for Neuroimaging, London, UK

2. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example Conclusion

3. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example 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. Introductionfrom functional segregation to functional integration localizing brain activity: functional segregation effective connectivity analysis: functional integration u1 u1 A B u1 u1 X u2 B A u2 « Where, in the brain, did my experimental manipulation have an effect? » « How did my experimental manipulation propagate through the network? » u2

6. Introductionwhy do we use dynamical system theory? 1 2 1 2 3 1 2 3 1 2 time 3 3 u

7. IntroductionDCM: evolution and observation mappings Hemodynamic observation model:temporal convolution Electromagnetic observation model:spatial convolution neural states dynamics fMRI EEG/MEG • simple neuronal model • slow time scale • complicated neuronal model • fast time scale inputs

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

9. 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 Daunizeau, Kiebel et al., Neuroimage, 2009

10. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example Conclusion

11. Neural ensembles dynamicsmulti-scale perspective 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

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

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

14. 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

15. Neural ensembles dynamicsfrom meso- to macro-scale lateral (homogeneous) density of connexions local wave propagation equation (neural field): 0th-order approximation: standing wave

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

17. Observation mappingsthe electromagnetic forward model

18. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example Conclusion

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

20. generative modelm Bayesian inferencelikelihood and priors likelihood prior posterior

21. 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”:

22. Bayesian inferencethe variational Bayesian approach free energy : functional of q mean-field: approximate marginal posterior distributions:

23. Bayesian inferenceEM in a nutshell Specify generative forward model (with prior distributions of parameters) Evoked responses Expectation-Maximization algorithm Iterative procedure: • Compute model response using current set of parameters • Compare model response with data • Improve parameters, if possible • Posterior distributions of parameters • Model evidence

24. Bayesian inferenceDCM: key model parameters 1 2 3 u state-state coupling input-state coupling input-dependent modulatory effect

25. 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

26. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example Conclusion

27. Examplemodels for deviant response generation Garrido et al., (2007), NeuroImage

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

29. ExampleMMN: temporal hypotheses Models for Deviant Response Generation Do forward and backward connections operate as a function of time? Peristimulus time 1 Peristimulus time 2 Garrido et al., PNAS, 2008

30. ExampleMMN: (best) model fit time (ms) time (ms) Garrido et al., PNAS, 2008

31. ExampleMMN: group-level model comparison across time Garrido et al., PNAS, 2008

32. Overview DCM: introduction Neural ensembles dynamics Bayesian inference Example Conclusion

33. 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

34. 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

35. Many thanks to: Karl J. Friston (FIL, London, UK) Klaas E. Stephan (UZH, Zurich, Switzerland) Stefan Kiebel (MPI, Leipzig, Germany)