Dynamic causal modelling :: Andre Marreiros, Klaas Stephan, Karl Friston, Welcome & University of Zurich :: Scholarpedia (2010) :: http://www.scholarpedia.org/articles/Dynamic_causal_modeling
Summary and review of the above article
Dynamic causal modelling (DCM) was created in order to estimate the functioning of connections between different brain regions. DCM infers the causal structure of distributed systems. It uses a Bayesian system to study how current data was created. This can be formulated in terms of differential equations. The aim is to work out the hidden neuronal processing that has given rise to actually measured responses. Bayesian methods select the neural processing most likely to have given rise to the measured neural processing. This approach allows the testing of theories as to how activity in particular neuronal populations effects the processing of other neuronal populations.
With dynamic causal modelling data is normally derived from brain scanning of the effects of sensory inputs. An input may produce a response in the primary visual cortex, or it may have a more indirect influence on the attentional system. Neural processing that comes between such inputs and observed outputs such as neural blood flow are described here as the ‘hidden’ states that DCM is designed to discover.
DCM attempts to distinguish between different possible models for how the outputs arise. An equation can be used to track how changes in one area of neuronal activity have been caused by activity in other areas, thus attempting to account for both external inputs and internal brain processing.
An initial value ‘A’ can represent the relationship between the activities of neural populations in the absence of external inputs. A second value, ‘B’, can represent the change in this processing produced by the external input. A final value, ‘C’ is intended to represent the effect on the ‘hidden’ neural populations that are causal links between the ‘A’ and ‘B’ populations. This represents the connectivity between a series of brain regions. The connectivity between these neural populations can lead to an observed change in blood oxygen level (BOLD). Differential equations can describe the changing relations between such a series of neuronal populations.
In dealing with evoked responses in the brain, dynamical causal modelling has been used to show how a response could arise from the connections between neural populations. Evoked responses are measured by EEG rather than fMRI. EEG data allows a much closer tracking of neuronal activity than the BOLD system. The DCM model can represent the activity of neuronal subpopulations and the relationship of pyramidal neurons and interneurons in different layers of the cortex. The model is a method of deciding which of a choice of possible theories about the connectivity that generates observed data is the most likely to be correct. A common approach with DCM is to search for the best model amongst a number of a priori plausible models and then make further assumptions on the basis of the winning model. DCM comprises a combination of physical modelling on the basis of differential equations and Bayesian statistics.
An example of DCM involves the processing of visual motion with the subject attending to possible changes in the velocity of dots on a screen. In this instance neural processing was tracked in both the primary (V1) and higher (V5) visual cortex and also in the superior parietal cortex. Three models or theories for how connectivity functioned here were proposed for understanding connectivity between the primary and the higher visual cortex. Bayes factors favoured the first proposed model. DCM makes it possible to model how activity in one neuronal population influences connection strengths with other populations. In one case, it was claimed that there was a 99% chance that the response of the higher cortex to the primary cortex was influenced by the parietal area.
Granger causality analysis in neuroscience :: Anil Seth, Adam Barrett, Lionel Barnet :: Journal of Neuroscience, 25 February 2015 :: http://www.jneurosci.org/content/35/8/3293.full
Summary and review of the above paper
One objective in neuroscience is to progress beyond simply identifying activity in particular brain regions, and to move on to identifying the causal relations between brain regions. The aim is to predict the causes of subsequently measured activity using statistical methods. This analysis can be applied to the neural connectivity underlying perception, cognition and behaviour. Mechanistic models are seen as being capable of explaining how observed data is arrived at. One method in neuroscience is dynamic causal modelling (DCM) which applies a combination of differential equations and a Bayesian framework to assess which neural models give the best predictions of observed outputs.
In Granger causality there is a concept of causes being used to predict effects. Grainger causality uses VAR models, in which the value of a variable at a particular time is based on a weighted sum of its own past, plus the past of a number of other variables. With Granger analysis, a variable ‘X’ causes another variable ‘Y’ if ‘X’ contains information that predicts something about the outcome for ‘Y’ that cannot be found in the past of ‘Y’. This indicates an information flow from ‘X’ to ‘Y’.
Normally the process involves a comparison of two VAR models. The application of Granger causality is most commonly used to interpret neuroimaging, where the aim is to move beyond identifying active brain regions, to understanding the connections between these brain regions. Granger causality has the important advantage that causal influences can be related to particular brain frequency bands. This is important in relation to neuroscience theories that attribute particular functions to particular frequency bands. Thus its application to data on frequency ranges has indicated top-down influences in the alpha and beta ranges, and bottom-up influences in the gamma range. These findings supported existing predictive frameworks.
Granger causality appears to be less specific about connectivity than dynamic causal modelling, but against this it is possible to apply Granger to larger neural areas. Granger is more interested in information flow, while DCM is more interested in the underlying physical connections.