Dynamic causal modeling: Difference between revisions

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'''Dynamic causal modeling''' (DCM) is a [[Bayes factor|Bayesian model comparison]] procedure for comparing models of how data were generated. Dynamic causal models are formulated as [[Stochastic differential equation|stochastic]] or [[Ordinary differential equation|ordinary differential equations]] (i.e., nonlinear [[State space|state-space]] models in continuous time). These equations model the dynamics of [[Hidden Markov model|hidden states]] in the nodes of a [[Graphical model|probabilistic graphical model]], where conditional dependencies are parameterized in terms of directed [[Brain connectivity estimators|effective connectivity]].

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 ==

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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. in neuroimaging, other approaches such as [[Psychophysiological Interaction| psychophysiological interaction (PPI)]] analysis may be more appropriate; especially for discovering key nodes for subsequent DCM.

The variational Bayesian methods used for model estimation are based on the on the Laplace assumption that the posterior over parameters is Gaussian. This approximation can fail in the context of highly non-linear models, where local minima can 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 usually 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 ==