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Dynamic Causal Modelling (DCM) is a methodology and software framework for specifying models of neural dynamics, estimating their parameters and comparing their evidence <ref>{{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>. It enables hypotheses to be tested about the interaction of neural populations (effective connectivity) using functional neuroimaging data e.g., [[functional magnetic resonance imaging]] (fMRI), [[magnetoencephalography]] (MEG)
DCM is used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context). The basic idea is to construct reasonably realistic models of interacting brain regions. These models are then supplemented with a forward model of how the hidden states of each brain region (e.g., neuronal activity) cause the measured responses. This enables the best model and its parameters (i.e., effective connectivity) to be identified from observed data. [[Bayesian model comparison]] is used to select the best model(s) based on their their evidence, which can then be characterised in terms of their parameters (e.g. connection strengths). This enables one to test hypotheses about how brain regions communicate; e.g., whether an experimental manipulation modulates the coupling between neural populations.▼
== Procedure ==
▲DCM is used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context). The basic idea is to construct reasonably realistic models of interacting brain regions. These models are then supplemented with a forward model of how the hidden states of each brain region (e.g., neuronal activity) cause the measured responses. This enables the best model(s) and
Experiments using DCM 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=http://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>:
# Experimental design. Formulate specific hypotheses and conduct a neuroimaging experiment to test those hypotheses.▼
▲# Experimental design. Formulate specific hypotheses and conduct a neuroimaging experiment
#Data preparation. Pre-process the acquired data (e.g. select relevant data features and remove confounds).
# Model specification. Specify one or more forward models (DCMs) of how the data were caused.
#Model estimation. Fit the model(s) to the data to determine their evidence and parameters.
# Model comparison. Compare the evidence for the models using Bayesian Model Comparison, at the single-subject level or at the group level, and inspect the parameters of the model(s).
Each of these steps is briefly reviewed below.▼
== 1. Experimental design ==▼
Functional neuroimaging experiments are typically task-based or [[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, for example, sensory evoked responses in the early visual cortex. The second class of inputs exerts their effects vicariously, through a modulation of the coupling among nodes, 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. To enable efficient estimation of driving and modulatory effects, a 2x2 [[Factorial experiment|factorial experimental design]] is often used - with one factor modelled as the driving input and the other as the modulatory input. ▼
Resting state experiments have no experimental manipulations within the period of the neuroimaging recording. Instead, endogenous fluctuations in brain connectivity during the scan are of interest, or the differences in connectivity between scans or subjects. The DCM framework includes models and procedures for resting state, described below..▼
▲Functional neuroimaging experiments are typically task-based or [[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, for example, [[Evoked potential|sensory evoked responses]] in the early visual cortex. The second class of inputs exerts their effects vicariously, through a modulation of the coupling among nodes, for example, the influence of attention on the processing of sensory information. These two types of input - driving and modulatory - are
▲Resting state experiments have no experimental manipulations within the period of the neuroimaging recording. Instead, endogenous fluctuations in brain connectivity during the scan are of interest, or the differences in connectivity between scans or subjects. The DCM framework includes models and procedures for resting state data, described below..
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Dynamic Causal Models (DCMs) are nonlinear state-space 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. Various models have been developed for use with DCM and the experimenter selects their preferred model based on the types of hypothesis they wish to address and the type of data they have collected.
==== Functional MRI ====
The neural model in DCM for fMRI uses a simple mathematical device - a [[Taylor series|Taylor approximation]] -
Support for resting state analysis 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}}</ref>, which estimates both neural fluctuations and connectivity parameters in the time ___domain using a procedure called [[Generalized filtering|Generalized Filtering]]. A faster and more accurate solution was introduced which operates in the frequency ___domain, called DCM for Cross-Spectral Densities (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=http://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|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=PMC4295921|pmid=25463471}}</ref>. Both of these can be applied to large-scale brain networks by using priors based on functional connectivity<ref>{{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=PMC5796644|pmid=29400357}}</ref>. Another recent development is Regression DCM. This also operates in the frequency ___domain, but linearizes the model under certain simplifications, such as a fixed (canonical) haemodynamic response function. The means that the model can be inverted rapidly as a [[General linear model|General Linear Model]] and can be applied to large-scale brain networks.
==== EEG / MEG ====
EEG and MEG data can support the estimation of more biologically detailed neural models than fMRI, as they have richer dynamics with higher temporal resolution.
The predominant model is DCM for evoked responses (DCM for ERP). It is a biologically plausible neural mass model, based on earlier work by Jansen and Rit (1995) and Lopes da Silva et al. (1974), which emulates the activity of a cortical area using three neuronal subpopulations. Each subpopulation rests on two operators. The first transforms the pre-synaptic firing rate into a Post-Synaptic Potential (PSP), by convolving a synaptic response function (kernel) by the pre-input. As a result, this is referred to as a convolution model. The second operator, a sigmoid function, transforms the membrane potential into a firing rate of action potentials. DCM for LFP (Local Field Potentials) extended this model to include the effects of specific ion channels on spike generation.
'''A short paragraph on the CMC model please?'''
'''A short paragraph on
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Model inversion or estimation is implemented in DCM using a [[Variational Bayesian methods|variational Bayesian]] optimisation scheme. It provides two useful quantities. The log marginal likelihood or model evidence <math>\ln{p(y|m)}</math> is the probability of observing of the given data under the model. This cannot be calculated exactly and in DCM it 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 named Bayesian model comparison. Model estimation also provides estimates of the parameters <math>p(\theta|y)</math>, for example the connection strengths, which maximise the free energy. Where models differ only in their priors, [[Bayesian model reduction|Bayesian Model Reduction]] can be used to rapidly the derive the evidence and parameters for nested or reduced models from a full model.
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Neuroimaging studies typically investigate effects which 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) and Parametric Empirical Bayes (PEB). Random effects BMS posits that subjects differ in terms of which model generated their data - e.g. drawing a random subject from the population, there would be a 25% chance their data were generated by model 1 and a 75% chance their data were generated by model 2. The analysis pipeline for the BMS approach procedure follows a series of steps:
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