'''Dynamic causal modeling''' (DCM) is a framework for specifying models, fitting them to data and comparing their evidence using [[Bayes factor|Bayesian model comparison]]. procedureThe formodels, comparingreferred modelsto ofas howdynamic datacausal weremodels generated.(DCMs), Dynamicare causalnonlinear [[State space|state-space]] models arein formulatedcontinuous astime, specified using [[Stochastic differential equation|stochastic]] or [[Ordinary differential equation|ordinary differential equations]] (i.e.,nonlinearDCM was initially developed for identifying models of [[StateDynamical spacesystem|state-spaceneural dynamics]]<ref modelsname=":2">{{Cite injournal|last=Friston|first=K.J.|last2=Harrison|first2=L.|last3=Penny|first3=W.|date=2003-08|title=Dynamic continuouscausal timemodelling|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>. TheseIn this setting, differential equations modeldescribe the dynamicsinteraction of [[Hiddenneural Markovpopulations, model|hiddenwhich states]]directly inor theindirectly nodesgive ofrise ato functional neuroimaging data e.g., [[Graphicalfunctional model|probabilisticmagnetic graphicalresonance modelimaging]] (fMRI), where[[magnetoencephalography]] conditional(MEG) dependenciesor are[[electroencephalography]] (EEG). parameterizedParameters in termsthese ofDCMs quantify the directed [[Braininfluences connectivityor estimators|effective connectivity among neuronal populations, which can be estimated from the available data using [[Bayesian inference|Bayesian]] statistical methods.
DCM was initially developed for identifying models of [[Dynamical system|neural dynamics]], estimating their parameters and comparing their evidence..<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>. DCM allows one to test competing models of interactions among neural populations using functional neuroimaging data e.g., [[functional magnetic resonance imaging]] (fMRI), [[magnetoencephalography]] (MEG) or [[electroencephalography]] (EEG).
== Procedure ==
DCM is usually used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context). TheModels basicof ideainteracting isbrain toregions constructare reasonablyspecified realisticwhich modelsdescribe ofthe interactinginteraction brainof regionsneural populations. These models are then supplemented with a forward model of how the hidden states of each brain region (e.g., neuronal activity) give rise to measured responses. Having specified This enables the best model(s) and their parameters (i.e. effective connectivity) to be identified from 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>:
