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{{short description|
'''Dynamic causal modeling''' ('''DCM''') is a framework for specifying models, fitting them to data and comparing their evidence using [[Bayes factor|Bayesian model comparison]]. It uses nonlinear [[State space|state-space]] models in continuous time, specified using [[Stochastic differential equation|stochastic]] or [[
▲'''Dynamic causal modeling''' (DCM) is a framework for specifying models, fitting them to data and comparing their evidence using [[Bayes factor|Bayesian model comparison]]. It uses 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 testing hypotheses about [[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|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 models quantify the directed influences or effective connectivity among neuronal populations, which are estimated from the data using [[Bayesian inference|Bayesian]] statistical methods.
== Procedure ==
DCM is typically used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context). A model of interacting neural populations is specified, with a level of biological detail dependent on the hypotheses and available data. This is coupled with a forward model describing how neural activity gives rise to measured responses. Estimating the generative model identifies the parameters (e.g. connection strengths) from the observed data. [[Bayesian model comparison]] is used to compare models based on their evidence, which can then be characterised in terms of parameters.
DCM studies typically involve the following stages
# Experimental design. Specific hypotheses are formulated and an experiment is conducted.
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== 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). These experimental variables can change neural activity through direct influences on specific brain regions, such as [[
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 in the next section.
== Model specification ==
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), which are generated via an observation function <math>g</math> with parameters <math>\theta^{(h)}</math>. Additive observation noise <math>\epsilon</math> completes the observation model. Usually, the neural parameters <math>\theta^{(n)}</math> are 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.
[[File:DCM for fMRI.svg|alt=DCM for fMRI neural circuit|thumb|The neural model in DCM for fMRI. z1 and z2 are the mean levels of activity in each region. Parameters A are the effective connectivity, B is the modulation of connectivity by a specific experimental condition and C is the driving input.
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 blood oxygen level dependent (BOLD) response and the MRI signal,<ref name="
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.
[[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.]]
DCM for EEG and MEG data use more biologically detailed neural models than fMRI, due to the higher temporal resolution of these measurement techniques. These can be classed into physiological models, which recapitulate neural
* Physiological models:
** Convolution models:
*** DCM for evoked responses (DCM for ERP).<ref>{{Cite journal|
*** DCM for LFP (Local Field Potentials).<ref>{{Cite journal|
*** Canonical Microcircuit (CMC).<ref>{{Cite journal|
***Neural Field Model (NFM).<ref>{{Cite journal|
** Conductance models:
***Neural Mass Model (NMM) and Mean-field model (MFM).<ref>{{Cite journal|
****
* Phenomenological models:
**DCM for phase coupling.<ref>{{Cite journal|
== 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|
Model estimation also provides estimates of the parameters <math>p(\theta|y)</math>, for example connection strengths, which maximise the 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|
# Specify and estimate multiple DCMs per subject, where each DCM (or set of DCMs) embodies a hypothesis.
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# Calculate the average connectivity parameters across models using Bayesian Model Averaging. This average is weighted by the posterior probability for each model, meaning that models with greater probability contribute more to the average than models with lower probability.
Alternatively, Parametric Empirical Bayes (PEB) <ref name="
# Specify a single 'full' DCM per subject, which contains all the parameters of interest.
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== Validation ==
Developments in DCM have been validated using different approaches:
* 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.
* Construct validity assesses consistency with other analytical methods. For example, DCM has been compared with Structural Equation Modelling <ref>{{Cite journal|
* Predictive validity assesses the ability to predict known or expected effects. This has included testing against iEEG / EEG / stimulation <ref>{{Cite journal|
== 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="
The variational Bayesian methods used for model estimation in DCM are based on the Laplace assumption, which treats the posterior over parameters as Gaussian. This approximation can fail in the context of highly non-linear models, where local minima may preclude the free energy from serving as a tight bound on log model evidence. Sampling approaches provide the gold standard; however, they are time
== Software implementations ==
DCM is implemented in the [[Statistical parametric mapping|Statistical Parametric Mapping]] software package, which serves as the canonical or reference implementation (http://www.fil.ion.ucl.ac.uk/spm/software/spm12/). It has been re-implemented and developed in the Tapas software collection (https://www.tnu.ethz.ch/en/software/tapas.html {{Webarchive|url=https://web.archive.org/web/20190203134649/https://www.tnu.ethz.ch/en/software/tapas.html |date=2019-02-03 }}) and the VBA toolbox (https://mbb-team.github.io/VBA-toolbox/).
== References ==▼
{{Reflist}}
== Further reading ==
{{Scholia}}
* [http://www.scholarpedia.org/article/Dynamic_causal_modeling Dynamic Causal Modelling on Scholarpedia]
* Understanding DCM: ten simple rules for the clinician<ref>{{Cite journal|last1=Kahan|first1=Joshua|last2=Foltynie|first2=Tom|date=December 2013|title=Understanding DCM: Ten simple rules for the clinician|journal=NeuroImage|volume=83|pages=542–549|doi=10.1016/j.neuroimage.2013.07.008|pmid=23850463|issn=1053-8119|doi-access=free}}</ref>
*
[[:Category:Neuroimaging]]▼
▲== References ==
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