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]]. It uses nonlinear [[State space|state-space]] models in continuous time, specified using [[Stochastic differential equation|stochastic]] or [[ordinary differential equation]]s. DCM was initially developed for testing hypotheses about [[Dynamical system|neural dynamics]].<ref name="Friston 2003">{{Cite journal|last=Friston|first=K.J.|last2=Harrison|first2=L.|last3=Penny|first3=W.|date=August 2003|title=Dynamic causal modelling|journal=NeuroImage|volume=19|issue=4|pages=1273–1302|doi=10.1016/s1053-8119(03)00202-7|pmid=12948688|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 ==

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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="Friston 2003"/> 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=June 1998|title=Dynamics of blood flow and oxygenation changes during brain activation: The balloon model|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=October 2000|title=Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics|journal=NeuroImage|volume=12|issue=4|pages=466–477|doi=10.1006/nimg.2000.0630|pmid=10988040|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=November 2007|title=Comparing hemodynamic models with DCM|journal=NeuroImage|volume=38|issue=3|pages=387–401|doi=10.1016/j.neuroimage.2007.07.040|pmid=17884583|pmc=2636182|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=January 2008|title=Dynamic causal modelling for fMRI: A two-state model|journal=NeuroImage|volume=39|issue=1|pages=269–278|doi=10.1016/j.neuroimage.2007.08.019|pmid=17936017|issn=1053-8119|citeseerx=10.1.1.160.1281}}</ref> and non-linear influences of neural populations on the coupling between other populations.<ref name="Stephan 2008">{{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=August 2008|title=Nonlinear dynamic causal models for fMRI|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.zora.uzh.ch/id/eprint/49235/1/Li_Neuroimage_2011.pdf|journal=NeuroImage|volume=58|issue=2|pages=442–457|doi=10.1016/j.neuroimage.2011.01.085|pmid=21310247|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=July 2014|title=A DCM for resting state fMRI|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=February 2015|title=Construct validation of a DCM for resting state fMRI|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=March 2013|title=Network discovery with large DCMs|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="Razi 2017">{{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=October 2017|title=Large-scale DCMs for resting-state fMRI|journal=Network Neuroscience|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=July 2017|title=Regression DCM for fMRI|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, due to the higher temporal resolution of these measurement techniques. 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="Hodgkin 1952">{{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|journal=The Journal of Physiology|volume=116|issue=4|pages=473–496|doi=10.1113/jphysiol.1952.sp004718|pmid=14946714|issn=0022-3751|pmc=1392209}}</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=September 1973|title=A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue|journal=Kybernetik|volume=13|issue=2|pages=55–80|doi=10.1007/bf00288786|pmid=4767470|issn=0340-1200}}</ref> and Freeman <ref>{{Cite book|date=1975|title=Mass Action in the Nervous System|doi=10.1016/c2009-0-03145-6|isbn=9780122671500|last1=Freeman|first1=Walter J}}</ref> in the 1970s and involve a convolution of pre-synaptic input by a synaptic kernel function. Some of the specific models used in DCM are as follows:

* Physiological models:

** Convolution models:

*** DCM for evoked responses (DCM for ERP).<ref>{{Cite journal|last=David|first=Olivier|last2=Friston|first2=Karl J.|date=November 2003|title=A neural mass model for MEG/EEG|journal=NeuroImage|volume=20|issue=3|pages=1743–1755|doi=10.1016/j.neuroimage.2003.07.015|pmid=14642484|issn=1053-8119}}</ref><ref>{{Citation|last=Kiebel|first=Stefan J.|date=2009-07-31|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|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=September 2007|title=A neural mass model of spectral responses in electrophysiology|journal=NeuroImage|volume=37|issue=3|pages=706–720|doi=10.1016/j.neuroimage.2007.05.032|pmid=17632015|pmc=2644418|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=November 2012|title=Canonical Microcircuits for Predictive Coding|journal=Neuron|volume=76|issue=4|pages=695–711|doi=10.1016/j.neuron.2012.10.038|pmid=23177956|pmc=3777738|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=February 2017|title=Dynamic causal modelling revisited|journal=NeuroImage|volume=199|pages=730–744|doi=10.1016/j.neuroimage.2017.02.045|pmid=28219774|pmc=6693530|issn=1053-8119}}</ref>

***Neural Field Model (NFM).<ref>{{Cite journal|last=Pinotsis|first=D.A.|last2=Friston|first2=K.J.|date=March 2011|title=Neural fields, spectral responses and lateral connections|journal=NeuroImage|volume=55|issue=1|pages=39–48|doi=10.1016/j.neuroimage.2010.11.081|pmid=21138771|pmc=3049874|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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* 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="Friston 2003" /><ref name="Stephan 2008" />).

* 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=January 2004|title=Modelling functional integration: a comparison of structural equation and dynamic causal models|journal=NeuroImage|volume=23|pages=S264–S274|doi=10.1016/j.neuroimage.2004.07.041|pmid=15501096|issn=1053-8119|citeseerx=10.1.1.160.3141}}</ref> and other neurobiological computational models.<ref>{{Cite journal|last=Lee|first=Lucy|last2=Friston|first2=Karl|last3=Horwitz|first3=Barry|date=May 2006|title=Large-scale neural models and dynamic causal modelling|journal=NeuroImage|volume=30|issue=4|pages=1243–1254|doi=10.1016/j.neuroimage.2005.11.007|pmid=16387513|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|journal=PLOS Biology|volume=6|issue=12|pages=2683–97|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=February 2008|title=Preictal short-term plasticity induced by intracerebral 1 Hz stimulation|journal=NeuroImage|volume=39|issue=4|pages=1633–1646|doi=10.1016/j.neuroimage.2007.11.005|pmid=18155929|issn=1053-8119|url=https://www.hal.inserm.fr/inserm-00381199/file/David_Manuscript.pdf}}</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=October 2010|title=Dynamic Causal Modelling and physiological confounds: A functional MRI study of vagus nerve stimulation|journal=NeuroImage|volume=52|issue=4|pages=1456–1464|doi=10.1016/j.neuroimage.2010.05.021|pmid=20472074|issn=1053-8119|url=https://www.hal.inserm.fr/inserm-00498678/file/Manuscript_Author.pdf}}</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|journal=Frontiers in Computational Neuroscience|volume=6|pages=103|doi=10.3389/fncom.2012.00103|pmid=23346055|pmc=3548242|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=August 2011|title=An In Vivo Assay of Synaptic Function Mediating Human Cognition|journal=Current Biology|volume=21|issue=15|pages=1320–1325|doi=10.1016/j.cub.2011.06.053|pmid=21802302|pmc=3153654|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|journal=PLoS ONE|volume=6|issue=8|pages=e22790|doi=10.1371/journal.pone.0022790|pmid=21829652|pmc=3149050|issn=1932-6203}}</ref>

== Limitations / drawbacks ==