Dynamic Causal Modelling Dynamic Causal Modelling (DCM) for fMRI (DCM) for fMRI Wellcome Trust Centre for Neuroimaging University College London Andre Marreiros Andre Marreiros
Mar 28, 2015
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: positive modulation
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Neurodynamics: reciprocal connections
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Simulated response
Haemodynamics: reciprocal connections
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green: neuronal activity
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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LG = lingual gyrusFG = fusiform gyrus
Visual input in the - left (LVF) - right (RVF)visual field.z1 z2
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hemodynamicmodel
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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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• Empirically determineda priori distributions.
• Computed separately for each area
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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
sf (rCBF)induction -flow
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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
ηθ|y
neuronal stateequation CuzBuAz j
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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:
ηθ|y
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