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Dynamic Causal Modelling (DCM) for fMRI Wellcome Trust Centre for Neuroimaging University College London Andre Marreiros.

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Presentation on theme: "Dynamic Causal Modelling (DCM) for fMRI Wellcome Trust Centre for Neuroimaging University College London Andre Marreiros."— Presentation transcript:

1 Dynamic Causal Modelling (DCM) for fMRI Wellcome Trust Centre for Neuroimaging University College London Andre Marreiros

2 Thanks to... Stefan Kiebel Lee Harrison Klaas Stephan Karl Friston

3 Overview Dynamic Causal Modelling of fMRI Definitions & motivation The neuronal model (bilinear dynamics) The Haemodynamic model The neuronal model (bilinear dynamics) The Haemodynamic model Estimation: Bayesian framework DCM latest Extensions

4 Principles of organisation Functional specialization Functional integration

5 Neurodynamics: 2 nodes with input u2u2 u1u1 z1z1 z2z2 activity in is coupled to via coefficient

6 Neurodynamics: positive modulation u2u2 u1u1 z1z1 z2z2 modulatory input u 2 activity through the coupling

7 Neurodynamics: reciprocal connections u2u2 u1u1 z1z1 z2z2 reciprocal connection disclosed by u2u2

8 Simulated response Haemodynamics: reciprocal connections Bold Response Bold Response a 11 a 22 a 12 green: neuronal activity red: bold response

9 Haemodynamics: reciprocal connections Bold with Noise added Bold with Noise added a 11 a 22 a 12 green: neuronal activity red: bold response

10 LG left LG right RVFLVF FG right FG left Example: modelled BOLD signal Underlying model (modulatory inputs not shown) LG = lingual gyrus Visual input in the FG = fusiform gyrus - left (LVF) - right (RVF) visual field. blue:observed BOLD signal red:modelled BOLD signal (DCM) left LG right LG

11 Use differential equations to describe mechanistic model of a system System dynamics = change of state vector in time Causal effects in the system: –interactions between elements –external inputs u System parameters : specify exact form of system overall system state represented by state variables change of state vector in time

12 Example: linear dynamic system LG left LG right RVFLVF FG right FG left LG = lingual gyrus FG = fusiform gyrus Visual input in the - left (LVF) - right (RVF) visual field. z1z1 z2z2 z4z4 z3z3 u2u2 u1u1 state changes effective connectivity external inputs system state input parameters

13 Extension: bilinear dynamic system LG left LG right RVFLVF FG right FG left z1z1 z2z2 z4z4 z3z3 u2u2 u1u1 CONTEXT u3u3

14 Bilinear state equation in DCM/fMRI state changes connectivity m external inputs system state direct inputs modulation of connectivity

15 BOLD y y y hemodynamic model Input u(t) activity z 2 (t) activity z 1 (t) activity z 3 (t) effective connectivity direct inputs modulation of connectivity The bilinear model c1c1 b 23 a 12 neuronal states λ z y integration Neuronal state equation Conceptual overview Friston et al. 2003, NeuroImage

16 important for model fitting, but of no interest for statistical inference The hemodynamic Balloon model 5 hemodynamic parameters: Empirically determined a priori distributions. Computed separately for each area },,,,{ h

17 Diagram Dynamic Causal Modelling of fMRI Model inversion using Expectation-maximization State space Model fMRI data y Posterior distribution of parameters Network dynamics Haemodynamic response Model comparison Priors

18 Constraints on Connections Hemodynamic parameters Models of Hemodynamics in a single region Neuronal interactions Bayesian estimation posterior prior likelihood term Estimation: Bayesian framework

19 stimulus function u modelled BOLD response observation model hidden states state equation parameters Specify model (neuronal and hemodynamic level) Make it an observation model by adding measurement error e and confounds X (e.g. drift). Bayesian parameter estimation using Bayesian version of an expectation-maximization algorithm. Result: (Normal) posterior parameter distributions, given by mean η θ|y and Covariance C θ|y. Overview: parameter estimation η θ|y neuronal state equation

20 Activity in z1 is coupled to z2 via coefficient a21 Haemodynamics: 2 nodes with input a 11 a 22 Dashed Line: Real BOLD response

21 Inference about DCM parameters: single-subject analysis Bayesian parameter estimation in DCM: Gaussian assumptions about the posterior distributions of the parameters Use of the cumulative normal distribution to test the probability by which a certain parameter (or contrast of parameters c T η θ|y ) is above a chosen threshold γ: η θ|y

22 Model comparison and selection Given competing hypotheses, which model is the best? Pitt & Miyung (2002), TICS

23 V1 V5 SPC Motion Photic Attention V1V5SPC Motion Photic Attention V1 V5SPC Motion Photic Attention Attention 0.23 Model 1: attentional modulation of V1V5 Model 2: attentional modulation of SPCV5 Model 3: attentional modulation of V1V5 and SPCV5 Comparison of three simple models Bayesian model selection:Model 1 better than model 2, model 1 and model 3 equal Decision for model 1: in this experiment, attention primarily modulates V1V5

24 potential timing problem in DCM: temporal shift between regional time series because of multi- slice acquisition Solution: –Modelling of (known) slice timing of each area. 1 2 slice acquisition visual input Extension I: Slice timing model Slice timing extension now allows for any slice timing differences. Long TRs (> 2 sec) no longer a limitation. (Kiebel et al., 2007)

25 input Single-state DCM Intrinsic (within-region) coupling Extrinsic (between-region) coupling Two-state DCM Extension II: Two-state model

26 Extension III: Nonlinear DCM for fMRI Here DCM can model activity- dependent changes in connectivity; how connections are enabled or gated by activity in one or more areas. The D matrices encode which of the n neural units gate which connections in the system. Can V5 activity during attention to motion be explained by allowing activity in SPC to modulate the V1- to-V5 connection? The posterior density of indicates that this gating existed with 97.4% confidence. V1 V5 SPC attention 0.03 (100%) motion 0.04 (100%) 1.65 (100%) 0.19 (100%) 0.01 (97.4%)

27 Conclusions Dynamic Causal Modelling (DCM) of fMRI is mechanistic model that is informed by anatomical and physiological principles. DCM is not model or modality specific (Models will change and the method extended to other modalities e.g. ERPs) DCM combines state-equations for dynamics with observation model (fMRI: BOLD response, M/EEG: lead field). DCM uses a deterministic differential equation to model neuro-dynamics (represented by matrices A,B and C) DCM uses a Bayesian framework to estimate these


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