Dynamic Causal Modelling (DCM) Dynamic Causal Modelling (DCM) for fMRIfor fMRI

Dynamic Causal Modelling (DCM) Dynamic Causal Modelling (DCM) for fMRIfor fMRI

Wellcome Trust Centre for Neuroimaging

University College London

Andre MarreirosAndre Marreiros

Thanks to...

Stefan KiebelLee HarrisonKlaas StephanKarl Friston

Overview

Dynamic Causal Modelling of fMRIDynamic Causal Modelling of fMRI

Definitions & motivationDefinitions & motivation

The neuronal model (bilinear dynamics)

The Haemodynamic model

The neuronal model (bilinear dynamics)

The Haemodynamic model

Estimation: Bayesian frameworkEstimation: Bayesian framework

DCM latest ExtensionsDCM latest Extensions

Principles of organisation

Functional specializationFunctional specialization Functional integrationFunctional integration

Neurodynamics: 2 nodes with input

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Neurodynamics: reciprocal connections

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red: bold response

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RVF LVF

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Example: modelled BOLD signalUnderlying 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

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

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Example: linear dynamic system

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Visual input in the - left (LVF) - right (RVF)visual field.z1 z2

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bilinear dynamic system

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Neuronal state equation ),,( nuzFz Conceptual overview

Friston et al. 2003,NeuroImage

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The hemodynamic “Balloon” model

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Diagram

Dynamic Causal Modelling of fMRIDynamic Causal Modelling of fMRI

Model inversion using

Expectation-maximization

State space Model

fMRI data y

Posterior distribution of parameters

Network dynamics

Haemodynamicresponse

Model comparison

Priors

Constraints on•Connections

•Hemodynamic parameters

Models of•Hemodynamics in a single region

•Neuronal interactions

Bayesian estimation

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Estimation: Bayesian framework

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• 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 ηθ|y and Covariance Cθ|y.

Overview:parameter estimation

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Activity in z1 is coupled to z2 via coefficient a21

Haemodynamics: 2 nodes with input

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Dashed Line: Real BOLD response

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 cT ηθ|y) is above a chosen threshold γ:

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Model comparison and selection

Given competing hypotheses, which model is the best?

Pitt & Miyung (2002), TICS

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Model 1:attentional modulationof V1→V5

Model 2:attentional modulationof SPC→V5

Model 3:attentional modulationof V1→V5 and SPC→V5

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 V1→V5

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• 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.

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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)

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Extension II: Two-state model

Extension III: Nonlinear DCM for fMRI

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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.

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Conclusions

Dynamic Causal Modelling (DCM) of fMRI is mechanistic model that is informed by anatomical and physiological principles.

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 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 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 deterministic differential equation to model neuro-dynamics (represented by matrices A,B and C)

DCM uses a Bayesian framework to estimate theseDCM uses a Bayesian framework to estimate these