Dynamic causal modeling: Difference between revisions

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'''Dynamic causal modeling''' (DCM) is a framework for specifying models, fitting them to data and comparing their evidence using [[Bayes factor|Bayesian model comparison]]. TheIt models, referred to as dynamic causal models (DCMs), areuses nonlinear [[State space|state-space]] models in continuous time, specified using [[Stochastic differential equation|stochastic]] or [[Ordinary differential equation|ordinary differential equations]]. DCM was initially developed for identifyingtesting modelshypotheses ofabout [[Dynamical system|neural dynamics]]<ref name=":2">{{Cite journal|last=Friston|first=K.J.|last2=Harrison|first2=L.|last3=Penny|first3=W.|date=2003-08|title=Dynamic causal modelling|url=https://doi.org/10.1016/S1053-8119(03)00202-7|journal=NeuroImage|volume=19|issue=4|pages=1273–1302|doi=10.1016/s1053-8119(03)00202-7|issn=1053-8119}}</ref>. In this setting, differential equations describe the interaction of neural populations, which directly or indirectly give rise to functional neuroimaging data e.g., [[functional magnetic resonance imaging]] (fMRI), [[magnetoencephalography]] (MEG) or [[electroencephalography]] (EEG). Parameters in these DCMsmodels quantify the directed influences or effective connectivity among neuronal populations, which can beare estimated from the available data using [[Bayesian inference|Bayesian]] statistical methods.

== Procedure ==

DCM is usuallytypically used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context). ModelsA model of interacting brainneural regionspopulations areis specified, whichwith describea level biological detail dependent on the interactionhypotheses ofand neuralavailable populationsdata. TheseThis areis supplementedcoupled with a forward model ofdescribing how the hidden states of each brain region (e.g., neuronalneural activity) givegives rise to measured responses. Having specified This enablesEstimating the bestgenerative model(s) andidentifies theirthe parameters (i.e.g. effectiveconnection connectivitystrengths) tofrom be identified fromthe observed data. [[Bayesian model comparison]] is used to compare models based on their evidence, which can then be characterised in terms of parameters (e.g. connection strengths).

DCM studies typically involve the following stages <ref name=":0">{{Cite journal|last=Stephan|first=K.E.|last2=Penny|first2=W.D.|last3=Moran|first3=R.J.|last4=den Ouden|first4=H.E.M.|last5=Daunizeau|first5=J.|last6=Friston|first6=K.J.|date=2010-02|title=Ten simple rules for dynamic causal modeling|url=https://dx.doi.org/10.1016/j.neuroimage.2009.11.015|journal=NeuroImage|volume=49|issue=4|pages=3099–3109|doi=10.1016/j.neuroimage.2009.11.015|issn=1053-8119}}</ref>:

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# Model specification. One or more forward models (DCMs) are specified for each dataset.

#Model estimation. The model(s) are fitted to the data to determine their evidence and parameters.

# Model comparison. The evidence for each model is used for Bayesian Model Comparison (at the single-subject level or at the group level) orto select the best model(s). Bayesian model averaging (BMA) is used to providecompute a weighted average of parameter estimates, averaged over different models.

The key stepsstages are briefly reviewed below.

== Experimental design ==

Functional neuroimaging experiments are typically either task-based or examine brain activity at rest ([[Resting state fMRI|resting state]]). In task-based experiments, brain responses are evoked by known deterministic inputs (experimentally controlled stimuli) that embody designed changes in sensory stimulation or cognitive set. These experimental or exogenous variables can change neural activity in one of two ways. First, they can elicit responses through direct influences on specific brain regions. This would include, forsuch example,as [[Evoked potential|sensory evoked responsespotentials]] in the early visual cortex., Theor second class of inputs exerts their effects vicariously, throughvia a modulation of coupling among nodesneural populations; for example, the influence of attention on the processing of sensory information. These two types of input - driving and modulatory - are parameterized separately in DCM<ref name=":2" />. To enable efficient estimation of driving and modulatory effects, a 2x2 [[Factorial experiment|factorial experimental design]] is often used - with one factor serving as the driving input and the other as the modulatory input <ref name=":0" />.

Resting state experiments have no experimental manipulations within the period of the neuroimaging recording. Instead, hypotheses are tested about the coupling of endogenous fluctuations in neuronal activity, or in the differences in connectivity between sessions or subjects. The DCM framework includes models and procedures for analysing resting state data, described belowin the next section.

== Model specification ==

All models in DCM have the following basic form:

Dynamic Causal Models (DCMs) are nonlinear state-space [[Dynamical system|dynamical with models]] in continuous time, parameterized in terms of directed effective connectivity between brain regions. Unlike [[Bayesian network|Bayesian Networks]], DCMs can be cyclic, and unlike [[Structural equation modeling|Structural Equation modelling]] and [[Granger causality]], DCM does not depend on the theory of Martingales; i.e., it does not assume that random fluctuations' are serially uncorrelated. All models in DCM have the following basic form:

<math>\begin{align}

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\end{align}</math>

The first equality describes the change in neural activity <math>z</math> with respect to time (i.e. <math>\dot{z}</math>), which cannot be directly observed using non-invasive functional imaging modalities. The evolution of neural activity over time is controlled by a neural function <math>f</math> with parameters <math>\theta^{(n)}</math> and experimental inputs <math>u</math>. The neural activity in turn causes the timeseries <math>y</math>, (second equality)., The timesserieswhich are generated via a observation function <math>g</math> with parameters <math>\theta^{(h)}</math>. Additive observation noise <math>\epsilon</math> completes the observation model. Usually, the key parameters of interest are the neural parameters <math>\theta^{(n)}</math> whichare of key interest, which for example, represent connection strengths that may change under different experimental conditions.

Specifying a DCM requires selecting a neural model <math>f</math> and observation model <math>g</math> and setting appropriate [[Prior probability|priors]] over the parameters; e.g. selecting which connections should be switched on or off.

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The neural model in DCM for fMRI is a [[Taylor series|Taylor approximation]] that captures the gross causal influences between brain regions and their change due to experimental inputs (see picture). This is coupled with a detailed biophysical model of the generation of the BOLD response and the MRI signal<ref name=":2">{{Cite journal|last=Friston|first=K.J.|last2=Harrison|first2=L.|last3=Penny|first3=W.|date=2003-08|title=Dynamic causal modelling|url=https://doi.org/10.1016/S1053-8119(03)00202-7|journal=NeuroImage|volume=19|issue=4|pages=1273–1302|doi=10.1016/s1053-8119(03)00202-7|issn=1053-8119}}</ref>, based on the Balloon model of Buxton et al.<ref>{{Cite journal|last=Buxton|first=Richard B.|last2=Wong|first2=Eric C.|last3=Frank|first3=Lawrence R.|date=1998-06|title=Dynamics of blood flow and oxygenation changes during brain activation: The balloon model|url=https://dx.doi.org/10.1002/mrm.1910390602|journal=Magnetic Resonance in Medicine|volume=39|issue=6|pages=855–864|doi=10.1002/mrm.1910390602|issn=0740-3194}}</ref>, which was supplemented with a model of neurovascular coupling <ref>{{Cite journal|last=Friston|first=K.J.|last2=Mechelli|first2=A.|last3=Turner|first3=R.|last4=Price|first4=C.J.|date=2000-10|title=Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics|url=https://dx.doi.org/10.1006/nimg.2000.0630|journal=NeuroImage|volume=12|issue=4|pages=466–477|doi=10.1006/nimg.2000.0630|issn=1053-8119}}</ref><ref>{{Cite journal|last=Stephan|first=Klaas Enno|last2=Weiskopf|first2=Nikolaus|last3=Drysdale|first3=Peter M.|last4=Robinson|first4=Peter A.|last5=Friston|first5=Karl J.|date=2007-11|title=Comparing hemodynamic models with DCM|url=https://dx.doi.org/10.1016/j.neuroimage.2007.07.040|journal=NeuroImage|volume=38|issue=3|pages=387–401|doi=10.1016/j.neuroimage.2007.07.040|pmid=17884583|issn=1053-8119}}</ref>. Additions to the neural model have included interactions between excitatory and inhibitory neural populations <ref>{{Cite journal|last=Marreiros|first=A.C.|last2=Kiebel|first2=S.J.|last3=Friston|first3=K.J.|date=2008-01|title=Dynamic causal modelling for fMRI: A two-state model|url=https://doi.org/10.1016/j.neuroimage.2007.08.019|journal=NeuroImage|volume=39|issue=1|pages=269–278|doi=10.1016/j.neuroimage.2007.08.019|issn=1053-8119}}</ref> and non-linear influences of neural populations on the coupling between other populations<ref name=":3">{{Cite journal|last=Stephan|first=Klaas Enno|last2=Kasper|first2=Lars|last3=Harrison|first3=Lee M.|last4=Daunizeau|first4=Jean|last5=den Ouden|first5=Hanneke E.M.|last6=Breakspear|first6=Michael|last7=Friston|first7=Karl J.|date=2008-08|title=Nonlinear dynamic causal models for fMRI|url=https://doi.org/10.1016/j.neuroimage.2008.04.262|journal=NeuroImage|volume=42|issue=2|pages=649–662|doi=10.1016/j.neuroimage.2008.04.262|issn=1053-8119|pmc=2636907|pmid=18565765}}</ref>.

DCM for resting state studies was first introduced in Stochastic DCM<ref>{{Cite journal|date=2011-09-15|title=Generalised filtering and stochastic DCM for fMRI|url=https://www.sciencedirect.com/science/article/pii/S1053811911001406|journal=NeuroImage|language=en|volume=58|issue=2|pages=442–457|doi=10.1016/j.neuroimage.2011.01.085|issn=1053-8119|last1=Li|first1=Baojuan|last2=Daunizeau|first2=Jean|last3=Stephan|first3=Klaas E|last4=Penny|first4=Will|last5=Hu|first5=Dewen|last6=Friston|first6=Karl}}</ref>, which estimates both neural fluctuations and connectivity parameters in the time ___domain, using [[Generalized filtering|Generalized Filtering]]. A more efficient scheme for resting state data was subsequently introduced which operates in the frequency ___domain, called DCM for Cross-Spectral Density (CSD) <ref>{{Cite journal|last=Friston|first=Karl J.|last2=Kahan|first2=Joshua|last3=Biswal|first3=Bharat|last4=Razi|first4=Adeel|date=2014-07|title=A DCM for resting state fMRI|url=https://dx.doi.org/10.1016/j.neuroimage.2013.12.009|journal=NeuroImage|volume=94|pages=396–407|doi=10.1016/j.neuroimage.2013.12.009|pmid=24345387|pmc=4073651|issn=1053-8119}}</ref><ref>{{Cite journal|last=Razi|first=Adeel|last2=Kahan|first2=Joshua|last3=Rees|first3=Geraint|last4=Friston|first4=Karl J.|date=2015-02|title=Construct validation of a DCM for resting state fMRI|url=https://doi.org/10.1016/j.neuroimage.2014.11.027|journal=NeuroImage|volume=106|pages=1–14|doi=10.1016/j.neuroimage.2014.11.027|issn=1053-8119|pmc=4295921|pmid=25463471}}</ref>. Both of these can be applied to large-scale brain networks by constraining the connectivity parameters based on the functional connectivity<ref>{{Cite journal|last=Seghier|first=Mohamed L.|last2=Friston|first2=Karl J.|date=2013-03|title=Network discovery with large DCMs|url=https://doi.org/10.1016/j.neuroimage.2012.12.005|journal=NeuroImage|volume=68|pages=181–191|doi=10.1016/j.neuroimage.2012.12.005|issn=1053-8119|pmc=3566585|pmid=23246991}}</ref><ref name=":4">{{Cite journal|last=Razi|first=Adeel|last2=Seghier|first2=Mohamed L.|last3=Zhou|first3=Yuan|last4=McColgan|first4=Peter|last5=Zeidman|first5=Peter|last6=Park|first6=Hae-Jeong|last7=Sporns|first7=Olaf|last8=Rees|first8=Geraint|last9=Friston|first9=Karl J.|date=2017-10|title=Large-scale DCMs for resting-state fMRI|url=https://doi.org/10.1162/NETN_a_00015|journal=Network Neuroscience|language=en|volume=1|issue=3|pages=222–241|doi=10.1162/netn_a_00015|issn=2472-1751|pmc=5796644|pmid=29400357}}</ref>. Another recent development for resting state analysis is Regression DCM<ref>{{Cite journal|last=Frässle|first=Stefan|last2=Lomakina|first2=Ekaterina I.|last3=Razi|first3=Adeel|last4=Friston|first4=Karl J.|last5=Buhmann|first5=Joachim M.|last6=Stephan|first6=Klaas E.|date=2017-07|title=Regression DCM for fMRI|url=https://doi.org/10.1016/j.neuroimage.2017.02.090|journal=NeuroImage|volume=155|pages=406–421|doi=10.1016/j.neuroimage.2017.02.090|pmid=28259780|issn=1053-8119}}</ref> implemented in the Tapas software collection (see [[#Software implementations|Software implementations]]). Regression DCM operates in the frequency ___domain, but linearizes the model under certain simplifications, such as having a fixed (canonical) haemodynamic response function. The enables rapid estimation of large-scale brain networks.

[[File:DCM for ERP and CMC.svg|thumb|Models of the cortical column used in EEG/MEG/LFP analysis. Self-connections on each population are present but not shown for clarity. Left: DCM for ERP. Right: Canonical Microcircuit (CMC). 1=spiny stellate cells (layer IV), 2=inhibitory interneurons, 3=(deep) pyramidal cells and 4=superficial pyramidal cells.]]

==== EEG / MEG ====

DCM for EEG and MEG data use more biologically detailed neural models than fMRI, asdue to the higher temporal resolution of these measurement techniques supports more refined models of neural dynamics. These can be classed into physiological models, which recapitulate neural circuity, and phenomenological models, which focus on reproducing particular data features. The physiological models can be further subdivided into two classes. [http://www.scholarpedia.org/article/Conductance-based_models Conductance-based models] derive from the equivalent circuit representation of the cell membrane developed by Hodgkin and Huxley in the 1950s<ref name=":5">{{Cite journal|last=Hodgkin|first=A. L.|last2=Huxley|first2=A. F.|date=1952-04-28|title=The components of membrane conductance in the giant axon ofLoligo|url=https://dx.doi.org/10.1113/jphysiol.1952.sp004718|journal=The Journal of Physiology|volume=116|issue=4|pages=473–496|doi=10.1113/jphysiol.1952.sp004718|issn=0022-3751}}</ref> . Convolution models were introduced by [[Wilson–Cowan model|Wilson & Cowan]]<ref>{{Cite journal|last=Wilson|first=H. R.|last2=Cowan|first2=J. D.|date=1973-09|title=A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue|url=https://dx.doi.org/10.1007/bf00288786|journal=Kybernetik|volume=13|issue=2|pages=55–80|doi=10.1007/bf00288786|pmid=4767470|issn=0340-1200}}</ref> and Freeman <ref>{{Cite journal|date=1975|title=Mass Action in the Nervous System|url=https://dx.doi.org/10.1016/c2009-0-03145-6|doi=10.1016/c2009-0-03145-6|isbn=9780122671500}}</ref> in the 1970s and involve a convolution of pre-synaptic input by a synaptic kernel function. TheSome of the specific models used in DCM are as follows:

* Physiological models:

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*** DCM for evoked responses (DCM for ERP)<ref>{{Cite journal|last=David|first=Olivier|last2=Friston|first2=Karl J.|date=2003-11|title=A neural mass model for MEG/EEG:|url=https://dx.doi.org/10.1016/j.neuroimage.2003.07.015|journal=NeuroImage|volume=20|issue=3|pages=1743–1755|doi=10.1016/j.neuroimage.2003.07.015|issn=1053-8119}}</ref><ref>{{Citation|last=Kiebel|first=Stefan J.|date=2009-07-31|url=https://dx.doi.org/10.7551/mitpress/9780262013086.003.0006|work=Brain Signal Analysis|pages=141–170|publisher=The MIT Press|isbn=9780262013086|last2=Garrido|first2=Marta I.|last3=Friston|first3=Karl J.|doi=10.7551/mitpress/9780262013086.003.0006|chapter=Dynamic Causal Modeling for Evoked Responses|title=Brain Signal Analysis}}</ref>. This is a biologically plausible neural mass model, extending earlier work by Jansen and Rit<ref>{{Cite journal|last=Jansen|first=Ben H.|last2=Rit|first2=Vincent G.|date=1995-09-01|title=Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns|url=https://dx.doi.org/10.1007/s004220050191|journal=Biological Cybernetics|volume=73|issue=4|pages=357–366|doi=10.1007/s004220050191|issn=0340-1200}}</ref>. It emulates the activity of a cortical area using three neuronal sub-populations (see picture), each of which rests on two operators. The first operator transforms the pre-synaptic firing rate into a Post-Synaptic Potential (PSP), by [[Convolution|convolving]] pre-synaptic input with a synaptic response function (kernel). The second operator, a [[Sigmoid function|sigmoid]] function, transforms the membrane potential into a firing rate of action potentials.

*** DCM for LFP (Local Field Potentials)<ref>{{Cite journal|last=Moran|first=R.J.|last2=Kiebel|first2=S.J.|last3=Stephan|first3=K.E.|last4=Reilly|first4=R.B.|last5=Daunizeau|first5=J.|last6=Friston|first6=K.J.|date=2007-09|title=A neural mass model of spectral responses in electrophysiology|url=https://dx.doi.org/10.1016/j.neuroimage.2007.05.032|journal=NeuroImage|volume=37|issue=3|pages=706–720|doi=10.1016/j.neuroimage.2007.05.032|issn=1053-8119}}</ref>. Extends DCM for ERP by adding the effects of specific ion channels on spike generation.

*** Canonical Microcircuit (CMC)<ref>{{Cite journal|last=Bastos|first=Andre M.|last2=Usrey|first2=W. Martin|last3=Adams|first3=Rick A.|last4=Mangun|first4=George R.|last5=Fries|first5=Pascal|last6=Friston|first6=Karl J.|date=2012-11|title=Canonical Microcircuits for Predictive Coding|url=https://dx.doi.org/10.1016/j.neuron.2012.10.038|journal=Neuron|volume=76|issue=4|pages=695–711|doi=10.1016/j.neuron.2012.10.038|pmid=23177956|issn=0896-6273}}</ref>. Used to address hypotheses about laminar-specific ascending and descending connections in the brain, which underpin the [[predictive coding]] account of functional brain architectures. The single pyramidal cell population from DCM for ERP is split into deep and superficial populations (see picture). A version of the CMC has been applied to model multi-modal MEG and fMRI data<ref>{{Cite journal|last=Friston|first=K.J.|last2=Preller|first2=Katrin H.|last3=Mathys|first3=Chris|last4=Cagnan|first4=Hayriye|last5=Heinzle|first5=Jakob|last6=Razi|first6=Adeel|last7=Zeidman|first7=Peter|date=2017-02|title=Dynamic causal modelling revisited|url=https://doi.org/10.1016/j.neuroimage.2017.02.045|journal=NeuroImage|doi=10.1016/j.neuroimage.2017.02.045|issn=1053-8119}}</ref>.

***Neural Field Model (NFM)<ref>{{Cite journal|last=Pinotsis|first=D.A.|last2=Friston|first2=K.J.|date=2011-03|title=Neural fields, spectral responses and lateral connections|url=https://dx.doi.org/10.1016/j.neuroimage.2010.11.081|journal=NeuroImage|volume=55|issue=1|pages=39–48|doi=10.1016/j.neuroimage.2010.11.081|pmid=21138771|issn=1053-8119}}</ref>. Extends the models above into the spatial ___domain, modelling continuous changes in current across the cortical sheet.

** Conductance models:

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== Model estimation ==

Model inversion or estimation is implemented in DCM using [[Variational Bayesian methods|variational Bayes]] under the [[Laplace's method|Laplace assumption]]<ref>{{Citation|last=Friston|first=K.|date=2007|url=https://dx.doi.org/10.1016/b978-012372560-8/50047-4|work=Statistical Parametric Mapping|pages=606–618|publisher=Elsevier|isbn=9780123725608|last2=Mattout|first2=J.|last3=Trujillo-Barreto|first3=N.|last4=Ashburner|first4=J.|last5=Penny|first5=W.|doi=10.1016/b978-012372560-8/50047-4|chapter=Variational Bayes under the Laplace approximation|title=Statistical Parametric Mapping}}</ref>. This provides two useful quantities: the log marginal likelihood or model evidence <math>\ln{p(y|m)}</math> is the probability of observing of the data under a given model. Generally, this cannot be calculated explicitly and is approximated by a quantity called the negative variational free energy <math>F</math> , referred to in machine learning as the Evidence Lower Bound (ELBO). Hypotheses are tested by comparing the evidence for different models based on their free energy, a procedure called Bayesian model comparison.

Model estimation also provides estimates of the parameters <math>p(\theta|y)</math>;, for example, connection strengths, which maximise variationalthe free energy. Where models differ only in their priors, [[Bayesian model reduction|Bayesian Model Reduction]] can be used to derive the evidence and parameters of nested or reduced models analytically and efficiently.

== Model comparison ==

Neuroimaging studies typically investigate effects that are conserved at the group level, or which differ between subjects. There are two predominant approaches for group-level analysis: random effects Bayesian Model Selection (BMS)<ref>{{Cite journal|last=Rigoux|first=L.|last2=Stephan|first2=K.E.|last3=Friston|first3=K.J.|last4=Daunizeau|first4=J.|date=2014-01|title=Bayesian model selection for group studies — Revisited|url=https://dx.doi.org/10.1016/j.neuroimage.2013.08.065|journal=NeuroImage|volume=84|pages=971–985|doi=10.1016/j.neuroimage.2013.08.065|issn=1053-8119}}</ref> and Parametric Empirical Bayes (PEB)<ref name=":1">{{Cite journal|last=Friston|first=Karl J.|last2=Litvak|first2=Vladimir|last3=Oswal|first3=Ashwini|last4=Razi|first4=Adeel|last5=Stephan|first5=Klaas E.|last6=van Wijk|first6=Bernadette C.M.|last7=Ziegler|first7=Gabriel|last8=Zeidman|first8=Peter|date=2016-03|title=Bayesian model reduction and empirical Bayes for group (DCM) studies|url=https://doi.org/10.1016/j.neuroimage.2015.11.015|journal=NeuroImage|volume=128|pages=413–431|doi=10.1016/j.neuroimage.2015.11.015|issn=1053-8119|pmc=4767224|pmid=26569570}}</ref>. Random effectsEffects BMS posits that subjects differ in terms of which model generated their data - e.g. drawing a random subject from the population, there might be a 25% chance that their brain is structured like model 1 and a 75% chance that it is structured like model 2. The analysis pipeline for the BMS approach procedure follows a series of steps:

# Specify and estimate multiple DCMs per subject, where each DCM (or set of DCMs) embodies a hypothesis.

# Perform randomRandom effectsEffects BMS to estimate the proportion of subjects whose data were generated by each model

# Calculate the average connectivity parameters across models using Bayesian Model Averaging. This average is weighted by the posterior probability for each model., This meansmeaning that models with greater probability contribute more to the average than models with lower probability.

Alternatively, oneParametric can use parametric empiricalEmpirical Bayes (PEB) <ref name=":1" /> to considercan be used, which specifies a hierarchical model over parameters (e.g., connection strengths). It eschews the notion of different models at the level of individual subjects, and assumes that people differ in the (parametric) strength of connections. The PEB approach models distinct sources of variability in connection strengths across subjects using fixed effects and between-subject variability (random effects). The PEB procedure is as follows:

# Specify a single 'full' DCM per subject, which contains all the parameters of interest.

# Specify a Bayesian [[General linear model|General Linear Model (GLM)]] to model the parameters (the full posterior density) from all subjects at the group level.

# Test hypotheses by comparing the full group-level model to reduced group-level models where certain combinations of connections have been switched off.

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* Face validity establishes whether the parameters of a model can be recovered from simulated data. This is usually performed alongside the development of each new model (E.g. <ref name=":2" /><ref name=":3" />).

* Construct validity assesses consistency with other analytical methods. For example, DCM has been compared with Structural Equation Modelling <ref>{{Cite journal|last=Penny|first=W.D.|last2=Stephan|first2=K.E.|last3=Mechelli|first3=A.|last4=Friston|first4=K.J.|date=2004-01|title=Modelling functional integration: a comparison of structural equation and dynamic causal models|url=https://dx.doi.org/10.1016/j.neuroimage.2004.07.041|journal=NeuroImage|volume=23|pages=S264–S274|doi=10.1016/j.neuroimage.2004.07.041|issn=1053-8119}}</ref> and other neurobiological computational models <ref>{{Cite journal|last=Lee|first=Lucy|last2=Friston|first2=Karl|last3=Horwitz|first3=Barry|date=2006-05|title=Large-scale neural models and dynamic causal modelling|url=https://dx.doi.org/10.1016/j.neuroimage.2005.11.007|journal=NeuroImage|volume=30|issue=4|pages=1243–1254|doi=10.1016/j.neuroimage.2005.11.007|issn=1053-8119}}</ref>.

* Predictive validity assesses the ability to predict known or expected effects. This has included testing against iEEG / EEG / stimulation <ref>{{Cite journal|last=David|first=Olivier|last2=Guillemain|first2=Isabelle|last3=Saillet|first3=Sandrine|last4=Reyt|first4=Sebastien|last5=Deransart|first5=Colin|last6=Segebarth|first6=Christoph|last7=Depaulis|first7=Antoine|date=2008-12-23|title=Identifying Neural Drivers with Functional MRI: An Electrophysiological Validation|url=http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0060315|journal=PLOS Biology|language=en|volume=6|issue=12|pages=e315|doi=10.1371/journal.pbio.0060315|issn=1545-7885|pmc=2605917|pmid=19108604}}</ref><ref>{{Cite journal|last=David|first=Olivier|last2=Woźniak|first2=Agata|last3=Minotti|first3=Lorella|last4=Kahane|first4=Philippe|date=2008-02|title=Preictal short-term plasticity induced by intracerebral 1 Hz stimulation|url=https://doi.org/10.1016/j.neuroimage.2007.11.005|journal=NeuroImage|volume=39|issue=4|pages=1633–1646|doi=10.1016/j.neuroimage.2007.11.005|issn=1053-8119}}</ref><ref>{{Cite journal|last=Reyt|first=Sébastien|last2=Picq|first2=Chloé|last3=Sinniger|first3=Valérie|last4=Clarençon|first4=Didier|last5=Bonaz|first5=Bruno|last6=David|first6=Olivier|date=2010-10|title=Dynamic Causal Modelling and physiological confounds: A functional MRI study of vagus nerve stimulation|url=https://dx.doi.org/10.1016/j.neuroimage.2010.05.021|journal=NeuroImage|volume=52|issue=4|pages=1456–1464|doi=10.1016/j.neuroimage.2010.05.021|issn=1053-8119}}</ref><ref>{{Cite journal|last=Daunizeau|first=J.|last2=Lemieux|first2=L.|last3=Vaudano|first3=A. E.|last4=Friston|first4=K. J.|last5=Stephan|first5=K. E.|date=2013|title=An electrophysiological validation of stochastic DCM for fMRI|url=https://dx.doi.org/10.3389/fncom.2012.00103|journal=Frontiers in Computational Neuroscience|volume=6|doi=10.3389/fncom.2012.00103|issn=1662-5188}}</ref> and against known pharmacological treatments <ref>{{Cite journal|last=Moran|first=Rosalyn J.|last2=Symmonds|first2=Mkael|last3=Stephan|first3=Klaas E.|last4=Friston|first4=Karl J.|last5=Dolan|first5=Raymond J.|date=2011-08|title=An In Vivo Assay of Synaptic Function Mediating Human Cognition|url=https://dx.doi.org/10.1016/j.cub.2011.06.053|journal=Current Biology|volume=21|issue=15|pages=1320–1325|doi=10.1016/j.cub.2011.06.053|issn=0960-9822}}</ref><ref>{{Cite journal|last=Moran|first=Rosalyn J.|last2=Jung|first2=Fabienne|last3=Kumagai|first3=Tetsuya|last4=Endepols|first4=Heike|last5=Graf|first5=Rudolf|last6=Dolan|first6=Raymond J.|last7=Friston|first7=Karl J.|last8=Stephan|first8=Klaas E.|last9=Tittgemeyer|first9=Marc|date=2011-08-02|title=Dynamic Causal Models and Physiological Inference: A Validation Study Using Isoflurane Anaesthesia in Rodents|url=https://dx.doi.org/10.1371/journal.pone.0022790|journal=PLoS ONE|volume=6|issue=8|pages=e22790|doi=10.1371/journal.pone.0022790|pmid=21829652|issn=1932-6203}}</ref>.

== Limitations / drawbacks ==

DCM is a hypothesis-driven approach for investigating the interactions among pre-defined regions of interest. It is not ideally suited for exploratory analyses<ref name=":0" />. Although methods have been implemented for automatically searching over reduced models ([[Bayesian model reduction|Bayesian Model Reduction]]) and for modelling large-scale brain networks<ref name=":4" />, these methods require an explicit specification of model space. inIn neuroimaging, other approaches such as [[Psychophysiological Interaction| psychophysiological interaction (PPI)]] analysis may be more appropriate for exploratory use; especially for discovering key nodes for subsequent DCM analysis.

The variational Bayesian methods used for model estimation in DCM are based on the on the Laplace assumption, thatwhich treats the posterior over parameters isas Gaussian. This approximation can fail in the context of highly non-linear models, where local minima canmay preclude the free energy from serving as a tight bound on log model evidence. Sampling approaches provide the gold standard; however, they are time consuming to run and have usuallytypically been used to validate the variational approximations in DCM<ref>{{Cite journal|last=Chumbley|first=Justin R.|last2=Friston|first2=Karl J.|last3=Fearn|first3=Tom|last4=Kiebel|first4=Stefan J.|date=2007-11|title=A Metropolis–Hastings algorithm for dynamic causal models|url=https://dx.doi.org/10.1016/j.neuroimage.2007.07.028|journal=NeuroImage|volume=38|issue=3|pages=478–487|doi=10.1016/j.neuroimage.2007.07.028|issn=1053-8119}}</ref>.

== Software implementations ==