dynamic causal modelling theory
DESCRIPTION
Dynamic Causal Modelling THEORY. Hanneke den Ouden Donders Centre for Cognitive Neuroimaging Radboud University Nijmegen Functional Imaging Laboratory (FIL) Wellcome Trust Centre for Neuroimaging University College London. SPM Course FIL, London 22-24 October 2009. - PowerPoint PPT PresentationTRANSCRIPT
Dynamic Causal Modelling THEORY
SPM Course FIL, London22-24 October 2009
Hanneke den Ouden
Donders Centre for Cognitive NeuroimagingRadboud University Nijmegen
Functional Imaging Laboratory (FIL)Wellcome Trust Centre for NeuroimagingUniversity College London
Functional specializationFunctional specialization Functional integrationFunctional integration
Principles of Organisation
Overview
• Brain connectivity
• Dynamic causal models (DCMs)
– Basics
– Neural model
– Hemodynamic model
– Parameters & parameter estimation
– Inference & Model comparison
• Recent extentions to DCM
• Planning a DCM compatible study
Structural, functional & effective connectivity
• anatomical/structural connectivity= presence of axonal connections
• functional connectivity = statistical dependencies between regional time series
• effective connectivity = causal (directed) influences between neurons or neuronal populations
Sporns 2007, Scholarpedia
For understanding brain function mechanistically, we can use DCM to
create
models of causal interactions among neuronal populations
to explain regional effects in terms of interregional connectivity
Overview
• Brain connectivity
• Dynamic causal models (DCMs)
– Basics
– Neural model
– Hemodynamic model
– Parameters & parameter estimation
– Inference & Model comparison
• Recent extentions to DCM
• Planning a DCM compatible study
• Cognitive system is modelled at its underlying neuronal level (not directly accessible for fMRI).
• The modelled neuronal dynamics (x) are transformed into area-specific BOLD
signals (y) by a hemodynamic model (λ). λ
x
y
The aim of DCM is to estimate parameters at the neuronal level such that the modelled and measured BOLD signals are optimally similar.
Basics of DCM: Neuronal and BOLD level
DCM: Linear Model
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• Cognitive system is modelled at its underlying neuronal level (not directly accessible for fMRI).
• The modelled neuronal dynamics (x) are transformed into area-specific BOLD
signals (y) by a hemodynamic model (λ). λ
x
y
Basics of DCM: Neuronal and BOLD level
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important for model fitting, but of no interest for statistical inference
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signal BOLD
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The hemodynamic model
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• 6 hemodynamic parameters:
• Computed separately for each area (like the neural parameters) region-specific HRFs!
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Friston et al. 2000, NeuroImageStephan et al. 2007, NeuroImage
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neural state equation
hemodynamic state equations
Estimated BOLD response
Measured vs Modelled BOLD signalRecapThe aim of DCM is to estimate- neural parameters {A, B, C}- hemodynamic parameters such that the modelled (x) and measured (y) BOLD signals are maximally similar.
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X1 X2 X3u1
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Overview
• Brain connectivity
• Dynamic causal models (DCMs)
– Basics
– Neural model
– Hemodynamic model
– Parameters & parameter estimation
– Inference & Model comparison
• Recent extentions to DCM
• Planning a DCM compatible study
DCM parameters = rate constants
dxax
dt 0( ) exp( )x t x at
The coupling parameter a determines the half life of x(t), and thus describes the speed of the exponential change
Integration of a first-order linear differential equation gives anexponential function:
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a/2ln
If AB is 0.10 s-1 this means that, per unit time, the increase in activity in B corresponds to 10% of the activity in A
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Example: context-dependent decay
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Penny, Stephan, Mechelli, Friston NeuroImage (2004)
Constraints on• Haemodynamic parameters • Connections
Models of• Haemodynamics in a single region• Neuronal interactions
Bayesian estimation
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Estimation: Bayesian framework
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Conceptual overview
Neuronal states
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Driving input(e.g. sensory stim)
Modulatory input(e.g. context/learning/drugs)
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BOLD Response
Parameters are optimised
so that the predicted
matches the measured
BOLD response
But how confident are
we in what these
parameters tell us?
Overview
• Brain connectivity
• Dynamic causal models (DCMs)
– Basics
– Neural model
– Hemodynamic model
– Parameters & parameter estimation
– Inference & Model comparison
• Recent extentions to DCM
• Planning a DCM compatible study
Model comparison and selection
Given competing hypotheses, which model is the best?
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Pitt & Miyung (2002) TICS
Inference about DCM parameters:
Bayesian single subject analysis
• The model parameters are distributions that have a mean ηθ|y and covariance Cθ|y.
– Use of the cumulative normal distribution to test the probability that a certain parameter is above a chosen threshold γ: ηθ|
y
Classical frequentist test across Ss
• Test summary statistic: mean ηθ|y
– One-sample t-test:Parameter > 0?
– Paired t-test:parameter 1 > parameter 2?
– rmANOVA: e.g. in case of multiple sessions per subject
DCM roadmap
fMRI data
Posterior densities of parameters
Neuronal dynamics
Haemodynamics
Model comparison
Bayesian Model inversion
State space Model
Priors
Overview
• Brain connectivity
• Dynamic causal models (DCMs)
– Basics
– Neural model
– Hemodynamic model
– Parameters & parameter estimation
– Inference & Model comparison
• Recent extentions to DCM
• Planning a DCM compatible study
Two-state DCM
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Extensions to DCM
• Ext. 1: two state model– excitatory & inhibitory
• Ext. 2: Nonlinear DCM– Gating of connections by
other areas
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Planning a DCM-compatible study
• Suitable experimental design:– any design that is suitable for a GLM – preferably multi-factorial (e.g. 2 x 2)
• e.g. one factor that varies the driving (sensory) input• and one factor that varies the contextual input
• Hypothesis and model:– Define specific a priori hypothesis– Which parameters are relevant to test this hypothesis?– If you want to verify that intended model is suitable to
test this hypothesis, then use simulations– Define criteria for inference– What are the alternative models to test?
So, DCM….
• enables one to infer hidden neuronal processes from fMRI data
• tries to model the same phenomena as a GLM
– explaining experimentally controlled variance in local responses
– based on connectivity and its modulation
• allows one to test mechanistic hypotheses about observed effects
• is informed by anatomical and physiological principles.
• uses a Bayesian framework to estimate model parameters
• is a generic approach to modeling experimentally perturbed dynamic
systems.
– provides an observation model for neuroimaging data, e.g. fMRI, M/EEG
– DCM is not model or modality specific (Models will change and the method
extended to other modalities e.g. ERPs)
Some useful references• The first DCM paper: Dynamic Causal Modelling (2003). Friston et
al. NeuroImage 19:1273-1302.
• Physiological validation of DCM for fMRI: Identifying neural drivers
with functional MRI: an electrophysiological validation (2008). David et
al. PLoS Biol. 6 2683–2697
• Hemodynamic model: Comparing hemodynamic models with DCM
(2007). Stephan et al. NeuroImage 38:387-401
• Nonlinear DCMs:Nonlinear Dynamic Causal Models for FMRI (2008).
Stephan et al. NeuroImage 42:649-662
• Two-state model: Dynamic causal modelling for fMRI: A two-state
model (2008). Marreiros et al. NeuroImage 39:269-278
• Group Bayesian model comparison: Bayesian model selection for
group studies (2009). Stephan et al. NeuroImage 46:1004-10174
• Watch out for: 10 Simple Rules for DCM, Stephan et al (in prep).
Time to do a DCM!
Dynamic Causal ModellingPRACTICAL
SPM Course FIL, London22-24 October 2009
Andre Marreiros
Hanneke den Ouden
Donders Centre for Cognitive NeuroimagingRadboud University Nijmegen
Functional Imaging Laboratory (FIL)Wellcome Trust Centre for NeuroimagingUniversity College London
DCM – Attention to MotionParadigm
Parameters - blocks of 10 scans
- 360 scans total
- TR = 3.22 seconds
Stimuli 250 radially moving dots at 4.7 degrees/s
Pre-Scanning
5 x 30s trials with 5 speed changes (reducing to 1%)
Task - detect change in radial velocity
Scanning (no speed changes)
F A F N F A F N S ….
F - fixation
S - observe static dots + photic
N - observe moving dots + motion
A - attend moving dots + attention
Attention to Motion in the visual system
Results
Büchel & Friston 1997, Cereb. CortexBüchel et al. 1998, Brain
V5+
SPCV3A
Attention – No attention
- fixation only- observe static dots + photic V1- observe moving dots + motion V5- task on moving dots + attention V5 + parietal cortex
Attention to Motion in the visual system
Paradigm
V1
V5
SPC
Motion
Photic
Attention
V1
V5
SPC
Motion
PhoticAttention
Model 1attentional modulationof V1→V5: forward
Model 2attentional modulationof SPC→V5: backward
Bayesian model selection: Which model is optimal?
DCM: comparison of 2 models
Ingredients for a DCM
Specific hypothesis/question
Model: based on hypothesis
Timeseries: from the SPM
Inputs: from design matrix
Attention to Motion in the visual system
Paradigm
V1
V5
SPC
Motion
Photic
Attention
V1
V5
SPC
Motion
PhoticAttention
Model 1attentional modulationof V1→V5: forward
Model 2attentional modulationof SPC→V5: backward
DCM – GUI basic steps
1 – Extract the time series (from all regions of interest)
2 – Specify the model
3 – Estimate the model
4 – Review the estimated model
5 – Repeat steps 2 and 3 for all models in model space
6 – Compare models
Attention to Motion in the visual system