|
=== Model specification ===
Dynamic Causal Models (DCMs) are nonlinear state-space models in continuous time that model the dynamics of hidden states in the nodes of a probabilistic graphical model, where conditional dependencies are 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.
==== DCM for fMRI ====
The neural model in DCM for fMRI uses a simple mathematical device - a [[Taylor series|Taylor approximation]] - to capture the gross causal causal influences between brain regions and their change due to driving and modulatory inputs. This is coupled with a detailed biophysical model of the generation of the BOLD response and the MRI signal, based on the Balloon model of Buxton et al. and later extended by Friston et al. and Stephan et al. The neural model was extended to include the interaction of excitatory and inhibitory neural populations and non-linear influences of neural populations on the coupling between other populations.
The neural model was extended to include the interaction of excitatory and inhibitory neural populations and non-linear influences of neural populations on the coupling between other populations. Support for resting state analysis was first introduced in Stochastic DCM, 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 that models resting state fMRIwhich dataoperates in the frequency ___domain, called DCM for Cross-Spectral Densities (CSD). A limitationBoth of DCMthese ofcan CSD,be relativeapplied to Stochasticlarge-scale brain networks by using priors based on functional connectivity. Another recent development is Regression DCM. This also operates in the frequency ___domain, isbut linearizes the model under certain simplifications, such as a fixed (canonical) haemodynamic response function. The means that itthe cannotmodel can be inverted rapidly as a [[General linear model|General time-varyingLinear connectivityModel]] (modulatoryand inputs)can be applied to large-scale brain networks.
==== DCM for EEG / MEG ====
EEG and MEG data can support the estimation of more biologically detailed neural models than fMRI, thanksas tothey theirhave muchricher dynamics with higher temporal resolution.
The predominant model is DCM for evoked responses. It is a biologically plausible neural mass model, used for understanding how event-related responses result from the dynamics of coupled neural populations. The neural mass model in DCM for ERPwhich emulates the activity of a cortical area using three neuronal subpopulations, assigned to granular and agranular layers. A population of excitatory pyramidal (output) cells receive inputs from inhibitory and excitatory populations of [[interneurons]], via intrinsic connections (which are confined to the cortical sheet). Within this model, excitatory interneurons can be regarded as spiny stellate cells found predominantly in layer four and in receipt of forward connections. Excitatory pyramidal cells and inhibitory interneurons are considered to occupy agranular layers and receive backward and lateral inputs.
'''A short paragraph on on the CMC model please - same length as the one above.'''
This model was elaborated
== Model estimation ==
| 