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Dynamic Causal Modelling for event-related responses

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Presentation on theme: "Dynamic Causal Modelling for event-related responses"— Presentation transcript:

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 Introduction structural, 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 functional segregation functional integration
Introduction from functional segregation to functional integration localizing brain activity: functional segregation effective connectivity analysis: functional integration u1 u1 X u2 A B u2 u1 Jusqu’à récemment, on utilisait la neuroimagerie pour localiser les régions impliquées dans telle ou telle tâche cognitive. J’ai travaillé sur le développement de méthodes liées à ce problème pendant ma thèse. Cela a donné lieu à la publication de 8 articles dont 4 en premier auteur. Aujourd’hui, on va plus loin et on analyse la connectivité cérébrale « effective ». En fait, on cherche à savoir quelle est la nature de l’information qui passe d’une région A à une région B. L’approche DCM se base sur des modèles réalistes décrivant la façon dont le cerveau est cablé, et comment il répond à la stimulation expérimentale. En fittant ces modèles aux données, on peut alors montrer qu’une connexion est modulée par une propriété des stimuli qu’on manipule expérimentalement (comme la récompense à un choix). Si tel est le cas, on a montré que cette connexion véhiculait l’information sur la récompense. J’ai contribué aux aspects statistique et neurobiologique de DCM. Cela a mené à la publication de 18 articles dont 8 en premier ou dernier auteur. « Where, in the brain, did my experimental manipulation have an effect? » « How did my experimental manipulation propagate through the network? »

6 Introduction why do we use dynamical system theory?
1 2 1 2 3 1 2 1 2 3 time 3 3 u

7 Introduction DCM: 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 Introduction DCM: 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 Introduction DCM for EEG-MEG: auditory mismatch negativity
sequence of auditory stimuli S S S D S S S S D S standard condition (S) deviant condition (D) t =200 ms S-D: reorganisation of the connectivity structure rIFG rSTG rA1 lSTG lA1 rIFG rSTG rA1 lSTG lA1 Daunizeau, Kiebel et al., Neuroimage, 2009

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

11 Neural ensembles dynamics multi-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 dynamics from micro- to meso-scale
: post-synaptic potential of j th neuron within its ensemble 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 dynamics synaptic kinematics
post-synaptic potential EPSP depolarization (mV) membrane IPSP time (ms)

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

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

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

17 Observation mappings the electromagnetic forward model

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

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

20 Bayesian inference likelihood and priors
generative model m posterior

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

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

23 Bayesian inference EM 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 23

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

25 Bayesian inference model comparison for group studies
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 Example models for deviant response generation
Garrido et al., (2007), NeuroImage

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

29 Example MMN: 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 29

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

31 Example MMN: group-level model comparison across time
Bayesian model comparison across subjects. (A) Comparison of the model with backward connections (FB) against the model without (F), across all subjects over the peristimulus interval 180–260 ms. The dots correspond to differences in log-evidence for 11 subjects over time. The solid line shows the average log-evidence differences over subjects [this is proportional to the log-group Bayes factor (Bf) or to the differences in the free energy of the two models (ΔF); see Materials and Methods for details]. The points outside the gray zone imply very strong inference (≥99% confidence that one model is more likely), i.e., model FB supervenes over F for positive points and the converse for negative points. (B) Histogram showing the number of subjects in each of seven levels of inference on models with and without backward connections across the peristimulus interval 180–260 ms. Garrido et al., PNAS, 2008

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

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

34 Conclusion DCM for EEG/MEG: variants
input depolarization 1st and 2d order moments 100 200 300 50 150 250 100 200 300 -100 -80 -60 -40 -20 100 200 300 -100 -80 -60 -40 -20  second-order mean-field DCM 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)  DCM for induced responses  DCM for phase coupling

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


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